E58 | Macro Paper Warehouse

Balance-Sheet Policy and the Term Premium: High-Frequency Evidence

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

When a central bank shrinks its balance sheet, how much do long-term interest rates actually move — and through which channel? Using minute-by-minute market data around balance-sheet announcements, the authors estimate that much of the long-rate response works through the term premium rather than through changed expectations of future short rates. The result is an estimate for their 2009–2024 sample under their identifying assumptions — evidence consistent with a term-premium channel, not a universal constant.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. Does balance-sheet policy move long rates through the term premium or through expected short rates?

The paper estimates that a substantial share of the long-rate response operates through the term premium, with a smaller role for revised short-rate expectations — though it frames this as identification within their window, not a structural decomposition that holds in all regimes. This sits against a literature that has split the response into a signaling channel and a portfolio-balance channel; the contribution here is using intraday yields to isolate the announcement effect from contaminating macro news.

Q2. How is the effect identified, and why high-frequency?

By measuring yield changes in narrow windows around scheduled balance-sheet announcements, so that other macroeconomic news is unlikely to move rates within the window. The maintained assumption is that within a tight enough window, the announcement is the dominant shock — a standard high-frequency identification premise. The authors note the assumption is weaker around unscheduled communications, and restrict the main sample accordingly.

Q3. What does this imply for the pace of balance-sheet runoff?

If transmission runs through the term premium, the pace and predictability of runoff plausibly matter for long rates — but the paper presents this as suggestive, stopping short of a calibrated policy rule. The reading is that quantity and communication interact, consistent with prior work on announcement effects, rather than that runoff has a single mechanical effect on yields.

Key concepts

term premium: The extra return investors require for holding a long-term bond instead of rolling over short-term ones — here, the part of long rates not explained by expected future short rates.
balance-sheet policy: A central bank changing the size or composition of its asset holdings (expansion via purchases, runoff via “quantitative tightening”) as a policy tool distinct from setting the short-term rate.
high-frequency identification: Inferring a policy action’s effect from price moves in a very short window around the announcement, on the assumption that little else moves markets inside that window.

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

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

Layer 1 — Overview

Research Question

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

Data and Setting

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

Methodology

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

Main Findings

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

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

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

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

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

Scope Conditions

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

Layer 2 — Q&A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Key Concepts

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

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

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

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

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

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

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

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

Central Bank Digital Currency with Collateral-Constrained Banks

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

The paper analyzes the implications of introducing a retail central bank digital currency (CBDC) that competes with commercial bank deposits for household liquidity, in a model where banks must post government bonds as collateral to access central bank lending. The authors revisit Niepelt’s (2022) “equivalence of payment systems” result and find that equivalence survives even under a collateral constraint: the central bank can still offer loans to banks that replicate the no-CBDC equilibrium allocation, but at a lending rate lower than Niepelt’s unconstrained rate, because tighter terms are needed to incentivize sufficient loan uptake when banks must redirect portfolio holdings toward government bonds to qualify. A structural cost remains: banks must hold government bonds as collateral at the expense of extending credit to firms, so equivalence in allocation does not imply full neutrality — banks’ business models and the government’s intermediation role change even when aggregate output and prices are unchanged. In the dynamic extension where the central bank does not sterilize the CBDC introduction, banks respond by narrowing deposit spreads to attract inflows, with the result that a CBDC ramp-up to 5 percent of steady-state output expands rather than contracts bank credit to firms.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is the equivalence of payment systems result and how does the collateral constraint change it?

Brunnermeier and Niepelt (2019) and Niepelt (2022) established that the central bank can neutralize the real effects of CBDC introduction by lending to banks at an appropriate rate to replace lost deposit funding, a result the present paper revisits by adding a collateral requirement on central bank lending — specifically, that banks must hold eligible government bonds up to a fraction θb of their central bank loan value. Under this constraint, Proposition 1 shows that equivalence survives: there exists a central bank lending rate that replicates the no-CBDC equilibrium allocation and price system. However, this lending rate is lower than Niepelt’s unconstrained rate by a factor increasing in the restrictiveness of the constraint (lower θb requires a lower lending rate), because when banks are collateral-constrained, cheaper terms are needed to induce them to borrow enough from the central bank to offset deposit outflows.

Q2. What is Corollary 1 and why does “full neutrality” fail?

Corollary 1 states that even when the central bank achieves allocation equivalence by setting the appropriate lending rate, banks must redirect portfolio holdings from firm loans to government bonds to meet the collateral requirement — crowding out bank credit to firms by an amount equal to the bond uptake, with the crowding-out diminishing as the collateral constraint becomes less restrictive (higher θb). This is the sense in which “full neutrality” fails under the collateral constraint: aggregate output and prices are unchanged, but the composition of credit changes — banks extend less to firms and hold more government bonds — and the government or household sector must absorb the gap in firm financing. In the limiting case where CBDC and deposits are equally valuable to households (λ = 1), the government alone compensates for the reduction in bank loans, effectively expanding its own intermediation role.

Q3. What does the dynamic extension show about bank disintermediation?

Simulating a gradual and near-permanent increase in CBDC to 5 percent of steady-state output without central bank sterilization, the paper finds that banks respond by narrowing their deposit interest spread to attract deposit inflows, such that total deposits do not fall and bank loans to firms expand rather than contract — the opposite of the disintermediation hypothesis. The mechanism relies on the assumption that banks have market power in their regional deposit markets (each bank is a monopsonist): in response to CBDC competition, the bank voluntarily reduces the rent it extracts on deposits (the spread between the risk-free rate and the deposit rate), attracting more deposit inflows. This deposit inflow, combined with central bank loan uptake, expands the bank’s balance sheet and increases credit extension to firms. The result stands in contrast to models with competitive deposit markets, where banks cannot respond to CBDC competition through deposit pricing.

Q4. What changes even if credit is not reduced?

Even when the dynamic model shows credit expansion rather than contraction, the paper establishes that CBDC introduction alters banks’ balance sheet composition and business model: banks shift toward holding more government bonds and away from firm loans, the government assumes a larger credit intermediation role, and the aggregate distribution of capital ownership changes — constituting the form of non-neutrality that survives even when total credit is unchanged. This is what Corollary 1 calls the failure of “full neutrality”: the real allocation equivalence holds at the aggregate level, but the sectoral distribution of who provides credit to firms shifts from the banking sector toward the public sector. The paper interprets this as a structural consequence of the collateral requirement on central bank lending that is absent in the frictionless equivalence benchmark.

Key concepts

equivalence of payment systems : the theoretical result (from Brunnermeier-Niepelt 2019 and Niepelt 2022) that the central bank can ensure the same equilibrium allocation whether or not CBDC exists, by adjusting its lending terms to banks; this paper revisits and extends the result to environments with a collateral constraint.

collateral constraint (θb) : the requirement in this model that banks hold eligible government bonds as a fraction of the central bank loans they take on; adding this friction to Niepelt’s framework preserves equivalence in allocation but requires a lower central bank lending rate and crowds out bank loans to firms.

disintermediation : the concern that CBDC adoption would cause households to shift en masse from bank deposits to CBDC, reducing bank funding and contracting bank credit; the paper finds this does not occur in either the equivalence analysis or the dynamic extension.

monopsony in deposits : the market structure assumption that each regional bank is the sole deposit provider in its region, giving it pricing power over deposit rates; this is what enables banks in the dynamic model to narrow the deposit spread in response to CBDC competition, generating deposit inflows rather than outflows.

full neutrality : a stronger invariance result requiring that not only the equilibrium allocation but also banks’ balance sheet composition and business model are unchanged by CBDC introduction; the paper shows this fails under the collateral constraint even when allocation equivalence holds.

Central bank reputation with noise

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

Layer 1 — Overview

Research Question. How does noise in the mapping from central bank actions to realized inflation affect the existence and character of reputational equilibria in monetary policy? Specifically, can a central bank that faces uncertainty about whether it is perceived as “hawkish” or “dovish” sustain a pure strategy separating equilibrium, and how should each type behave as a function of its current reputation?

Model and Methodology. Amador and Phelan build on the monopolistic-competition, cash-in-advance framework of Chari, Christiano, and Eichenbaum (1998) and extend it to allow for (i) two central bank types — hawkish (type 1, high penalty γ₁ for inflationary actions) and dovish (type 2, lower penalty γ₂ < γ₁) — whose identity is private information; (ii) type switching governed by a Markov process, with probability δ that a hawkish bank is replaced by a dovish one and probability ε that a dovish bank is replaced by a hawkish one; and (iii) noise between the central bank’s chosen action μᵢ and realized money growth μₐ, which is drawn from a density f(μₐ|μᵢ) with full support. The equilibrium concept is pure symmetric Markov perfect equilibrium, in which all strategies are functions only of the public Bayesian posterior ρ that the current central bank is hawkish. The paper proceeds analytically to characterize no-pooling results and then computationally to demonstrate existence of separating equilibria.

Main Findings.

No pooling equilibria exist (analytical). Propositions 2 and 3 establish that no pure symmetric Markov equilibrium can have both types choosing the same positive action for any reputation ρ, as long as γ₁ ≠ γ₂ and Assumption 1 (pricing distortion sufficiently severe) holds. The intuition: if both types pool, realized inflation is uninformative, reputation does not change, and there are no dynamic incentives — but different static incentives (γ₁ ≠ γ₂) then imply different optimal actions, a contradiction.
Without sufficient noise, separating equilibria also fail to exist. In the no-noise limit, Bayesian updating forces the dovish bank’s reputation to jump to its maximum after one period of mimicking the hawkish action, making mimicry cheap when the discount factor β is high or the type-persistence probability ε is low. This makes the incentive-compatibility constraint for the dovish bank very difficult to satisfy, potentially precluding existence of a separating equilibrium.
With sufficient noise, pure strategy separating equilibria exist and have appealing properties (computational). The benchmark parameterization sets α = 1, σ = 5, β = 0.99, h(μ) = 0.5μ², ε = δ = 0.02, and the noise distribution such that the hawkish type’s unconstrained target would deliver mean inflation of 2% and the dovish type’s 3%. Under these parameters:
- In the full-information (known-type) world: price P = 1.313 for the hawkish type and P = 1.338 for the dovish type, with E[log(c) − αc] = −1.0297 and −1.0320 respectively, versus the efficient benchmark of −1.
- In the reputational equilibrium, both types choose lower inflationary actions than they would absent reputation considerations — because reputation is valuable (higher ρ lowers household prices and thus improves welfare for both types).
- Both types’ optimal actions are U-shaped in reputation ρ: they are most restrained — choosing the lowest inflationary actions — when ρ is middling (interior), because Bayesian updating is most sensitive (and thus the reputation cost of inflating is greatest) at interior beliefs, while it is difficult to move extreme beliefs.
- Average equilibrium inflation is 2.1%, which lies below the weighted average of unconstrained type targets (2.5% given equal switching probabilities), demonstrating that reputation concerns compress inflation outcomes.
Ergodic distribution of reputation remains interior. Starting from ρ = 0.5, expected reputation conditional on being hawkish stays below 0.63 and conditional on being dovish stays above 0.38, reflecting that noise and type switching prevent reputation from collapsing to its extremes.
Welfare implications. The hawkish type is made worse off by ongoing household uncertainty (relative to the reference game in which type is immediately revealed), while the dovish type is made better off. Households are better off under continuing uncertainty than under immediate revelation, unless reputation is near its maximum — because uncertainty suppresses inflationary temptations for both types.

Scope Conditions. Results apply within a monopolistic-competition, cash-in-advance economy with discrete time, infinite horizon, and Markov strategies. The no-pooling result requires Assumption 1 (the pricing distortion is sufficiently severe that the central bank has a positive incentive to inflate from μ = 0). The no-noise existence failure is an informal argument holding fixed discount and type-switching parameters. Computational results are specific to the benchmark parameterization but are verified to be robust to variation in β, σ, γ₁, γ₂, ε, and δ.

Layer 2 — Q&A

Q1: What is the fundamental time-inconsistency problem in the underlying Chari et al. (1998) economy, and how does the paper extend it?

A1: In the Chari et al. (1998) monopolistic-competition cash-in-advance economy, households exploit market power when setting prices, and the cash-in-advance constraint depresses consumption efficiency; this creates an ex-post temptation for the central bank to inflate and partially offset these distortions, even though in equilibrium such inflation is anticipated and only worsens inefficiencies. Equilibrium consumption equals (1/α) × ((σ−1)/σ) × (β/(1+μ)), compounding a monopoly distortion (σ−1)/σ < 1 and a cash-in-advance distortion β/(1+μ) < 1 below the efficient level 1/α. Amador and Phelan add household uncertainty about the central bank’s type — captured by the Bayesian posterior ρ that the bank is hawkish — allowing reputation to be endogenously determined and to feed back into equilibrium pricing.

Q2: Why does reputation matter only through differences in inflation costs γᵢ and not through differences in effective discount factors alone?

A2: Proposition 1 establishes that if γ₁ = γ₂ (equal inflation penalties), then even if the two types have different effective discount factors β₁ = β(1−δ) ≠ β₂ = β(1−ε), there exists a pooling Markov equilibrium in which both types choose the same action μ* and reputation plays no role. When both types have identical static incentives, they will always choose the same action given that reputation doesn’t affect payoffs in such an equilibrium. Hence the relevant dimension of heterogeneity for reputation to matter is the inflation cost parameter γᵢ, not patience.

Q3: What is the formal argument that no pooling equilibrium can exist when γ₁ ≠ γ₂?

A3: Propositions 2 and 3 provide the formal argument. If both types pool at any reputation ρ with a common positive action μ, Bayesian updating implies that ρ⁺ is independent of the money growth realization μₐ. The first-order condition for type i then reduces to the static condition (∂E[log(c) − αc|μ]/∂μ) = γᵢh’(μ), which cannot hold simultaneously for types 1 and 2 since γ₁ ≠ γ₂ and h’(μ) > 0 for μ > 0. This logic rules out pooling at the stationary reputation ρ* = ε/(δ+ε) in Proposition 2 and at any reputation where μ > 0 in Proposition 3.

Q4: Why does noise facilitate the existence of separating equilibria?

A4: Without noise, if types separate, observing the hawkish action reveals the bank is hawkish with certainty, pushing reputation to its maximum (1−δ) in a single period. This makes mimicry extremely cheap for the dovish type when β₂ is large or ε is small: the incentive compatibility condition requires that the dovish type’s static gain from choosing its own action exceeds the value gain from jumping to the best possible reputation, which is a very stringent requirement. With noise, mimicry generates only a probabilistic shift in beliefs rather than a discrete jump to the extreme, so the dovish type must maintain the hawkish action repeatedly to achieve a reputational gain — making mimicry costly enough that the incentive compatibility condition can be satisfied.

Q5: What is the “reference game” and what analytical purpose does it serve?

A5: The reference game is a variant in which the central bank’s type is fixed and is revealed to households immediately after they set prices at date t = 0. From t = 1 onward, the game reduces to the full-information, single-type game of Section 4. This allows the authors to isolate the “direct” effect of reputation — the fact that expected type affects equilibrium prices today — from the “indirect” or strategic effect of the central bank actively managing its reputation. In the numerical example, the reference-game prices form the upper dashed line in Figure 1, while the actual game’s prices form the lower solid line, with the gap between them attributable to the central bank’s incentive to restrain inflation in order to protect reputation.

Q6: What are the equilibrium price and welfare levels in the benchmark numerical example, and how do they compare to efficient and full-information benchmarks?

