E43 | Macro Paper Warehouse

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

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

Layer 1 — Core Argument

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

Layer 2 — Q&A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Key Concepts

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

Overview

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

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

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

Main Findings.

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

Q&A

Q1: Why does the paper restrict estimation to bonds with maturity greater than one year? Short-maturity Treasury notes exhibited particularly large estimated bond-specific pricing errors in preliminary analysis, which the authors attribute to a liquidity premium: short-term government debt was used for transactions and thus commanded a money-like premium that a common discount function cannot accommodate. To keep this liquidity premium from distorting estimates of the longer end of the curve, these bonds are excluded from the main estimation. Short-maturity bonds are then studied separately as an “out-of-sample” exercise (the short-rate disconnect).

Q2: How does the Dynamic Nelson-Siegel model with stochastic volatility solve the cross-sectional sparsity problem? The DNS model parameterizes the entire yield curve at each date using only three latent factors — level (L), slope (S), and curvature (C) — which follow a driftless random walk. The stochastic volatility component, captured in the covariance matrix Σt, governs how much information is pooled across adjacent time periods. When Σt → 0, the yield curve is assumed constant (full pooling); when Σt → ∞, estimates are date-by-date (no pooling). By allowing Σt to vary, the model pools more heavily in sparse periods and less during wars when yields change rapidly. The companion paper (Payne et al. 2023a) confirms via information criteria that stochastic volatility and correlated shocks improve fit without overfitting.

Q3: What is the bond-specific pricing error and why is it essential for historical data? Assumption 3 adds to each bond i a Gaussian pricing error with mean zero and bond-specific standard deviation σ(i)_m (scaled by Macaulay duration to approximate yield-space errors). This allows bonds with idiosyncratic contract features — call options, conversion clauses, ambiguous payment currency — to inform the common yield curve without unduly distorting it. Bonds with larger σ(i)_m receive less weight in estimation. In modern datasets, researchers pre-select homogeneous bonds and use time-specific pricing errors; the historical sparsity prevents that approach here.

Q4: How large were Civil War yields compared to prior estimates, and why does the discrepancy arise? The paper’s posterior median for the 10-year gold zero-coupon yield peaks at approximately 16% near the end of the Civil War. Homer and Sylla (2004) report a peak of 6% at the start of the war. The discrepancy arises because Homer and Sylla used bonds trading close to par, but during the Civil War no federal bonds traded at gold-price par (Lincoln’s re-election was uncertain in summer 1864; 100 greenback dollars could be purchased for 40 gold dollars, implying 6% coupon bonds were priced at 40% of par, implying yields in excess of 15%). This paper uses the full universe of Treasury bonds at monthly frequency and allows all bonds — regardless of trading price — to inform the yield curve.

Q5: When did US debt cease to carry a default risk premium relative to UK debt, and how is this measured? The authors compare yields-to-maturity on gold-denominated UK consols to those on hypothetical gold-denominated US consols promising the same coupon flows. Because both countries were on a gold standard for most of the period and UK consols were the 19th-century safe asset, the spread is interpreted as a risk premium on US debt. US yields fell below UK yields persistently after approximately 1905, indicating that US debt was priced as a safe asset well before World War I. US yields were temporarily close to UK yields in the 1820s but the spread re-widened after the Jacksonian era, state defaults in the 1840s, and the Civil War. The spread closed only after Civil War disruptions resolved, the National Banking System matured, and gold-greenback parity was restored in 1879.

Q6: What is the “nominal anchor” finding during the greenback era, and what econometric method uncovers it? During 1862–1878, the federal government issued non-convertible greenback dollars alongside gold bonds. The greenback depreciated substantially (to 40 cents per gold dollar in 1864), yet greenback-paying bonds traded near par, implying greenback yields near 6%. The authors model the greenback yield curve as a product of the gold discount function and a “multiplier” z(j)_t capturing the expected future gold-to-greenback exchange rate at each horizon j (Assumption 4). The exchange rate expectations are estimated via a time-varying VAR(2) model of the gold-to-greenback and gold-to-goods exchange rates (Assumption 5), jointly constrained by the prices of greenback bonds via an interest-rate parity condition. The resulting estimates show that throughout the greenback era — even during large wartime depreciations — investors’ long-run expectations of the exchange rate remained anchored near gold parity, consistent with anticipated eventual resumption.

