Monetary-Policy-Rules | Macro Paper Warehouse

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 and Endogenous Financial Crises

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

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

Summary of a published paper based on the NBER working paper full text, AI-assisted, pending human review. See the linked original for the authoritative claims and full conditions.

Layer 1: Overview

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

In depth

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

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

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

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

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

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

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

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

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

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

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

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

Key Concepts

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

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

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

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

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

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

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

Layer 1: Overview

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

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

In depth

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

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

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

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

Q3. How does monetary policy discipline sovereign borrowing?

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

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

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

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

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

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

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

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

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

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

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

Key Concepts

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

Monetary Policy and the Drifting Natural Rate of Interest

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

This paper analyzes how monetary policy should respond to a long-run natural interest rate that can drift permanently — following a bounded random walk with upper bound 3 percent and lower bound 0 percent — when the zero lower bound (ZLB) on nominal interest rates is a binding constraint. The central result is that the long-run neutral rate (the real policy rate consistent with stable inflation in long-run equilibrium) should fall more than one-for-one with the long-run natural rate as the latter approaches zero, because the mere risk of future ZLB episodes — even when the economy is currently away from the ZLB — imparts a persistent downward bias on inflation expectations that can only be offset by maintaining a pre-emptive expansionary bias. Quantitatively, the model implies that the neutral rate should be zero as soon as the long-run natural rate falls to 75 basis points — well above the near-zero estimates prevailing in the late 2010s — and that the ZLB would bind one-third of the time under optimal policy when the natural rate fluctuates between 0 and 3 percent. Price level targeting with a 10-basis-point upward drift closely approximates optimal commitment policy and has the advantage of not requiring knowledge of the natural rate level.

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 empirical fact motivates the model?

Empirical analyses of the long-run natural rate — the real interest rate prevailing over a long-run equilibrium in which nominal rigidities are absent — consistently find that it is time-varying in a manner best described by a random walk, meaning it can drift without reverting to a constant long-run level. The paper cites Holston, Laubach, and Williams (2017), Fiorentini et al. (2018), and Hamilton et al. (2016) as the main empirical references. Holston et al. (2017) place the long-run natural rate at between 0 and 1 percent in the U.S. and possibly slightly negative in the euro area as of 2016. The paper draws one central lesson: because the natural rate is time-varying and its future level is uncertain, a model with constant natural rate will give unreliable guidance for monetary policy, especially at low natural rate levels near zero.

Q2. What is the model and what are the key equilibrium concepts?

The paper embeds a new Keynesian model in which the long-run natural rate follows a bounded random walk with upper bound 3 percent and lower bound 0 percent, calibrated to post-WWII U.S. TFP data, and studies optimal monetary policy under commitment while imposing the zero lower bound. A critical distinction separates two notions of the long-run equilibrium interest rate: the “long-run natural rate” (denoted ¯r) is the real rate that would prevail in flexible-price equilibrium, determined by fundamentals outside the central bank’s control; the “neutral rate” (r*) is the real policy rate consistent with stable inflation in the long run, which the central bank operationally targets. The two coincide in standard models with constant ¯r, but diverge in this paper because ZLB risk drives a wedge between them.

Q3. What is the main theoretical result?

Under optimal commitment, the neutral rate r should fall more than one-for-one with the long-run natural rate ¯r — that is, the central bank should maintain a negative gap (r < ¯r) that widens as ¯r falls toward zero — because permanent downward movements in ¯r make future ZLB binding episodes permanently more likely, creating a persistent downward bias on inflation expectations that requires pre-emptive accommodation even in periods when the ZLB is not currently binding.** This result contrasts with the existing literature on optimal commitment at the ZLB, which has emphasized forward guidance — the promise to maintain low rates even after the economy recovers from a ZLB episode — as the primary stabilization tool. The paper shows that forward guidance alone is not sufficient when ¯r can permanently drift lower, because each downward drift permanently raises the probability of future ZLB episodes, reducing the central bank’s scope for fulfilling future inflation promises.

Q4. What are the quantitative implications?

