Asset-Pricing | Macro Paper Warehouse

A Cognitive Theory of Reasoning and Choice

Mon, 01 Jan 0001 00:00:00 +0000

Bordalo, Gennaioli, Lanzani, and Shleifer develop a cognitive theory of choice in which a decision maker’s attention to the features of options is determined by her categorization of the current problem against a memory database of problems she solved in the past. The core claim is that before solving a problem, the decision maker asks “what kind of problem is this?” and resolves it by selecting the category — indexed by a prototype attention-plus-context vector and a time-discounted frequency — whose similarity to the current problem is maximized. This problem recognition step then pins down which features (price, quality, probabilities) receive attention, which in turn shapes valuation and choice.

The model formalizes two-step choice. In step one (recognition), the decision maker jointly chooses an attention vector alpha_P and a category c* to maximize a separable similarity function S[(alpha_P, kappa_P), (alpha_c, kappa_c)] weighted by category frequency F_c, plus a Type I extreme-value shock that yields a logit probability over categories. In step two, she maximizes perceived value over the menu using the endogenously determined weights. Perceived hedonic value of feature i shrinks toward the menu average when alpha_{P,i} < 1; perceived probabilities compress toward uniform when the event-attention weight falls below 1, producing probability overweighting of unlikely events. Full attention recovers expected utility.

The model yields three structural predictions that hold without changing tastes or information. First, within-person multi-modal attention: because categorization is stochastic, the same person can cluster on entirely different features (e.g., the base rate vs. the likelihood in an inference problem) across otherwise identical choice occasions. Second, systematic context-driven instability: when an irrelevant context feature kappa_{P,i} drifts away from a category’s diagnostic kappa_{c,i}, the probability of that category falls discontinuously, causing a discrete switch in the attention profile and hence in valuation. Third, experience-driven heterogeneity: people more frequently exposed to a category (higher F_c) are more likely to use it, producing persistent differences in price elasticities or probability weighting at constant income and tastes.

Applied to riskless consumer choice, the paper introduces two categories — “buying” (full attention to price, partial to quality: alpha_{M_g}=1 > alpha_{Q_g}=alpha) and “consuming” (full attention to quality, partial to price: alpha_{Q_g}=1 > alpha_{M_g}=alpha). A jam problem categorized as buying yields valuation v = alphaq - etap; categorized as consuming, v = q - alphaetap. The valuation jumps discontinuously as context crosses a threshold kappa*, which shifts when relative category frequency F_{buy}/F_{con} changes. This framework accounts for context-dependent price elasticities (Wakefield and Inman 2003), poverty-driven excess price focus (Shah et al. 2018), de-commoditization through advertising, and mental accounting anomalies including opportunity cost neglect and the sunk cost fallacy — both arising because con neglects capital gains (alpha_{con,Delta_M}=0) and buy neglects quality shocks (alpha_{buy,Delta_Q}=0).

Applied to statistical judgment, the paper introduces two categories — “frequency estimation” (attention alpha_1=1 to a single i.i.d. draw from a known DGP) and “agnostic inference” (attention alpha_S=1 to the share of heads as a sufficient statistic). The threshold N* separates recognition: for sequence length N_P < N*(F_{freq}/F_{inf}), the decision maker categorizes as frequency and correctly assesses odds; for N_P >= N*, she switches to inference and overweights balanced sequences, producing the Gambler’s Fallacy. The same competition between categories also accounts for base rate neglect, conjunction fallacy, and correlation neglect, with the bias strengthening as sequences grow longer.

Applied to risky choice, bottom-up salience — sensory prominence and contrast — interacts with categorization. A publicity shock drawing attention to a low-probability contamination risk raises similarity to “consuming,” triggering a category switch that amplifies attention to quality broadly and reduces attention to price, producing large valuation drops disproportionate to the actual probability shift. This mechanism generates the framing effects of prospect theory without a stable S-shaped utility function: gains and losses frames correspond to different contexts activating different categories.

Scope conditions: the theory applies when features and their values are fully known to the decision maker (no uncertainty about attributes), so the distortions take the form of altered sensitivity to known features rather than missing information. The set of categories C is taken as given in the formal analysis, though the authors discuss endogenization as future work.

Q: What is the paper’s central departure from standard rational inattention and noisy-perception models?

A: Standard models (Sims 2003, Woodford 2012, Enke and Graeber 2023) produce unimodal, stably weighted valuations — the decision maker’s weighting of features is a smooth function of payoff-relevant costs or priors. In this paper, the weighting is determined by problem recognition, which is discrete and stochastic, producing within-person multi-modal attention: the same person can cluster on entirely different features across identical problems. The authors cite direct evidence from Bordalo, Conlon, Gennaioli, Kwon, and Shleifer [20] showing bimodal clustering on base rates vs. likelihoods in statistical problems, a pattern inconsistent with stable-weighting models.

Q: How is perceived value distorted when the attention weight on a hedonic feature is below 1?

A: The perceived value of hedonic feature i is u_i(alpha_P) = alpha_{P,i} * u_i + (1 - alpha_{P,i}) * u_bar_i, where u_bar_i is the average value of that feature across options in the menu. An attention weight of zero collapses perceived variation in that feature to zero; full attention recovers the true value. The implication is that under-attention shrinks the decision maker’s effective sensitivity to a known attribute, causing systematic under- or over-valuation relative to a rational benchmark while tastes (marginal utilities) are held fixed.

Q: How is perceived probability distorted?

A: With attention weight alpha_{P,W} on event W, the perceived probability of event e is P(e)^{alpha_{P,W}} / sum_{e’} P(e’)^{alpha_{P,W}}, which compresses the distribution toward uniform as alpha_{P,W} falls toward 0 and recovers the true distribution at alpha_{P,W}=1. In the jam example, under-attention to the small probability of spoilage causes the decision maker to overestimate the risk of contamination. For multi-dimensional event vectors the formula generalizes multiplicatively, allowing “editing out” of entire event dimensions (e.g., urn selection in a balls-and-urns problem) when their attention weight hits zero.

Q: What is the mechanism for context-dependent price elasticity?

A: When context kappa_P is below threshold kappa*(F_{buy}/F_{con}), the decision maker categorizes the problem as “buying” and her valuation is v = alphaq - etap, giving a high price sensitivity (coefficient eta) and attenuated quality sensitivity (coefficient alpha < 1). Above kappa*, she categorizes as “consuming” and valuation is v = q - alphaetap, reversing the emphasis. Because the threshold kappa* is increasing in relative frequency F_{buy}/F_{con}, a decision maker with more buying experience has a higher threshold and thus acts as more price-elastic at any given context level. These elasticity differences arise without any change in the true marginal utility of money eta or quality q.

Q: How does the model generate the sunk cost fallacy and opportunity cost neglect as a unified phenomenon?

A: Both anomalies arise because buying and consuming categories selectively neglect shocks. In the football example, recognizing the problem as “buying” activates alpha_{buy,Delta_Q}=0, so the blizzard quality shock Delta_q<0 is ignored and the decision maker drives to the game as if the shock did not occur — the sunk cost fallacy. In the wine example, recognizing the problem as “consuming” activates alpha_{con,Delta_M}=0, so the capital gain Delta_p is ignored and the decision maker reports a zero or purchase-price cost — opportunity cost neglect. The unifying mechanism is that each category attends only to the features diagnostic of its prototypical experiences: buying attends to price paid and normal quality; consuming attends to realized quality and partly to price, but not to capital gains.

Q: What comparative static does the model predict for sunk cost susceptibility based on experience?

A: People with higher F_{buy} (more buying experiences, e.g. poverty experiences or having recently purchased but not yet consumed the good) exhibit more sunk cost fallacy and less opportunity cost neglect. Conversely, season ticket holders face many consuming experiences relative to one buying event, raising F_{con} and thus reducing susceptibility to the sunk cost fallacy for sports events. Making the blizzard more salient in the description shifts similarity toward “consuming,” also reducing the sunk cost fallacy through a different channel (bottom-up salience rather than experience).

Q: What is the paper’s explanation for the Gambler’s Fallacy, and what distinguishes it from prior accounts?

A: The Gambler’s Fallacy arises when sequence length N_P exceeds threshold N*(F_{freq}/F_{inf}), causing the decision maker to switch from the frequency category (which attends to the 50:50 fairness of the coin) to the inference category (which attends to the share of heads). Under inference, the decision maker treats balanced and unbalanced sequences as representatives of their “share of heads equivalence class,” and the class of balanced sequences is larger, so balanced sequences receive higher estimated probability — the Gambler’s Fallacy. This differs from Rabin and Vayanos (2010), where the bias stems from a belief that the coin is drawn from a pool; here the decision maker knows the coin is fair (kappa_{P,U}=0.5) but the inference representation causes question substitution rather than a wrong model of the DGP.

Q: How does the model make the Gambler’s Fallacy testable beyond length effects?

A: The model predicts the bias is stronger for decision makers who recently solved many inference problems (lower F_{freq}/F_{inf}), and weaker when the 50:50 nature of flips is made bottom-up salient in the choice context (because salience raises similarity to the frequency category, hindering recognition of inference). These cognitive proxies — experience frequencies and bottom-up salience — are orthogonal to the statistical content of the problem and thus allow identification of the mechanism separately from changes in information or incentives.

Q: How does the model produce framing effects in risky choice without a stable S-shaped utility function?

A: Gains and losses frames are modeled as different context vectors kappa_P that differentially increase similarity to a “safe outcome” category or a “risk” category. Recognizing the problem as the safe-outcome category shifts attention toward the certain option; recognizing it as the risk category shifts attention toward variance. The reversal of preferences between gain and loss frames (the Asian Disease problem, Tversky and Kahneman 1981) thus emerges from context-driven re-categorization rather than from a fixed probability weighting function. The novel prediction is that framing effects should be stronger for decision makers with more experience with the category activated by each frame, and weaker when bottom-up salience of the alternative frame’s features is raised.

Q: How does bottom-up salience interact with top-down categorization in the contamination example?

A: A publicity shock alpha_{delta,Q_b}>0 raises baseline attention to the spoiled-jam quality feature, increasing the similarity of the current problem to the “consuming” category (where quality is focal). This triggers a category switch for marginal agents, activating the full consuming attention profile — which attends to quality broadly, not just to contamination specifically, and reduces attention to price. The resulting valuation drop is therefore disproportionate to the actual probability of contamination and exhibits price insensitivity, because re-categorization shifts the entire attention profile rather than just updating a single probability.

Q: How does the model relate to and distinguish itself from case-based decision theory (Gilboa and Schmeidler 1995) and analogical reasoning (Mullainathan 2002, Fryer and Jackson 2008)?

A: In Gilboa-Schmeidler and related models, the decision maker uses past cases to resolve uncertainty about unknown attributes of current options; attention is full and the mechanism is extrapolation of payoffs from similar cases. In Mullainathan (2002) memory-based model, categories again serve to fill in missing information. In this paper, there is no uncertainty about attributes — features and their values are fully known — and the distortion instead takes the form of altered sensitivity to known features through selective attention. This allows the model to produce biases even in simple problems with full data disclosure, and to explain phenomena like base rate neglect and price insensitivity that are not primarily about missing information.

Q: What does the model predict about within-person versus across-person distributions of valuations?

A: Within a person, attention is multi-modal (bimodal in the two-category case) because categorization is stochastic. However, if many categories are possible across the population, the aggregate distribution of valuations can appear approximately unimodal even though each individual’s distribution is not. This distinction is empirically important: a researcher observing average choices may incorrectly infer smooth preference heterogeneity when the underlying mechanism is discrete category switching.

Q: What cognitive proxies does the model propose for empirical identification?

A: The theory links endogenous attention and choice to three observable (or measurable) proxies: (1) past experience frequencies F_c, measurable from administrative histories, surveys about past exposure, or experimental manipulation of training; (2) contextual similarity, measurable from field or experimental variation in irrelevant context features; and (3) bottom-up salience, experimentally controllable via prominence or contrast manipulations. The key identification logic is that these proxies are payoff-irrelevant — they do not change tastes, information, or the objective choice problem — yet predict systematic shifts in choice through their effect on recognition.

Problem Recognition: The first step in the decision maker’s choice process, in which she jointly selects an attention vector alpha_P and a category c* by maximizing weighted similarity between the current problem (characterized by its context vector kappa_P) and the prototype of a past category (alpha_c, kappa_c), multiplied by the category’s time-discounted frequency F_c. Recognition is not about resolving uncertainty over attributes but about selecting which known attributes to attend to.

Category: A partition element of the decision maker’s memory database, indexed by a prototype attention-plus-context vector (alpha_c, kappa_c) and a frequency scalar F_c. The prototype encodes both the context features diagnostic of experiences in that category (binary alpha_{c,i} for i in Phi_K) and the attention to hedonic and event features (alpha_{c,i} for i in Phi_H union Phi_E) used when solving problems in that category. Examples in the paper: “buying” and “consuming” for riskless choice; “frequency estimation” and “agnostic inference” for statistical judgment.

Attention Weight (alpha_{P,i}): A scalar in [0,1] assigned to feature i of the current problem P. For hedonic features, alpha_{P,i}<1 collapses perceived variation toward the menu average; for event features, alpha_{P,i}<1 compresses perceived probabilities toward uniform. Full attention alpha_{P,i}=1 recovers expected utility. Attention weights are the endogenous output of the recognition step, not fixed preference parameters.

Contextual Similarity S: A separable function measuring how close the current problem (alpha_P, kappa_P) is to a category prototype (alpha_c, kappa_c). It decreases in discrepancies in the attention vector (measured by a strictly increasing, convex function d) and in discrepancies in the values of context features diagnostic of the category (d_i(kappa_{P,i}, kappa_{c,i}) * alpha_{c,i}). Endogenous attention to context is set to reduce sensitivity to discrepancies, not to eliminate them.

Mental Accounting (as categorization): In the paper’s account, non-fungibility, sunk cost fallacy, and opportunity cost neglect all arise because buying and consuming categories selectively attend to different monetary and quality features. The sunk cost effect is alpha_{buy,Delta_Q}=0; opportunity cost neglect is alpha_{con,Delta_M}=0. Mental accounts are not separate budget constraints but the by-product of category-specific attention profiles that were calibrated to normal-state experiences and do not generalize to shocks.

Bottom-up Salience: Exogenous attention to a feature driven by sensory prominence (described by alpha_{delta,i} in the problem’s presentation vector) or payoff contrast (the DM attends more to features where her option’s value deviates more from the menu average relative to total menu variance). Bottom-up salience raises baseline attention to a feature before top-down categorization acts, and can trigger a category switch by raising similarity to the category for which that feature is focal.

Gambler’s Fallacy via Question Substitution: In the model, the Gambler’s Fallacy arises when a long sequence length kappa_{P,N} causes recognition of the “agnostic inference” category, which focuses attention on the share of heads alpha_S=1. The decision maker then treats sequences as representatives of a “share of heads equivalence class,” and since the balanced class is larger than the unbalanced class, balanced sequences are assigned higher estimated probability. This is not a belief that the coin is unfair; it is question substitution induced by the inference representation.

A Housing Portfolio Channel of QE Transmission

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper identifies and quantifies a housing portfolio channel of quantitative easing (QE) transmission that operates through household portfolio rebalancing toward second homes (as opposed to the well-studied bank credit channel). The central question is whether, and how much, the ECB’s formal adoption of QE in January 2015 induced households with larger pre-existing bond holdings to shift wealth into residential real estate—specifically second homes held for investment—and what the downstream effects on regional housing market outcomes were.

Setting and Motivation

Germany is used as the empirical laboratory because it experienced a sustained housing boom from 2009 onward that was not accompanied by a household credit boom—a “housing boom without a credit boom.” The national house price-to-rent ratio rose markedly from 2009, especially accelerating after QE adoption in 2015, while the stock of mortgage credit to households as a share of GDP was flat or declining. This decoupling makes Germany well-suited for isolating a non-credit portfolio rebalancing mechanism.

Data

Household-level data come from the Deutsche Bundesbank’s Panel on Household Finances (PHF), a triennial survey fielded in 2011, 2014, and 2017, from which the authors construct a panel of 1,651 households. The key exposure variable is each household’s pre-QE (2014) share of total wealth invested in bonds, both directly and indirectly via mutual funds and insurance. Regional housing outcomes (prices, rents, rental yields) are from Bulwiengesa AG for all 401 German administrative regions (Kreise) at annual frequency, and listing data come from Immoscout 24, Germany’s largest online real estate platform.

Methodology

The household-level analysis uses a difference-in-differences (DiD) specification comparing changes in housing portfolio shares between the pre-QE wave (2014) and the post-QE wave (2017), against the pre-period change (2011 to 2014), with the degree of exposure measured by the 2014 bond share. The specification includes household and time fixed effects. A parallel-trends check using all three survey waves (Figure 2) shows that more- and less-exposed households tracked identically before QE adoption, diverging sharply thereafter. Two indirect placebo tests—using households’ share in non-financial, non-housing assets as a spurious treatment, and using the change in non-financial assets as a spurious outcome—both return null results, supporting the identification assumption. For regional housing outcomes, the authors use a panel regression interacting lagged ECB debt-securities-to-GDP (the QE intensity measure) with a regional exposure variable—the 2008 pre-QE share of refugees housed in independent accommodations—across 401 regions from 2010 to 2017.

Main Findings with Quantitative Magnitudes

Benchmark portfolio rebalancing: A household with an ex-ante bond share that is 10 percentage points higher (roughly the interquartile range of the bond share distribution) increases its portfolio share of second homes by 1.72 to 1.87 percentage points more than a less-exposed household after QE adoption, conditional on household and time fixed effects. This result is statistically significant at the 1% level across multiple specifications and is robust to alternative bond share definitions, alternative portfolio denominators, and controlling for negative interest rate policy exposure (via initial deposit shares).
Equity rebalancing: Controlling for risk aversion does not attenuate the second-home result. Strikingly, households with larger ex-ante bond shares reduce, rather than increase, their equity shares after QE (coefficient: −0.042, significant at 5%), ruling out the interpretation that the housing result merely picks up broad rebalancing toward all risky assets. This implies that cash purchases of second homes are funded by liquidating bonds, drawing down deposits, and also selling equities.
Heterogeneity—household characteristics: Rebalancing is stronger for (a) bank-advised households (triple-interaction significant at 5%), (b) financially more literate households (significant at 1%), and (c) households aged 40–60 (significant at 5%), consistent with a lifetime-income-peak, tax-optimization motive rather than a bequest motive. The result for age 61+ is positive but statistically insignificant.
Tax-motive heterogeneity: In Germany, rented-out second homes (or those declared for future letting) benefit from substantial tax deductions not available for owner-occupied primary residences, with the advantage rising in marginal tax rates. Rebalancing is stronger for higher-income households (triple interaction with income per capita positive and significant, especially after controlling for deposit shares) and for church-affiliated households, who face an additional 8–9% church tax surcharge on their regular tax bill, amplifying the tax gain from rental property deductions. For church members, the income-interaction triple coefficient is statistically significant; for non-church members it is not, directly linking the rebalancing gradient to the church tax burden.
Buy-to-let motive: The benchmark result is driven entirely by households that already owned a second home in the pre-QE period and were generating rental income from it (coefficient 0.821, significant at 1%); households without a pre-owned second home show a near-zero, statistically insignificant coefficient (0.000). This establishes that the rebalancing is driven by experienced buy-to-let investors, not vacation-home buyers or commuters.
Credit channel control: The portfolio rebalancing result is not driven by credit access or credit growth. The triple interactions of the bond-share × Post term with both (a) pre-QE leverage (mortgage credit to housing wealth) and (b) post-QE mortgage credit growth are statistically insignificant. Restricting the sample to households with no mortgage credit growth leaves the main coefficient essentially unchanged (0.175, significant at 1%). Nonetheless, an independent credit-channel effect is also present: mortgage credit growth has its own positive and significant effect on second-home share increases, confirming the two channels operate in parallel but independently.
Regional housing market outcomes—prices and yields: In regions more exposed to rental market tightness (higher refugee-in-independent-accommodation share), QE is associated with larger declines in rental yields. A one-standard-deviation increase in QE (approximately 4.3 pp higher ratio of ECB debt securities to GDP) reduces the rental yield in the 75th-percentile-exposure region relative to the 25th-percentile region by 2 to 12 basis points per year (depending on whether the refugee share or the renter share is used as the exposure measure). As ECB holdings rose from 7% of GDP in 2014 to 24% in 2017, the cumulative implied rental yield decline at the regional interquartile range is 8 to 48 basis points, sizable relative to the average regional rental yield decline of 140 basis points (from 7.4% to 6.0%) over the same period. House prices increase more than rents in more exposed regions.
Regional housing market outcomes—listings: Using Immoscout 24 data, both sale and rental listings decline in more exposed regions as QE expands, but the ratio of sale to rental listings falls significantly: sale listings decrease significantly more than rental listings in more exposed regions. This relative shift in supply toward the rental market is interpreted as evidence consistent with the buy-to-let motive documented at the household level and as potentially having benign implications for housing affordability through increased rental supply.

Scope Conditions

All household-level findings are conditional on the German institutional setting: Germany’s combination of a low-homeownership norm, substantial tax incentives favoring rental properties, triennial household survey data spanning one pre- and one post-QE wave, and a housing boom that was decoupled from household credit prior to 2015. The regional results apply to 401 German administrative regions (Kreise) over 2010–2017, using exposure instruments that are argued to capture rental-market tightness or depth rather than direct household bond holdings.

In depth

Q1. What is the housing portfolio channel of QE transmission, and how does it differ mechanically from the credit channel?

A: In the housing portfolio channel, the ECB’s bond purchases reduce the net supply of bonds available to private investors, raising bond prices and reducing expected bond returns. Under the assumption that bonds and houses are substitutes in household portfolios, households with larger initial bond positions rebalance toward housing to restore their target allocation, bidding up house prices. This mechanism operates through changes in risk premia rather than through future short-term rates or bank reserves and loan supply. The credit channel, by contrast, operates through increased bank reserves enabling expanded mortgage lending. The authors show empirically that the two channels operate in parallel and independently, but that greater prior credit access and post-QE mortgage credit growth do not amplify the portfolio rebalancing effect.

Q2. What is the key exposure variable and why is it a valid identification strategy?

A: The exposure variable is each household’s 2014 (pre-QE) share of total wealth invested in bonds, including both direct holdings and indirect holdings via mutual funds and insurance companies. The logic, drawn from the bank-portfolio-rebalancing literature (Rodnyansky and Darmouni, 2017; Luck and Zimmermann, 2020) and from the authors’ own portfolio model, is that the larger a household’s bond share, the stronger its incentive to rebalance when the central bank reduces bond supply. Identification rests on the parallel-trends assumption: Figure 2 shows that before 2015, more- and less-exposed households (defined by a median split on the 2014 bond share) followed identical trends in second-home shares; the trends diverge sharply post-QE. Two indirect placebo tests corroborate this: using a spurious treatment variable (non-financial, non-housing asset share) and using a spurious outcome (change in non-financial, non-housing asset share) both yield null results.

Q3. What is the benchmark magnitude of the portfolio rebalancing effect and how robust is it?

A: A 10-percentage-point higher 2014 bond share (the approximate interquartile range) is associated with a 1.72–1.87 percentage point larger increase in the second-home portfolio share post-QE relative to the pre-QE period (Table 3, columns 1–2, significant at 1%). This result is robust to: scaling second-home shares by a model-consistent denominator (bonds + housing + deposits, column 3); using total housing wealth instead of second-home wealth alone (column 4); using the count of second homes rather than their value share to rule out valuation-effect confounds (column 5); using direct bond holdings without imputation, or indirect holdings only, as alternative exposure measures (columns 7–8, where the coefficients are if anything larger at 0.403 and 0.420); controlling for a broad set of time-varying household characteristics including net worth, age, household size, financial literacy, and risk aversion (Table 4, range 0.19–0.23); and explicitly controlling for the deposit-share post-interaction to rule out the negative interest rate policy as a driver (column 6, main bond coefficient unchanged at 0.122).

Q4. Do households with higher bond exposure also rebalance toward equities after QE?

A: No. Column (7) of Table 4 shows that households with larger ex-ante bond shares reduce their equity shares after QE adoption (coefficient: −0.042, significant at 5%). This rules out the interpretation that the second-home finding merely captures broad rebalancing toward all risky assets due to general risk-appetite changes. Combined with the evidence that deposit shares also decline (though not precisely estimated), the result implies that households fund second-home purchases by selling bonds, drawing down deposits, and reducing equity positions.

Q5. Which household characteristics amplify the rebalancing, and what do they reveal about the mechanism?

A: Five characteristics are shown to amplify rebalancing (Table 5 and Table 7): (1) being actively advised by a bank on asset allocation (triple interaction significant at 5%), consistent with banks that own real estate agencies steering clients toward property; (2) higher financial literacy (significant at 1%), consistent with more informed investors acting more quickly on QE-induced return differentials; (3) middle age (40–60), significant at 5%, but not older age (61+), ruling out bequest motives and pointing to households near their lifetime income peak optimizing their tax burden; (4) higher income per capita (positive and significant, especially among church members), reflecting the progressive German tax schedule that makes property-related deductions more valuable; and (5) church affiliation (the income-triple interaction is significant only for church members, who face an 8–9% church tax surcharge, amplifying the tax advantage of rental property ownership). Tenure status (renter vs. owner of main residence) shows that both groups rebalance, but the triple interaction is significant only at 10%, suggesting the effect is not confined to existing homeowners.

Q6. How is the buy-to-let motive established directly in the data, as opposed to vacation-home or commuter motives?

A: The authors use variation in whether households owned a second home and generated rental income from it before QE adoption (Table 8). Households that owned a second home and reported rental income in the pre-QE wave rebalance very strongly (coefficient 0.821 on Bonds × Post, significant at 1%). Households that owned a second home but did not generate rental income show a positive but imprecisely estimated coefficient (0.641, significant at 10% in a very small sub-sample of 138 households). Critically, households that did not own any second home prior to QE show a coefficient of essentially zero (0.000). This pattern establishes that rebalancing is driven by experienced buy-to-let investors rather than by households acquiring second homes for personal use, and is consistent with the income-seeking motive documented in the Australian context by Gargano and Giacoletti (2022).

Q7. How does the paper demonstrate that the effect is independent of the credit channel, while also acknowledging the credit channel operates?

A: The paper employs three complementary tests (Table 6). First, triple interactions of the Bonds × Post coefficient with pre-QE leverage (mortgage-to-housing-wealth ratio) and with post-QE mortgage credit growth are both statistically insignificant (columns 5–6 of Table 5), meaning that greater credit access does not amplify the bond-share rebalancing effect. Second, restricting the sample to households with zero mortgage credit growth between 2014 and 2017 leaves the main coefficient unchanged at 0.175 (column 1 of Table 6). Third, including the two credit variables as additional controls only marginally reduces the bond-share coefficient without affecting its significance (columns 2–3 of Table 6). At the same time, column 3 of Table 6 shows that mortgage credit growth does have its own statistically significant positive effect on second-home shares (coefficient 0.009, significant at 1%), confirming a separate, independently operating credit channel.

Q8. How is regional exposure to the channel proxied, given that household survey data cannot be aggregated to the regional level?

A: Because the 1,651-household panel provides only 3–4 observations per region on average across 401 German Kreise, the authors cannot construct representative regional averages of household bond shares. Instead, they use the pre-QE (2008) share of refugees housed in independent accommodation in each region as developed by Bednarek et al. (2021), arguing that a larger refugee share creates tighter rental housing market conditions and therefore makes buy-to-let investment more attractive. For robustness, they also use the 2011 census share of renters in each region as an alternative measure of rental market depth. Both regional exposure variables take higher values in urban areas (refugee share: 21% urban vs. 10% rural; renter share: 70% urban vs. 46% rural), consistent with household-level rebalancing being stronger in urban regions.

Q9. What are the quantitative effects on regional rental yields, house prices, and rents?

A: Table 9 shows that a one-standard-deviation increase in QE (approximately 4.3 percentage points higher ECB debt securities-to-GDP ratio) reduces the rental yield in a region at the 75th percentile of the refugee-share exposure distribution relative to the 25th percentile by 2 basis points per year (using the refugee share) to 12 basis points per year (using the renter share). Comparing the 5th vs. 95th percentile of exposure, the yield differential is 5–24 basis points per year. Over the full 2014–2017 QE expansion (from 7% to 24% of GDP), the cumulative implied rental yield decline at the interquartile range of exposure is 8 to 48 basis points—sizable relative to the average regional decline of 140 basis points. House prices increase more than rents in more exposed regions. Using the Campbell-Shiller decomposition, about 70% of return variation is attributable to future price-to-rent increases, 36% to lower future rent growth (consistent with more rental supply), and only 5% to discount rate differentials.

Q10. What do the listing data reveal about the supply implications of the channel?

A: Table 10 shows that QE reduces both sale and rental listings in more exposed regions (both significant at 1%), consistent with the aggregate national decline visible from 2015 onward. Critically, the ratio of sale listings to rental listings declines significantly in more exposed regions: sale listings fall more than rental listings (columns 3 and 6, significant at 1% with both exposure measures). This relative shift implies that the share of properties available for rent increases relative to properties available for sale in regions more exposed to the portfolio rebalancing channel, providing evidence of an expanded rental supply. This finding is interpreted as a potentially beneficial side effect of QE-induced buy-to-let investment for housing affordability, to the extent that a larger rental supply mitigates rent increases even as house prices rise.

Q11. What is the theoretical model underlying the empirical analysis?

A: The model (Appendix C) features a representative local household with mean-variance preferences managing a portfolio of bonds, housing, and cash (equities are omitted for tractability). Preferred habitat investors segment both the national bond market and the local housing market. QE reduces the fixed net supply of bonds, raising bond prices and reducing expected bond returns. Under the substitutability of bonds and houses, households rebalance toward housing to restore optimal allocation, bidding up house prices; the larger the initial bond share, the larger the required rebalancing. Housing supply constraints determine how much rebalancing depresses expected housing returns (rental yields). The model does not unambiguously predict the response of the cash (deposit) share, motivating the empirical investigation reported in column (6) of Table 3.

Q12. What are the aggregate household balance sheet patterns consistent with the individual-level results?

A: Table 1 shows that Germany’s aggregate household real estate share rose from 55% of total assets in 2014 to 56–57% in 2017–2018, while the bond share declined by roughly 0.5 percentage points. The homeownership rate declined by about 2 percentage points over the sample period (from 52.5% in 2014 to 51.4–51.5% in 2017–2018), consistent with an increasing share of landlords and renters—which is compatible with the buy-to-let mechanism since more than 60% of German renters lease from other households. Household leverage also declined (loans-to-assets from 13% in 2014 to 12% in 2017), consistent with portfolio rebalancing rather than credit-driven housing acquisition. The deposit share remained constant over the period, weighing against the negative-interest-rate policy as a driver of portfolio rebalancing.

Key Concepts

Housing portfolio channel of QE transmission: The paper’s central concept—a mechanism by which central bank bond purchases (QE) induce households holding bonds to rebalance their portfolios toward second homes held for investment (buy-to-let), operating through changes in risk premia (bond prices and expected returns) rather than through bank lending channels or future short-term interest rates.

Ex-ante bond share (QE exposure measure): Each household’s share of total wealth invested in bonds (direct holdings plus indirect holdings via mutual funds and insurance) measured in the 2014 pre-QE survey wave. Used as a continuous household-level treatment intensity: the larger this share, the stronger the portfolio pressure to rebalance when the ECB reduces bond supply to the private sector. Corresponds roughly to 10 percentage points per interquartile range.

Buy-to-let motive: In the paper’s usage, the investment purpose of purchasing second homes specifically to rent them out—or to declare them for future letting—in order to exploit Germany’s substantial tax advantages for rented properties (depreciation allowances, deductibility of mortgage interest, management costs, and property taxes against rental income), which are unavailable for owner-occupied primary residences. Distinguished from vacation-home or commuter motives by the presence of pre-QE rental income.

Segmented housing markets / preferred habitat investors: Assumptions embedded in the paper’s theoretical model (following Flavin and Yamashita, 2002; Gete and Reher, 2018; Greenwald and Guren, 2021) that local real estate markets are insulated from national or international housing markets, and that some investors have a binding preference to hold bonds or local housing, so that QE-induced price changes in the bond market are not fully arbitraged away by shifting into liquid alternatives.

Parallel trends (DiD validity): The identifying assumption that, absent QE, households with larger and smaller initial bond shares would have followed the same trajectory in their second-home portfolio shares. The paper documents this graphically using all three survey waves (Figure 2) and supports it with two indirect placebo tests involving unrelated treatment and outcome variables.

Regional rental yield: The rent-to-price ratio at the regional (Kreise) level, derived from Bulwiengesa data. Used as the primary regional outcome variable because it jointly captures discount rate, rent-growth, and price-to-rent dynamics. A Campbell-Shiller decomposition decomposes its predictive content into three components: discount rates (5%), future rent growth (36%), and future price-to-rent ratio changes (70%) in the German regional panel.

Sale-to-rental listing ratio: The ratio of sale listings to rental listings for apartments on Immoscout 24, used as a quantity-side outcome variable. A decline in this ratio in more-exposed regions is interpreted as evidence of a relative increase in rental supply, consistent with the buy-to-let motive and with potentially beneficial implications for housing affordability.

Church tax (Kirchensteuer): A German institutional feature—formally affiliated church members pay an additional 8–9% surcharge on their regular income tax bill (varying by state). Because the tax advantage of owning rental property is proportional to the marginal tax rate, church members face a higher effective marginal tax rate and thus derive larger tax benefits from buy-to-let investment, producing stronger QE-induced portfolio rebalancing for this sub-group.

A Preferred-Habitat Model of Term Premia, Exchange Rates, and Monetary Policy Spillovers

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Core Argument

The paper develops a two-country preferred-habitat model in which currency and bond markets are populated by different investor clienteles — currency traders with price-elastic demand for foreign assets, and bond investors whose preferences are habitat-specific by country and maturity — with segmentation partly overcome by global arbitrageurs who have limited capital and bear mean-variance risk. Risk premia in the model are time-varying, connected across markets, and consistent with the empirical violations of Uncovered Interest Parity (UIP) and the Expectations Hypothesis (EH): in particular, currency carry trade (CCT) and bond carry trade (BCT) strategies earn abnormally high expected returns in ways that co-vary across the two markets in a manner the standard frictionless model cannot generate. Through these time-varying, connected risk premia, large-scale bond purchases (QE) lower domestic bond yields, lower foreign bond yields, and depreciate the purchasing country’s currency; short-rate cuts also lower foreign yields, but with smaller effects than bond purchases. A key structural finding, quantified in the estimated model calibrated to US and Eurozone data, is that currency returns are nearly uncorrelated with long-maturity bond returns — an exchange-rate disconnect — yet the currency market is instrumental in transmitting bond demand shocks across countries, because arbitrageurs hedge their cross-currency positions in bond markets and vice versa. Sterilized foreign-exchange interventions have strong effects on the exchange rate but weak effects on bond yields, while QE/QT has weak effects on the exchange rate but sizeable effects on foreign bond yields — a sharp asymmetry that follows directly from the disconnect.

In depth

Q1. Why do UIP and EH fail in the standard model, and what changes in this model?

In the standard model with perfect capital mobility, risk premia are constant, so the yield curve depends only on expectations of the domestic short rate and the exchange rate absorbs short-rate differentials exactly. In this model, arbitrageurs bear the residual risk when currency traders and bond clienteles are unwilling to absorb excess supply or demand at prevailing prices. Because arbitrageurs have limited capital (captured by a risk-aversion parameter a ≥ 0 that can also represent capital or Value-at-Risk constraints in reduced form), they demand compensation — time-varying risk premia — for holding currency and maturity risk. When a = 0, arbitrageurs are risk-neutral, UIP and EH both hold, and the model collapses to the standard frictionless benchmark.