Q7: How did political events affect exchange rate expectations during and after the Civil War? The time-varying VAR captures shifts in exchange rate expectations associated with identifiable political events. Grant’s victory in 1869 (which resolved uncertainty about whether debts would be honored in gold) coincided with an increase in the price of greenbacks, a decrease in expected greenback appreciation, and a closing of the gap between greenback and gold 10-year yields. In the early 1870s, following the Panic of 1873 and uncertainty about resumption, investors came to expect that gold-greenback discrepancies would persist almost indefinitely, causing gold and greenback yields to converge. The Resumption Act of January 1875 then shifted 2-year and 10-year expectations back toward parity.

Q8: What is the short-rate disconnect and what does it reveal about the National Banking Era? The short-rate disconnect is the difference between observed yields-to-maturity for bonds with less than one year to maturity and the yields-to-maturity implied by the model estimated on bonds with more than one year maturity. A positive disconnect means short-maturity bonds yielded less than long-maturity bonds conditional on the model — indicating a liquidity premium on short-term debt. The authors find a persistent premium of 0.25 to 0.5 percentage points through most of the 19th century, reflecting scarcity of money-like assets when state bank notes circulated at variable discounts. The premium disappeared from approximately the 1880s to World War I, coinciding with the mature National Banking Era after greenback-gold parity was restored in January 1879. The authors interpret this as evidence that the National Banking Acts (1862–1866), which allowed National Banks to issue standardized bank notes backed by long-term US government bonds, ultimately succeeded in supplying liquid assets and equalizing the pricing of short- and long-term federal debt — but only after the currency risk from the greenback period had been resolved.

Q9: How does the composite long-term yield series (Officer-Williamson / Homer-Sylla) distort historical narratives? The composite series combines Homer and Sylla US federal yields (1798–1861), New England Municipal bond yields (1862–1899), and corporate bond yields (1900–1940). The paper shows that this composite series substantially underestimates the increase in US federal borrowing costs during Civil War deficits (peak of 6% vs. this paper’s 16%) and overstates post-Civil War borrowing costs by mixing in riskier private obligations. The authors argue that earlier findings of no strong association between 19th-century interest costs and deficits (Evans 1985, 1987) may reflect the composite series’ failure to accurately capture federal borrowing costs during large deficit episodes.

Q10: How did the yield curve slope change after the Civil War and what explains it? The term spread (10-year minus 2-year gold yield) was typically negative before the Civil War and positive after the late 1870s. Major wars caused sharp temporary decreases (inversions). The authors connect the sign switch to a change in long-run inflation dynamics documented in a companion paper (Payne et al. 2023b): long-run inflation was hard to predict before the Civil War and easier to predict after, suggesting gold bonds provided a better inflation hedge in the pre-war period (negative inflation-risk premium), which is consistent with asset pricing theory producing a downward-sloping yield curve. After the Civil War, as inflation became more predictable, the inflation-risk premium became positive and the yield curve turned upward-sloping.

Q11: What did the National Banking Acts seek to do and was the puzzle of bank note under-issuance resolved? The National Banking Acts (1862, 1863, 1865, 1866) authorized federally chartered banks to issue bank notes up to 90% of the par or market value of eligible US Treasury bonds deposited as collateral, subject to a 1% annual tax on notes outstanding (0.5% after 1900), compared to a 10% tax on state bank notes. The intended goals were to increase the supply of short-term liquid assets and to increase bank demand for long-term federal debt, thereby lowering long-term yields and eliminating the short-rate disconnect. A long-standing puzzle (Friedman-Schwartz, Cagan, Champ, Calomiris-Mason) held that yields on eligible Treasuries did not fall enough to equal the note tax rate, implying under-issuance. The paper’s analysis of the short-rate disconnect offers a resolution: if one focuses on the disconnect rather than the yield-tax spread, the National Banking Acts appear to have largely achieved their goals by the 1880s — but only after greenback-gold parity was restored, suggesting that currency devaluation risk had initially restrained bank note issuance, as hypothesized by Cagan (1965).

Key Concepts

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

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

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

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

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

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

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

Expectation-driven term structure of equity and bond yields

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

Overview

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

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

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

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

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

Main Findings.