The model implies that the neutral rate r reaches zero when the long-run natural rate ¯r is at 75 basis points — a level that was well above the near-zero estimates of ¯r prevailing at the end of the 2010s — and that the ZLB binds one-third of the time under optimal policy when ¯r fluctuates between 0 and 3 percent.* The 75 basis-point threshold means that a central bank operating in an environment where ¯r has declined to its estimated late-2010s levels would already be constrained to a neutral rate of zero under optimal policy. The one-third ZLB frequency is higher than what would be predicted by models with constant ¯r at typical calibrations, reflecting the permanent nature of ¯r shocks and their cumulative effect on the neutral rate.

Q5. What do the adjustment dynamics look like after a negative ¯r shock?

Following a permanent reduction in ¯r, the real policy rate adjusts gradually rather than immediately — remaining temporarily above the new long-run neutral rate during the transition — implying that monetary policy is contractionary along the adjustment path and that a permanent decline in ¯r is followed by a temporary disinflation before the economy settles at the new r.* This history-dependence of optimal commitment policy means the central bank does not immediately jump to the new, lower r* after a ¯r shock; it moves gradually, making the short-run policy stance more contractionary than the long-run position. The temporary disinflation is consistent with the general principle of history-dependence of optimal policy under commitment.

Q6. What role does price level targeting play?

Price level targeting variants — particularly a rule with an optimally chosen upward drift of 10 basis points — closely approximate the economic outcomes achieved under optimal commitment policy in the model, with the practical advantage that such rules do not require the central bank to know or estimate the current level of the long-run natural rate ¯r. The Eggertsson-Woodford (2003) price level target works well in models with constant ¯r by generating positive inflation expectations in the wake of deflationary ZLB episodes. Adding a small upward drift of 10 basis points strengthens this property under a drifting ¯r, because it provides additional buffer against the downward expectations bias that permanent ¯r drift generates. Under price level targeting rules, the neutral rate reaches the ZLB as soon as ¯r falls below 1 percent.

Key concepts

long-run natural rate (¯r) : the real interest rate prevailing over a long-run equilibrium in which nominal rigidities are absent; in this paper modelled as a bounded random walk with upper bound 3 percent and lower bound 0 percent, calibrated to post-WWII TFP data.

neutral rate (r)* : the real policy rate consistent with stable inflation in the long run; distinct from ¯r in this paper because ZLB risk drives a negative gap (r* < ¯r) that widens as ¯r approaches zero.

zero lower bound (ZLB) : the constraint that nominal policy rates cannot fall below zero; in this model the reason that permanent reductions in ¯r create a persistent downward bias on inflation expectations even when the ZLB is not currently binding.

expansionary bias : the paper’s finding that optimal commitment policy should maintain r* < ¯r — a pre-emptive accommodation away from the ZLB — to offset the downward bias on inflation expectations created by the risk of future ZLB episodes.

price level targeting : a monetary policy rule in which the central bank targets the price level rather than the inflation rate; shown in this paper to approximate optimal commitment policy and to have the practical advantage of not requiring knowledge of ¯r.

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.

Optimal monetary policy with uncertain private sector foresight

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

Central banks must set policy under uncertainty about how private-sector expectations form, which changes how monetary policy transmits to output and inflation. This paper studies optimal time-consistent monetary policy using a New Keynesian finite-horizon planning (NK-FHP) model in which households and firms have limited foresight: they solve structural problems only up to a finite horizon, and update their beliefs about longer-run inflation by averaging over past data. In this setting—unlike in standard New Keynesian models—an “inflation scares” problem can arise: agents’ longer-run inflation expectations can deviate persistently from the central bank’s target, generating costly and prolonged disinflations. The authors formally characterize optimal policy when the planning horizons of private-sector agents are uncertain and a risk of inflation scares is present, showing that risk-management considerations modify the standard “leaning against the wind” principle with a novel preemptive motive: the optimal policy responds more aggressively to the risk of unanchoring to prevent inflation scares from materializing. An estimated version of the model is used to quantify how much this preemptive motive mattered during the post-pandemic inflation surge.

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 NK-FHP model and how does it differ from standard New Keynesian models?