Q2. What are the three types of agents and what does each do?

Currency traders hold foreign assets and have a demand that is downward-sloping (price-elastic, with slope coefficient αe ≥ 0) in the log exchange rate; their demand also shifts with a stochastic currency demand factor γt. They can be interpreted as households engaged in expenditure switching or central banks managing reserve levels. Bond investors form clienteles, each with a preferred-habitat demand for bonds of a specific country and maturity that is downward-sloping in the log bond price (slope αj(τ)) and shifts with a country-specific bond demand factor βjt; examples are pension funds and insurance companies whose liabilities are long-dated and denominated in their home currency. Global arbitrageurs trade the currency and all bonds of both countries, maximizing mean-variance utility over instantaneous wealth changes; they bridge the segmented markets and their positions pin down equilibrium risk premia.

Q3. What is the equilibrium structure and which factors drive prices?

The equilibrium exchange rate and bond prices are log-affine functions of five stochastic factors: the home short rate iHt, the foreign short rate iFt, the currency demand factor γt, and the two bond demand factors βHt and βFt. These factors follow a mean-reverting (Ornstein-Uhlenbeck) system. The equilibrium is characterized by a scalar nonlinear system (25 equations in the general case) whose solution pins down the loadings of prices on each factor. This affine structure means each asset’s risk premium is the product of the arbitrageur’s risk-aversion coefficient, the factor covariance matrix, and arbitrageur net positions, which are themselves determined by market-clearing.

Q4. How does a conventional short-rate cut transmit domestically and internationally in the model?

Following a home short-rate cut, arbitrageurs find it attractive to enter the CCT — borrow home currency, invest in foreign currency. If currency traders’ demand is price-elastic (αe > 0), arbitrageurs’ equilibrium foreign-currency holdings rise, and the expected return on the CCT rises too (arbitrageurs must be compensated for the increased risk). This attenuation effect means the foreign currency appreciates less than implied by UIP: the exchange rate response is dampened. Simultaneously, arbitrageurs enter the home BCT (borrow at the home short rate, invest in long home bonds); if home bond investors’ demand is price-elastic (αH(τ) > 0), arbitrageurs’ long-bond holdings rise and the BCT’s expected return rises, attenuating the transmission to domestic long-maturity yields (which fall less than EH would imply). A propagation effect to foreign bond yields arises through arbitrageur hedging: by taking long positions in foreign currency (CCT), arbitrageurs become exposed to the risk that the foreign short rate drops and the foreign currency depreciates; long-maturity foreign bonds provide a natural hedge (their price rises when the foreign short rate drops), so arbitrageurs increase foreign bond demand, depressing foreign yields. This international transmission of conventional policy is absent from the standard model.

Q5. How does unconventional policy (QE/QT) transmit domestically and to the exchange rate and foreign yields?

Following QE purchases of home bonds, their prices rise; arbitrageurs accommodate by holding fewer home bonds, which reduces their exposure to home short-rate risk. With less home-rate risk, arbitrageurs become more willing to hold foreign currency (which depreciates when the home short rate rises, offering a natural hedge against the home rate risk they have shed). The increased foreign-currency position in turn makes arbitrageurs more willing to hold foreign bonds (which hedge the foreign-currency position against foreign rate changes). The net result in the model is: QE lowers domestic bond yields, lowers foreign bond yields, and depreciates the home currency. The quantitative finding from the estimated model is that QE/QT effects on foreign bond yields are sizeable and stronger than those of conventional short-rate policy.

Q6. What explains the exchange-rate disconnect, and how can the currency market still transmit bond demand shocks?

In the estimated model, variance decompositions reveal that long-maturity bond yields in each country are driven primarily by bond demand factors (βHt and βFt), while the exchange rate is driven primarily by the currency demand factor (γt); short rates account for a small fraction of movements in both, and each factor type accounts for negligible variation in the other asset class’s price. The disconnect between bond yields and the exchange rate arises because bond demand shocks in the two countries move the exchange rate in opposite directions — a home bond demand shock that lowers home yields also raises the exchange rate via arbitrageur hedging, while a foreign bond demand shock moves the exchange rate in the opposite direction. These offsetting effects make the exchange rate nearly uncorrelated with long-maturity bond yields. However, bond demand shocks in one country are transmitted to bond yields in the other country through the currency market: arbitrageurs hedge their bond positions using the currency, so a shock to home bond demand moves arbitrageurs’ currency positions, which in turn affects their willingness to hold foreign bonds. Cross-country bond yield comovement is therefore positive and sizeable, despite the exchange-rate disconnect.

Q7. What are the model’s implications for foreign exchange intervention?

A sterilized purchase of foreign currency by the home or foreign central bank — which shifts the currency demand factor — has strong effects on the exchange rate but weak effects on bond yields. This follows directly from the variance decomposition: the exchange rate loads heavily on the currency demand factor and bond yields load lightly on it. The asymmetry mirrors the QE result in reverse: QE shifts bond demand factors, which load heavily onto bond yields and lightly onto the exchange rate; FX intervention shifts the currency demand factor, which loads heavily onto the exchange rate and lightly onto bond yields. The model thus delivers a sharp policy instrument separation between QE/QT (primarily a bond yield tool) and FX intervention (primarily an exchange-rate tool), with each having spillovers in the other dimension that are quantitatively weaker.

Q8. How is the relationship between currency risk premia and bond risk premia captured, and what empirical regularities does the model match?

The model’s risk premia are linked through the shared arbitrageur portfolio: the price of each risk factor is proportional to the covariance between that factor and the arbitrageur’s overall portfolio return, so a shock that changes arbitrageurs’ currency positions also changes the compensation required for bond positions, and vice versa. The estimated model is reported to match closely the violations of UIP (CCT profitability) and EH (BCT profitability) documented in the literature, and the ways in which these violations are connected — including findings that yield-curve slope differentials predict CCT profitability, and that CCT profitability declines when carried out with long-maturity rather than short-maturity bonds. These matches are described as consistent with the empirical regularities, not structural identification of the underlying causes.

Q9. What is the role of segmented versus global arbitrage, and why does the distinction matter?

The paper considers both cases. Under segmented arbitrage, separate arbitrageur pools operate in the currency market (risk aversion ae), home bond market (aH), and foreign bond market (aF); first-order conditions for each pool reflect only their own portfolio risk, so the prices of risk factors differ across markets. Under global arbitrage, a single pool of arbitrageurs trades all assets, and their shared portfolio means the price of each risk factor is the same across currency and bond markets — this is the mechanism through which bond demand shocks in one country propagate through the currency market to bond yields in the other. Global arbitrage is the primary specification; segmented arbitrage serves as a benchmark to isolate the hedging-based transmission channel that requires global positions.

Q10. How does the model relate to and extend predecessor frameworks?

The model extends Vayanos and Vila (2021) — a closed-economy preferred-habitat yield curve model — to two countries by adding a currency market and a second country’s bond market, with arbitrageurs who are global rather than country-specific. In the currency dimension, the attenuation of UIP deviations parallels Gabaix and Maggiori (2015), which models exchange-rate dynamics with financially constrained intermediaries but without a yield curve. The two-country structure allows the paper to simultaneously study term premia (EH violations), exchange rate dynamics (UIP violations), and their connection, and to quantify the effects of QE, conventional monetary policy, and FX intervention within a single internally consistent framework estimated on US-Eurozone data.

Key Concepts

Preferred-habitat demand: A bond investor’s demand for bonds of a specific country and maturity that does not arise from portfolio optimization over the full menu of available assets, but rather from institutional constraints or liability-matching motives (e.g., pension funds matching long-dated domestic liabilities). In the model, preferred-habitat demand is price-elastic with slope αj(τ) and shifts with a country-specific bond demand factor βjt; the elastic component means that as bond prices rise, clientele demand falls, so arbitrageurs must absorb the residual supply and require a risk premium to do so.

Global arbitrageur: An investor who trades the currency and bonds of both countries simultaneously, bridging the segmented currency and bond markets. In the model, global arbitrageurs maximize mean-variance utility over instantaneous wealth changes; their shared portfolio across all asset classes is the mechanism through which shocks in one market create hedging-driven demand in other markets, generating the cross-market linkages in risk premia and monetary policy transmission.

Currency carry trade (CCT): A strategy that borrows at the home short rate and invests at the foreign short rate, profiting when the foreign currency does not depreciate enough to offset the interest rate differential. Under UIP, the CCT earns zero expected return; the model generates a positive expected CCT return — a currency risk premium — when arbitrageurs are risk-averse and currency traders’ demand is price-elastic. In the paper’s notation, the CCT return is det/et + (iFt − iHt)dt.

Bond carry trade (BCT): A strategy that borrows at the short rate and invests in long-maturity bonds of the same country, profiting when long yields fall or when expected short rates are below current long yields. Under EH, the BCT earns zero expected return; the model generates a positive expected BCT return — a term premium — when arbitrageurs are risk-averse and bond clientele demand is price-elastic.

Exchange-rate disconnect: The empirical and model finding that movements in the exchange rate are nearly uncorrelated with movements in long-maturity bond yields, even though both are endogenously determined in the same model. The disconnect arises in the estimated model because long bond yields are driven primarily by bond demand factors, while the exchange rate is driven primarily by the currency demand factor, and the two sets of factors move the exchange rate in offsetting directions so that their net effect on bond yield-exchange rate covariance is approximately zero.

Attenuation effect: The dampening of monetary policy transmission to asset prices caused by the need to compensate risk-averse arbitrageurs for the increased risk they bear when accommodating the policy-induced excess demand. In the currency market, a home short-rate cut causes the CCT’s expected return to rise (arbitrageurs must be paid more to hold foreign currency), which means the foreign currency appreciates less than UIP predicts. In the bond market, a short-rate cut causes the BCT’s expected return to rise (term premia increase), so long yields fall less than EH predicts.

Propagation effect: The international transmission of a domestic monetary policy shock to foreign asset prices through arbitrageur hedging. A home short-rate cut causes arbitrageurs to increase their foreign-currency position (CCT); this exposes them to the risk of foreign short-rate declines (which depreciate the foreign currency), and long-maturity foreign bonds hedge this risk; so arbitrageurs increase foreign bond demand, depressing foreign yields. This channel is absent from the standard model where risk premia are constant.

Log-affine equilibrium: The conjectured and verified form of the equilibrium in which the log exchange rate and log bond prices are affine (linear plus constant) functions of the five state factors (iHt, iFt, γt, βHt, βFt). This structure allows the model to be solved as a system of ordinary differential equations and scalar equations, and enables closed-form or numerically tractable characterization of risk premia, variance decompositions, and policy effects.

Bond demand factor (βjt): A stochastic variable that shifts the intercept of bond clientele demand in country j, independent of maturity τ. A positive shock to βjt increases desired bond holdings of country-j clienteles at any given price, forcing arbitrageurs to shed country-j bonds, which lowers bond yields. The factor follows a mean-reverting process and in the estimated model is found to be the primary driver of long-maturity yields in both countries.

Currency demand factor (γt): A stochastic variable that shifts the intercept of currency traders’ demand for foreign assets, independent of the exchange rate level. A positive shock to γt increases desired foreign asset holdings of currency traders, so arbitrageurs reduce their foreign-currency position, which affects their bond positions through hedging. In the estimated model, γt is the primary driver of exchange-rate movements.

Summary based on LSE Research Online accepted version (accepted manuscript). AI-assisted, human review pending.

Aggregate demand externality and self-fulfilling default cycles

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question. Why do corporate defaults cluster in recurring episodes rather than occurring smoothly? The paper asks whether observable fundamental factors — firm characteristics and macroeconomic variables — are sufficient to account for the clustered default patterns documented in the data, and, if not, what theoretical mechanism can explain them.

Empirical Motivation. Using Moody’s historical default rate data, the authors document that the long-run average corporate bond default rate during 1866–2008 was approximately 1.50%, yet defaults were highly episodic: the worst three-year period during the Great Depression totaled 12.88%, and the three-year period 1873–1875 after the railroad boom reached 35.80%. A Markov switching regression on post-war default rate data (1951–2017) strongly rejects a linear no-switch model in favor of a two-regime model across all information criteria (AIC, HQ, SC, and log-likelihood). The estimated high-default regime has a mean default rate of 1.93% (unconditional mean µ/(1−ρ)) — roughly eight times the 0.23% mean of the low-default regime — and a standard deviation nearly six times larger. The high-default regime persists on average 5.81 years (transition probability of staying ≈ 0.83), while the low-default regime lasts approximately 7.52 years (staying probability ≈ 0.87).

Model. The authors build a continuous-time general equilibrium model with Dixit-Stiglitz monopolistic competition (CES aggregation with elasticity σ) and an endogenous entry/exit/default mechanism. Households are risk-neutral and also act as entrepreneurs. At each instant, δµ new project blueprints are invented; entrepreneurs borrow to invest, then face an idiosyncratic liquidity shock z drawn from a Pareto distribution G(z). Entrepreneurs continue if z ≤ Z*, a cutoff determined by the continuation value of the firm, and default otherwise. Continuing firms become monopolists for a new variety until that variety becomes obsolete at a Poisson rate δ. Each operating firm must borrow working capital constrained by its firm value Vt (collateral constraint wtnjt ≤ θVjt). The entire equilibrium reduces to a two-dimensional dynamical system in (Mt, Vt), where Mt is the number of operating firms (state variable) and Vt is the firm value (control variable).

Key Mechanism — Demand Externality and Positive Feedback. Under CES aggregation, each firm’s gross revenue is y_jt^(1–1/σ) · Y_t^(1/σ), making individual firm revenue increasing in aggregate output Yt. A decline in Yt lowers firm profits and firm value Vt, which raises the default threshold Z* and increases the fraction of projects that are abandoned. Fewer operating firms further depress Yt, closing a positive feedback loop. This static strategic complementarity (through CES) is combined with dynamic strategic complementarity through the borrowing constraint: higher expected future firm value relaxes current working capital constraints, raising current production.

Multiple Equilibria and Global Dynamics. The two-locus phase diagram (˙Mt = 0 and ˙Vt = 0) yields multiple intersections — and hence multiple steady states — when productivity A lies in an intermediate range (A < A < Ā). When A > Ā, a single good saddle-point equilibrium exists. When A < A, no equilibrium can be sustained. In the intermediate range, a good steady state (low default rate, high firm value) coexists with a bad steady state (high default rate, low firm value). The good steady state is always a saddle; the bad steady state is a sink (locally indeterminate, κ < κ_Hopf) or a source (locally determinate but globally indeterminate, κ > κ_Hopf), depending on parameter κ = 1 + (θ + ρ)/δ.

Bogdanov-Takens Bifurcation. Using global dynamical methods, the paper demonstrates richer indeterminacy than local analysis permits. Near the Bogdanov-Takens point (κ, Ā), the system can exhibit: (a) infinite equilibrium trajectories converging to the bad steady state; (b) saddle-loop bifurcation at κ = κ_SL ≈ 14.25 (under the baseline calibration); (c) stable or unstable periodic orbits for κ ∈ (κ_Hopf, κ_SL) — endogenous business cycles in a perfect-foresight equilibrium; and (d) multiple trajectories from near the source that converge to the good saddle equilibrium.

Simulation of Clustered Defaults. With a two-state Markov process for productivity (Ah = 10, Al = 9.34) and pessimistic sentiment shifts (the “ugly” state), the model replicates the cluster pattern: in the good/high-productivity state, the default rate is near zero; when productivity falls to low and sentiment turns pessimistic, the default rate can spike to approximately 12%, consistent with the Great Depression observation. Critically, the paper shows that the cluster pattern is generated only under global dynamics — restricting to local dynamics produces substantially smaller fluctuations in the default rate, confirming that the ugly (sink) equilibrium is essential.

Policy. A countercyclical subsidy to non-defaulting entrants — financed by a lump-sum tax, calibrated as tr(Vt) = τ(VG − Vt) — shifts the ˙Mt = 0 locus downward and can eliminate the bad steady state entirely, leaving only the good saddle-path equilibrium. The paper provides a closed-form sufficiency condition for τ (Proposition 7).

Scope Conditions. Multiple equilibria require: (i) productivity in the intermediate range A < A < Ā; (ii) the elasticity of substitution σ not too large (below a threshold σ̄ that itself depends on µ); (iii) the borrowing constraint binding (δ > θσ/((σ–1)κ), which can always be ensured by choosing δ sufficiently large). Clustered defaults in the simulation require the joint occurrence of a negative fundamental shock (productivity falling from high to low) and a shift to pessimistic sentiment; either factor alone generates only limited default amplification.

In depth

Q1. What is the core empirical motivation for the model, and what does the regime-switching analysis establish?

The paper documents that the corporate bond default rate, drawn from Moody’s data covering 1866–2008, clusters sharply in episodes: the long-run average is 1.50%, yet the worst three-year period of the Great Depression totaled 12.88% and 1873–1875 reached 35.80%. A Markov switching regression on 1951–2017 data strongly rejects a linear no-regime-switch model across all four criteria (log-likelihood, AIC, HQ, SC). The two-regime model identifies a high-default regime with unconditional mean 1.93% and standard deviation roughly six times the low-default regime’s, a persistence probability of approximately 0.83 (duration ≈ 5.81 years), and a low-default regime with unconditional mean 0.23% and persistence approximately 0.87 (duration ≈ 7.52 years). The regime-switching result supports the prior literature’s claim (Das et al. 2007; Duffie et al. 2009; Azizpour et al. 2018) that observable fundamentals alone cannot account for clustered defaults.

Q2. How does the Dixit-Stiglitz CES structure generate a demand externality that links aggregate output to individual firm default decisions?

Under CES aggregation with elasticity σ, each firm’s gross revenue equals y_jt^(1–1/σ) · Y_t^(1/σ) (equation 7), so aggregate output Yt directly enters individual firm revenue. Each firm takes Yt as given, yet the aggregation of all firms’ output determines Yt. When aggregate output falls — because more firms have defaulted and exited production — each remaining firm’s revenue and profit fall, reducing the firm’s continuation value Vt. A lower Vt tightens the borrowing constraint (wtnjt ≤ θVjt), reduces working capital, and raises the probability that the firm’s idiosyncratic liquidity shock will exceed the default threshold Z*, producing further defaults. This positive feedback constitutes the demand externality: individual firms’ decisions are strategic complements, both statically (through CES demand) and dynamically (through the borrowing constraint on working capital).

Q3. What is the two-dimensional dynamical system that summarizes the equilibrium, and what do the two loci look like in the phase diagram?

The entire equilibrium reduces to two differential equations in (Mt, Vt): ˙Mt = –δ[Mt – µG(Z(Vt))] and ˙Vt = κδVt[1 – F(Vt, Mt)], where F captures the ratio of monopoly profit to firm value including the borrowing constraint. The ˙Mt = 0 locus slopes strictly upward because a higher firm value Vt raises the default cutoff Z* and lowers the fraction of entrants who default, so more firms survive and Mt rises until absorption equals entry. This locus has a minimum at Mm = µG(zm) because firm value must exceed the threshold that sustains the credit market. The ˙Vt = 0 locus is non-monotonic: it first slopes upward (more firms raise aggregate demand and profit through the scale/externality channel) and then slopes downward (more firms tighten the labor market, raising wages and lowering profits). The two opposing channels make the ˙Vt = 0 locus hump-shaped, creating the possibility of two intersections and hence two steady states.

Q4. Under what conditions do multiple steady states exist, and what does each look like?

Multiple steady states exist when productivity A satisfies A < A < Ā, where A and Ā are closed-form thresholds given by Equations (A.3) and (A.4), and the elasticity of substitution σ is below a threshold σ̄ (Equation A.5). When A < A, neither locus intersects and no equilibrium is sustainable. When A > Ā, a single good saddle-point equilibrium exists. In the multiple-equilibria range, the good steady state has a higher firm value and a smaller fraction of firms defaulting; the bad steady state has a lower firm value and a higher default rate. Under the paper’s numerical calibration (A = 10, η = 6.5, Zmin = 0.88), the low default rate at the good steady state is approximately 1.5% and the high default rate at the bad steady state is between 12% and 13%.

Q5. What are the local dynamics around each steady state, and how does parameter κ determine whether the bad steady state is a sink or a source?

Proposition 5 shows that the good steady state is always a saddle point, ensuring a unique convergent path for initial Mt near Mg_0. The bad steady state’s local nature depends on κ = 1 + (θ + ρ)/δ and the critical value κ_Hopf = 1 + ψ/(θMb_0Vb_0). When κ is between 1 and κ_Hopf, the Jacobian trace is negative and the bad steady state is a sink with one order of indeterminacy: given Mt close to Mb_0, infinitely many initial values of the control variable Vt satisfy all equilibrium conditions. When κ > κ_Hopf, the bad steady state is a source point; the economy diverges from it. Because κ does not affect the steady-state locations (Proposition 3), one can vary κ to change the dynamic character without moving the equilibria in the phase diagram.

Q6. What does the global dynamics analysis reveal that local analysis misses?

Global analysis via Bogdanov-Takens bifurcation (Proposition 6) reveals three classes of dynamics absent from local analysis. First, even in the saddle-source case (locally determinate), there exist multiple equilibrium trajectories diverging from near the bad (source) steady state and converging to the good (saddle) steady state; these paths satisfy all equilibrium conditions including transversality but are incorrectly ruled out by local methods. Second, at the critical value κ_SL ≈ 14.25 (under the baseline calibration), a homoclinic saddle-loop orbit connects the saddle point to itself — all trajectories interior to the loop converge to the bad steady state. Third, for κ between κ_Hopf and κ_SL, periodic orbits arise in a perfect-foresight equilibrium with no external shocks. For example, at κ = 14.9, the phase diagram displays a unique periodic orbit around the bad steady state, with two distinct initial values of Vt for any given Mt near the orbit — endogenous, perpetual oscillations without any exogenous driving force. Numerical experiments confirm that Mt = 0.23 admits two rational-expectations values of Vt (2.09 and 3.55) on the saddle path alone, illustrating abundant indeterminacy even at the endpoint.

Q7. How does the paper simulate the clustered default pattern and what is the role of the “ugly” equilibrium?

The paper constructs a three-state Markov economy: “good” (high productivity Ah = 10, single saddle equilibrium, near-zero default rate), “bad” (low productivity Al = 9.34, saddle-path equilibrium, modestly elevated defaults), and “ugly” (low productivity, sink-path equilibrium, sharply elevated defaults). The ugly state is reached when, upon a productivity decline, firms adopt pessimistic expectations and the economy slides to the high-default sink instead of remaining on the low-default saddle path. Transition probabilities are set so that the average ugly-state duration is approximately 6 years and roughly 45% of periods are ugly, consistent with the regime-switching estimates. With Zmin = 0.2 and η = 15, the ugly-state default rate can reach approximately 12%, matching the Great Depression observation. The counterfactual experiment deletes the ugly state (pGU = 0) and resets pGB = 0.45: the resulting default rate stays close to zero with no cluster pattern, demonstrating that global dynamics (the ugly sink) rather than the fundamental shock alone generate the clustering.

Q8. Can purely sentiment-driven cycles generate the clustered default pattern?

Section 6.2 fixes productivity at a low level (A = 9.53) and drives switches between the bad (saddle path) and ugly (sink path) states by pure sentiment shocks alone (πBU and πUB). The simulated default rate does spike upward when sentiment turns pessimistic, but the rises are generally more modest than in the combined fundamental-plus-sentiment exercise, and the default rate can no longer be characterized as countercyclical. The authors conclude that the realistic observed default cluster is the result of a combination of negative fundamental shocks and pessimistic sentiment shifts; either ingredient alone is insufficient to replicate all features of the data.

Q9. How does the collateral constraint on working capital create dynamic strategic complementarity?

Following Jermann and Quadrini (2012), Liu and Wang (2014), and Lian and Ma (2021), each operating firm must borrow to pay wages each period, subject to the constraint wtnjt ≤ θVjt. Since Vt is forward-looking (the discounted present value of the firm’s monopoly profit stream), optimistic expectations about future output raise Vt, relax the borrowing constraint, allow firms to hire more labor and produce more output today, and thereby validate optimism. This intertemporal complementarity means that the equilibrium is sensitive not only to current fundamentals but also to beliefs about the future, opening the channel for sentiment-driven multiple equilibria and self-fulfilling cycles.

Q10. What is the policy remedy for the bad equilibrium, and how does it work?

Proposition 7 establishes that a countercyclical lump-sum-tax-financed subsidy to non-defaulting entrants, tr(Vt) = τ(VG − Vt), with τ exceeding a computable threshold, eliminates the bad steady state. The subsidy works by effectively raising the value of continuing for a firm at any given Vt and Mt, shifting the ˙Mt = 0 locus downward until it lies below the ˙Vt = 0 locus everywhere in the relevant range, eliminating the second intersection and leaving only the good saddle-path equilibrium. The numerical illustration uses parameters from Section 6 with A = 9.67 and τ = 1/3 to demonstrate that the bad steady state vanishes and the phase diagram has a single equilibrium. The subsidy is self-limiting: in normal conditions when firm value is already high (Vt ≈ VG), the transfer is near zero.

Cui and Kaas (2021) show default cycles from self-fulfilling beliefs in a fully competitive firm environment, focusing on intertemporal default coordination. The present paper differs in three respects. First, firms engage in monopolistic competition under CES preferences, and the main novel mechanism is cross-firm default contagion through the demand externality — which can produce multiple equilibria even in a static setting, without any intertemporal coordination. Second, the paper examines the joint role of fundamental shocks and aggregate-demand externalities together, showing that multiple equilibria arise only in the presence of sufficiently low productivity (A < A < Ā), making indeterminacy contingent on external fundamentals rather than structural parameters alone. Third, the continuous-time framework with full global analysis via Bogdanov-Takens bifurcation allows characterization of periodic orbits and the interaction of the ugly sink path with Markov productivity regimes — dynamics not covered in Cui and Kaas (2021).

Q12. What is the markup prediction of the model, and is it consistent with empirical evidence?

Under Dixit-Stiglitz CES with elasticity σ, the equilibrium markup of each intermediate good equals σ/(σ–1) at the firm level. However, the measured gross markup — which includes the effective collateral constraint — is predicted to comove positively with the default rate in the model, and hence the markup is countercyclical. The paper notes this is consistent with the well-documented empirical regularity in Bils (1987) and Rotemberg and Woodford (1999). Additionally, the model replicates the finding in Gilchrist and Zakrajšek (2012) that a low default rate is associated with a high firm entry rate.

Key Concepts

Demand Externality (Dixit-Stiglitz type). In the paper’s sense, this is the mechanism by which individual firms’ revenues depend on aggregate output Yt through the CES aggregator: each firm’s gross revenue is y_jt^(1–1/σ) · Y_t^(1/σ). Each firm takes Yt as given, but the aggregation of all firms’ output determines Yt. This creates a positive spillover: more operating firms raise aggregate output, which raises each firm’s revenue, and vice versa. The paper uses this as the central transmission channel for self-fulfilling defaults, in contrast to prior literature that emphasized debt networks or asymmetric information contagion.

Self-Fulfilling Default Cycle. A dynamic equilibrium path in which pessimistic expectations about aggregate output are validated: if firms anticipate that more other firms will default (lowering Yt), their own continuation value Vt falls, raising the probability that their idiosyncratic liquidity shock will exceed the default threshold, increasing actual defaults, further lowering Yt, and so on. The paper distinguishes this from shock-amplifier stories by constructing a model with multiple rational-expectations equilibria in which the aggregate default rate is determined in part by initial beliefs.

Bogdanov-Takens Bifurcation. A mathematical tool for global dynamics analysis applied to two-dimensional continuous-time systems. In the paper, it is used to characterize system behavior when the parameters (κ, A) are near the point (κ̄, Ā) at which the Jacobian has two zero eigenvalues. Near this point, the system can exhibit saddle-loop bifurcations, Hopf bifurcations, homoclinic orbits, and stable or unstable periodic orbits — all of which are invisible to local linearization analysis. The paper uses this to establish that indeterminacy is more pervasive than local analysis suggests.

Good / Bad / Ugly Steady States. In the paper’s three-regime framework: the “good” state is the unique saddle-point equilibrium under high productivity Ah, with near-zero default rates; the “bad” state is the saddle-path equilibrium under low productivity Al, with modestly elevated defaults; the “ugly” state is the sink-path equilibrium under low productivity, characterized by self-fulfilling high default rates (up to ~12%). The ugly state is reached only when pessimistic sentiment coincides with the low-productivity regime, and it is the ugly state that generates the cluster pattern in simulation.

Collateral Constraint on Working Capital. The firm-level borrowing constraint wtnjt ≤ θVjt, where θ is the collateral ratio and Vjt is the firm’s continuation value. This constraint means that higher expected future profits — by raising Vt — relax the current borrowing limit, increase current labor demand and output, and create dynamic strategic complementarity between current and future production. It is this constraint, combined with the CES demand externality, that makes the dynamical system two-dimensional and generates the non-monotonic ˙Vt = 0 locus.

Global Indeterminacy. The existence, given an initial state variable Mt, of multiple equilibrium trajectories — each satisfying all equilibrium conditions including transversality — that converge to different steady states or follow periodic paths. In the paper, global indeterminacy arises even when the system is locally determinate (e.g., in the saddle-source case): trajectories diverging from near the source steady state can converge to the saddle steady state along multiple paths, none of which is detectable by local linearization.

Periodic Orbit (Endogenous Cycle). In the paper, a closed trajectory in the (Mt, Vt) phase plane that the economy follows indefinitely in perfect-foresight equilibrium without any exogenous shocks. Such orbits exist for κ ∈ (κ_Hopf, κ_SL), are stable if S < 0 and unstable if S > 0 (where S is a computable quantity defined in Equation A.13). Their existence demonstrates that business cycles can arise purely from internal forces — the demand externality and borrowing constraint — consistent with the view in Beaudry, Galizia, and Portier (2020).

Auctions with Frictions: Recruitment, Entry, and Limited Commitment

Mon, 01 Jan 0001 00:00:00 +0000

This paper develops an auction model that jointly incorporates three frictions pervading informal price-formation processes: (1) costly recruitment by the seller, (2) costly participation by bidders, and (3) the seller’s inability to commit to a recruitment level or reserve price. The authors argue these frictions are especially prevalent in markets for idiosyncratic assets such as mergers and acquisitions, real estate, and home repair contracting, where auction houses like Christie’s and Sotheby’s command fees of 20–30% of revenues precisely because they reduce the underlying inefficiencies.

The model features a single seller who exerts recruitment effort gamma at cost gamma*s, generating a Poisson-distributed number of contacted bidders with mean gamma. Each contacted bidder independently decides whether to pay entry cost c > 0 to learn their private value and participate in a first-price auction (FPA). The seller cannot commit to gamma (which is unobservable to bidders) or to a reserve price. Two scenarios are analyzed: PO (participation-observable, where bidders observe the number of entrants before bidding) and PU (participation-unobservable).

The central tension is between the seller’s incentive to recruit more bidders to intensify competition and raise revenue, and bidders’ rational concern that excessive recruitment makes entry unprofitable. Because the seller cannot commit, this tension generates several novel inefficiency results.

In the PO scenario, the seller’s marginal revenue from recruitment Ro’(lambda) is single-peaked, meaning there is a minimum profitable participation scale lambda_o below which the seller will never recruit. Combined with a maximum participation level lambda-bar_c above which bidders will not enter (defined by U(lambda-bar_c) = c, where U is the bidder’s expected payoff), no-trade equilibrium is the unique outcome whenever lambda-bar_c < lambda_o — even for arbitrarily small recruitment cost s. This result holds because with unobservable effort, bidders correctly anticipate the seller will target participation above lambda_o, making entry unprofitable. When lambda-bar_c > lambda_o, three regimes arise: (i) no trade if s exceeds a threshold s-bar_o; (ii) an interior equilibrium with full entry (q* = 1) and lambda* = lambda_o(s) for intermediate s; and (iii) for small s, an equilibrium with lambda* = lambda-bar_c and partial entry q* = Ro’(lambda-bar_c)/s < 1. In regime (iii), total recruitment cost lambda*(s/q*) equals the constant lambda-bar_c * Ro’(lambda-bar_c) regardless of s — so even as s approaches zero, wasteful recruitment costs do not vanish, because they are determined by incentive constraints rather than by technology.

In the PU scenario, a no-trade equilibrium always exists for all parameter values, because the seller cannot credibly disclose participation, creating self-reinforcing expectations of zero competition. The seller’s recruitment incentive xi(lambda) is strictly weaker than Ro’(lambda) in the PO scenario (proven via revenue equivalence: Ro’(lambda) = xi(lambda) + a positive term reflecting how greater participation induces more aggressive bidding). This yields ranking reversals: for intermediate s and small c, the PO scenario dominates PU; but for small s or large c, the PU scenario’s weaker recruitment incentive reduces wasteful over-recruitment, making PU preferable. These comparisons translate directly to a comparison of FPA and SPA with unobservable participation: the two formats are not equivalent in the presence of recruitment and entry frictions because they generate different recruitment incentives.

A sampling-curse mechanism drives near-complete market unraveling when sellers have privately known recruitment costs drawn from a continuous uniform distribution on [0, s_o]. Because low-cost sellers recruit more, a contacted bidder believes the seller is more likely to have low costs — and hence to have recruited many other bidders — making entry unprofitable. Proposition 3 establishes a threshold c-hat such that for c in (c-hat, c-bar), as the lower bound of the cost distribution approaches zero, the fraction of seller types that remain inactive approaches one — near-complete unraveling — even though each type would be active if its cost were commonly known.

Q: What is the paper’s main modeling innovation relative to the existing literature? A: The paper’s central novelty is combining all three frictions — costly recruitment by the seller, costly participation by bidders, and limited seller commitment — in one model. The existing literature had studied entry and recruitment separately; Szech (2011) examined costly recruitment with costless entry; McAfee and McMillan (1987) and Levin and Smith (1994) studied costly entry with an exogenously given number of potential bidders; Milgrom (1987) and McAfee and Vincent (1997) studied limited commitment to a reserve price with a fixed bidder set. None combine all three.

Q: What is the “minimum profitable scale” result and why does it arise? A: Because the seller cannot commit to a reserve price, the first few bidders are complementary — they stimulate competitive bidding, causing the seller’s marginal revenue Ro’(lambda) to be initially increasing, then decreasing (single-peaked). This means the seller’s profit Pi_o(lambda, q) is maximized either at zero or at a participation level above a minimum scale lambda_o, defined by Ro’(lambda_o) = s-bar_o. The seller will never choose a participation level between 0 and lambda_o.

Q: Under what conditions does the market completely shut down in the PO scenario? A: No-trade is the unique equilibrium outcome whenever lambda-bar_c < lambda_o, where lambda-bar_c is defined by U(lambda-bar_c) = c (the participation break-even level) and lambda_o is the seller’s minimum profitable scale. This condition arises when entry costs c are large enough relative to the competitive dynamics. Importantly, no trade occurs for every recruitment cost s > 0, including arbitrarily small s — commitment failure alone can cause complete market breakdown even when recruiting bidders is nearly costless.

Q: What is the inefficiency in regime (iii) of Proposition 2 (small s, PO scenario)? A: When s < Ro’(lambda-bar_c), equilibrium has lambda* = lambda-bar_c and q* = Ro’(lambda-bar_c)/s < 1. The total recruitment cost is lambda* * (s/q*) = lambda-bar_c * Ro’(lambda-bar_c), a strictly positive constant independent of s. As s approaches zero, total recruitment effort and its cost do not vanish — they are pinned by incentive constraints. This waste could be avoided if the seller could commit to an effort level below lambda-bar_c, illustrating that commitment failure creates persistent inefficiency even when the technology of recruitment is inexpensive.