A6: The efficient benchmark delivers log(c) − αc = −1 with consumption c* = 1/α = 1. Under full information with only the hawkish type present, P = 1.313 and E[log(c) − αc] = −1.0297; under only the dovish type, P = 1.338 and E[log(c) − αc] = −1.0320. In the reputational equilibrium, prices lie below the full-information mixed benchmark for any given ρ (the solid line in Figure 1 lies below the dashed reference-game line), reflecting that the central banks’ desire to maintain reputation leads both types to restrain inflation beyond what the direct price effect alone would induce.

Q7: How does the U-shape of optimal central bank actions in reputation arise, and what does it imply for policy?

A7: The U-shape arises because Bayesian updating is most powerful at interior beliefs: for extreme reputations (near ε or 1−δ), any given realization of money growth moves the posterior relatively little, so the reputational cost of inflating is small. For interior (middling) reputations, the same action shifts the posterior substantially, making reputation more sensitive to inflation choices and thus increasing the marginal cost of inflating. Both types therefore choose their minimum inflationary actions at middling reputations. The policy implication is that a hawkish central bank with a very low reputation (following a run of high realized inflation outcomes) should not dramatically tighten, because further contraction does relatively little for its reputation until nature delivers enough favorable realizations to move it to a more interior range.

Q8: What happens to the ergodic distribution of reputation and inflation, and what does this imply about the persistence of reputational dynamics?

A8: Starting from ρ = 0.5, expected reputation remains in the interior: above 0.38 for the dovish type and below 0.63 for the hawkish type. The ergodic distribution of ρ (Figure 5) concentrates at interior values rather than the poles, showing that noise and type switching prevent reputation from stabilizing at extremes. The ergodic inflation distribution (Figure 6) has an average of 2.1%, compared to 2% under an all-hawkish world and 3% under an all-dovish world. Because ε = δ (types are equally likely in the long run), the unconstrained-type-weighted average would be 2.5%, so reputational incentives reduce equilibrium average inflation by approximately 0.4 percentage points.

Q9: Who gains and who loses from ongoing type uncertainty relative to immediate revelation?

A9: The hawkish type’s value function (Figure 3a) lies below the reference-game dashed line for intermediate reputations, indicating that the hawkish type is made worse off by uncertainty — it must bear the cost of restraining inflation beyond what is statically optimal in order to signal its type, but the households partially “blame” it for high realized inflation regardless. The dovish type (Figure 3b) is made better off under continuing uncertainty because its reputation benefits from households’ inability to perfectly distinguish types. Households (Figure 3c) are better off under uncertainty unless reputation is very high, because uncertainty suppresses inflation temptations for both types and keeps prices lower.

Q10: What happens to equilibrium behavior under robustness checks on key parameters?

A10: When the discount factor β or the elasticity of substitution σ decreases, both types inflate more and prices rise. When the hawkish type’s penalty γ₁ decreases (becomes less hawkish), both types inflate more and prices rise. When the dovish type’s penalty γ₂ decreases (becomes more dovish), the dovish type inflates more and, somewhat counterintuitively, the hawkish type inflates less, leaving prices roughly unchanged but slightly higher. When switching probabilities ε or δ increase, prices rise and both types inflate more, analogously to a decrease in β. Across all robustness exercises, the dovish type never inflates less than the hawkish type — consistent with Proposition 1’s implication that the inflation-cost difference γ₁ − γ₂ is the fundamental driver of separation.

Key Concepts

Hawkish type (type 1): A central bank that receives a relatively large negative payoff γ₁h(μᵢ) for taking inflationary actions, where γ₁ > γ₂. In the paper’s own sense, this type is not behavioral — it optimizes fully and can choose any action — but has a strong intrinsic cost to inflation, making it prefer lower money growth rates ceteris paribus.

Dovish type (type 2): A central bank with a lower penalty parameter γ₂ < γ₁ for inflationary actions. Like the hawkish type, it is fully strategic and optimizing, differing only in the magnitude of its intrinsic inflation cost.

Reputation (ρ): The Bayesian posterior probability that households assign to the current central bank being the hawkish type. It is the single payoff-relevant state variable in the Markov equilibrium, evolving through Bayes’ rule applied to realized money growth and type-switching probabilities.

Pure symmetric Markov perfect equilibrium: An equilibrium in which all households set the same price and consume the same amount (symmetry), and all strategies — prices P(ρ), central bank actions μ₁(ρ) and μ₂(ρ), and household consumption c(μₐ, ρ) — depend on history only through the current reputation ρ (Markov). The paper focuses exclusively on pure (non-mixed) strategy equilibria.

Pooling equilibrium: An equilibrium in which both types choose the same action μ₁(ρ) = μ₂(ρ) at some reputation ρ. The paper proves analytically that no pooling equilibrium can exist when γ₁ ≠ γ₂ and the pricing distortion is sufficiently severe (Assumption 1).

Separating equilibrium: An equilibrium in which μ₁(ρ) ≠ μ₂(ρ) for all ρ, so that realized money growth outcomes are informative about type and reputation evolves non-trivially. The paper argues that sufficient noise is necessary for such equilibria to exist.

Effective discount factor (βᵢ): The discount factor net of type-switching: β₁ = β(1−δ) for the hawkish type (which survives as hawkish with probability 1−δ) and β₂ = β(1−ε) for the dovish type. Central banks care only about payoffs while they are active, so effective discounting captures both time preference and expected tenure.

Noise (disconnection between actions and outcomes): The stochastic wedge between the central bank’s chosen action μᵢ and realized money growth μₐ, governed by a density f(μₐ|μᵢ) with full support. In the paper’s framework, noise is not merely a nuisance but a structural feature that makes reputational equilibria possible by preventing single-period complete revelation of type.

Credit Easing versus Quantitative Easing: Evidence from Corporate and Government Bond Purchase Programs

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

Using security-level data on individual corporate bond prices and the Bank of England’s published purchase quantities across its gilt purchase programs (QE1: £200bn, QE2: £125bn, QE3: £50bn, QE4: £60bn) and Corporate Bond Purchase Scheme (CBPS: £10bn of investment-grade sterling corporate bonds), this paper estimates supply effects of QE and CE on UK corporate bond prices, credit spreads, and new issuance separately, exploiting cross-sectional variation in quantities purchased as identifying variation via an instrumental variables approach. In the case of QE alone, supply effects on corporate bond prices are significant at announcement and larger over the full stock-effect horizon, but pass-through to credit spreads is found to be limited to the default-free component of corporate yields under normal market conditions — an exception is QE1 during the financial crisis, when QE’s cross-asset supply effects also significantly lowered credit spreads in the longer run. CE via the CBPS is found to be more effective than QE in reducing credit spreads for higher-rated investment-grade bonds even under normal conditions, and is the only program that generates a statistically significant increase in sterling corporate bond issuance. The results are consistent with QE and CE working through partially distinct channels — QE primarily affecting the default-free component of corporate yields, CE additionally compressing the credit-spread component — and complementing each other for higher-rated bonds.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is the empirical strategy and why use a security-level approach?

The paper uses a two-stage instrumental variables (IV) approach at the individual corporate bond level, with pre-program bond characteristics — maturity, yield-curve fitting errors, the BoE’s prior ownership share in the gilt bucket — serving as instruments for the expected distribution of purchases across bonds, allowing isolation of the supply channel from signaling and duration channels. The security-level approach offers three advantages over aggregate or event-study methods: it enables construction of “substitute buckets” (bonds whose maturity is close to the purchased bonds’) to estimate cross-asset supply effects; it permits direct comparison of the price elasticity with respect to gilt purchases (cross-asset effect) versus corporate bond purchases (within-asset effect); and it allows estimation of both the announcement-day effect and the stock effect — the cumulative price and spread change over the life of each program — which captures the longer-run portfolio-rebalancing contribution separately from the initial market reaction.

Q2. What are QE’s effects on corporate bond prices and credit spreads?

For QE alone (QE1–3), the instrumented gilt substitute purchases have positive and statistically significant effects on corporate bond prices at announcement across all three programs — in the case of QE1, the average 30 basis-point decline in corporate yields on the announcement day is attributed in full to QE supply effects in the paper’s regression. The stock effect — estimated over the full life of each program — is significantly larger than the announcement-day effect, consistent with gradual portfolio rebalancing as predicted by Greenwood, Hanson, and Liao (2018). However, except for QE1, the supply effects do not carry through to credit spreads in either the short run or the longer run, which the paper interprets as consistent with QE working primarily through the default-free component of the corporate yield: corporate yields fell in line with gilt yields, but spreads over gilts were unchanged.

Q3. When does QE affect credit spreads?

QE1’s cross-asset supply effects significantly lowered credit spreads in the longer run, even though QE2 and QE3 do not generate significant credit spread compression in either the short or long run, suggesting that the supply channel interacts with the liquidity channel specifically under conditions of financial market distress. The paper interprets the QE1 exception as reflecting the severe disruption during the 2008–09 financial crisis: when capital mobility across markets is constrained and liquidity premia are elevated, central bank purchases of safe assets may also improve trading conditions in indirectly targeted, less liquid markets such as the corporate bond market, reducing the liquidity component of corporate spreads. This interaction does not appear to be operative in the more normal market conditions of QE2 and QE3.

Q4. How does CE compare to QE in reducing credit spreads and stimulating issuance?

CE via the CBPS is found to be more effective than QE in reducing credit spreads for higher-rated investment-grade bonds even under normal financial market conditions, and a corporate bond’s price sensitivity to its own CBPS purchases is substantially higher than its price sensitivity to gilt substitute purchases; CE is also the only program with a statistically significant positive effect on new sterling corporate bond issuance. Across QE1–3, there is no statistically significant impact of gilt purchases on sterling corporate issuance, while CBPS purchases have positive and statistically significant effects on new sterling corporate bond issuance. The paper characterizes CE and QE as complementary for higher-rated bonds: CE’s credit-spread reduction layers on top of QE’s default-free component effect, making the total stock effect larger than either program alone.

Q5. What happens for lower-rated investment-grade bonds?

For lower-rated investment-grade bonds, the evidence for both cross-asset QE supply effects and within-asset CE supply effects is weaker, and the paper suggests that CE’s stimulation of new bond issuance may have counterbalanced its positive price effects for these bonds through the dilutive effect of new supply. The mechanism is that CE’s reduction in the cost of corporate bond issuance for lower-rated firms induced enough new bond issuance to partially offset the price increase from CBPS purchases, consistent with the issuance channel being most active for the market segment where CBPS created the largest pricing improvement. This dilution effect implies that the net price benefit of CE for lower-rated bonds is smaller than the gross supply-effect estimate.

Key concepts

stock effect : the cumulative effect of the total quantity of bonds purchased under a program on bond prices and spreads, estimated over the full life of the program; in this paper the stock effect is significantly larger than the announcement-day effect, consistent with gradual portfolio rebalancing.

cross-asset supply effect : the pass-through of government bond (gilt) purchase supply shocks to the prices of corporate bonds — an asset class not directly targeted by QE; the paper provides the first estimates of this cross-market supply channel at the security level.

credit spread : the difference between the yield on a corporate bond and the yield on a risk-free government bond of the same maturity; the paper finds QE pass-through is generally limited to the default-free component of corporate yields rather than the credit spread.

default-free component : the part of a corporate bond’s yield attributable to the risk-free interest rate rather than credit risk; the paper finds that QE supply shocks affect this component but generally leave the credit spread unchanged in normal market conditions.

within-asset substitution effect : the price effect of CE purchases on the bonds directly purchased and their corporate bond substitutes, as distinct from cross-asset effects; the paper finds this effect is substantially larger in magnitude than the cross-asset QE effect on corporate bonds.

issuance channel : the mechanism by which lower corporate borrowing costs induced by CE stimulate new corporate bond issuance; the paper finds this channel operates under CE (CBPS) but not under QE (gilt purchases).

Dollar Dominance and the Transmission of Monetary Policy

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

Layer 1 — Summary

An emerging view in international macroeconomics contends that dollar invoicing of exports renders monetary policy ineffective for non-U.S. countries: because export prices are allegedly sticky in dollars, exchange rate depreciations cannot shift expenditure toward domestic goods, muting the classical Mundell-Fleming channel. McLeay and Tenreyro argue that this view rests on empirical assumptions that are not borne out by the data: goods priced in dollars tend to have more flexible prices and higher elasticities of substitution, not the monopoly power and sticky dollar prices assumed in dominant currency pricing (DCP) models. They propose a mixed currency pricing (MCP) framework that incorporates heterogeneous price flexibility and intra-sector international competition, and show that even with dollar pricing, depreciating the currency by loosening monetary policy can still boost exports and activity materially. The limit to any expansion is not demand, but supply capacity: after a depreciation, domestic dollar costs fall, flexible-price exporters lower prices slightly and gain large market share due to high demand elasticities, and the expansion runs until rising marginal costs offset the initial depreciation — producing limited reduced-form dollar pass-through as an equilibrium result rather than evidence of nominal stickiness. Empirical tests using monetary policy shocks in a sample of emerging and developing economies, case studies of Canada and Chile as commodity exporters, and three large devaluation episodes all find significant, material increases in exports and aggregate activity following exchange-rate depreciations, consistent with the MCP model’s predictions.

Layer 2 — Q&A

Q1. What is the specific empirical claim that DCP models rest on, and how do McLeay and Tenreyro challenge it?

DCP models (e.g., Gopinath et al. 2020) posit that exporters invoicing in dollars have monopoly power and face nominal rigidities that keep their dollar export prices sticky. The observable implication used to motivate this assumption was limited exchange rate pass-through to dollar export prices. McLeay and Tenreyro show that low pass-through is equally consistent with a flexible-price, high-elasticity equilibrium. When demand elasticities are high, firms optimally absorb exchange rate changes through quantities rather than prices; the reduced-form pass-through coefficient is small even without any nominal friction. Low pass-through is therefore not informative about the degree of nominal rigidities, and using it to calibrate sticky-price DCP models and draw normative conclusions about exchange rate policy is unwarranted.

Q2. What are the three empirical facts that motivate the MCP framework’s assumptions?

Fact 1: Homogeneous products (commodities and commodity-like goods traded on organized exchanges or reference-priced, following Rauch 1999) represent a large share of goods exports, exceeding 70% for developing economies, around 60% for emerging economies, and around 35% for advanced economies; Sub-Saharan Africa, Latin America, and the Middle East all have shares above 50%. Fact 2: Homogeneous and more competitively produced goods have more flexible prices, documented across multiple countries — for instance, Nakamura and Steinsson (2008) find a median monthly price-change frequency of 10.8% for finished-good producer prices but 98.9% for crude materials. Fact 3: Dollar (vehicle currency) invoicing is most prevalent precisely in these homogeneous, competitive-good sectors; classical work by McKinnon (1979) and Magee and Rao (1980) emphasized that vehicle-currency invoicing facilitates continuous price comparability in competitive markets, and panel regressions corroborate a positive relationship between the share of exports invoiced in dollars and the homogeneous-goods share of exports.

Q3. What is the mechanism through which depreciation boosts exports in the MCP model, and why does this generate low observed pass-through?