In the NK-FHP model, households and firms are boundedly rational because they evaluate state-contingent paths only up to a finite horizon; beyond that horizon they extrapolate longer-run beliefs by averaging over past data, making those beliefs adaptive rather than anchored at the target. When agents have long planning horizons, the model approximates rational expectations: inflation expectations are well anchored, disinflations are relatively costless, and policy transmits quickly. When planning horizons are short, longer-run inflation expectations can become unanchored, disinflations are costly, and policy transmission lags lengthen. The NK-FHP model thus nests both extremes and provides micro-foundations for the “inflation scares” discussed by Goodfriend (1993).

Q2. What is the “inflation scares problem” and why does it matter for optimal policy?

An inflation scare occurs when agents’ longer-run inflation expectations deviate persistently from the central bank’s target because agents with short planning horizons update beliefs adaptively, and past high inflation feeds forward into current expectations. This creates a welfare-relevant asymmetry: once expectations become unanchored, a disinflation is costly in output because the central bank must build credibility against backward-looking expectations. The standard NK model with rational expectations does not generate this problem—rational agents’ inflation expectations are pinned to the target irrespective of history—so it cannot address the design of policy specifically to prevent scares from materializing.

Q3. What is the “preemptive motive” and how does it modify the leaning-against-the-wind principle?

Optimal time-consistent policy under uncertain private-sector foresight adds a preemptive motive to the standard leaning-against-the-wind (LATW) principle: the central bank contracts demand not just in response to current output-gap and inflation deviations, but also to prevent expectations from becoming unanchored. Under the standard NK LATW result (Clarida, Galí, and Gertler 1999), the policymaker responds to the means of output and inflation. Under uncertain and potentially short-horizon foresight, optimal policy also depends on the distribution of output and inflation, as well as agents’ beliefs about future inflation—specifically, whether those beliefs risk drifting away from target. The preemptive motive implies a more aggressive policy response to the risk of an inflation scare even before the scare has fully materialized.

Q4. How does the paper relate to the post-pandemic inflation experience?

Using parameter estimates from an estimated version of the NK-FHP model, the paper applies the optimal policy framework to quantify how much the preemptive motive matters during the recent post-pandemic inflation surge. The model—which has been shown in related work (Gust, Herbst, and López-Salido 2022, 2024) to fit macroeconomic time series substantially better than hybrid NK models and to account for initial underreaction and subsequent overreaction of inflation forecasts—is well suited to analyze an episode where longer-run inflation expectations initially remained anchored but later showed signs of drift. The paper’s quantification indicates that risk-management considerations, including the preemptive motive, significantly affect the optimal policy path.

Key concepts

finite-horizon planning (NK-FHP) : a bounded-rationality framework (Woodford 2018) in which agents evaluate only those state-contingent paths within a finite planning horizon, updating beliefs about events beyond the horizon adaptively from past data.

inflation scares : episodes (Goodfriend 1993) in which agents’ longer-run inflation expectations deviate persistently from the central bank’s target, making disinflation costly; the NK-FHP model provides micro-foundations for such scares.

preemptive motive : the additional incentive for a policymaker to tighten beyond what current output-gap and inflation deviations alone would prescribe, specifically to prevent longer-run inflation expectations from becoming unanchored.

time-consistent policy under uncertainty : optimal policy that does not rely on commitment and hence accounts for future re-optimization; in this model it must also account for the non-additive uncertainty arising from a distribution of planning horizons.