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

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

Q&A

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Key Concepts

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

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

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

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

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

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

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

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

How Do Rising U.S. Interest Rates Affect Emerging and Developing Economies? It Depends

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

Layer 1 — Overview

Research Question

This paper examines how the effects of rising U.S. interest rates on emerging market and developing economies (EMDEs) depend on the underlying source of the interest rate increase. Specifically, it asks: what mix of inflation, reaction, and real shocks has driven changes in U.S. interest rates in recent years; how do these different shock types affect EMDE financial markets, capital flows, borrowing costs, and fiscal outcomes; and how do they affect the likelihood of EMDE financial crises?

Motivation and Context

Written in late 2022 against the backdrop of the Federal Reserve’s most aggressive tightening cycle since the 1990s, the paper argues that the standard practice of treating all interest rate increases as equivalent is misleading. Whether rising U.S. rates reflect strengthening growth, rising inflation expectations, or a perceived hawkish shift in the Fed’s reaction function carries very different implications for EMDEs already burdened by post-COVID debt at record highs and scarring from the pandemic.

Methodology

Three distinct empirical approaches are used, chosen to match the data frequency and parsimony requirements of each research question.

A sign-restricted Bayesian VAR model with stochastic volatility is estimated on monthly U.S. data (January 1982 - September 2022) using four variables: 2-year Treasury yield, 10-year Treasury yield, S&P 500 index, and 5-year breakeven inflation expectations. Sign restrictions identify three shocks: (i) real shocks raise both yields, equity prices, and inflation expectations; (ii) inflation shocks raise yields and inflation expectations but lower equity prices; (iii) reaction shocks raise yields but lower both equity prices and inflation expectations.
Panel local projection models (Jorda 2005) are estimated at quarterly frequency for 17-38 EMDEs over 1997Q2-2019Q4, excluding the 2008Q4-2009Q4 global financial crisis and the COVID-19 pandemic. The models link the VAR-identified quarterly shock series (normalized to represent a 25-basis-point move in the 2-year yield) to EMDE financial, real, and fiscal variables, including local-currency bond yields, EMBI+ sovereign spreads, capital flows, real GDP components, CPI inflation, the real effective exchange rate, primary fiscal balance, government revenues, expenditures, gross debt, and debt composition.
A panel logit model with random effects is estimated on annual data for 139 EMDEs over 1985-2018, linking the three shock types to the probability of banking, currency, and sovereign debt crises (as defined by Laeven and Valencia 2020).

Key Findings

Shock decomposition: Real shocks account for the largest share of variance in 2-year U.S. yields over the full sample (39 percent at a 10-month horizon); inflation shocks explain 14 percent and reaction shocks 13 percent. However, since the start of 2022, reaction and inflation shocks together account for approximately three-quarters of the cumulative increase in yields, with real shocks playing a negligible role.

Financial market and macroeconomic spillovers: Conditional on a 25-basis-point shock, reaction shocks produce significantly adverse EMDE outcomes: widening sovereign spreads (EMBI+), declining capital flows, real exchange rate depreciation, and unlike inflation shocks, statistically significant declines in private consumption and fixed investment. Inflation shocks raise domestic EMDE CPI significantly. By contrast, real shocks are associated with declining sovereign spreads, rising capital flows, real exchange rate appreciation, and higher real exports, with other real GDP components unaffected.

Fiscal outcomes: In response to inflation and especially reaction shocks, EMDE governments improve their primary balances almost exclusively through expenditure cuts, consistent with tighter credit availability constraining fiscal space. Real shocks also improve primary balances, but through both revenue gains and expenditure reductions. Government debt declines in response to all three shock types, though the decline is statistically significant only for real shocks.

Debt composition: Reaction shocks shift debt composition toward shorter maturities and foreign-currency instruments (the latter reflecting exchange rate depreciation mechanically raising the local-currency value of foreign-currency debt). Real shocks shift composition toward longer maturities and higher external creditor participation, consistent with improved market access.

Heterogeneity by credit rating: Investment-grade and noninvestment-grade EMDEs show broadly similar responses to reaction shocks, with the exception of statistically larger yield responses for noninvestment-grade economies. The paper notes this finding contrasts with several prior studies that find stronger fundamentals buffer spillovers.

