Financial-Stability | Macro Paper Warehouse

A Tale of Two Bailouts and Their Impact on Subprime Consumer Debt

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

This paper examines the effects of the Troubled Asset Relief Program (TARP) and the Paycheck Protection Program (PPP)—two government bailout programs during the Global Financial Crisis and the COVID-19 crisis, respectively—on subprime consumer debt, using over 11 million credit bureau observations of individual consumer debt combined with banking, bailout, and local market data. TARP and PPP are found to have opposite effects: subprime consumers in markets with more TARP institutions experienced significantly increased debt burdens following the bailouts, while PPP was associated with reduced subprime consumer debt. Both programs are treated as quasi-natural experiments due to their rapid, largely unanticipated assembly. The findings yield policy implications regarding bailout structures and the conditions attached to bailout funds.

In depth

Q1. What are the two bailout programs studied and why are they treated as natural experiments?

TARP (2008) and PPP (2020) are treated as quasi-natural experiments because they were assembled quickly during crisis conditions and were largely unanticipated, providing relatively exogenous financial shocks to markets based on the presence of eligible institutions, rather than on prior local demand for credit. Both programs had distinct structures and intended targets—TARP aimed at stabilizing financial institutions directly, while PPP aimed at supporting small business payrolls to prevent employment losses—making their differential effects on subprime consumer debt informative about the channels through which bailout design matters.

Q2. How did TARP affect subprime consumer debt and why?

Subprime consumers in markets with more TARP institutions had significantly increased debt burdens following TARP, consistent with a channel in which bank stabilization via TARP relaxed credit supply conditions (especially for lower-quality borrowers) or with a moral hazard channel in which TARP-recipient banks extended credit more aggressively knowing they had government backing. Subprime mortgages played a central role in the buildup to the GFC, growing from 2.5% to 8.4% of mortgage balances outstanding between 2001 and 2007; the finding that TARP increased rather than reduced subprime debt burdens raises concerns about whether bank stabilization programs sufficiently constrain the subsequent lending behavior of recipient institutions.

Q3. How did PPP affect subprime consumer debt and why?

PPP was associated with reduced subprime consumer debt, consistent with a channel in which the payroll support prevented the expected wave of unemployment-driven debt distress and credit score deterioration that would otherwise have converted prime consumers into subprime borrowers during the COVID-19 crisis. Prior to PPP, the COVID-19 recession—with unemployment peaking at 14.7% in April 2020—was expected to cause a ballooning of subprime consumer debt; the failure of this ballooning to materialize and the actual decline in subprime debt is attributed in part to PPP’s employment and income support function.

Q4. What are the policy implications for bailout design?

The opposite effects of TARP (which increased subprime debt) and PPP (which reduced it) yield policy implications for bailout structures and the conditions attached to bailout funds: bailouts directed at banks without explicit restrictions on subsequent lending behavior may inadvertently stimulate the accumulation of high-risk household debt, while bailouts directed at supporting household incomes and employment may reduce systemic credit risk. These findings suggest that the distribution channel of bailout funds (through banks vs. directly to households and employers) has first-order effects on the resulting debt accumulation and credit risk in the household sector.

Key concepts

TARP (Troubled Asset Relief Program) : the 2008 U.S. government program that provided capital injections to financial institutions during the Global Financial Crisis; found in this paper to be associated with increased subprime consumer debt burdens in affected markets. PPP (Paycheck Protection Program) : the 2020 U.S. government program that provided small business loans/grants to support payrolls during the COVID-19 crisis; found in this paper to be associated with reduced subprime consumer debt, opposite to TARP’s effect. subprime consumer debt : obligations of consumers with low credit scores; the paper’s key outcome measure; elevated levels associated with systemic credit risk (as seen in the buildup to the GFC) and used as a barometer of financial vulnerability in the household sector.

Bank Opacity and Safe Asset Moneyness

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

This paper studies when a bank is more effective as a supplier of privately produced money-like safe assets (repo, commercial paper), finding that a bank produces safer, more liquid assets when (1) its return on equity (ROE) is relatively lower, and (2) it is relatively more opaque about its balance sheet. A three-period model is presented in which safe asset investors focus on the left tail of the bank asset value distribution that ultimately determines the debt’s moneyness: a higher ROE signals riskier investment activities with higher return volatility, exposing investors to greater left-tail risk and lowering the moneyness of the bank’s debt. Bank opacity mitigates the strength of the ROE-moneyness relationship because opacity limits investors’ ability to infer asset risk, making it optimal for the banking system to maintain a certain level of opacity. Empirical tests on dealer banks and money market mutual funds’ (MMFs) funding relationships confirm that higher ROE leads to MMF withdrawal due to lower moneyness of safe assets.

In depth

Q1. Why does higher ROE lower the moneyness of a bank’s safe assets?

Higher ROE signals that a bank is more likely to be engaging in riskier investment activities with higher return volatility, which exposes safe asset investors—who care almost entirely about the left tail of the bank asset value distribution—to a higher likelihood of complete insolvency, lowering the moneyness of the bank’s debt. The intuition is asymmetric: for a debt holder, the upside is limited to the contracted interest rate, while the downside involves potential total loss if the bank becomes insolvent. A higher ROE thus signals higher left-tail risk rather than higher credit quality from the safe asset investor’s perspective, contradicting the positive signal that higher ROE sends to equity investors.

Q2. How does the model formalize the moneyness concept?

In the three-period model, the bank issues a money-like safe asset (deposit) to finance itself, and the household holds it both to transfer wealth intertemporally and to use it as a medium of exchange; moneyness captures both the safety and the liquidity of the asset as experienced by the holder. The model embeds the Gorton-Pennacchi (1990) and Dang-Gorton-Holmström (2012) notion that money-like assets are purposefully designed to be information-insensitive, so that investors have little incentive to acquire private information about them. The model shows how ROE—a piece of public information—nonetheless predicts moneyness and triggers withdrawal.

Q3. Why is bank opacity an equilibrium feature that improves moneyness?

Bank opacity mitigates the predictive power of ROE for the moneyness of safe assets because if investors cannot observe detailed information about the bank’s asset side, they cannot fully infer the riskiness of the investments backing the bank’s debt from the ROE signal, making it optimal for the banking system to maintain a certain level of opacity to preserve the information-insensitive character of its safe assets. This result is consistent with Dang et al. (2017)’s argument that banks are intentionally opaque: opacity is not merely a byproduct of complexity but a deliberate design feature that preserves the moneyness of privately produced safe assets.

Q4. What is the empirical evidence using MMF and dealer bank data?

Empirical tests using data on MMF funding of dealer banks confirm that higher bank ROE leads to MMF withdrawal from the bank, consistent with the model’s prediction that higher ROE reduces the moneyness of the bank’s safe assets for institutional investors; the relationship is attenuated for more opaque banks, consistent with the model’s opacity mechanism. The wholesale banking sector (dealer banks and institutional investors like MMFs) is the natural testing ground because its participants are more informed than retail depositors and therefore more sensitive to signals about the riskiness of the assets backing the bank’s debt.

Key concepts

moneyness of safe assets : the degree to which a financial asset is safe and liquid—traded at par with no questions asked; determined in this paper by how well a bank’s debt protects investors against the left tail of the bank asset value distribution. return on equity (ROE) as a risk signal : the paper’s key insight that, for safe asset investors (debt holders), higher bank ROE signals riskier investments with higher return volatility rather than lower credit risk; this contrasts with the positive signal ROE sends to equity investors. information-insensitive safe asset : a financial asset purposefully designed to be immune to private information acquisition by investors (Gorton-Pennacchi 1990; Dang et al. 2012); bank opacity preserves this property by limiting investors’ ability to infer asset-side risk from public signals.

Comment on 'Asset Bubbles and Overlapping Generations' by Tirole

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

Tirole (1985) studied an overlapping generations model with capital accumulation and showed that the emergence of asset bubbles can resolve the capital over-accumulation problem when the economy is dynamically inefficient. His Proposition 1(c) claims that a bubble can emerge if and only if the dividend growth rate exceeds the bubbleless steady-state interest rate. This comment identifies an error in that proposition: the stated condition is necessary but not sufficient for bubble existence. The paper constructs an explicit counterexample in which the dividend growth rate exceeds the bubbleless interest rate but no bubble equilibrium exists, and separately constructs a case in which a bubble exists even when the condition in Proposition 1(c) fails. Corrected necessary and sufficient conditions for bubble existence are derived, and the implications of the correction for the welfare results and the relationship between dynamic inefficiency and bubbles are characterized.

In depth

Q1. What is the error in Tirole’s Proposition 1(c)?

The error is in the sufficiency direction: Tirole argued that whenever the dividend growth rate exceeds the bubbleless interest rate, a bubble equilibrium exists; Pham and Toda construct a parameter configuration satisfying this condition where no bubble equilibrium exists, because the continuity argument used in Tirole’s proof fails at boundary parameter values. The necessity direction — that bubble existence requires this rate comparison — is not challenged.

Q2. How do the corrected conditions change the interpretation of dynamic inefficiency?

Tirole’s original result linked bubbles tightly to dynamic inefficiency (r < g), providing a clean condition for when bubbles are both feasible and welfare-improving by absorbing excess saving. The correction weakens this link: bubble existence requires additional structural conditions beyond the rate comparison, meaning dynamic inefficiency is a necessary but not sufficient condition for bubbles in the Tirole framework. Policy prescriptions based on the r < g condition for bubble welfare analysis need qualification.

Key concepts

dynamic inefficiency : the OLG condition in which the interest rate falls below the growth rate, making intergenerational transfers from young to old welfare-improving; related to but not sufficient for bubble existence under the corrected Tirole conditions.

bubble existence condition : the necessary and sufficient conditions under which an asset bubble can emerge and persist in the Tirole OLG model; the corrected version requires more than the dividend-growth-rate-exceeds-interest-rate comparison of the original Proposition 1(c).

Cyberattacks on Small Banks and the Impact on Local Banking Markets

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

This paper studies what happens to local banking markets when a small bank suffers a successful cyberattack, using a stacked difference-in-differences design on 16 cyber incidents at small U.S. banks drawn from the Privacy Rights Clearinghouse database over 2005–2017. Attacked small banks experience a deposit growth rate roughly 22 percentage points lower than matched control banks in the two years following a breach, reflecting depositors’ loss of confidence in the targeted institution’s cybersecurity capacity. The deposit attrition is sharply stronger in counties with lower digital literacy, consistent with less-informed depositors placing disproportionate weight on a visible security failure. Deposit losses do not flow evenly to all competitors: positive spillovers accrue only to the dominant or largest banks in the local market, not to other small banks, concentrating market share toward large incumbents. Affected small banks subsequently attract riskier mortgage borrowers — proxied by higher loan-to-value ratios and lower FICO scores — suggesting that the deposit-cost pressure from a cyberattack induces yield-seeking behavior. The aggregate effect is a reduction in credit access for informationally opaque small borrowers that slows local small-establishment growth.

In depth

Q1. What is the identification strategy and what variation does it exploit?

The paper uses a stacked difference-in-differences design that stacks sub-experiments around each of the 16 cyberattack events, comparing the attacked small bank against a matched set of control banks in the same local market that did not experience a breach, with the event window centered on the quarter of the reported breach. The primary data source for cyber incidents is the Privacy Rights Clearinghouse (PRC) database, which records data breaches across industries; the paper restricts attention to incidents at U.S. commercial banks with total assets below a size threshold that classifies them as small. The stacking design allows each attack event to contribute its own two-by-two (pre/post, treated/control) comparison while controlling for time fixed effects across all events, which is important because cyberattacks cluster in certain periods. Identification relies on the parallel-trends assumption: absent the cyberattack, the deposit growth trajectory of the attacked bank would have evolved like that of matched local competitors. The paper validates this assumption with pre-trend tests and provides a battery of robustness checks including alternative matching procedures and excluding events that coincide with other bank-specific news.

Q2. How large is the deposit effect at attacked small banks and what is the direction of deposit flows?

Attacked small banks see deposit growth rates approximately 22 percentage points lower than control banks over the two years following a breach, a decline that is economically large relative to the unconditional mean deposit growth rate in the sample. The market-share impact is of the order of 1 percentage point lower for the attacked bank. Crucially, the deposit outflows do not disperse evenly to all rivals: the paper finds positive and statistically significant deposit spillovers only at the dominant large bank (or banks) in the local market, with no measurable increase at competing small banks. This asymmetric spillover is consistent with depositors fleeing to scale — perceiving large banks as having the technological resources and regulatory scrutiny to maintain cybersecurity — rather than simply seeking any alternative.

Q3. What role does digital literacy play in moderating the deposit response?

The deposit effect is significantly stronger in counties with below-median digital literacy, measured using population-weighted indices of internet connectivity and self-reported computer use from the American Community Survey, suggesting that less-digitally-literate depositors rely more heavily on observable security signals — such as a publicized breach — when assessing bank safety. In high-digital-literacy counties, the average customer may already have some prior belief about cyber risk across institutions and may discount a single breach as less informative, dampening the flight-to-quality response. In low-digital-literacy counties, the breach is a more salient and credibility-destroying event. The heterogeneity is quantitatively meaningful and survives controlling for MSA-level income, education, and urbanization.

Q4. How does the competitive position of large banks in the local market moderate the spillover?

When a large bank holds a dominant market position prior to the attack — measured by having a market share above the 75th percentile of the local deposit distribution — the positive deposit spillover to that large bank is more than 30 percentage points larger than in markets where large banks hold a weaker position, pointing to a flight-to-incumbency effect that operates on top of the flight-to-scale effect. This finding implies that cyberattacks on small banks are particularly concentrating in markets where large banks are already dominant: the attack accelerates an existing market-share gradient rather than creating a new one. The result has policy relevance for local banking market competition: communities that already have concentrated banking sectors are more exposed to structural concentration following cyber events.

Q5. Do deposit rates at attacked small banks rise or fall, and does this signal a funding-cost channel?

Deposit rate evidence in the working paper suggests that attacked small banks do not uniformly raise deposit rates to retain customers, which is consistent with the deposit outflows being driven by non-price concerns about security rather than competitive pricing, and which rules out a simple funding-cost-through-repricing mechanism. The absence of a strong deposit-rate increase at the attacked bank indicates that depositors are responding to a qualitative signal about the bank’s cybersecurity capacity rather than being price-insensitive. This matters for the economic interpretation: the mechanism is loss of depositor confidence rather than increased funding costs passed through from the attack’s direct remediation expenses.

Q6. What happens to the loan portfolio and borrower risk profile of attacked small banks after a breach?

In the post-attack period, affected small banks shift their mortgage originations toward riskier borrowers, with originations showing higher average loan-to-value ratios and lower average FICO scores relative to the pre-attack period and relative to control banks, consistent with yield-seeking behavior driven by the deposit-funding squeeze. This borrower-quality deterioration implies a second-order financial stability concern beyond the immediate deposit loss: attacked banks may take on more risk in the loan book at precisely the moment when their funding base is weakening. The evidence is thus consistent with a mechanism in which the cyberattack triggers a cascade — deposit loss → funding pressure → reach-for-yield → loan-quality deterioration.

Q7. What are the real-economy consequences at the local market level?

Counties that experience a cyberattack on a local small bank show lower subsequent small-establishment growth relative to control counties, measured using County Business Patterns data on establishments with fewer than 20 employees, consistent with reduced small-business credit availability as small banks contract lending. Large banks that absorb deposit inflows from the attacked institution do not offset this credit reduction: the deposit inflows do not translate into proportionate increases in small-business or small-mortgage lending, reflecting the well-documented diseconomy of scale in relationship lending by large institutions. The real-economy effect is concentrated in counties where small banks had a larger pre-attack share of local deposits and credit, consistent with the mechanism that the effect operates through credit-supply disruption rather than demand shocks.

Q8. How does this paper relate to the literature on bank runs and financial contagion?

Unlike classic bank-run models in which depositor withdrawals are self-fulfilling or triggered by sunspot-like coordination failures, this paper’s results suggest that cyberattacks constitute an information event that rationally updates depositors’ beliefs about the attacked bank’s technological competence, generating a fundamentals-based run on the specific institution rather than systemic panic. The results complement the emerging literature on cyber risk in financial institutions (e.g., Kashyap and Wetherilt 2019, Eisenbach et al. 2022) by documenting market-level spillovers and real effects beyond the attacked institution. The finding that large banks absorb deposits following attacks on small banks also connects to the “too-big-to-fail” literature by showing that size confers a competitive advantage in moments of localized financial stress.