Robust Real Rate Rules

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

The paper proposes and analyzes real rate rules — monetary policy rules of the form i_t = r_t + φπ_t (φ > 1), where r_t is the current-period real interest rate observed via TIPS yields or inflation swap markets. The central analytical result is that combining this rule with the Fisher equation i_t = r_t + E_t[π_{t+1}] immediately yields E_t[π_{t+1}] = φπ_t, whose unique non-explosive solution is π_t = 0 for all t. This proof uses only the Fisher equation — not the aggregate Euler equation — making the determinacy result robust to household heterogeneity, hand-to-mouth consumers, non-rational household or firm expectations, active fiscal policy, missing transversality conditions, and any specification of intertemporal or nominal-real links. The Fisher equation itself requires only two deep-pocketed, fully-informed, rational agents to arbitrage between nominal and real bonds — a much weaker assumption than aggregate Euler equation rationality. Under the real rate rule, inflation is decoupled from the Phillips curve: causation runs monetary policy → inflation, then inflation → output gap, not the reverse; the Phillips curve determines the output gap residually given already-determined inflation. In a three-equation New Keynesian model with a mark-up shock ζ_t and cost-push shock ω_t, the output gap satisfies x_t = −(ζ_t/(κ(φ − ρ_ζ))) − (ω_t/κ), where the Euler equation plays no role in inflation determination. The rule is globally stable under learning via a contraction argument using Gautschi’s inequality: even if financial market participants hold incorrect prior beliefs, the learning process converges to the target inflation. With a time-varying inflation target π*_t, the modified rule i_t = r_t + φ(π_t − π*_t) implements any target path determinately — π_t = π*_t for all t, including optimal Ramsey paths — making real rate rules observationally equivalent to any other monetary policy specification. The Taylor principle (φ_π > 1) is neither necessary nor sufficient for determinacy in richer models (Bilbiie 2008 TANK; Leeper-Leith 2016 FTPL); the real rate rule achieves determinacy without invoking Euler equation structure. An additional result: with long-maturity government debt, a stable inflation equilibrium always exists under the real rate rule regardless of whether fiscal policy is active or passive — the fiscal theory of the price level fails to produce unique outcomes in this setting.

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 real rate rule, and why does it achieve determinacy without requiring the aggregate Euler equation?

The real rate rule i_t = r_t + φπ_t (φ > 1) combined with the Fisher equation i_t = r_t + E_t[π_{t+1}] immediately gives E_t[π_{t+1}] = φπ_t, whose unique non-explosive solution is π_t = 0 for all t; the proof is complete at this step, requiring no information about how households form expectations or optimize intertemporally. Standard Taylor-rule determinacy proofs rely on the aggregate Euler equation to close the system — the IS curve determines aggregate demand as a function of the real interest rate; deviation from determinacy arises when the Euler equation-Phillips curve system allows self-fulfilling expectation spirals. The real rate rule bypasses this entirely: the Fisher equation alone pins down the inflation path. The Fisher equation is a no-arbitrage condition between nominal and real bonds; it holds as long as two “deep-pocketed, fully-informed, rational agents” can trade both types of bonds — a condition that does not require aggregate household rationality, representative agent assumptions, or any specific consumption theory. Hand-to-mouth households, heterogeneous expectations, learning dynamics, and non-Ricardian fiscal regimes all leave the Fisher equation intact as long as some agents are pricing both asset classes. The consequence is that the Euler equation in the three-equation NK model becomes residual under the real rate rule: it determines the path of real interest rates given already-determined inflation and output gap, but plays no role in choosing among inflation equilibria.

Q2. What does the real rate rule imply about causation between inflation and the output gap?

Under the real rate rule, the Phillips curve operates in reverse relative to standard models: inflation is determined first (by the Fisher equation and the monetary rule), and the Phillips curve then determines the output gap as a residual; cost-push and demand shocks cannot amplify or dampen inflation variance under the rule. In the standard three-equation NK model with a mark-up shock ζ_t (law of motion ζ_t = ρ_ζ ζ_{t-1} + ε_{ζ,t}) and cost-push shock ω_t, the output gap under the real rate rule is x_t = −ζ_t/(κ(φ − ρ_ζ)) − ω_t/κ — a closed-form solution determined entirely by shocks, where the Euler equation does not appear. Inflation is π_t = 0 at all t (zero target): shocks affect the output gap but not inflation. Under an augmented rule that also responds to the output gap (i_t = r_t + φ_π π_t + φ_x x_t), determinacy still holds as long as a Phillips curve linking inflation and the output gap exists and the Taylor principle φ_π > 1 holds — providing additional policy degrees of freedom without sacrificing robustness. The decoupling of inflation from the Phillips curve is consistent with the empirical finding of Dotsey, Fujita, and Stark (2018) that the Phillips curve ceased to forecast inflation after 1984 — compatible with the hypothesis that the Fed’s post-Volcker behavior moved toward more real-rate-rule-like rules, giving the Fisher equation stronger anchor over inflation.

Q3. How does global stability under learning extend the determinacy result beyond local uniqueness?