With sticky wages (representing non-tradable input price stickiness more broadly), a monetary policy-induced depreciation lowers the domestic cost of production when expressed in dollars. For competitive exporters facing highly elastic demand, even a small reduction in the dollar price translates into a substantial gain in export quantities. Firms therefore lower their dollar prices slightly, trading some profit margin for a large increase in market share. As exports expand, domestic marginal costs rise (firms move up the upward-sloping marginal cost curve), partially offsetting the depreciation’s effect on dollar costs. In equilibrium, the net dollar price movement is small — producing the observed limited pass-through — but the quantity response is large. In the perfectly competitive limit (relevant for commodity exporters), the dollar price is unchanged by the world market, and the entire adjustment is through an expansion of export volumes until rising domestic marginal costs absorb the depreciation. The implied observation is identical to a sticky-price model for prices, but “the implications for export quantities are diametrically opposed.”

Q4. How does the MCP model nest existing frameworks, and what does it add relative to the DCP and PCP benchmarks?

The MCP (mixed currency pricing) framework nests sticky-price DCP as a special case (by setting demand elasticities low and allowing full price stickiness) and produces behavior close to PCP (producer currency pricing) in the flexible-price, high-elasticity limit — restoring the allocative properties of the exchange rate from Obstfeld and Rogoff (1995). The distinctive addition is intra-sector international competition: domestic exporters face competition from international competitors producing highly substitutable varieties of the same good, so substitution elasticities can be high at the variety level even when macro-level elasticities between goods remain low. This follows a bottom-up approach to elasticities as in Feenstra et al. (2018). The model also allows heterogeneous nominal rigidities across producers, with exporters of dollar-invoiced homogeneous goods having flexible prices while non-tradable input prices (wages) remain sticky — the source of monetary non-neutrality and the mechanism for real exchange rate effects.

Q5. What is the role of supply capacity, and why is it “the limit” rather than demand?

In the sticky-price DCP model, the constraint on the export response is on the demand side: dollar prices do not move, so demand is unchanged, and there is no export response at all. In the MCP model, demand responds immediately to the cost reduction — the constraint that eventually stops the expansion is supply capacity, captured by the slope of the marginal cost curve and macroeconomic constraints on non-tradable inputs. With a flat marginal cost curve (plentiful supply capacity), exports expand materially; with a steep curve or hard capacity constraints, the increase in marginal cost fully offsets the depreciation before much quantity adjustment occurs. This supply-side framing reorients the policy question: the limiting factor for monetary policy’s external effectiveness is not whether dollar prices can move, but whether the domestic economy has the productive capacity to expand tradable output. This also connects the paper to the Salter-Swan two-good framework and to Schmitt-Grohé and Uribe (2021).

Q6. What do the macroeconomic empirical tests find, and how do they distinguish the MCP from sticky-price DCP?

The paper uses three empirical exercises. First, using a sample of developing and emerging economies, monetary policy expansions that generate exchange rate depreciations cause significant increases in both exports and aggregate economic activity — consistent with the MCP model’s material export response and inconsistent with the DCP prediction of no export channel. Second, focusing on Canada and Chile as commodity exporters where the MCP assumptions (competitive markets, flexible export prices) are especially applicable, the aggregate results are corroborated and sectoral evidence provides additional support. Third, three case studies of large devaluations in the sample document that they are followed by material increases in exports relative to trend. In all exercises, the direction and magnitude of export and output responses are consistent with a functioning expenditure-switching channel, even where exports are priced in dollars.

Q7. How does the paper reinterpret the pass-through evidence that motivated sticky-price DCP models, and what does this imply for normative conclusions?

Standard reduced-form pass-through regressions relate the change in dollar export prices to changes in the exchange rate. These regressions typically omit or fail to fully capture movements in marginal cost. In the MCP model, flexible-price firms fully pass through changes in marginal cost; the observed limited pass-through to export prices is an equilibrium result of the offsetting rise in marginal costs as export volumes expand, not evidence of a nominal friction. Because the standard regressions omit marginal cost dynamics, they risk attributing the equilibrium quantity-driven equilibrium to a pricing friction. This has direct normative implications: the case made by the IMF (2019, 2020) that dollar invoicing worsens the cost-benefit calculation for flexible exchange rates — and may bolster the case for capital controls — rests on interpreting low pass-through as evidence of stickiness. If low pass-through instead reflects high demand elasticities and supply-side adjustment, the normative argument for constraining exchange rate flexibility is weakened.

Q8. How does the paper relate to the purchasing power parity puzzle and the Mussa puzzle?

The MCP framework offers explanations for two classic international macro puzzles without assuming nominal rigidities in export prices. On the PPP puzzle (the volatility and persistence of the real exchange rate, Rogoff 1996): in the MCP model, exporters’ optimal reset prices move very little after exchange rate changes — not because of stickiness, but because demand is elastic and marginal costs rise quickly. This predicts limited movement in relative export prices, consistent with empirical evidence in Blanco and Cravino (2020) and Itskhoki and Mukhin (2025). On the Mussa puzzle (the large jump in nominal and real exchange rate volatility after the Bretton Woods collapse): the model’s mechanism via sticky wages is consistent with evidence that depreciations produce slow adjustment of non-tradable prices (Burstein, Eichenbaum, and Rebelo 2005), generating real exchange rate movements despite limited response in traded-good dollar prices.

Key Concepts

Dominant currency pricing (DCP): A framework in which non-U.S. exporters set and maintain prices in U.S. dollars, with sticky dollar prices. As formulated by Gopinath et al. (2020), DCP predicts that exchange rate depreciations by non-U.S. countries do not reduce dollar export prices and therefore do not stimulate export demand — muting the expenditure-switching channel of monetary policy.

Mixed currency pricing (MCP): The framework introduced in this paper. It allows heterogeneous price flexibility and market structure across export sectors, nesting both sticky-price DCP and flexible-price PCP as special cases. Dollar-priced exports face elastic demand from international competition, have flexible prices, and respond to depreciations through quantities rather than prices. Non-traded inputs (wages) remain sticky, providing the source of monetary non-neutrality.

Expenditure-switching channel: The mechanism by which exchange rate depreciations redirect spending toward domestically produced goods, boosting exports and aggregate demand. In PCP models, this works through a fall in relative export prices. In the MCP model, it works through an expansion in export quantities even when dollar prices change little.

Exchange rate pass-through (to export prices): The elasticity of dollar export prices with respect to the nominal exchange rate. In sticky-price DCP models, low pass-through reflects a nominal friction (prices cannot adjust). In the MCP model, low pass-through reflects high demand elasticities and offsetting marginal cost increases: it is an equilibrium outcome, not a friction, and therefore does not imply that export volumes are unresponsive.

Intra-sector international competition: The market structure feature central to the MCP framework. Domestic exporters of a given good compete with foreign suppliers of highly substitutable varieties, making their demand elastic at the variety level even if aggregate elasticities across different goods categories are low. This follows Armington (1969) as implemented by Feenstra et al. (2018).

Supply capacity constraint: In the MCP model, the binding constraint on how much a depreciation can boost exports. With high demand elasticities, demand for domestic exports expands freely; the limit is set by how quickly rising domestic marginal costs absorb the improvement in export profitability. The supply constraint replaces the demand constraint that operates (mechanically, via zero price response) in sticky-price DCP models.

Homogeneous goods (Rauch 1999 classification): Goods traded on organized commodity exchanges or reference-priced in trade publications, as opposed to differentiated goods. McLeay and Tenreyro use this classification to establish that dollar-invoiced exports are disproportionately homogeneous, competitive, and flexible-priced — contrary to the DCP assumption of monopoly power and price stickiness.

Summary based on published open-access version. AI-assisted, human review pending.

Inference Based on Time-Varying SVARs Identified with Sign Restrictions

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

Layer 1 — Overview

Research Question. The paper asks how to conduct valid Bayesian inference in time-varying structural vector autoregressions (SVARs) identified with sign restrictions, a setting in which existing algorithms are shown to be theoretically flawed. As an empirical illustration, the authors use the new framework to examine three questions about the 2022–2023 Federal Reserve tightening cycle: (i) how did the Fed respond to the state of the economy; (ii) how would more dovish or hawkish stances have fared; and (iii) was the Fed behind the curve in 2021, and at what cost?

Methodology. The paper defines a class of rotation-invariant time-varying SVARs, building on Bognanni (2018). A model belongs to this class when its prior over sequences of structural parameters is invariant to orthogonal transformations of those sequences—i.e., it assigns equal prior density to all observationally equivalent structural parameter sequences (Proposition 1 establishes that observational equivalence corresponds exactly to orthogonal rotation of the sequence). The authors prove an if-and-only-if characterization (Proposition 2): a prior belongs to this class if and only if the induced prior over sequences of orthogonal matrices is uniform and independent of the time-varying reduced-form parameters.

A specific member of this class, the Random Correlations SVAR (RC-SVAR), is constructed by combining a prior over time-varying reduced-form parameters based on Archakov and Hansen’s (2021) parametrization of correlation matrices with a uniform prior over sequences of orthogonal matrices. The RC-SVAR is preferred over alternatives (Primiceri 2005’s decomposition, which is order-dependent; Bognanni’s 2018 discounted Wishart model, whose marginal likelihood significantly underperforms) because, for the type of empirical applications considered, it generally implies a higher log-predictive score than most orderings of the Primiceri (2005) model.

The authors introduce three algorithms. Algorithm 1 (simple acceptance sampling) is theoretically correct but computationally infeasible when sign restrictions span many periods because the probability of satisfying all restrictions simultaneously converges to zero as sample length T grows. Algorithm 2, the current approach in the literature (Baumeister and Peersman 2013; Bognanni 2018; Debortoli, Galí and Gambetti 2020), draws orthogonal matrices period-by-period from the sign-restriction-truncated uniform distribution; the authors show this does not draw from the correct target posterior because the resulting prior over orthogonal matrices is not independent of the reduced-form parameters and therefore the prior does not satisfy the rotation-invariance condition. Algorithm 3, the paper’s contribution, uses a Gibbs sampler that incorporates the Particle Gibbs with Ancestor Sampling (PGAS) method of Lindsten, Jordan and Schon (2014) to draw sequentially from the correct target posterior conditional on sign restrictions over an arbitrary number of periods.

An important additional contribution is the allowance for time-varying sign restrictions—restrictions that are imposed only in selected periods—enabling researchers to tailor identification to institutional knowledge about when particular restrictions are economically appropriate.

Data and Empirical Application. The RC-SVAR is estimated at a quarterly frequency with five variables: output growth (log difference of real GDP), core inflation (log difference of core PCE price index), the federal funds rate, money growth (log difference of M2), and the Moody’s Baa corporate bond yield relative to the 10-year Treasury yield (credit spread). The sample runs from 1959:Q1 to 2023:Q2, with a constant and two lags (n=5, p=2, m=11). Four independent MCMC chains of 20,000 draws are used, keeping every tenth draw after discarding the first 2,500; 1,800 particles approximate the reduced-form posterior and 3,600 particles approximate the posterior of the orthogonal matrices.

Main Findings. Decomposing the unexpected change in the federal funds rate from 2022:Q2 to 2023:Q2 into contributions from the predictable component, the systematic monetary policy response to non-monetary-policy shocks, and pure monetary policy shocks, the authors find that the lion’s share of the unpredictable rate increase was a systematic response to non-monetary policy shocks. Monetary policy shocks contributed about 100 basis points of the unexpected change in the federal funds rate by 2023:Q2 (out of roughly 4.99 percentage points of cumulative actual funds rate).

In the Dovish Fed counterfactual—where the response of the federal funds rate to contemporaneous inflation is halved for the first quarter of 2022—the economy would have marginally overheated, with inflation running persistently above 5 percent. In the Hawkish Fed counterfactual—where the response to inflation is doubled—inflation would have quickly declined at a small output cost: focusing on posterior medians, real GDP in 2023:Q2 would have been about 0.7 percent lower than in the data, though the lower envelope of the 68 percent probability bands indicates the output cost could have been as large as 3.1 percent.

Regarding the “behind the curve” question, the model finds evidence that the Fed was accommodative in 2021 (expansionary monetary policy shocks in that period), consistent with Summers (2021b). However, monetary policy shocks contributed only about 0.6 percentage points to annualized core inflation during 2021:Q2–2021:Q4 on a cumulative basis; the larger and dominant source of the unexpected inflation surge was non-monetary policy shocks. A comparison of the RC-SVAR with a constant-parameter SVAR identified only by Restriction 1 (Uhlig 2005) shows substantively different conclusions: the constant-parameter model attributes the unexpected increase in the federal funds rate to shocks that affect money growth and credit spreads, without a clear connection to the real economy, whereas the RC-SVAR links the rate increases to shocks that made the economy run hotter.

Layer 2 — Q&A

Q1: What is the fundamental theoretical flaw in existing algorithms for time-varying SVARs identified with sign restrictions, and why does it matter?

Existing algorithms (e.g., Baumeister and Peersman 2013; Bognanni 2018; Debortoli, Galí and Gambetti 2020) draw orthogonal matrices period-by-period from the uniform distribution restricted to those matrices satisfying the sign restrictions at each t. This construction implicitly defines a marginal density for the orthogonal matrices conditional on the reduced-form parameters that is not uniform: it is proportional to the reciprocal of the volume of the sign-restriction-satisfying subset of the orthogonal group, which depends on the reduced-form parameters. Consequently, the prior over structural parameters implied by these algorithms does not assign equal density to observationally equivalent sequences of structural parameters, violating Proposition 2’s necessary and sufficient condition. The resulting posteriors are therefore not correctly targeted to the desired posterior, meaning inference is distorted in a way that cannot be corrected by importance reweighting without prohibitive computation.

Q2: What does Proposition 1 establish, and how does it generalize the constant-parameter case?

Proposition 1 proves that two sequences of time-varying structural parameters are observationally equivalent if and only if there exists a sequence of orthogonal matrices such that one sequence is obtained from the other by post-multiplying each period’s structural parameters by the corresponding orthogonal matrix. This directly mirrors the constant-parameter result in Rubio-Ramírez, Waggoner and Zha (2010) and Uhlig (2005), where a single orthogonal matrix produces observational equivalence. The extension to sequences is non-trivial because the law of motion couples parameter draws across time, but the likelihood’s separability across periods preserves the period-by-period orthogonal rotation structure.

Q3: What is Proposition 2, and what is its practical implication for constructing valid priors?

Proposition 2 states that the prior over time-varying structural parameters satisfies the rotation-invariance condition (Equation 3) if and only if the induced prior over the time-varying orthogonal reduced-form parameters does not depend on the sequence of orthogonal matrices—equivalently, the prior over (Qt) is uniform over the product of orthogonal groups and is independent of the reduced-form parameters (Bt, Σt). The practical implication is constructive: any prior over time-varying reduced-form parameters (Bt, Σt), combined with an independent uniform prior over sequences of orthogonal matrices, automatically produces a rotation-invariant SVAR. This means that widely-used priors for reduced-form time-varying VARs (Primiceri 2005, Bognanni 2018, the new RC prior) can all be adapted for structural analysis without modification, as long as the orthogonal matrices are drawn uniformly and independently of the reduced-form parameters.

Q4: Why do models with heteroskedastic structural shocks (identification via heteroskedasticity) not belong to the class of rotation-invariant SVARs?

In models identified through heteroskedasticity, the time-varying structural parameters take the form (A Ψt^{-1/2}, F Ψt^{-1/2}), where Ψt is a time-varying diagonal matrix. For any permissible sequence, post-multiplying by a non-diagonal orthogonal matrix at one period produces a sequence where the ratio of structural parameters across consecutive periods is not diagonal, which violates the permissibility constraint of those models. Thus, the class of rotation-invariant SVARs and models identified through heteroskedasticity are mutually exclusive when the heteroskedastic specification has constant impulse responses up to scale—a restriction that the authors note has been criticized as a potential weakness of the heteroskedasticity-based approach.