Key Concepts

stacked difference-in-differences : an event-study design in which multiple treatment events are each assigned their own pre/post comparison window, the sub-experiments are then stacked into a single dataset, and pooled regressions with event-by-period fixed effects estimate the average treatment effect; used in this paper to exploit variation across 16 separate cyberattack events at small banks.

Privacy Rights Clearinghouse (PRC) database : a publicly available database of data-breach incidents across industries in the United States, which the paper uses as the primary source for identifying confirmed cyberattacks on commercial banks; the paper restricts to incidents classified as hacking or skimming rather than physical theft or accidental exposure.

deposit spillover : the increase in deposit inflows to competitor banks in the same local market following a cyberattack on a rival institution; in this paper, measured as the change in deposit growth at non-attacked banks relative to their own pre-attack trends.

flight-to-scale : the pattern in which depositors shift funds from smaller to larger banks following a cyber incident, driven by the belief that larger banks have superior cybersecurity resources; the paper documents that this flight benefits only the largest local bank rather than all large banks.

digital literacy : a county-level index measuring residents’ familiarity with digital technologies, internet access, and computer use; used in the paper to test whether depositor reactions to cyberattacks are stronger where depositors have less prior information about cyber risk.

reach-for-yield : the tendency of a bank with a weakened funding base to shift its loan portfolio toward higher-yielding, riskier borrowers to maintain net interest margins; documented in this paper as a behavioral response of attacked small banks in the post-breach period.

From Interaction to Business Fluctuations: How Credit Network Explains Cycles

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

Layer 1: Overview

This paper investigates how the endogenous structure of credit, deposit, and interbank networks shapes business cycle fluctuations and large financial crises in the U.S. economy. Ciola and Tedeschi build and estimate a microfounded heterogeneous-agents macroeconomic model in which households, firms, and banks interact through decentralized matching in three markets — deposits, credit, and interbank lending — with agents choosing partners based on both posted interest rates and the size of the counterpart, generating a preferential-attachment mechanism that endogenously concentrates the financial sector. The structural parameters governing network formation are estimated on U.S. quarterly interest rate and GDP growth data from 1947 to 2019 via an Extended Method of Simulated Moments (EMSM) procedure combined with a Bayesian Adaptive Random Walk Metropolis–Hastings sampler; the calibrated model reproduces the empirical autocorrelation structure of these series. The model’s key finding is that preferential attachment endogenously concentrates roughly three-quarters of deposits, credit, and interbank transactions into a single hub bank, whose dominance raises markups, suppresses deposit rates, and depresses aggregate capital accumulation relative to the initial symmetric state. Bank runs against this hub — rare but endogenously generated when households reallocate deposits simultaneously — collapse the interbank market completely and produce deep recessions that last multiple quarters, with recovery requiring approximately five years.

In depth

Q1. What is the model’s core structure and how do agents interact?

The model consists of a fixed number of households (N_H = 1,000), banks (N_I = 10), and firms (N_F = 1,000) who interact in deposit, credit, and interbank markets through a decentralized preferential-attachment matching mechanism in which agents assess both current interest rates and the size of potential counterparts. Households deposit savings in a single bank chosen based on a fitness index combining the bank’s promised deposit rate and its size (used as a proxy for long-run quality), and they search for a new partner each period with probability ζ_H. Firms borrow from one bank at a time, also choosing based on a fitness that weighs the promised profit share against bank size, and switch with probability ζ_F. Banks set interest rates in all three markets to maximize expected profits, exploiting their monopolistic power (higher when they are larger), subject to a balance sheet constraint that links deposits, credit extended to firms, and interbank borrowing. The interbank market exists specifically to cover unexpected deposit withdrawals: when a bank’s deposits fall below its outstanding credit, it borrows in the interbank market or closes credit lines.

Q2. How does the estimation methodology work and what parameters does it identify?

The paper employs the Extended Method of Simulated Moments (EMSM) of Smith (1993) and Gourieroux et al. (1993), which minimizes the weighted distance between the coefficients of a VAR auxiliary model estimated on observed U.S. data and on H simulated time series generated from a given structural parameter vector, with the optimal weighting matrix set to the inverse of the Newey–West covariance of the auxiliary parameter estimates. Because gradients of the criterion function are not analytically available for this nonlinear agent-based model, the authors use a two-step approach: first, a Particle Swarm Optimization (PSO) algorithm explores the parameter space to locate a neighborhood of the global minimum; second, a Bayesian Adaptive Random Walk Metropolis–Hastings (ARWMH) algorithm generates posterior draws from the structural parameter distribution using the chi-square distributional properties of the EMSM criterion function. The estimated structural parameters include the nine network formation parameters {ω_X, ζ_X, ψ_X} for each of the three markets — governing competition intensity, switching probability, and the weight agents assign to counterpart size — while the production coefficient (α = 0.37) and household discount factor (β = 0.997) are calibrated directly to U.S. labor share and real interest rate data. Estimation uses 1947:Q1–2019:Q4 U.S. real GDP growth and real interest rate data; with three VAR lags and d = 9 structural parameters, the overidentification chi-square test can be assessed.

Q3. What are the long-run dynamics and how does the financial network concentrate?

Starting from an equal distribution of agents across banks, the model converges to a pseudo-steady-state in which a single hub bank intermediates approximately three-quarters of deposits, credit lines, and interbank transactions, because the preferential-attachment mechanism is self-reinforcing: larger banks attract more depositors (providing more stable funding), more firms (generating more profit), and more interbank counterparts, which further enlarges their size and attractiveness. This concentration has clear aggregate consequences: as the hub’s monopolistic power grows, it widens the markup over the perfect competition interest rate in the credit market and the markdown below it in the deposit market, reducing the deposit rate paid to households and thereby depressing household capital accumulation. Simulations across 1,000 independent replicas show that the aggregate production level in the pseudo-steady-state is below the initial competitive equilibrium, credit and interbank interest rates rise, and approximately 10% of total capital circulates through the interbank market as periphery banks rely on the hub for liquidity provision.

Q4. How do cyclical fluctuations and crises emerge endogenously?

Business cycles arise from the continuous reallocation of household deposits across banks, which generates endogenous liquidity shocks that do not require an exogenous crisis trigger: when a critical mass of households simultaneously reallocates away from the hub — a rare but endogenous event driven by the stochastic matching process — the hub faces a severe liquidity shortage, must close credit lines and interbank lending, and produces a systemic economic contraction. In a representative 100-year simulation, aggregate production fluctuates around a stable trend with mild recessions most of the time, but the model occasionally generates a catastrophic bank run against the hub. When this occurs, the hub’s weighted degree in all three markets collapses to near zero within one or two quarters, the interbank market freezes completely, and firm production stops because firms cannot immediately reallocate their credit demand to alternative banks. The impulse response to a sudden reduction in hub deposit centralization shows that aggregate production falls sharply in the short run (as credit contracts) and only surpasses its pre-run level after approximately five years (20 quarters).

Q5. What does the VAR impulse response analysis reveal about recovery dynamics?

An estimated VAR on all simulations — with aggregate production and the volume, centralization, and interest rates of each of the three markets as endogenous variables — shows that a negative shock to deposit market centralization (i.e., a bank run against the hub) triggers an immediate spike in deposit interest rates (as competing banks compete for the displaced funds), a contraction in credit and interbank supply (as periphery banks lack sufficient liquidity to expand), and a rise in credit interest rates (as the pool of surviving credit lines is concentrated in the most profitable projects). In the medium run, higher deposit rates promote household capital accumulation, which ultimately expands the aggregate supply of productive capital; at the same time, the dissolution of the old hub reduces the sector’s average monopolistic markup, permanently lowering credit market interest rates. This self-correcting mechanism underlies the five-year recovery window and also illustrates why prompt policy intervention during hub-collapse crises is particularly effective — early stabilization prevents the reinforcing deposit-withdrawal spiral that deepens the contraction.

Q6. What is the paper’s contribution relative to existing macroeconomic network literature?

The paper makes three distinct contributions over prior agent-based macroeconomic network models: first, it treats households as active depositors whose reallocation choices generate endogenous liquidity shocks rather than simply passive shock absorbers; second, it models banks as profit-maximizing agents that optimally set interest rates exploiting market power rather than assuming perfect competition or regulatory constraints; and third, it produces a Bayesian estimator of all structural parameters rather than relying on calibration to observed moments. Prior work in this tradition (Delli Gatti et al. 2010; Riccetti et al. 2013; Lenzu and Tedeschi 2012) typically either omits households from the deposit market or assumes exogenous mechanisms of crisis formation. By endogenizing all three sources of network dynamics — deposit, credit, and interbank — and estimating the model on U.S. data, the paper provides a framework in which large financial crises emerge as intrinsic system properties rather than imposed scenarios, and quantifies the structural parameters driving them.

Key Concepts

preferential attachment : a matching mechanism in which agents preferentially form links with larger counterparts; in this model it causes households and firms to favor large banks, endogenously concentrating the financial sector into a hub-and-spoke structure with a dominant hub bank.

hub bank : the single largest financial intermediary that endogenously emerges in the model’s long-run equilibrium, intermediating approximately three-quarters of deposits, credit lines, and interbank transactions; its size confers monopolistic power but makes it the systemic node whose failure triggers economy-wide crises.

Extended Method of Simulated Moments (EMSM) : the estimation strategy used to identify the nine network formation structural parameters; it minimizes the weighted distance between VAR coefficients estimated on observed U.S. data and on model-simulated data, with a Bayesian ARWMH sampler used to generate the posterior distribution given the chi-square-distributed criterion function.

endogenous bank run : the crisis mechanism in this model — a simultaneous reallocation of household deposits away from the hub, triggered by the stochastic matching process rather than an external shock, that freezes the interbank market and produces a deep recession lasting approximately five years (20 quarters) in impulse response analysis.

Hedge funds and the Treasury cash-futures basis trade

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

The U.S. Treasury market is the deepest and most liquid fixed-income market in the world, yet in March 2020 it experienced unprecedented dysfunction—widening bid-ask spreads, skyrocketing repo rates, and diverging arbitrage spreads that prompted massive Federal Reserve intervention. This paper documents the rise and near-collapse of the Treasury cash-futures basis trade—an arbitrage strategy among hedge funds exploiting a persistent disconnect between cash Treasury prices and futures prices—as a central feature of that episode. Using regulatory datasets on hedge fund exposures and repo transactions, the authors show that at its peak the basis trade accounted for an estimated $400–$500 billion in positions, constituting more than 60% of total hedge fund Treasury exposure, more than 70% of hedge fund repo borrowing, and more than 25% of primary dealers’ repo lending. A model and empirical evidence link the trade’s growth after 2016 to broader Treasury market developments, and show how the trade’s reliance on short-term repo financing creates both margin risk and rollover risk. In March 2020 many of these risks materialized, though the unwinding of basis positions was likely a consequence rather than the primary cause of the stress; prompt Federal Reserve intervention may have prevented a liquidity spiral.

In depth

Q1. What is the Treasury cash-futures basis trade and why did it become popular?

The basis trade exploits the arbitrage relationship Pₜ,τ = ΣBₜ,ₛcₛ + Bₜ,T Fₜ,τ,T: when futures prices are too high relative to the present value of the deliverable bond, traders go “long the basis” by buying the cash bond and shorting the futures, financing the long position in the overnight repo market. The trade became popular following 2016 as demand for long Treasury futures positions grew (from institutional investors seeking leveraged duration exposure) while the supply of warehousing capacity from dealers contracted under post-crisis regulatory constraints. Hedge funds stepped in as the marginal warehouser, exploiting the resulting premium embedded in futures prices. The trade is nearly zero net-cash but requires continuous repo rollover.

Q2. How large did the trade become and how was its size estimated?

Using regulatory data—specifically CFTC Form 40 (hedge fund futures positions), SEC Form PF (AUM and derivatives exposures), and FR 2004 (primary dealer repo data)—the authors estimate basis trade positions peaked at $400–$500 billion, comprising more than 60% of hedge fund Treasury exposure, more than 70% of hedge fund repo borrowing, and more than 25% of primary dealer repo lending to hedge funds. The data allow the authors to identify basis positions directly, distinguishing them from outright long Treasury positions, by matching the simultaneous long cash / short futures pattern that defines the trade. The estimates underscore that hedge funds had become systemically important participants in Treasury market intermediation.

Q3. What financial stability risks does the basis trade create?

The basis trade creates two interrelated risks: margin risk (variation margin calls on futures positions can force immediate liquidation) and rollover risk (if repo lenders withdraw funding, the cash Treasury position must be sold). The paper’s model formalizes how limits to arbitrage—specifically repo market illiquidity and margin requirements—impair risk-sharing between dealers and holders of long futures positions. These constraints mean that even a moderate adverse price move can trigger a self-reinforcing cycle: higher basis volatility → margin calls → forced sales → further basis widening → further margin calls.

Q4. What happened in March 2020 and what was the Federal Reserve’s role?

Beginning in early March 2020, the COVID-19 pandemic triggered a “dash for cash” that disrupted Treasury market functioning: bid-ask spreads widened dramatically, repo rates spiked, and the cash-futures basis moved sharply against basis traders, generating large margin calls. The authors find that while Treasury market disruptions spurred hedge funds to sell Treasuries, the unwinding of the basis trade was likely a consequence rather than a primary cause of the stress. The Federal Reserve intervened by dramatically expanding Treasury purchases from dealers and offering unlimited repo and reverse repo facilities, which likely prevented a liquidity spiral by removing the constraint on dealer intermediation capacity. The paper argues this episode highlights structural vulnerabilities in Treasury market intermediation arising from the shift of warehousing capacity to hedge funds.

Key concepts

Treasury cash-futures basis trade : an arbitrage strategy in which a trader simultaneously holds a long position in cash Treasury bonds (funded via repo) and a short position in Treasury futures, profiting from the convergence of cash and futures prices at delivery.

warehousing role of hedge funds : the function of holding Treasury bonds on behalf of institutional investors who want long futures exposure, financed in the repo market; this creates a link between Treasury, futures, and repo markets and exposes the system to repo rollover and margin risk.

rollover risk : the risk that short-term repo lenders decline to roll over funding at maturity, forcing the borrower to sell the collateral asset (Treasury bonds) at potentially distressed prices.

How Bad Are Weather Disasters for Banks?

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

Using FEMA disaster declarations matched to SHELDUS property-damage estimates and Call Report data for 1995–2018, this paper finds that weather disasters — even at their most severe — have had modest effects on U.S. bank safety over the last quarter century. For single-county banks exposed to 95th-percentile disasters, Z-scores decline by roughly 9 percent at a five-year horizon under the panel estimates; reaching failure thresholds from sample mean Z-score levels would require a disaster approximately 6.7 standard deviations more destructive than a 95th-percentile event. Federal disaster aid does not appear to be the primary driver of this resilience, since banks exposed to weather events without FEMA declarations exhibit similar stability. Instead, the paper points to a loan demand channel — multi-county bank lending increases roughly 0.25 percentage points per standard deviation of damage at five years without an accompanying interest-rate increase — and to local banks’ apparent avoidance of mortgage lending in flood-prone areas beyond what official flood maps predict, consistent with local information about true flood risk limiting exposure before disasters strike.

In depth

Q1. How severe are weather disaster effects on bank safety?

The paper finds that weather disasters at any severity level produce small and often statistically insignificant effects on the key bank safety measures — charge-offs, capital ratios, return-on-assets volatility, and Z-scores — at single-county banks, with the largest measured effect being roughly a 9 percent decline in Z-scores at the 95th percentile of disaster damage at a five-year horizon. The regression framework uses bank and state-year fixed effects, with SHELDUS damage as the continuous severity measure and FEMA disaster declarations as a binary indicator. For multi-county banks, charge-offs increase by roughly 10 percent at five years, but net income also rises, suggesting disaster-area loan demand partially offsets credit losses. The paper’s calculation is that pushing a typical bank from its mean Z-score of 135.9 to the failure threshold would require a Z-score decline of 127.9 — far exceeding the estimated −9 percent impact of a 95th-percentile disaster, which would need to be approximately 6.7 standard deviations more destructive to close that gap.

Q2. Is bank resilience an artifact of federal disaster aid?