Equilibrium determinacy is a local result (unique bounded solution near the target); the real rate rule additionally provides global stability under learning — even if financial market participants start with prior beliefs far from zero, the learning process converges to π_t = 0, preventing self-fulfilling sunspot equilibria from taking hold in the first place. The proof (Appendix D, using Gautschi’s inequality) establishes that the mapping from current beliefs to future beliefs is a contraction in the appropriate norm: since E_t[π_{t+1}] = φπ_t with φ > 1 drives realized inflation to zero, agents who update beliefs based on observed prices will progressively correct any initial error. This contrasts with Taylor rules, which are only locally determinate — an economy that starts at a non-zero sunspot inflation level may remain there if the sunspot is self-fulfilling. The global stability result also provides a response to the Cochrane (2022) critique that indeterminate equilibria under standard Taylor rules are “everywhere”: under the real rate rule, the only globally stable equilibrium is the target. The interest rate smoothing variant (Section 1.5) — fully smoothed real rate rule, θ > 0 — provides additional robustness: it requires agents to believe only that the central bank responds positively to inflation (not that φ > 1 specifically), and still generates identical inflation dynamics; this is more credible as a commitment device because the specific magnitude of φ cannot be directly observed.

Q4. How can the real rate rule implement arbitrary inflation dynamics, including optimal policy?

With a time-varying inflation target π_t, the modified rule i_t = r_t + φ(π_t − πt) implements any target inflation path determinately: the Fisher equation gives E_t[π{t+1} − π*_{t+1}] = φ(π_t − π*_t), whose unique solution is π_t = π*_t for all t, so realized inflation tracks the announced target exactly.** The CB must announce π*_t each period; this announcement may respond to the output gap, cost-push shocks, or any other variable. For example, to stabilize inflation while accommodating a cost-push shock, the CB sets π*t as a function of ω_t; realized inflation then follows this target, and the Phillips curve determines the output gap residually. There are two constraints: (1) the CB must be able to compute a reasonable approximation to E_t[π*{t+1}] — achievable via inflation futures, inflation swap markets, or an internal forecasting model; (2) the target path itself must not be explosive (a target that amplifies its own past realizations would generate explosive equilibria). Under these constraints, the paper formally proves (Appendix E.5) that real rate rules with time-varying targets can replicate the outcomes of any other monetary regime. This implies: (a) real rate rules can implement Ramsey-optimal policy, attaining the highest possible welfare; (b) it is empirically impossible to test whether a central bank is following a general real rate rule — any observed inflation and interest rate dynamics are consistent with some choice of π*_t. The Smets-Wouters (2007) estimated rule for the US illustrates: at the posterior mode, the correlation between the rule component z_t and the real interest rate r_t is 0.63, with both variables having standard deviation 0.46%, suggesting the Fed is already approximately two-thirds of the way toward a simple robust real rate rule.

Q5. Why does the Taylor principle fail in richer models, and how does the real rate rule avoid those failures?

The Taylor principle (φ_π > 1) is sufficient for determinacy in the benchmark three-equation NK model with a representative rational agent, but it is neither necessary nor sufficient in richer environments: Bilbiie (2008) shows that with enough hand-to-mouth consumers, higher φ_π can destabilize the economy; Leeper-Leith (2016) shows that following the Taylor principle can generate explosive inflation under the fiscal theory when nominal debt is present. Bilbiie (2008, 2019) inverts the Euler equation for the representative rational household when hand-to-mouth agents dominate: the aggregate consumption Euler equation has a negative intertemporal substitution sign, making the system’s eigenvalues switch. With enough hand-to-mouth agents, φ_π > 1 actually generates explosive equilibria (indeterminacy flips). Under the real rate rule, the Euler equation is disconnected from inflation determination entirely — Bilbiie’s mechanism cannot operate because the inflation equation relies only on the Fisher equation, not on whether the Euler equation has positive or negative sign. Similarly, the paper’s Section 2 result on fiscal robustness: with long-maturity government debt (Appendix B), a stable inflation equilibrium always exists under the real rate rule regardless of whether fiscal policy is active or passive. This implies the fiscal theory of the price level (FTPL) cannot uniquely determine inflation under the real rate rule — there is always a stable solution — so FTPL determinations are not unique, which may be of independent theoretical interest. The proof uses the contracting property of the non-linear real rate rule in the fully non-linear model, showing the target gross inflation Π* is always a solution of the bond-pricing fixed-point equation and that it is approached from all starting points via iteration.