Crisis probabilities: A 25-basis-point increase in 2-year U.S. yields driven by a reaction shock almost doubles the baseline probability of financial crisis in the average EMDE, from 3.5 percent to 6.6 percent. Extrapolating the nonlinear logit relationship to the 114-basis-point reaction-shock-driven increase in 2-year yields that occurred from January through September 2022 implies the probability of financial crisis in the average EMDE rising approximately 36 percentage points, to nearly 40 percent. The paper cautions that no comparable yield episode occurred in the 1985-2018 estimation sample, so this extrapolation carries substantial uncertainty. Inflation shocks are associated with only small, statistically insignificant changes in crisis probability; real shocks reduce the probability of sovereign debt crisis while raising currency crisis probability by less than reaction shocks do.

Historical episode analysis: The 2013 taper tantrum was dominated by reaction shocks, causing 10-year yields to rise by approximately 100 basis points; sovereign spreads widened by 60 basis points in the May-June 2013 window and capital flows dropped sharply. The 2022 tightening episode was driven by reaction and inflation shocks (reaction shocks adding 114 basis points to 2-year yields through September 2022), with five-year breakeven inflation expectations breaching 3 percent for the first time in the two-decade history of the series. The 2004-2006 build-up to the global financial crisis involved a mix of all three shock types with real shocks prominent, and EMDE financial conditions remained broadly benign.

Layer 2 — Q&A

Q1: How are the three shock types identified, and what makes this identification strategy credible?

The identification uses sign restrictions imposed on a Bayesian VAR with stochastic volatility. A real shock is identified as one that simultaneously raises 2-year yields, 10-year yields, S&P 500 equity prices, and inflation expectations. An inflation shock raises all yields and inflation expectations but lowers equity prices the equity decline signals that higher rates are not accompanied by stronger growth prospects. A reaction shock raises all yields but lowers both equity prices and inflation expectations the fall in inflation expectations distinguishes it from an inflation shock and signals that markets perceive the Fed is tightening beyond what current inflation warrants. Covering both short- and long-maturity yields in the sign restrictions ensures the identified shocks capture both conventional and unconventional (e.g., quantitative easing tapering) policy moves.

Q2: What share of 2-year yield variation do the three shocks each explain over the full sample?

At a 10-month horizon, real shocks explain 39 percent of the forecast error variance in 2-year U.S. Treasury yields, making them the dominant driver over the full sample (January 1982 - September 2022). Inflation shocks account for 14 percent and reaction shocks for 13 percent. Together the three identified shocks explain roughly two-thirds of total yield variation; the remaining one-third reflects residual or unclassified movements.

Q3: How did the composition of shocks driving 2-year yields change from 2021 into 2022?

Starting in September 2021, as inflation mounted and the Fed pivoted toward aggressive tightening, reaction and inflation shocks became the dominant drivers of 2-year yield increases. By September 2022, reaction and inflation shocks together accounted for approximately three-quarters of the cumulative increase in yields from the beginning of 2022, with reaction shocks alone contributing 114 basis points to the 2-year yield.

Q4: What are the financial market effects of a 25-basis-point reaction shock on EMDEs?

Reaction shocks produce significant adverse effects on EMDE financial markets within one quarter: 10-year local-currency government bond yields rise significantly, EMBI+ sovereign spreads widen significantly, capital flows decline significantly, and the real effective exchange rate depreciates significantly. Short-term (3-month) yields and equity prices also deteriorate, but these movements are not statistically significant at conventional levels.

Q5: How do financial market effects of inflation shocks compare to reaction shocks?

Inflation shocks generate adverse directional effects similar to reaction shocks rising 10-year yields, declining capital flows, real exchange rate depreciation, and falling equity prices but with the notable difference that, except for equity prices, these effects are generally not statistically significant. The paper thus finds that reaction shocks are more potent drivers of EMDE financial market tightening than inflation shocks.

Q6: How do real shocks affect EMDE financial conditions?

Real shocks produce outcomes broadly opposite to those from inflation and reaction shocks. They are associated with significant declines in EMBI+ sovereign spreads, significant increases in capital flows, significant real effective exchange rate appreciation, and significant increases in equity prices. Ten-year government bond yields do rise consistent with global bond market integration but this occurs alongside improving risk sentiment, not financial stress.