Q: Why does a no-trade equilibrium always exist in the PU scenario but not always in the PO scenario? A: In the PU scenario, if bidders expect zero participation, they bid zero conditional on being contacted; the seller then has no incentive to recruit, validating the expectation. This equilibrium is self-sustaining for all parameter values (Claim 2). In the PO scenario, the equilibrium refinement (requiring that off-path beliefs not support negative seller payoff at lambda = 0 when trade equilibria exist) rules out no-trade equilibria when lambda-bar_c > lambda_o and s is not too large; specifically, Proposition 2 shows that no-trade equilibrium is unique only when s > s-bar_o or lambda-bar_c < lambda_o.

Q: What drives the ranking reversal between PO and PU scenarios? A: The core result is Claim 3: Ro’(lambda) > xi(lambda) for all lambda > 0, meaning the marginal incentive to recruit is strictly stronger under PO than PU. This follows from revenue equivalence: Ro’(lambda) = xi(lambda) + (d/d lambda-hat) Ru(lambda, beta_{lambda-hat})|_{lambda-hat=lambda}, and the second term is strictly positive because greater expected participation induces more aggressive bidding. For intermediate s and small c, stronger PO recruitment incentives support higher participation and revenue. For small s or large c, those same stronger incentives generate wasteful over-recruitment in PO, making PU preferable.

Q: How does the paper connect its PO/PU comparison to a comparison of first- and second-price auctions? A: In any standard auction where the highest-value bidder wins, payoff and revenue equivalence imply that the bidder payoff function U(lambda) and seller revenue Ro(lambda) are identical. In particular, the dominant-strategy equilibrium of the SPA (where bidders bid their true values regardless of participation) generates the same outcomes as the PO equilibrium, because with truthful bidding the observability of participation is irrelevant. Therefore, comparing PO and PU with an FPA is equivalent to comparing the SPA and FPA with unobservable participation. The two formats are not revenue-equivalent when recruitment and entry frictions are present: their ranking depends on s and c in exactly the way described for PO vs. PU.

Q: What is the “sampling curse” and how does it cause market unraveling? A: The sampling curse arises when sellers have privately known recruitment costs. Because a lower-cost seller optimally recruits more bidders, the probability of any given bidder being contacted is higher when the seller has a lower cost. Conditional on being contacted, a bidder therefore believes the seller more likely has a low cost and thus has recruited many competitors, reducing the value of entry. In the binary-type case (Claim 8), if sL is sufficiently small relative to sH, the low-cost seller must recruit so many bidders that entry becomes unattractive; the resulting low q* makes the marginal recruitment cost sH/q* prohibitively high for the high-cost type, driving it out (lambda*_H = 0).

Q: What does Proposition 3 establish about near-complete unraveling with a continuum of seller types? A: With seller costs uniformly distributed on [s-bar, s_o], Proposition 3 establishes a threshold c-hat strictly between 0 and c-bar such that: (i) for c in (c-hat, c-bar), as s-bar approaches zero, the fraction of seller types with zero recruitment approaches one — near-complete market unraveling; (ii) for c < c-hat, all seller types remain active regardless of how small s-bar is. This is striking because for any commonly known s in (0, s_o), the PO scenario supports trade for all c < c-bar; unraveling arises purely from the interaction of private cost information and the sampling curse, not from any type’s cost being intrinsically too high.

Q: What does the welfare analysis say about equilibrium efficiency? A: The welfare-maximizing participation level lambda_w satisfies U(lambda_w) = c + s (equating the marginal bidder’s surplus to the full social cost of one more participant), with full entry q_w = 1. In equilibrium under PO, q* < 1 in some cases (wasted recruitment) and lambda* differs from lambda_w for almost all (s, c) pairs — both excessive participation (lambda* > lambda_w) and deficient participation (lambda* < lambda_w) can arise. Full efficiency requires Ro’(lambda*) = s and U(lambda*) = s + c simultaneously, but since both U and Ro’ are independent of s and c as parameters, these equalities generically fail.

Q: Does the seller benefit from being able to commit to recruitment effort? A: Claim 10 shows that with observable effort in the PO scenario, the seller commits to gamma-hat = min{lambda-bar_c, lambda_o(s)} when lambda-bar_c >= lambda_o, and to lambda-bar_c (if profitable) when lambda-bar_c < lambda_o. Commitment strictly improves the seller’s profit whenever gamma-hat = lambda-bar_c: it enables positive trade when lambda-bar_c < lambda_o and Ro(lambda-bar_c) > lambda-bar_c * s (otherwise impossible without commitment), and it saves recruitment costs when lambda-bar_c > lambda_o and Ro’(lambda-bar_c) > s. However, the commitment outcome is always welfare-inefficient: lambda-bar_c > lambda_w whenever s > 0.

Q: What anecdotal evidence do the authors cite for the model’s relevance? A: Subramanian (2010) and Boone and Mulherin (2004, 2009) show that the majority of merger and acquisition auctions are “informal” — mixtures of auctions and negotiations rather than structured processes with rules laid out in advance — and that sellers are typically unable to credibly commit to participation levels. Milgrom (2003) states from consulting experience that marketing an auction is often more critical than clever mechanism design. Fees of 20–30% of revenues paid to intermediaries like Christie’s and Sotheby’s are offered as quantitative evidence of the magnitude of the inefficiencies that such intermediaries reduce. Home repair contracting is cited as a familiar informal-auction setting where both recruitment and entry costs are material.

Recruitment effort (gamma): The seller’s costly action of contacting potential bidders, modeled as a Poisson process with mean gamma at cost gamma*s; unobservable to bidders in the baseline model.

Participation-observable (PO) vs. participation-unobservable (PU) scenarios: The two variants of the model; in PO, bidders observe the total number of entrants n before bidding; in PU, they do not observe n and the seller cannot credibly disclose it.

Minimum profitable scale (lambda_o): The smallest positive participation level the seller will ever choose in equilibrium, defined as the value where Ro’(lambda_o) equals the peak of the average revenue curve s-bar_o. The seller always recruits either zero bidders or at least lambda_o, due to the initial complementarity of bidders (they stimulate each other’s bids) under no-commitment-to-reserve-price.

Break-even participation level (lambda-bar_c): The maximum participation level at which a bidder’s expected gross payoff U(lambda) equals the entry cost c; bidders will not enter if they expect participation above lambda-bar_c.

Sampling curse: The adverse-selection mechanism arising when sellers have privately known recruitment costs: because low-cost sellers recruit more, a contacted bidder infers the seller is more likely to have a low cost and thus to have recruited many competitors, making entry less attractive and potentially driving higher-cost seller types out of the market.

xi(lambda): The seller’s marginal revenue with respect to recruitment in the PU scenario, defined as the total derivative of Ru(lambda, beta_{lambda-hat}) evaluated where actual and expected participation coincide (lambda-hat = lambda). Strictly less than Ro’(lambda) for all lambda > 0, reflecting that in PU the seller loses the ability to leverage bidder aggression via observable competition.

Wasteful recruitment: The equilibrium phenomenon in which total recruitment cost lambda*(s/q*) remains at the positive constant lambda-bar_c * Ro’(lambda-bar_c) even as s approaches zero, because incentive constraints — not technology — pin the equilibrium effort level.

Central bank communication by ??? The economics of monetary policy leaks

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper investigates the economics of monetary policy leaks — anonymous disclosures of confidential information by insiders to the media — focusing on three central questions: (1) Are leaks random accidents, strategic individual disclosures, or institutionally authorized “plants”? (2) Do leaks shape public (financial market) views, and by how much? (3) Can attributed (named) communication by central bank officials mitigate the effects of leaks?

Data and Setting

The authors study the Eurosystem (ECB and euro area National Central Banks) over January 2002 to December 2021. Their primary data source is a novel database of 368 unique policy-relevant leaks — assembled by manually filtering and classifying more than a million news items from Reuters, Bloomberg, and Market News International archives — with precise minute-level timestamps. Topics covered include: policy rates (178 leaks), unconventional monetary policy/UMP (207 leaks), economic growth (47), inflation (41), and euro exchange rate (36); individual leaks may cover multiple topics. They complement this with a dataset of 7,883 attributable public statements by ECB Governing Council members, identified via keyword filtering and machine learning classification of the Reuters News Archive.

Methodology

The paper employs four main empirical strategies. First, high-frequency event studies using asymmetric windows (5 minutes before to 30 minutes after an event) compare absolute market reactions in OIS rates across the full term structure (3M to 10Y) and in the EURO STOXX 50 across leaks, 5,000 randomly sampled placebo events, and attributable statements. Second, Poisson regression models relate the number of leaks per policy meeting to proxies for Governing Council disagreement (Italian-German sovereign yield spread, inter-quartile range of national inflation rates, number of attributable statements per meeting) and a dummy for quarterly macroeconomic projection releases. Third, a regression framework tests whether leaks move market expectations toward the subsequent policy outcome — identifying whether leaks are informative about the direction of policy. Fourth, an augmented version of the Tillmann (2021) model relates end-of-day changes in longer-term OIS rates to high-frequency monetary policy surprises, interacted with dummies for post-announcement leaks and attributable statements.

Main Findings

Incidence and timing. The number of Eurosystem leaks peaked at 36 in 2019 (more than four per policy meeting on average) before declining by more than one third following the start of Christine Lagarde’s presidency in November 2019. Leaks cluster around policy meetings and, since 2015, have shifted notably from before meetings to after meetings, a shift driven by leaks related to UMP. Leaks occur even during the ECB’s quiet period, when policy-makers are formally restricted from public statements on policy-sensitive topics.

Leaks are not accidents. Poisson regressions reveal that the number of leaks per meeting is significantly and positively associated with proxies for Governing Council disagreement: every additional percentage point in the Italian-German sovereign yield spread is associated with approximately half an additional leak per meeting. The propensity of a policy change increases by four to six percentage points with each additional pre-meeting leak (statistically significant at the 5% or 10% level). The specification explains around 15% of the variation in leak counts.

Market impact. Market movements around leaks are up to 85% larger than those around placebo events. Leaks trigger market reactions that are consistently larger than those of attributable statements by individual Governing Council members across the entire OIS term structure and in equities — a result robust to controlling for distance to policy meetings. Rate leaks mainly move the short and medium end of the yield curve; UMP leaks affect the long end and equities. Leaks about general economic conditions (growth, inflation, exchange rate) produce little statistically significant market response.

Leaks are uninformative about policy direction. Conditional on a pre-meeting leak occurring, the average leak does not move market rates closer to the levels prevailing directly after the subsequent policy announcement. By contrast, attributable statements systematically do reduce this distance. This asymmetry implies that leaks predominantly reflect minority opinions within the Governing Council. Consistent with this, leaks counteract prevailing trends in market expectations at the short end of the yield curve (as established by a negative coefficient on the interaction between the prevailing seven-day pre-leak trend and the leak dummy).

Leaks are not plants; attributed communication mitigates their effects. Post-announcement leaks dampen the transmission of monetary policy surprises to longer-term rates (negative and significant interaction coefficient in the augmented Tillmann framework). Attributed statements by ECB Executive Board members, by contrast, systematically move in the direction opposite to the preceding leak across most of the yield curve, partially reversing leak-induced market moves. More intense pre-leak attributable communication is also associated with lower market impact of the subsequent leak, across most maturities. These results jointly indicate that most Eurosystem leaks originate from individual insiders with minority opinions rather than constituting institutional plants.

Scope Conditions

Results pertain to the Eurosystem committee setting, where decision-making is broadly consensus-based and voting records are not published; they may not fully generalize to institutions with concentrated decision-making power. The study measures effects on financial markets, not broader public opinion.

In depth

Q1. How is a “leak” defined in this paper, and how are Eurosystem leaks identified empirically?

A leak is defined as a disclosure of confidential information by an insider to the media with an expectation of anonymity. Eurosystem leaks are identified from Reuters, Bloomberg, and Market News International archives (2002–2021) using keyword-driven pre-filtering followed by manual classification of “candidate” items. The resulting database contains 1,253 news items that aggregate to 368 unique policy-relevant leaks with minute-level timestamps. Policy-relevant leaks touch on: policy rates, unconventional monetary policy tools, economic growth, inflation, or the euro exchange rate; leaks about local economic conditions, banking regulation, or managerial appointments are excluded.

Q2. What are the broad trends in the number and topic composition of Eurosystem leaks over 2002–2021?

The number of leaks rose sharply in the second half of the sample, peaking at 36 in 2019 (more than four per meeting on average). Since Christine Lagarde took over the ECB presidency in November 2019, leaks fell by more than one third from that peak. The topic composition shifted substantially over time: policy-rate leaks predominated in the earlier period, while leaks related to UMP came to dominate in the 2015–2021 sub-period.

Q3. How does the timing of leaks within the policy meeting cycle change across sub-periods?

In the full sample, leaks cluster in the run-up to policy meetings and immediately following announcement days (both on the announcement day itself and the following Friday). Since 2015, a notable shift occurs from pre-meeting to post-meeting timing, driven specifically by leaks related to UMP. The authors attribute this shift to the expectation-management role of UMP: post-meeting leaks allow dissenting insiders to reshape market expectations that are otherwise guided by official press releases and press conferences.

Q4. What regression evidence supports the view that leaks are not random accidents?

Poisson regressions of the number of leaks per meeting on disagreement proxies find significant positive coefficients on: the lagged Italian-German sovereign yield spread (about half a leak more per meeting for each additional percentage point of spread), the inter-quartile range of national inflation rates, and the number of attributable statements per meeting. Meetings coinciding with the release of quarterly macroeconomic projections also attract significantly more leaks. These results are robust to replacing the disagreement proxies with a binary dissent index based on Q&A sessions at ECB press conferences (Tillmann, 2021), even after excluding disagreement-related leaks from the dependent variable to address endogeneity. The model explains about 15% of the variation in leak counts.

Q5. Does the number of pre-meeting leaks predict policy changes?

Yes. The propensity of a monetary policy change increases by four to six percentage points with each additional pre-meeting leak (significant at the 5% or 10% level). This signal about the propensity of change (not the direction) is hard to square with the random accidents hypothesis.

Q6. How large are the financial market reactions to leaks relative to placebo events and to attributable statements?

Market movements around leaks are up to 85% larger than the average size of market reactions to 5,000 randomly sampled placebo events. When leaks are compared directly to attributable statements (with leaks as the baseline and fixed effects for year, month, weekday, and hour), average absolute market moves around leaks are consistently larger across the entire term structure of OIS rates and for the EURO STOXX 50. This result is robust to differences in distance to policy meetings, with size differences across the full term structure persisting for periods far from meetings; near meetings, differences narrow but the average market reaction to leaks never falls below that to attributable statements.

Q7. Do the market effects of leaks differ by topic?

Yes. Leaks about policy rates primarily move the short and medium end of the yield curve. Leaks about UMP tools affect the long end of the curve and equities. Leaks about general economic conditions (growth, inflation, euro exchange rate) do not produce statistically significant market reactions, consistent with the interpretation that economic condition leaks require more interpretation before their implications for the policy path become apparent.

Q8. Do leaks move market expectations in the direction of the subsequent policy outcome?

No. The average pre-meeting leak does not reduce the absolute distance of market rates to post-announcement levels. This result holds across maturities from 3M to 10Y and is robust to separating leaks inside and outside the ECB’s quiet period. Attributable statements, by contrast, systematically reduce this distance (Table 7). The failure of leaks to align expectations with outcomes is interpreted as evidence that leaks predominantly reflect minority views within the Governing Council rather than information held by the decisive voter.

Q9. Do leaks counteract or reinforce prevailing trends in market expectations?

Leaks counteract prevailing trends. The regression of market reactions to leaks and placebo events on the seven-day pre-event trend reveals a significantly negative interaction between the trend and the leak dummy at the short end of the yield curve. This result is driven specifically by leaks about policy rates.

Q10. Do post-announcement leaks dampen the transmission of monetary policy surprises to longer-term rates?

Yes. In the augmented Tillmann (2021) framework, the interaction of the high-frequency 2Y monetary policy surprise with a dummy for post-announcement leaks is negative and significant for 2Y, 5Y, and 10Y OIS rates. In contrast, the interaction with a dummy for post-announcement attributable statements is positive and significant across maturities, indicating that attributed communication reinforces the official policy signal. These two results jointly show that leaks weaken official policy announcements while attributed communication strengthens them.

Q11. Does more intense pre-leak attributable communication reduce the market impact of subsequent leaks?

Yes. Using an intensity measure that weights each attributable statement by the inverse of its distance in hours to the subsequent leak (covering a window from 36 hours to 30 minutes before the leak), the paper finds a significant negative relationship between pre-leak communication intensity and the absolute market reaction to the leak, controlling for year, month, weekday, and hour fixed effects. This holds across most maturities.

Q12. Does the market impact evidence support the “plant” hypothesis?

No. If leaks were institutional plants intended to prepare markets for new policy, one would expect the ECB Executive Board — which controls official communication — to subsequently reinforce the signal from leaks. Instead, attributable statements by ECB-affiliated Governing Council members are systematically negatively correlated with the market direction of the preceding leak across the yield curve, with significant coefficients at medium maturities. NCB Governor statements show weaker and more ambiguous effects, potentially because their statements generate smaller average market movements rather than reflecting a lack of willingness to counteract leaks.

Q13. Why do markets react to leaks even though leaks are generally uninformative about policy outcomes?

The paper offers three candidate explanations: (1) automated trading algorithms that do not distinguish between attributed and anonymous communication; (2) leaks serve as a coordination device in the spirit of Morris and Shin (2002), amplifying even noisy signals; (3) media-reporting models such as Nimark (2014) and Chahrour et al. (2021) predict that “man-bites-dog” news — unusual events such as revelations of committee disagreement — shift beliefs beyond their true information content. Leaks are unusual both in frequency (far less common than attributed statements) and in content (they reveal disagreement that rarely surfaces in official communication).

Q14. What are the implications for the measurement of monetary policy shocks from high-frequency identification?

The paper notes that Eurosystem leaks frequently occur shortly before or after official policy announcements. Pre-announcement leaks can shift market expectations before the start of standard event windows, reducing the measured surprise component of official announcements. Post-meeting leaks dampen the end-of-day effects of announcements. In both cases, standard high-frequency surprise instruments extracted from official announcements alone may miss the full extent of new information available to market participants, suggesting that accounting for leaks could improve the relevance of high-frequency instruments used in monetary policy identification.

Q15. What are the implications for the design of central bank quiet periods?

The ECB’s quiet period ends with the policy announcement, whereas the Federal Reserve’s extends to the day after the meeting. Based on the finding that post-announcement leaks dampen policy announcement effects while post-announcement attributed statements reinforce them, the paper suggests that permitting attributed communication shortly after policy decisions may help mitigate the market impact of post-announcement leaks.

Key Concepts

Monetary policy leak (“sources story”): In this paper, a leak is defined as a disclosure of confidential information emanating from an insider within the Eurosystem (ECB or NCB staff or policy-makers) that is transmitted to financial media with an expectation of anonymity for the source. The paper excludes whistle-blower cases and focuses on leaks where anonymity keeps attention on the content rather than the identity of the source. Leaks are distinct from “plants” (formally authorized institutional disclosures intended to advance the institution’s goals) and from “pleaks” (the middle ground).

Plant: An authorized or semi-authorized anonymous disclosure of confidential information made for the purpose of advancing the public institution’s own goals and interests, as distinct from a leak that originates from an individual insider’s personal agenda. The paper tests and rejects the plant hypothesis for most Eurosystem leaks on the basis that ECB Executive Board members’ attributed statements systematically counteract the market impact of leaks.

Single voice principle: The ECB’s communication norm requiring that Governing Council members discuss and resolve disagreements internally while publicly representing the official policy stance. This principle creates a setting where individual members with minority views may resort to anonymous communication as a way to express dissent “off-protocol.”

Quiet period (purdah): The ECB’s rule requiring policy-makers to refrain from public statements on policy-related topics in the seven days before each Governing Council monetary policy meeting. Leaks cluster during this period despite the restriction, supporting the non-random interpretation of leaks.

Attributable (named) statement: A public statement clearly attributed to a specific, named member of the ECB Governing Council, reported as a breaking-news headline. Attributable statements serve both as a comparison benchmark for measuring the market impact of leaks and as a mitigation instrument when they counteract leak-induced market moves.

Pre-leak communication intensity (lambda): The paper’s measure of the intensity of attributable communication in the 36-hour window before a given leak, defined as the sum of inverse time distances (in hours) from each attributable statement to the leak. A higher value means more recent and/or more numerous attributed statements precede the leak.

High-frequency event study window: The paper uses an asymmetric window starting 5 minutes before and ending 30 minutes after a leak’s timestamp. Market reactions are measured as the change in the median OIS quote during the 10 minutes after the window versus the 10 minutes before, matching methodology used for both leaks and attributable statements to ensure comparability across communication types.

Post-announcement leak dummy: An indicator taking the value of one if at least one leak occurs between the end of the official ECB monetary policy announcement window (15:50 CET) and end of trading hours on the announcement day. Used in the augmented Tillmann (2021) regression to measure whether leaks dampen the transmission of monetary policy surprises to longer-term rates.

Coarse Bayesian Updating

Mon, 01 Jan 0001 00:00:00 +0000

This paper introduces and axiomatically characterizes Coarse Bayesian updating, a generalization of Bayes’ rule designed to accommodate the wide empirical evidence that individuals systematically deviate from standard Bayesian belief revision. The research question is: what is the minimal, tractable, axiomatically grounded generalization of Bayes’ rule that can accommodate heterogeneous non-Bayesian behaviors — including under-reaction, over-reaction, asymmetric updating, limited perception, and motivated reasoning — while remaining portable to standard economic settings?

The paper takes as primitive a finite state space Omega = {1, …, N} and an updating rule mu: S -> Delta assigning posterior beliefs to signals, where signals represent likelihood profiles from stochastic information structures. No data are used; the methodology is axiomatic decision theory combined with analysis of the model’s implications in static, dynamic, and decision-theoretic settings.

A Coarse Bayesian agent is characterized by (i) a partition of the probability simplex Delta into convex cells, and (ii) a representative distribution for each cell, one of which is the prior. Upon observing a signal, the agent determines which cell contains the Bayesian posterior and adopts the representative of that cell as his posterior belief. The agent need not point-identify the Bayesian posterior; he merely approximates it by identifying which cell it belongs to.

The central characterization result (Theorem 1) establishes that an updating rule has a Coarse Bayesian representation if and only if it satisfies three axioms: Homogeneity (beliefs depend only on likelihood ratios of the signal, not its scale), Cognizance (if two signals induce the same belief, then a garbled signal indicating one of them was generated also induces that belief), and Confirmation (if a signal is perfect evidence of some feasible belief, the agent adopts that belief). The representation — partition, representative points, and prior — is unique.

Proposition 1 shows that, under mild regularity conditions, strengthening any of the three axioms to an if-and-only-if form forces the agent to be perfectly Bayesian. This identifies the Coarse Bayesian framework as a qualitatively small but substantively rich departure from Bayes’ rule. The converse statements identify three necessary non-Bayesian behaviors exhibited by any proper Coarse Bayesian: (i) treating some signals as equivalent when a Bayesian would not; (ii) collapsing to a default belief when uncertain between two signals the agent would otherwise distinguish; (iii) false extrapolation — arriving at a belief via signals that are not perfect evidence of it.

In dynamic settings, Pooled Coarse Bayesian rules (which apply the full signal history at each period) are invariant to signal ordering and pooling and converge whenever Bayesian beliefs do, though to the representative point of the cell containing the true state rather than the true state itself. Sequential Signal Distortion rules are invariant to signal ordering but not pooling, and beliefs converge almost surely — but not necessarily to the true state (Example 1 illustrates convergence to the wrong state in a two-state setting). Sequential Coarse Bayesian rules need not satisfy either form of path-independence and need not converge at all.

In the decision-theoretic application (Section 4), a Coarse Bayesian’s value of information is posterior-separable and generally violates the Blackwell (1951) information ordering — more informative experiments need not be valued more highly. Two Coarse Bayesians are shown to be identical (same cells and representative points) if and only if they benefit from the same Blackwell improvements, providing a behavioral identification result. Agents with finer partitions are more sophisticated (higher ex-ante value of information), while agents with larger distortions from Bayesian posteriors are more biased (larger worst-case losses relative to a Bayesian). Neither greater sophistication nor lower bias implies being better off at all menus or signal realizations.

Q: What are the three axioms that characterize Coarse Bayesian updating, and what property of Bayes’ rule does each capture? A: Homogeneity requires that beliefs depend only on likelihood ratios of the signal — if two signals are proportional (s ~ t), they induce the same posterior. Cognizance requires that if two signals induce the same belief, then a garbled signal indicating that one of them was generated also induces that belief (mu_{s+t} = mu_s when mu_s = mu_t). Confirmation requires that if a signal is perfect evidence of some feasible belief — i.e., the Bayesian posterior at that signal equals a candidate belief — then the agent adopts that belief. Each axiom is satisfied by standard Bayesian updating.

Q: In what sense is Coarse Bayesian updating a “small” departure from Bayes’ rule? A: Proposition 1 establishes that strengthening any one of the three axioms to an if-and-only-if form forces the agent to be perfectly Bayesian. The converses are: (i) different likelihood ratios lead to different posteriors; (ii) if a garbled signal does not change beliefs, then the two signals must induce the same belief individually; (iii) if a signal induces the same posterior as another, then it must be perfect evidence of that posterior. Any Coarse Bayesian satisfying any one of these is in fact perfectly Bayesian, meaning the three axioms together come very close to fully characterizing Bayesian rationality.

Q: What non-Bayesian behaviors does the model generate as special cases? A: The framework generates under-reaction (representative points of cells close to the prior boundary), over-reaction (representative points at the far boundary), asymmetric updating (favoring one state, making upward revision easier than downward), limited perception (the agent retains the prior unless the Bayesian posterior is sufficiently far from the prior), extreme-belief aversion (the agent applies Bayes’ rule except when posteriors are near degenerate distributions), and reactions to unexpected news (non-Bayesian behavior only when signals have low prior probability). In each case the Coarse Bayesian Representation provides an axiomatic foundation via Axioms 1–3.

Q: What are the three necessary non-Bayesian behaviors exhibited by any proper (non-Bayesian) Coarse Bayesian? A: These follow from the negations of properties (i)-(iii) in Proposition 1. First, there exist signals s and t that are not proportional yet induce the same posterior — the agent treats informationally distinct signals as equivalent. Second, there exist signals s and t such that mu_s ≠ mu_t but mu_{s+t} = mu_s — signals the agent distinguishes individually collapse to a default when the agent is uncertain which one was generated. Third, there exist signals s and t with mu_s = mu_t where t is not perfect evidence of mu_s — a form of false extrapolation. Together, these three biases account for all non-Bayesian behavior the model generates.

Q: How does the model accommodate globally uniform biases like always-under-reaction, and how common does it predict such behavior to be? A: Global under-reaction requires representative points of cells to sit on their cell boundaries (as close to the prior as possible given the partition). This is a non-generic, hairline case — representative points generically lie in the interior of their cells, so a typical Coarse Bayesian under-reacts to some signals and over-reacts to others depending on which cell the Bayesian posterior falls into. The model additionally predicts local stability: if an agent over-reacts to signal s, nearby signals typically produce the same response; if an agent is Bayesian at s, nearby signals are almost surely also Bayesian.

Q: What does the model imply about dynamic updating under sequential signal-by-signal processing versus pooled processing? A: Pooled Coarse Bayesian rules apply the full signal history at each period, are invariant to both signal ordering and signal pooling, and converge almost surely whenever Bayesian beliefs converge — but to the representative point of the cell containing the true state, not necessarily the true state itself. Sequential Signal Distortion rules are invariant to signal ordering but not signal pooling, and also yield almost-sure convergence though potentially to the wrong state (Example 1 shows this for a two-state setting). Sequential Coarse Bayesian rules need not be invariant to either form of path-dependence and need not converge at all.

Q: How does the paper provide a behavioral identification of the model’s parameters? A: Theorem 1 establishes that the partition, representative points, and prior are uniquely determined by the agent’s updating rule alone — they are identifiable from observable updating behavior without additional assumptions. In the decision-theoretic setting of Section 4, a stronger result holds: two Coarse Bayesians are identical (same cells and same representative points) if and only if they benefit from the same Blackwell improvements across all menus (decision problems). This means the model’s parameters can be uniquely identified from menu-contingent rankings of Blackwell-comparable experiments.

Q: Does the Coarse Bayesian framework respect the Blackwell information ordering, and what characterizes when Blackwell improvements are beneficial? A: Unlike Bayesians, Coarse Bayesians typically violate the Blackwell ordering — they need not assign higher ex-ante value to more informative experiments. The paper characterizes the menus (decision problems) for which a given Coarse Bayesian benefits from Blackwell improvements, and shows this characterization runs deep: the complete set of such menus fully identifies the agent’s representation.

Q: How do the sophistication and bias orderings relate to welfare? A: An agent is more sophisticated if he employs a finer partition; more-sophisticated agents have a higher ex-ante value of information. An agent is more biased if his updating rule exhibits larger distortions from Bayesian posteriors; greater bias is characterized by greater worst-case losses relative to a Bayesian. Crucially, neither greater sophistication nor lower bias implies the agent is better off at all menus or signal realizations — welfare improvements require the agent to be perfectly Bayesian on a strictly larger set of signal realizations, giving rise to a third ordering that jointly refines the other two.

Q: How does the model relate to Wilson (2014) and Ortoleva (2012)? A: Wilson (2014) studies optimal updating for a boundedly rational agent with K memory states over binary decisions: each memory state is associated with a convex set of posteriors and a representative, so the optimal protocol is a dynamic Coarse Bayesian updating procedure. However, Wilson’s parameters are endogenous (determined by signal structure, stakes, and the bound K), whereas Coarse Bayesian updating does not require optimality or a bound on the number of cells — the model can accommodate behavior (e.g., Bayesian updating except at “extreme” signals) that Wilson’s model cannot. Ortoleva’s (2012) Hypothesis Testing model applies Bayes’ rule when the prior probability of a signal exceeds a threshold epsilon and otherwise uses a maximum-likelihood criterion; Coarse Bayesian updating can accommodate similar behavior, and the paper shows that Coarse Bayesian rules can be expressed as Maximum-Likelihood rules when there are only two states, but neither class subsumes the other in general — Maximum-Likelihood rules may violate Confirmation.

Q: What are the main limitations of the Coarse Bayesian framework? A: The paper identifies four. First, only likelihood ratios of the realized signal matter — sensitivity to framing and extraneous environmental features are ruled out. Second, beliefs must be probability distributions, so phenomena like the conjunction fallacy (where subjects assign higher probability to a conjunction than a component event) are outside the model’s scope. Third, the model exhibits discontinuities when signal perturbations move the Bayesian posterior across a cell boundary — a feature shared with Wilson (2014), Ortoleva (2012), and related models. Fourth, cells must be convex (driven by Cognizance); dropping Cognizance allows non-convex cells but removes the normative foundation that agents correctly forecast their own updating behavior.

Coarse Bayesian Representation: A pair consisting of a partition P of the probability simplex Delta into convex cells and a profile of representative distributions (one per cell, including the prior), such that the agent’s posterior after observing signal s equals the representative of the cell containing the Bayesian posterior B(mu_e|s).

Homogeneity: The axiom that if two signals are proportional (s ~ t, meaning s = lambda*t for some lambda > 0), they induce the same posterior belief — updating depends only on likelihood ratios, not signal scale.

Cognizance: The axiom that if signals s and t induce the same posterior, then the garbled signal s+t (indicating that either s or t was generated) also induces that belief — the agent correctly forecasts his own updating behavior.

Confirmation: The axiom that if a signal constitutes perfect evidence of some feasible belief (i.e., the Bayesian posterior equals a candidate belief), the agent adopts that belief — candidate beliefs are adopted when the signal confirms them exactly.

Signal Distortion Representation: An equivalent representation of Coarse Bayesian behavior as a function d: S -> S that distorts signals before Bayesian updating is applied (mu_s = B(mu_e|d(s))), satisfying properties analogous to the three axioms; equivalent to the partition representation in static settings but distinct in dynamic settings.

Blackwell Information Ordering: The partial order on experiments under which sigma is more informative than sigma’ if sigma can be obtained from sigma’ by a garbling; Bayesians always weakly prefer more informative experiments in this ordering, but Coarse Bayesians typically do not.

Sophistication Ordering: The partial order under which one Coarse Bayesian is more sophisticated than another if he employs a finer partition; more-sophisticated agents exhibit greater responsiveness to information as measured by ex-ante value of information.

Bias Ordering: The partial order under which one Coarse Bayesian is more biased than another if his updating rule exhibits larger distortions away from Bayesian posteriors; greater bias is characterized by larger worst-case losses relative to a Bayesian benchmark.

Contextually Private Mechanisms

Mon, 01 Jan 0001 00:00:00 +0000

Haupt and Hitzig introduce a framework for comparing the privacy properties of different mechanism protocols. The core research question is: when a designer commits to implementing a social choice rule, how much superfluous private information must they inevitably learn about agents, and how should they design the elicitation protocol to minimize that exposure?

The setting is a finite-player extensive-form game in which a designer elicits agents’ private types through a dynamic protocol to compute a social choice function. The authors explicitly exclude cryptographic tools and trusted mediators, working under the minimal assumption that the designer learns information if and only if an agent discloses it. This assumption is motivated by the historical prevalence of live dynamic auction formats — ascending formats at Sotheby’s, descending formats at Aalsmeer, oral ascending formats used by the U.S. Forest Service for timber, multi-round clock auctions for radio-spectrum allocation — and by settings where mediating technology is unavailable or costly.

The central object is the contextual privacy violation. A protocol produces a contextual privacy violation for agent i at type profile θ if the designer can distinguish θ_i from some alternative type θ’_i while holding other agents’ types fixed, yet the social choice rule assigns the same outcome at both profiles. Violations are defined at the level of individual agent–state pairs, not aggregated ex ante. A protocol is fully contextually private if it produces no violations; it is maximally contextually private if its set of violations is inclusion-minimal among all protocols that implement the same rule.

The main characterization result (Theorem 1) connects privacy to pivotality: a social choice function admits a fully contextually private protocol if and only if, on every product subset of the type space where agents are collectively pivotal, at least one agent is individually pivotal. The contrapositive is what drives the paper’s impossibility results: whenever a rule contains a region where no single agent’s report changes the outcome but a group’s joint report does, any implementing protocol must produce contextual privacy violations.

Using this characterization, the authors establish that the first-price auction rule (Proposition 2) and serial dictatorship (Proposition 3) admit fully contextually private protocols. Conversely, k-item Vickrey auction rules (Proposition 4) and any stable school-choice rule (Proposition 5) do not admit fully contextually private protocols, because these rules contain type-space regions where agents are only collectively — not individually — pivotal.

For k-item Vickrey auctions, the authors study maximally contextually private protocols. They establish (Proposition 6) that, for a class of social choice rules on totally ordered type spaces that contains k-item Vickrey auctions, it is without loss to consider only protocols consisting of threshold queries that are monotonically increasing or decreasing after an initial guess. This reduction identifies two key design dimensions: the initial query posed to each agent, and the order in which agents are queried.

The main constructive result (Theorem 2) proves that an ascending-join protocol is maximally contextually private for the k-item Vickrey auction. Proposition 7 formalizes the sense in which this protocol protects privacy by delaying queries to certain bidders — it repeatedly asks agents whether they can rule out a particular outcome, and postpones questioning agents whose privacy it is protecting.