The paper presents evidence that federal disaster aid is not the primary source of bank resilience, since banks exposed to weather events that did not receive FEMA disaster declarations exhibit similarly modest effects on bank safety measures. The test is designed to separate the insurance mechanism (FEMA aid replacing household income and debt service capacity) from intrinsic bank resilience. The fact that non-FEMA disasters produce comparable stability redirects attention to the demand-side and local-knowledge channels as the more fundamental explanations for the resilience finding.

Q3. What is the loan demand channel and how large is it?

Multi-county banks experience an increase in lending of roughly 0.25 percentage points per standard deviation of SHELDUS damage at a five-year horizon, and the authors find no accompanying increase in loan interest rates, which is consistent with a demand-side shift rather than a tightening of lending standards. The demand interpretation is that disasters create a wave of borrowing demand as households and firms repair or replace damaged assets, and the increased loan volume helps offset the increase in charge-offs. The pattern is found at multi-county banks — which can serve affected and unaffected areas simultaneously — but not at single-county banks, consistent with lending capacity mattering for capturing the demand increase.

Q4. What does “local knowledge” mean in this context?

Local banks originate approximately 6.4 percent fewer log mortgage dollars per application in FEMA flood zones than would be predicted by the official flood map classifications alone, with the gap widening to 7–8 percent in areas that have experienced more than five FEMA flood declarations compared to areas with fewer than three, which is consistent with local lenders holding information about true flood risk not captured in official maps. The finding is consistent with local banks having access to community-level information — observed flooding history, property-level characteristics, local drainage and elevation — that is not incorporated into official FEMA flood zone classifications. This pre-disaster selectivity limits mortgage accumulation in the highest-risk areas before disasters occur.

Q5. What are the implications for climate risk assessment?

The paper explicitly frames the historical resilience documented for 1995–2018 as informing rather than settling assessments of physical risk to banks from future climate change, since more frequent or more severe disasters could overwhelm the demand-offset and local-knowledge mechanisms that the paper identifies as sustaining bank performance. The key qualification is temporal scope: the demand-side recovery effect requires that affected areas have the income and economic capacity to service new loans, and the local-knowledge effect requires that banks have experienced enough repeated flooding to develop accurate private flood risk assessments. Both conditions could become less reliable as climate change alters the frequency, geography, and severity of weather events relative to the historical distribution.

Key concepts

Z-score : a bank-level distance-to-insolvency measure equal to (return on assets + capital ratio) divided by return-on-assets volatility; higher values indicate greater distance from failure; used here as the primary measure of disaster impact on bank safety.

SHELDUS : the Spatial Hazard Events and Losses Database for the United States, providing county-level property damage estimates for weather events; used in this paper as the continuous measure of disaster severity in panel regressions.

single-county bank : a bank whose entire depositor base is drawn from one county, making it fully exposed to local disaster effects with no geographic diversification across other counties.

loan demand channel : the mechanism by which disasters increase demand for credit from households and firms repairing or replacing damaged assets, generating new loan volume that partially offsets credit losses at banks serving affected areas.

local knowledge : the paper’s label for the informational advantage that local banks appear to have about true flood risk beyond what official FEMA flood zone classifications capture, inferred from lower mortgage originations in areas with a history of repeated flooding.

International Reserve Management Under Rollover Crises

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

The paper extends the Cole-Kehoe (2000) sovereign rollover crisis model to include international reserves and derives the joint optimal management of sovereign debt and reserves in a small open economy subject to potential creditor coordination failure. The central results are: (i) reserves are only valuable as a rollover-crisis defense when debt has sufficiently long maturity; (ii) the optimal exit path from the crisis zone requires holding zero reserves while gradually reducing debt, then jumping simultaneously to the optimal safe pair (a*, b*) by issuing new debt while accumulating reserves; (iii) this seemingly paradoxical debt-financed reserve accumulation lowers bond spreads because it moves the economy fully into the safe zone.

Environment: The government issues long-maturity bonds with Macaulay duration 1/δ (δ=1 is one-period debt; δ→0 is a consol). In each period, creditors decide whether to roll over. If the economy is in the crisis zone C (defined below), a sunspot ζ ∈ {0,1} with P(ζ=1) = λ determines whether a coordination failure occurs: if ζ=1 and the government is in C, creditors refuse to roll over, and the government must use reserves to service debt; if reserves are insufficient, the government defaults. The government also holds reserves a ≥ 0 earning the risk-free rate r.

Three-zone structure (Definition 1, Figure 1): the debt-reserve space (b,a) is partitioned into:

Safe zone S: b < b−(a) — government can meet its debt obligations even if the rollover crisis sunspot realizes (ζ=1); reserves are sufficient to cover the redemption shortfall
Crisis zone C: b−(a) ≤ b ≤ b+(a) — a rollover crisis is possible but not inevitable; if ζ=1, the government defaults unless reserves cover the gap; if ζ=0, the government refinances normally
Default zone D: b > b+(a) — the government defaults regardless of the sunspot because its debt burden exceeds any feasible repayment

Proposition 2 — Reserves expand the safe zone: Both boundaries b−(a) and b+(a) are increasing in reserves a. The slope of b−(a) with respect to a is steeper than the slope of b+(a), so as reserves rise: the safe zone expands, the crisis zone narrows, and the default zone shrinks. Reserves improve debt sustainability by shifting both zone boundaries to higher debt levels, but the benefit falls with debt because high-debt governments are closer to the default zone where reserves cannot compensate.

Proposition 3 — Positive reserves require long debt maturity: Optimal reserves a* > 0 requires that debt maturity is long enough (condition (18): δ < δ̄ for some threshold δ̄ < 1). The intuition is mechanical: if there is a rollover crisis with one-period debt (δ=1), the government must immediately repay the full face value b of all outstanding bonds; moderate reserve stocks a « b cannot cover this, making reserves useless. With long-maturity debt (δ<1), a rollover crisis only forces repayment of the near-term cash flow (δb plus coupon), which a much smaller reserve buffer a can cover. Hence reserves only provide value — and are only demanded — when debt has sufficient duration.

Proposition 4 — No reserves with one-period debt: When δ=1 (pure short-term debt), the optimal reserve level is zero: a* = 0. This follows directly from Proposition 3: one-period debt lies above the maturity threshold, so the safe zone cannot be expanded by any feasible reserve level.

Proposition 5 and Corollary 1 — Optimal exit strategy: The optimal exit path from the crisis zone is non-monotone in reserves:

While in the crisis zone, hold zero reserves (a=0) and reduce debt b through primary surpluses
Continue reducing debt until the government can reach the optimal safe pair (a*, b*) in a single period
In that final period, simultaneously issue new debt (increase b) AND accumulate reserves (increase a to a*), jumping directly from the safe zone to (a*, b*)

The counterintuitive simultaneous debt issuance in step 3 lowers bond spreads immediately because the reserve accumulation moves the economy firmly into the safe zone, eliminating rollover risk for creditors who then demand a lower yield premium. The optimal path delays all reserve accumulation until this transition step — building reserves gradually while in the crisis zone is suboptimal because partial reserves still leave the economy vulnerable to sunspot crises while incurring the return cost of holding low-yield liquid assets.

Proposition 6 — One-period exit condition: If the government’s current net foreign asset position NFA = a − q·b exceeds the NFA at (a*, b*), the government can exit the crisis zone in a single period.

Calibration (Italy 2012 sovereign debt crisis as the target economy):

Endowment: y = 1 (normalized); relative risk aversion: σ = 2; risk-free rate: r = 3% annually; discount factor: β = (1+r)^{−1}
Debt maturity: 1/δ = 7 years (corresponding to Italy’s average debt maturity in 2012)
Default cost: consumption floor c = 0.70 (government can guarantee 70% of normal consumption even in default, with the residual representing trade balance adjustment and output losses)
Rollover crisis probability: λ = 0.5% per quarter (calibrated to historical sovereign crisis frequency in the data)
Crisis zone midpoint parameter ϕ calibrated to set the midpoint of the crisis zone at 90% of GDP debt (consistent with Italy’s 2012 position at the crisis zone boundary)
Optimal safe pair: a* = 0.05 (5% of GDP in reserves); b* = 0.93 (93% of GDP in debt)
With reserves a = a*: bond price at b = b* is higher than without reserves; the b+(a) boundary shifts outward, confirming reserves improve debt sustainability
Without reserves (a=0): for the same debt level b = b*, bond price is lower and rollover risk is higher — the counterfactual quantifies the reserves premium

Sensitivity analysis:

Shorter debt maturity (1/δ = 4 years): optimal reserves rise substantially, to approximately 30% of GDP, because shorter maturity means the government must cover a larger fraction of face value in a rollover crisis
Higher risk aversion (σ > 2): optimal reserves increase (the welfare cost of default is higher, raising demand for precautionary reserves)
Higher default cost (lower consumption floor c): optimal reserves decrease (default is so costly to avoid that the government maintains a small debt stock in the safe zone even without reserves)

Policy implication: The standard IMF prescription to immediately accumulate reserves after a sovereign crisis is suboptimal for highly indebted governments. The paper prescribes the opposite sequence: first reduce debt through fiscal adjustment until the government can jump to (a*, b*) in a single step, then execute the jump by simultaneously issuing debt and accumulating reserves. Importantly, this jump increases both debt and reserves relative to the pre-jump position but is welfare-improving because it eliminates rollover risk — the yield reduction from entering the safe zone more than offsets the higher debt service.

Scope conditions: The model abstracts from: reserves serving exchange rate management or import coverage purposes (only rollover crisis defense modeled); a domestic banking sector; capital controls; negotiated renegotiation after default (default is assumed final). The rollover crisis mechanism is purely self-fulfilling (no fundamental triggers); the calibration is specific to Italy’s 2012 maturity structure, output level, and crisis zone midpoint.

In depth

Q1. What are the three zones, and how do reserves shift their boundaries?

The safe zone S is the set of (b,a) pairs where the government can repay even under a rollover crisis sunspot (ζ=1), because reserves cover the financing shortfall; the crisis zone C is where self-fulfilling rollover crises are possible but not inevitable (government survives if ζ=0); the default zone D is where the government defaults regardless of the sunspot because debt exceeds any payable amount. Reserves shift both boundaries of the crisis zone to higher debt levels (Proposition 2), with the S/C boundary b−(a) rising more steeply than the C/D boundary b+(a), so the safe zone expands and the crisis zone narrows as reserves increase. This shift is the core channel through which reserves improve debt sustainability: at any given debt level b, a higher a makes it more likely that b < b−(a) (i.e., the economy is in the safe zone).

Q2. Why do reserves only matter for long-maturity debt?

With one-period debt, a rollover crisis forces immediate repayment of the full face value b — a total that any realistic reserve stock a « b cannot cover, so reserves provide zero marginal benefit against rollover risk. With long-maturity debt (duration 1/δ), a rollover crisis only requires repayment of the current-period obligation (δb + coupon), which scales with δ; as δ → 0 (near-perpetuity), this obligation becomes arbitrarily small and any positive reserve stock can cover it. Proposition 3 formalizes this by showing that a* > 0 requires δ < δ̄ (a maximum maturity threshold), and Proposition 4 confirms that δ=1 (one-period debt) implies a*=0 regardless of other parameters.

Q3. Why should a government in the crisis zone hold zero reserves?

Holding reserves while in the crisis zone is costly because reserves earn the risk-free rate r, which is lower than the sovereign’s borrowing rate (which includes a rollover risk premium); the cost of holding reserves is therefore the spread between the sovereign’s borrowing cost and the risk-free rate. The benefit of reserves while in the crisis zone is partial: positive reserves reduce the probability of default in a rollover crisis but do not eliminate rollover risk entirely (the economy remains in C for moderate a). The return on accumulating reserves jumps discontinuously when crossing from C into S — only in the safe zone do reserves entirely eliminate rollover risk. Hence the optimal strategy concentrates all reserve accumulation at the transition step when the economy crosses into the safe zone.

Q4. Why does the optimal exit involve simultaneously issuing debt and accumulating reserves?

The jump to (a, b) requires the government to reach a higher reserve level a* and a higher-than-current debt level b* simultaneously; b* > current b because (a*, b*) is inside the safe zone at a debt level the government can afford, not at the minimum possible debt level.** The debt issuance at the moment of transition is financed at the safe-zone bond price (lower spread) rather than the crisis-zone price, making the gross financing cost of the extra debt affordable. More importantly, the simultaneous reserve accumulation moves the economy into the safe zone, raising the bond price immediately: creditors see that a = a* makes b = b* safe, and they lower the yield premium accordingly. This feedback means the jump is self-financing in terms of expected debt service — the yield reduction partially covers the cost of holding reserves.

Q5. Why is the IMF prescription of immediate reserve accumulation suboptimal?

The standard prescription is to begin accumulating reserves as soon as a crisis episode passes, which keeps the government in the crisis zone longer (because reserve accumulation diverts fiscal resources from debt reduction) while paying the spread cost on all reserves held at crisis-zone yields. The paper’s prescription is to instead prioritize debt reduction until the government can make the one-step exit (Proposition 6: NFA(current) > NFA(a*, b*)), then execute the jump. This path reaches the safe zone with total lower expected cost because: (i) time spent in the crisis zone is minimized; (ii) the carry cost of reserves (spread between borrowing rate and safe asset return) is paid only for the brief period of the transition, not throughout the exit path.

Q6. How do reserves affect bond prices and spreads?

Reserves reduce sovereign spreads through two channels: (i) a direct precautionary channel — for a government already in the safe zone, reserves make the safety guarantee more credible and support the high bond price; (ii) a zone-transition channel — crossing from the crisis zone to the safe zone by accumulating reserves to a eliminates the rollover risk premium that was embedded in crisis-zone yields.* In the calibration, at Italy’s 2012 debt level (≈127% of GDP), zero reserves implies the government is in the crisis zone or default zone — bonds trade at distressed prices. At the calibrated safe pair (a*=5%, b*=93%), bonds price at the risk-free rate plus a default risk premium that excludes rollover-crisis risk. The counterfactual (same b*, a=0) yields a lower bond price, quantifying the reserves’ contribution to debt sustainability.

Q7. What does the Italy 2012 calibration imply for actual Eurozone crisis management?

Italy’s 2012 debt-to-GDP ratio of approximately 127% places it well above the optimal target b=93%, suggesting Italy was not in the safe zone even had it held substantial reserves; the primary prescription for Italy at that moment — debt reduction, not reserve accumulation — follows directly from the model’s exit strategy (Propositions 5-6).* The model also implies that European bailout mechanisms (ESM, OMT) shifted the effective boundary of the safe zone by providing contingent external reserves, consistent with the empirical observation that ECB President Draghi’s “whatever it takes” announcement in July 2012 moved Italy’s bond yields toward safe-zone pricing without any actual reserve or debt movement.

Key concepts

rollover crisis : a self-fulfilling coordination failure in which creditors refuse to roll over maturing sovereign debt not because solvency fundamentals require default but because they expect other creditors to refuse; modeled by a sunspot ζ=1 with probability λ that triggers a crisis when the economy is in the crisis zone C.

safe zone : the set of (b,a) pairs where the government can service its debt even under the worst-case sunspot (ζ=1); defined by b < b−(a); entering the safe zone eliminates rollover risk entirely and immediately lowers bond yields to the risk-free rate plus a pure credit-risk premium.

crisis zone : the set of (b,a) pairs where rollover crises are possible but not certain; b−(a) ≤ b ≤ b+(a); the government survives if ζ=0 but defaults if ζ=1; bonds are priced to include a rollover risk premium while in this zone.

optimal exit strategy : Proposition 5 and Corollary 1 — the welfare-maximizing path out of the crisis zone; involves holding zero reserves while reducing debt, followed by a simultaneous jump to (a*, b*) that increases both reserves and debt, moving the economy immediately to the safe zone and eliminating rollover risk in a single step.

long-maturity debt advantage : the property (Proposition 3) that reserves only provide rollover-crisis protection when debt has sufficiently long maturity (δ < δ̄); with short-maturity debt, a rollover crisis forces repayment of the full face value, which no realistic reserve stock can cover; with long-maturity debt, only the near-term cash flow must be covered.

debt-financed reserve accumulation : the seemingly paradoxical simultaneous issuance of new long-maturity bonds and accumulation of reserves at the moment of exit (a=0→a*, b<b*→b*); welfare-improving because the jump moves the economy into the safe zone, lowering bond yields immediately and making the higher debt affordable.