Q7: What are the macroeconomic (real activity) effects of the three shock types?

Reaction shocks produce a statistically significant decline in real GDP components, particularly in private consumption expenditure and gross fixed capital formation (fixed investment), within one quarter. Real shocks lead to higher real exports consistent with beneficial demand spillovers from stronger U.S. activity while leaving other GDP components unchanged. Inflation shocks induce a large and statistically significant increase in domestic EMDE CPI inflation, while real shocks reduce it; neither produces significant real GDP effects beyond the export channel.

Q8: How do EMDE fiscal balances respond differently to the three shock types?

Both inflation and especially reaction shocks are followed by an improvement in the EMDE primary balance (smaller deficit or larger surplus), achieved almost exclusively through declines in government expenditure. The paper attributes this to tighter credit availability and higher borrowing costs constraining fiscal space. Real shocks also improve primary balances, but the mechanism differs: both revenue increases and expenditure decreases contribute to the improvement. Declines in gross government debt occur in response to all three shocks but are statistically significant only for real shocks.

Q9: How does the composition of government debt shift in response to the different shocks?

Following inflation and reaction shocks, debt held by external creditors declines significantly as a share of total government debt, consistent with reduced access to global credit markets. Short-term debt eventually rises following both shock types. Foreign-currency debt rises considerably following reaction shocks likely reflecting the mechanical effect of currency depreciation boosting the local-currency value of pre-existing foreign-currency obligations. Conversely, following real shocks, external creditor participation rises significantly (improved market access), foreign-currency debt shares remain broadly stable, and short-term debt declines significantly (consistent with maturity extension by fiscal authorities seeking to minimize rollover risk under favourable conditions).

Q10: Do investment-grade and noninvestment-grade EMDEs respond differently to reaction shocks?

The paper finds little evidence of important differences between investment-grade and noninvestment-grade EMDEs in their responses to reaction shocks across most variables. Noninvestment-grade economies do show statistically larger increases in 10-year bond yields, and larger increases in EMBI+ spreads and 3-month yields than investment-grade economies though the latter two differences are not statistically distinguishable. For fiscal, GDP, and capital flow outcomes, the two groups respond similarly. The paper notes this finding is inconsistent with several prior studies but consistent with others, concluding the role of fundamentals remains unresolved.

Q11: How does the probability of financial crisis in EMDEs respond to the three shock types?

In the baseline (explanatory variables at sample means), the average EMDE faces a 3.5 percent probability of experiencing any type of financial crisis in a given year, with currency and banking crises the most common and sovereign debt crisis the least. Reaction shocks drive by far the largest increase: a 25-basis-point increase in 2-year yields from a reaction shock almost doubles the crisis probability to 6.6 percent. Inflation shocks produce small and statistically insignificant effects. Real shocks reduce the probability of sovereign debt crisis (consistent with their benign effects on financial markets) while raising currency crisis probability by less than reaction shocks.

Q12: What does the nonlinear logit relationship imply for the 2022 tightening cycle specifically?

Because the logit function is nonlinear, a doubling of the shock size leads to a more-than-proportional increase in crisis probability. Applying the estimated model to the 114-basis-point reaction-shock contribution to 2-year yields from January to September 2022, the model implies that the probability of financial crisis in the average EMDE increased by approximately 36 percentage points, to nearly 40 percent. The paper emphasizes this estimate carries wide uncertainty because no comparable yield increase occurred during the 1985-2018 estimation period, placing this extrapolation well outside the sample’s support.

Q13: What crisis dynamics were already materializing in 2022 consistent with the model predictions?

By the time of writing (late 2022), seven EMDEs had experienced currency depreciations of at least 30 percent against the U.S. dollar meeting the Laeven and Valencia (2020) threshold for a currency crisis and 21 EMDEs had reached agreements with the IMF for additional financing. The paper notes these developments had occurred despite standard macroeconomic factors (interest rate differentials and flight-to-safety flows) not fully explaining the magnitude of depreciations.

Q14: What robustness tests were conducted, and did they alter the main conclusions?