The authors also show (Proposition 19) that the ascending-join protocol is minimally relatively informative among protocols that are maximally contextually private. Extensions cover group contextual privacy (Proposition 11) and individual contextual privacy (Proposition 8), showing that individual contextual privacy violations equal the union of contextual privacy violations and nonbossiness violations.

Q: What is a contextual privacy violation, precisely? A: A protocol produces a contextual privacy violation for agent i at type profile θ if the designer can distinguish θ_i from some alternative type θ’_i — holding all other agents’ types fixed — yet the social choice rule assigns the same outcome at both profiles. The violation is defined at the level of individual agent–state pairs. A single additional superfluous distinction at the same (i, θ) pair does not register as a second violation; the framework records whether any unnecessary disclosure occurs for that agent at that state, not the degree of overexposure.

Q: How does contextual privacy differ from relative informativeness? A: Relative informativeness compares two protocols by whether one distinguishes every pair of type profiles the other does, treating all disclosures as equally undesirable. Contextual privacy conditions the notion of a “violation” on the social choice rule: a distinction between θ_i and θ’_i counts as a violation only when the rule assigns the same outcome at both profiles. Relative informativeness thus penalizes the designer for learning information that is necessary to implement the rule, whereas contextual privacy imposes no penalty for learning pivotal information.

Q: What is the pivotality characterization (Theorem 1)? A: A social choice function admits a fully contextually private protocol if and only if, on every product subset of the type space where agents are collectively pivotal, at least one agent is individually pivotal. The necessity direction shows that if a collectively pivotal set exists where no agent is individually pivotal, any implementing iterative partition must contain an earliest node that distinguishes two type profiles leading to the same outcome. The sufficiency direction constructs a contextually private protocol inductively by always querying an individually pivotal agent, ensuring every distinction implies a different outcome.

Q: Which social choice rules admit fully contextually private protocols? A: The first-price auction rule (Proposition 2) and serial dictatorship (Proposition 3) admit fully contextually private protocols. The authors use Theorem 1 to show this: in both rules, any collectively pivotal region contains an individually pivotal agent. By contrast, k-item Vickrey auction rules (Proposition 4), any stable school-choice rule (Proposition 5), efficient allocations in housing assignment, and generalized median voting rules (Section B) do not admit fully contextually private protocols.

Q: Why do k-item Vickrey auctions fail full contextual privacy? A: Proposition 4 shows that k-item Vickrey auctions for k ≥ 1 do not admit fully contextually private protocols. The argument uses the necessary conditions from Theorem 1 (Corollaries 1 and 2): the Vickrey payment rule creates type-space regions where multiple agents together determine the price but no single agent is individually pivotal over the price, so any protocol implementing the Vickrey rule must produce violations for at least some agents at some type profiles.

Q: What is the ascending-join protocol and what does Theorem 2 establish? A: The ascending-join protocol is a specific dynamic elicitation protocol for k-item Vickrey auctions that repeatedly asks agents whether they can rule out a particular outcome, structured as threshold queries ascending from an initial guess. Theorem 2 proves that the ascending-join protocol is maximally contextually private for the k-item Vickrey auction. Proposition 7 formalizes the protection mechanism: the protocol delays queries to the bidders whose privacy it is protecting, querying them only when their responses become necessary for determining the outcome.

Q: What does Proposition 6 establish about the structure of maximally contextually private protocols? A: For a class of social choice rules on totally ordered type spaces that contains k-item Vickrey auctions, Proposition 6 shows it is without loss of generality to consider only protocols consisting of threshold queries that are monotonically increasing or decreasing in the threshold after an initial guess. This result serves as a theoretical reduction (enabling proofs that certain protocols are maximally private) and as a practical design principle (identifying the initial query and the ordering of agents as the two key design dimensions).

Q: How does contextual privacy relate to obviously dominant strategies? A: The paper treats privacy properties and incentive properties as largely orthogonal questions, to be analyzed separately. For the ascending-join protocol specifically, the authors verify obvious dominance — the most demanding incentive notion they consider — which requires that at every history, the worst-case payoff from the equilibrium action exceeds the best-case payoff from any deviation. This analysis proceeds after the contextual privacy properties of the protocol are established.

Q: What is group contextual privacy and why do the authors focus on individual-level violations instead? A: Group contextual privacy requires that whenever the designer learns any property of the joint type profile, that property must affect the outcome. The authors show (Proposition 11) that a protocol is fully group contextually private if and only if every query rules out at least one outcome. They argue this standard is extremely demanding and produces a very coarse partial order: improving in the group privacy order requires restructuring the entire protocol tree rather than making agent- or state-specific improvements. They also note that normative accounts of privacy, including Nissenbaum’s contextual integrity theory, center on individual rather than group information.

Q: How does individual contextual privacy relate to nonbossiness? A: Individual contextual privacy (Proposition 8) requires that if two type profiles differing only in agent i’s type are distinguished, they must lead to different allocations for agent i — presuming a private allocation domain. The paper shows that the set of individual contextual privacy violations equals the union of contextual privacy violations and nonbossiness violations: individual contextual privacy is violated precisely when either (a) agent i’s superfluous type information is revealed, or (b) agent i is “bossy” — able to change others’ outcomes without changing their own.

Q: What is the relationship between the ascending-join protocol and minimal relative informativeness? A: Proposition 19 shows that the ascending-join protocol is not only maximally contextually private but also minimally relatively informative among protocols that are maximally contextually private. That is, among all maximally contextually private protocols, the ascending-join protocol reveals the smallest total amount of information about the type profile in the relative informativeness order. This establishes relative informativeness as a useful refinement for selecting among contextually privacy-equivalent protocols.

Q: What motivates the exclusion of cryptographic tools and trusted mediators from the framework? A: The authors work under the minimal assumption that the designer learns information if and only if an agent directly discloses it — no commitment to forget, anonymize, or cryptographically conceal. They motivate this on two grounds: first, many real-world auction formats are live and dynamic with no mediating technology; second, advanced cryptography is often costly in time, money, or computation, and studying the no-mediator benchmark can explain the historical prevalence of dynamic protocols and inform auction design in environments where cryptography may become unavailable (for example, due to quantum computing). The authors cite a Danish sugar-beet auction as a case where designers themselves questioned whether full multiparty computation was necessary.

Contextual privacy violation: A protocol produces a contextual privacy violation for agent i at type profile θ if the designer can distinguish θ_i from some alternative type θ’_i — holding other agents’ types fixed — yet the social choice rule assigns the same outcome at both profiles. The violation is assigned at the level of individual agent–state pairs.

Maximally contextually private protocol: A protocol whose set of contextual privacy violations is inclusion-minimal among all protocols that implement the same social choice rule — equivalently, a protocol that lies on the Pareto frontier of implementation and contextual privacy, such that no other implementing protocol weakly reduces every violation and strictly reduces at least one.

Iterative partition: A directed rooted tree whose nodes are subsets of the type space, where each non-leaf node is split into children by partitioning on a single agent’s type. Any protocol is equivalent (in terms of what the designer learns) to a partitional protocol induced by an iterative partition (Proposition 1).

Individual pivotality: On a product set of type profiles, agent i is individually pivotal if there exist two subsets of agent i’s types such that every type profile from one subset leads to a different outcome than every type profile from the other subset, holding others’ types fixed.

Collective pivotality: Agents are collectively pivotal on a product set if there exist two type profiles in that set with different outcomes. Collective pivotality without any agent being individually pivotal is precisely the condition that forces contextual privacy violations (Theorem 1).

Ascending-join protocol: A specific dynamic protocol for k-item Vickrey auctions that poses threshold queries in ascending order after an initial guess, repeatedly asking agents whether they can rule out a particular outcome. It is maximally contextually private (Theorem 2) and minimally relatively informative among maximally contextually private protocols (Proposition 19), and it achieves privacy protection by delaying queries to agents whose privacy it protects (Proposition 7).

Relative informativeness: A partial order on protocols defined by: protocol P is less relatively informative than P’ if every pair of type profiles P distinguishes is also distinguished by P’. Unlike contextual privacy, relative informativeness treats all disclosures as equally undesirable and does not condition on the social choice rule. The paper positions it as a useful refinement for selecting among contextually privacy-equivalent protocols.

Costs of Financing U.S. Federal Debt Under a Gold Standard: 1791-1933

Mon, 01 Jan 0001 00:00:00 +0000

Overview

This paper constructs a new dataset of US federal bond prices and uses it to estimate the full term structure of yields on gold-denominated US federal debt from 1791 to 1933 — the entire gold standard era. The core research question is how the costs of financing US federal debt evolved over this period and what monetary, fiscal, and financial policy changes drove that evolution, with the ultimate aim of understanding how the US built fiscal capacity and transformed its debt from a “junk bond” into a global “safe asset.”

Data and Methodology. The authors compile monthly prices, quantities, and descriptions of all US Treasury securities from 1776 to 1960 (the Hall et al. 2018 dataset). Bonds with less than one year to maturity are excluded from the main estimation due to liquidity premia. The primary estimation uses a Dynamic Nelson-Siegel (DNS) model with stochastic volatility (Diebold and Li 2006; Hautsch and Yang 2012), estimated by Bayesian MCMC. A key methodological innovation is the addition of bond-specific idiosyncratic pricing errors (Assumption 3), which allows the authors to include bonds with heterogeneous contract features — call options, indefinite maturities, conversion features — that characterize 19th-century US debt without either dropping them from the sample or having their idiosyncrasies distort the common yield curve. The data are “big” in the time-series dimension but sparse in the maturity (cross-sectional) dimension, frequently offering fewer than five price observations per month; the DNS framework pools information across time to address this sparsity.

For the greenback period (1862–1878), the authors extend the approach by modeling the greenback yield curve as a function of the gold yield curve and a time-varying VAR model of exchange rate expectations (Assumptions 4–5). Only nine greenback-denominated bonds exist in the sample, most of them short-term; the VAR is estimated jointly using exchange rate data and the relative prices of greenback and gold bonds.

Main Findings.

Long-run decline in yields. The 10-year gold-denominated zero-coupon yield fell from approximately 8% in 1800 to approximately 2% in 1900, consistent with global secular decline trends, but the trajectory stabilized near 2% after 1900 — suggesting US debt began to play a distinctive “safe-asset” role from the turn of the 20th century.
War spikes were much larger than previously understood. The paper’s estimate of the 10-year gold yield reaches a peak of approximately 16% near the end of the Civil War. This is substantially higher than the Homer and Sylla (2004) peak of 6% at the start of the war. The discrepancy arises because Homer and Sylla used bonds trading at par — which did not exist during the Civil War — while this paper uses the full universe of bonds at monthly frequency.
Yield curve slope switched sign. The term spread (10-year minus 2-year gold yield) was typically negative before the Civil War (inverted yield curve) and turned persistently positive afterward. The authors link this switch to a change in long-run inflation predictability: inflation was relatively hard to forecast before the Civil War and easier to forecast after, consistent with a negative inflation-risk premium in the pre-war period.
Default risk premium disappeared around 1905. Comparing hypothetical gold-denominated US consols to UK consols (the 19th-century benchmark safe asset), US yields were persistently above UK yields until approximately 1905, when US yields fell below UK yields. This indicates that US federal debt acquired safe-asset characteristics well before World War I, foreshadowing the shift in global reserve asset status during and after Bretton Woods.
Nominal anchor during the Civil War. Despite a 60% depreciation of the greenback against gold during the Civil War (100 greenback dollars could be purchased for as few as 40 gold dollars in summer 1864), investors expected greenbacks to eventually return to gold parity. Estimated long-run exchange rate expectations remained anchored at one-for-one parity throughout the period. This kept greenback-denominated bond yields flat at approximately 6% — bonds traded around par — explaining the “Civil War yield puzzle” noted by Friedman and Schwartz (1963).
Short-rate disconnect. Short-maturity government bonds (less than one year) traded with a premium of approximately 0.25 to 0.5 percentage points relative to model-implied yields throughout most of the 19th century, reflecting scarcity of money-like assets. This premium effectively disappeared from the 1880s until World War I — coinciding with the National Banking Era — and then reappeared in the 1920s after the Federal Reserve created a secondary market for Certificates of Indebtedness.

In depth

Q1. Why does the paper restrict estimation to bonds with maturity greater than one year?

Short-maturity Treasury notes exhibited particularly large estimated bond-specific pricing errors in preliminary analysis, which the authors attribute to a liquidity premium: short-term government debt was used for transactions and thus commanded a money-like premium that a common discount function cannot accommodate. To keep this liquidity premium from distorting estimates of the longer end of the curve, these bonds are excluded from the main estimation. Short-maturity bonds are then studied separately as an “out-of-sample” exercise (the short-rate disconnect).

Q2. How does the Dynamic Nelson-Siegel model with stochastic volatility solve the cross-sectional sparsity problem?

The DNS model parameterizes the entire yield curve at each date using only three latent factors — level (L), slope (S), and curvature (C) — which follow a driftless random walk. The stochastic volatility component, captured in the covariance matrix Σt, governs how much information is pooled across adjacent time periods. When Σt → 0, the yield curve is assumed constant (full pooling); when Σt → ∞, estimates are date-by-date (no pooling). By allowing Σt to vary, the model pools more heavily in sparse periods and less during wars when yields change rapidly. The companion paper (Payne et al. 2023a) confirms via information criteria that stochastic volatility and correlated shocks improve fit without overfitting.

Q3. What is the bond-specific pricing error and why is it essential for historical data?

Assumption 3 adds to each bond i a Gaussian pricing error with mean zero and bond-specific standard deviation σ(i)_m (scaled by Macaulay duration to approximate yield-space errors). This allows bonds with idiosyncratic contract features — call options, conversion clauses, ambiguous payment currency — to inform the common yield curve without unduly distorting it. Bonds with larger σ(i)_m receive less weight in estimation. In modern datasets, researchers pre-select homogeneous bonds and use time-specific pricing errors; the historical sparsity prevents that approach here.

Q4. How large were Civil War yields compared to prior estimates, and why does the discrepancy arise?

The paper’s posterior median for the 10-year gold zero-coupon yield peaks at approximately 16% near the end of the Civil War. Homer and Sylla (2004) report a peak of 6% at the start of the war. The discrepancy arises because Homer and Sylla used bonds trading close to par, but during the Civil War no federal bonds traded at gold-price par (Lincoln’s re-election was uncertain in summer 1864; 100 greenback dollars could be purchased for 40 gold dollars, implying 6% coupon bonds were priced at 40% of par, implying yields in excess of 15%). This paper uses the full universe of Treasury bonds at monthly frequency and allows all bonds — regardless of trading price — to inform the yield curve.

Q5. When did US debt cease to carry a default risk premium relative to UK debt, and how is this measured?

The authors compare yields-to-maturity on gold-denominated UK consols to those on hypothetical gold-denominated US consols promising the same coupon flows. Because both countries were on a gold standard for most of the period and UK consols were the 19th-century safe asset, the spread is interpreted as a risk premium on US debt. US yields fell below UK yields persistently after approximately 1905, indicating that US debt was priced as a safe asset well before World War I. US yields were temporarily close to UK yields in the 1820s but the spread re-widened after the Jacksonian era, state defaults in the 1840s, and the Civil War. The spread closed only after Civil War disruptions resolved, the National Banking System matured, and gold-greenback parity was restored in 1879.

Q6. What is the “nominal anchor” finding during the greenback era, and what econometric method uncovers it?

During 1862–1878, the federal government issued non-convertible greenback dollars alongside gold bonds. The greenback depreciated substantially (to 40 cents per gold dollar in 1864), yet greenback-paying bonds traded near par, implying greenback yields near 6%. The authors model the greenback yield curve as a product of the gold discount function and a “multiplier” z(j)_t capturing the expected future gold-to-greenback exchange rate at each horizon j (Assumption 4). The exchange rate expectations are estimated via a time-varying VAR(2) model of the gold-to-greenback and gold-to-goods exchange rates (Assumption 5), jointly constrained by the prices of greenback bonds via an interest-rate parity condition. The resulting estimates show that throughout the greenback era — even during large wartime depreciations — investors’ long-run expectations of the exchange rate remained anchored near gold parity, consistent with anticipated eventual resumption.

Q7. How did political events affect exchange rate expectations during and after the Civil War?

The time-varying VAR captures shifts in exchange rate expectations associated with identifiable political events. Grant’s victory in 1869 (which resolved uncertainty about whether debts would be honored in gold) coincided with an increase in the price of greenbacks, a decrease in expected greenback appreciation, and a closing of the gap between greenback and gold 10-year yields. In the early 1870s, following the Panic of 1873 and uncertainty about resumption, investors came to expect that gold-greenback discrepancies would persist almost indefinitely, causing gold and greenback yields to converge. The Resumption Act of January 1875 then shifted 2-year and 10-year expectations back toward parity.

Q8. What is the short-rate disconnect and what does it reveal about the National Banking Era?

The short-rate disconnect is the difference between observed yields-to-maturity for bonds with less than one year to maturity and the yields-to-maturity implied by the model estimated on bonds with more than one year maturity. A positive disconnect means short-maturity bonds yielded less than long-maturity bonds conditional on the model — indicating a liquidity premium on short-term debt. The authors find a persistent premium of 0.25 to 0.5 percentage points through most of the 19th century, reflecting scarcity of money-like assets when state bank notes circulated at variable discounts. The premium disappeared from approximately the 1880s to World War I, coinciding with the mature National Banking Era after greenback-gold parity was restored in January 1879. The authors interpret this as evidence that the National Banking Acts (1862–1866), which allowed National Banks to issue standardized bank notes backed by long-term US government bonds, ultimately succeeded in supplying liquid assets and equalizing the pricing of short- and long-term federal debt — but only after the currency risk from the greenback period had been resolved.

Q9. How does the composite long-term yield series (Officer-Williamson / Homer-Sylla) distort historical narratives?

The composite series combines Homer and Sylla US federal yields (1798–1861), New England Municipal bond yields (1862–1899), and corporate bond yields (1900–1940). The paper shows that this composite series substantially underestimates the increase in US federal borrowing costs during Civil War deficits (peak of 6% vs. this paper’s 16%) and overstates post-Civil War borrowing costs by mixing in riskier private obligations. The authors argue that earlier findings of no strong association between 19th-century interest costs and deficits (Evans 1985, 1987) may reflect the composite series’ failure to accurately capture federal borrowing costs during large deficit episodes.

Q10. How did the yield curve slope change after the Civil War and what explains it?

The term spread (10-year minus 2-year gold yield) was typically negative before the Civil War and positive after the late 1870s. Major wars caused sharp temporary decreases (inversions). The authors connect the sign switch to a change in long-run inflation dynamics documented in a companion paper (Payne et al. 2023b): long-run inflation was hard to predict before the Civil War and easier to predict after, suggesting gold bonds provided a better inflation hedge in the pre-war period (negative inflation-risk premium), which is consistent with asset pricing theory producing a downward-sloping yield curve. After the Civil War, as inflation became more predictable, the inflation-risk premium became positive and the yield curve turned upward-sloping.

Q11. What did the National Banking Acts seek to do and was the puzzle of bank note under-issuance resolved?

The National Banking Acts (1862, 1863, 1865, 1866) authorized federally chartered banks to issue bank notes up to 90% of the par or market value of eligible US Treasury bonds deposited as collateral, subject to a 1% annual tax on notes outstanding (0.5% after 1900), compared to a 10% tax on state bank notes. The intended goals were to increase the supply of short-term liquid assets and to increase bank demand for long-term federal debt, thereby lowering long-term yields and eliminating the short-rate disconnect. A long-standing puzzle (Friedman-Schwartz, Cagan, Champ, Calomiris-Mason) held that yields on eligible Treasuries did not fall enough to equal the note tax rate, implying under-issuance. The paper’s analysis of the short-rate disconnect offers a resolution: if one focuses on the disconnect rather than the yield-tax spread, the National Banking Acts appear to have largely achieved their goals by the 1880s — but only after greenback-gold parity was restored, suggesting that currency devaluation risk had initially restrained bank note issuance, as hypothesized by Cagan (1965).

Key Concepts

Dynamic Nelson-Siegel (DNS) model with stochastic volatility: A parametric yield curve model (Diebold-Li 2006) parameterizing zero-coupon yields at each date as a function of three latent factors — level (L), slope (S), curvature (C) — following a driftless random walk. The paper extends this with time-varying shock volatilities (stochastic volatility) to allow the degree of information pooling across time periods to vary with institutional and wartime disruptions. Used here to handle cross-sectional sparsity in historical bond data.

Bond-specific pricing error: A Gaussian pricing error with bond-specific standard deviation σ(i)_m (scaled by Macaulay duration) added to each bond’s observed price. Allows bonds with heterogeneous and idiosyncratic contract features (call options, conversion clauses) to inform a common discount function without distorting it, by automatically down-weighting “peculiar” bonds through higher estimated σ(i)_m.

Short-rate disconnect (liquidity premium): The systematic difference between observed yields-to-maturity on bonds with less than one year to maturity and yields implied by a pricing kernel fitted on bonds with more than one year to maturity. Interpreted as a money-like convenience yield (liquidity premium) on short-term debt: when money-like assets are scarce, short-term bonds are overpriced (lower yields) relative to the term structure implied by longer maturities. Measured here as an out-of-sample fit residual from the DNS model.

Denomination risk: The risk that the unit of account in which bond payments are promised may change in value relative to gold. During the greenback era (1862–1878), bonds denominated in greenbacks carried denomination risk because greenbacks could depreciate against gold. The paper distinguishes denomination risk from default risk by estimating separate gold and greenback yield curves and modeling exchange rate expectations.

Nominal anchor: The phenomenon in which long-run market expectations of the gold-to-greenback exchange rate remained anchored near gold parity (one-for-one) even during large short-run depreciations during the Civil War. Inferred from the observation that greenback-denominated bonds traded near par (yield ~6%) while the spot greenback depreciated by up to 60% against gold, implying investors anticipated eventual full appreciation.

Default risk premium (US-UK yield spread): The difference between yields on hypothetical gold-denominated US consols and yields on UK consols. Since both were on a gold standard (so inflation expectations are similar), and UK consols were the 19th-century benchmark safe asset, the spread is interpreted as the compensation investors demanded for the risk that the US might default or alter payment terms. Persistently positive until approximately 1905, then became negative.

Convenience yield: An implicit yield that accrues to holders of money-like or safe assets because of their use in transactions or as collateral. In this paper, it emerges as the spread between yields on US federal bonds and other low-risk bonds in the late 19th century, reflecting increased demand for Treasuries as reserves under the National Banking System. Historically identified via the short-rate disconnect disappearing in the National Banking Era.

Dynamic Concern for Misspecification

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper asks how an agent who fears that none of their probabilistic models is the correct description of the data-generating process (DGP) should update that fear as evidence accumulates, and what long-run behavior such an agent exhibits. The central contribution is making the concern for misspecification endogenous: the better the agent’s structured models explain past observations, the less concerned the agent becomes.

Decision Criterion

The agent posits a finite-dimensional parametric set of structured models Θ, holds a prior µ over Θ, and evaluates each action according to an average robust control criterion. This criterion takes a weighted average (over models) of robust control assessments, where each assessment penalizes expected utility for probability distributions that deviate from the structured model in terms of relative entropy, scaled by a misspecification concern parameter λ > 0. A standard subjective expected utility maximizer is the limiting case as λ → 0 (no concern), and a maxmin agent is approached as λ → ∞.

Endogenous Misspecification Concern

The concern parameter λ is updated each period as a function of the likelihood ratio test (LRT) statistic of the structured models against unstructured alternatives, scaled by a time-normalizing sequence βₜ: λ(hₜ) = LRT(hₜ, Θ) / (2βₜ). The sequence βₜ determines how demanding the agent is in evaluating model fit.

Taxonomy of Agent Types

Three types emerge based on the speed of βₜ:

Statistician type (βₜ = ct, linear): applies a time scaling that keeps the LRT asymptotically informative about the degree of misspecification. This is the unique type satisfying both safety (long-run average payoff at least ε-close to the maxmin guarantee, almost surely) and consistency under almost correct specification (no ε-regret when misspecification is small).
Lenient type (t = o(βₜ)): attributes unexplained evidence to sampling variability; corresponds to the Law of Large Numbers intuition.
Demanding type (βₜ = o(t)): overly penalizes small discrepancies, analogous to the Law of Small Numbers fallacy (Tversky and Kahneman, 1971).

Standard SEU maximization fails safety; robust control with an invariant λ (Hansen and Sargent, 2001; 2022) fails consistency under almost correct specification.

Long-Run Convergence Results (Theorem 1)

For a misspecified agent (no θ ∈ Θ with qθ_{a*} = p*_{a*}), the nature of the limit action a* depends on the agent type:

Lenient type: a* is a Berk-Nash equilibrium — an SEU best reply to beliefs supported on the models with minimum relative entropy from the true DGP.
Demanding type: a* is a maxmin equilibrium — a worst-case best reply to all models absolutely continuous with respect to the true DGP.
Statistician type: if behavior converges, a* is a c-robust equilibrium — a robust control best reply to beliefs on the relative entropy minimizers, with the concern for misspecification endogenously set at minθ R(p*{a*} || qθ{a*}) / c.

For a correctly specified agent (Proposition 2), every limit action is a self-confirming equilibrium, regardless of the agent type.

Cycles and Limit Frequency (Section 4, Theorem 2)

The statistician type’s behavior need not converge. In natural settings, the agent cycles between actions: playing a “safe” action whose consequences are well-explained by Θ reduces concern for misspecification, eventually leading to a riskier action whose poorly-explained consequences raise concern again, inducing a return to the safe action. The paper proves that every limit frequency (empirical distribution over actions) is a mixed c-robust equilibrium — a generalization that allows mixing while tying the concern for misspecification to the frequency-weighted average relative entropy of each action.

Empirical Applications

Monetary policy cycles (Sargent 1999, 2008): In a central bank model where the true DGP includes increased inflation variability under aggressive policy (a feature absent from the bank’s structured models), no pure c-robust equilibrium exists for small c. The model predicts persistent cycles between conservative and aggressive policy. The frequency of the conservative policy is increasing in the strength of the exploitable inflation-unemployment trade-off (θ₁π + θ₁a).
Labor supply under complex tax schedules (Rees-Jones and Taubinsky, 2020): Agents with a “schmeduling” heuristic (linearizing the tax schedule) are misspecified. Berk-Nash equilibrium predicts these agents exert excess effort, with the bias increasing in the complexity (convexity) of the tax code. The c-robust equilibrium attenuates this bias: conditional on the equilibrium, minθ R(p*_a || qθ_a) > 0, so agents maintain positive concern for misspecification and pull back from the biased recommendation. The paper rationalizes the empirical finding that approximately 40% of agents hold the schmeduling belief but only about 20% fewer agents act on it — consistent with endogenous concern reducing the behavioral impact of the biased model.

Axiomatization (Section 5)

The paper axiomatizes the static average robust control criterion (Theorem 3) using: a Variational Axiom (from Maccheroni, Marinacci, and Rustichini, 2006a), a Structured Savage axiom (Sure-Thing Principle for bets on the model identity), an Intramodel Sure-Thing Principle (STP for bets conditional on the model), and Uniform Misspecification Concern (the agent is equally concerned about misspecification regardless of which model is identified as best-fitting). Three additional dynamic axioms characterize preference evolution: Constant Preference Invariance (utility index stable over time), Dynamic Consistency over Models (Bayesian updating over structured models), and Q-Likelihood (misspecification concern increases in the LRT). A novel Asymptotic Frequentism axiom characterizes the statistician type: preferences must become arbitrarily similar (in a precise quantitative sense) after sufficiently long histories with the same outcome frequency.

In depth

Q1. What is the average robust control criterion and how does it generalize prior decision criteria?

A: An agent evaluates action a by averaging over structured models θ a robust control assessment: for each θ, minimize expected utility over probability distributions within relative entropy distance (penalized by 1/λ) of qθ_a, then integrate over θ with prior µ. This nests SEU (λ → 0, perfect trust in models), standard robust control of Hansen and Sargent (2001) (µ is Dirac, single benchmark model), and maxmin expected utility of Gilboa and Schmeidler (λ → ∞). The key extension is allowing µ to be nondegenerate, so the agent is simultaneously uncertain about the best-fitting model and about whether any model is exact.

Q2. What is the role of the likelihood ratio test statistic in driving misspecification concern?

A: The LRT statistic compares the maximum likelihood of the structured models against the best unstructured alternative. It diverges almost surely when the agent is misspecified, regardless of how close the structured models are to the true DGP. The concern parameter λ(hₜ) = LRT(hₜ, Θ) / (2βₜ) uses a time-scaling sequence βₜ to keep this statistic interpretable. Without scaling, a misspecified agent’s concern would always explode to infinity.

Q3. Why does linear time scaling (βₜ = ct) uniquely characterize the statistician type as rational?

A: Proposition 1 establishes two properties: (1) ε-safety — every βₜ = ct-optimal policy achieves average payoff at least ε below the maxmin guarantee, almost surely; (2) ε-consistency under almost correct specification — for DGPs sufficiently close to Θ, the agent avoids long-run regret. Part 2 of Proposition 1 shows that no βₜ with βₜ = o(t) or t = o(βₜ) satisfies both properties simultaneously. SEU fails safety; invariant-λ robust control fails consistency.

Q4. What is a c-robust equilibrium and how does it differ from a Berk-Nash equilibrium?

A: A Berk-Nash equilibrium (Esponda and Pouzo, 2016) requires the action to be an SEU best reply to beliefs supported on the relative entropy minimizers of the true DGP. A c-robust equilibrium requires the same support condition but with the best reply taken under the average robust control criterion, where the concern for misspecification λ equals minθ R(p*{a*} || qθ{a*}) / c — that is, the minimum relative entropy scaled by 1/c. The endogenous λ is positive whenever the agent is misspecified, so the agent does not fully trust even the best-fitting model.

Q5. How does the paper explain that misspecified lenient types converge to Berk-Nash while demanding types converge to maxmin?

A: For the lenient type (t = o(βₜ)), the time scaling makes the concern for misspecification converge to 0 (the LRT grows slower than βₜ relative to t), so the agent effectively behaves as an SEU maximizer with beliefs on the KL-minimizing models — the Berk-Nash condition. For the demanding type (βₜ = o(t)), the LRT diverges relative to βₜ, so λ → ∞ and the agent’s preferences converge to worst-case evaluation over all models absolutely continuous with the true DGP — the maxmin condition. These are Theorem 1, parts 1 and 2.

Q6. Why does the statistician type exhibit cycles rather than convergence?

A: Section 4 and Corollary 1 show in the monetary policy application that no pure c-robust equilibrium exists for small c. Intuitively, the conservative policy (a=0) is a best reply to a high misspecification concern, but it produces outcomes well-explained by Θ, which drives concern down. The aggressive policy (a=1) is a best reply to a low concern, but it generates increased inflation variability not captured in Θ, which drives concern up sharply. There is no fixed point that is self-sustaining, so the agent cycles. Theorem 2 shows that the empirical frequency of actions still converges to a mixed c-robust equilibrium.

Q7. What are the quantitative comparative statics for the monetary policy cycles?

A: Corollary 1 establishes that there exists a threshold c̄ > 0 such that for all c ≤ c̄: (1) no pure c-robust equilibrium exists; (2) a mixed c-robust equilibrium exists; and (3) in the maximal and minimal equilibria, the frequency of the conservative policy α*(0) is increasing in θ₁π + θ₁a — a larger exploitable trade-off between inflation and unemployment implies more time spent on the aggressive policy.

Q8. How does the model rationalize the Rees-Jones and Taubinsky (2020) labor supply finding?

A: Rees-Jones and Taubinsky (2020) find that approximately 40% of agents have incentive-compatible beliefs consistent with the schmeduling heuristic (linearizing a convex tax schedule), but approximately 20% fewer agents act according to that heuristic. In a Berk-Nash equilibrium, the schmeduling agent exerts excess effort relative to the optimum; the more convex the tax code, the larger the excess. In a c-robust equilibrium, the agent retains a positive misspecification concern proportional to the deviation between the convex tax schedule and the linear approximation. Higher effort levels are more exposed to uncertainty in the marginal rate (the misspecified term θ+ε multiplies a higher average income z), so the concern for misspecification provides a natural force that reduces effort below the Berk-Nash prediction. The paper notes this finding is also consistent with an alternative interpretation in Rees-Jones and Taubinsky where all agents hold schmeduling beliefs but under-respond behaviorally.

Q9. What is the mixed c-robust equilibrium and why does it always exist?

A: A mixed c-robust equilibrium is a mixed action α* ∈ Δ(A) such that beliefs ν are supported on the relative entropy minimizers Θ(α*) — computed as the parameter minimizing the α*-weighted average relative entropy across actions — and every action in the support of α* is a best reply under the average robust control criterion with λ = minθ Σ_a α*(a) R(p*_a || qθ_a) / c. Proposition 3 proves existence by mapping this fixed-point condition to a Nash equilibrium in an auxiliary game between the agent and two adversarial Nature players, then invoking Reny (1999) on that game. A pure c-robust equilibrium need not exist, but mixing over actions allows the concern for misspecification to be calibrated to the frequency of poorly-explained actions.

Q10. How does Theorem 2 formally connect cycles to mixed c-robust equilibria?

A: Theorem 2 states that if βₜ = ct for all t and α* is a βₜ-limit frequency (i.e., the empirical action distribution converges to α* with positive probability under some optimal policy), then α* is a mixed c-robust equilibrium. The intuition is that when α* places weight on both a well-explained action and a poorly-explained action, the time-averaged relative entropy stabilizes at a fixed level, producing a stable endogenous concern for misspecification that makes the agent asymptotically indifferent between the actions in the support — sharply reducing the incentive to break the cycle.

Q11. What does the axiomatization contribute beyond the learning results?

A: The axiomatization (Section 5, Theorem 3) provides behavioral foundations observable from choices, without assuming the internal LRT mechanism. Two primary axioms pin down the average robust control criterion within the variational class: Structured Savage (Sure-Thing Principle for bets over model identity) and Uniform Misspecification Concern (equal concern for misspecification regardless of which model is revealed as best-fitting). Dynamic Consistency over Models pins down Bayesian updating. Q-Likelihood axiomatizes that the concern for misspecification is ordinally increasing in the LRT. The novel Asymptotic Frequentism axiom (Axiom 9) pins down the quantitative speed of adjustment: long histories with the same empirical frequency must induce asymptotically similar preferences, and Proposition 5 shows this implies λ_{hₜ} / (LRT(hₜ, Q) / (2tₙ)) converges to a finite limit — exactly the statistician type’s linear scaling.

Q12. What is the correlation between behavioral biases that the model predicts?

A: The paper derives three novel empirical predictions about the cross-sectional and time-series correlation of uncertainty attitudes: (1) long-run uncertainty aversion positively correlates with initial misspecification and with belief in the Law of Small Numbers; (2) these correlations are causal — repeated model failures and overly demanding evaluation induce a shift toward cautious behavior; (3) even holding misspecification and probability reasoning fixed, limit uncertainty attitudes are stochastic, depending on whether the limit action’s outcomes are well-explained by the structured models.

Q13. How does Example 2 (Correlation Neglect) show that endogenous concern can amplify rather than attenuate biases?

A: In a double auction, a buyer who mistakenly treats their own valuation and the ask price as independent (Correlation Neglect, Esponda, 2008) bids below the optimum in Berk-Nash equilibrium. In a c-robust equilibrium, the positive correlation between valuations and prices produces a strictly positive minθ R(p*{a*} || qθ{a*}), so the agent maintains misspecification concern. Since lower bids are accepted with lower probability (and thus are less sensitive to model misspecification), the endogenous concern drives the agent to bid even lower — amplifying the bias rather than attenuating it. This example illustrates that the direction of the correction depends on the geometry of how the misspecification interacts with the payoff structure.