Q5: Why is the Random Correlations SVAR (RC-SVAR) chosen as the baseline, and how does it compare to alternatives?

The RC-SVAR uses the Archakov and Hansen (2021) parametrization of correlation matrices to define a prior over time-varying reduced-form parameters that is order-invariant (unlike Primiceri 2005, which produces n! different elements depending on variable ordering) and avoids the highly restrictive structure of Bognanni’s (2018) discounted Wishart model, which significantly underperforms in marginal likelihood. For the empirical applications considered, Arias, Rubio-Ramírez and Shin (2023) show the RC-SVAR generally achieves a higher log-predictive score than most orderings of the Primiceri (2005) model, motivating its use as the baseline. The theoretical results apply to any member of the rotation-invariant class, so the algorithm is not specific to the RC-SVAR.

Q6: Why are time-varying sign restrictions important, and how are they implemented in the monetary policy application?

Time-varying sign restrictions allow researchers to impose identification restrictions only in periods where those restrictions are economically appropriate, adhering to the principle “If you know it, impose it; if you do not know it, do not impose it” (Uhlig 2017). In the monetary policy application, Restriction 2 (which constrains the contemporaneous elasticities in the policy rule to plausible ranges, following Arias, Caldara and Rubio-Ramírez 2019) is not imposed during three exceptional periods: 1979:Q4–1982:Q4 (non-borrowed reserves targeting under Volcker), 2009:Q1–2015:Q3 (quantitative easing following the Great Recession), and 2020:Q2–2021:Q4 (QE and effective zero lower bound during COVID-19). Restriction 1 (sign restrictions on impulse responses to a monetary policy shock, following Uhlig 2005) is imposed throughout the entire sample.

Q7: What do the estimated contemporaneous elasticities reveal about how monetary policy has changed over time?

The model estimates show substantial time variation. The contemporaneous elasticity of the federal funds rate to output growth exhibits three peaks: during Arthur Burns’s chairmanship in 1974 (capturing the sharp rate cut during the 1974–1975 recession), during Volcker’s chairmanship in 1983–1984 (when annualized real GDP growth averaged 6.8 percent), and during Greenspan’s tenure in 2001 (when the federal funds rate fell from 6.4 percent in December 2000 to 1.8 percent by end-2001). Outside these peaks, the elasticity averaged about 0.1, implying a 0.1 percentage point rise in the annualized federal funds rate per 1 percentage point increase in annualized GDP growth. The elasticity to inflation averaged about 0.3 percentage points per 1 percentage point rise in annualized core inflation, with a range from above 0.5 in the early 1970s and early Volcker years down to about 0.15 during Yellen’s tenure. The elasticity to the credit spread moved from about −1.4 at the beginning of Burns’s tenure to −2.2 at the end of Nixon’s presidency, then declined through the mid-1970s to the Great Recession, and stood at about −1 by mid-2023.

Q8: What is the exact decomposition of the 2022–2023 tightening cycle into predictable, systematic non-monetary, and monetary policy shock components?

Table 1 from the paper shows the federal funds rate decomposition. In 2022:Q2, the predictable component was 0.27 percentage points, the unpredictable component due to systematic response to non-monetary shocks was 0.24 pp, and the unpredictable component due to monetary policy shocks was 0.26 pp, summing to 0.77 pp. By 2023:Q2, these were 1.70 pp (predictable), 2.25 pp (systematic/non-monetary), and 1.04 pp (MP shocks), totaling 4.99 pp. Thus, at the tightening cycle’s end in 2023:Q2, the systematic response to non-monetary shocks accounted for about two-thirds of the unpredictable component (2.25 / (2.25 + 1.04) ≈ 68 percent), consistent with the broader literature finding that most variation in policy instruments is driven by the systematic component of policy.

Q9: How do the Hawkish and Dovish Fed counterfactuals work, and what do they imply?

The Hawkish (Dovish) counterfactual replaces the estimated contemporaneous response to inflation in the policy rule with one that is twice (half) as large as the estimated response for the first quarter of 2022, then simulates history forward from 2022:Q2 under the modified rule. Under the Dovish Fed, the economy would have marginally overheated with output rising above CBO potential GDP estimates, and inflation would have run persistently above 5 percent. Under the Hawkish Fed, posterior medians show inflation quickly declining at a cost of about 0.7 percent of real GDP in 2023:Q2 relative to the data; the lower envelope of the 68 percent probability bands shows the output cost could have been as large as 3.1 percent. A parallel set of counterfactuals, designed to be robust to the Lucas critique by working through one-time monetary policy shocks rather than changes to the reaction function, yields broadly similar results.

Q10: What does the comparison with Romer and Romer (2023a) reveal about the model’s monetary policy shock series?

Romer and Romer (2023a) identify a contractionary monetary policy shock in July 2022 (2022:Q3) using a narrative approach. The RC-SVAR’s estimated monetary policy shock series is broadly consistent with this finding: the model detects a contractionary shock in 2022:Q3 and, like Romer and Romer, also finds some evidence of a contractionary shock in 2022:Q2 (though they characterized it as “signs but not definitive evidence”). Beyond the Romer-Romer estimation window, the RC-SVAR additionally finds evidence of an expansionary monetary policy shock in 2023:Q1, when the Fed decelerated the pace of rate increases from 50 to 25 basis points.

Q11: How does the RC-SVAR’s inference on the 2022–2023 tightening cycle differ from that of a constant-parameter SVAR identified only with Restriction 1?

Two salient differences emerge. First, through the lens of the constant-parameter SVAR, monetary policy shocks contribute insignificantly to unexpected output growth between 2022:Q2 and 2023:Q2; in fact, the posterior median output response to a contractionary monetary policy shock is positive in that model (consistent with Uhlig 2005’s finding), implying that the positive monetary policy shocks needed to explain the rate increase would propel rather than reduce output. In the RC-SVAR, the posterior median output response to a contractionary shock is negative, so contractionary monetary policy shocks worked to decelerate output against a backdrop of non-monetary shocks that made the economy run hotter. Second, in the constant-parameter SVAR, non-monetary policy shocks that drive the unexpected increase in the federal funds rate do not propagate through output or inflation, whereas in the RC-SVAR they do—yielding a much more coherent macroeconomic narrative for the tightening cycle.

Q12: What does the model find about whether the Fed was behind the curve in 2021, and what were the consequences?

The model’s 2021:Q1 forecasts predicted the federal funds rate would reach about 0.6 percent by end-2021, consistent with a view that rate normalization was already warranted. The actual federal funds rate remained at its effective lower bound through 2021:Q4, and the shock decomposition shows that the cumulative unexpected change in the funds rate during 2021:Q2–2021:Q4 was driven by expansionary monetary policy shocks—supporting the view that monetary policy was accommodative and the FOMC fell behind the curve. However, monetary policy shocks contributed only about 0.6 percentage points (annualized) to the unexpected increase in core inflation during this period; the dominant and larger source of the inflation surge was non-monetary policy shocks. The model therefore finds that the delay in tightening was not the primary driver of the 2021 inflation surge.

Q13: Do time-varying sign restrictions materially affect inference, as demonstrated in Section 6.8?

Yes. Comparing the baseline identification scheme (Restrictions 1 and 2, with Restriction 2 not imposed during exceptional periods) against an alternative scheme that imposes both restrictions throughout the entire sample reveals differences in the estimated monetary policy shocks, particularly in 2021:Q4. Under the alternative scheme, there was an expansionary monetary policy shock in 2021:Q4, while the baseline finds the shock was nearly centered around zero. Additionally, for 2021:Q2, the alternative scheme implies the contemporaneous output response to an expansionary monetary policy shock is more likely to have been positive, whereas the baseline scheme yields a different posterior distribution for this response. These differences illustrate that imposing or omitting restrictions in specific periods affects inference about structural shocks and impulse responses at economically important junctures.

Key Concepts

Rotation-Invariant Time-Varying SVAR: A class of time-varying SVAR models whose prior over sequences of structural parameters satisfies: for every permissible sequence of structural parameters and every sequence of orthogonal matrices, the orthogonally-rotated sequence is also permissible and receives the same prior density. This ensures the prior does not break the observational equivalence among structural parameter sequences related by orthogonal rotation, so that identification comes solely from the imposed restrictions.

Observational Equivalence in Time-Varying SVARs: Two sequences of time-varying structural parameters are observationally equivalent if and only if there exists a sequence of orthogonal matrices such that one sequence equals the other sequence post-multiplied period-by-period by the corresponding orthogonal matrix. This definition extends Rothenberg’s (1971) concept to the time-varying setting and directly implies the rotation-invariance restriction.

Random Correlations SVAR (RC-SVAR): A specific member of the rotation-invariant class constructed by using the Archakov and Hansen (2021) parametrization of correlation matrices to define the prior over time-varying reduced-form parameters, combined with a uniform prior over sequences of orthogonal matrices. The prior is order-invariant and, for the empirical applications considered, generally achieves higher log-predictive scores than the workhorse Primiceri (2005) model.

Time-Varying Sign Restrictions: Sign restrictions imposed only on selected time periods rather than uniformly across the sample, implemented by allowing the restriction function St() to differ across t (including the possibility that no restriction is imposed at some t). This allows researchers to tailor identification to periods in which the theoretical or institutional knowledge motivating the restriction is deemed applicable—e.g., imposing policy-rule contemporaneous restrictions only when the federal funds rate is the primary policy instrument.

Particle Gibbs with Ancestor Sampling (PGAS): The sequential Monte Carlo method (from Lindsten, Jordan and Schon 2014) used in the paper’s Algorithm 3 to draw the sequence of structural parameters At from its conditional posterior given the sign restrictions. PGAS conditions on the previous Gibbs draw of the structural parameter sequence to ensure an invariant distribution, which is the key property that makes the Gibbs sampler valid for drawing from the correct target posterior.

Systematic Component of Monetary Policy: In the paper’s structural monetary policy equation, the linear combination of contemporaneous endogenous variables (output growth, inflation, money growth, credit spread) that enters the federal funds rate equation, weighted by the contemporaneous elasticities ψ. It represents the portion of interest rate variation that is a predictable, rule-based response to economic conditions, as distinguished from the monetary policy shock (the residual).

Contemporaneous Elasticity: The coefficient ψi,t in the monetary policy equation measuring the response of the federal funds rate to a one-unit contemporaneous change in variable i at time t, defined directly in terms of the structural parameter matrix At. The paper’s time-varying framework allows these elasticities to evolve over the sample, revealing historically distinct episodes of how aggressively the Fed responded to output growth, inflation, money growth, and credit spreads.

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.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

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 Policy, Employment Shortfalls, and the Natural Rate Hypothesis

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

This paper examines optimal monetary policy under discretion when the loss function is asymmetric — placing greater weight on employment shortfalls than on equivalently sized employment strength. The model satisfies the natural rate hypothesis (NRH): monetary policy is neutral in the long run, so persistent accommodation of above-potential activity raises inflation expectations without permanently boosting employment. The central paradox the paper establishes is that an asymmetric shortfalls-oriented loss function, despite its stated goal of reducing shortfalls, exacerbates them: the mechanism runs through the NRH expectation-adjustment channel, which creates an inflationary bias structurally analogous to the Barro-Gordon result. Mandating a central bank objective that is more symmetric than the social loss function — a conservative-in-asymmetry design — lowers both the frequency of activity shortfalls and the inflationary bias. As a corollary, the analysis implies that monetary accommodation of labor market strength requires justifications beyond the asymmetric costs of shortfalls, such as permanent effects of strong labor markets on economic potential.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. How does the asymmetric loss function exacerbate employment shortfalls?

The mechanism runs through the natural rate hypothesis: under a loss function that places no weight on activity above potential, the optimal policy fully accommodates positive supply shocks by allowing above-potential output, but the NRH then raises the expectational baseline, making shortfalls more frequent as the perceived natural rate adjusts upward. Because the central bank treats above-potential activity as costless, it does not resist the accumulation of above-potential output in good states; expectations of future activity then rise, effectively moving the benchmark against which shortfalls are measured, and making shortfalls a more common outcome. The asymmetric policy thus generates a self-defeating dynamic: attempts to minimize shortfalls through accommodation of strength create an expectational environment in which shortfalls are more frequent.

Q2. How does the inflationary bias emerge?

The inflationary bias is structurally analogous to the Barro-Gordon (1983) time-inconsistency result: the central bank’s asymmetric desire to reduce shortfalls leads it to ease policy more aggressively than a symmetric loss function would warrant, and this tendency transmits into persistently higher inflation through the NRH expectations-adjustment channel. The classic Barro-Gordon mechanism operates through the desire to push output above its natural rate; here the analog is the desire to push activity above the shortfalls threshold. The paper’s model is constructed so that no Barro-Gordon bias exists in the baseline symmetric case, isolating the asymmetry as the sole source of the inflationary bias.

Q3. What policy prescription follows from the analysis?

The paper recommends mandating a central bank objective that is more symmetric than the social loss function, analogous to Rogoff’s (1985) conservative-central-banker result but applied to the dimension of asymmetry rather than the level of inflation aversion. A mandate that requires the CB to weight above-potential and below-potential activity more equally than society does lowers both the frequency and depth of shortfalls and reduces inflationary bias, improving welfare relative to a CB that faithfully implements the asymmetric social preference. The paper further shows that optimal policy under this design does not accommodate fluctuations from aggregate demand shocks, implying that accommodation of labor market strength requires other justifications — such as permanent productivity effects — not the shortfalls-cost asymmetry alone.

Key concepts

shortfalls asymmetry : the specification in which the central bank’s or social loss function places greater weight on employment below its natural rate than on equivalently sized employment above it; the paper’s central object of analysis.

natural rate hypothesis (NRH) : the assumption that monetary policy is neutral in the long run — persistent monetary accommodation does not permanently raise employment above its natural rate but does raise the price level; imposes the constraint that bounds the central bank’s ability to durably lower shortfalls.

inflationary bias : the systematic tendency of a central bank operating under a shortfalls-oriented asymmetric loss function to allow above-target inflation on average; emerges in this model via the NRH expectations-adjustment channel, analogous to but distinct from the Barro-Gordon result.

Money Markets, Collateral and Monetary Policy

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

The paper studies the euro area interbank money markets during the global financial crisis (2007–09) and sovereign debt crisis (2010–15), documenting four empirical regularities and building a quantitative general equilibrium model to evaluate their macroeconomic impact and the role of central bank policy. The central finding is that the ECB’s collateral policy — lending to banks at haircuts more favorable than private markets — prevented output and investment from falling roughly twice as much as they would have under a passive constant-balance-sheet policy.