Loose Monetary Policy and Financial Instability

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

This paper provides the first long-run causal evidence that a persistently loose stance of monetary policy — defined as extended periods of low interest rates relative to the neutral rate — significantly raises the probability of a financial crisis several years later. Using a long historical panel of 18 advanced economies (approximately 1870–2020, excluding world wars), the paper estimates local projection (LP) regressions in which the stance is measured as the 5-year backward moving average of (r – r*), with r* from the Del Negro–Giannoni–Gaballo–Tambalotti (DGGT) factor model. The OLS baseline finds that a 1 percentage-point (pp) looser average stance over a 5-year window raises the 3-year financial crisis probability by 2.2pp at a 5–7 year horizon and 3.3pp at a 7–9 year horizon, against an unconditional base of 10.5%. To address the endogeneity of monetary policy to pre-existing economic conditions, the authors construct an instrumental variable based on the international trilemma of open-economy finance: for countries pegging their exchange rate, changes in the base-country interest rate orthogonal to domestic economic conditions provide exogenous variation in domestic rates, weighted by a capital mobility index. IV estimates are substantially larger: 1pp looser average stance raises crisis probability by 5.5pp at 5–7 years and 15.5pp at 7–9 years, indicating that OLS understates the causal effect because accommodative policy is endogenously adopted during recessions when crisis risk is already low. The same loose-policy stance significantly raises the probability of entering R-zones — periods of credit market overheating identified by Greenwood, Hanson, Shleifer, and Sørensen (2022) as harbingers of financial crisis — and, with a lag of 6–9 years, raises the probability of historically low GDP growth (below the 20th percentile of the cross-country distribution). The evidence supports a growth-risk tradeoff: loose policy may deliver short-term stimulus, but at a meaningful cost in medium-term financial fragility and real tail risk.

Data and sample (Section 2): 18 advanced economies, long historical panel from the 1870s to 2020, excluding the world war episodes (pre-1914, interwar, and 1939–1945 conflicts), yielding an unbalanced panel of roughly 1,500 country-year observations. Financial crisis dates from the Jordà–Schularick–Taylor (2017) Macrofinancial History Database. The stance measure is r_{i,t} − r*{i,t}, where r*{i,t} is country-specific and time-varying, estimated from a factor model (DGGT); the 5-year backward moving average smooths over cyclical fluctuations and captures the sustained character of monetary accommodation that theory associates with financial fragility buildup. The unconditional 3-year financial crisis probability in the post-WWII sample is 10.5%.

Empirical methodology (Section 3): Local projections (Jordà 2005) with financial crisis indicator B_{i,t} as the outcome and 5-year backward MA of stance as the key regressor, estimated at horizons h = 0 to 12 years:

B_{i,t+h} = α_{i} + β_{h} · stance_{i,t} + γ_{h} · X_{i,t} + ε_{i,t+h}

Controls X_{i,t} include: lagged B (crisis history), lagged stance, lagged log GDP growth, lagged credit-to-GDP growth, lagged inflation, and lagged short-term rate — plus global controls (cross-country averages) to absorb common factors. Country fixed effects α_{i} and Driscoll–Kraay (1998) standard errors with h lags account for serial correlation and cross-sectional dependence. The coefficient −100β_{h} converts to the change in 3-year crisis probability (in percentage points) per 1pp tighter stance, so a positive −100β_{h} means a looser stance raises crisis probability.

OLS baseline results (Section 4.1): The baseline LP-OLS model (Figure 3, panel (a)) finds no significant association between stance and crisis probability in the first 4 years after the policy window — loose monetary policy does not immediately raise crisis risk. Crisis probability rises meaningfully from horizons 5 onward:

5–7 year horizon: +2.2pp crisis probability per 1pp lower average stance
7–9 year horizon: +3.3pp crisis probability per 1pp lower average stance
Very loose indicator (stance at the 20th percentile, approximately −2.5%): +13pp at the peak horizon; when stance = −1%, crisis probability is approximately 16% (vs unconditional 10.5%)
Alternative chronology (Baron–Verner–Xiong 2021, bank equity crash events): +5.3pp at the 8-year horizon per 1pp lower stance — broadly consistent with the baseline

R-zone analysis (Section 4.2): Greenwood, Hanson, Shleifer, and Sørensen (2022) define R-zones as periods when household or business credit grows anomalously fast — a pre-crisis credit overheating indicator. LP-OLS estimates show:

1pp lower average stance → +3.2pp household R-zone probability within 5 years; +1.8pp business R-zone probability
Very-loose binary indicator (bottom quintile of stance) → +9.6 to 10.8pp R-zone probability These magnitudes confirm that the financial instability buildup operates through the canonical credit channel: loose monetary policy inflates credit volumes first, with financial crises following several years later.

Eurozone periphery illustration (Section 4.2): The pre-2008 divergence between the ECB’s common stance and country-specific neutral rates is shown in Figure 10. Core eurozone countries (Belgium, Denmark, France, Germany, Netherlands) experienced tight-to-neutral effective stances during 2003–2008, while periphery countries (Ireland, Italy, Portugal, Spain) faced loose stances of up to approximately −10pp. The periphery’s credit boom — in total credit, household credit, mortgage credit, and house prices — far exceeded the core’s over 2002–2008, consistent with the LP-OLS estimates. This pattern motivates the IV strategy.

IV construction (Section 4.3): The instrument follows Jordà, Schularick, and Taylor (2020) and uses the international monetary trilemma. For countries pegging their exchange rate (identified by exchange rate stability), the domestic interest rate is mechanically tied to the base country’s rate; the instrument is:

z_{i,t} = k_{i,t} × (ΔR_{b(i,t),t} − ΔR̂_{b(i,t),t})

where k_{i,t} is a Chinn–Ito capital mobility index, b(i,t) is the base country for country i in year t, ΔR_{b,t} is the actual change in the base country’s interest rate, and ΔR̂_{b,t} is the predicted change obtained from a first-stage regression of base-country rates on base-country economic conditions. The residual captures shifts in the base country’s rate that are orthogonal to economic fundamentals and are transmitted to pegged countries via the exchange rate commitment — exogenous from the perspective of the pegged country. Ten lags of z are used as instruments for the 5-year moving average of stance. The Kleibergen–Paap (2006) test for weak instruments exceeds 10 across all first-stage regressions.

IV second-stage results (Figure 11): The IV estimates are substantially larger than OLS throughout the horizon:

5–7 year horizon: +5.5pp crisis probability per 1pp lower average stance (vs +2.2pp OLS)
7–9 year horizon: +15.5pp per 1pp lower average stance (vs +3.3pp OLS)
With stance = −1%, the IV-implied crisis probability is 16% at 5–7 years; at 7–9 years, medium-term crisis risk more than doubles from the unconditional 10.5% to over 20%
These IV estimates are 2.5× to 5× the OLS, implying substantial attenuation bias in OLS: monetary policy is endogenously loosened during downturns when crisis risk is already low, so reverse causality compresses the OLS coefficient toward zero

IV R-zones (Figure 13): LP-IV estimates for household and business R-zones confirm the LP-OLS direction — loose monetary policy raises the likelihood of entering credit market overheating as defined by Greenwood et al. (2022), at economically relevant magnitudes in the post-WWII period.

Growth-risk tradeoff (Section 5): To close the circle between monetary policy, financial fragility, and real activity, the paper estimates LP models with tail real growth indicators as outcomes. Define Low-Output-Growth_{i,t} = 1{Δ₃(log Y_{i,t}) < 20th percentile} — an indicator for historically low 3-year real GDP per capita growth. The 20th percentile in the sample corresponds to positive growth of 1.32%. Results (Figure 14a):

No significant relationship between stance and Low-Output-Growth probability in the first 4–5 years — consistent with the idea that short-term stimulus benefits materialize before financial fragility builds
At horizons 6–9 years: when stance is 1pp looser, the probability that Low-Output-Growth turns on rises by 2pp (at 8 years) and 3pp (at 9 years), significant at the 32% (5%) level at h=8 (h=9)
For Barro–Ursua (2008) disaster events (peak-to-trough falls in real GDP per capita of ≥10%, 3.2% of sample observations): the disaster probability follows a similar hump — slightly lower disaster risk in the short term under loose policy (the stimulus dividend), followed by materially higher disaster risk at 7–9 years (Figure 14b)
Conclusion: loose monetary policy produces a growth-risk tradeoff, where short-run stimulus gains are offset by elevated medium-term tail risk in financial and real activity

Scope conditions: The paper documents empirical regularities from long historical data; it does not build or estimate a structural model, so it cannot formally decompose the mechanisms driving the reduced-form effects (risk-taking channel, credit-boom channel, or asset-price inflation). The stance measure (r − r*) depends on estimates of the time-varying neutral rate, which carries its own uncertainty; robustness using alternative r* measures is presented. The IV relies on countries pegging their exchange rate, which varies across time and countries; results may not generalize to monetary unions or fully flexible exchange rate regimes where the trilemma applies differently. The sample of 18 advanced economies may not be representative of emerging market contexts. The analysis is positive, not normative: it does not compute welfare-optimal monetary policy rules that account for the intertemporal tradeoff.

In depth

Q1. Why does the paper measure stance as a 5-year backward moving average rather than the contemporaneous rate gap?

The 5-year moving average captures the sustained character of loose monetary policy that theory associates with financial fragility accumulation; a single quarter of low rates does not meaningfully alter bank balance sheets or credit market dynamics, but several years of below-neutral rates allow risk appetite to build up gradually through reach-for-yield behavior, leveraging, and lending standard erosion. The backward average also corresponds more naturally to the length of a typical financial cycle (Borio 2014), over which excessive credit and asset price growth gradually accumulates before a crisis materializes. Using the contemporaneous rate gap would miss the cumulative nature of the stance and would likely attenuate the estimated effect toward zero because any individual year’s rate is highly endogenous to the current cyclical position.

Q2. Why are the IV estimates so much larger than the OLS estimates, and what does this imply about the direction of endogeneity bias?

The IV estimates (5.5pp at 5–7 years, 15.5pp at 7–9 years) are roughly 2.5× to 5× the OLS estimates (2.2pp and 3.3pp), implying that OLS is severely attenuated by reverse causality: central banks endogenously loosen policy during recessions and financial downturns — precisely the states in which crisis risk is temporarily depressed — so the OLS coefficient conflates the true causal effect (loose policy raises crisis risk) with an offsetting correlation (loose policy coincides with post-crisis low-risk states). The trilemma IV isolates the exogenous component of the stance — changes transmitted to pegged countries by the base-country’s monetary decisions that are orthogonal to the pegged country’s own economic conditions — and strips away this endogeneity, revealing that the true causal effect on crisis risk is substantially larger than OLS suggests. This finding matters for policy: it implies that the textbook concerns about risk-taking and financial cycle effects of low rates are not only statistically detectable but quantitatively much more important than naive correlations suggest.

Q3. How does the trilemma instrument achieve exogenous variation in domestic monetary conditions?

For countries pegging their exchange rate, the trilemma forces domestic interest rates to shadow the base country’s rate (usually the US, Germany, or the UK); when the base country cuts rates for reasons driven by its own domestic conditions — unrelated to the pegged country’s economic state — the pegged country inherits looser monetary conditions through the exchange rate commitment. The instrument refines this logic by: (i) using the residual of the base-country rate change after partialling out the base country’s own macro fundamentals, eliminating the component of the base-country cut that might be correlated globally with crisis risk; and (ii) weighting by the capital mobility index k_{i,t}, so that the instrument is strongest when capital flows freely and the trilemma constraint is tightest. The exclusion restriction requires that these exogenous shifts in the base-country rate affect the pegged country’s financial crisis probability only through the channel of domestic monetary conditions, not through other international spillovers (e.g., trade or capital flow channels).

Q4. What is the timing pattern of crisis risk accumulation and what explains the absence of an effect in the first four years?

Crisis risk does not rise in the first 4 years after a period of loose monetary policy, rises sharply at 5–7 years (5.5pp IV), and peaks at 7–9 years (15.5pp IV) — the “slow burn” pattern reflects the lag between credit market overheating and realized financial crises. The mechanism links stance to crisis through the intermediary of credit booms: the paper shows (Figure 13) that R-zones (credit overheating) build within 5 years of loose policy, and the literature (Schularick–Taylor 2012; Jordà–Schularick–Taylor 2015) has established that credit booms predict financial crises with similar multi-year lags. The short-term absence of elevated crisis risk is consistent with — and not in tension with — the Barro–Ursua disaster results, which show lower disaster probability in the short term under loose policy, capturing the genuine stimulus dividend before the financial fragility materializes.

Q5. What are R-zones and what role do they play in the paper’s chain of evidence?

R-zones (Greenwood, Hanson, Shleifer, and Sørensen 2022) are periods when household or business credit grows anomalously fast relative to historical norms, identified as leading indicators of subsequent financial distress; the paper uses them to establish a link in the causal chain: loose monetary policy → credit overheating → financial crisis, providing a mechanism-level bridge between the reduced-form IV results. The R-zone regressions show that loose policy raises the household R-zone probability by 3.2pp and business R-zone by 1.8pp within 5 years (OLS; LP-IV confirms the direction), implying that the credit channel is active within the financial cycle window before the eventual crisis materializes. This is important because it distinguishes the paper’s finding from a pure statistical correlation between stance and crisis: the financial system’s credit overheating is a detectable intermediate state that connects loose policy to the eventual fragility outcome.

Q6. What does the growth-risk tradeoff finding imply for the welfare calculus of monetary accommodation?

The short-term benefits of loose policy (higher output, lower unemployment in the first 4–5 years) are offset in expectation by a materially elevated probability of historically severe output collapses at 6–9 year horizons; the Barro–Ursua disaster evidence further suggests a slight reduction in disaster risk in the short term followed by a large increase at medium horizons, which is exactly the intertemporal tradeoff that makes evaluating accommodative policy difficult in real time. The growth-risk tradeoff does not by itself deliver an optimal policy prescription — the tradeoff between near-term stimulus and medium-term tail risk depends on the discount rate, the size of the respective effects, and the welfare cost of financial crises — but it establishes that any evaluation of prolonged accommodative policy that considers only its near-term benefits is incomplete. The finding is consistent with the Growth-at-Risk literature (Adrian et al. 2019, 2022) and with the BIS’s documented concerns about financial cycle risks during the 2010s low-rate environment.

Q7. Why is the endogeneity of monetary policy to financial conditions particularly important for this paper’s identification?

A central objection to any empirical relationship between low rates and subsequent financial crises is that central banks loosen policy in response to financial stress and economic weakness — states in which crisis risk is already elevated or depressed by pre-existing vulnerabilities; the OLS coefficient would then reflect the reverse-causal channel (crisis risk → loose policy) as much as the forward-causal channel (loose policy → crisis risk), making it impossible to infer causation. The trilemma IV directly addresses this by exploiting variation in monetary conditions that is literally determined by a different country’s central bank for that country’s domestic reasons — making it extremely implausible that the pegged country’s crisis risk influenced the base country’s rate decision in ways that satisfy the exclusion restriction. The result that IV exceeds OLS by 2.5–5× implies the endogeneity was strongly attenuating (loose policy coincides with low-risk states, biasing OLS downward), and the true causal effect of sustained accommodation on crisis risk is considerably larger than the raw correlations would suggest.

Q8. How does the paper relate to and distinguish itself from the theoretical risk-taking channel literature?

The paper is entirely empirical and does not propose a structural model; it complements the theoretical risk-taking channel literature (Borio–Zhu 2012; Dell’Ariccia–Laeven–Marquez 2014; Bekaert–Hoerova–Lo Duca 2013) by providing the first long-run causal evidence that the reduced-form prediction of that literature — loose policy raises systemic financial fragility — holds in the historical data. Existing empirical work had focused on high-frequency or cross-sectional responses of individual bank risk metrics to monetary policy surprises; the paper’s long-run LP approach is better suited to capturing the slow financial cycle dynamics that theory predicts and cannot be identified in event-study windows. The IV strategy resolves the identification problem that had stymied prior cross-country empirical work, where reverse causality confounded the relationship.