Key Concepts

Average Robust Control Criterion: The decision criterion proposed in the paper. An agent evaluates action a by taking the expectation over structured models θ (with prior µ) of min_{p_a ∈ Δ(Y)} [E_{p_a}[u(a,y)] + (1/λ) R(p_a || qθ_a)]. This is a weighted average of robust control assessments, each penalizing distributions that deviate from a structured model in relative entropy. The parameter λ > 0 governs the intensity of misspecification concern, with SEU as the limit at λ → 0 and maxmin at λ → ∞.

Endogenous Misspecification Concern: Unlike prior robust control models where λ is fixed or set externally, here λ(hₜ) = LRT(hₜ, Θ) / (2βₜ) is a function of how well the structured models explain the observed history hₜ via the likelihood ratio test statistic. The better the models explain past data, the smaller λ becomes and the less the agent hedges.

Statistician Type: An agent who scales the likelihood ratio test statistic with a linear time sequence βₜ = ct for some c > 0. This is the unique agent type satisfying both ε-safety (guaranteed long-run average payoff above the maxmin guarantee minus ε) and ε-consistency under almost correct specification (no long-run regret when misspecification is small). The statistician type’s linear scaling is the only one for which the LRT statistic retains asymptotic informativeness about the degree of misspecification.

c-Robust Equilibrium: A fixed-point concept for the long-run behavior of the statistician type. Action a* is a c-robust equilibrium if it is an average robust control best reply to beliefs supported on Θ(a*) = argmin_θ R(p*{a*} || qθ{a*}), with misspecification concern λ = minθ R(p*{a*} || qθ{a*}) / c. This generalizes Berk-Nash equilibrium by incorporating an endogenous hedging motive proportional to the minimum relative entropy between the true DGP and the best structured model.

Mixed c-Robust Equilibrium: A generalization of c-robust equilibrium to mixed actions α* ∈ Δ(A) for environments where no pure equilibrium exists. The beliefs are supported on the models minimizing the α*-weighted average relative entropy, and the misspecification concern is tied to that average entropy. Every βₜ-limit frequency is a mixed c-robust equilibrium (Theorem 2). This concept characterizes the long-run time-average behavior when the statistician type cycles.

Law of Small Numbers (LSN) Type / Demanding Type: An agent for whom βₜ = o(t), meaning the time scaling grows sub-linearly. This agent is excessively sensitive to early model failures (analogously to the Law of Small Numbers fallacy of Tversky and Kahneman, 1971, where short-run frequencies are treated as the long-run norm). The long-run behavior of such a type converges to maxmin behavior rather than robust control.

Asymptotic Frequentism (Axiom 9): A novel axiom requiring that conditional preferences after sufficiently long histories with the same empirical outcome frequency must be arbitrarily similar (in a quantitative sense defined by measuring rods x, y, E) to a limiting preference. This axiom axiomatically pins down the statistician type’s linear time scaling: it implies that the ratio λ_{hₜ} / (LRT(hₜ, Q) / (2t)) converges to a finite limit c, exactly characterizing βₜ = ct.

Berk-Nash Equilibrium: The equilibrium concept (Esponda and Pouzo, 2016) that describes the long-run behavior of lenient (SEU) agents learning under misspecification. An action a* is a Berk-Nash equilibrium if it is an SEU best reply to beliefs supported on Θ(a*) — the KL-minimizing models — without any additional hedging against misspecification. The current paper shows that lenient types converge to Berk-Nash equilibria, while statistician types converge to c-robust equilibria that differ by incorporating a positive misspecification concern.

Expectation-driven term structure of equity and bond yields

Mon, 01 Jan 0001 00:00:00 +0000

Overview

Research Question. What drives the joint historical dynamics of the term structure of equity yields and nominal bond yields — and can a single unified equilibrium model explain the procyclical equity yield slope, the switch in bond-stock correlation from positive to negative after the late 1990s, the maturity-declining predictability of dividend strip returns, and standard aggregate stock market puzzles?

Key Departure from Prior Literature. Existing equilibrium models (habit formation, long-run risk, disaster risk) rely on time-varying risk premia to explain asset prices. Recent survey evidence challenges this: De La O and Myers (2021) show that most aggregate stock price movements are driven by cash-flow growth expectations rather than return expectations, and Van Binsbergen et al. (2013) show that equity yields are driven mainly by dividend growth expectations. This paper constructs an equilibrium model in which equity (bond) yield variation is attributable to subjective dividend growth (GDP growth) expectations, with a constant subjective risk premium implied by CRRA utility.

Model Architecture. The representative agent has CRRA utility with risk-aversion coefficient γ = 4 and subjective discount factor β = 1.0065 (calibrated to the average 10-year equity yield). The agent departs from rational expectations by having the “belief in the law of small numbers” (Tversky and Kahneman 1971): she perceives small samples to represent their population as well as large samples, leading to subjective learning gains that differ from the rational Kalman gain. The subjective belief updating rule is a modified Kalman filter in which the likelihood is exaggerated by factor (1+θ), producing a subjective learning gain ν that exceeds the Kalman gain K when overreaction applies and falls below it when underreaction applies.

The model has three blocks of fundamentals, each decomposed into a stable and a transitory component. (1) Real GDP growth is decomposed into PCE growth (stable, with a random-walk trend state µ_g) and a volatile gap component (stationary state x_g, persistence ρ_g = 0.941). (2) Inflation is decomposed into core inflation (stable, with trend state µ_π) and a volatile gap (persistence ρ_π = 0.932). (3) Real aggregate dividend is decomposed into a long-duration dividend component dl (levered on log real GDP with leverage λ = 3) and the share of long-duration dividend ds (stationary with persistence ρ_d = 0.94). This cross-sectional decomposition uses firm-level long-term earnings growth (LTG) forecasts from IBES as a model-free equity duration measure.

Estimation. State-space parameters are estimated by maximum likelihood with the Kalman filter on data from NYSE/NASDAQ/AMEX firms (CRSP/Compustat), quarterly, from 1987Q4 to 2019Q4. Subjective learning gains are estimated by minimizing RMSE between model-implied expectations and consensus forecasts: 1-year real GDP growth and inflation from the Survey of Professional Forecasters (SPF, 1981Q3–2019Q4), and 1-year aggregate dividend growth extended from De La O and Myers (2021) to 2019Q4. Equity yield data are from Giglio et al. (2021); bond yields are end-of-quarter zero-coupon nominal yields from Gürkaynak et al. (2007).

Main Findings.

Equity Term Structure Dynamics. The model’s subjective dividend growth expectations drive equity yields. The 1-year model-implied equity yield correlates 0.68 with data; the 10-year correlates 0.79; the 10Y–1Y slope correlates 0.59 with data. Consistent with “belief in the law of small numbers,” the agent overreacts to dividend news (estimated learning gains νl_d = 0.166 and νs_d = 0.458, both below their Kalman gains, which under the level-to-growth translation implies overreaction to dividend growth news, confirmed by negative CG(2015) regression slope coefficients of −0.69 at 1Y and −0.97 at 5Y).
Procyclical Equity Yield Slope. During recessions, the average equity yield slope (10Y–1Y) in the model is −3.77%; during expansions it is +3.96%, matching the data (−5.50% in recessions, +3.93% in expansions). The sign reversal is driven primarily by the dividend-specific component of the decomposition: in recessions, short-run dividend growth expectations fall much more sharply than long-run expectations.
Bond Pricing. The model’s 1-year and 10-year nominal bond yields achieve correlations of 0.92 and 0.95 with their data counterparts, inheriting the explanatory power of Zhao (2020) for the bond market. The agent underreacts to GDP growth and inflation news (estimated learning gains well below Kalman gains, confirmed by positive CG(2015) slope coefficients of +2.08 at 1Y for GDP growth and +1.01 at 1Y for inflation).
Bond-Stock Correlation Switch. In data, 10Y bond vs. dividend strip return correlation (5Y strip) goes from +0.46 before 2000 to −0.49 after 2000. The model produces +0.14 before and −0.56 after (for the 5Y strip). Decomposing the change in bond-stock return covariance: the “inflation real effect” (correlation between expected inflation and real growth) accounts for approximately 27–31% of total changes (for 5Y to 10Y strips); the “real growth correlation” channel — stronger co-movement between real GDP and real dividend growth expectations after 2000 — accounts for approximately 89–95% of total changes. The paper identifies this real bond hedging channel as the dominant and previously unexamined driver.
Dividend Strip Return Predictability. The price-dividend ratio predicts annual market excess returns with R² of 10.3% (data) vs. 9.0% (model). Strip return predictability is downward-sloping by maturity: in data, the R² is 20.2% for 5-year strips and 14.5% for 10-year strips; the model generates 14.2% and 10.4% respectively. This is decomposed into three sources: bond return predictability (small contribution), dividend forecast error predictability (dominant for short maturities), and forecast revision predictability (negative contribution that offsets). The downward slope occurs because current news has smaller impact on long-term dividend expectations.
Aggregate Market Puzzles. The model-implied log dividend-price ratio correlates 0.86 with data, with AR(1) coefficient 0.96 (data: 0.95). Model-implied average market return is 9% (data: 8%); annualized return volatility 12% (data: 16%). The model replicates the switch of the bond-stock aggregate return correlation from +0.13 before 2000 to −0.46 after 2000 (data: +0.39 to −0.64).

Scope Conditions. Results apply to U.S. equity and bond markets over 1987Q4–2019Q4 (with bond learning using data back to 1959Q1). The model assumes a representative agent with CRRA utility and constant subjective risk premium. It is silent on the term structure of expected returns in the statistical sense (which requires identification of latent states under the physical measure). The aggregate market results require a reduced-form specification for stochastic equity duration H_t linked to the value-weighted LTG average.

In depth

Q1. What is the core psychological mechanism generating subjective beliefs, and how does it differ from the diagnostic expectations approach?

The agent has the “belief in the law of small numbers” (Tversky and Kahneman 1971): she treats small samples as equally representative of their population as large samples. Formally, this is embedded by exaggerating the likelihood in the Bayesian update: p(x_t|I_t) ∝ p(y_t|x_t)^{1+θ} × p(x_t|I_{t-1}), where θ captures the magnitude of cognitive bias. The resulting subjective learning gain ν = (1+θ)P̃ / [(1+θ)P̃ + σ²_ε] can exceed the Kalman gain K when θ is large (overreaction) or fall below it when θ is small (underreaction). This differs from diagnostic expectations (Bordalo et al. 2019, 2020a,b), which are based on the representativeness heuristic; the paper notes the two notions of news are highly correlated in simulation (Table IA.2) and that both can imply overreaction.

Q2. Why does the model generate overreaction to dividend growth news even though the dividend-level learning gains are smaller than the Kalman gains?

The model separates dividend learning into level and growth. Section 2.2 derives that underreaction to dividend level news (νl_d < Kl_d, νs_d < Ks_d, estimated values 0.166 and 0.458 against Kalman gains 0.19 and 0.49 respectively) translates into overreaction to dividend growth news. This is confirmed by the CG(2015) rationality test: regressing forecast errors on lagged forecast revisions yields slope coefficients of −0.69 (1Y) and −0.97 (5Y) for real dividend growth, both statistically significant (t-statistics −3.63 and −3.22). In contrast, the same test yields positive slope coefficients for GDP growth (2.08 at 1Y) and inflation (1.01 at 1Y), confirming underreaction for these series.

Q3. How well does the model match subjective dividend growth expectations in the survey data?

The model-implied 1-year subjective dividend growth forecast is estimated by minimizing RMSE against the consensus dividend growth forecast series (extended from De La O and Myers 2021 to 2019Q4, with a replication correlation of 0.92 over the overlapping sample). The unconditional correlation between model-implied and data 1-year forecasts is 0.80. Although only 1-year forecasts are used in estimation, the model also achieves a correlation of 0.80 for 2-year forecasts, providing an out-of-sample validation.

Q4. What explains the higher volatility of short-term equity yields relative to long-term equity yields?

Short-term subjective dividend growth expectations are more volatile because the agent’s short-run expectation mean-reverts toward the less volatile long-run (levered) GDP growth expectation. In the model’s two-component dividend structure, the transitory dividend-share component xd has persistence ρ_d = 0.94 and its effect on equity yields decays as maturity increases (via the factor (1−ρ^n_d)/n). Similarly, the effect of the transitory GDP growth state x_g decays with maturity. Long-term equity yields are thus anchored by the slower-moving trend components µ_g and µ_d. In the data from Giglio et al. (2021), 1-year yields have a standard deviation of 8.89% annualized vs. 2.70% for 10-year yields; the model generates 8.22% and 1.89% respectively.

Q5. What is the quantitative importance of the “real growth correlation” channel vs. the “inflation real effect” channel in explaining the bond-stock correlation switch?

For the switch in bond-stock return correlation (using the 10-year nominal bond and various maturity dividend strips), the decomposition in Table 4 shows that the “real growth correlation” channel accounts for 89.1% (5Y strip), 92.1% (7Y strip), and 94.8% (10Y strip) of total bond-stock covariance changes, while the “inflation real effect” (correlation between expected inflation and expected real growth) accounts for 27.3%, 29.3%, and 31.1% respectively. The “volatility of shocks to expected inflation and real growth” makes a negative contribution (−16.4%, −21.4%, −25.9%), mostly attributable to more volatile beliefs during the 2008 global financial crisis. The real growth correlation channel reflects that after 2000, real bonds provide a better hedge to aggregate real dividend risks because real GDP growth expectations and real dividend growth expectations became more positively correlated.

Q6. Does the same real growth correlation story hold for the “Fed model” (bond-stock yield correlation)?

Yes, but with a quantitatively different balance. For yield correlations (Table 5), the “real growth correlation” channel accounts for 72.4%–80.1% of bond-stock yield covariance changes (5Y to 10Y strip), while the “inflation real effect” now accounts for 41.2%–43.9%. The inflation real effect is proportionally larger for yield levels because persistent expected inflation correlates strongly with the level of expected real GDP growth — even though inflation expectations do not move fast enough at high frequency to explain return correlation, they co-move strongly with expected growth at low frequency.

Q7. How does the model generate a downward-sloping term structure of return predictability?

The strip excess return is decomposed into three components (Equation 44): maturity-matched bond excess return (Bond), dividend forecast error within the holding period (FE), and forecast revision regarding dividend growth after the holding period (FR). For short maturities, bond predictability contributes little (R² ≈ 6.7% for 5Y strip), while FE predictability (R² ≈ 31.5%) and FR predictability (R² ≈ 35.6%) dominate. As maturity increases, the current news has smaller impact on long-term dividend expectations, reducing the predictability of FE (R² ≈ 26.6% for 10Y) and FR (R² ≈ 26.5% for 10Y). Taken together, total model-implied strip R² declines from 14.2% (5Y) to 10.4% (10Y), matching the data pattern (20.2% to 14.5%). The paper identifies forecast revision predictability as a new channel not previously documented.

Q8. Why do forecast errors and forecast revisions have opposite signs in the predictability regressions?

Bad news (high equity yields, i.e., low current stock prices) triggers excessively pessimistic subjective dividend growth expectations because the agent overreacts to dividend news. These overly pessimistic forecasts tend to be disappointed in the future — actual dividend realizations exceed the forecast — producing positive subsequent forecast errors (FE is positively predicted by high yields, with R² ≈ 31.5% for 5Y strips). However, as dividend levels mean-revert, higher subsequent realizations cause the agent to revise down the forecast for dividend growth thereafter, leading to negative forecast revisions (FR is negatively predicted by high yields, with R² ≈ 35.6% for 5Y strips, opposite sign from FE). The net effect on return predictability is thus a combination of positive (FE) and negative (FR) contributions.

Q9. How does the model handle the aggregate market dividend-price ratio and its persistence?

The aggregate stock price is modeled as the sum of dividend strip prices up to a stochastic horizon H_t, which is parameterized as a linear function of the value-weighted average of LTG forecasts: H_t = a + b·LTG_t. Parameters a and b are estimated by minimizing RMSE between model-implied and data log dividend-price ratio. The model-implied ratio achieves a correlation of 0.86 with data, an AR(1) coefficient of 0.96 (data: 0.95), and an annualized volatility of 26% (data: 30%). The time-variation is driven entirely by strip yield variations and exogenous LTG movements.

Q10. Is the overreaction to dividend news and underreaction to GDP/inflation news consistent in a single framework?

Yes. The model’s subjective learning framework (based on “belief in the law of small numbers”) generates both over- and underreaction depending on the estimated subjective learning gain relative to the Kalman gain. For GDP growth and inflation, the learning gains (ν*_g = 0.012, νgap_g = 0.065; ν*_π = 0.049, νgap_π = 0.228) are below their Kalman gains (0.29 and 0.67 for GDP components; 0.67 and 0.48 for inflation components), producing underreaction. The paper hypothesizes this is related to the Fed’s dual mandate: agents rationally assign lower weight to GDP and inflation shocks expecting the Fed will stabilize them. For dividend growth, a level-to-growth translation converts level underreaction into growth overreaction.

Q11. What are the robustness checks, and what do they show?

The paper checks three alternative equity duration measures: those from Dechow et al. (2004), Weber (2018), and Gonçalves (2021b), as well as the book-to-market ratio following Lettau and Wachter (2007). Table IA.1 shows that replacing LTG with these measures still produces model-implied equity yields that replicate key data moments with high time-series correlations. Changing the cross-sectional breakpoint for long-duration dividends from the median LTG to the 40th or 60th percentile leaves results similar. The paper also presents an Internet Appendix extension in which the agent has ambiguity about real GDP and dividend growth (model misspecification fear), yielding equity yields and returns even closer to data.

Q12. What is the paper’s contribution to the bond market relative to Zhao (2020)?

The bond pricing block closely follows Zhao (2020), inheriting its explanatory power for bond market stylized facts. The model’s 1-year and 10-year nominal bond yields achieve correlations of 0.92 and 0.95 with data, respectively. The new contribution is the joint model covering both equity and bond markets simultaneously, enabling the decomposition of bond-stock covariance and the identification of the real growth correlation as the dominant driver of the bond-stock correlation switch — a channel not addressed by Zhao (2020), which focused on bond market puzzles alone.

Key Concepts

Equity Yield (Dividend Strip Yield). Defined as ey^(n)_t = (1/n)(d$_t − p^(n)_t), where p^(n)_t is the log price of the n-period dividend strip (a claim to the nominal dividend n periods ahead) and d$_t is the log nominal aggregate dividend. It decomposes into the bond yield, a subjective dividend growth component, and a (constant) risk premium component.

Belief in the Law of Small Numbers. A cognitive bias (Tversky and Kahneman 1971) in which the agent perceives small samples to represent their population as well as large samples. Modeled by exaggerating the likelihood in Bayesian updating: p(x_t|I_t) ∝ p(y_t|x_t)^{1+θ} × p(x_t|I_{t-1}). This generates a subjective learning gain ν that can exceed the Kalman gain (overreaction) or fall below it (underreaction) depending on θ and the signal-to-noise ratio.

Subjective Learning Gain. The coefficient ν in the subjective Kalman filter update ẽ_t x_t = ρẽ_{t-1}x_{t-1} + ν(y_t − ρẽ_{t-1}x_{t-1}). It equals (1+θ)P̃ / [(1+θ)P̃ + σ²_ε], where P̃ is the subjective predictive variance. When ν > K (the rational Kalman gain), the agent overreacts to news; when ν < K, the agent underreacts.

Long-Duration Dividend Component. The portion of aggregate real dividend (dl_t) attributable to “long-duration” firms — those with above-median analyst LTG forecasts in CRSP/Compustat/IBES data. Levered on log real GDP with leverage parameter λ = 3, it carries aggregate risk. The complementary short-duration dividend share ds_t is stationary and carries no aggregate risk. The decomposition allows the model to exploit cross-sectional cash-flow duration information when learning about future aggregate dividend growth.

Real Growth Correlation Channel. A bond-stock covariance component defined as Cov(RGDP^(N), RDIV^(n)), where RGDP^(N) is the real GDP growth expectation component of 10-year nominal bond returns and RDIV^(n) is the real dividend growth expectation component of n-period strip returns. This channel captures whether real bonds hedge aggregate real dividend risks. The paper shows this channel accounts for approximately 89–95% of the post-2000 bond-stock covariance change for dividend strips.

Inflation Real Effect. The covariance component Cov(INFL^(N)_B, RGDP^(n) + RDIV^(n)), defined as the correlation between shocks to expected inflation (embedded in nominal bond returns) and shocks to expected real growth (in strip returns). In the paper’s framework this is distinct from the standard inflation risk premium story, as it concerns the correlation between subjective beliefs rather than realized covariances under the physical measure.

Forecast Error (FE) and Forecast Revision (FR) Predictability. Two of three components of realized strip excess return (Equation 44). FE = ∆d${t+1:t+h} − ẽ_t∆d${t+1:t+h} is the realized dividend growth forecast error within the holding period; FR = (ẽ_{t+h} − ẽ_t)∆d$_{t+h+1:t+n} is the forecast revision for dividend growth beyond the holding period. Because the agent overreacts to dividend news, bad news triggers overly pessimistic forecasts (positive subsequent FE) and, as dividends mean-revert, downward forecast revisions (negative FR). These two have opposite signs in predictive regressions, generating the downward-sloping term structure of return predictability.

Fed Model. The empirical positive correlation between equity yields (real) and nominal bond yield levels. The paper shows that this yield-level correlation switched from strongly positive (≈ 0.85 before 2000) to significantly negative (≈ −0.60 to −0.62 after 2000) for 5Y–10Y dividend strips, and that the same real growth correlation and inflation real effect decomposition applies, albeit with the inflation real effect proportionally larger (≈ 40%) for yield levels than for returns (≈ 30%) because persistent inflation expectations co-move with the level of expected real GDP growth.

Inequality and asset prices during Sudden Stops

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper studies the cross-sectional dimension of Fisher’s (1933) debt-deflation mechanism as it operates during Sudden Stop crises — episodes characterized by large, abrupt reversals in the current account. The central question is how the distribution of wealth and leverage across households shapes the macroeconomic dynamics of financial crises, and whether greater inequality makes Sudden Stops more or less severe.

Data and Methodology

The empirical analysis uses panel microdata from the Mexican Family Life Survey (MxFLS) across three waves (2002, 2005, 2009), covering a representative sample of approximately 8,400 households in 150 localities. The 2009 wave captures a Sudden Stop in which Mexico’s current account reversed by 1.5 percentage points of GDP, per capita consumption fell 7 percent, and housing prices fell 4 percent below pre-crisis trend by 2010. Households are sorted by net wealth and leverage ratio — defined as total debt divided by total assets — to identify how balance sheet heterogeneity drove differentiated asset-holding dynamics during the crisis.

The theoretical framework is a Bewley small open economy model with heterogeneous agents, incomplete markets, aggregate risk (simultaneous shocks to the international interest rate and total factor productivity), and an occasionally-binding loan-to-value (LtV) collateral constraint. Households hold two assets: a one-period risk-free international bond and a risky domestic collateralizable asset (land). Households face persistent non-insurable idiosyncratic risk in both labor income and dividend returns; the latter creates an endogenous risk-wealth tradeoff, since larger asset holdings raise future income volatility while simultaneously expanding debt capacity. The model is calibrated to Mexican data — matching the leverage ratio distribution in 2005 (10 percent of households financially constrained) and a net foreign asset position of −35 percent of GDP — and solved using the FiPIt algorithm combined with the Krusell-Smith stochastic-simulation approach.

Main Findings with Quantitative Magnitudes

The empirical evidence from Mexico’s 2009 crisis reveals sharply divergent asset dynamics across the household balance sheet distribution. Wealthy households (top net-wealth decile) with low leverage increased their real estate holdings by 61.4 percent (annualized, relative to the average) between 2005 and 2009, consistent with a crisis-dampening effect whereby unconstrained agents absorb fire-sales. Wealthy households in the top decile of both net wealth and leverage ratio — financially constrained — reduced their real estate holdings by 36.6 percent, consistent with a crisis-amplifying effect. Cross-country descriptive evidence shows that Sudden Stop episodes are associated with significantly larger contractions in consumption and GDP in more unequal economies (Gini index, World Bank data, 58 Sudden Stop episodes identified by Bianchi and Mendoza 2020).

In the calibrated model, the crisis-dampening effect dominates relative to the representative agent baseline: the heterogeneous-agents economy produces a smaller decline in asset prices (−0.99 percent vs. −2.57 percent in the representative agent model during crisis episodes), but a larger and more persistent consumption decline (−2.97 percent vs. −1.17 percent) and current account reversals (1.56 percentage points vs. 0.09 percentage points). The wealth Gini index generated by the calibrated model is 0.61, close to the untargeted 2005 Mexican estimate of 0.73. The aggregate equity premium generated is 5.1 percent, close to the data estimate of 6.5 percent; of this, 55.3 percent is attributable to the risk component, 35.9 percent to the persistence effect, and 8.6 percent to the constraint effect.

When comparing the baseline emerging economy (wealth Gini 0.61) to an advanced economy calibration in which idiosyncratic dividend risk is set to zero (wealth Gini 0.29), crises are milder and less frequent in the more equal economy: consumption drops 1.0 percentage point less, asset prices drop 0.2 percentage points less, and the net foreign debt position is 6.2 percentage points larger relative to GDP. The implied slope coefficient from the model relating consumption declines during Sudden Stops to the income Gini (−11.1) closely matches the cross-country empirical estimate (−11.5). An economy with an income Gini index 0.10 points lower experiences a decline in consumption 1.1 percentage points smaller during a crisis.

An impulse response to a two-standard-deviation aggregate shock confirms that, conditional on starting from a perfectly equal (symmetric) initial distribution via complete redistribution, declines in consumption and asset prices are approximately 0.5 percentage points smaller than in the baseline economy with the stationary ergodic distribution as initial condition.

Redistributive Dividend Tax

A flat 30 percent dividend income tax, redistributed as lump-sum transfers, reduces Sudden Stop severity by lowering average asset prices by 9.6 percent relative to the benchmark, which shrinks effective debt capacity and limits bond adjustment during crises. The average current account reversal during a crisis falls by 0.54 percentage points, and aggregate consumption falls by 0.63 percentage points less than in the benchmark. Crisis probability under the benchmark threshold falls from 4.3 to 1.83 percent (less than half). Average welfare improves by a gain equivalent to 2.8 percent of consumption. However, 26.7 percent of households — those more leveraged and three times wealthier than the beneficiaries — experience welfare losses averaging 6.8 percent of consumption, due to asset price declines and tighter financial conditions.

Overall Conclusion

Both the empirical evidence and the model suggest that economies with lower inequality, whether due to reduced idiosyncratic risk (as in advanced versus emerging economy calibrations) or wealth redistribution across agents with identical idiosyncratic risk processes, experience less severe Sudden Stop crises.

In depth

Q1. What are the two cross-sectional channels through which household heterogeneity affects the debt-deflation mechanism, and in which direction do they move asset prices?

A1: The dampening effect operates when unconstrained wealthy households — who hold diversified portfolios and have precautionary savings in bonds — purchase fire-sold assets from constrained households, relieving downward pressure on asset prices. The amplifying effect operates when highly leveraged households, once pushed into binding credit constraints by declining asset prices, must further liquidate asset positions, deepening the price decline and tightening the collateral constraint for additional households via the pecuniary externality. These two effects move in opposite directions, so the net effect of inequality on crisis severity is theoretically ambiguous and depends on calibration.

Q2. What specific empirical evidence from Mexico’s 2009 Sudden Stop supports both cross-sectional effects?

A2: Using MxFLS microdata, Table 1 in the paper shows that wealthy households (top net-wealth decile) with low leverage (deciles I–VII of leverage) increased their real estate holdings by 61.4 percent between 2005 and 2009 — evidence for the dampening effect. Wealthy households in the top decile of both net wealth and leverage reduced their real estate holdings by 36.6 percent — evidence for the amplifying effect. Between 2005 and 2009, the share of financially constrained households (leverage ratio above 0.168, the 90th percentile) increased by 1.7 percentage points, while the share of financial savers dropped by 5.0 percentage points. The pre-crisis period (2002–2005) shows no comparable divergence, ruling out a mechanical mean-reversion explanation.

Q3. What is the risk-wealth tradeoff, and why is it central to generating a realistic wealth and leverage distribution in the model?

A3: The risk-wealth tradeoff arises because idiosyncratic dividend risk is endogenous to asset holdings: holding more risky domestic assets increases debt capacity (relaxing borrowing constraints) but also raises future income volatility, since the variance of household flow income is convex in asset holdings. For households earning high dividend realizations, there exists a threshold beyond which precautionary savings motives — driven by rising income risk — dominate the benefit from expanded debt capacity, causing these households to begin accumulating bonds and eventually become net savers. This mechanism generates an empirically plausible distribution in which some households are financially constrained at the LtV limit, others are unconstrained borrowers, and a fraction are net savers holding both domestic assets and positive international bonds.

Q4. How does the model calibration match the stationary distribution of Mexican households?

A4: Three parameters governing the dividend income risk process (average dividend yield, autocorrelation, and standard deviation) are jointly calibrated to match three statistics from the MxFLS 2005 distribution of households: 14.1 percent financial savers (data: 14.2 percent), 75.9 percent unconstrained indebted (data: 75.8 percent), and 10.0 percent financially constrained (data: 10.0 percent). The collateral fraction κ = 0.168 is set equal to the 90th percentile of the leverage ratio distribution in 2005, reflecting that the average delinquency rate for commercial bank household credit was 10.3 percent between 2004 and 2008. The discount factor β = 0.90 matches the average net foreign asset position relative to GDP of −35 percent for Mexico.

Q5. How does the heterogeneous-agents model compare to the representative agent model in terms of crisis dynamics?

A5: In the heterogeneous-agents benchmark, the average current account reversal during a Sudden Stop is 1.56 percentage points, consumption falls 2.97 percent, and asset prices fall 0.99 percent below the steady state. In the representative agent model with the same average leverage ratio (κ = 0.12), the current account reversal is only 0.09 percentage points, consumption falls 1.17 percent, and asset prices fall 2.57 percent. The crisis-dampening effect in the heterogeneous economy produces a smaller asset price drop but a larger consumption decline, because leveraged households must make larger consumption adjustments when hit by negative idiosyncratic shocks in addition to the aggregate shock. Impulse response analysis shows the heterogeneous-agents economy generates current account reversals 1.9 percentage points larger than the representative agent, and consumption responses approximately four times larger.

Q6. What is the mechanism by which comparing emerging and advanced economy calibrations shows that lower inequality leads to less severe crises?

A6: The advanced economy calibration sets idiosyncratic dividend risk to zero, eliminating the risk-wealth tradeoff and resulting in a wealth Gini of 0.29 (compared to 0.61 in the baseline). Without dividend risk, households have weaker incentives to accumulate assets as a precautionary buffer against income volatility, so they hold less debt on average and the long-run net foreign debt relative to GDP is 6.2 percentage points larger (i.e., less debt). During a Sudden Stop under this calibration, consumption drops 1.0 percentage point less, asset prices drop 0.2 percentage points less, and the economy is less frequently in crisis. The model-implied slope of consumption decline on income Gini is −11.1, matching the cross-country empirical estimate of −11.5.

Q7. What does the impulse response analysis reveal about the effect of wealth redistribution on crisis severity, holding idiosyncratic risk constant?

A7: The impulse response analysis compares the baseline heterogeneous-agents economy (with the stationary ergodic distribution as the initial condition) against a version in which all households are given a perfectly symmetric initial distribution — identical bond and asset holdings equal to long-run averages — while retaining the same idiosyncratic risk processes. The symmetric initial condition corresponds to a complete redistribution of wealth without changing fundamentals. In the first three periods after a two-standard-deviation aggregate shock, the symmetric economy shows declines in consumption and asset prices approximately 0.5 percentage points smaller than the baseline. This demonstrates that even holding the risk environment constant, reducing wealth dispersion mitigates crisis severity.

Q8. How does the equity premium decomposition work in the heterogeneous-agents model, and which components are quantitatively most important?

A8: The aggregate equity premium is decomposed into five components (Equation 7 in the paper): a constraint effect (positive, increasing in the measure and intensity of constrained households), a risk effect (positive, from the negative covariance between the individual stochastic discount factor and individual equity return, weighted more heavily on constrained households), a persistence effect (positive, from the covariance between idiosyncratic dividend return and asset holdings, since high-dividend households accumulate more assets), a trading cost effect (approximately zero in aggregate), and a no-short-sales effect (negative, since households at the short-sales constraint add to asset demand without increasing the marginal benefit of saving). In the calibrated model, the equity premium is 5.1 percent; the risk effect accounts for 55.3 percent, the persistence effect for 35.9 percent, and the constraint effect for 8.6 percent.

Q9. What is the mechanism by which the dividend income tax reduces crisis severity?

A9: A flat 30 percent dividend income tax lowers average after-tax dividend returns, reducing households’ incentive for precautionary accumulation of domestic assets and weakening the risk-wealth tradeoff. As a result, households demand fewer domestic assets and fewer international bonds in normal times. The reduced demand for the domestic asset lowers the equilibrium asset price by 9.6 percent on average relative to the benchmark, which — through the pecuniary externality embedded in the LtV constraint — tightens borrowing constraints, raising the share of financially constrained households from 5.6 to 7.8 percent. Nevertheless, the reduction in equilibrium debt positions means that during a crisis, bond adjustments and consumption drops are more limited: the average current account reversal during crises falls by 0.54 percentage points, and aggregate consumption falls by 0.63 percentage points less than in the benchmark. Crisis probability under the benchmark threshold falls from 4.3 to 1.83 percent.

Q10. Who benefits and who loses from the dividend income tax, and by how much?

A10: Among the simulated population, 73.3 percent of households experience welfare gains averaging 6.2 percent of consumption in consumption-equivalent terms, while 26.7 percent experience welfare losses averaging 6.8 percent of consumption. The average welfare gain across all households is equivalent to 2.8 percent of consumption. The households experiencing losses are more leveraged and three times wealthier on average than those that benefit; the policy reduces their net worth through lower asset prices and tightens their financial constraints. The welfare analysis accounts for the transition to the new tax policy.

Q11. Why does the representative agent model miss the cross-sectional effects that are central to the paper’s mechanism?

A11: In the representative agent model, all households behave identically and either collectively want to buy or sell assets, but since there is no one to trade with domestically, actual asset holdings remain unchanged by cross-sectional forces. Additionally, the average debt constraint multiplier in the representative agent equals the single household’s multiplier, whereas in the heterogeneous model a small fraction of highly constrained households can have much larger individual multipliers, amplifying the aggregate debt-deflation effect. In the calibrated stationary model, 10 percent of constrained households own 7.7 percent of assets and have a consumption share of 9.0 percent, while 75.9 percent of unconstrained indebted households hold 88.1 percent of assets with a consumption share of 78.1 percent — distributional features invisible to a representative agent.

Q12. What robustness does the model validation provide for the quantitative results?

A12: The model reproduces the untargeted net wealth and asset distributions across deciles from MxFLS 2005 closely, with slight underestimation at the top deciles; the exception is the bottom decile of debt (where the model cannot generate households with negative net wealth since default is not modeled). The aggregate law of motion for the Krusell-Smith algorithm fits with R² = 0.99 for bond position and R² = 0.93 for asset price, and Den Haan (2010) accuracy checks show maximum forecast errors of 2.8 (current account) and 1.1 (asset price). The model replicates the untargeted magnitude of current account reversals observed in Mexican Sudden Stops. The wealth Gini of 0.61 is close to the untargeted 2005 Mexican estimate of 0.73, and the equity premium of 5.1 percent is close to the data estimate of 6.5 percent.