The VAR decomposition was re-estimated using weekly rather than monthly data. The three-shock model was simplified to two shocks (real versus monetary, combining inflation and reaction). The VAR was extended to include real GDP and PCE inflation with contemporaneous exclusion restrictions to insulate shock identification from current macroeconomic conditions. Inflation expectations were replaced with the Haubrich, Pennacchi, and Ritchken (2012) model-based measure throughout, rather than only pre-2003. For the crisis probability models, panel probit with random effects and panel logit with fixed effects were estimated alongside the baseline panel logit with random effects. In all cases, the results were not materially different: inflation and reaction shocks remained more adverse than real shocks for EMDE financial and fiscal variables, and only reaction shocks produced statistically significant increases in overall crisis probability. One noteworthy robustness finding: when combining inflation and reaction into a single monetary shock, the relative importance of the inflation component appears somewhat larger than when the two are separated.

Q15: What are this paper’s main contributions relative to existing literature?

The paper makes three stated contributions. First, it is the first to decompose the evolution of U.S. interest rates over the COVID-19 pandemic recession, subsequent recovery, and 2021-22 inflation surge into the separate contributions of real, inflation, and reaction shocks. Second, it extends prior work on EMDE spillovers (e.g., Arteta et al. 2015; Hoek, Kamin, and Yoldas 2021, 2022) by showing how different shock types affect government budget balances, revenues, expenditures, and debt composition, and by expanding the EMDE country sample. Third, it is the first to examine how real, inflation, and reaction shocks differentially affect the probability of banking, currency, and sovereign debt crises in EMDEs.

Key Concepts

Reaction shock: In this paper’s framework, a change in U.S. interest rates caused by a perceived shift in the Federal Reserve’s reaction function toward a more hawkish policy stance. Identified as a shock that raises both 2-year and 10-year Treasury yields while simultaneously lowering equity prices and lowering inflation expectations. The fall in inflation expectations distinguishes this shock from an inflation shock and signals that markets believe the Fed is tightening beyond what current inflation alone would warrant.

Inflation shock: A change in U.S. interest rates caused by rising expectations of U.S. inflation. Identified as a shock that raises both yields and inflation expectations but lowers equity prices. The equity decline signals that higher rates reflect inflationary pressure rather than improved growth prospects.

Real shock: A change in U.S. interest rates driven by improved prospects for U.S. real economic activity. Identified as a shock that simultaneously raises both yields, equity prices, and inflation expectations. The equity increase distinguishes this shock from the other two and signals that higher rates are accompanied by strengthening U.S. growth.

Sign-restricted Bayesian VAR with stochastic volatility: The paper’s primary model for decomposing U.S. yield movements. Sign restrictions on four variables (2-year yield, 10-year yield, S&P 500, 5-year inflation expectations) identify the three shock types without requiring timing restrictions. Stochastic volatility is incorporated to handle the heteroskedastic financial data and the COVID-19 period’s unusual size and nature; the model covers February 1982 to September 2022 at monthly frequency.

Panel local projection (Jorda 2005): The empirical framework linking the VAR-identified shock series to EMDE outcomes at quarterly frequency. Direct estimation of impulse responses at each horizon h avoids the misspecification accumulated in iterated VAR forecasts and permits straightforward incorporation of state-dependent (investment-grade vs. noninvestment-grade) heterogeneity via a dummy-variable interaction specification.

Capital flows (as used in this paper): Defined specifically as increases in net portfolio and other investment liabilities of EMDEs, excluding foreign direct investment liabilities. This definition isolates the more volatile, financially driven flows rather than the longer-horizon FDI component.

Financial crisis typology (Laeven and Valencia 2020): The crisis classification underlying the logit analysis. Sovereign debt crises are defined as a government default or restructuring of debt owed to private creditors. Banking crises require significant distress in the banking system combined with significant policy intervention measures. Currency crises are defined as a sharp nominal depreciation of at least 30 percent against the U.S. dollar. The paper uses these definitions from Laeven and Valencia (2020), extended through 2018 in Kose et al. (2021).

Primary budget balance improvement via expenditure compression: In the paper’s framework, the fiscal adjustment mechanism triggered specifically by inflation and reaction shocks: EMDE governments improve their primary balance (reduce deficits or increase surpluses) almost exclusively by cutting expenditures, rather than raising revenues, as a response to the credit tightening and higher borrowing costs associated with adverse U.S. interest rate shocks.

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.