Four empirical observations (Section 2, 2003–2015):

The share of unsecured interbank borrowing declined throughout the euro area; banks substituted toward secured (repo) transactions — the secured share rose from roughly 42% to 90% of turnover
Private market haircuts on Southern sovereign bonds (IT, ES, PT) rose dramatically during the sovereign debt crisis, peaking at 25.16% in 2012–2013 (vs 3% in 2010) — while the ECB kept its haircuts nearly unchanged, creating a “haircut gap”
Bank borrowing from the ECB increased eight-fold in Southern regions as the haircut gap widened
Household deposits at banks remained stable throughout

Model architecture (Section 3): Two regions (North: DE/FR; South: IT/ES/PT) share a common central bank. Each period is divided into a morning and afternoon. In the morning, banks choose portfolios subject to a Gertler-Karadi (2011) leverage constraint (fraction λ of assets can be diverted by the manager) and a central bank collateral constraint (CB loans require bonds pledged at CB haircut η). In the afternoon, banks face idiosyncratic liquidity shocks ω~iid F(ω) on deposits. Connected banks (fraction ξ) can borrow unsecured in the afternoon interbank market. Unconnected banks (fraction 1−ξ) must cover their maximum possible payment outflow ωmaxD by holding reserves or pledging bonds as collateral in the private secured market (at haircut 1−η̃^γ). Five inequality constraints — the morning leverage constraint, a CB collateral constraint, and three short-sale constraints (bonds, deposits, capital) — can each switch between binding and slack; the model requires a non-linear solution (Dynare Levenberg-Marquardt mixed complementarity solver).

Calibration (Table 2, quarterly frequency):

Standard: capital share θ = 0.33, depreciation δ = 0.02, discount factor β = 0.994, Frisch inverse ε = 0.40, government spending g = 0.566
Bond maturity 1/κ = 5.952 years; dividend fraction φ = 0.025; leverage constraint λ = 0.701
Pre-crisis interbank structure: ξ = 0.42 (42% connected), haircuts η̃ = η = 0.97 (3%)
Maximum liquidity shock ωmax = 0.10; foreign sector bond demand elasticity ρ = 1.757
6 targeted moments (Table 3, exact fit): Govt/GDP = 0.20; bank leverage = 6; annual bond spread = 0.2%; bank share of bond holdings = 23%; foreign sector share = 64%; annual inflation = 2%
Non-targeted moments broadly matched: central bank bond holdings/GDP, government debt/GDP

Two shock processes (Section 5.2):

ξ shock (permanent, onset t=1 corresponding to 2009 Q1): connected share log(ξt) transitions from ξ−1 = 0.42 to ξ∞ = 0.10 with AR(1) persistence ρξ = 0.95
η̃S shock (temporary-persistent, onset t=13 corresponding to 2012 Q1): Southern private haircut recovery factor follows AR(2) with ρη1 = 1.65, ρη2 = −0.70 and an initial impulse ε13 = −0.11; model haircuts peak at 25%, matching the data peak of 25.16%

Comparative statics (Section 6.1):

ξ shock alone: As the share of unconnected banks rises from 0.58 to 0.89 (pre- to post-2008 average), the capital stock falls 10% on aggregate and output declines 1.8% in the new steady state; no CB intervention occurs because CB and private haircuts are equal — banks have no incentive to use CB funding
η̃S shock alone (without prior ξ shift): Output falls only 0.15% even as private haircuts reach 40% in comparative statics; the muted effect arises because collateral markets are segmented in the baseline — Northern banks hold only Northern bonds (unaffected haircuts), fully counteracting Southern banks’ investment decline

Dynamic analysis (Section 6.2): In the full simulation combining both shocks:

The ξ shock causes an immediate output and investment overshoot below the new steady-state: anticipating future crowding-out of capital (unconnected banks hold bonds/reserves rather than investing), bank net worth falls immediately and leverage declines, pushing output below the eventual new steady state before gradual recovery
The η̃S shock (at t=13) additionally tightens collateral constraints for unconnected banks in the South; they endogenously switch to holding money as collateral, which integrates money markets across regions and creates a pecuniary externality on Northern banks (all banks now face the same higher collateral price for money) — a sharp contrast to the segmented-market comparative statics where Northern banks were unaffected
CB take-up peaks at 2.5% of total bank assets under CO policy, closely matching the data

CO policy vs CB policy counterfactual (Section 6.2.3, Figure 10):

Under the CO policy (benchmark: ECB keeps CB haircut at 3% while private market haircuts rise to 25%), unconnected banks in the South substitute expensive deposit funding for cheaper CB funding, reducing the collateral premium for money and directly benefiting Northern unconnected banks (pecuniary externality channel)
Under the CB policy (counterfactual: constant balance sheet, CB haircut = 100%), this substitution is impossible; collateral scarcity is unmitigated; the Northern banks’ spillover is larger
Main result: output and investment fall around twice as much on impact under the CB policy; the CB policy also produces a stronger post-crisis rebound as higher initial capital returns raise bank leverage
Conclusion: the ECB’s collateralized lending operations were crucial in containing the crisis, working through a haircut-gap channel that reduced the premium on collateral and attenuated the pecuniary externality between North and South

Scope conditions: Sovereign default risk on government bonds is treated as exogenous (the model does not endogenize default); the paper notes this would require a separate analysis linking haircuts to default probabilities. Prices are set one period in advance (not a full NK model), which disciplines inflation dynamics but is not a full monetary policy analysis. The model abstracts from the ECB’s Securities Markets Programme (sterilized asset purchases, not in scope). The two-region framework aggregates heterogeneous countries into North and South. Results depend on the perfect-foresight assumption; uncertainty about the path of shocks would introduce additional precautionary effects.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. Why did the decline in unsecured interbank lending harm the real economy?

Unsecured interbank borrowing allows banks to pool idiosyncratic liquidity shocks without holding any liquid buffer; when unconnected banks (unable to borrow unsecured) must instead cover their maximum possible afternoon deposit outflow ωmaxD by holding bonds or reserves, they divert balance sheet capacity away from capital investment, crowding it out. As the share of unconnected banks rises from 42% to 90%, this crowding-out effect operates through two channels: (i) direct diversion of assets from productive capital to unproductive liquidity buffers; (ii) higher demand for collateral raises the collateral premium on bonds, increasing the effective cost of deposit funding and inducing all banks — even connected ones — to downsize their balance sheets through the leverage constraint.

Q2. Why was the steady-state impact of Southern haircuts muted while the dynamic impact was large?

In the baseline steady-state, collateral markets are segmented: Northern unconnected banks hold only Northern bonds (unaffected by Southern haircuts) and Southern unconnected banks hold only Southern bonds; in comparative statics, Northern banks absorb the capital freed by Southern banks’ disinvestment and the aggregate effect is small (−0.15% output for haircuts rising to 40%). In the dynamic model, however, the prior ξ shock has already pushed Northern unconnected banks to hold money as collateral (since high bond demand from all unconnected banks raises bond prices until money becomes the cheaper alternative); when Southern haircuts then spike, Southern banks also switch to money as collateral — and since money is a non-regional collateral, its price spike affects all unconnected banks simultaneously, integrating the previously segmented collateral markets and transmitting the Southern shock to the North.

Q3. How does the CO policy’s “haircut gap” channel work?

Under CO policy, the ECB maintains its haircut at 3% while private markets charge 25%; for each unit of collateral, a bank can access (1−0.03)=0.97 units from the ECB but only (1−0.25)=0.75 units from the private repo market — a 22-percentage-point haircut gap that makes ECB funding more efficient per unit of collateral pledged. When private haircuts rise, unconnected Southern banks face a collateral scarcity that makes deposit funding more expensive (higher afternoon constraint tightening); under CO policy, they optimally substitute toward CB funding, reducing their dependence on expensive deposits and mitigating the collateral premium spike. This directly benefits Northern unconnected banks because the reduced collateral premium for money (driven by Southern banks switching out of money as collateral) relaxes their own afternoon constraints without any direct exposure to Southern bonds.

Q4. Why does the CB policy produce a stronger post-crisis rebound?

The CB policy’s larger initial output and investment decline implies a larger undershoot below the new (post-ξ) steady state; during the recovery phase, banks face elevated returns on capital investment because capital is below its steady-state level; these higher returns raise bank net worth and allow more aggressive leverage, producing a steeper rebound than under the CO policy where the downturn was mitigated. This “larger crisis, faster recovery” tradeoff means the CB policy does not necessarily produce lower total welfare than the CO policy over the full cycle — the welfare comparison requires integrating the entire path, not just comparing the initial impact.

Q5. What makes the model require a non-linear solution?

The model features five inequality constraints that each can switch between binding and slack as parameters change: the morning leverage constraint, a collateral constraint on CB loans, and three short-sale constraints (kt,i ≥ 0, Bt,i ≥ 0, Dt,i ≥ 0). Standard linearized DSGE methods assume constraints are either always binding or always slack; here, for instance, connected banks begin holding positive money balances only when the share of unconnected banks rises past a threshold (0.61 in comparative statics), at which point the collateral premium rises enough to equalize returns on bonds and money — a kink that requires tracking which constraints are active. The Dynare Levenberg-Marquardt mixed complementarity solver handles these transitions, with T=400 periods imposed to ensure convergence to steady state.

Q6. What is the role of the leverage constraint in transmitting interbank frictions to the real economy?

The leverage constraint (Gertler-Karadi 2011) limits each bank’s total assets to Vt,i/λ; when money market frictions reduce the bank’s value Vt,i — either directly (collateral premia reduce bond prices and thus net worth) or through lower expected future net worth — the binding leverage constraint forces a proportional reduction in all assets including capital. This is the channel through which a purely financial friction in interbank markets (collateral scarcity) translates into a real investment decline: the leverage constraint links bank net worth to lending capacity, and interbank frictions that depress net worth also shrink investment. The result that “output and investment fall around twice as much” under CB policy is quantitatively driven by this chain: CB policy mitigates the collateral premium, preserving net worth and thus the lending capacity of banks.

Q7. Why do household deposits remain stable even as interbank markets are disrupted?

The model’s equilibrium has banks absorbing shocks through their balance sheet structure (switching between deposit funding, CB funding, bonds, and money) rather than through deposit supply; household deposits Dt,i are determined by households’ intertemporal optimization and the deposit rate, both of which are relatively insulated from the interbank friction. The friction operates within the banking system (between banks, or between banks and the CB), not in the retail deposit market; the afternoon liquidity shocks are interbank in nature (payment flows between banks) and are settled without household involvement. This matches Observation 4 from the data (stable household deposits) and is consistent with the mechanism: banks’ portfolio recomposition toward CB funding or bonds is a liability-side substitution that leaves retail deposits intact.

Key concepts

haircut gap channel : the mechanism through which the ECB’s policy of maintaining favorable haircuts (3%) on collateral while private market haircuts spike (to 25%) provides effective relief from collateral scarcity; banks can access more liquidity per unit of pledged collateral from the ECB than from the private repo market, inducing substitution from deposit funding to CB funding when the private haircut gap widens.

connected vs. unconnected banks : the model’s key bank heterogeneity; connected banks (fraction ξ) can borrow unsecured in the afternoon interbank market and therefore need no liquidity buffer; unconnected banks must cover their maximum afternoon payment outflow ωmaxD with reserves or pledged bond collateral, crowding out capital investment — the shift from ξ = 0.42 to ξ = 0.10 is the model’s representation of the euro area secured-market shift.

pecuniary externality (North-South spillover) : the channel through which a rise in Southern bond haircuts affects Northern banks even though Northern bonds are not repriced; when Southern banks switch to holding money as collateral, the demand for money rises, pushing up its collateral price; Northern unconnected banks (already holding money after the ξ shock) pay the higher price, tightening their afternoon constraint and reducing their capital investment indirectly.

collateral premium : the shadow price on bonds arising from their dual role as investment assets (in the morning) and collateral for afternoon liquidity (in the private repo or CB markets); when the afternoon constraint is binding, the collateral premium is positive — bonds are valued above their pure investment return — and determines how much of a bank’s balance sheet is diverted from capital to liquidity buffers.

CO policy vs CB policy : the paper’s two scenarios for the ECB’s response; CO policy (benchmark) maintains collateralized lending at a fixed (favorable) CB haircut, allowing CB balance sheet expansion as private haircuts rise; CB policy (counterfactual) keeps the balance sheet constant (CB haircut = 100%, no CB lending), forcing all liquidity needs to be met through private markets — the comparison isolates the macroeconomic value of the ECB’s lender-of-last-resort function.

Motivating banks to lend? Credit spillover effects of the Main Street Lending Program

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

Overview

Research Question. Minoiu, Zarutskie, and Zlate ask whether participation in the Main Street Lending Program (MSLP)—a Federal Reserve emergency facility launched in mid-2020 to channel credit to small and mid-sized firms during the COVID-19 pandemic—caused banks to lend more outside the program. The authors focus on credit spillover effects: did MSLP-participating banks ease standards and expand volumes on their general commercial and industrial (C&I) loan books, beyond the direct loans originated under the program itself?

Institutional Context. The MSLP opened for lender registration on June 15, 2020 and began accepting loan submissions on July 6, 2020, expiring December 31, 2020. Of $600 billion in available SPV capacity, only $16.05 billion was actually deployed, making overall take-up approximately 2.7% of capacity. Despite this, the program required participating banks to retain 5% of each loan’s credit risk while offloading 95% to the SPV, and charged borrowers LIBOR plus 300 bps. Registration rate among all Call Report banks was 11.7% (614 out of 5,242 banks), with participation rising steeply with bank size: from 6.5% of banks in the below-$1-billion asset group to 63.8% of banks with assets above $50 billion.

Data and Methodology. The analysis draws on multiple data sources: (a) supervisory Y-14Q H1 loan-level data covering C&I loans above $1 million commitments, reported by 32 bank holding companies (BHCs) that account for roughly three-quarters of total U.S. C&I loans; (b) Y-14Q A9 loan portfolio segment data for small business C&I loans (below $1 million commitments) from 22 BHCs; (c) quarterly Senior Loan Officer Opinion Survey (SLOOS) microdata for April, July, and October 2020, providing bank-level assessments of lending standard changes, loan terms, demand shifts, and stated reasons for tightening; (d) Dealscan syndicated loan originations for 262 banks (51 MSLP participants); and (e) bank balance sheet data from Call Reports, including the Ellul-Yerramilli risk management index (RMI) for 16 BHCs. The core empirical design is a difference-in-differences (DiD) comparing MSLP-participating vs. non-participating banks before (2020:Q1–Q2) and after (2020:Q3) program implementation. To address nonrandom selection, the authors instrument MSLP participation with three variables: (i) a dummy for banks that cited registration as “too burdensome” in the September 2020 supplementary SLOOS; (ii) a dummy for banks with prior experience pledging loan collateral at the Fed’s discount window; and (iii) a dummy for banks with prior experience pledging securities collateral at the discount window. Firm×quarter fixed effects absorb time-varying credit demand at the borrower level (Khwaja-Mian design), and bank×borrower fixed effects further control for relationship-specific lending patterns.

Main Findings — Extensive Margin (Large Business Loans). In the Y-14Q H1 data, MSLP banks were 30–32% more likely to renew existing loans than non-MSLP banks in 2020:Q3, with the probability of renewal 1.6–1.7 percentage points higher (against a sample average renewal rate of 5.3%). New loan originations were 22–27% more likely at MSLP banks, or 1.1–1.4 percentage points higher (against a sample average origination rate of 5.1%). 2SLS estimates are similar in magnitude to OLS, indicating selection bias is modest.

Main Findings — Extensive Margin (Small Business Loans and Survey Data). In the A9 small business segment data, MSLP lenders had 17.3% more small business loan accounts outstanding in 2020:Q3 than non-MSLP banks. In SLOOS microdata, MSLP banks were approximately 15 percentage points less likely to report tightening C&I lending standards in 2020:Q3 (conditional on demand controls), compared to an actual tightening rate of 37.5%. This effect is larger for small (more financially constrained) firms (16–17 percentage points) than for large firms (13–14 percentage points).