Key Concepts

Sudden Stop: An episode characterized by a large, abrupt reversal in the current account, typically triggered by a sudden halt in foreign capital inflows. In this paper, Sudden Stops are modeled as endogenous crises that arise from the interaction of a negative aggregate shock (simultaneous rise in the international interest rate and decline in total factor productivity) with an occasionally-binding LtV collateral constraint. The paper follows Bianchi and Mendoza (2020) in identifying 58 such episodes over the past four decades.

Debt-deflation mechanism (cross-sectional dimension): The paper studies Fisher’s (1933) debt-deflation spiral — in which declining asset prices tighten credit constraints, forcing further asset sales, further depressing prices — through the lens of household heterogeneity. The cross-sectional dimension refers to the fact that different households (wealthy unconstrained vs. highly leveraged constrained) respond differently to price declines, generating two opposing effects: dampening (wealthy buyers absorb fire-sales) and amplifying (constrained households fire-sell additional assets).

Risk-wealth tradeoff: A novel feature of the model in which holding more risky domestic assets simultaneously (a) expands debt capacity by relaxing the LtV constraint and (b) increases future income volatility through higher exposure to idiosyncratic dividend risk, since the variance of household flow income is convex in asset holdings. This tradeoff generates the endogenous transition of households from indebted to net-saver status and gives rise to the empirically plausible distribution of savers, unconstrained borrowers, and constrained households.

Loan-to-value (LtV) collateral constraint: A borrowing limit requiring that households’ international debt (negative bond holdings) cannot exceed a fixed fraction κ of the market value of their domestic asset holdings. In the paper, κ = 0.168 (the 90th percentile of the Mexican leverage ratio distribution in 2005). The constraint is occasionally binding and generates a pecuniary externality: households fail to internalize that their individual portfolio choices affect the aggregate asset price, which in turn determines the borrowing limits of all other households.

Pecuniary externality: The externality arising from the LtV constraint in which each household’s choice of asset holdings affects the equilibrium asset price, thereby changing the borrowing limits of all households simultaneously. This externality drives the debt-deflation spiral and is the source of Sudden Stop crises in the model: no single household internalizes the aggregate impact of its fire-sales on credit conditions.

Fire-sale: In the context of this paper, the forced liquidation of domestic asset holdings by financially constrained households during a crisis. Fire-sales are triggered when the LtV constraint becomes binding, forcing households to sell assets to reduce debt; the resulting price decline tightens the constraint further, producing additional fire-sales. The paper documents that, during Mexico’s 2009 Sudden Stop, wealthy constrained households (top decile of both net wealth and leverage) reduced real estate holdings by 36.6 percent, while wealthy unconstrained households increased holdings by 61.4 percent.

Dampening and amplifying effects: Two opposing cross-sectional effects on asset prices during a crisis. The dampening effect: unconstrained wealthy households purchase depressed assets fire-sold by constrained households, relieving downward pressure on prices and weakening the debt-deflation spiral. The amplifying effect: highly leveraged households that are pushed into binding constraints by falling prices must also fire-sell assets, further depressing prices and tightening financial conditions. The net impact on crisis severity depends on which effect dominates, which the paper establishes empirically and quantitatively is inequality-dependent.

Equity premium decomposition: A decomposition derived in the paper (Equation 7) that expresses the aggregate excess return on the risky domestic asset as the sum of five components: a constraint effect (positive, from the measure and intensity of binding LtV constraints), a risk effect (positive, from the covariance of individual stochastic discount factors with individual equity returns), a persistence effect (positive, from the covariance of idiosyncratic dividend returns with asset holdings due to return persistence), a trading cost effect (approximately zero in aggregate), and a no-short-sales effect (negative). In the calibrated model, the risk and persistence effects account for 91 percent of the 5.1 percent equity premium.

Permanent Capital Losses after Banking Crises

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper investigates two interrelated questions about historical banking crises: (1) whether bank losses during banking crises are primarily temporary or permanent in nature, and (2) whether policy interventions — particularly liquidity-based interventions — are effective at restoring bank capitalization after such crises. The paper positions these questions against a theoretical divide: models stressing temporary price dislocations (binding borrowing constraints, depositor fragility, information frictions) versus models in which crises reflect fundamental and permanent deterioration in the value of bank assets.

Data and Methodology

The authors construct three new historical datasets spanning 46 economies from 1870 to 2019. The first is a country-level panel of annual and monthly bank and nonfinancial equity index total returns, building on Baron, Verner, and Xiong (2021). The second is an individual-bank-level dataset covering the ten largest banks per country across 17 economies (from Jordà, Schularick, and Taylor 2017), containing equity returns, balance sheet quantities, net income decomposed into write-downs and trading income, and equity issuance within ±5-year windows around each crisis. The third is a new database of the monthly starting dates of policy interventions — extraordinary central bank liquidity support, blanket liability guarantees, and government recapitalizations — extending the databases of Laeven and Valencia (2020) and Metrick and Schmelzing (2024).

Bank equity crises are identified using a real-time, data-driven indicator requiring: (1) a greater than 30% annual decline in the bank equity index and (2) the failure of a top-20 bank within the country. This definition yields 76 bank equity crises, nearly all of which overlap with prior narrative-based chronologies (Reinhart-Rogoff, JST, Laeven-Valencia), and results are robust to all alternative crisis definitions examined.

Main Findings

Permanent losses. In the year of a bank equity crisis onset, bank equity experiences average abnormal returns of -68 log-points (or -49% in arithmetic terms), while nonfinancial equity falls by -36 log-points (-30%). Over the subsequent five years, bank equity does not earn elevated returns relative to the country’s unconditional average — point estimates are consistently negative, and significantly so in years three and four after crisis onset. Bank equity does not recover to its pre-crisis level. By contrast, nonfinancial equity earns cumulative abnormal returns of roughly 30 log-points (35% arithmetic) over five years, recovering to pre-crisis trend, consistent with a discount-rate-driven decline for nonfinancial firms.

Earnings-driven, not discount-rate-driven. Panel regressions at both the country and individual-bank level show coefficients of roughly 1 to 2 on the relationship between the initial bank equity return in the crisis year and the subsequent five-year change in real dividends and real earnings. The initial equity decline thus predicts a roughly commensurate long-run decline in banks’ dividends and earnings, inconsistent with the temporary-loss view’s prediction of discount-rate-driven declines that should subsequently reverse.

Short-run bounce-backs are modest and transient. At the monthly frequency, bank equity does rebound modestly from its trough — the bounce-back averages only about 30% of the initial decline, even assuming perfect market timing. This gain partially reverses after approximately twelve months, so cumulative five-year returns remain not elevated above the unconditional average.

Write-downs, not fire sales, drive losses. Realized book losses in the first year of crisis onset account for only about 30% of market-value losses — contrary to what fire-sale models predict. By year five, cumulative book losses reach roughly 35% of pre-crisis book equity and approximately 100% of market-value losses. Decomposing net income, write-downs track cumulative book losses closely and fully account for market-value losses by year five. Trading losses (from securities sales and asset dispositions) account for only a small share on average, though for banks in the top quartile of securities-to-assets ratios, immediate accounting losses are larger and more trading-loss-driven — consistent with fire-sale dynamics being important specifically for banks with large tradable securities portfolios.

Nonperforming loans confirm the mechanism. At the country level, larger bank equity declines are associated with higher peak NPL rates in the subsequent five years (adjusted R² of 0.53 excluding two outliers; 0.606 for the 2008-2010 subsample only). No analogous relationship exists for nonfinancial equity returns.

Policy interventions are insufficient. Liquidity-based interventions (extraordinary central bank support and blanket guarantees) implemented after bank equity crises are followed by an approximately 20% short-run rebound in bank equity, which reverses between months 12 and 36. No large or permanent increase in bank value follows. Government recapitalization programs have historically been small (averaging 24% of pre-crisis book equity and 43% of realized losses), narrow (65% classified as narrow, median of five banks recapitalized), and delayed. Banks cannot self-recapitalize through high post-crisis profitability.

Crisis type matters. Panic-only crises (banking panics without large bank equity declines, N=85) exhibit very different dynamics: bank equity recovers to pre-crisis levels within five years, dividends fall only temporarily, liquidity interventions produce large and permanent rebounds, and macroeconomic output losses are smaller. In 75% of bank equity crises, the bank equity decline strictly precedes the banking panic, indicating that fundamental weaknesses — not liquidity shocks escalating into solvency problems — are the primary driver. Only 19 cases (25%), labelled “mismanaged banking panics” (including the U.S. Great Depression), saw the panic precede the equity decline, mostly in the pre-1945 Gold Standard era. Early liquidity intervention is essentially a necessary condition for averting incipient crises, but it is effective only when a steep bank equity decline has not yet occurred.

In depth

Q1. How do the authors define a “bank equity crisis” and why does the definition matter for their empirical strategy?

A bank equity crisis is defined as the first year when (1) the bank equity index declines by more than 30% in annual excess total returns in any year within the past five years, and (2) a top-20 bank (ranked by assets) fails within the country. This purely data-driven, real-time definition avoids the look-ahead bias inherent in narrative-based chronologies. The authors identify 76 such crises. Results are robust to using Reinhart-Rogoff, JST, Laeven-Valencia, and 30%-decline-only definitions, alleviating concerns that the differential bank versus nonfinancial equity dynamics are mechanical artifacts of the crisis identification approach.

Q2. What is the quantitative magnitude of the initial equity shock to banks versus nonfinancial firms at crisis onset?

In the year of a bank equity crisis, the average abnormal cumulative log excess total return is -68 log-points for bank equity and -36 log-points for nonfinancial equity (corresponding to -49% and -30% in arithmetic abnormal returns, respectively). These are relative to the country’s unconditional average returns, estimated using country fixed effects in panel regressions.

Q3. Do bank stocks earn elevated returns after banking crises, as temporary-loss models predict?

No. Over the five years following crisis onset, bank equity point estimates of cumulative abnormal returns are consistently negative, and significantly so at years three and four. Bank equity does not recover to its pre-crisis level at any horizon out to five years (and Figure A.9 extends to ten years with similar conclusions). This pattern holds across advanced and emerging economies, before and after 1945, excluding the Global Financial Crisis, and across a variety of methods for computing abnormal returns. Even for surviving banks — excluding those that failed or exited — the pattern holds.

Q4. How do the earnings and dividend dynamics of banks versus nonfinancial firms differ after crises?

For banks, both real dividends per share and real earnings per share remain well below their long-term average five years after crisis onset, with no recovery visible by year five. For nonfinancial firms, dividends and earnings decline at crisis onset but rebound, though only slowly through year five. Panel regressions at both the country and individual-bank level find coefficients of approximately 1 to 2 on the relationship between the crisis-year bank equity return and the five-year-ahead change in real dividends and real earnings — indicating a roughly commensurate earnings-driven decline, not a transitory discount-rate shock.

Q5. What is the magnitude of the short-run bounce-back in bank equity, and does it represent a profit opportunity?

Even with perfect knowledge of the crisis trough (which is not available in real time), the rebound in bank equity from trough to peak averages only about 30% of the initial decline. This gain partially reverses within approximately twelve months, so that cumulative five-year abnormal returns remain not elevated above the unconditional average. Trading strategies that account for risk and factor returns (market, value, size, momentum, global equity) yield even lower risk-adjusted returns, strengthening the conclusion that bank equity is not cheap at crisis troughs.

Q6. How do write-downs compare to trading losses in explaining the accounting losses of banks during crises?

Realized book losses in the first year of crisis onset account for only about 30% of market-value losses. By year five, cumulative book losses reach approximately 35% of pre-crisis book equity and roughly 100% of market-value losses. Decomposing net income, write-downs (revaluations of assets remaining on the balance sheet — loan loss provisions, impairments, goodwill write-downs) track cumulative book losses closely and fully account for market-value losses by year five. Trading losses (realized gains and losses from securities trading and all asset sales) account for only a small share of total losses on average.

Q7. Under what conditions do fire sales rather than write-downs dominate the accounting losses?

For banks in the top quartile of the ratio of securities to total assets, immediate accounting losses in the first year of crisis onset are substantially larger and driven to a significant extent by trading losses rather than write-downs. The six bank equity crises with the highest securities-to-assets ratios (weighted across banks) all occurred during the 2007-2008 crisis (Belgium, France, Germany, Switzerland, the U.K., and the U.S.), when fire sales of securitized assets were significant. Banks holding mostly loans (bottom quartile of securities-to-assets) show slower-to-materialize book losses driven predominantly by write-downs.

Q8. How do nonperforming loan rates relate to the magnitude of bank equity declines across crises?

At the country level, more negative unlevered bank equity returns at crisis onset are statistically significantly associated with higher peak NPL rates over the subsequent five years. The adjusted R² for the full available sample is 0.233, rising to 0.533 after excluding two outliers (U.S. 1990, Sweden 1991). For the 2008-2010 crisis episodes only, the adjusted R² is 0.606. No analogous association between NPL rates and nonfinancial equity returns is found, suggesting the mechanism is specific to the banking sector’s asset-quality deterioration.

Q9. Do liquidity-based interventions (central bank support or blanket guarantees) restore bank capitalization after bank equity crises?

No. Following the implementation of liquidity-based interventions during bank equity crises, bank equity prices initially continue to decline for about two months, then rise by approximately 20%, but this gain reverses between months 12 and 36. Bank equity values remain persistently low thereafter. This is inconsistent with models in which forceful lender-of-last-resort interventions accomplish the same result as direct recapitalizations. The authors caution that interventions are not randomly assigned — deeper crises may receive stronger interventions — so the analysis cannot identify counterfactual outcomes.

Q10. What are the historical characteristics of government recapitalization programs?

Based on a new database covering all government recapitalization programs across 17 economies since 1870, recapitalizations have historically been small (averaging 24% of pre-crisis book equity and 43% of realized market-value losses), narrow (65% classified as narrow, with a median of five banks recapitalized), and delayed. Total equity issuance (government and private combined) is only a small fraction of realized losses. Government-funded issuance accounts for about one-fourth of total bank equity issuance. The U.S. TARP after 2008 was unusual in being both broad (over 700 banks) and timely (about one month after the Lehman collapse). Japan’s crisis of the 1990s is a prominent example of extreme delay, with the first recapitalization program implemented in March 1999, nearly a decade after the real estate collapse began.

Q11. How do “panic-only crises” differ from bank equity crises in terms of equity dynamics and policy effectiveness?

Panic-only crises (N=85) are banking panics without a 30% bank equity decline. They feature significant initial negative returns followed by elevated bank equity returns that bring valuations back to pre-crisis levels within five years. Dividends fall only temporarily. Liquidity interventions during panic-only crises produce a full rebound in bank equity in the month of intervention, contrasting sharply with the modest and transient response observed in bank equity crises. Panic-only crises are also associated with shallower real GDP declines and smaller bank credit contractions than bank equity crises.

Q12. In what fraction of bank equity crises does the bank equity decline precede the banking panic, and what does this imply about the root cause?

In 57 of the 76 bank equity crises (75%), the bank equity decline strictly precedes the emergence of the banking panic. This timing implies that most bank equity crises are not liquidity shocks that evolved into solvency problems — rather, fundamental weaknesses in the banking system are already present at the early stages of the crisis. Only 19 cases (25%), called “mismanaged banking panics,” saw the panic precede the equity decline; these occurred predominantly in the pre-1945 period, often in countries on the Gold Standard with limited central bank capacity.

Q13. Under what conditions can early liquidity interventions avert an incipient banking crisis?

Of 183 episodes of incipient liquidity shocks in which a prior 30% bank equity decline had not yet occurred, 126 received early liquidity interventions, of which 92 were successfully averted (approximately 50% of the original 183 episodes). The two strongest predictors of a successfully averted crisis — essentially necessary conditions — are: (1) the pre-panic bank equity decline remains below 30%, and (2) liquidity intervention occurs within one month of the panic. War outbreak and single-bank focus of the run are additional factors that substantially increase the probability of aversion. Combining the small-equity-decline and early-intervention conditions predicts averted panics with a true-positive rate of 99% (91/92), though with a 24% false-positive rate.

Q14. Does cross-sectional heterogeneity at the bank level confirm the permanent-loss interpretation?

Yes. Sorting the ten largest banks by country into five bins by market-to-book (M/B) ratio at crisis onset shows monotonic relationships with five-year outcomes. The most distressed banks (M/B below 0.2) experience reduced credit growth of 26 percentage points and reduced income-to-book-equity of 87 percentage points (both cumulative over five years) relative to the healthiest banks (M/B above 0.8). The M/B ratio at crisis onset is persistently low in subsequent years, because market values crash permanently while book values are sticky (slow write-down recognition). These results hold with crisis fixed effects, meaning the patterns reflect within-crisis cross-sectional variation, not merely crisis-level heterogeneity.

Q15. Do crises preceded by credit booms have worse post-crisis outcomes for banks?

Yes. Crises preceded by above-median growth in the credit-to-GDP ratio (from pre-crisis trough to peak) are associated with an additional 60 log-point abnormal decline in bank equity excess total returns occurring around year three after crisis onset, persisting through year five. By contrast, crises not preceded by credit booms earn bank equity returns similar to the country’s unconditional average after the initial decline. This supports the hypothesis that credit-boom-driven crises involve unexpected future deterioration in asset quality, possibly linked to persistently negative housing returns (which do not recover to pre-crisis levels within five years after banking crises).

Key Concepts

Bank equity crisis (paper-specific definition): An episode identified in real time when two criteria are jointly met for the first time: (1) the bank equity index declines by more than 30% in annual excess total returns within any year of the past five years, and (2) a top-20 bank (ranked by total assets within the country) fails. This definition is purely data-driven and does not require any look-ahead information. It produces 76 crises across 46 economies from 1870 to 2019.

Permanent-loss view: The theoretical interpretation that banking crises primarily reflect fundamental, lasting deterioration in the value of bank assets — arising either from fire sales that permanently destroy value or (more commonly in the authors’ evidence) from deterioration in asset quality (rising nonperforming loans, loan impairments). Under this view, bank equity declines are earnings-driven rather than discount-rate-driven and do not reverse even after funding and market liquidity are restored.

Temporary-loss view: The theoretical interpretation that bank losses during crises are primarily due to temporary price dislocations — assets held by financial intermediaries trade at sharp discounts due to binding borrowing constraints or depositor fragility, but recover their fundamental value once central banks provide liquidity support. Under this view, bank equity should earn elevated future returns after crises, and forceful liquidity interventions should be equivalent to direct recapitalizations in restoring bank value.

Write-downs (paper-specific definition): Revaluations of assets that remain on the balance sheet, reflecting expected future reductions in cash flows. They include loan loss provisions, additions to loan loss reserves, write-downs of fixed assets, and goodwill impairments. Distinguished from trading income (realized gains and losses from securities trading and all asset dispositions). Write-downs are subject to accounting discretion and are recognized slowly over multiple years after crisis onset, while equity markets price in expected total losses rapidly at crisis onset.

Trading income (paper-specific definition): Realized gains and losses from securities trading and all asset sales, including sales of real estate, loans, and subsidiary divisions. Unlike write-downs, trading losses must be recognized immediately (they are realized transactions), so large trading losses at crisis onset would be evidence consistent with fire-sale dynamics.

Panic-only crises: Banking panics (sustained bank runs or depositor withdrawals) that do not coincide with a greater-than-30% bank equity decline. Identified as N=85 in the full sample. These episodes are characterized by temporary equity declines, full recovery within five years, large positive responses to liquidity interventions, and smaller macroeconomic output losses — consistent with the temporary-loss view.

Mismanaged banking panics: The minority of bank equity crises (19 cases, 25%) in which the banking panic occurred first or concurrently with the 30% bank equity decline, rather than the equity decline preceding the panic. Concentrated in the pre-1945 period, often in Gold Standard countries with limited central bank flexibility. The U.S. Great Depression is the prominent example.

Averted crisis: An incipient liquidity shock to the banking sector that fully recedes within two months without any bank failures or 30% bank equity declines. Empirically, all averted crises in the sample had not yet experienced a 30% bank equity decline and all received early liquidity interventions (within one month of the incipient panic onset).

Racial Disparities in Housing Returns

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper estimates the racial/ethnic gap in realized housing returns using administrative data on individual housing transactions, and investigates the mechanisms that generate those gaps. The central question is: why do Black and Hispanic homeowners accumulate less housing wealth than White homeowners, even as minority homeownership rates have risen substantially over the last century?

Data and Methodology

The authors merge three primary data sources. First, a nationwide panel of residential property records from ATTOM covering 146.8 million arm’s-length home purchases from 1990 to 2020, which records transaction prices, mortgage characteristics, and property-level identifiers. Second, Home Mortgage Disclosure Act (HMDA) records, which contain self-reported race and ethnicity for mortgage applicants. Third, supplementary administrative sources including McDash mortgage servicing records, Equifax credit bureau data, Fannie Mae/Freddie Mac/ABSNet modification records, and the Survey of Income and Program Participation (SIPP). After applying sample restrictions — including requiring an observed purchase price, a linked HMDA record, an arm’s-length repeat sale, a combined loan-to-value ratio of at most 102.5%, and an ownership spell of at least 12 months — the baseline analysis sample comprises 13.6 million ownership spells for Black, Hispanic, and White homeowners who purchased homes with a mortgage between 1990 and 2016 in 40 states. Ownership spells unsold by March 2020 have their value imputed using the FHFA county-level house price index, a procedure that is conservative in that it understates racial gaps.

The authors construct two complementary return measures. The unlevered return compares the annualized ratio of sale price to purchase price. The levered return (internal rate of return) sets the net present value of all homeowner cash flows — down payment, monthly mortgage payments, implicit rent, maintenance, taxes, insurance, transaction costs, and limited liability in foreclosure — equal to zero.

Main Findings

Among mortgaged home purchases, mean annual unlevered returns are 0.5% for Black homeowners, 0.6% for Hispanic homeowners, and 2.8% for White homeowners, implying Black-White and Hispanic-White gaps of approximately 2.3 percentage points per year. Mean annual levered returns are 1.6%, −3.0%, and 6.6% for Black, Hispanic, and White homeowners respectively, yielding gaps of 5.0 and 9.6 percentage points. After adjusting for the approximately one-fourth of purchases made in cash (for which no racial gap is found), preferred estimates of the unlevered gap are 1.9 (Black-White) and 1.4 (Hispanic-White) percentage points.

Distressed sales — foreclosures and short sales — statistically account for the entire gap in returns. Within non-distressed sales, the Black-White gap in annual unlevered returns falls to less than 40 basis points, and the Hispanic-White gap reverses sign. Two distinct factors drive the role of distressed sales: (1) Black and Hispanic homeowners are approximately twice as likely as White homeowners to experience a distressed sale, and (2) minority homeowners live in neighborhoods where distressed sale price discounts are larger — estimated at 39%–40% for Black and Hispanic homeowners versus 28% for White homeowners. A Blinder-Oaxaca decomposition indicates that equalizing distressed sale rates (holding the distressed sale penalty fixed) would eliminate 84.6% of the Black-White unlevered returns gap and 133.6% of the Hispanic-White gap, confirming that the frequency margin dominates the severity margin.

A counterfactual wealth-accumulation exercise using PSID data shows that equalizing housing returns reduces the Black-White gap in housing wealth at retirement by 37%. Equalizing first-time purchase rates reduces the gap by only 1%, illustrating that promoting homeownership without addressing the returns gap is largely ineffective. Equalizing both returns and purchase rates reduces the gap by 49%.

Mechanisms

Approximately one-third of the gap in unlevered returns can be explained by purchase year and county fixed effects, with much of this timing effect attributable to the Great Recession. Controlling additionally for income, family structure, gender, and leverage reduces the gap by a further ~0.3 percentage points, leaving a substantial residual. About half of the racial gap in mortgage default can be attributed to observable credit risk (family structure, income, leverage, credit score). The remainder is associated with unobservable liquidity shortfalls and income instability: median liquid wealth among Black and Hispanic homeowners is $2,400 and $5,400 respectively, and minority homeowners are 2–4 percentage points more likely to transition to unemployment conditional on pre-unemployment income. Using quasi-experimental variation from adjustable-rate mortgage resets, the paper shows that in response to a 10% increase in monthly payments, White homeowners increase 90-day mortgage default by 3.0 percentage points after 12 months, while Black and Hispanic homeowners show increases of 4.5 and 7.1 percentage points respectively — excess sensitivity that is not captured by credit scores. The early-2000s credit supply expansion through private securitization and portfolio lending channels (as distinct from GSE/FHA) contributed to 61.5% of the 6.2-percentage-point increase in the Black-White distressed-sale gap between the 2002 and 2006 purchase cohorts, and 52.0% of the 12.2-percentage-point increase in the Hispanic-White gap. Evidence from the National Survey of Mortgage Originations suggests that Black homeowners hold overoptimistic expectations about future house price growth and income growth relative to their realized outcomes, which may explain why high-risk minority households do not self-select out of homeownership.

Scope Conditions

Results pertain to mortgaged home purchases (approximately three-fourths of all purchases) by Black, Hispanic, and White homeowners in 40 states (non-disclosure states excluded), with primary coverage from 2000 to 2016. No racial gap in returns is found for cash purchases. The racial gap in non-distressed returns is small and not economically meaningful, so the findings specifically pertain to the realized-return distribution that includes the distressed-sale tail.

In depth

Q1. How large is the racial gap in housing returns, and how does it compare to previously documented racial disparities in housing costs?

A: Among mortgaged purchases, Black and Hispanic homeowners each realize annual unlevered returns approximately 2.3 percentage points lower than White homeowners; levered return gaps are 5.0 percentage points (Black-White) and 9.6 percentage points (Hispanic-White). In dollar terms, this translates to a difference of roughly $5,920 per year for the average Black homeowner and $6,762 per year for the average Hispanic homeowner on a ten-year holding horizon. These gaps are an order of magnitude larger than previously documented racial disparities in housing costs, such as post-origination interest rate disparities of about 40 basis points (~$500 annually for a $200,000 home) or inflated property tax assessments amounting to $300–$390 per year.

Q2. What is the role of distressed sales in explaining racial gaps in returns, and how do frequency versus severity contribute?

A: Distressed sales statistically account for nearly the entire racial gap in realized housing returns. Within non-distressed sales, the Black-White unlevered gap falls to less than 40 basis points and the Hispanic-White gap inverts. Two channels operate: (1) Black and Hispanic homeowners are approximately twice as likely as White homeowners to experience a distressed sale; and (2) within distressed sales, minority homeowners realize lower returns because they tend to live in neighborhoods with larger distressed-sale price discounts (estimated at 39–40% below imputed market value for Black and Hispanic homeowners, vs. 28% for White homeowners). A Blinder-Oaxaca decomposition indicates that equalizing distressed sale frequency (holding severity fixed) would close 84.6% of the Black-White gap and 133.6% of the Hispanic-White gap, so the frequency margin is quantitatively dominant.

Q3. Are racial differences in house price appreciation responsible for the gap in non-distressed returns?

A: No. Among non-distressed sales, realized returns closely track county-level FHFA house price index growth for Black, Hispanic, and White homeowners alike, essentially one-for-one regardless of race. There is no economically meaningful racial gap in house price appreciation conditional on avoiding a distressed sale. This finding implies that the gap in average realized returns is not generated by differential neighborhood-level appreciation but rather by the incidence of distressed sales and the price penalties they entail.

Q4. How much of the racial gap in housing returns can be explained by observable homeowner characteristics such as income, family structure, and leverage?

A: Controlling for county and purchase year fixed effects reduces the raw Black-White and Hispanic-White unlevered returns gaps from 2.3 to 1.5 and 1.6 percentage points, respectively. Additionally controlling for income, family structure (gender and co-applicant status), and leverage reduces the gap by a further ~0.3 percentage points. Even among the ostensibly safest group — high-income couples with low leverage — the Black-White (Hispanic-White) gap in unlevered returns is 0.7 (0.5) percentage points. Among high-leverage, low-income, single-male homeowners the gap is 1.8 (1.7) percentage points. Gaps exist within every demographic subgroup, and neighborhoods (Census tract fixed effects) explain roughly half of the remaining gap for Black homeowners and one-third for Hispanic homeowners, but substantial residual gaps persist even within neighborhood.

Q5. What observable credit risk characteristics explain racial differences in mortgage default?

A: Raw racial gaps in 90-day mortgage delinquency are 2.6 percentage points (Black-White) and 1.8 percentage points (Hispanic-White). Controlling for purchase year and county reduces these to 2.2 and 1.6 percentage points respectively. Controlling for family structure, income, leverage, and credit score reduces the gaps to 0.98 and 0.94 percentage points — implying that observable characteristics explain approximately 55% and 41% of the Black-White and Hispanic-White default gaps respectively. Credit scores contribute the most explanatory power among these controls, while mortgage contract characteristics (a test of differential lender treatment) contribute negligibly.

Q6. What is the evidence that liquidity and income instability — factors not observable to lenders — explain the residual racial gap in default?

A: Survey data from SIPP reveal that median liquid wealth (bank accounts, stocks, bonds) for Black and Hispanic homeowners is only $2,400 and $5,400 respectively, while minority homeowners are 2–4 percentage points more likely to transition to unemployment conditional on pre-unemployment income. In SIPP mortgage delinquency regressions, controlling for liquidity, job loss in the prior year, and income reduces the Black-White coefficient by about 30% and the Hispanic-White coefficient by about 41% (and 29% and 70% respectively when also controlling for income level, current loan-to-value, and family composition). In administrative data using ARM payment resets as liquidity shocks, a 10% increase in monthly payments raises 90-day default by 3.0 percentage points for White homeowners, 4.5 percentage points for Black homeowners, and 7.1 percentage points for Hispanic homeowners after 12 months. This excess sensitivity is not substantially reduced by controlling for credit scores, income, or leverage — indicating that the liquidity risk of minority homeowners is largely unobservable to lenders at origination.

Q7. Is there evidence that strategic default explains higher minority distress rates?

A: No meaningful evidence supports strategic default as a driver of excess minority distress. Using quasi-experimental variation in ex-post leverage from diverging option ARM indices (following Gupta and Hansman 2022), the paper finds large causal impacts of leverage on default but no evidence that these impacts are larger for minority homeowners. Separate survey evidence from the NSMO shows a statistically insignificant Black-White difference of 0.05 percentage points (s.e. 0.65) in agreement that “it is okay to default if it is in the borrower’s financial interest” (relative to a White mean of 6.1%). The absence of larger leverage-driven default responses combined with the presence of larger payment-shock-driven responses points specifically to liquidity — not strategic behavior — as the relevant mechanism.

Q8. What is the evidence for information frictions contributing to excess minority homeownership risk?

A: Black homeowners in the NSMO report future house price expectations that are 0.07 standard deviations more optimistic than White homeowners, conditional on past price experiences, yet realized house price growth in the subsequent two years is actually 1.1 percentage points lower for Black homeowners. Although Black homeowners are 2.8 percentage points more likely to report past personal financial crises, their stated expectations about future financial crises are similar to those of White homeowners — despite 90-day default rates that are 2.5 percentage points higher in the first two years post-origination. Black homeowners also report income growth expectations 0.3 standard deviations higher than White homeowners, while SIPP and CPS data show minorities are more likely to experience income losses. These patterns of overoptimistic expectations relative to realized outcomes are consistent with information frictions causing high-risk minority households to suboptimally select into homeownership.

Q9. How much of the racial gap in distress can be attributed to the early-2000s credit supply expansion?

A: The paper identifies the expansion as concentrated in portfolio loans and privately securitized mortgages, which are distinct from GSE/FHA mortgages that did not exhibit a comparable supply increase. Between the 2002 and 2006 purchase cohorts, the Black-White gap in distressed sales rose by 6.2 percentage points overall but only 2.4 percentage points among GSE/FHA loans. A decomposition using this contrast attributes 61.5% of the overall 6.2-percentage-point increase to the credit supply expansion. Analogously, 52.0% of the 12.2-percentage-point increase in the Hispanic-White gap between 2002 and 2006 is attributed to credit supply. Within-race decompositions find that credit supply accounts for 42%, 30%, and 35% of the increase in distress relative to 2002 for Black, Hispanic, and White homeowners respectively, for mortgages originated 2004–2006.

Q10. What is the implied contribution of the returns gap to the racial wealth gap?

A: Using a simple wealth accumulation model calibrated to PSID data on first-time homebuyer rates and home values (average first home for Black households: $142,587; for White households: $208,621), the paper finds an estimated Black-White gap in housing wealth at retirement of $169,389 versus an observed PSID gap of $182,771. Equalizing housing returns would reduce this gap by 37%. In contrast, equalizing first-time purchase rates alone reduces the gap by only about 1%, because low returns nullify the benefit of purchasing earlier. Equalizing both returns and purchase rates reduces the gap by 49%. Housing wealth in the primary home constitutes 43% of total net wealth for the average retirement-age Black household in PSID, implying the returns gap explains a quantitatively large share of the overall racial wealth gap.

Q11. What do the COVID-19 pandemic forbearance experience and mortgage modification evidence imply for policy?

A: Quasi-experimental estimates using servicer-level variation in modification propensity show that mortgage modifications cause economically large increases in housing returns for Black, Hispanic, and White homeowners alike, suggesting that since minority homeowners are more likely to become distressed, expanded modifications would disproportionately benefit them. The pandemic experience provides macroeconomic confirmation: after the onset of COVID-19 forbearance and foreclosure moratoria in March 2020, the Black-White gap in unlevered returns and distressed sales fell by approximately half, while the Hispanic-White gap (whose pre-pandemic distress convergence was already underway) remained comparatively stable. Administratively, Black homeowners who default are already 3–7 percentage points more likely than observationally similar White homeowners to receive a modification, even controlling for neighborhood and servicer, suggesting servicers partially internalize the larger distressed-sale discounts in minority neighborhoods.

Q12. Are neighborhood-level factors — specifically distressed-sale price discounts from illiquid real estate markets — important for explaining racial heterogeneity in returns conditional on distress?

A: Yes. Using MLS data on median days-on-market as a measure of real estate market thickness, the paper shows that distressed sale discounts are substantially larger in less-liquid markets, with discounts experienced by Black homeowners approximately 13 percentage points lower in the least-thick markets relative to the thickest. Black and Hispanic homeowners are disproportionately likely to realize distressed sales in thin markets. Regular sale returns are not affected by market thickness. This establishes that neighborhood market illiquidity is a second-order channel through which neighborhood-level factors contribute to the racial gap — primarily by amplifying the severity of distressed sale penalties rather than by affecting ordinary house price appreciation.

Key Concepts

Distressed sale: In this paper’s usage, an ownership spell that ends in either a foreclosure (where a lender seizes and sells the property after payment default) or a short sale (where the lender allows the homeowner to sell for less than the outstanding mortgage balance without holding the homeowner liable for the deficiency). Distressed sales are the central mediating factor between race and housing returns.

Unlevered return: The annualized ratio of sale price to purchase price, capturing property-level capital gains without reference to the financing structure. Computed as (P_sale / P_purchase)^(1/T) − 1. Does not capture leverage amplification or limited homeowner liability in foreclosure.

Levered return (internal rate of return): The discount rate that sets the net present value of all homeowner cash flows to zero, including down payment at purchase; monthly payments (principal, interest, taxes, insurance, maintenance); implicit rent; and the net proceeds at sale (property sale price minus outstanding principal balance, subject to a floor of $0.01 capturing limited liability). This measure accounts for both the amplifying effect of leverage on gains and the homeowner’s limited liability in underwater foreclosures.

Distressed sale frequency versus severity: The two distinct components through which distressed sales generate racial gaps. Frequency refers to the higher probability that a minority homeowner’s ownership spell terminates in a distressed sale. Severity refers to the larger price discount at distressed sale that minority homeowners experience, concentrated in neighborhoods with illiquid real estate markets. The paper’s decomposition finds frequency is the dominant margin.