Q6. How is the real rate rule implemented in practice, and what are the policy implications for central bank design?

Implementation uses TIPS yields (Treasury Inflation-Protected Securities) or inflation swap markets as real-time signals for r_t; the central bank sets i_t = TIPS_yield_t + φπ_t without estimating the natural rate (r) or output gap, eliminating the key measurement error in standard rules.* The key operational advantage over standard Taylor-type rules: standard rules require estimating the natural rate r* (now known to be mismeasured; Holston-Laubach-Williams 2017 revisions) and the output gap (subject to large real-time revisions); the real rate rule bypasses both because r_t is directly observable from financial markets (it equals the TIPS yield to a risk premium). The CB must also compute E_t[π*_{t+1}] to set the time-varying target; inflation futures or swap markets provide a forward-looking market price for this purpose. The paper discusses Hall and Reis (2016) “indexed payment on reserve” rules, which use a different mechanism (central bank liability indexation) to achieve similar robustness goals but do not rely on the Fisher equation as directly. Adão, Correia, and Teles (2011) achieve related results via complete nominal bond indexation. The real rate rule is more transparent and simpler to communicate: the CB says “we will raise the policy rate one-for-one with the real rate plus respond to inflation with coefficient φ.” For a smoothed version, communicating “we respond positively to inflation” — without specifying exactly how much — is sufficient for determinacy, and arguably more credible as a commitment. Section 4 (not covered here) develops a ZLB-adapted version of the rule for zero lower bound episodes that rules out explosive inflation equilibria at the bound.

Key concepts

real rate rule : the monetary policy rule i_t = r_t + φπ_t (φ > 1), where r_t is the current real interest rate observed from TIPS or inflation swap markets; achieves equilibrium determinacy via the Fisher equation alone, without invoking the aggregate Euler equation, making it robust to heterogeneous agents, hand-to-mouth consumers, non-rational expectations, and active fiscal policy.

Fisher equation : the no-arbitrage condition i_t = r_t + E_t[π_{t+1}] linking the nominal policy rate, real rate, and expected inflation; in the context of the real rate rule, it is the only structural equation needed for determinacy; requires only two deep-pocketed rational agents to arbitrage between nominal and real bonds — not aggregate household rationality.

inflation decoupling : the property under the real rate rule that the Phillips curve determines the output gap residually given already-determined inflation, rather than operating as a transmission mechanism for cost-push or demand shocks into inflation; implies that only monetary policy shocks and Fisher equation shocks can move inflation — cost-push and demand shocks affect the output gap but not the price level.

Taylor principle failure : the result (Bilbiie 2008) that standard Taylor rules can fail to deliver determinacy in models with hand-to-mouth consumers or heterogeneous agents — because the inverted aggregate Euler equation can flip eigenvalue signs — and (Leeper-Leith 2016) that following the Taylor principle can generate explosive inflation under the fiscal theory of the price level with nominal debt; the real rate rule avoids both failures by relying on the Fisher equation rather than the Euler equation for inflation determination.

global stability under learning : the property that even if financial market participants start with beliefs far from the inflation target, the learning process converges to the target under the real rate rule, proven via a contraction argument using Gautschi’s inequality; stronger than local determinacy (which only guarantees uniqueness near the target), ruling out self-fulfilling sunspot equilibria from any starting point.

fiscal theory robustness : the paper’s finding that with long-maturity government debt, the real rate rule always implies a stable inflation equilibrium regardless of whether fiscal policy is active (non-Ricardian) or passive (Ricardian); equivalently, the fiscal theory of the price level cannot uniquely determine inflation under the real rate rule because a stable solution always coexists with any fiscal regime.