Main Findings — Intensive Margin. On loan terms, MSLP banks charged spreads that were approximately 9 basis points lower on renewed/originated C&I loans in the Y-14Q data, and 13.5 basis points lower in the Dealscan syndicated loan sample, compared to non-MSLP banks in 2020:Q3. 2SLS estimates are somewhat larger (19–30 bps). In the Dealscan sample, MSLP banks also extended syndicated loans that were 11.2% larger (about $2.4 million more given a $22 million average loan size). Survey data confirm MSLP banks were less likely to tighten most individual loan terms.

Aggregate Magnitude. The authors estimate that, in the absence of the MSLP, total loan renewals and originations at Y-14Q reporting banks in 2020:Q3 would have been approximately 10% lower. Scaling to the broader banking sector, the estimated credit spillover effect is approximately $44.8 billion in C&I lending—nearly three times the $16.05 billion in direct MSLP loan purchases.

Mechanism. Survey and objective evidence both point to reduced risk aversion as the primary channel, rather than immediate balance sheet constraint relief. MSLP banks were significantly less likely to cite “reduced tolerance for risk” as a reason for tightening lending standards after the program’s introduction, while showing no differential propensity to cite capital or liquidity deterioration. Banks with higher risk management index scores (more risk-averse institutions) exhibited larger spillover effects on two of three lending margins. Indicators of immediate balance sheet tightness (excess capital cushions, cost of capital, core deposit reliance) do not predict larger spillovers, with a partial exception for lower excess capital and higher loan loss reserves — suggesting future rather than current balance sheet constraints may have played some role.

Scope Conditions and Robustness. The backstop mechanism is explicitly tied to the program’s credibility period: the spillover effects are smaller in 2020:Q4, consistent with the Treasury’s November 19, 2020 announcement that the program would not be extended, which diminished its backstop role. Placebo regressions using 2018 and 2019 data find no differential lending behavior between MSLP and non-MSLP banks before the program, supporting parallel trends. Results are robust to controls for PPP participation, credit line drawdown exposure, loan loss provisioning, and bank-level loan portfolio cyclicality.

Q&A

Q1: What precisely is the “spillover effect” that the paper measures, and how does it differ from the direct effect of the MSLP? A: The direct effect is the $16.05 billion in MSLP loans purchased by the SPV — credit extended specifically through the program. The spillover effect refers to changes in banks’ general C&I lending behavior outside the program: renewals and originations of non-MSLP loans, changes in lending standards and terms for all business borrowers, and changes in small business loan volumes. The sample in the Y-14Q regression explicitly excludes MSLP loans themselves, so the estimates reflect only the indirect, broader credit effects.

Q2: What instruments does the paper use for MSLP participation, and why are they plausibly exogenous? A: Three IVs are employed: (1) a dummy for banks that cited program registration as “too burdensome” as a very important reason for not joining (from the September 2020 supplementary SLOOS); (2) a dummy for banks that pledged loan collateral at the Fed’s discount window in December 2019; and (3) a dummy for banks that pledged securities collateral at the discount window in the same period. The exclusion restriction argument is that (1) reflects banks’ administrative capacity and prior Fed engagement rather than underlying balance sheet strength or lending appetite, and that (2) and (3) reflect familiarity with Fed collateral processes in ways that made a loan-based program easier to understand and join — without independently affecting lending standards or volumes in 2020:Q3.

Q3: How large are the spillover effects on the extensive margin of large corporate lending? A: In the Y-14Q H1 data across 32 BHCs, MSLP banks renewed loans 1.6–1.7 percentage points more frequently and originated new loans 1.1–1.4 percentage points more frequently in 2020:Q3, relative to non-MSLP banks. Against sample averages of 5.3% renewal rate and 5.1% origination rate, these translate to MSLP banks being 30–32% more likely to renew and 22–27% more likely to originate loans. The 2SLS estimates are broadly similar in magnitude, suggesting that self-selection bias in OLS is limited.

Q4: What are the estimated aggregate dollar spillovers from the MSLP? A: The paper calculates that, in the absence of the program, total loan renewals and originations at Y-14Q H1 MSLP banks in 2020:Q3 would have been lower by approximately $33.6 billion (derived from 44,274 bank-borrower pairs × 1.38 existing loans per pair × 3.06 percentage points of extra loan activity × $17.98 million average loan size). Scaling to all Y-14Q banks (MSLP and non-MSLP alike), the shortfall would represent roughly a 10% reduction in total 2020:Q3 loan renewals and originations. Extrapolating to the full banking sector (since Y-14Q banks cover about 75% of total C&I lending), and assuming similar spillover magnitudes for banks outside the sample, total MSLP spillovers amount to roughly $44.8 billion — approximately three times the $16.05 billion in direct MSLP loan purchases.

Q5: What is the estimated effect on C&I lending standards using survey data? A: Using SLOOS microdata, the paper estimates that MSLP banks were approximately 15 percentage points less likely to tighten C&I lending standards in 2020:Q3 compared to non-MSLP banks, after controlling for demand conditions. The actual tightening rate in 2020:Q3 was 37.5%, meaning the counterfactual tightening rate absent the program would have been approximately 5 percentage points higher. In a further hypothetical where all SLOOS sample banks had participated, the counterfactual tightening rate would have been nearly 10 percentage points higher than actual.

Q6: Are spillover effects larger for small or large borrowers, and what does this imply? A: The SLOOS-based estimates show that MSLP banks were 16–17 percentage points less likely to tighten lending standards for small firms (annual sales below $50 million), compared to 13–14 percentage points less likely for large and middle-market firms — a statistically significant difference. The authors interpret this as consistent with the MSLP reducing risk aversion broadly, with the largest effect on borrowers facing greater credit constraints where uncertainty about creditworthiness was highest.

Q7: What evidence supports the risk aversion (psychological backstop) mechanism over the balance sheet constraint mechanism? A: From SLOOS data, MSLP banks were significantly less likely (at the 1% level) to cite “reduced tolerance for risk” as a reason for tightening lending standards after the program’s introduction, while showing no differential likelihood of citing deteriorating capital or liquidity positions as reasons. Furthermore, splitting banks by the risk management index (RMI), the spillover effects are stronger for high-RMI (more risk-averse) banks on two of three lending outcomes. Conversely, proxies for immediate balance sheet constraints — excess capital cushions, core deposit ratios, equity issuance, and cost of capital — do not yield consistently stronger spillover effects for more constrained banks. The only partial exception is lower excess capital and higher loan loss reserves, which are associated with more loan renewals, suggesting future rather than current balance sheet constraints may have contributed.

Q8: What is the risk management index (RMI), and how is it used here? A: The RMI is an index developed by Ellul and Yerramilli (2013) that captures the strength of a bank’s internal risk management function, constructed from variables including whether the bank has a chief risk officer (CRO), the CRO’s executive status and relative compensation, risk committee member experience, and meeting frequency. Available for 61 BHCs over 2011–2013, it is matched to 16 BHCs in the Y-14Q H1 sample and used as a pre-COVID proxy for institutional risk aversion. Banks above the median RMI show larger MSLP spillover effects on loan renewals and tightening standards, consistent with the interpretation that the MSLP reduced effective risk aversion more for banks that had higher baseline risk-consciousness.

Q9: How do the authors address the concern that PPP participation — not MSLP participation — might drive the results? A: First, they test directly that MSLP participation does not predict outstanding PPP/federally-guaranteed loan balances (in Q2 or Q3 2020) in the A9 loan segment data, finding no correlation. Second, they add an interaction of PPP loan balances (divided by total assets) × Post to the baseline regression in Table A10 and find that while PPP lending is positively associated with loan renewals and originations, the MSLP bank × Post coefficient remains statistically significant and similar in magnitude to the baseline, ruling out PPP participation as the driver of the baseline results.

Q10: What explains the low take-up of the MSLP despite its large designed capacity? A: Survey responses from the September 2020 supplementary SLOOS indicate several demand- and supply-side constraints: banks reported they could generally meet credit demand outside the program; borrower leverage limits (capped at 4–6× EBITDA depending on facility) were seen as too restrictive; the LIBOR plus 300 bps interest rate was high relative to historical pricing for eligible firms; and registration and loss-sharing arrangements were viewed as burdensome and uncertain. The paper interprets these findings as consistent with banks treating the MSLP primarily as a backstop — a facility they would activate only if economic conditions deteriorated significantly — rather than a primary lending channel.

Q11: How does the paper address the threat that MSLP participation reflects bank-level cyclicality in loan portfolios? A: Table 10 controls for bank-specific C&I loan portfolio cyclicality, measured as the correlation between each bank’s C&I loan growth and aggregate banking-sector C&I loan growth estimated over 1985:Q1–2021:Q2 using two functional forms. The MSLP bank × Post coefficient estimates remain very similar to the baseline after including these controls, ruling out the concern that MSLP participants were simply banks with naturally more procyclical or countercyclical lending patterns.

Q12: What happens to the estimated spillover effects in 2020:Q4, and what does this reveal? A: The paper shows (Table A6) that extending the sample to include 2020:Q4 yields somewhat smaller estimated spillover effects than in the baseline 2020:Q3 period. The authors attribute this to the November 19, 2020 announcement by Treasury Secretary Mnuchin that the MSLP would not be extended beyond year-end, which effectively ended the program’s backstop role and — consistent with the psychological backstop mechanism — reduced banks’ confidence in the program’s future availability and thus the spillover motivation.

Q13: Does the paper find spillover effects on intensive margin loan terms, and how large are they? A: On loan spreads, MSLP banks charged approximately 9 basis points lower spreads on floating-rate C&I loans renewed or originated in 2020:Q3 in the Y-14Q data (2SLS: 19 bps), and approximately 13.5 bps lower spreads in the Dealscan syndicated loan sample (2SLS: 30 bps). The 9 bps OLS estimate implies the average spread across all LIBOR-indexed C&I loans in 2020:Q3 would have been approximately 4 bps higher absent the program (i.e., 0.43 × 9 bps), relative to an actual average spread of 235 bps — an effect the authors characterize as economically small. On loan size, the Dealscan evidence indicates MSLP banks extended syndicated loans that were 11.2% larger (2SLS: 25% larger).

Key Concepts

Credit Spillover Effects: As used in this paper, spillover effects refer to the impact of MSLP participation on participating banks’ lending behavior outside and beyond the program itself — specifically, changes in loan renewal rates, new loan origination rates, lending standards, and loan terms for non-MSLP C&I loans. This is distinct from the direct effect (i.e., loans originated through the MSLP proper).

Psychological Backstop: The paper’s term for the mechanism by which the MSLP reduced participating banks’ effective risk aversion without necessarily easing their immediate balance sheet constraints. By committing to provide lending support if conditions deteriorated, the program built banks’ confidence to lend ex ante, functioning as “insurance” against bad outcomes rather than a direct funding facility. The mechanism is distinguished from balance sheet easing by the fact that constrained and unconstrained banks exhibited similar spillover effects.

Extensive Margin of Lending: The binary dimension of lending activity — specifically, whether a bank renews an existing loan or originates a new loan within a bank-borrower pair. In this paper, measured as the share of existing loan commitments within each bank-borrower pair that are renewed or newly originated each quarter. Contrasted with the intensive margin.

Intensive Margin of Lending: The quantitative dimension of existing lending relationships — specifically, the average loan size and average spread on loans renewed or originated in a given period, conditional on a loan being extended.

Senior Loan Officer Opinion Survey (SLOOS): A quarterly Federal Reserve survey of senior lending officers at large U.S. banks covering self-reported changes in C&I lending standards, terms (including spreads, maximum loan size, maturity, covenants, collateral requirements), demand conditions, and — in supplementary editions — reasons for changing standards. Used in this paper both as an outcome variable (tightening standards) and as a control variable (changes in loan demand) and as a source of IV variation (burden of MSLP registration).

Risk Management Index (RMI): An index developed by Ellul and Yerramilli (2013) measuring the strength of a bank’s internal risk management function, combining information on the presence and compensation of a chief risk officer, risk committee composition, and meeting frequency. Used in this paper as a pre-pandemic proxy for institutional risk aversion to test whether the MSLP disproportionately reduced risk aversion in banks with stronger risk controls.

Difference-in-Differences with Granular Fixed Effects: The primary identification strategy, comparing changes in lending outcomes between MSLP-participating and non-participating banks before (2020:Q1–Q2) and after (2020:Q3) program implementation. The paper uses firm×quarter fixed effects following Khwaja and Mian (2008) to absorb borrower-level credit demand, and bank×borrower fixed effects following Chodorow-Reich (2013) to absorb relationship-specific supply factors — isolating the bank credit supply effect attributable to MSLP participation.

Originate-and-Distribute Feature (of MSLP): The MSLP’s design in which banks originate MSLP loans but sell 95% of the credit exposure to the SPV, retaining only 5%. This feature was intended to free up balance sheet capacity for further lending. The paper tests whether this channel (easing current balance sheet constraints) explains the observed spillovers, finding limited support relative to the risk aversion reduction channel.

Soft landing and inflation scares

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

Layer 1 — Overview

Research Question

Why did the 2021–2023 US inflation surge end in a soft landing — disinflation without a major recession — while the Volcker disinflation of 1979–1987 required substantial output losses? And was the timing and strength of the Federal Reserve’s reaction to the inflation surge decisive in achieving this outcome?

Methodology and Model

The paper develops and estimates a micro-founded Heterogeneous-Expectation New Keynesian (HENK) model in which agents hold idiosyncratic, dispersed beliefs about the long-run (steady-state) level of inflation. The key departure from full-information rational expectations (FIRE) is that information about the long-run value of inflation is dispersed and sticky: agents update their beliefs through pairwise social learning (SL), adopting the forecasting model of the agent whose belief produced lower recent inflation forecast errors. This tournament process — inspired by genetic algorithms — generates a time-varying cross-sectional distribution of subjective inflation beliefs.

The model admits a closed-form solution that retains the entire time-varying distribution of beliefs and can be estimated with standard full-information Bayesian methods using the inversion filter (Cuba-Borda et al. 2019). The FIRE benchmark is nested as the special case in which the average belief deviation from the target is zero at all times.

Estimation uses four US macroeconomic observables (output gap, CPI inflation, one-quarter-ahead average SPF inflation expectation, and the proxy funds rate of Choi et al. 2022 that captures both conventional and unconventional monetary policy) over 1985Q1–2023Q4. A formal model comparison rejects the RE null hypothesis (p < 0.0001) in favor of the HENK specification.