Unobservable liquidity risk: Default risk arising from insufficient liquid wealth (cash, bank deposits, liquid securities) and income instability that is not captured by credit scores or other characteristics observable to lenders at mortgage origination. The paper’s ARM-reset event study shows this risk generates excess minority default responses even conditional on credit score and income.

Information friction (overoptimism): The tendency of minority homeowners, particularly Black homeowners, to hold expectations about future house prices, personal financial crises, and income growth that are more optimistic than their realized outcomes and than observationally similar White homeowners’ expectations. The paper uses this to explain why high-risk minority households do not self-select out of homeownership despite the high cost of distressed sales.

Credit supply channel: The mechanism by which the early-2000s expansion of private securitization and portfolio lending — channels that exhibited substantially greater growth among Black and Hispanic borrowers than among White borrowers — contributed to increased rates of minority distress during the Great Recession. Distinguished from GSE/FHA channels that did not exhibit comparable credit expansion and serve as the counterfactual.

Search Frictions and Product Design in the Municipal Bond Market

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

This paper investigates whether intermediaries in the U.S. municipal bond market strategically exploit product design to increase search frictions and, through that channel, capture rents. Specifically, it asks: do underwriters who negotiate bond design with local governments have an incentive to add nonstandard provisions that raise their own competitive advantage in subsequent secondary-market intermediation, even at the expense of issuing governments and their taxpayers?

Setting and Data

The study focuses on tax-exempt general obligation and revenue bonds issued via negotiated sales by local governments (counties, cities, school districts, and other special-purpose governments) from 2010 to 2013, tracking all secondary-market transactions through 2014. The final sample comprises 13,118 bond issues with a total face value of $266.9 billion. Bond attribute data come from Mergent; transaction data come from the Municipal Securities Rulemaking Board (MSRB). Issuer financial health, demographics, and economic conditions are drawn from the Census and American Community Survey; state revolving-door regulations are compiled from the National Conference of State Legislatures database. Structural estimation uses a subsample of 927 bonds concentrated in the five states that enacted revolving-door regulations during the study period and neighboring border counties.

Identification Strategy

A core empirical challenge is that unobserved factors may jointly determine bond complexity and market outcomes. The authors exploit panel variation in state-level revolving-door regulations — laws that restrict former public officials from taking employment at firms regulated by their former agencies for a “cool-off” period — as an instrument for bond complexity. Between 2010 and 2013, three states (Arkansas 2011, Indiana 2010, Maine 2013) enacted new legislation covering state officials, and two states (New Mexico 2011, Virginia 2011) extended existing regulations to cover local officials. A difference-in-differences regression, with county and year-month fixed effects, shows that adopting revolving-door regulations covering local officials reduces bond complexity by 6% on average (coefficient −0.064, p < 0.01). Regulations targeting only state officials, who are not directly involved in bond negotiations, yield smaller and statistically fragile effects. Placebo checks on auctioned bonds, where underwriters cannot influence design, show no effect, and there is no evidence of pre-existing trends in complexity.

Main Findings

Flexibility vs. liquidity trade-off: A 1% increase in the bond complexity index lowers the number of negative credit-watch events (a proxy for default risk) by 0.002, a 3% decrease relative to the mean of 0.074, confirming that nonstandard provisions provide genuine financial flexibility. However, increasing the complexity index from its mean (1.46) to the 75th percentile (1.69) raises the intermediation spread — the cost for an investor to buy and immediately sell a bond — by 17 basis points (a 14% increase over the average of 120 basis points), confirming that complexity raises trading frictions. For context, the average intermediation spread of 120 basis points is large relative to the 30–60 basis point bid-ask spread of corporate bonds in 2010–2013.
Underwriter incentive to complicate: Increasing complexity from the mean to the 75th percentile raises the underwriter’s market share in secondary-market intermediation by 1.4 percentage points, an 11% increase over the average underwriter share of 12.2%. The underwriter’s gross profits from intermediation also increase with complexity.
Structural estimates — search costs: For a median bond, average dealer search costs amount to 10% of monthly gross profits ($2,625 per month). The underwriter’s exclusive initial sales generate a client network that lowers its effective search costs by 21% relative to an average dealer, more than offsetting its initial geographical disadvantage (for 72% of bonds, the underwriter’s baseline search cost exceeds the median dealer’s). Nonstandard provisions increase both the initial search cost parameter (φ₀) and the network-effect parameter (φ₁): a 1% increase in the complexity index increases φ₀ by 3.79% and φ₁ by 1.66%, implying complex bonds raise search costs broadly but amplify the advantage of a large client network — a position the underwriter occupies via exclusive primary-market sales.
Investor demand: Nonstandard provisions do not substantially change the average investor valuation but substantially increase the dispersion: the standard deviation of investor valuations is 0.003 for simple bonds and 0.013 for complex bonds, consistent with complex bonds being niche products that investors “either love or loathe.”
Government cost: The marginal cost of paying debt obligations is convex in complexity, reaching a minimum at an interior level of provisions; the government’s marginal financial cost increases by 42% when a median bond is stripped of all nonstandard provisions, reflecting the value of payment flexibility.
Conflict of interest: The estimated weight that government officials place on underwriter payoffs in the absence of revolving-door regulations (ψ₀) is 0.34, implying the underwriter’s value accounts for 6.7% of the government official’s payoff under the median unregulated issuer. With revolving-door regulations in place, ψ₁ is essentially zero.

Counterfactual Policies (on representative bond: face value $6.45 million, maturity 7.7 years)

Standardization mandate (ban on all nonstandard provisions): The coupon rate falls from 2.81% to 2.16% (−23%), average dealer search costs fall 47%, and investor surplus rises 13.3%. However, the marginal financial cost (c₀) rises by 41% (from 0.615 to 0.871), so the issuer’s total debt payment cost — principal plus interest, weighted by c₀ — rises by 35%, from $5.13 million to $6.96 million. The standardization policy harms issuers even while saving 7.8% of raw principal-and-interest payments ($8,349K to $7,997K), because the loss of flexibility more than offsets the liquidity gain.
Issuer-driven design (issuer sets complexity to minimize its own debt payment cost, then negotiates the coupon): Complexity falls 19% to 1.14, the interest rate falls to 2.37%, total issuer cost falls 1.5%, investor surplus rises 6%, and the underwriter’s secondary-market payoff falls 19.9%.
Underwriter intermediation ban (underwriter excluded from trading after six months): Complexity falls 5.7% to 1.33, the coupon falls to 2.59%, issuer cost falls 1.5%, but investor surplus falls 1.84% and even other dealers are worse off by 3.97%, because the underwriter’s information on primary-market buyers is lost, offsetting the liquidity gains from lower complexity.

In depth

Q1. What are the five nonstandard bond features tracked as proxies for complexity, and how are they combined into a single index?

Following Harris and Piwowar (2006), the paper focuses on five features that are particularly difficult for investors to price: (i) multiple or serial bonds per issue (as opposed to a single bond), (ii) call provisions allowing early redemption, (iii) sinking fund provisions requiring periodic debt retirement, (iv) nonstandard interest payment frequencies (other than semiannual), and (v) variable or floating interest rates. The complexity index is constructed as the simple average of the latter four provisions across bonds within an issue, plus a dummy for whether the issue contains multiple bonds.

Q2. Why do revolving-door regulations that target local officials reduce complexity more than those targeting state officials?

State officials are not directly involved in bond origination negotiations — they can only indirectly influence local governments through budget allocations. Local officials negotiate directly with underwriters and are thus the proximate counterparties whose incentives the regulations alter. Accordingly, revolving-door regulations covering local officials reduce complexity by 6% (coefficient −0.064, p < 0.01 with full controls), whereas regulations targeting only state officials produce a smaller effect (approximately 2%) that loses statistical significance once issuer financial health controls are added.

Q3. How does the paper validate that revolving-door regulations are a valid instrument for bond complexity?

The paper provides three pieces of evidence. First, the regulations have no effect on the credit ratings of bonds issued prior to their enactment, on the annual amount of bond issuance, or on the maturity length and sale method conditional on issuance — confirming the regulations do not alter governments’ risk management or underlying financing needs. Second, the regulations have no effect on complexity for competitively auctioned bonds, where underwriters cannot influence design — a direct placebo test. Third, a pre-trend analysis (Figure A1) finds no differential trend in complexity in states that subsequently adopted regulations.

Q4. What is the mechanism by which underwriters benefit from adding nonstandard provisions, and why does this advantage not diminish over time?

Underwriters purchase and distribute the entire bond issue at origination, giving them an exclusive network of investors who initially purchased the bonds. In the secondary market, knowing who owns a bond allows the underwriter to locate buyers and sellers with lower search effort. For complex bonds, this advantage is amplified: nonstandard provisions make investor education and persuasion more costly, increasing the value of pre-existing client relationships. The network-effect parameter φ₁ — which governs how rapidly search costs fall as a dealer’s cumulative trades grow — itself rises with complexity (by 1.66% per 1% increase in the complexity index), so the underwriter’s head start in client network accumulation translates into a persistently larger cost advantage precisely for the most complex bonds.

Q5. How large is the underwriter’s search cost advantage in equilibrium, and what drives it?

At the equilibrium meeting rate, the underwriter’s effective search cost of maintaining a given meeting rate is 21% lower than that of an average dealer. This advantage arises despite the underwriter having a higher initial search cost type (φ₀ of $3,609 vs. $3,216 for the average dealer at λ = 1), because for 72% of bonds the underwriter has less local trading experience than the median dealer. The advantage is entirely driven by the underwriter’s network: its exp(−φ₁ log(b)) cost discount factor averages 0.34, 32% lower than the average dealer’s 0.50. The underwriter meets investors 20% more frequently than the average dealer (0.23 vs. 0.19 per month), despite higher absolute search expenditures ($3,045 vs. $2,625 per month).

Q6. How does bond complexity affect investor demand — mean or dispersion of valuations?

Structural estimates show that increasing the complexity index by 1% increases the standard deviation of investor valuations (γ₂) by 4.60% but has no statistically significant effect on the mean valuation (coefficient −0.085, standard error 0.561). This pattern is consistent with complex bonds being niche products — they attract a subset of investors with specific preferences for the embedded features (e.g., certain tax or cash-flow attributes), while being unappealing to most investors. The standard deviation of valuations is 0.003 for a low-complexity bond (25th percentile) and 0.013 for a high-complexity bond (75th percentile).

Q7. What does the structural estimate of ψ₀ imply about the degree of collusion between government officials and underwriters?

The estimated collusion parameter without revolving-door regulations (ψ₀ = 0.34) implies that, for the median unregulated issuing government, the underwriter’s value from secondary-market trading accounts for 6.7% of the government official’s objective function. This is a substantial weight: it means officials act partly as agents for the underwriter rather than purely for taxpayers. With revolving-door regulations (ψ₁ ≈ 0), this collusive weight is essentially eliminated, explaining the empirical reduction in complexity found in Table 2.

Q8. What are the effects of a full standardization mandate on each class of market participant, and why does the issuer lose overall despite paying a lower coupon?

Under standardization, the coupon falls 23% (from 2.81% to 2.16%) and the raw principal-plus-interest payment falls 7.8% (from $8,349K to $7,997K). However, the marginal financial cost c₀ rises 41% (from 0.615 to 0.871), reflecting the loss of payment flexibility previously provided by call provisions and other features; the total issuer cost — c₀A(1 + rT) — rises by 35% (from $5.13 million to $6.96 million). Investors gain 13.3% in surplus because they value liquidity and, on average, do not value nonstandard features. The underwriter loses 36.6% of its secondary-market value while other dealers gain 36.1%, as standardization erodes the underwriter’s network advantage.

Q9. Why does the issuer-driven design scenario outperform standardization in terms of total issuer cost, even though complexity does not fall to zero?

Under issuer-driven design, the government minimizes its total cost of debt payment c₀A(1 + rT), accounting for both the flexibility value of provisions and their effect on the negotiated coupon. The optimal complexity index is 1.14 — positive, but 19% below the current baseline of 1.41 — because some provisions genuinely lower c₀ by allowing flexible debt service. The cost of search frictions (and hence the liquidity premium embedded in the coupon) falls 32% and the negotiated coupon falls to 2.37%, sufficient to reduce total issuer cost by 1.5%. By contrast, full standardization imposes a complexity of zero, which overshoots: c₀ rises more than the coupon savings compensate, increasing total costs by 35%.

Q10. What are the net welfare effects of the underwriter intermediation ban, and why is investor surplus negative despite lower complexity?

The ban reduces complexity by 5.7%, lowering the coupon to 2.59% and reducing issuer costs by 1.5%. However, the underwriter’s client network — built during exclusive initial sales — is a productive resource that improves match quality in the secondary market; banning the underwriter from trading after six months wastes this information. Average dealer search costs rise 1.2% and the meeting rate falls 1.7%, net of the complexity reduction. Investors face bonds with lower coupons and higher effective search frictions, so their surplus falls 1.84%. Non-underwriter dealers also lose 3.97% because lower coupons reduce the rents extractable from intermediation.

Q11. How is the structural model estimated, and what role do revolving-door regulations play in the estimation?

Estimation proceeds in three steps. In Step 1, bond-specific trading market parameters (investor demand, dealer search costs, meeting rates, bargaining parameters) are recovered separately for each bond by minimizing squared differences between observed and simulated trading prices, quantities, and transaction timing. In Step 2, IV regressions using revolving-door regulations and their interactions with county/state attributes as instruments for endogenous complexity map Step 1 parameters to bond attributes, addressing the endogeneity of complexity in determining search costs and investor demand. In Step 3, GMM moment conditions derived from Nash bargaining first-order conditions for the equilibrium complexity and coupon rate identify government preference parameters (θ_c, ψ₀, ψ₁), using the orthogonality condition that unobserved financing cost shocks are mean-zero conditional on observed attributes, regulations, and bond supply from neighboring counties.

Q12. Does the underwriting market show signs of concentration that might amplify the conflict-of-interest problem?

Yes. The mean state-level Herfindahl-Hirschman Index (HHI) for underwriting is 0.12, with the top three firms covering 45% of the market on average. For smaller deals (under $10 million), concentration is markedly higher: mean HHI of 0.24 and top three firms covering 64% of the market. Repeat relationships are common — 41% of bonds issued in 2011–2017 were underwritten by a firm that had underwritten a prior bond for the same issuer within five years — reflecting both informational advantages of local presence and potentially entrenched relationships that may increase government officials’ susceptibility to underwriter influence.

Key Concepts

Complexity index (nonstandard provisions): A bond-level measure computed as the simple average, across bonds within an issue, of four nonstandard features — call provisions, sinking fund provisions, nonstandard interest payment frequency, and variable/floating interest rates — plus a dummy for whether the issue contains multiple bonds. Used as the primary measure of bond complexity in all regressions and the structural model.

Revolving-door regulation: A state-level law restricting former public officials or employees from engaging in lobbying or taking employment at regulated firms for a specified “cool-off” period (typically one to two years) after leaving office. The paper uses the presence and scope of such regulations (whether they cover state officials, local officials, or both) as a source of exogenous variation in government officials’ incentives to align with underwriter interests.

Intermediation spread: The logarithm of the average dealer-to-investor sale price minus the logarithm of the average dealer-from-investor purchase price for a given bond. Used as the empirical measure of trading frictions; the sample average is 120 basis points.

Network effect in search (φ₁): The parameter governing how a dealer’s cumulative prior trades with investors in a given bond reduce its cost of meeting new investors for that bond. A higher φ₁ means a larger client network translates into steeper cost savings. The paper estimates that φ₁ itself increases with bond complexity, so complex bonds amplify the advantage of dealers (especially the underwriter) who accumulate large client networks.

Marginal cost of debt payment (c₀): A bond- and issuer-specific parameter capturing the effective cost to the government of repaying each dollar of principal and interest, net of the flexibility benefits provided by nonstandard provisions. Normalized to one for a bond with zero nonstandard provisions at average issuer characteristics; estimated to be convex in complexity with an interior minimum, implying some nonstandard provisions are beneficial from the government’s perspective.

Collusion weight (ψ): The weight a government official places on the underwriter’s secondary-market value from trading when negotiating bond design. Estimated at ψ₀ = 0.34 in the absence of revolving-door regulations (implying the underwriter’s interest accounts for 6.7% of the official’s objective) and at ψ₁ ≈ 0 when such regulations are present.

Underwriter dual role: The institutional arrangement in which the same investment bank (i) negotiates and purchases the entire bond from the issuing government at origination, and (ii) subsequently acts as a dealer in the bond’s secondary market. This dual role creates an incentive to design complex bonds that strengthen the underwriter’s competitive advantage in secondary intermediation via network effects in search.

Issuer-driven design: A counterfactual policy scenario in which the government sets the complexity level to minimize its total cost of debt payment — accounting for both the flexibility value of provisions and the anticipated effect on the negotiated coupon rate — before bargaining with the underwriter only over the coupon. This policy allows some nonstandard provisions (complexity index 1.14 vs. baseline 1.41) and reduces total issuer cost by 1.5% relative to the baseline.

Stock market participation and macro-financial trends

Mon, 01 Jan 0001 00:00:00 +0000

This paper documents a puzzle for canonical limited-participation models: when U.S. stock market participation rose from 31.6% to 53% between 1989 and 2007—a period also characterized by the Great Moderation—the equity premium and stock return volatility increased rather than fell as those models would predict. The paper resolves this puzzle using an RBC model with concentrated capital ownership in which capitalists have external habit utility with a habit stock that depends on aggregate per capita consumption. As participation rises, the representative capitalist’s consumption converges to aggregate consumption, shrinking the surplus-consumption ratio and raising endogenous average risk-aversion; this risk-aversion channel dominates the conventional risk-sharing channel (which predicts a lower equity premium under higher participation). The model implies that higher participation generates a sizeable rise in both the equity premium and stock return volatility while reducing the risk-free rate and aggregate consumption volatility—jointly explaining the observed U.S. macro-financial patterns. Household-level data from the Consumption Expenditure Survey (1984–2017) and cross-state variation support the model’s mechanism.

Summary based on a working paper version, AI-assisted and human-reviewed. See the linked published article for the authoritative version.

In depth

Q1. What is the puzzle the paper addresses?

Existing limited-participation models predict that higher stock market participation should reduce the equity premium (by improving risk-sharing), yet the U.S. experienced a rising equity premium and higher stock return volatility precisely during the period of sharp participation growth (1989–2007), at the same time as the Great Moderation. The standard channel predicts that as more households access financial markets, the representative capitalist’s risk burden falls and the covariance between capitalists’ consumption and equity returns declines, lowering the equity premium. The data contradict this prediction, motivating the paper’s novel mechanism.

Q2. What is the novel risk-aversion channel?

As stock market participation rises, the representative capitalist’s consumption converges toward aggregate per capita consumption, shrinking the surplus-consumption ratio and thereby raising the endogenous effective risk-aversion of the economy—this risk-aversion channel dominates the conventional risk-sharing channel. The key assumption is that capitalists’ habit stock depends on aggregate per capita consumption. The surplus-consumption ratio (the gap between the capitalist’s consumption and the habit level) determines risk-aversion in the external habit utility framework. As participation rises, the capitalist’s consumption approaches the habit level, increasing risk-aversion and the equity premium, even as aggregate consumption volatility falls.

Q3. What are the model’s predictions for macro-financial variables?

In the model economy, an increase in stock market participation generates a sizeable rise in both the equity premium and the volatility of stock returns, a moderate increase in the price-dividend ratio, and a fall in the average risk-free rate and aggregate consumption volatility—jointly accounting for the U.S. macro-financial experience since the 1980s. The rise in equity premium and stock volatility produced by higher participation substantially counteracts the shrinking effect due to lower aggregate uncertainty from the Great Moderation, providing a unified explanation for the co-movement of these macro-financial trends.

Q4. What is the empirical evidence supporting the mechanism?

Household-level data from the U.S. Consumption Expenditure Survey (1984–2017) show that the model-implied average risk-aversion for the representative stockholder trended upward over time closely tracking the rate of participation, while the stockholder-to-aggregate consumption ratio trended downward; cross-state data document a negative relationship between participation and the stockholder-to-aggregate consumption ratio. Both the time-series and cross-sectional patterns are consistent with the model’s prediction that higher participation compresses the gap between stockholder and aggregate consumption, the key driver of the risk-aversion channel.

Key concepts

participation puzzle : the empirical regularity that only a fraction of the population participates in the stock market; exploited in asset pricing models to explain the equity premium with plausible average risk-aversion; this paper studies the consequences of the upward trend in participation since the 1980s. surplus-consumption ratio : the gap between the capitalist’s consumption and their habit level, normalized by consumption; the key state variable in external habit utility models; determines endogenous risk-aversion so that a shrinking surplus-consumption ratio raises risk-aversion. risk-aversion channel : the novel mechanism introduced in this paper: as stock market participation rises, the capitalist’s consumption converges to aggregate consumption, shrinking the surplus-consumption ratio and raising endogenous risk-aversion and thus the equity premium; dominates the conventional risk-sharing channel in the model. risk-sharing channel : the conventional channel in limited-participation models: higher participation improves risk-sharing, reducing the covariance between stockholder consumption and equity returns and tending to depress the equity premium; present in the model but dominated by the risk-aversion channel.

The Price of Housing in the United States, 1890–2006

Mon, 01 Jan 0001 00:00:00 +0000

Lyons, Shertzer, Gray, and Agorastos construct the first consistent, annual, quality-adjusted market rent and home sales price series for American cities spanning 1890–2006. The paper addresses a fundamental data gap: no annual city-level series existed for market rents at any point in the 20th century, and no annual city-level sales price series existed prior to 1975. Existing national series—the BLS Rent of Primary Residence (RoPR) for rents and the Shiller index for sales—carry well-documented methodological limitations that the authors argue have produced materially misleading stylized facts about long-run U.S. housing markets.

The Historical Housing Prices (HHP) dataset draws on just under 2.7 million newspaper real estate listings from 30 U.S. cities across 1890–2006. Listings must contain a price, a size measure (rooms or bedrooms), property type (house or apartment), and a location indicator. The authors construct hedonic price indices using a rolling-windows methodology—baseline three-year rolling windows with annual step size—that controls for size, type, and standardized within-city location, allowing coefficients to vary over time rather than imposing a fixed vector across the full century. City-level indices are aggregated to national indices using population weights from census data interpolated between census years. Listed prices serve as proxies for transaction prices; the authors validate these against census distributions and against post-1975 FHFA and Case-Shiller series.

The paper’s findings revise several established stylized facts. First, real market rents did not fall over the 20th century as implied by the RoPR series. Instead, real rental price levels were approximately 20% higher in 2006 than in 1890, fluctuating within a relatively narrow band. The RoPR series, by contrast, implies a near-halving of real rents between 1914 and 2006. Second, the paper documents a substantial interwar housing boom-bust absent from the Shiller index: real sales prices rose approximately 47% between 1920 and 1928, then fell 27% by 1935, with the 1928 peak not recovered in real terms until 1968. Third, contrary to the Shiller index’s depiction of minimal housing price growth from 1950 to 1995, the HHP series shows real sales prices rising 21% between 1953 and 1974—a period for which Shiller relies on a truncated sample of government-backed mortgages that excluded higher-valued homes.

On the return to homeownership, the paper finds average nominal housing returns across 1890–2006 of approximately 11% per year, composed of 3.8% capital gain and 7.2% rental return. Gross market rental yields exceeded 8% annually for much of 1900–1945, fell to 7% by 1960, and to 3% by 2006. Capital gains were largely unimportant before the 1940s and became the dominant return component only from 1970 onward; the post-1980 period with sustained capital gains is characterized as historically anomalous. Returns varied substantially across cities, with some cities outperforming the S&P 500 in the prewar era while most underperformed equities from 1981–2006.

The paper also examines implications for the CPI. The HHP series implies nominal rents grew at approximately 3.5% per year from 1914 to 2006, versus 2.6% per year for the RoPR component. A back-of-the-envelope alternative CPI using HHP rental data yields overall price growth of 3.3% per year rather than the official 3.1%, suggesting the measured increase in U.S. living standards since World War I may be modestly overstated. Finally, cross-city analysis shows that land constraints and, increasingly, regulatory constraints explain divergence in price growth across cities, with the role of zoning becoming more pronounced after 1980.

Q: What is the core data source and how are the indices constructed? A: The HHP dataset comprises just under 2.7 million newspaper real estate listings from 30 U.S. cities, 1890–2006, sampled from real estate sections (typically the last Sunday of each month). Valid listings require price, size, property type, and within-city location. Hedonic indices are estimated using rolling three-year windows with annual steps, controlling for size, type, and standardized location, allowing hedonic coefficients to evolve over time rather than imposing a fixed vector. City indices are aggregated to national indices using population-weighted census data interpolated between census years.

Q: Why are the HHP series based on listing prices rather than transaction prices, and how is this limitation addressed? A: Transaction-price records require local archival effort infeasible across 30 cities over 116 years, and rental transaction data are essentially unavailable historically. The authors argue that hedonic mix-adjustment makes listed prices strong predictors of selling prices during normal market conditions, and that a substantial share of houses transact at their exact listing price. Validation against census distributions and against post-1975 FHFA and Case-Shiller series supports the approach; the authors acknowledge listing prices may diverge from transaction prices at cyclical peaks and troughs.

Q: What does the paper find about the long-run trajectory of real market rents, and how does this revise existing understanding? A: The HHP series shows real rental price levels in 2006 were approximately 20% higher than in 1890 or 1914, fluctuating within a relatively narrow band over the century. The BLS RoPR series implies real rents fell by nearly half between 1914 and 2006. The HHP findings align with the most influential proposed corrections to the RoPR by Gordon & van Goethem (2007) for 1915–1939 and broadly with Crone et al. (2010) in terms of overall growth levels for 1940–1995, though the HHP series shows a sharper rental spike after World War II rent controls were lifted that the BLS methodology captures only with deliberate lag.

Q: What does the paper find about the interwar housing cycle, and why does the Shiller index miss it? A: The HHP series documents that real sales prices rose approximately 47% between 1920 and 1928, then fell 27% by 1935, with the 1928 nominal peak not regained until 1946 and the real peak not until 1968. The Shiller index for 1890–1934 is based on a 1934 survey of owner recollections of past transaction prices and assessed values, which the authors argue reflects homeowners’ lack of awareness of the changing value of their homes over prior decades. The HHP finding is consistent with census data, Nicholas & Scherbina’s study of New York City, and Fishback & Kollmann’s analysis of New Deal reports.

Q: What does the paper find about the 1953–1974 period, and what explains the divergence from the Shiller index? A: The HHP series shows housing sales prices increased 21% in real terms between 1953 and 1974, while the Shiller index (based on the Home Purchase Component of the CPI) implies a moderate decline of around 10%. The Shiller index for this period uses a truncated sample of government-backed mortgages subject to FHA loan limits; when the authors truncate their own data using the same statutory FHA limits ($30,000 in 1973, $45,000 in 1974, $60,000 in 1977), approximately 50% of their 1971–1979 listings are excluded and their truncated series matches the Shiller index more closely. This supports the Greenlees (1982) critique of downward bias in the Home Purchase CPI component.

Q: What are the long-run return components to homeownership at the national level? A: Average nominal housing returns across 1890–2006 were approximately 11% per year: 3.8% capital gain and 7.2% rental return. Before World War II (1890–1945), average nominal rental returns ranged from 7.9% to 8.3% per sub-period while capital gains averaged near zero or negative in real terms. Only in 1981–2006 did capital gains (averaging 5.8%) exceed the rental return (averaging 5.3%). The return to housing has thus been dominated by rental income over the long run, with the post-1980 era of sustained capital gains constituting a historical anomaly.

Q: How do rental yields evolve over the sample period? A: Gross market rental yields exceeded 8% annually for much of 1900–1945, with spikes after both World Wars and a dramatic fall from nearly 11% to below 7% during the early 1920s boom, consistent with a bubble dynamic before the Great Depression. Yields fell to approximately 7% by 1960 and to 3% by 2006. City-level heterogeneity was substantial: rental returns exceeded 15% in some cities in the two decades before the Great Depression, and most cities saw returns above 10% nominally during 1930–1945, while even by 1981–2006 cities like Phoenix and St. Louis averaged above 12%.

Q: What does the paper find about housing and the business cycle? A: Real growth rates in GDP and housing prices moved in the same direction in 72 of 116 years for sales prices and 65 of 116 years for rental prices. The paper identifies three major downturns where falling rents led falling prices which led falling GDP: the Great Depression (rents fell from 1924, prices from 1929, GDP from 1930), the early 1990s recession (rents from 1988, prices from 1990, GDP from 1991), and the end-of-sample period (rents from 2002). Only after World War I (1920–21) and World War II (1945–46) did clear economic contractions occur without equivalent housing price downturns.

Q: What does the paper find about cross-city variation in housing returns, and what does this imply for the volatility puzzle? A: Capital gains and rental returns vary substantially across cities and time periods; some cities saw returns exceeding the S&P 500 before World War II (including New York and Chicago), while most underperformed equities from 1981–2006. The authors argue that the apparently low volatility of housing returns at the national level documented by Jordà et al. (2019) is partly an aggregation artifact: local housing markets with very different trajectories are combined into a national index, dampening measured variance. The mild positive correlation between city-level capital gains and rental returns has an R² of 0.24.

Q: What are the implications for CPI measurement? A: The HHP series implies nominal rents grew at approximately 3.5% per year from 1914 to 2006, compared with 2.6% per year for the BLS RoPR component, with higher growth concentrated in the years after both World Wars and in the 1965–1985 period. A back-of-the-envelope alternative CPI substituting HHP rental data yields overall price growth of 3.3% per year rather than the official 3.1%. If rental price growth before 1985 is understated in the BLS data, then there has been less improvement in the U.S. standard of living since World War I than was previously understood.

Q: What does the paper find about the role of supply constraints in explaining cross-city price divergence? A: Natural land constraints are positively linked to price growth throughout the 20th century, with the relationship sharpest during 1930–1945 (before the postwar suburban expansion) and again after 1980. Regulatory constraints—measured at the turn of the millennium—have become an increasingly important driver of cross-city price differences, consistent with zoning functioning as a tax (Gyourko & Krimmel 2021). The paper also finds evidence suggesting land-use regulations are partly driven by expectations of future price growth, consistent with the homeowner-voter hypothesis (Fischel 2015; Trounstine 2018).

Q: How does the paper validate its series against existing sources? A: The HHP rental series aligns closely with the Rees and Jacobs (1961) series for 1890–1914. For sales, the HHP series matches the Case-Shiller-Weiss and FHFA repeat-sales indices at both national and city level after 1990 despite methodological differences. The paper finds approximately 25% more price growth than the CSW series over 1975–2006 (117% versus 90% in the 30 HHP cities), attributing some of the divergence to OFHEO appraisal-based valuations before 1992 and the HHP coverage of the broader owned housing market beyond single-family homes.

Historical Housing Prices (HHP) Project: A dataset of just under 2.7 million newspaper real estate listings from 30 U.S. cities, 1890–2006, used to construct annual, quality-adjusted hedonic price indices for both rented and owned housing segments at the city and national level.
Rolling-windows hedonic methodology: An index construction approach that runs sequential hedonic regressions over two-, three-, or five-year overlapping windows with annual step size, allowing the coefficients on size, type, and location to evolve over time rather than imposing a fixed vector across the full sample period, reducing bias from unobserved quality changes.
Market rent vs. contract rent: Market rent (the listing price for a rental unit actively advertised) is conceptually distinct from contract rent (the rent paid by tenants currently in situ), which is what the BLS RoPR series measures. Market rents adjust to vacancy and lease resets faster than contract rents, producing substantially more short-run volatility and a materially different long-run trend.
Gross rental yield (rent-to-price ratio): Annual rental income from a property divided by its market sales price, computed as RI_{c,t} / HPI_{c,t}. Gross yields exceeded 8% annually for much of 1900–1945 and fell to 3% by 2006 nationally, making rental income the dominant component of total housing returns for most of the century.
Total return to housing: The sum of the capital gain (percentage change in sales price) and the rental return (rental income divided by sales price), computed at annual, city, and national frequency for 1890–2006. The average nominal total return was approximately 11% per year, with 3.8% from capital gains and 7.2% from rental income.
Rent of Primary Residence (RoPR): The BLS survey-based series measuring changes in contract rents for a rotating panel of rental units, used as the shelter component of the CPI. The HHP series implies this series understates rental price growth by approximately 0.9 percentage points per year (3.5% vs. 2.6% nominal growth), concentrated in post-World War periods and 1965–1985, due to tenant non-response bias and delayed incorporation of new construction.
Supply constraints and cross-city divergence: Natural land constraints (geographic barriers to development) and regulatory constraints (zoning and land-use regulation) that limit housing supply, both positively associated with price growth, with regulatory constraints becoming increasingly important after 1980 and consistent with the hypothesis that land-use regulations are partly driven by homeowner expectations of future price appreciation.

Unconventional monetary policy spillovers and the (in)convenience of Treasuries

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 — Overview

Research Question

The paper asks why unconventional monetary policy (UMP) spillovers from the European Central Bank (ECB) to the U.S. Treasury yield curve vary so substantially over time, and whether the time-varying “convenience” of Treasuries — their non-pecuniary premium as the world’s preeminent safe asset — can explain that variation. The core claim is that a declining convenience yield on Treasuries makes them more substitutable with other safe sovereign bonds, thereby amplifying the portfolio-balance channel through which foreign large-scale asset purchases (LSAPs) depress U.S. term premia.

Data and Methodology

The authors use high-frequency identification of ECB monetary policy surprises following Altavilla et al. (2019), defined as the first principal component of intraday changes in 1-, 3-, 6-, 12-, and 24-month euro OIS rates plus 5- and 10-year German and French bond yields, measured in the 10-20 minute window bracketing each ECB decision press conference. Surprises are normalized so that one unit raises the 24-month euro OIS by 10 basis points. The sample runs from March 2001 to December 2023, covering approximately 265-268 ECB announcement dates. U.S. zero-coupon Treasury yields come from Gürkaynak et al. (2007); the yield is decomposed into an expected short-rate path and a term premium using the shadow-rate term structure model (SRTSM) of Wu and Xia (2016). The convenience yield on Treasuries is proxied by the spread between the 10-year Treasury yield and the maturity-matched overnight index swap (OIS) rate, so that a positive (and rising) spread indicates declining convenience. Structural breaks in the convenience yield are identified via the Bai-Perron test.

The empirical strategy has three main components: (i) 700-business-day rolling regressions of Treasury yields and their decomposition on ECB surprises to document time variation; (ii) interaction regressions (following equation 5/9) that condition the ECB shock effect on lagged convenience-yield proxies, net Treasury supply, intermediary balance-sheet constraints (proxied by G10 covered-interest-parity deviations), and inflation-anchoring indicators; and (iii) a policy decomposition following Swanson (2021) that decomposes ECB surprises into “target,” “forward guidance,” and “LSAP” components. These empirical findings are rationalized in a two-country preferred-habitat model, extending Gourinchas, Ray, and Vayanos (in press) (GRV) by allowing the demand-slope parameter governing investor price elasticity to vary with the convenience yield. Functional derivatives and Malliavin calculus are used to characterize dynamic impulse responses to elasticity shifts.