Key concepts

monetary policy stance : in this paper, the 5-year backward moving average of the policy rate gap (ri,t − r*i,t), where r* is the time-varying natural rate from the DGGT factor model; the sustained character of the measure captures the cumulative accommodation relevant for financial cycle dynamics, as opposed to short-lived rate cuts that do not materially affect bank portfolio decisions or credit standards.

trilemma IV : the paper’s instrumental variable for monetary stance, constructed for exchange-rate pegging countries as the capital-mobility-weighted residual of base-country interest rate changes (orthogonal to the base country’s own macro conditions); exploits the international monetary trilemma — a country pegging its exchange rate surrenders monetary autonomy and must match the base country’s rate regardless of its own economic conditions — to generate exogenous variation in the domestic stance.

local projections (LP) : the empirical methodology (Jordà 2005) estimating a separate OLS regression for each horizon h = 0,…,12, with the future crisis indicator (or R-zone, or low growth indicator) at horizon h as the outcome and the current stance measure as the key regressor; provides flexible impulse response functions without imposing the dynamic restrictions of a VAR, and allows the timing of crisis risk buildup to emerge directly from the data.

R-zones : periods of credit market overheating as defined by Greenwood, Hanson, Shleifer, and Sørensen (2022) in which household or business credit grows anomalously fast; used in this paper as an intermediate-state indicator that links loose monetary policy (identified 1–4 years earlier) to subsequent financial crisis (materializing 5–9 years later), supporting the credit-channel interpretation of the reduced-form IV results.

growth-risk tradeoff : the paper’s characterization of the intertemporal welfare consequences of sustained monetary accommodation; loose policy delivers short-term output gains (visible as slightly lower disaster probability at short horizons) but raises the probability of historically low real GDP growth at 8–9 year horizons by 2–3pp and elevates medium-term financial crisis risk by up to 15.5pp per 1pp looser average stance, implying that assessments of accommodative policy based only on near-term stimulus benefits substantially understate the medium-term costs.

Monetary and Macroprudential Policy and Welfare in an Estimated Four‐Agent New Keynesian Model

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

This paper introduces a four-agent estimated New Keynesian DSGE model—comprising banked simple households, underbanked simple households, firm owners, and bank owners—to examine agent-specific and social welfare effects of monetary and macroprudential policy, estimated on U.S. quarterly data (1985Q1–2016Q4) via Bayesian methods. The model features two layers of endogenous default probability (for borrowers and banks), nominal, real, and financial frictions, and trend inflation and stochastic growth. The optimal bank capital requirement ratio (CRR) is estimated at 12.6%, which is 2.1% above Basel III’s 10.5%; increasing CRR up to approximately 12.2% raises welfare for all four agent types, though with smaller gains for credit-reliant simple households and firm owners. Countercyclical capital buffers benefit firm owners and bank owners with smaller gains for simple households. Coordinated monetary and macroprudential policy yields higher social welfare than non-coordinated policies.

In depth

Q1. Why does the paper use four agent types instead of the usual borrower-saver distinction?

The standard borrower-saver split lumps together all interest-earning agents—including both simple deposit-holding households and wealthy bank owners—so that macroprudential policies that shift surplus from borrowers to savers appear to benefit the simple household and the banker equally; the four-agent framework separates these groups and allows for heterogeneous welfare effects. Population shares are calibrated using Compustat and the Survey of Consumer Finances (firm owners and bank owners as shareholders of non-financial and financial firms) and the National Survey of Unbanked and Underbanked Households (underbanked simple households with very limited access to banking services).

Q2. What is the optimal CRR and how does it compare to existing benchmarks?

The optimal social CRR is estimated at 12.6%, which is 2.1% higher than Basel III’s 10.5%, 4.6% higher than Basel II’s 8%, and 3.6% higher than the 9% optimal CRR of Mendicino et al. (2019) who use a borrower-saver welfare framework. Increasing the CRR up to approximately 12.2% improves welfare for all four agent types, though unequally: simple households and firm owners who rely on credit see smaller gains. Above 12.2%, stricter CRR harms firm owners and simple households (tighter credit reduces activity), while bank owners continue to gain via higher capital income share until the CRR exceeds 25.9%, above which even bank owners are harmed as loans fall dramatically.

Q3. How do countercyclical capital buffers and loan loss provisions affect welfare by agent type?

Countercyclical capital buffers support firm owners and bank owners with smaller gains for the two simple household types; countercyclical loan loss provisions improve social welfare only for specific shocks and benefit underbanked simple households and firm owners at the expense of bank owners and banked simple households. The asymmetry reflects the different income streams: bank owners’ income derives primarily from loan returns and capital gains on bank equity, while underbanked simple households are most sensitive to credit availability. Loan loss provisions affect the timing of income recognition and loss absorption, generating distributional trade-offs that differ from those of capital requirements.

Q4. What are the gains from coordinating monetary and macroprudential policy?

Coordinating monetary and macroprudential policy yields higher social welfare than assigning each policy to an independent authority targeting its own objective, demonstrating that the interaction between interest rate policy and bank capital regulation matters for welfare outcomes. Investment shocks (27.41% of GDP growth variance) and financial risk shocks (~20%) are quantitatively important in this interaction. The model’s rich friction structure means that optimal monetary policy must account for how macroprudential policy changes the credit supply environment, and vice versa; failing to coordinate creates inefficiencies that coordinated policy avoids.

Key concepts

four-agent model : the model’s typology distinguishing banked simple households, underbanked simple households, firm owners, and bank owners; enables agent-specific welfare analysis of macroprudential policy with heterogeneous income streams and credit access. optimal capital requirement ratio (CRR) : the bank capital-to-assets ratio that maximizes social welfare; estimated at 12.6% in this model; 2.1% above Basel III’s current 10.5% requirement. countercyclical capital buffer (CCyB) : a macroprudential tool requiring banks to hold additional capital during economic expansions to be released in downturns; shown here to benefit firm owners and bank owners with smaller gains for simple households. dynamic loan loss provisions : a macroprudential tool requiring banks to build provisions against future expected losses during expansions; shown here to have welfare effects that depend on the source of the shock and to benefit different agent types than capital requirements.

Monetary Policy and Endogenous Financial Crises

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

This paper asks whether a central bank should deviate from strict inflation targeting (SIT) to promote financial stability, studying the question in a textbook New Keynesian model augmented with capital accumulation and microfounded endogenous credit-market crises. The model embeds two financial frictions — limited contract enforcement and asymmetric information about firm productivity — that together generate fragile credit markets in which, when productive firms’ marginal return on capital falls below a threshold, the credit market collapses (a “financial crisis”). The calibrated model matches the empirical regularity that economies spend roughly 8% of time in financial crises. The central finding is threefold: (1) monetary policy affects crisis probability both in the short run (via output and markups) and in the medium run (via capital accumulation dynamics); (2) a Taylor-type rule that responds to output fluctuations — rather than SIT — reduces crisis incidence and raises welfare, with TR93 (φ_y = 0.125) generating a 0.016% permanent consumption equivalent gain over SIT; (3) prolonged unexpected monetary easing followed by abrupt tightening is itself a mechanism that can trigger financial crises. These findings imply a genuine price-versus-financial-stability tradeoff and challenge the “divine coincidence” view that SIT is sufficient in the presence of financial frictions.

Layer 1: Overview

Boissay, Collard, Galí, and Manea build a New Keynesian model with capital accumulation and endogenous credit-market crises to study whether central banks should deviate from inflation targeting to promote financial stability. The model departs from the textbook three-equation NK framework in four ways: capital accumulation that allows persistent booms, firm heterogeneity in productivity that generates a credit market, financial frictions (limited enforcement and asymmetric information) that make the credit market fragile, and global (nonlinear) solution methods that can capture the boom-bust dynamics. A financial crisis — credit-market collapse — occurs when productive firms’ marginal return on capital falls below the minimum loan rate that unproductive firms require to willingly lend. The model is calibrated so that the economy spends 8% of time in crisis (consistent with cross-country evidence from Reinhart and Rogoff, Laeven and Valencia, and Baron et al.) and the additional parameter governing financial frictions (the proportion μ = 2.42% of unproductive firms) is chosen to match this target. Three main findings emerge: monetary policy operates through short-run aggregate demand channels and a medium-run capital accumulation channel; a Taylor-type rule that responds to output improves welfare over SIT, with TR93 raising permanent consumption by 0.016% relative to SIT; and discretionary loosening followed by abrupt tightening can itself generate crises.

In depth

Q1. How do financial crises arise in the model, and what is the triggering condition?

A financial crisis in the model is a credit-market breakdown in which the credit market collapses to autarky: unproductive firms stop lending because the loan rate they can credibly demand falls below the return on holding idle capital. The friction generating this fragility is a combination of limited contract enforcement (firms that borrow to purchase capital can abscond with sale proceeds) and asymmetric information about idiosyncratic productivity. Together, these frictions imply that productive firms cannot borrow beyond an incentive-compatible leverage cap, and that the minimum loan rate required to induce unproductive firms to lend is a positive threshold $\bar{r}^k = \mu/(1-\mu) - \delta$. A crisis occurs if and only if productive firms’ marginal return on capital $r_t^k$ falls below this threshold — which happens at the end of a protracted boom when the economy has accumulated excess capital, driving down marginal productivity. The average simulated crisis is triggered by a roughly three-standard-deviation negative TFP shock (around 1.5% below steady state) hitting an economy where the capital stock has been elevated by a long sequence of positive shocks. The same shock would not trigger a crisis at lower capital stocks — the capital overhang is a necessary precondition.

Q2. Through what channels does monetary policy affect financial stability, and how do short-run and medium-run channels differ?

The paper identifies three channels: a Y-channel (output), an M-channel (markups), and a K-channel (capital accumulation), with the K-channel operating only in the medium run through expectations about the policy rule. In the short run, a rate hike that compresses output and raises markups reduces the marginal return on capital, pushing the economy closer to a crisis — a destabilizing short-run effect. In the medium run, however, a commitment to lean against output booms (high φ_y) slows capital accumulation during expansions through two mechanisms: (i) it reduces investors’ expected returns from expansion, dampening incentives to accumulate capital; and (ii) it provides households with implicit insurance against aggregate shocks, reducing precautionary savings. Because capital accumulation is slow, these medium-run effects only materialize over multiple years and require that the central bank pre-commit to the rule. Expectations of the rule thus shape the boom dynamics before any crisis.

Q3. What does the welfare comparison across Taylor rules reveal about the price-versus-financial-stability tradeoff?

Responding to output raises welfare in the presence of financial frictions, even though it reduces welfare in the frictionless benchmark, generating a genuine price-versus-financial-stability tradeoff. Under strict inflation targeting, the welfare loss relative to the first best is 0.11% in consumption equivalent variation, entirely attributable to financial crises (since SIT eliminates price distortions). Responding more aggressively to output (higher φ_y) reduces crisis incidence from 9.85% of time (under SIT) to as low as 0.45% (under φ_y = 0.75), but raises inflation volatility. The welfare gain is non-monotone in φ_y: under the baseline φ_π = 1.5, welfare is highest around φ_y ≈ 0.5–0.6, and declines for higher φ_y as markup volatility (M-channel) more than offsets the financial stability gain. TR93 (φ_y = 0.125) already delivers 0.016% higher permanent consumption than SIT.

Q4. What is the role of monetary policy discretion in generating financial crises?

The model shows that sustained discretionary loosening followed by abrupt tightening can itself trigger a crisis, formalizing the “rates too low for too long” narrative of the 2007-08 Global Financial Crisis. Using only monetary policy shocks (either AR(1) with ρ = 0.5, σ = 0.25% or i.i.d.) as the source of aggregate uncertainty, the average simulated crisis follows a long period of unexpectedly accommodative policy that feeds an investment boom, with the crisis triggered by three consecutive unexpected rate hikes (persistent shock case) or a single 60-basis-point jolt (i.i.d. case) at the end of the boom. This is consistent with empirical evidence (Schularick, Ter Steege, and Ward 2021) that unanticipated rate hikes at the end of a boom are more likely to trigger crises than prevent them.

Q5. How much additional welfare gain is available from a “backstop” commitment that forestalls crises entirely?

A nonlinear backstop rule — under which the central bank deviates from its normal rule just enough to prevent a crisis whenever one would otherwise occur — nearly eliminates the welfare cost of financial crises, requiring only modest policy deviations. Under SIT, the backstop improves welfare by 0.11% in consumption equivalent variation — the full cost of crises — leaving a residual welfare loss of only 0.0013% relative to the first best. The backstop requires rate cuts of on average 20 basis points below TR93, or tolerance of 0.6 percentage points of extra inflation above the SIT target, in the periods when a crisis would otherwise emerge. The tradeoff is that backstopping increases the frequency with which the central bank must intervene, since knowing that the bank will intervene can increase the financial sector’s risk-taking (fragility).

Q6. How does the paper’s approach to microfounding crises compare to reduced-form alternatives?

Unlike Woodford (2012) and Gourio, Kashyap, and Sim (2018), who use reduced-form functions linking credit or leverage gaps to crisis probability, this paper derives crisis probability and severity endogenously from first principles, with implications for the policy prescriptions. Because crises and their depth are both endogenous to policy, the model can determine not only how policy affects the probability of a crisis but also how it affects the size of the output loss conditional on a crisis. This distinction matters: the model shows that not all credit booms are equally dangerous — a boom accompanied by genuine productivity gains carries lower crisis risk than an equivalent capital accumulation driven by precautionary saving externalities. The endogenous crisis mechanism also implies that some forms of leaning that superficially appear to reduce crisis probability may actually increase it by raising markup volatility, an effect absent from reduced-form models.

Key Concepts

divine coincidence : the standard New Keynesian result that strict inflation targeting (SIT) simultaneously eliminates output gap fluctuations and is welfare-optimal in the absence of financial frictions; the paper shows this coincidence breaks down when the credit market is fragile, because SIT does not internalize the externalities driving capital overhang and crisis risk.

financial crisis (in the model) : the autarkic equilibrium of the credit market, in which productive firms’ marginal return on capital falls below the minimum loan rate required for unproductive firms to willingly lend; characterized by credit-market collapse, capital misallocation (unproductive firms retain idle capital), severe output loss, and inflationary pressure.

K-channel of monetary policy on financial stability : the medium-run mechanism by which a commitment to respond strongly to output fluctuations dampens capital accumulation during booms, reducing the likelihood of the excess capital overhang that triggers crises; operates through expectations and requires multi-year lead times, distinguishing it from the short-run output (Y) and markup (M) channels.

savings glut externality : the tendency of households to over-accumulate capital relative to the socially efficient level in anticipation of a crisis, because individual households do not internalize the aggregate effect of their precautionary saving on the economy’s distance from the credit-market collapse threshold; identified by Boissay, Collard, and Smets (2016) and present in this model as a driver of endogenous boom-bust dynamics.

backstop rule : a nonlinear monetary policy rule in which the central bank follows a standard Taylor or SIT rule in normal times but commits to deviating just enough from that rule to forestall a financial crisis whenever one would otherwise emerge; shown to nearly eliminate the welfare cost of crises at the cost of modest and infrequent policy deviations, with the side effect of increasing the frequency of needed interventions.

Monetary Policy and Sovereign Risk in Emerging Economies (NK-Default)

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

Layer 1: Overview

This paper develops a New Keynesian small open economy model with endogenous sovereign default — the NK-Default framework — and uses it to study the interplay between monetary policy and sovereign risk in emerging markets. The core finding is that sovereign default risk amplifies inflation volatility through an expectations channel: when default risk rises, forward-looking firms increase prices in expectation of high future inflation and depressed consumption during a potential default, so that current inflation rises even before any default occurs. Conversely, tight monetary policy disciplines government overborrowing by raising the cost of domestic monetary distortions, which the government internalizes by reducing its borrowing. Calibrated to eight emerging-market inflation targeters (Brazil, Chile, Colombia, Mexico, Peru, Philippines, Poland, South Africa) over 2004–2019, the model quantitatively matches the positive comovement of spreads with inflation and nominal rates, and the temporary nature of inflation events (approximately 4.5% inflation spike, 2.3% spread increase, resolved within roughly a year). Counterfactual experiments find that default risk accounts for approximately 50% of both inflation business-cycle volatility and the inflation increase during these events, and that a 1% tighter monetary policy would reduce spreads by about 0.3% during inflation events. An interest rate rule augmented to respond to default risk dominates strict inflation targeting in welfare and reduces mean spreads by 2.2 percentage points; strict inflation targeting is not the optimal monetary regime when sovereign risk is present.