Main Findings With Quantitative Magnitudes

Inflation scares are endogenous: In the model, inflation scares arise whenever repeated above-target inflation outcomes validate and diffuse above-target beliefs through social interactions. Under the historical scenario, the share of agents holding long-run inflation beliefs between 1 and 3 percent (annualized) falls to 40 percent in mid-2022 before recovering above 90 percent by end-2023, indicating a partial but not complete unanchoring of expectations.
Timing dominates strength: Counterfactual simulations show that the timing — not the strength — of the Fed’s reaction to the inflation surge is the key determinant of inflation expectations management and subsequent macroeconomic outcomes. Varying the Taylor-rule inflation coefficient by +/-10 percent (moving from 1.64 to 2.00) produces negligible differences in inflation and output gap dynamics, with welfare ratios of 1.052 and 0.981 relative to benchmark respectively under the ad-hoc loss function. By contrast, varying the timing via the interest-rate smoothing parameter by +/-10 percent produces much larger divergences.
The Fed fell behind the curve: Under a scenario in which the Fed had strictly followed its estimated Taylor rule (removing the negative monetary policy shocks observed from mid-2020 to mid-2022), inflation would have peaked approximately 3 percentage points lower on a yearly basis. Inflation expectations would have remained lower for almost a year longer, and the subsequent rise in expectations would have been more gradual and lower-peaking. Crucially, the output gap in this preemptive-tightening scenario would have been only briefly negative (in 2022Q2) and not deep enough to trigger a recession.
Further delays would have been highly costly: A delay of the tightening by one, two, four, or eight quarters would have produced successively worse outcomes. A two-year delay generates runaway inflation and 100 percent loss of target credibility (complete unanchoring). A delay of approximately three quarters would have resulted in a sizable, self-reinforcing entrenchment of above-target inflation expectations. The welfare cost of an eight-quarter delay is 5.76 times the benchmark loss under the ad-hoc measure (1.167 under the microfounded measure).
Early rate cuts would have reignited inflation: A counterfactual 100-basis-point cut as early as 2022Q3 would have pushed annual inflation approximately 2 percent above the historical scenario through end-2023, with inflation expectations rebounding by about 1 percent (annualized) immediately after the cut. Under no early-cut scenario would inflation or expectations have converged back to target by end-2023.
Expectation heterogeneity amplifies shocks: Greater initial dispersion in beliefs amplifies and prolongs the impact of all shocks (demand, supply, monetary policy, expectation). After a one-standard-deviation cost-push shock, higher initial belief dispersion produces larger and more persistent deviations in inflation, output, and interest rates. The model-implied interquartile range of beliefs is correlated 0.538 with the SPF interquartile range and the cross-sectional standard deviation is correlated 0.483 (both p < 0.001).
Historical decomposition: Over the 2010s, negative expectation shocks account for a substantial fraction of the persistent below-target inflation (“missing inflation”). From approximately mid-2022 onward, positive expectation shocks account for most of the variance of inflation in the model. The recent disinflation is attributed to a combination of: easing supply pressures, normalization of monetary policy, and re-anchoring of inflation expectations.

Scope Conditions

Results are conditional on the estimated HENK model applied to US data, 1985Q1–2023Q4, using a stylized three-equation NK backbone (no labor market dynamics, no financial sector, no capital). The proxy funds rate is more volatile than the federal funds rate, which affects the welfare comparison for large preemptive tightening scenarios. Counterfactual scenarios are implemented through unexpected monetary policy shocks; anticipated shocks would only strengthen the inflationary effects of delays.

Layer 2 — Q&A

Q1: What is the core mechanism by which an inflation scare can develop in the HENK model?

A: When inflation repeatedly exceeds the target — whether due to shocks or delayed policy — agents whose beliefs are already above-target incur lower forecast errors than those anchored at the target. During pairwise social interactions (the tournament step of social learning), above-target beliefs spread through the population because they are selected as the “better” forecasting model. The resulting upward shift in the average belief feeds higher inflation through the New Keynesian Phillips Curve, which validates above-target beliefs further, creating a self-reinforcing loop. This mechanism differs from rational-expectations models, where beliefs mean-revert automatically.

Q2: How does the model retain a closed-form solution despite the nonlinearity of the social-learning process?

A: Two assumptions deliver the closed-form. First, beliefs are private and dispersed (Assumption 1): agents observe only the belief of their matched mate, not the population distribution. Second, a quasi-rational-expectations (quasi-RE) observer treats aggregate beliefs as a random walk in expectations (Assumption 2: a martingale). Under these conditions, the aggregate subjective inflation expectation equals the average subjective belief about steady-state inflation plus the rational-expectations forecast. This augmented minimum-state-variable (MSV) solution can be estimated with full-information methods (the inversion filter) via standard Dynare tooling.

Q3: What data are used and how are observables mapped to model variables?

A: The estimation uses four quarterly US observables from 1985Q1–2023Q4: the output gap (real GDP from FRED, HP-filtered with a one-sided adjusted filter); the CPI inflation rate (CPIAUCSL, FRED); one-quarter-ahead average CPI inflation expectation from the Survey of Professional Forecasters (CPI3); and the proxy funds rate of Choi et al. (2022), which captures both QE and QT so that unconventional monetary policy is reflected in the instrument. Inflation and expectations are demeaned by the sample average to express them as deviations from steady state. The discount factor is calibrated at 0.99; all other parameters are estimated via Bayesian methods with Metropolis-Hastings (8 parallel chains x 100,000 iterations, acceptance rate ~30%).

Q4: What are the key estimated parameter values for the social-learning block?

A: The posterior mean of the decay parameter in the fitness evaluation (discounting of past forecast errors) is 0.775, implying a half-life of past forecast errors of approximately 3 quarters. The frequency of news shocks has a posterior mean of 0.436, meaning approximately 40 percent of agents receive an inflation news shock every quarter. The standard deviations of the aggregate and idiosyncratic news shocks are very small (posterior means of 0.0004 and 0.0006, respectively) but strictly positive. The 95 percent confidence intervals for both exclude zero.

Q5: How does the HENK model outperform the RE benchmark in fitting the data?

A: Formal model comparison rejects the RE null (p < 0.0001) with equal prior model weights (50/50). On second moments, only the HENK model replicates positive autocorrelation in inflation (0.428 vs. 0.162 for RE, against an empirical interval of [0.239; 0.579]), in inflation expectations (0.824 vs. 0.161, empirical interval [0.839; 0.927]), and in inflation forecast errors (0.122 vs. -0.145). Additionally, the HENK model reproduces the untargeted cross-sectional dispersion of beliefs over the business cycle, including the increase during the GFC and the COVID-19 era and the low dispersion during the Great Moderation — with correlations of 0.538 and 0.483 between model and SPF dispersion measures.

Q6: What does the historical shock decomposition reveal about the recent inflation surge?

A: The decomposition (Section 3.3) shows that in the initial phase of the COVID-19 shock (2020Q2-Q3), negative demand and monetary policy shocks drove inflation down. Adverse cost-push (supply) shocks dominate from early 2021 into 2022. Expectation shocks — the contribution of dispersed beliefs — are negative throughout the 2010s (explaining part of the “missing inflation”) and remain briefly negative at the pandemic’s onset before turning sharply positive and driving most of the variance of inflation in the final two years of the sample (2022-2023). The loose monetary policy stance (negative monetary policy shocks from mid-2020 to mid-2022, visible in the Taylor-rule residuals) also contributes substantially to the inflation dynamics.

Q7: What does the Taylor-rule counterfactual show, and why doesn’t preemptive tightening cause a recession in the model?

A: Removing the monetary policy shocks after 2020Q4 so that the proxy rate follows the estimated Taylor rule would have reduced the inflation peak by approximately 0.75 percentage points per quarter (equivalent to about 3 percentage points annualized) and kept expectations lower-anchored for almost a year longer. The output gap under the Taylor-rule scenario is only briefly negative (2022Q2) and does not constitute a recession. This occurs because the preemptive tightening exploits the sluggishness of subjective expectations stemming from information frictions: by raising rates earlier when beliefs are still anchored (or only weakly above target), the CB prevents the social-learning mechanism from diffusing above-target beliefs, which in turn softens the stabilization trade-off between inflation and output.

Q8: What is the U-shaped welfare relationship between preemptive tightening size and welfare?

A: Both the ad-hoc and microfounded welfare measures show a U-shaped relationship as the size of the front-loaded tightening in 2021Q1 increases from 100 bps to 400 bps to 800 bps. At 100 bps, the welfare ratio is 0.336 (ad-hoc, improvement over benchmark at 1.0); at 400 bps it improves further to 0.304; but at 800 bps (front-loading the entire subsequent tightening cycle) the ratio rises to 0.555, reflecting that the output costs of a very large early rate increase become prohibitive amid the series of supply shocks that hit in 2022. The maximum welfare gain in the microfounded criterion occurs at a slightly larger early increase than in the ad-hoc criterion, attributed to the absence of a financial sector and use of the more volatile proxy funds rate.

Q9: Does increasing the hawkishness of the Taylor rule compensate for falling behind the curve?

A: No. Varying the inflation reaction coefficient by +/-10 percent (to 2.00 for “hawk” and 1.64 for “dove”) from the posterior mean of approximately 1.82 produces negligible differences in inflation and output gaps. The hawkish scenario achieves marginally earlier rate increases but does not reduce the inflation gap relative to the historical benchmark. Welfare ratios are 0.960 (hawkish, slight improvement) and 1.057 (dovish, slight deterioration) under the ad-hoc measure, and 0.981 and 1.052 under the microfounded measure. The joint simulations varying both smoothing (timing) and hawkishness (strength) confirm that timing is the dominant factor: the two “earlier reaction” scenarios are clustered together and well-separated from the two “later reaction” scenarios, regardless of the inflation coefficient.

Q10: How does the model handle the role of initial belief dispersion in monetary policy transmission?

A: Impulse response function exercises varying the initial standard deviation of beliefs (as a share of the maximum model-generated standard deviation under the filtered shocks) show that greater initial dispersion uniformly amplifies and prolongs the macroeconomic response to all shock types (demand, cost-push, monetary policy, expectation). The mechanism is: greater dispersion means the population contains more “extreme” (far-from-target) beliefs; a shock that temporarily moves inflation off target temporarily validates extreme beliefs (lower forecast errors), causing them to spread in social interactions and shift the average belief further from target. This raises nominal rates (through the Taylor rule), deepens output losses, and prolongs the return to steady state.

Q11: What are the implications of early interest rate cuts in the counterfactual scenarios?

A: A 100-basis-point cut in any quarter from 2022Q3 through 2023Q2 would have reignited inflation expectations. The 2022Q3 scenario is most severe: expectations rebound approximately 1 percentage point higher (annualized) immediately post-cut, and annual inflation remains on average 2 percent above the historical path through end-2023. Across all early-cut scenarios, neither inflation nor inflation expectations would have returned to target by end-2023; instead, inflation would have been landing approximately 2 percent above the 2 percent target. The welfare ratios for early cuts range from 1.200 (cut in 2022Q3) down to 1.079 (cut in 2023Q2) under the ad-hoc measure — all welfare-worsening.

Key Concepts

Inflation scare (Goodfriend 1993, as used in this paper): A situation in which the public’s long-run inflation expectations become unanchored from the central bank’s target, making beliefs about above-target steady-state inflation self-fulfilling via the New Keynesian Phillips Curve. In the HENK model, a scare arises endogenously when above-target inflation outcomes repeatedly validate above-target beliefs, causing them to spread through social interactions. Measured in the paper by the share of idiosyncratic beliefs falling between 1 and 3 percent (annualized); lower share = more severe scare.

Social learning (SL): The belief-updating mechanism in which agents are paired at random each period and compare their inflation forecasting models; the agent whose model produced lower recent forecast errors (measured by the discounted sum of squared forecast errors with half-life approximately 3 quarters) is adopted by both members of the pair. This evolutionary tournament process — analogous to a genetic algorithm — generates a nonlinear, history-dependent distribution of beliefs that can drift persistently away from the target.

Steady-state learning: The restriction that agents’ heterogeneous beliefs concern only the low-frequency (intercept) component of inflation — i.e., their subjective perception of the steady-state inflation rate — while the rest of their inflation forecast (the effects of transitory shocks and lagged variables) coincides with rational expectations. This assumption, combined with internal rationality, permits a closed-form MSV solution of the HENK model.

Internal rationality: The assumption that each agent uses a perceived law of motion that is consistent with the true MSV solution of the HENK economy (including the effect of heterogeneous beliefs on dynamics), even if their intercept differs from the rational-expectations value. Agents internalize how the aggregate deviation of expectations from RE affects inflation, but they disagree about the long-run level.

Quasi-rational-expectations (quasi-RE) observer: An observer (or central bank) who, lacking information about how individual private beliefs are formed and aggregated, treats aggregate beliefs as a martingale — i.e., the expected future aggregate belief equals its current value. This assumption closes the model and permits estimation with full-information (inversion filter) methods, while preserving consistency between subjective beliefs and the law of motion.

Belief dispersion / expectation heterogeneity: The time-varying cross-sectional standard deviation (or interquartile range) of idiosyncratic beliefs in the population. In the model this is an endogenous, history-dependent outcome of the SL process. Greater dispersion amplifies the response of all macroeconomic variables to any shock by providing more “extreme” beliefs that can gain traction in pairwise tournaments when inflation temporarily deviates from target. Measured empirically by the interquartile range and standard deviation of individual SPF forecasts.

Proxy funds rate (Choi et al. 2022): A summary measure of the US monetary policy stance that incorporates both conventional interest rate policy and the effects of unconventional policies (quantitative easing and tightening), used in the paper in place of the federal funds rate to capture the full stance of monetary policy in the estimation and historical decomposition.

Inversion filter (Cuba-Borda et al. 2019): A computationally efficient estimation algorithm that, rather than the Kalman or particle filter, inverts the observation equation analytically to recover the sequence of structural shocks for a given parameter vector. It enables full-information Bayesian estimation of the nonlinear HENK model by separating the linear part of the solution from the nonlinear social-learning residual.

Taylor Rule Deviations Across Horizons: A Practical Tool for Monetary Policy

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

Layer 1 — Overview

Research Question

The paper addresses a fundamental limitation of the standard Taylor rule as a monetary policy stance gauge: the rule is defined solely for the overnight federal funds rate (FFR) and cannot assess stance across the maturity spectrum of the yield curve. This limitation becomes acute when the FFR hits its effective lower bound (ELB) and the Federal Reserve resorts to unconventional monetary policy (UMP) instruments—quantitative easing and forward guidance—that are explicitly intended to influence longer maturities. The authors ask: can the Taylor rule idea be extended across the yield curve horizon to produce a maturity-specific monetary policy stance measure that remains informative even during ELB episodes?

Methodology and Data

The paper proposes the “Taylor rule yield curve,” which extends the original Taylor rule to points in time in the future horizon (maturities of 1 through 10 years). The Taylor rule expected rate at maturity h is defined as the average of h annual one-period-ahead Taylor-rule-implied short-term rates, each computed from professional forecasters’ expectations of inflation and the output gap h years ahead. The market counterpart is the Overnight Index Swap (OIS) rate for the corresponding maturity. The “Taylor rule deviation” (TRD) at maturity h is then the difference between the Taylor rule expected rate and the market OIS rate at that maturity—interpretable as the average expected monetary policy stance from the current period through h years ahead.

Data sources: inflation and GDP growth forecasts from Consensus Economics (1–5 years ahead, and 6–10 year average); output gap forecasts constructed using Congressional Budget Office potential output estimates; natural rate of interest estimates from Holston, Laubach, and Williams (2017) available from the Federal Reserve Bank of New York; FFR, core CPI inflation, and GDP growth from FRED; OIS rates from Bloomberg (available from 2002/Q1). Two Taylor rule coefficient sets are examined: the “original” rule (α = 0.5, β = 0.5) and the “balanced” rule (α = 0.5, β = 1.0), with the balanced rule as baseline. An inertia parameter of ρ = 0.85 (quarterly) is assumed, implying annual persistence of approximately 0.52. The sample period runs from 2000/Q1 to 2018/Q4 for the Taylor rule yield curve itself, and from 2002/Q1 to 2017/Q4 for OIS-based TRD analysis.