On the Optimal Design of a Financial Stability Fund

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

Layer 1 — Overview

Research Question

This paper asks how to optimally design a Financial Stability Fund (Fund) for a union of sovereign countries that must simultaneously (i) prevent sovereign default, (ii) provide risk-sharing and consumption smoothing, (iii) respect countries’ sovereignty (limited enforcement on both sides), (iv) address moral hazard from governments’ non-contractable policy reform effort, and (v) never impose permanent transfers or incur undesired expected losses. The paper develops the formal theory of such a Fund and evaluates it quantitatively against an incomplete-markets economy with sovereign default (IMD), calibrated to euro area “stressed countries” (Greece, Italy, Portugal, Spain — the GIPS).

Model Setup and Methodology

The Fund is modeled as a long-term contract between a risk-neutral lender (the Fund) and a risk-averse, relatively impatient borrower (a small open-economy sovereign). The government maximizes lifetime utility over consumption, leisure, and effort, where effort is private information (non-contractable) and determines the distribution of future endogenous government expenditure shocks. Two-sided limited enforcement (LE) constraints govern the contract: the borrower’s constraint ensures the country never prefers autarky-with-default to staying in the Fund; the lender’s constraint ensures the Fund never prefers investing at the risk-free rate to continuing the contract. The lender’s constraint is set with Z = 0 in the benchmark, meaning the Fund never accepts any expected permanent transfers — no ex-ante or ex-post redistribution.

Because LE and moral hazard (MH) constraints are forward-looking, standard dynamic programming cannot be applied directly. The paper uses recursive contracts (a Saddle-Point Functional Equation, SPFE) with a discounted relative Pareto weight x as the co-state variable. The SPFE characterizes the constrained-efficient allocation. The paper then proves two welfare theorems, providing a novel decentralization of the Fund contract as a recursive competitive equilibrium (RCE) with state-contingent long-term bonds, Pigouvian taxes on Arrow securities (budget-neutral in equilibrium), and endogenous borrowing limits.

The benchmark (IMD) economy features long-term non-contingent defaultable debt modeled following Chatterjee–Eyigungor, with asymmetric default penalties and probabilistic market re-entry after default (λ = 0.264). Both economies are calibrated to GIPS data for 1980–2015 using a panel Markov regime-switching AR(1) productivity process with three regimes (crisis, intermediate, normal). Key parameters: β = 0.929, r = 2.48%, δ = 0.814, κ = 0.083, labor share α = 0.566.

Main Findings with Quantitative Magnitudes

Borrowing capacity: The Fund supports a long-run average debt-to-GDP ratio of 191 percent, compared with 78.6 percent in the IMD economy — more than double — while eliminating default episodes entirely. At the state-level, the maximum debt capacity of the Fund ranges from roughly 99–293 percent of GDP across states, versus 1.6–184 percent in the IMD economy; capacity in bad states (low θ, high g) under the IMD falls to under 2 percent, while the Fund can absorb close to 100 percent even in the worst state.
Consumption volatility: The relative volatility of consumption to output falls from 139 percent in the IMD economy to 36 percent under the Fund, reflecting greatly improved risk sharing through state-contingent payments.
Primary surplus co-movement: The cyclical correlation of the primary surplus with output rises from 0.23 (mildly procyclical — consistent with some consumption smoothing but limited by borrowing constraints and default risk) in the IMD to 0.94 under the Fund, enabling counter-cyclical primary deficits during crises.
Effort: The long-run mean effort is 17 percent higher under the Fund than in the IMD economy in normal times, reflecting the Fund’s long-horizon incentive structure. However, during a crisis, effort is lower under the Fund than under the IMD — the Fund deems high effort in a crisis not part of the efficient allocation, in contrast to the IMD where spreads and borrowing constraints impose austerity-like discipline.
Welfare gains: Starting from zero initial debt, the consumption-equivalent steady-state average welfare gain of the Fund is approximately 8.5 percent (ergodic mean-weighted), ranging from 7.0 percent in the best state (high θ, low g) to 10.3 percent in the worst state (low θ, high g). In a counterfactual crisis simulation initialized at pre-crisis GIPS levels (70 percent debt-to-GDP, 0.8 percent spread), the welfare gain rises to approximately 10.59 percent in consumption-equivalent terms, exceeding the zero-debt benchmark of 8.57 percent for the same shock state.
Welfare decomposition: For the two worst-shock states examined, higher debt capacity (channel iii) and state-contingent insurance (channel iv) together account for more than 90 percent of total welfare gains — specifically, 63.65 percent and 28.10 percent for (θl, gh), and 51.92 percent and 41.39 percent for (θl, gl), respectively. The direct costs of default (output penalty and market exclusion) together contribute less than 10 percent of total gains.
Spreads: The IMD economy generates positive spreads reflecting default risk. The Fund economy generates only non-positive spreads in equilibrium — negative spreads arise when the lender’s limited enforcement constraint is binding (i.e., when continuing to lend risks permanent Fund losses, so the Fund restrains the borrower). This negative spread is interpretable as a Debt Sustainability Analysis signal.