In depth

Q1. What is the structural architecture of the NK-Default model?

The NK-Default framework combines the standard New Keynesian small open economy model of Gali and Monacelli (2005) with the Eaton-Gersovitz (1981) sovereign default structure extended to long-term foreign-currency debt, producing a model in which households, firms, a monetary authority, and a fiscal government all interact. Households consume domestic and foreign goods and supply labor; intermediate goods producers are monopolistically competitive and set prices subject to Rotemberg (1982) quadratic adjustment costs, generating a forward-looking New Keynesian Phillips Curve (NKPC); the monetary authority follows a nominal interest rate rule targeting domestic goods inflation; and the government borrows internationally in long-term foreign-currency perpetuity bonds, choosing each period whether to repay or default, with default leading to temporary exclusion from international financial markets and a transitory productivity reduction. The bond price schedule compensates risk-neutral international lenders for expected losses from default and falls with the government’s indebtedness. A key methodological choice is the use of global solution methods rather than local approximations, because the nonlinear dynamics around default are central to the mechanisms.

Q2. What is the default amplification mechanism, and how does it transmit to inflation?

Default amplification operates through an expectations channel encoded in the forward-looking NKPC: when default risk rises, firms’ expectations of higher future inflation (during the inflation that would accompany a default event) and lower future consumption (because default depresses productivity and restricts borrowing) both increase, causing firms to raise current prices, generating current inflation without any contemporaneous policy change. Formally, the NKPC relates current inflation π to a unit-cost term and to the expectation term E[Y’u’_C(π’-π)π’], which increases with default risk because default states feature high inflation and high marginal utility. The resulting current inflation increase then triggers the monetary authority’s interest rate rule to tighten, which in turn depresses consumption through the Euler equation, amplifying the monetary distortion (wedge). In the simplified quasi-linear preferences setting, higher borrowing B’ increases functions F and M — the expectation terms in the NKPC and Euler equation — and Proposition 1 establishes formally that higher borrowing raises default risk, inflation, the nominal domestic rate, and the monetary wedge under Assumption 1.

Q3. How does monetary policy discipline sovereign borrowing?

Tight monetary policy disciplines government overborrowing because the government internalizes the additional costs that monetary distortions impose on the economy: when the monetary authority raises interest rates, the resulting monetary wedge — the gap between the marginal product of labor and households’ marginal rate of substitution — acts as an additional cost on borrowing from the government’s perspective, discouraging excessive debt accumulation. Proposition 2 establishes this formally: under Assumption 2 (one-time deviation from constrained efficiency), a policy rate i > i_ST (above the strict-inflation-targeting rate) generates a positive monetary wedge that modifies the government’s optimal borrowing condition with an additional term reflecting the cost to the sovereign of the higher wedge its borrowing induces. Contractionary monetary policy thus reduces the incentive to borrow and lowers equilibrium default risk. The paper also derives Proposition 3: a default-risk monetary rule of the form i = ī·Φ^αD can achieve the constrained-efficient default risk and an arbitrarily small monetary wedge simultaneously, by choosing αD appropriately — meaning that targeting default risk can address both the pricing friction and the overborrowing incentive.

Q4. What are the quantitative findings on default amplification and the disciplining mechanism?

Quantitatively, default risk accounts for approximately 50% of inflation business-cycle volatility and approximately 50% of the inflation increase during the temporary inflation events (4.5 p.p. inflation spike, 2.3 p.p. spread increase, nominal rate rise from baseline 5–6% to 8–9%), based on comparison with a reference model without default. For the disciplining mechanism, panel-data regressions using monetary policy shocks recovered from estimated Taylor rules across the eight countries find that a 1% contractionary monetary shock reduces sovereign spreads, consistent with model predictions. During the inflation events, a 1% tighter monetary policy would have reduced spreads by approximately 0.3 percentage points. Comparing alternative monetary policy regimes against strict inflation targeting (which implements flexible-price allocation): the baseline interest rate rule (responding only to inflation) reduces mean spreads by 0.5 percentage points relative to strict inflation targeting; an augmented rule that also responds to default risk reduces mean spreads by 2.2 percentage points. Welfare under the baseline rule exceeds that under strict inflation targeting, and welfare under the default-risk rule exceeds both, with the ranking holding across all robustness extensions.

Q5. How does the model fit the data across targeted and untargeted moments?

The model is calibrated to match key business-cycle statistics of the eight emerging-market inflation targeters and successfully replicates several untargeted moments, including the positive correlations of spreads with inflation (mean 0.5 across countries in data) and nominal rates (mean 0.3), the relative volatility of inflation to output (mean 0.8), and the mean spread level of approximately 2%. The temporary inflation events — constructed as windows around periods of elevated inflation — are matched with a combination of low productivity shocks and expansionary monetary shocks, and the model’s impulse response functions for inflation, output, nominal rates, and spreads during these events align with the empirical paths. The model also fits the positive elasticity of inflation expectations to default risk and the negative elasticity of spreads to monetary policy shocks, both of which are estimated from data and used as untargeted validation moments. Structurally, the model is parameterized to match the mean and volatility of inflation, spreads, and the correlation of spreads with output (mean -0.5 across countries), among other moments.

Q6. How do the model’s results hold up across extensions, especially local currency debt and discretionary monetary policy?

The main results — default amplifies inflation, tight monetary policy disciplines borrowing, and the default-risk rule dominates strict inflation targeting — are robust across all extension economies, including the case of local currency sovereign debt, alternative default costs (no productivity loss, endogenous domestic financial frictions), and loose monetary policy during defaults. In the local currency debt extension, which introduces the classic incentive to erode debt via inflation, the paper shows that monetary discretion delivers substantially worse outcomes: average inflation doubles relative to the commitment case and — crucially — sovereign spreads also double under discretion, because market participants anticipate the inflationary incentive. This result shows that the disciplining benefits of commitment in monetary policy rules extend to the sovereign debt dimension: the country’s ability to commit to a rule lowers spreads by reducing the expected future inflation that lenders must be compensated for. The endogenous financial frictions extension — in which banking sector health depends on nominal rates and spreads — generates similar monetary-fiscal interactions, confirming that the mechanisms are not specific to the productivity-cost assumption.

Q7. What is the paper’s relationship to the literature on nominal rigidities and sovereign default?

The NK-Default framework differs critically from related papers that introduce downward nominal wage rigidity (e.g., Na, Schmitt-Grohe, Uribe, Yue 2018; Bianchi, Ottonello, Presno 2023) in that price-setting frictions arise from optimal forward-looking pricing by monopolistically competitive firms under Rotemberg costs, not from a mechanical wage floor, so that inflation expectations matter for current inflation and output in a standard NKPC. This means that expected future default events — through their effects on expected inflation and expected marginal utility — transmit to current equilibrium in a way that downward-rigid-wage models cannot replicate. The paper also differs from the literature studying the inflation incentive for local-currency debt dilution (e.g., Calvo 1988; Du, Pflueger, Schreger 2020): the baseline model assumes foreign-currency debt and a rule-based monetary authority that has no incentive to inflate away debt, so the mechanisms operate through expectations and discipline rather than through the debt-erosion channel. The paper connects these strands in the local-currency extension.

Q8. What are the welfare and policy implications for central bank mandates in emerging markets?

The paper provides formal support for monetary policy rules that respond to financial or sovereign-risk conditions — beyond standard inflation targeting — in emerging economies: the welfare ranking is default-risk rule > baseline rule > strict inflation targeting, with the gap between the default-risk rule and strict inflation targeting driven by lower mean and volatility of spreads, which reduce the frequency and severity of default amplification events. Strict inflation targeting, which delivers the flexible-price allocation, is not optimal because it leaves the overborrowing incentive of the fiscal government unchecked, generating excessive default risk that feeds back into inflation volatility through the expectations channel. A monetary rule with sufficient responsiveness to inflation or to default risk disciplines fiscal behavior and reduces welfare costs from both pricing frictions and default risk, suggesting that emerging-market central bank mandates that focus exclusively on inflation targeting at the expense of financial stability considerations may be suboptimal relative to rules that jointly address monetary and fiscal distortions.

Key Concepts

NK-Default framework: the paper’s model combining a New Keynesian small open economy (Gali-Monacelli structure with Rotemberg price-setting frictions and a Taylor-type interest rate rule) with the Eaton-Gersovitz endogenous sovereign default structure extended to long-term foreign-currency perpetuity bonds; the joint treatment of monetary policy and sovereign risk for emerging economies.
default amplification: the mechanism by which elevated sovereign default risk increases current inflation and depresses output through the forward-looking NKPC expectations channel: firms raise prices in anticipation of high future inflation and low consumption during a potential default, so current inflation rises even without any contemporaneous fiscal action; established as Proposition 1 in the simplified model and confirmed quantitatively.
monetary discipline: the mechanism by which contractionary monetary policy raises the cost of government borrowing through monetary distortions (the monetary wedge), inducing the fiscal government to reduce its indebtedness and thereby lowering equilibrium default risk; established as Proposition 2 and confirmed empirically using panel-data regressions of spreads on monetary policy shocks.
monetary wedge: the deviation of the marginal product of labor from households’ marginal rate of substitution between labor and consumption, arising from price-setting frictions; serves as the quantitative measure of monetary distortions and is the channel through which monetary policy affects government borrowing incentives.
default-risk monetary rule: an interest rate rule of the form i = ī·Φ^αD that responds directly to the one-period-ahead default probability Φ; shown in Proposition 3 to achieve both the constrained-efficient level of government debt and an arbitrarily small monetary wedge simultaneously, by incorporating an additional cost of borrowing for the fiscal government through the rule’s response.
temporary inflation events: empirical regularities in eight emerging-market inflation targeters in which inflation, spreads, and nominal policy rates temporarily spike together (inflation rises approximately 4.5%, spreads by 2.3%, within roughly one year) before reverting to lower levels; the model replicates these patterns using a combination of low productivity shocks and expansionary monetary shocks.

Redemption Fees and Gates in the Lab

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

Layer 1: Overview

This paper uses laboratory experiments to evaluate the effectiveness of two liquidity management tools — redemption fees and redemption gates — in reducing runs on money market funds (MMFs), explicitly accounting for preemptive run behavior where investors withdraw before a fee or gate is triggered to avoid being harmed by its imposition. The experimental design is based on a Diamond–Dybvig framework modified following Engineer (1989), in which four investors must decide whether to withdraw before learning their own liquidity type (patient or impatient), generating a setting where preemptive runs are theoretically possible even without fear of fund default. Three treatments are compared: a laissez-faire baseline, a gates treatment (withdrawals suspended after cash reserves are exhausted), and a fees treatment (a redemption fee charged on withdrawals once cash reserves are exhausted). Across 15-period session halves, redemption fees produce significantly lower withdrawal rates than both the baseline and gates treatments, with the gap emerging primarily after the first ten periods as participants adapt to the tool; gates, contrary to the theoretical prediction that they reduce the risk factor of the no-run equilibrium, do not lower withdrawal rates relative to the baseline — and in the full-session analysis, gates actually generate significantly higher withdrawal rates than the baseline, consistent with preemptive runs accelerating when investors fear losing access to their funds. The overall finding is that neither tool eliminates fund fragility, but fees offer a modest and delayed stabilizing effect while gates are counterproductive, lending empirical support to the SEC’s 2023 regulatory shift away from gates and toward fees in MMF regulation.

In depth

Q1. What is the experimental design and why does it explicitly study preemptive runs?

The experiment models a fund with four investors, each holding a demandable claim worth 1 ECU in period 1; the fund holds 2 ECUs in cash and a project that pays 2R ECUs in period 2 if allowed to mature but only 1 ECU if liquidated early, and investors must make their period-1 withdrawal decision before learning whether they are impatient (need period-1 funds) or patient (can wait), mirroring the Engineer (1989) setup where preemptive runs arise from the risk of being locked in rather than from fundamental insolvency concerns. The key feature is that an investor who expects fees or gates to be imposed faces an incentive to withdraw early to avoid either losing access (gates) or paying a fee (fees) at precisely the moment their liquidity need arises, which is exactly the preemptive run mechanism observed empirically during the COVID-19 MMF turmoil of spring 2020. Investors are sequentially asked whether they wish to withdraw in a random order without observing others’ choices, and they learn their type only in the evening of period 1 after having already made the morning withdrawal decision. In the treatment with gates, the fund suspends payouts entirely once its 2 ECU cash reserve is exhausted (i.e., after two withdrawals), forcing the third and fourth investors to wait for period 2 regardless of their type. In the treatment with fees, the fund charges a redemption fee on the third and fourth period-1 withdrawals instead of suspending them.

Q2. How does the theoretical risk factor framework generate the paper’s main hypothesis?

The paper uses the concept of the “risk factor of the no-run equilibrium” — defined as the probability p at which an investor becomes indifferent between staying invested and withdrawing when all other investors stay with probability p — to rank the three treatments by their predicted effectiveness: fees should generate the lowest risk factor and thus the highest tendency toward the no-run equilibrium, followed by gates, with the baseline highest. Fees dominate gates on the risk factor because fees still permit withdrawal in period 1 (albeit at a cost), meaning an impatient investor who remained invested can still access funds when needed, whereas under gates an impatient investor who is locked out has no recourse. This additional flexibility of fees means that the downside of remaining invested is smaller under fees than under gates, making the no-run equilibrium relatively more attractive under fees. The paper’s design tests whether this theoretical ranking carries through to actual investor behavior in the lab, where cognitive limitations, learning dynamics, and strategic uncertainty may produce deviations from the prediction.

Q3. What are the main experimental results on withdrawal rates?

Pooled over the first 15 periods of the first session halves (where no spillovers from prior experience occur), withdrawal rates are 30.3% in the baseline, 31.7% in gates, and 27.6% in fees; proportion tests confirm that fees produce significantly lower withdrawal rates than both baseline and gates at the 5% level, but no significant difference is found between baseline and gates — gate withdrawal rates are actually slightly higher than the baseline, contradicting the directional hypothesis. In the robustness check using both session halves (full 30 periods), the pattern sharpens: overall withdrawal rates are 30.3% (baseline), 33.4% (gates), and 25.4% (fees), with gates now significantly higher than baseline (p = 0.000) as well as significantly higher than fees, indicating that gates actively encourage preemptive withdrawal rather than deterring it. Withdrawal rates in the fees treatment exhibit a distinctive time pattern: they start higher than the other treatments in the first 5 periods (the Fees × Period interaction in the regression is negative and significant, while the main Fees coefficient is positive and significant, indicating an initially elevated but steeply declining trajectory), with the fee benefit materializing only from period 11 onward — consistent with the European Commission’s (2023) observation that European MMF investors more familiar with fees show less preemptive behavior than U.S. investors.

Q4. What does the regression analysis reveal about the treatment effects and dynamics?

Random-effects panel linear probability models of the binary withdrawal decision confirm that the fees treatment produces a significantly negative trend (Fees × Period coefficient negative and statistically significant) while the baseline shows no time trend and gates show no significant deviation from baseline trends, and that prior round experience — specifically the number of withdrawal requests in the immediately preceding round — is a strong positive predictor of withdrawal (approximately 6 percentage points per additional prior-round withdrawal request), while longer-run experience before the last round carries no significant predictive power. The inclusion of individual-level controls in Model (4) shows that higher risk tolerance is associated with significantly lower withdrawal rates (a surprising finding relative to prior experimental literature, which the authors suggest may reflect the preemptive nature of the decision making risk tolerance relevant through attitudes toward liquidity timing risk rather than through classic strategic risk). The regression analysis confirms that gates’ ineffectiveness is not explained by observable participant characteristics: the gates dummy is never significant and the gates-period interaction is not significantly different from the baseline, ruling out the possibility that session-level composition differences drive the null result for gates.

Q5. Does switching regulatory regime across session halves generate behavioral change?

Switching from the baseline to fees in the second session half produces a significant reduction in withdrawal rates in the final 5-period block consistent with Hypothesis 2, and switching from fees to gates in the second half produces a significant increase in withdrawal rates in the final 5-period block; however, switching from baseline to gates and from gates to fees produce no significant differences between session halves at the 5% level. The modest switching effects suggest that the fee benefit takes time to emerge regardless of prior regime experience — a finding consistent with the general pattern that fee effectiveness materializes only after participants have had multiple rounds of exposure. This regime-switching analysis also rules out a strong order effect as an explanation for the observed fee benefit: the fee advantage over baseline is present even when comparing within the same session halves and is not driven by participants carrying in stabilizing prior knowledge from the fees treatment.