Main Findings with Quantitative Magnitudes

Rising spillovers post-GFC, concentrated at long maturities. Rolling regressions show that ECB-to-U.S. spillovers were statistically indistinguishable from zero during the conventional-policy era but grew significantly after 2010, well before the ECB’s Expanded Asset Purchase Programme (EAPP) launched in 2015 and before “whatever it takes” (summer 2012). Spillovers began to dissipate not when ECB purchases ended (March 2022) but when the Fed announced tapering in November 2021 — consistent with the convenience channel rather than mere co-movement in LSAP volumes. A Bai-Perron test detects five structural breaks in the relationship between ECB surprises and 10-year Treasury yields.
Term-premium dominance, amplified by inconvenient Treasuries. At average convenience-yield levels, a one-standard-deviation ECB loosening shock (lowering the 24-month euro OIS by 10 basis points) reduces the 10-year Treasury yield by approximately 4.4 basis points (column 5, Table 2). When the Treasury convenience yield is one standard deviation below its historical average (i.e., Treasuries are less convenient), the spillover increases by 1.64 basis points, making the total effect approximately 6.1 basis points — a shift from the bottom 20th to below the 12th percentile of the unconditional distribution of daily Treasury yield changes. This amplification operates entirely through the term premium; the expected path of short rates shows no statistically significant sensitivity to the convenience yield interacted with ECB shocks.
Net Treasury supply amplification. Conditional on the net publicly available U.S. debt stock (Treasury debt less Fed holdings, as a percent of GDP), a one-standard-deviation ECB shock at average supply reduces the 10-year yield by approximately 3.9 basis points; when net supply is one standard deviation above its historical average (approximately 7.6 percentage points of GDP), the same shock generates a 5.35 basis-point decline — a 50-percent amplification (Table 5, column 5).
Intermediary constraints amplification. Conditioning on the first principal component of G10 CIP deviations against the dollar (a proxy for intermediary balance-sheet tightness), a CIP deviation one standard deviation above average amplifies the ECB spillover from approximately 3.9 basis points to 6.2 basis points (Table 7).
Inflation anchoring. Periods when inflation expectations lie outside the interquartile range of the historical distribution are associated with larger spillovers to 10-year Treasury yields, an effect that is statistically significant both above the 75th and below the 25th percentile of expectations, with point estimates of the interaction coefficient reaching approximately 5.0-5.3 basis points (Table 6).
Policy asynchronicity. Spillovers are especially pronounced when the Federal Reserve is tightening while the ECB is easing. The rolling regressions show term-premium spillovers become dominant (relative to expected-path spillovers) post-2014, coinciding with U.S. normalization. The calibrated model shows that, during policy asynchronicity combined with lower convenience, the home short-rate tightening is partially offset by capital inflows induced by foreign QE, with the attenuation especially pronounced at intermediate and long maturities and persistent across multiple periods.
Alternative channels ruled out. Horse-race regressions against the VIX, MOVE index, Economic Policy Uncertainty (EPU) index, Monetary Policy Uncertainty (MPU) index, and 30-day EUR/USD spot variance show none of these candidates displaces the convenience channel. Short-rate-risk decompositions (Bundick et al. 2017) and equity-orthogonal risk premium shocks (Leombroni et al. 2021) cannot explain the post-Taper Tantrum timing pattern of rising term-premium spillovers.

Scope Conditions

All empirical results apply to ECB-to-U.S. spillovers; the paper explicitly leaves Bank of England-to-U.K. Gilt spillovers for future work.
The portfolio-balance amplification through convenience is specific to unconventional monetary policy (LSAP shocks); target and forward-guidance components drive spillovers through different channels (expected short-rate path) and do not exhibit the same convenience-contingent amplification.
The mechanism operates through preferred-habitat investors demanding sovereign-grade credit; the Bund convenience yield does not amplify U.S. spillovers, consistent with Bunds being an imperfect representation of the full portfolio requiring substitution under ECB capital-key-based purchases.

In depth

Q1. How do the authors measure ECB monetary policy surprises, and why do they prefer this measure?

A1: Surprises are the first principal component of intraday changes in 1-, 3-, 6-, 12-, and 24-month euro OIS rates plus 5- and 10-year German and French bond yields, measured from 10-20 minutes pre-announcement to 10-20 minutes post-press conference. This cross-section of yields is preferred because it summarizes shocks to the overall stance of policy both at and away from the effective lower bound, including effects on different parts of the yield curve. The composite measure therefore subsumes both conventional rate actions and unconventional (LSAP, forward guidance) dimensions. Surprises are normalized so one unit raises the 24-month euro OIS by 10 basis points.

Q2. What is the key empirical fact about the timing of spillover emergence and dissipation?

A2: Rolling regressions show ECB spillovers to U.S. Treasury yields became statistically significant when the rolling window began integrating observations starting in approximately 2010 — substantially before the ECB’s EAPP (2015) and even before “whatever it takes” (summer 2012). Moreover, spillovers began to dissipate not when the ECB’s Pandemic Emergency Purchase Programme ended (March 2022) but when the Fed announced tapering in November 2021. This timing pattern is inconsistent with a simple “both central banks doing QE simultaneously” explanation and instead points to the importance of Federal Reserve balance sheet behavior for the convenience of Treasuries.

Q3. How do the authors decompose the Treasury yield, and what does the decomposition reveal about the channel of transmission?

A3: Following standard term-structure decomposition, the n-year yield equals the expected path of short-term rates over the maturity plus a maturity-specific term premium. Rolling regressions on this decomposition show that term-premium spillovers dominate expected-path spillovers, especially post-2014 when the Federal Reserve is out of sync with other advanced economies. Early ECB UMP spillovers showed a more even mix of expected-path and term-premium effects; later spillovers loaded much more heavily on the term premium. This is consistent with the portfolio balance channel — LSAPs remove duration risk and compress term premia, and this effect transmits internationally.

Q4. How is the convenience yield proxied, and why does the paper use this proxy in particular?

A4: The authors use the spread between the sovereign bond yield and the maturity-matched overnight index swap rate (Y − OIS), expressed so that a larger spread (sovereign yield higher than OIS) reflects less convenience. Prior to the GFC, Treasury yields ran below swap rates (negative spread, high convenience); post-GFC, the spread reversed and turned positive, reflecting deterioration in Treasury specialness. This proxy is preferred because it captures the relative convenience as priced by the marginal investors the model focuses on — those with sovereign credit quality preferences and arbitrageurs — rather than broader measures such as the Treasury-to-corporate spread.

Q5. What is the quantitative impact of convenience yield variation on the size of ECB spillovers to U.S. yields?

A5: In the most conservative specification (Table 2, column 5), an ECB loosening shock that lowers 24-month euro OIS by 10 basis points reduces the 10-year Treasury yield by 4.4 basis points when the convenience yield is at its historical average. When the convenience yield falls one standard deviation below average (Treasuries are less convenient), the spillover increases by 1.64 basis points to approximately 6.1 basis points. A one-standard-deviation change in 10-year Treasury yields in the sample is 5.86 basis points; the 4.4 bp response falls in the bottom 20th percentile of unconditional daily yield changes, while the 6.1 bp response falls below the 12th percentile.

Q6. Does the amplification of spillovers from ECB shocks by Treasury inconvenience operate through the term premium or the expected short-rate path?

A6: The amplification operates entirely through the term premium. In Table 2, columns 7 and 8, the interaction coefficient between the ECB shock and the convenience yield proxy is positive and statistically significant for the 10-year term premium but is not statistically different from zero for the expected path of short rates. The authors interpret this as confirming the portfolio balance channel: displaced Bund investors substitute into Treasuries, raising Treasury prices and compressing term premia, with no mechanical connection to market participants’ updating of expected future Federal Reserve policy rates.

Q7. How does net Treasury supply interact with the size of ECB spillovers?

A7: Net U.S. Treasury supply (debt outstanding as a percent of GDP, less Fed holdings) is strongly positively correlated with the swap spread, confirming the link between supply and convenience. Interaction regressions (Table 5) show that a one-standard-deviation ECB shock at average net supply reduces 10-year yields by 3.9 basis points. When net supply is one standard deviation above average (approximately 7.6 percentage points of GDP), the same shock generates a 5.35 basis-point decline — roughly a 50 percent amplification. The point estimates suggest this operates primarily through term premia, though those interaction coefficients are statistically insignificant in the term premium specification.

Q8. How do intermediary balance-sheet constraints relate to Treasury convenience and ECB spillover amplification?

A8: The authors follow Du, Hébert, and Huber (2023) in using deviations from covered interest parity (CIP) among G10 currencies against the dollar as a proxy for the shadow cost of intermediary balance-sheet constraints. When CIP deviations are at historical average, the ECB spillover to 10-year Treasury yields is approximately 3.9 basis points; when CIP deviations are one standard deviation above average, the spillover rises to approximately 6.2 basis points. The authors also use the plausibly exogenous variation from quarter-end “window dressing” (per Correa, Du, and Liao 2020): LSAP-type ECB surprises landing near quarter-end generate larger spillovers to the term premium, and the further into the quarter an announcement occurs, the larger the LSAP shock’s effect on the term premium — consistent with balance-sheet constraints amplifying the portfolio balance channel.

Q9. What is the theoretical model, and what is the key innovation relative to the baseline GRV framework?

A9: The paper extends the two-country preferred-habitat model of Gourinchas, Ray, and Vayanos (in press), in which segmented investors demand bonds of specific maturities and currencies while capital-constrained global arbitrageurs partially bridge the segmentation. The key innovation is allowing the demand-slope parameter α_j(τ) — which in GRV is fixed and governs how inelastic investors are with respect to price — to vary over time as a function of the convenience yield. When Treasuries are special (high convenience), α_H(τ) is large, demand is inelastic, and foreign shocks have limited pass-through. When convenience falls, α_H(τ) shrinks, demand becomes more elastic, investors reallocate more aggressively in response to yield differentials, and U.S. term premia respond more strongly to ECB purchases. Functional derivatives and Malliavin calculus are used to characterize both instantaneous and dynamic amplification effects.

Q10. What does the calibrated model predict about the maturity structure of spillover amplification?

A10: In the calibration exercise (Figure 4), the elasticity perturbation is modeled as a smooth function (transformed Cauchy distribution) centered at the 10-year maturity, and the ECB QE shock is a purchase concentrated at the 5-year maturity amounting to 10 percent of euro-area GDP. The marginal change in the home yield impulse response (the quantity ∂²_{α_H,b} log P^τ_{Hs}) is positive across nearly all maturities and horizons, but is most pronounced around the 5-year maturity and during the first few periods after the shock — where the ECB purchase profile and the demand perturbation are most closely aligned in tenor. Amplification effects are persistent across horizons due to the dynamic multiplier in Theorem 3.1.

Q11. How does the model rationalize the 2019 yield curve inversion?

A11: In August 2019, the 10-year Treasury yield fell below short-term rates despite a robust domestic labor market, while the Fed was raising rates and the ECB remained accommodative. The model’s asynchronicity exercise (Section 3.3) shows that combining a home short-rate increase with ongoing foreign QE and a contemporaneous decline in Treasury convenience produces attenuated or even reversed yield curve responses. More elastic investors facing a flatter demand curve shift into longer-term Treasuries — whose relative yields remain attractive globally — resulting in a yield-curve inversion driven not by recession expectations but by asymmetric monetary policy and a time-varying convenience premium.

Q12. Do alternative explanations — risk sentiment, policy uncertainty, exchange rate volatility — explain the time variation in ECB spillovers?

A12: No. Horse-race regressions in Table 9 condition the ECB shock on lagged VIX, MOVE index, Economic Policy Uncertainty (Baker et al. 2016), Monetary Policy Uncertainty (Husted et al. 2020), and 30-day EUR/USD spot variance. None of these measures displaces the baseline convenience-yield interaction, which remains statistically significant across all specifications. Elevated EPU is associated with smaller spillovers (consistent with uncertainty impairing substitution), but this does not reduce the magnitude or significance of the convenience-yield interaction. Exchange-rate variance does not alter spillover size. A rolling regression decomposing the term premium into a short-rate-uncertainty component (Bundick et al. 2017) and a residual shows the empirical pattern is more consistent with the residual — not the short-rate-volatility channel. An equity-orthogonal risk premium shock (Leombroni et al. 2021) explains some term premium effects in the early GFC period (2008-2012) but cannot rationalize the post-Taper Tantrum pattern of growing term-premium spillovers.

Q13. How does the Swanson (2021) decomposition confirm the portfolio balance channel?

A13: Following Swanson (2021), the authors decompose ECB surprises into a “target surprise” (change in 3-month OIS futures), a “forward guidance surprise” (residual from projecting 24-month futures onto the target surprise), and an “LSAP surprise” (residual from projecting French and German 10-year bond yields onto target and forward guidance). In the full sample (Table 3), LSAP shocks drive spillovers to U.S. yields exclusively at higher maturities and exclusively through the term premium; they have no statistically significant impact on the expected path of short rates. Conditioning LSAP shocks on the convenience yield (Table 4, panel c) shows that it is specifically LSAP-type announcements combined with Treasury inconvenience that generate larger medium- and long-term term-premium spillovers, confirming the portfolio balance mechanism.

Q14. What are the implications for fiscal and monetary policy?

A14: The paper argues that the persistently low long-term rates and yield curve inversions observed between the GFC and the COVID-19 pandemic were driven partly by ECB LSAPs amplified by U.S. quantitative tightening, which increased net Treasury supply, reduced Fed absorption, constrained dealer balance sheets, and lowered Treasury convenience. Simultaneously, U.S. monetary tightening raised short-term rates while ongoing ECB easing depressed long rates, reshaping the yield curve in a manner consistent with the model. More broadly, the effectiveness of conventional domestic monetary policy tightening is attenuated when the convenience yield is compressed and foreign QE is ongoing — not because the short rate fails to move, but because more elastic investors reallocate around it. This suggests policy asynchronicity, combined with declining convenience, creates a constraint on monetary independence that may require more forceful or coordinated policy action.

Key Concepts

Convenience yield (Treasury convenience premium) The non-pecuniary value that investors derive from holding U.S. Treasury securities over and above cash flows and credit risk — arising from their deep and liquid markets, broad regulatory compatibility, high-quality collateral function, and reserve-currency status. Operationalized in this paper as the spread between the n-year Treasury yield and the maturity-matched overnight index swap (OIS) rate; a positive and rising spread indicates declining convenience, not increasing yield risk.

Portfolio balance channel (of unconventional monetary policy transmission) The mechanism by which large-scale asset purchases by one central bank displace investors from their target allocations, inducing them to substitute into other assets — including foreign sovereign bonds — thereby compressing yields and term premia in those markets. Distinguished from the signaling/expected-path channel in that it operates through changes in duration risk (term premia) rather than revisions to expected future short rates, and is unique to UMP because it targets long-duration assets.

Preferred habitat investors Investors with persistent, institutionally determined demand for bonds of specific maturities and issuers (e.g., insurance companies, pension funds), arising from regulatory constraints, risk management practices, or balance sheet matching. Their demand is modeled as relatively price-inelastic when assets command a convenience premium, and more elastic when that premium erodes.

Demand-slope parameter α_j(τ) In the extended GRV preferred-habitat model, the parameter governing the price elasticity of preferred-habitat investor demand for country-j bonds of maturity τ. Large values imply inelastic demand (strong habitat preferences), small values imply elastic demand and greater cross-border substitutability. The paper’s key innovation is treating this parameter as time-varying — specifically, as a function of the observed Treasury convenience yield rather than a fixed structural constant.

Policy asynchronicity The condition in which the Federal Reserve is tightening monetary policy (raising rates or conducting quantitative tightening) while other advanced-economy central banks (specifically the ECB) are simultaneously easing through LSAPs. The paper argues that asynchronicity interacts with a declining convenience yield to amplify ECB spillovers to U.S. term premia and attenuate the effectiveness of Federal Reserve tightening at the long end of the yield curve.

Swap spread (as inconvenience proxy) The spread of the sovereign bond yield over the maturity-matched OIS rate (Y − OIS). Expressed so that a larger positive value indicates greater Treasury inconvenience. Prior to the GFC, 10-year Treasury yields ran below swap rates (negative spread); post-GFC, this relationship reversed, with the spread turning persistently positive and exhibiting structural breaks consistent with Bai-Perron tests.

Exorbitant privilege The benefit the United States accrues from the global dominance of its sovereign debt and currency, which structurally insulates U.S. financial markets from foreign monetary policy shocks through inelastic global demand for Treasuries. The paper argues this insulation is not structural but endogenous and state-dependent: erosion of exorbitant privilege — operationalized as a declining convenience yield — substantially increases U.S. vulnerability to foreign monetary shocks.

Gâteaux/Malliavin functional derivative (as used in the model) Mathematical tools used to characterize how the impulse response function of the yield curve to policy shocks changes when the demand-slope parameter α_k(τ) is perturbed. The mixed Gâteaux differential ∂²_{α_k,b} log P^(τ)_{js} captures both the instantaneous amplification (direct pass-through increase) and the intertemporal propagation (dynamic multiplier) of a foreign policy shock under lower convenience, enabling a tractable decomposition of state-contingent spillover magnitudes across maturities and horizons.

Why Is Intermediating Houses So Difficult? Evidence from iBuyers

Mon, 01 Jan 0001 00:00:00 +0000

This paper examines frictions in dealer intermediation in durable consumer goods markets, using iBuyers — technology-driven real estate companies such as Opendoor and Offerpad — as a lens. The central research question is why dealer intermediation, which provides immediate liquidity by purchasing assets onto a balance sheet and reselling, is so limited in the U.S. housing market (valued at $50 trillion and representing roughly 70% of the median household’s net worth) relative to other durable goods markets such as automobiles.

The authors use CoreLogic deed transaction data and MLS listing data from five markets with substantial iBuyer presence (Phoenix, Las Vegas, Dallas, Orlando, and Gwinnett County, Georgia) over 2013–2018, covering arm’s-length, non-foreclosure single-family home and condominium transactions. They supplement this with Redfin ZIP-level data on listing speed and American Community Survey demographics. iBuyers are identified as Opendoor, Offerpad, Knock, Zillow, and Redfin.

The empirical analysis documents that iBuyers grew from roughly 1% market share in Phoenix in 2015 to about 6% by 2018, acting as balance-sheet intermediaries who hold properties for a median of 105 days. iBuyers purchase homes at a 3.1 percentage point (pp) discount relative to comparable homes sold in the same ZIP-quarter, and sell at a 2.2 pp premium relative to other institutional sellers, for a combined gross spread of approximately 5.3 pp (reported in the abstract and body as ~5%). Sellers to iBuyers show a 6.8 pp higher rate of market exit post-sale and a 4.0 pp higher probability of purchasing before selling, consistent with demand for immediacy from impatient, relocating households.

Two key frictions constrain intermediation. First, adverse selection: iBuyers rely on algorithmic valuation models (AVMs) that explain over 80% of price variation in iBuyer transactions versus only 68% in non-iBuyer transactions, leaving a residual of soft information (odor, neighbor quality) that sellers know but algorithms cannot capture. iBuyer presence is over three times greater in the lowest pricing-uncertainty tercile versus the highest, and a one standard deviation increase in pricing uncertainty reduces iBuyer presence by 1.23 pp within a ZIP and reduces gross spread per transaction by 1.5 pp. Second, underlying illiquidity: iBuyers are almost entirely absent in market segments where the probability of sale within three months (PSALE) falls below 50%, despite strong seller demand.

To quantify these frictions, the authors build and calibrate a continuous-time directed search equilibrium model with a dealer intermediary subject to adverse selection. Six parameters are calibrated to match empirical moments: iBuyer market share (5%), purchase discount (3.1 pp), sale premium (2.2 pp), iBuyer concentration in the most versus least liquid PSALE quartiles, impatient seller fraction, and median iBuyer holding time. The calibrated adverse selection parameter (α = 0.35) means the intermediary correctly identifies 35% of low-quality homes as such; the impatient seller share (μ = 0.18) means 18% of unmatched sellers are highly impatient; and the vacancy depreciation rate (d = 0.02) means 2% per period for unoccupied homes. External validation via a difference-in-differences comparison of Phoenix against other markets yields model-consistent predictions of a 0.5 pp reduction in time on market and a 0.8 pp increase in house prices.

Counterfactual experiments reveal that introducing a 30-day acquisition delay (rather than near-instantaneous) reduces iBuyer market share from 5% to below 2%; eliminating the signal entirely (α = 0) drops market share to just above 1%; and enabling iBuyers to rent vacant properties during the holding period could raise market share above 7.5 pp. A 50% reduction in PSALE reduces iBuyer market share roughly proportionally.

The calibrated model is then applied to other durable goods markets by varying informational asymmetry, liquidity, and depreciation parameters. Cars — more homogeneous (year/make/model/mileage fully characterizes value), mobile (transportable across markets), and depreciating primarily through use — are predicted to support dealer intermediary market shares of 40–55%, consistent with observed U.S. car dealer market share of ~50%. Reducing the depreciation rate from the housing level (d = 0.02) to a car-like level (d = 0.005) alone increases intermediary market share by about 5 pp. Houses — heterogeneous, immobile, and depreciating through time rather than use — are predicted to support near-zero intermediation under pre-iBuyer technology. The authors also explain COVID-19 iBuyer suspensions (reduced market liquidity made resale untenable) and Zillow’s November 2021 exit (very liquid markets eroded the iBuyer speed premium, worsening adverse selection while rapid price appreciation degraded AVM accuracy).

Q: What discount do iBuyers pay when purchasing homes, and what premium do they earn when selling? A: iBuyers purchase homes at a 3.1 pp discount relative to comparable homes sold in the same ZIP code and quarter, with a t-statistic of 8.55. They sell at a 2.2 pp premium relative to other institutional sellers. The combined gross spread is approximately 5.3 pp (referred to throughout the paper as roughly 5%).

Q: How large is the iBuyer market share, and in which markets did they operate? A: iBuyer market share grew from approximately 1% in Phoenix in 2015 to roughly 6% by 2018. In Gwinnett County, Las Vegas, and Dallas/Orlando, shares reached approximately 4%, 4%, and 2% respectively by 2018. The analysis covers five markets: Phoenix, Las Vegas, Dallas, Orlando, and Gwinnett County (suburban Atlanta).

Q: What is the evidence that iBuyer sellers are impatient rather than simply lower-quality-house owners? A: Sellers to iBuyers exhibit a 6.8 pp higher rate of market exit (defined as purchasing a home outside the county or making no subsequent real estate purchase within 12 months), consistent with relocation-driven impatience. They also have a 4.0 pp higher probability of purchasing a new home before completing the sale of their current home, which is enabled by the iBuyer transaction’s speed facilitating mortgage approval conditional on the existing property’s sale.

Q: How do the authors measure adverse selection risk and what is its relationship to iBuyer presence? A: Adverse selection is proxied by the squared residual from a hedonic pricing regression — the variation in transaction prices unexplained by observable characteristics — computed at the ZIP-year level for non-iBuyer transactions. iBuyer presence is over three times greater in the lowest pricing-uncertainty tercile than in the highest. A one standard deviation increase in pricing uncertainty reduces iBuyer presence by 1.23 pp within a ZIP (controlling for ZIP fixed effects, local prices, house age, and square footage), and reduces gross spread per transaction by 1.5 pp.

Q: What role does underlying asset liquidity play in constraining iBuyer intermediation? A: iBuyers concentrate almost entirely in market segments where the ex ante probability of selling within three months (PSALE) exceeds 50%, and are essentially absent where PSALE falls below 50%. This holds even though sellers in low-PSALE segments have strong demand for immediacy, implying that illiquidity raises intermediation costs above the demand-side willingness to pay a discount.

Q: What does the model’s calibration reveal about the share of impatient sellers and the accuracy of iBuyer signals? A: The calibrated adverse selection parameter α = 0.35 means the intermediary correctly identifies 35% of low-quality homes as low quality (the signal is moderately but imperfectly informative). The calibrated impatient seller share μ = 0.18 means approximately 18% of unmatched sellers are highly impatient and willing to accept a significant price discount for immediacy. The vacancy depreciation rate d = 0.02 implies a 2% per period cost for unoccupied properties.

Q: How important is transaction speed to the iBuyer model? A: Introducing a 30-day acquisition delay (rather than near-instantaneous purchase) reduces iBuyer market share from 5% to below 2% — a reduction of more than 60%. The model mechanism is that the primary iBuyer customers are highly impatient sellers who place extreme value on immediate transactions; even a moderate delay substantially reduces their willingness to accept a price discount.

Q: What happens if iBuyers lose their ability to distinguish between high- and low-quality homes? A: Setting the signal accuracy to zero (α = 0, the “naive intermediary” case) causes iBuyer market share to fall from 5% to just above 1%. Without any quality signal, severe adverse selection forces the intermediary to offer substantially lower prices to break even, which in turn reduces the number of sellers willing to transact.

Q: How much would enabling iBuyers to rent vacant properties during the holding period affect market share? A: The rental-enabled iBuyer counterfactual shows that market share could increase above 7.5 pp from the baseline 5%, because rental income would allow iBuyers to offer higher purchase prices while offsetting carrying costs. This suggests that rental infrastructure or policy changes permitting temporary rentals would substantially expand the scope of dealer intermediation in housing.

Q: How does the model validate itself externally? A: The authors use a difference-in-differences design comparing Phoenix (earlier and larger iBuyer entry) to the other four markets. The model predicts iBuyer entry should reduce average time on market and increase house prices; the DiD results show a 0.5 pp reduction in time on market and a 0.8 pp increase in house prices in Phoenix relative to comparison markets post-entry, consistent with model predictions.

Q: Why did iBuyers suspend operations during the COVID-19 pandemic despite having a contactless technological advantage? A: The model explains the suspension through the liquidity channel: iBuyers’ value proposition depends on quickly reselling acquired properties, not merely on contactless buying. When market liquidity collapsed during lockdowns (transaction volumes fell sharply), iBuyers could not resell properties quickly, making intermediation unprofitable regardless of their purchasing-side technological advantage. As liquidity recovered, iBuyers resumed operations.

Q: What does the model say about Zillow’s exit from iBuying in November 2021? A: In very liquid markets, the iBuyer speed advantage shrinks because homeowners can sell quickly in the traditional market anyway, reducing the discount sellers accept when selling to an iBuyer. With a smaller discount, adverse selection worsens because only sellers with unfavorable private information (knowing their house has problems the algorithm overvalued) choose the iBuyer route. The pandemic-era housing market also featured rapid price appreciation that degraded AVM accuracy trained on historical data, compounding adverse selection. Zillow reported having significantly overpaid for homes, consistent with this mechanism.

Q: Why is dealer intermediation approximately 50% in car markets but near-zero historically in housing? A: The model, applied to car-market parameters, predicts 40–55% dealer intermediation, consistent with observed U.S. car market shares. Three structural differences explain the gap: (i) cars are more homogeneous (year/make/model/mileage sufficiently characterizes value), reducing adverse selection; (ii) cars are mobile and can be transported across markets, increasing effective liquidity; and (iii) cars depreciate primarily through use, so holding a car on a dealer lot incurs lower value loss than leaving a house vacant. Reducing the depreciation rate from the housing calibration (d = 0.02) to a car-like level (d = 0.005) alone raises predicted intermediary market share by about 5 pp.

Q: Does subjective value dispersion (heterogeneity in buyer preferences) play a large role in limiting intermediation? A: While subjective value dispersion plays a significant role in shaping search market equilibrium (affecting match quality and the gains from household-to-household search), the model finds its effect on the overall level of intermediation is comparatively less pronounced than informational asymmetry, market liquidity, or the opportunity cost of vacancy.

Q: What evidence supports the claim that iBuyers use algorithmic pricing? A: Observable property characteristics and ZIP-quarter fixed effects explain over 80% of price variation in iBuyer transactions, compared to only 68% in non-iBuyer transactions. The higher R-squared for iBuyer transactions is consistent with iBuyers relying on measurable, formalizable characteristics rather than soft information (such as odors or neighbor property conditions) that traditional buyers gather through physical visits.

Q: What are the structural limits on iBuyer expansion even with improved technology? A: Even with enhanced pricing technology (lower α), the scope for dealer intermediation remains narrow because strong incentives persist for iBuyers to avoid markets where algorithmic valuation is difficult, such as older and less homogeneous housing stock. The fundamental barriers — heterogeneity, immobility, and high vacancy opportunity cost — cannot be overcome by technology alone, meaning iBuyers are unlikely to reach the ~50% market share seen in automobile dealer markets.

iBuyers: Technology-driven real estate companies (principally Opendoor and Offerpad) that use automated valuation models and online platforms to make near-instantaneous cash offers on homes, functioning as dealer intermediaries who purchase properties onto their balance sheet and resell after a short holding period, thereby providing immediate liquidity to sellers who would otherwise wait 90+ days in the traditional listing process.

Dealer (Balance Sheet) Intermediation: A form of market-making in which an intermediary purchases an asset outright and holds it on its own balance sheet while finding a subsequent buyer, as distinct from matchmaking intermediaries (brokers) who connect buyers and sellers without taking ownership. The intermediary earns a gross spread between purchase and sale prices.

Adverse Selection (in iBuyer context): The problem arising because sellers possess soft private information about their property (odors, hidden defects, neighbor quality) that algorithmic valuation models cannot capture, while traditional buyers can acquire this information through physical visits. Because iBuyers price quickly without visits, they disproportionately attract sellers of unobservably lower-quality homes, as measured in the paper by the calibrated parameter α = 0.35 (the fraction of low-quality homes the intermediary correctly identifies).

Algorithmic Valuation Model (AVM): The pricing technology used by iBuyers to value homes near-instantaneously using observable property characteristics. The paper measures AVM performance by the R-squared of a hedonic regression: over 80% for iBuyer transactions versus 68% for non-iBuyer transactions, with the residual representing information the algorithm misses and traditional buyers discover through visits.

PSALE (Probability of Sale within 3 Months): An ex ante measure of a property’s underlying liquidity, estimated from a probit model on non-iBuyer listings, capturing the probability that a given home sells within three months of listing. The paper uses PSALE as the key liquidity variable; iBuyers are almost entirely absent where PSALE falls below 50%.

Occupancy Cost: The value loss incurred when a house is held vacant on an intermediary’s balance sheet — encompassing both foregone housing service flows (which continue to benefit occupants under traditional listing but are lost under iBuyer ownership) and ongoing maintenance and depreciation costs (calibrated at d = 0.02 per period). This cost distinguishes housing from goods like cars that depreciate primarily through use rather than time.

Gross Spread: The difference between the price at which an iBuyer sells a property and the price at which it purchased that property, expressed as a percentage of the acquisition price. The paper documents a gross spread of approximately 5% (combining the 3.1 pp purchase discount and the 2.2 pp sale premium), which is persistently positive over the sample period.

Asset-Pricing | Macro Paper Warehouse

A Cognitive Theory of Reasoning and Choice

A Housing Portfolio Channel of QE Transmission

Layer 1 — Overview

In depth

Q1. What is the housing portfolio channel of QE transmission, and how does it differ mechanically from the credit channel?

Q2. What is the key exposure variable and why is it a valid identification strategy?

Q3. What is the benchmark magnitude of the portfolio rebalancing effect and how robust is it?

Q4. Do households with higher bond exposure also rebalance toward equities after QE?

Q5. Which household characteristics amplify the rebalancing, and what do they reveal about the mechanism?

Q6. How is the buy-to-let motive established directly in the data, as opposed to vacation-home or commuter motives?

Q7. How does the paper demonstrate that the effect is independent of the credit channel, while also acknowledging the credit channel operates?

Q8. How is regional exposure to the channel proxied, given that household survey data cannot be aggregated to the regional level?

Q9. What are the quantitative effects on regional rental yields, house prices, and rents?

Q10. What do the listing data reveal about the supply implications of the channel?

Q11. What is the theoretical model underlying the empirical analysis?

Q12. What are the aggregate household balance sheet patterns consistent with the individual-level results?

Key Concepts

A Preferred-Habitat Model of Term Premia, Exchange Rates, and Monetary Policy Spillovers

Layer 1 — Core Argument

In depth

Q1. Why do UIP and EH fail in the standard model, and what changes in this model?

Q2. What are the three types of agents and what does each do?

Q3. What is the equilibrium structure and which factors drive prices?

Q4. How does a conventional short-rate cut transmit domestically and internationally in the model?

Q5. How does unconventional policy (QE/QT) transmit domestically and to the exchange rate and foreign yields?

Q6. What explains the exchange-rate disconnect, and how can the currency market still transmit bond demand shocks?

Q7. What are the model’s implications for foreign exchange intervention?

Q8. How is the relationship between currency risk premia and bond risk premia captured, and what empirical regularities does the model match?

Q9. What is the role of segmented versus global arbitrage, and why does the distinction matter?

Q10. How does the model relate to and extend predecessor frameworks?

Key Concepts

Aggregate demand externality and self-fulfilling default cycles

Layer 1 — Overview

In depth

Q1. What is the core empirical motivation for the model, and what does the regime-switching analysis establish?

Q2. How does the Dixit-Stiglitz CES structure generate a demand externality that links aggregate output to individual firm default decisions?

Q3. What is the two-dimensional dynamical system that summarizes the equilibrium, and what do the two loci look like in the phase diagram?

Q4. Under what conditions do multiple steady states exist, and what does each look like?

Q5. What are the local dynamics around each steady state, and how does parameter κ determine whether the bad steady state is a sink or a source?

Q6. What does the global dynamics analysis reveal that local analysis misses?

Q7. How does the paper simulate the clustered default pattern and what is the role of the “ugly” equilibrium?

Q8. Can purely sentiment-driven cycles generate the clustered default pattern?

Q9. How does the collateral constraint on working capital create dynamic strategic complementarity?

Q10. What is the policy remedy for the bad equilibrium, and how does it work?

Q11. How does this paper differ from Cui and Kaas (2021), the most closely related predecessor?

Q12. What is the markup prediction of the model, and is it consistent with empirical evidence?

Key Concepts

Auctions with Frictions: Recruitment, Entry, and Limited Commitment

Central bank communication by ??? The economics of monetary policy leaks

Layer 1 — Overview

In depth

Q1. How is a “leak” defined in this paper, and how are Eurosystem leaks identified empirically?

Q2. What are the broad trends in the number and topic composition of Eurosystem leaks over 2002–2021?

Q3. How does the timing of leaks within the policy meeting cycle change across sub-periods?

Q4. What regression evidence supports the view that leaks are not random accidents?

Q5. Does the number of pre-meeting leaks predict policy changes?

Q6. How large are the financial market reactions to leaks relative to placebo events and to attributable statements?

Q7. Do the market effects of leaks differ by topic?

Q8. Do leaks move market expectations in the direction of the subsequent policy outcome?

Q9. Do leaks counteract or reinforce prevailing trends in market expectations?

Q10. Do post-announcement leaks dampen the transmission of monetary policy surprises to longer-term rates?

Q11. Does more intense pre-leak attributable communication reduce the market impact of subsequent leaks?

Q12. Does the market impact evidence support the “plant” hypothesis?

Q13. Why do markets react to leaks even though leaks are generally uninformative about policy outcomes?

Q14. What are the implications for the measurement of monetary policy shocks from high-frequency identification?

Q15. What are the implications for the design of central bank quiet periods?

Key Concepts

Coarse Bayesian Updating

Contextually Private Mechanisms

Costs of Financing U.S. Federal Debt Under a Gold Standard: 1791-1933

Overview

In depth

Q1. Why does the paper restrict estimation to bonds with maturity greater than one year?

Q2. How does the Dynamic Nelson-Siegel model with stochastic volatility solve the cross-sectional sparsity problem?

Q3. What is the bond-specific pricing error and why is it essential for historical data?

Q4. How large were Civil War yields compared to prior estimates, and why does the discrepancy arise?

Q5. When did US debt cease to carry a default risk premium relative to UK debt, and how is this measured?

Q6. What is the “nominal anchor” finding during the greenback era, and what econometric method uncovers it?

Q7. How did political events affect exchange rate expectations during and after the Civil War?