Tokenomics: Optimal monetary and fee policies

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

The rapid proliferation of cryptocurrency tokens—roughly 10,000 outstanding with a total market capitalization around $3 trillion as of early 2024—raises new questions about the design of token monetary policy and fee structures. This paper makes two contributions. Empirically, using supply histories for approximately 2,000 tokens, it documents three systematic patterns: average token money growth rates decline with age and stabilize at about 0.2% per month; long-run money growth rates and convergence speeds are positively correlated across tokens in the cross-section; and tokens more widely held by retail investors have relatively lower long-run money growth rates and convergence speeds. Theoretically, the paper derives optimal issuance and fee policies for a profit-maximizing issuer in a dynamic model where commitment matters, showing that a fully committed (Ramsey) issuer who maximizes profits after the initial period makes choices that maximize the total utility value of all tokens, that without any commitment no equilibrium with a positive token price exists unless fees are charged, and that under partial commitment issuers with higher commitment credibility optimally choose lower long-run money growth rates and fee ratios.

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 are the three empirical facts about crypto monetary policies?

Fact 1: the average money growth rate across the ~2,000 tokens declines with cohort age and stabilizes at approximately 0.2% per month, with more recent cohorts converging faster to their long-run growth rates. Fact 2: in the cross-section of tokens, the estimated long-run money growth rate and the speed of convergence to it are positively correlated—tokens that will eventually have higher money growth also converge more quickly to that level. Fact 3: tokens whose circulating supply is widely distributed among retail investors (measured by the proportion of wallet addresses holding less than 0.1% of total supply) have both lower long-run money growth rates and lower convergence speeds. Together these facts suggest that the degree of decentralization of token ownership systematically influences the choice of monetary policy.

Q2. What are the main theoretical results about commitment?

Without any commitment, no equilibrium with a positive token price can be sustained if the issuer cannot charge user fees; fees create credibility by giving a Markov-perfect issuer an incentive to restrict future token issuance (to collect fees on legacy token holders), which supports a positive price. At the other extreme, with full commitment the Ramsey issuer maximizes profits subject to the full sequence of resource constraints, and a central analytical result is that at steady state the Ramsey issuer’s profit-maximizing choices are equivalent to maximizing the total utility value of all tokens outstanding. This equivalence—profit maximization = welfare maximization for token holders—holds because commitment prevents the issuer from diluting legacy holders; under full commitment, the issuer has no incentive to deviate from the policy that maximizes total token value.

Q3. What does partial commitment imply for policy design?

Under partial commitment (modeled as a probability of sticking to a given policy rather than re-optimizing), issuers with higher commitment probability optimally choose lower long-run money growth rates and reduce both the money growth rate and the fee ratio more slowly over time. This is because higher commitment credibility raises the present value of legacy tokens (users expect the issuer to honor its policy), which makes it optimal to extract less seigniorage and fewer fees in each period while sustaining a higher token price. The model is analytically solvable under partial commitment despite rich economic mechanisms, and the results help interpret Fact 3: tokens with more decentralized ownership (higher effective commitment due to governance constraints) exhibit lower money growth.

Q4. How do the model’s predictions compare with the Bitcoin and Ethereum cases?

Bitcoin exemplifies near-full commitment: its supply schedule is essentially deterministic and hard-coded, resembling the Ramsey policy, though the paper notes a non-zero probability of a fork that could alter the policy. Ethereum exemplifies frequent policy changes (the transition from proof-of-work to proof-of-stake altered issuance and burn rules significantly). Discretionary platforms like MakerDAO, which allow issuer discretion over token supply, more closely resemble the Markov-perfect benchmark. The paper’s framework covers this entire spectrum and predicts that tokens with more commitment (closer to Bitcoin) should have lower long-run money growth and slower convergence—consistent with the empirical facts.

Key concepts

token monetary policy : the issuer’s choice of the rate at which new tokens are minted over time (the money growth rate) and the fees charged per transaction; the paper shows these jointly determine the value of a token and the issuer’s profit.

Ramsey policy for tokens : the full-commitment profit-maximizing policy for a token issuer; a key result is that the Ramsey issuer’s profit-maximizing choices, after the initial period, are equivalent to maximizing the total utility value of all tokens.

partial commitment : a probabilistic commitment technology in which the issuer maintains a given policy with some probability and re-optimizes with the complementary probability; the paper uses this to model the spectrum between Bitcoin (high commitment) and more discretionary platforms.