Q6. What are the regulatory implications and how do the findings connect to the 2020 MMF turmoil?

The experimental findings directly inform the ongoing regulatory overhaul of MMF liquidity management tools, supporting the SEC’s 2023 decision to move away from gates toward mandatory swing pricing (which functions similarly to a fee) as the primary tool for U.S. MMFs, and providing micro-level behavioral evidence for why the 2014 fees-and-gates provisions failed to prevent the spring 2020 MMF runs even though they were in force. The preemptive run mechanism is empirically identified in the lab as a real and substantial phenomenon: withdrawal rates in the first round are if anything higher under fees than under the baseline, and the fee benefit only consolidates after participants have repeatedly experienced the tool, suggesting that investor familiarity is necessary for fee effectiveness — a condition that was likely not met in 2020. The finding that gates actively worsen run propensity in the full-session analysis provides the starkest regulatory implication: gates may be self-defeating by compressing investors’ effective option to wait, creating a focal first-mover advantage that accelerates exactly the run the gate is meant to stop.

Key Concepts

preemptive run : a run in which investors withdraw from a fund before their immediate liquidity need arises, driven by the strategic risk that fees or gates will be imposed at the exact moment they need liquidity; modeled here following Engineer (1989) and experimentally documented as a significant behavioral phenomenon that undermines both fees and gates.

risk factor of the no-run equilibrium : a measure based on risk dominance (Harsanyi and Selten 1988) defined as the probability p at which an investor becomes indifferent between withdrawing and remaining when all others stay with probability p; lower risk factor means the no-run equilibrium is more robust to coordination failure, and the paper predicts fees < gates < baseline in this ranking.

redemption gate : a liquidity management tool that suspends fund withdrawals once cash reserves are depleted, theoretically preventing fire sales but experimentally found to be ineffective and potentially counterproductive due to the preemptive run incentive it creates for investors who fear losing access to their funds.

redemption fee : a liquidity management tool that charges a cost on fund withdrawals during periods of redemption stress, internalizing liquidation losses into the withdrawing investor’s payoff; experimentally found to significantly reduce withdrawal rates relative to both baseline and gates, but only after a learning period of approximately 10 periods.

Regulating Credit Lines in the Presence of Fire‐Sale Externalities

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

This paper provides a contract-theoretic rationale for the special liquidity regulation of bank credit lines—a form of lending that has received little attention in the regulatory literature despite being the most important source of firm liquidity risk management. In the model, banks choose pre-arranged funding (committed before drawdowns accumulate) and ex-post funding (raised as drawdowns occur) to finance firms’ liquidity needs through credit lines. In states with high liquidity needs, banks cannot raise sufficient ex-post funding to meet all drawdowns and renege on some credit lines, forcing liquidations. Because each additional liquidation depresses the equilibrium liquidation value for all liquidated firms—a pecuniary externality—competitive banks choose insufficient pre-arranged funding in the private equilibrium. A minimum requirement on bank pre-arranged funding per committed (undrawn) funds in credit lines restores constrained efficiency, despite making credit lines more costly; welfare improves because more firms receive funding in high-liquidity states. The optimal regulatory ratio is increasing in the frequency of high-liquidity-need states, the value lost in liquidation, and the sensitivity of liquidation values to forced sales, and decreasing in the premium on pre-arranged funding.

In depth

Q1. Why can banks not fully meet credit line drawdowns in high liquidity need states?

In high liquidity need states, where many firms simultaneously draw on their credit lines, the revenues that banks receive from credit lines (interest payments and fees from the small share of firms that need no drawdown) shrink relative to the total drawdown demand, and the resulting shortfall cannot be fully met through ex-post funding raised from new investors because bank revenues are the collateral for such funding. The model captures the systemic nature of correlated liquidity shocks: when drawdowns are idiosyncratic, banks can cross-subsidize from non-drawing firms and raise ex-post funding easily; when drawdowns are highly correlated, these cross-subsidy revenues vanish and ex-post funding is insufficient, making pre-arranged funding essential for maintaining credit line insurance.

Q2. What is the pecuniary externality and why does it lead to under-provision of pre-arranged funding?

When a bank reneges on a credit line and the borrowing firm is liquidated, the forced sale of the firm’s assets depresses the equilibrium liquidation value—a fire-sale externality that reduces the payoff for all other firms being liquidated simultaneously; competitive banks do not internalize this negative spillover because, individually, each bank takes liquidation prices as given, leading the private equilibrium to feature too little pre-arranged funding and too frequent reneging relative to the constrained social optimum. This is a classic pecuniary externality (Lorenzoni 2008): the externality does not operate through a technological channel but through prices (liquidation values), so it is invisible to competitive agents who treat prices as parametric.

Q3. How does the minimum liquidity requirement on credit lines restore efficiency?

A minimum requirement mandating that banks hold a specified amount of pre-arranged funding per committed (undrawn) credit line funds induces competitive banks to internalize the social value of additional pre-arranged funding—namely, that more pre-arranged funding reduces the number of liquidated firms and raises equilibrium liquidation values—and thereby implements the constrained planner’s solution. This regulatory tool resembles the Basel III LCR (which requires banks to hold liquid assets equal to 5%-30% of undrawn credit lines, depending on the type of credit facility) and the NSFR (which requires stable funding equal to at least 5% of undrawn credit lines); the paper provides the first theoretical justification for precisely this type of regulation for credit lines and characterizes how the optimal ratio depends on economic fundamentals.

Q4. What are the determinants of the optimal regulatory ratio?

The optimal minimum pre-arranged funding requirement per committed funds in credit lines is higher when: (1) the premium on pre-arranged over ex-post funding is lower (making additional pre-arranged funding less costly at the margin); (2) high-liquidity-need states are more frequent (making the insurance value of pre-arranged funding higher in expectation); (3) liquidations are more costly (larger welfare losses per uninsured firm); and (4) liquidation values are more sensitive to the number of liquidations (a steeper fire-sale externality). This comparative statics result is policy-relevant: it implies that the Basel III framework’s one-size-fits-all approach to credit line liquidity ratios cannot be optimal across jurisdictions with different economic fundamentals, and national authorities should calibrate requirements to local conditions.

Key concepts

credit line pre-arranged funding : bank funding committed before credit line drawdowns accumulate; provides insurance against high-liquidity-need states by ensuring the bank can meet drawdowns even when ex-post funding is insufficient; corresponds to equity-like stable funding in Basel III terminology. fire-sale pecuniary externality on liquidation values : the depression of equilibrium firm liquidation values caused by simultaneous forced sales when many firms are liquidated after banks renege on credit lines; not internalized by competitive banks, leading to under-provision of pre-arranged funding in the private equilibrium. optimal credit line liquidity requirement : a minimum ratio of pre-arranged funding to committed (undrawn) credit line funds that restores constrained efficiency by internalizing the fire-sale externality; shown to be an increasing function of the frequency of high-liquidity-need states, liquidation costs, and liquidation-value sensitivity.

Self-Fulfilling Debt Crises with Long Stagnations

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

Layer 1: Overview

This paper asks whether sovereign debt crises can be self-fulfilling — triggered by lenders’ expectations of default rather than by weak fiscal fundamentals alone — and whether such crises are empirically plausible. Following the mechanism of Calvo (1988), high expected default probabilities require high interest rates to compensate lenders, but high interest rates in turn raise the cost of debt service and the probability of default, making the pessimistic expectations self-confirming. The key theoretical contribution is to show that this multiplicity of equilibria is state-dependent: it arises only in periods of stagnation, when the endowment process is in a persistent low-growth regime. The paper modifies a standard infinite-horizon sovereign default model (in the spirit of Eaton-Gersovitz and Arellano 2008) by introducing a two-state Markov regime-switching process for trend growth and by having the borrower choose current debt rather than debt at maturity — a timing assumption that is essential for multiplicity. Calibrating the output process to Argentina, Brazil, Italy, Portugal, and Spain using 1980–2017 data, the paper finds that for intermediate levels of debt and in low-growth states, interest rates can be either low (around 4%) or high (around 46%) depending on the coordination of lenders’ beliefs — a self-fulfilling crisis range that reproduces the qualitative features of the European sovereign debt crisis of 2010–2012 and the Argentine crisis of 1998–2002. In high-growth states, the multiplicity region is negligibly small or absent entirely.

In depth

Q1. What is the Calvo (1988) mechanism, and why does it require a bimodal endowment process?

The Calvo mechanism generates multiple equilibrium interest rates for a given level of debt: lenders’ expectation that the borrower will default in the low-output state forces them to charge a high interest rate to break even, but the high rate raises the debt service burden and makes default more likely, validating the pessimistic expectation. For this self-confirming loop to sustain multiple stable equilibria, the interest rate correspondence — mapping debt levels to possible interest rates — must have an upward-sloping region at both the low and high rate. A unimodal endowment distribution generates a correspondence with a downward-sloping high-rate segment (higher debt → lower high interest rate), which is inadmissible and eliminates multiplicity. A bimodal distribution with well-separated high and low growth states, as observed empirically in crisis-prone countries, generates an upward-sloping correspondence at both rates, creating a region of intermediate debt levels where either rate is an equilibrium.

The second key model feature is the timing of moves: the borrower chooses current debt (amount borrowed today) rather than debt at maturity (the repayment obligation). When the borrower chooses debt at maturity, it implicitly pins down the default probability and therefore the interest rate, eliminating multiplicity. When the borrower chooses current debt, the interest rate is determined by lenders and can take either the high or the low value consistent with break-even pricing, given the chosen debt level.

Q2. How does the paper calibrate the endowment process and what does the estimation reveal?

The paper estimates a two-state Markov regime-switching model for annual GDP per capita growth for Argentina, Brazil, Italy, Portugal, and Spain using data from 1980 to 2017, and finds clear evidence of a bimodal distribution with persistent high- and low-growth regimes across all five countries. Estimated using a Bayesian MCMC algorithm with the Kim (1994) filter, the posterior means for the benchmark cross-country calibration are: low-growth rate gL = −1.0% per year, high-growth rate gH = 3.0% per year, persistence of low-growth state pL = 0.60, persistence of high-growth state pH = 0.80, and standard deviation of transitory shocks σ = 0.015. The average gap between gL and gH across countries is approximately 6 percentage points, more than three times the standard deviation of the transitory shock — confirming the bimodal structure that is essential for multiplicity. Both growth regimes are persistent, with the low-growth state having 60–80% persistence across countries.

The quantitative model uses these estimates together with standard parameters: risk-free rate R* = 3.5%, recovery rate κ = 75%, discount factor β = 0.75, and risk aversion γ = 3. The sunspot process governing equilibrium selection is i.i.d. with a 5% probability of the bad (high-rate) sunspot in each period.

Q3. What does the calibrated model predict for interest rates and when do self-fulfilling crises occur?

In the calibrated quantitative model, the multiplicity region is present only in the low-growth state and for intermediate debt levels; in the high-growth state, the multiplicity region is either empty or negligibly small. In the low-growth state with intermediate debt, the interest rate schedule features two admissible equilibria: a low-rate equilibrium consistent with a low probability of default (1.7% in the benchmark simulation) and a high-rate equilibrium consistent with a high probability of default (60.1%). Both are sustained by self-confirming expectations. The scenario simulation illustrates this starkly: two economies starting from identical wealth and facing identical growth-shock sequences but different sunspot realizations in period t=2 (when they are in the low-growth state) face interest rates of 4.0% versus 46.4% and next-period default probabilities of 1.7% versus 60.1%, respectively, with no difference in fundamentals.

The model also generates endogenous austerity: borrowers optimally refrain from increasing debt to avoid discrete jumps in interest rates, both at the fundamental threshold (driven by the growth regime) and at the expectations-driven threshold (driven by the sunspot). In low-growth states facing the bad sunspot, the borrower either bunches at a low debt level below the multiplicity region or makes a discrete jump above it, echoing the binary fiscal-adjustment dynamics observed in crisis episodes.

Q4. How does the model interpret the European debt crisis and the role of the ECB?

The model provides a direct interpretation of the European sovereign debt crisis: the southern European economies (Italy, Spain, Portugal) entered a low-growth state around 2009–2010, which created conditions for the Calvo mechanism to operate; spreads jumped to high-rate equilibria driven by expectations rather than by fundamentals alone. The ECB’s announcement of the Outright Monetary Transactions (OMT) program in September 2012 — the commitment to purchase sovereign bonds in secondary markets — shifted lenders’ beliefs from the bad-sunspot equilibrium to the good-sunspot equilibrium, collapsing spreads substantially even without actual intervention. In the model’s language, a credible lender of last resort can eliminate the bad equilibrium by committing to lend at the low-rate schedule, rendering the high-rate self-fulfilling expectations non-viable. The Argentine crisis of 1998–2002 fits the model as an alternative trajectory: Argentina entered the low-growth state with a 7% spread on 35% debt-to-GDP and, without a lender of last resort intervention, eventually defaulted in 2002 — consistent with the bad-sunspot equilibrium path.

Q5. What role does persistence of the low-growth state play?

The persistence of the low-growth state (pL) is the key parameter governing the severity of self-fulfilling crises: higher pL generates higher equilibrium interest rates in the bad-sunspot equilibrium and a larger multiplicity region. Intuitively, if the economy is likely to remain in the low-growth state for a long time, the probability of default conditional on entry into the bad equilibrium is very high, requiring lenders to charge very high interest rates to break even. The higher the interest rate, the more debt service costs compress fiscal space, making default even more likely and potentially sustainable at even lower debt levels. The paper shows in robustness exercises that the multiplicity result is robust to reasonable perturbations in pL, κ (recovery rate), σ (transitory shock standard deviation), gL, and gH, with the key ingredient being the bimodal structure of the endowment process rather than any single parameter value.

Q6. What are the policy implications for lenders of last resort?

The central policy implication is that a lender of last resort — such as the ECB or the IMF — is justified precisely when fundamentals are weak, not because fundamentals alone cause the crisis but because weak fundamentals create conditions in which expectations can trigger a self-fulfilling crisis. Intervening in the bad-sunspot equilibrium by committing to supply funds at low-rate terms makes the high-rate equilibrium infeasible: lenders cannot expect default because the lender of last resort ensures the borrower can always roll over at low rates. The model thus rationalizes the design of the OMT: a credible commitment with no limit on size is sufficient to rule out the bad equilibrium without necessarily requiring actual asset purchases. The paper notes that such interventions will also have effects on the economy outside the period of crisis, since the availability of backstop financing may affect the equilibrium path more broadly.

Key Concepts

Calvo (1988) mechanism: the self-fulfilling loop in sovereign debt markets in which high lender expectations of default require high interest rates for break-even pricing, which raise the actual default probability and thereby confirm the initial pessimistic expectations; generates multiple equilibrium interest rates for a given debt level.
state-dependent multiplicity: the feature of the model in which multiple interest rate equilibria arise only in periods of low and persistent growth (stagnation), not in high-growth regimes; the central quantitative finding that self-fulfilling crises are empirically plausible only when growth fundamentals are weak.
endogenous austerity: the borrower’s optimal choice to hold debt below the multiplicity region to avoid discrete jumps in interest rates triggered by either fundamentals or expectations; reflected in the flat portions of the debt policy function and consistent with fiscal consolidation patterns observed in crisis episodes.
sunspot variable: the exogenous coordination device that selects among the multiple equilibrium interest rate schedules; takes a bad or good realization each period according to an i.i.d. process, with the bad sunspot selecting the high-rate schedule and the good sunspot selecting the low-rate schedule in the low-growth state.