Main Findings

First, the estimated Taylor rule expected rate curves show that after the onset of the Global Financial Crisis (GFC), the balanced-rule Taylor rate dropped completely below zero for all maturities up to 10 years. During 2008/Q4, the Taylor rule expected rate curve lay approximately 2–3 percentage points below the market rate curve across maturities, reflecting excessively tight market expectations relative to what the Taylor rule framework implied. By 2011/Q4, the market OIS curve fell below the Taylor rule expected rate curve for maturities beyond 4 years—indicating that explicit and forceful forward guidance (the August 2011 FOMC statement committing to “exceptionally low levels for the federal funds rate at least through mid-2013”) had driven market rates below the Taylor-implied accommodative path at the long end.

Second, VAR analysis for the sample period 2002–2017 shows that TRDs at both 2-year and 10-year maturities generate statistically significant impulse responses: positive TRD shocks—indicating a tighter-than-Taylor monetary policy stance—cause both the output gap and inflation to decrease. Importantly, this result holds during the ELB period when the FFR gap and shadow policy rate gap do not yield theoretically consistent impulse responses; in the 2002–2017 subsample, both the FFR gap and the shadow rate gap produce perverse (positive) responses of output and inflation to a tightening shock, presumably because the ELB binds and UMP operates outside the overnight rate. The OIS rates per se (without the Taylor rule expected rate subtracted) show mostly muted and statistically insignificant impulse responses in the same VAR framework. Granger causality tests (62 observations) confirm that TRDs Granger-cause OIS rates for both 2-year (F-statistic = 4.579, p = 0.014) and 10-year (F-statistic = 7.734, p = 0.001) maturities, while the reverse direction is not rejected in either case, highlighting TRDs’ informational superiority over raw OIS rates.

Third, TRDs for 2-, 5-, and 10-year maturities are positively correlated with the VIX in the same quarter (R² values of 0.34, 0.37, and 0.35 respectively), whereas the FFR gap is negatively correlated with the VIX (R² = 0.22). This positive TRD–VIX relationship holds during both ELB (2008/Q1–2015/Q3) and non-ELB subperiods, suggesting TRDs serve as a proxy for risk appetite in financial markets—with a loose-relative-to-Taylor monetary stance associated with lower risk aversion.

Fourth, a stylized New Keynesian model with anticipated future shocks to the Taylor rule (interpreted as “news shocks”) provides theoretical support. When agents learn of a future expansionary Taylor rule shock, they revise upward their expectations of future output and inflation, which—through consumption smoothing (Euler equation) and forward-looking pricing (New Keynesian Phillips curve)—produce contemporaneous expansionary effects. An extended model with habit formation, backward-looking price-setters, and interest rate smoothing generates hump-shaped and persistent IRs consistent with the empirical patterns. Simulations on model-generated data confirm that the TRD measure, but not the future interest rate or contemporaneous rate deviation, recovers statistically significant and correctly signed impulse responses in the VAR.

Scope Conditions

The methodology requires data on professional forecasters’ expectations of output and inflation at multi-year horizons, limiting applicability to countries for which such forecast data exist. Term premium components of OIS rates are excluded from the analysis, which the authors note may make estimates of forward guidance impact conservative. The analysis is confined to the United States for the period 2000/Q1–2018/Q4.

Layer 2 — Q&A

Q1: What is the precise mathematical definition of the Taylor rule deviation (TRD) at horizon h, and how does it differ from the conventional FFR gap?

A: The TRD at maturity h is defined as the difference between the market OIS rate at h-year maturity and the Taylor rule expected rate at that maturity. The Taylor rule expected rate is the average (across years k = 1 to h) of the Taylor-rule-implied short-term interest rates expected k years ahead, where each expected rate uses professional forecasters’ projections of inflation and the output gap at that horizon, together with the current natural rate of interest (assumed unchanged). The conventional FFR gap is the deviation of the overnight FFR from the contemporaneous Taylor rule rate—a scalar at a single point in time. The TRD generalizes this to any maturity: it equals the average expected monetary policy stance (accommodative or tight relative to Taylor) from the current period through h years ahead, capturing the cumulated sum of anticipated and unanticipated disturbances to the Taylor rule.

Q2: Why does the FFR gap fail as a monetary policy stance indicator during the ELB period, and why does the shadow rate gap not resolve this failure?

A: When the FFR hits the ELB, it is pinned near zero regardless of how accommodative the Federal Reserve’s actual policy intentions are; any further intended easing through forward guidance or quantitative easing is not reflected in the overnight rate’s level or its deviation from the Taylor rule. The authors show (Figure 8a, 2002–2017 subsample) that in a three-variable VAR with output gap, inflation, and FFR gap, a positive FFR gap shock generates increases in both output and inflation—the opposite of theoretically expected contractionary effects—because the ELB constrains the FFR while UMP operates through longer maturities. The shadow policy rate (Wu and Xia, 2016) drops below zero during the UMP period and conceptually summarizes the entire yield curve’s accommodation in a single synthetic overnight rate. However, Figure 8b shows that replacing the FFR with the shadow rate leaves the perverse VAR impulse responses qualitatively unchanged in the 2002–2017 subsample, because a single short-term summary rate cannot isolate the maturity-specific information that the TRD captures.

Q3: What does the VAR analysis reveal about TRDs’ ability to capture monetary policy effects at the ELB, and does the maturity of TRD matter?

A: For the 2002–2017 sample period (Figure 9a), VAR impulse responses with the TRD replacing the FFR gap show that a positive TRD shock causes statistically significant decreases in both the output gap and inflation—the theoretically expected contractionary response. This result holds for both 2-year and 10-year TRDs. The fact that the 10-year TRD also produces this correct result indicates that TRDs at long maturities can capture the stance reflected in forward guidance, which explicitly targets expectations about the future course of monetary policy well beyond overnight. The output gap response is quantitatively larger in magnitude than the inflation response across both maturities (figure axis ranges suggest output gap peaks at roughly ±1.0% versus inflation at ±0.2%), consistent with the theoretical model’s prediction that the output gap is more responsive to contemporaneous effects while inflation responds to both current and expected future conditions.

Q4: What is the role of the output gap component versus the inflation component in driving TRD changes?

A: Figures 6 and 7 decompose period-by-period first differences of TRDs into their output gap and inflation contributions for both 2-year and 10-year maturities. The output gap component is the main determinant of changes in TRDs across both maturities, reflecting the substantially volatile outlook on economic growth—especially around the GFC. The inflation component has a considerably smaller contribution, and this difference is even more pronounced for 10-year maturities than for 2-year maturities, reflecting the fact that professional forecasters’ inflation expectations change much less at longer horizons than near-term GDP growth expectations.

Q5: What does the Granger causality analysis reveal about the informational content of TRDs relative to OIS rates?

A: Table 1 reports Granger causality tests using 62 observations. For 2-year maturities, the null that TRD 2Y does not Granger-cause OIS 2Y is rejected at the 5% level (F = 4.579, p = 0.014), while the null that OIS 2Y does not Granger-cause TRD 2Y is not rejected (F = 0.999, p = 0.375). For 10-year maturities, the null that TRD 10Y does not Granger-cause OIS 10Y is rejected at the 1% level (F = 7.734, p = 0.001), while the reverse null is not rejected (F = 0.843, p = 0.436). This unidirectional causality—TRDs leading OIS rates but not vice versa—implies that TRDs contain information about future OIS rate movements not already embedded in current OIS rates, making TRDs informationally superior to raw OIS rates for assessing monetary policy stance.

Q6: How do TRDs relate to VIX, and does this relationship depend on whether the economy is at the ELB?

A: Figures 10 and 11 document that TRDs for 2-, 5-, and 10-year maturities are positively correlated with the VIX in the same quarter (R² values of approximately 0.34, 0.37, and 0.35 for 2Y, 5Y, and 10Y TRDs respectively), meaning that a tighter-than-Taylor monetary policy stance (positive TRD) is associated with higher market risk aversion. By contrast, the FFR gap shows a negative correlation with the VIX (R² = 0.22), the opposite sign. The same positive TRD–VIX correlation is observed when current TRDs are plotted against VIX four quarters later, though the R² values are smaller (ranging from approximately 0.04 to 0.05). Critically, Figure 11 shows that dividing the 2002/Q1–2017/Q4 sample into ELB (2008/Q1–2015/Q3) and non-ELB periods, the positive correlation between the 5-year TRD and VIX holds during both subperiods (R² = 0.37 for ELB current quarter, R² = 0.41 for ELB four quarters ahead), demonstrating that TRDs’ relationship with risk appetite is not an artifact of the ELB environment.

Q7: What does the theoretical New Keynesian model contribute, and what is the mechanism by which anticipated future Taylor rule shocks affect current macroeconomic variables?

A: The paper embeds anticipated future shocks to the Taylor rule (news shocks) in a stylized New Keynesian model with Euler equation, New Keynesian Phillips curve, and Taylor rule. When a one-period-ahead expansionary monetary policy shock (εh,t for h=1) is announced at time t, agents expect expansionary effects in period t+1 (higher output gap and inflation). Through consumption smoothing in the Euler equation, expected higher output in t+1 raises current consumption and thus current output. Through forward-looking pricing in the NKPC, expected higher future inflation raises current inflation. Analytically, the coefficients on the one-period-ahead shock (c_{1,y} and c_{1,π}) satisfy the same signs as the contemporaneous shock coefficients (c_{0,y} and c_{0,π}), confirming the contemporaneous impact. The model shows that for the inflation rate, the future shock has larger impact than the contemporaneous shock (|c_{1,π}| > |c_{0,π}|) because inflation responds to both current and future output gap in the NKPC; for the output gap, the future shock has smaller impact (|c_{1,y}| < |c_{0,y}|) because higher expected inflation raises the nominal interest rate via the Taylor rule’s endogenous feedback, partially offsetting the expansionary effect on current output.

Q8: How do simulations on model-generated data validate the VAR methodology for identifying TRD effects?

A: Figure 17 uses simulated data from the model with inertia (200 periods, corresponding to 50 years) to compare three interest rate measures in a three-variable VAR (output gap, inflation, interest rate measure): (i) the average future interest rate (I), (ii) the contemporaneous interest rate deviation (ε_{0,t}), and (iii) the H-period TRD with H = 8. When the future interest rate I is used, the identified monetary policy shock produces impulse responses with the opposite sign relative to the structural model, because the VAR captures reverse causality between the interest rate and the state of the economy. When the contemporaneous rate deviation ε_{0,t} is used, responses have the intended sign but are not statistically significant, because future anticipated shocks are not materialized in the current period’s rate. When the TRD is used, the identified shock generates statistically significant responses with the correct sign, validating TRD as the appropriate measure for capturing the effects of anticipated future monetary policy shocks in an empirical VAR framework.

Q9: How does the Taylor rule yield curve behave at specific historical episodes, and what do these patterns reveal about monetary policy stance?

A: During 2008/Q4, the Taylor rule expected rate curve (balanced rule) lay approximately 2–3 percentage points below the market OIS curve across all maturities, reflecting that markets expected a much faster policy normalization than the Taylor rule implied given the economic collapse—indicating excessively tight market expectations. By 2011/Q4, after successive rounds of forward guidance, the market OIS curve fell below the Taylor rule expected rate curve for maturities beyond 4 years, with the balanced-rule Taylor expected rates remaining negative for maturities up to 3 years. By 2013/Q4, mid- and long-term market expected rates were roughly aligned with Taylor rule expected rates. In 2015/Q4, when the Fed hiked for the first time post-GFC (while the Taylor rule short-term rate was still negative), the market curve almost perfectly matched the Taylor rule expected curve for maturities beyond one year. In 2017/Q4, the Taylor rule expected rate curve exceeded the market curve by approximately 0.5–1 percentage points, suggesting continued expansionary stance even after policy rate normalization began.

Q10: How robust are the results to the choice between the original and balanced Taylor rule specifications?

A: Robustness checks (Figures 12–14) compare results under the original rule (α = 0.5, β = 0.5) versus the baseline balanced rule (α = 0.5, β = 1.0). The original rule generates smaller fluctuations in Taylor rule expected rates, reflecting its lower coefficient on the more volatile output gap. However, the overall trajectories do not change significantly. The main qualitative difference emerges in 2011/Q4 and 2013/Q4: the balanced rule implies Taylor expected rates are negative for 1–3 year maturities (indicating the ELB was still binding even relative to medium-term Taylor-implied paths), while the original rule produces all-positive Taylor expected rates for these periods. For 2008/Q4, 2009/Q4, 2015/Q4, and 2017/Q4, both specifications yield similar pictures, and the central conclusions about TRDs’ macroeconomic relevance and relationship with risk appetite are robust to the specification choice.

Key Concepts

Taylor Rule Yield Curve: The paper’s proposed extension of the standard Taylor rule from the overnight federal funds rate to all points in the future yield curve horizon (1 through 10 years). For maturity h, it is the average of h annual Taylor-rule-implied expected short-term rates, each calculated using professional forecasters’ h-years-ahead projections of inflation and the output gap plus the current estimate of the natural rate. Not a market instrument but a model-derived benchmark yield curve representing the “neutral” rate at each horizon.

Taylor Rule Deviation (TRD): The gap between the market OIS rate at maturity h and the corresponding Taylor rule expected rate—that is, the deviation of market expectations from what the Taylor rule framework implies should prevail at that horizon. A positive TRD indicates market rates are above the Taylor-implied rate (tighter-than-neutral stance); a negative TRD indicates easier-than-neutral stance. The TRD at maturity h equals the average of expected monetary policy stance residuals from the current period through h years ahead.

Effective Lower Bound (ELB): The floor to which a central bank can reduce the nominal policy rate before further cuts become infeasible or counterproductive. In the paper’s empirical context, the FFR ELB episode for the United States runs from 2008/Q1 to 2015/Q3. During this period, the standard FFR gap and shadow rate gap measures fail to produce theoretically consistent VAR impulse responses.

Taylor Rule Expected Rate: The paper’s specific construct: the average of Taylor-rule-implied future short-term interest rates at each year of maturity, computed from professional forecasters’ consensus projections of inflation and output gap at multi-year horizons. Distinct from any market rate; serves as the “neutral” benchmark at each maturity against which OIS rates are compared.

Balanced vs. Original Taylor Rule: Two coefficient specifications used in the paper. The “original” rule (Taylor, 1993) sets the inflation gap coefficient α = 0.5 and the output gap coefficient β = 0.5. The “balanced” rule (Taylor, 1999) sets α = 0.5 and β = 1.0, placing greater weight on output stabilization; the paper uses the balanced rule as its baseline on the grounds that it better reflects the Federal Reserve’s dual mandate in recent years.

Anticipated Future Taylor Rule Shocks (News Shocks): Shocks to the Taylor rule that are known to agents at time t but materialize in a future period t+h. Following Laséen and Svensson (2011) and Del Negro et al. (2012), the paper embeds these in a New Keynesian model to show that anticipated future expansionary policy has contemporaneous expansionary effects through consumption smoothing and forward-looking pricing—the theoretical mechanism underpinning why TRDs at longer maturities affect current macroeconomic outcomes.

Risk-Taking Channel via TRD: The paper’s finding that TRDs for 2-, 5-, and 10-year maturities are positively correlated with VIX (R² ≈ 0.34–0.37 in the same quarter), holding in both ELB and non-ELB periods. A positive TRD (tighter-than-Taylor stance) corresponds to higher market risk aversion as measured by VIX, enabling TRDs to serve as a maturity-specific measure of risk appetite in financial markets—in contrast to the FFR gap, which shows the opposite (negative) correlation with VIX.