The Effects of Regulatory Office Closures on Bank Behavior

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

Using closures of U.S. bank regulatory offices between 2002 and 2013 as difference-in-differences shocks to the physical proximity between supervisors and the community banks they oversee, the paper asks whether a decentralized network of local supervisory offices produces safer banks. The authors first show closures are not predicted by the risk or performance of the supervised banks — offices near a regional main office with falling workload are the ones shut — which supports treating closures as plausibly exogenous to affected banks. Following a closure, banks previously supervised by the closed office increase total lending by about 6-10% and tilt toward riskier loans (e.g., commercial real estate), and overall risk-taking as measured by the Z-Score rises by roughly 19-32% of the sample mean, with larger increases in distance to the new office associated with riskier policies. Banks affected before the 2008-09 financial crisis subsequently exhibited more bad loans, higher charge-offs, and higher failure rates during the crisis. Examining channels, the authors find affected banks report lower and less timely loan-loss provisions (and more income-increasing provisions, making balance sheets more opaque), increase dividend payouts, and see lower risk-adjusted returns on assets — which they read as evidence that proximity lets supervisors enforce timelier provisioning, restrain payouts, and share expertise. On balance the authors interpret the results as implying that geographical proximity reduces informational frictions in supervisory monitoring and leads to more stable banks — that is, the monitoring-benefit view dominates the regulatory-capture view on average.

In depth

Q1. What is the paper’s research design and identification strategy?

The paper uses a difference-in-differences design built on closures of FDIC, Federal Reserve, and OCC regulatory offices from 2002 to 2013, comparing banks that lost their supervising office to nearby banks in the same county supervised by a different office. Because U.S. banks in the same geographic area may be supervised by one of three federal regulators, within a county where an office closed only banks supervised by that closed office should be affected, while similarly located banks supervised by another office serve as controls exposed to the same local economic conditions. The analysis draws on a hand-collected data set mapping regulatory office locations and focuses on community banks, which are tied to local markets and served by traveling rather than in-house examiners. The tightest specifications include county-quarter, regulatory-office-quarter, and bank fixed effects, and the authors report parallel pre-trends and, using a timing-effects model, effects that appear only after closures and not before.

Q2. Are office closures plausibly exogenous to the affected banks?

The authors report that office closures are unrelated to the risk, performance, assets, or loans of the banks the office supervised; instead, offices closest to a regional main office experiencing a falling workload are the ones closed. They read this as the reasons for closure residing with banks outside the closed office’s immediate vicinity and reflecting a rebalancing of supervisory resources within regions, which they argue alleviates reverse-causality concerns that poor bank performance could drive both office closures and subsequent higher risk-taking.

Q3. What happens to bank lending and risk-taking after a regulatory office closes?

Following a closure, affected banks increase total lending by 6-10% and increase overall risk-taking as measured by the Z-Score by 19-32% of the sample mean, directing new lending toward riskier loan categories such as commercial real estate. In addition, larger increases in physical distance to the new supervising office are associated with riskier policies, which the authors interpret as evidence that proximity alleviates informational frictions in collecting information from and communicating with banks. The paper reports that its analysis does not provide clear evidence that treated banks hold more capital after office closures.

Q4. Do these changes have consequences for bank fragility?

Banks affected by office closures prior to the 2008-09 financial crisis subsequently exhibited more bad loans, higher charge-offs, and were more likely to fail during the crisis. The authors present this as evidence that the additional lending and risk-taking following closures was not benign, and read it, collectively, as support for the view that a decentralized supervisory structure — by keeping supervisors proximate — leaves banks less fragile.

Q5. Through what channels does proximity appear to operate?

The authors examine three nonmutually exclusive channels — provisioning practices, payouts, and supervisory expertise — and report evidence consistent with each. On provisioning, affected banks report both lower and less timely loan-loss provisions and make greater use of income-increasing provisions, which leads to more opaque balance sheets. On payouts, affected banks significantly increase their dividend payouts to shareholders. On expertise, risk-adjusted returns on assets for affected banks decrease after closures, which the authors read as consistent with proximate supervisors advising banks toward more efficient risk-taking. They interpret the combined evidence as proximity reducing informational frictions in supervisory monitoring.

Q6. How do the authors position their contribution and interpret the findings overall?

The authors state that, to the best of their knowledge, they are the first to use regulatory office closures to study how geographical networks of offices matter for bank supervision, and they interpret their results as indicating that the monitoring-benefit view dominates the regulatory-capture view on average. They emphasize that both views — that proximity aids monitoring and that proximity risks capture — can operate simultaneously, so the empirical question is which dominates; the finding of riskier, more fragile banks after supervisors move farther away implies proximity’s monitoring benefits dominate. The paper frames the policy-relevant implication as: geographical proximity reduces informational frictions in supervisory monitoring and leads to more stable banks.

Key concepts

Regulatory office closure : the shutting of a local supervisory office of the FDIC, Fed, or OCC, used here as a shock that increases the physical distance between a community bank and its supervisor while leaving the bank’s regulator and the applicable rules unchanged.

Decentralized supervisory structure : the arrangement whereby a unified body of banking regulation is enforced through geographically dispersed networks of local supervisory offices, intended to give supervisors easier access to local (especially soft) information about banks.

Monitoring-benefit (proximity) view : the hypothesis that physical proximity lowers the cost of collecting soft information and communicating supervisory expectations, enabling supervisors to enforce safer bank policies.

Regulatory capture view : the alternative hypothesis that proximity to supervised banks can undermine monitoring, because closer contact fosters social/communal ties or career concerns that lead supervisors to cater to bank interests.

Loan loss provisions (LLPs) : accounting charges intended to reflect the expected future losses on a bank’s loan portfolio; under-provisioning can flatter short-term liquidity and performance while masking inadequate capital, and the paper finds affected banks report lower and less timely LLPs.

Z-Score : the accounting-based measure of bank risk the paper uses; the paper reports that overall risk-taking, as measured by the Z-Score, increases by 19-32% of the sample mean for banks affected by office closures.

Community banks : smaller banks tied to local markets and served by traveling rather than in-house examiners — the sample the paper focuses on.

Key concepts

Community banks : smaller banks tied to local markets and served by traveling rather than in-house examiners — the sample the paper focuses on.

Unequal and Unstable: Income Inequality and Bank Risk

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

This paper documents that U.S. metropolitan statistical areas with higher income inequality have a larger share of failed banks, higher average bank default probabilities, and greater dispersion of bank risk, using cross-sectional regressions across 178 MSAs and 5,543 banks over 2000–2019 with the Gini coefficient measured from the 2006 American Community Survey. A move from the 25th to the 75th percentile of the Gini distribution (0.429 to 0.460) is associated with a 0.124 percentage point higher share of failed banks, a large effect relative to the 0.3 percent mean failure rate in the sample. To account for these patterns, the paper builds a general equilibrium model in the Allen and Gale (2000) tradition in which banks compete to lend to households that differ by income and finance housing purchases with mortgages; competition and deposit insurance together induce some banks to lend to low-income (subprime) households at rates that carry negative expected present value, creating a segment of endogenously risky banks that fail with positive probability in the bad state. Income inequality expands the subprime borrower pool both directly — by shifting more households below the endogenous income cutoff — and indirectly — by raising the equilibrium cutoff itself via higher housing prices — leading to a larger share of risky banks. A key counterfactual result is that if deposit insurance premiums fully reflected bank-specific risk (eliminating risk-shifting), all banks would be safe regardless of the income distribution, isolating risk-shifting as the necessary friction.

In depth

Q1. What is the empirical design, and what does the data show?

The paper uses a cross-sectional dataset at the MSA level, covering 178 MSAs with 5,543 commercial and savings bank headquarters over 2000–2019, regressing several measures of bank risk on the Gini coefficient measured from the 2006 ACS (one-year survey) while controlling for MSA-level income, population, urbanization, and year fixed effects in panel extensions. Bank failure is the primary risk measure: the share of bank headquarters that failed (FDIC-confirmed failure dates, excluding 2008–2009 TARP years to avoid ambiguity about government support) is regressed on the Gini coefficient. Additional risk measures — banks’ predicted probabilities of default (from a logit model trained on financial ratios) and z-scores — are used to confirm that the Gini result is not driven entirely by crisis-period observations. The paper finds significant positive relationships between the Gini and: (i) the share of failed banks (Panel A), (ii) the risk of the most-risky banks per MSA (Panel B), (iii) average bank risk (Panel C), and (iv) the dispersion of bank risk across banks in the MSA (Panel D). Robustness checks use 3-year survey Gini coefficients, the income share of the top 5 percent as an alternative inequality measure, and panel regressions with MSA-level clustering; results are qualitatively unchanged. Poverty (share of households below the poverty line) is not significantly associated with bank risk, distinguishing inequality from the level of the lower tail.

Q2. What is the theoretical framework and what agents populate the model?

The model is a two-date (0 and 1) general equilibrium model with a continuum of households heterogeneous in income and a continuum of ex-ante identical, risk-neutral bankers; households finance housing purchases at date 0 with mortgage loans that are repaid at date 1, and bankers can choose at date 0 to operate a safe bank (solvent in both states) or a risky bank (insolvent in the bad state with probability q). Housing is produced by competitive firms with increasing marginal cost, so the equilibrium housing price P_0 is an increasing function of aggregate housing demand. Deposits are insured (explicitly or implicitly), and banks are subject to a minimum capital requirement (maximum leverage ratio ρ). The cost of bank capital exceeds the cost of deposits, so all banks lever to the maximum. Each bank’s cost of managing its balance sheet is quadratic in balance sheet size, which pins down individual bank size and allows a clean characterization of how many risky vs. safe banks exist in equilibrium.

Q3. What is the key sorting result between banks and borrowers (Proposition 1 and 2)?

In equilibrium, there is an endogenous income cutoff y such that households with income above y are prime borrowers served by safe banks at undistorted interest rates r_u(y), and households with income below y* are subprime borrowers served by risky banks at a uniform risk-shifting interest rate r_rs; crucially, subprime loans carry negative expected net present value because competition among risky banks drives r_rs below the break-even rate for a safe bank (Corollary 1).** The risk-shifting interest rate r_rs is lower than the undistorted rate for low-income borrowers because a risky bank only internalizes the loan payoff in the good state (where it is solvent) and benefits from the deposit insurance subsidy in the bad state (where it defaults and the fund covers depositor losses). Risky banks are therefore willing to lend at below-NPV rates, and competition among them drives r_rs to equality with their marginal cost conditional on survival. Safe banks rationally refuse to enter the subprime segment because they internalize the expected loss in the bad state. The clientele of safe and risky banks do not overlap in equilibrium.

Q4. How does income inequality affect the proportion of risky banks?

Income inequality raises the share of risky banks through two reinforcing channels: a direct channel that shifts a larger mass of households below the fixed cutoff y, expanding the subprime borrower pool, and an indirect channel that moves the cutoff y upward (because inequality raises the equilibrium housing price P_0, which in turn raises the default rate among any given income level, making more households effectively subprime) — under convex housing demand (plausible if n(y) is concave below a poverty-line income ymin), both channels reinforce each other.** Numerically, with a log-normal income distribution calibrated to the observed Gini range of 0.35–0.55, the model generates a monotone positive relationship between the Gini coefficient and (i) the proportion of risky banks, (ii) average bank default probability, and (iii) dispersion of bank default probabilities — matching the empirical patterns from Section 2. A Pareto income distribution produces a steeper relationship, suggesting the result is robust to distributional assumptions. The proportion of risky banks in Proposition 2 equals the subprime housing demand divided by the sum of subprime and weighted prime demand, and is therefore a smooth function of the income distribution H.

Q5. Why is risk-shifting — not borrower riskiness — the necessary friction?

Proposition 3 shows that if deposit insurance premiums fully reflected each bank’s individual default probability (i.e., if risk-shifting were not feasible), all banks would choose to be safe even when the income distribution places many households with high default rates below y, because a risky bank would have to pay higher deposit rates to attract insured deposits and would be unable to extract a competitive advantage from subprime lending.* The proposition isolates risk-shifting as a necessary condition: without it, the income distribution has no effect on bank risk. This result directly connects to Keeley’s (1990) observation that bank risk reflects the option value of limited liability plus deposit insurance. It also implies that policies that make deposit insurance premiums bank-risk-sensitive (such as risk-based FDIC premiums) could substantially mitigate the inequality–bank-risk nexus, though the paper notes that empirical evidence suggests current risk-based premiums do not fully internalize bank-specific risk.

Q6. How does housing supply elasticity interact with the inequality–bank-risk relationship?

When housing supply is inelastic (high marginal cost c_1), a mean-preserving spread in income raises the equilibrium housing price P_0 substantially, which raises the subprime cutoff y sharply via the indirect channel — and for very high values of c_1, this can actually push the cutoff above the top of the income distribution, putting all households into the prime segment and reducing the share of risky banks.* This asymmetry means that in regions with very inelastic housing supply (e.g., coastal urban areas with strict zoning), higher inequality may be associated with fewer risky banks because the high housing price forces even low-income households to borrow at rates where a safe bank is marginally competitive. Conversely, in regions with elastic housing supply, the indirect channel is weak and the direct channel dominates, so higher inequality unambiguously raises bank risk. The paper characterizes this interaction numerically using Figure 4, noting that the perverse (negative) relationship is theoretically possible but considered less empirically relevant in practice.

Q7. What are the model’s extensions and robustness?

The paper discusses four extensions that leave the central mechanism intact: (i) ex-ante heterogeneous banks, in which risky banks specialize in subprime mortgages and also finance risky firms; (ii) risk-weighted capital requirements, which permit risk-shifting as long as risk weights are not fully calibrated to bank-specific risk; (iii) a firm sector, in which risky banks serve risky small firms in addition to subprime households; and (iv) housing speculation by high-income households, which amplifies the risky-bank segment by creating additional demand for negative-NPV mortgages. In extension (iv), the high-income speculator demands a risky mortgage even though speculator income is above y*, creating an additional channel through which inequality can generate bank risk beyond the subprime-borrower mechanism. The discussion also addresses the baseline model’s assumptions about flat deposit rates and homogeneous bankers, arguing that relaxing either would introduce quantitative but not qualitative changes to the central sorting result.

Q8. What does the paper contribute relative to the literature on bank risk and inequality?

The paper’s empirical contribution is to document a robust cross-sectional positive relationship between income inequality and bank failure rates at the MSA level, a relationship that is not driven by poverty (the lower tail per se), is present for multiple bank-risk measures, and survives including the crisis years 2008–2009 in the bank-risk measures (though significance weakens). On the theory side, the contribution relative to the Cairo-Sim (2018) monetary policy and inequality work and the Allen-Gale (2000) rational bubbles framework is to endogenize the sorting of banks and borrowers into safe/risky pairs in response to the income distribution, and to show that this sorting — not borrower riskiness per se — generates the empirical bank-risk gradient. The model is purposefully simple (one period, no dynamics, no aggregate shock heterogeneity) to make the mechanism transparent; the authors acknowledge that a dynamic model with time-varying inequality might generate additional predictions about the timing of bank failures relative to inequality trends.

Key Concepts

subprime cutoff y* : the endogenous income level that separates prime (income above y*) from subprime (income below y*) borrowers; determined in equilibrium as the income level at which the undistorted mortgage rate for a safe bank equals the risk-shifting rate charged by a risky bank; shifts in response to the equilibrium housing price.

risk-shifting interest rate (r_rs) : the mortgage rate that a risky bank is willing to accept on a subprime loan, determined by the condition that the bank earns zero profit conditional on the good state (survival), without internalizing the loss imposed on the deposit insurance fund in the bad state; in the paper’s equilibrium, r_rs is uniform across all subprime borrowers.

undistorted interest rate (r_u(y)) : the mortgage rate that a safe bank requires from a household with income y, determined by the full expected return on the loan across both good and bad states; increasing in y because lower-income households have higher default rates in the bad state.

negative NPV subprime loans : mortgage loans to households with income below y* that carry a negative expected present value when the deposit insurance cost is internalized; attractive only to risky banks that do not internalize the bad-state payoff, and not to safe banks that must break even in expectation.

Allen-Gale (2000) rational bubbles framework : a one-period general equilibrium model in which banks lend to asset purchasers using deposit insurance, creating a wedge between private and social returns on risky assets; this paper adapts that framework to a mortgage/housing market with a continuous income distribution to generate endogenous bank sorting and an inequality channel.

direct vs. indirect channel of inequality : the direct channel (region A in Figure 2) operates by shifting more households below the existing cutoff y* as the income distribution spreads; the indirect channel (region B) operates by raising y* itself through higher equilibrium housing prices; both channels reinforce each other when housing demand is convex in income (n(y) convex below the poverty line).

deposit insurance subsidy : the implicit transfer from the deposit insurance fund to risky banks in the bad state; risky banks pay the same deposit rate as safe banks despite imposing expected losses on the fund, creating the wedge that makes subprime lending attractive to risky banks and not to safe banks.