Scope Conditions

Calibration is to GIPS countries over 1980–2015. The Fund assumes full exclusivity (absorbs all sovereign debt). A follow-up paper by other authors shows similar welfare gains hold when only a minimal fraction of debt is absorbed. The benchmark sets Z = 0 (no solidarity transfers); relaxing Z < 0 would allow greater risk sharing. The borrower is strictly more impatient than the lender (η = β(1+r) = 0.9684 < 1).

Layer 2 — Q&A

Q1: What are the two limited enforcement (LE) constraints in the Fund contract, and what do they individually prevent?

A: The borrower’s LE constraint (constraint 1) ensures the country’s continuation value under the Fund always weakly exceeds its outside option V°(s) — the value of defaulting and entering incomplete markets as a defaulter. This prevents the borrower from reneging on the Fund contract. The lender’s LE constraint (constraint 3) ensures the Fund’s expected net present value of transfers never falls below Z (set to 0 in the benchmark), preventing the Fund from making permanent expected losses. Together, these two constraints define an interval [x(s), x̄(s)] for the relative Pareto weight within which both parties remain voluntarily in the contract.

Q2: How does moral hazard enter the model, and what is the key assumption enabling the first-order-condition (FOC) approach?

A: Government effort e ∈ [0,1] is non-contractable; it shifts the distribution of future government expenditure shocks g in a first-order stochastically dominant direction (higher effort → lower expected g). The incentive compatibility constraint (ICC, constraint 2) imposes that the marginal cost of effort v′(e) equals the marginal benefit in terms of expected future utility changes. The FOC approach is validated by Assumption 1 (monotone likelihood ratio condition on the g-shock transition, and convexity of the CDF with respect to effort), which guarantees the ICC is sufficient as well as necessary. Without this assumption, the full optimization problem would need to replace the ICC, making the recursive formulation substantially more complex.

Q3: How does the paper achieve a recursive formulation despite forward-looking LE and MH constraints?

A: The paper uses the saddle-point Lagrangian approach (following Marcet–Marimon). Rather than tracking the full history of constraints, it introduces a discounted relative Pareto weight x ≡ [β(1+r)]^t · (µ_b,t / µ_l,t) as the sufficient co-state variable. The law of motion for x adjusts at each state realization: the borrower’s LE multiplier ν_b raises x (rewards the borrower), the lender’s LE multiplier ν_l lowers x (restrains the borrower), and the MH multiplier ρ̺ shifts x up or down depending on whether the realized g provides a positive or negative signal about effort (monotone likelihood ratio). This collapses the problem to a stationary Saddle-Point Functional Equation (SPFE) in (x, s).

Q4: What are the key properties of the optimal Fund allocation characterized in the paper?

A: (i) When neither LE constraint binds, consumption increases with x and is constant in s (perfect Pareto weight-determined risk sharing), labor supply is undistorted and increases in θ, and x declines over time due to borrower impatience (η < 1). (ii) When the borrower’s LE binds (x ≤ x̄(s)), consumption, labor, and x are pinned at x̄(s) and the borrower is prevented from receiving less. (iii) When the lender’s LE binds (x ≥ x̄(s)), the same constancy holds and the lender is prevented from being overexposed. Moral hazard introduces state-contingency in the inter-period evolution of x even when neither LE binds, via the likelihood ratio term. The paper shows that immiseration (consumption converging to zero) is prevented by the borrower’s LE constraint, even in the presence of moral hazard.

Q5: What is the modified inverse Euler equation in this model, and how does it differ from standard formulations?

A: In the standard pure moral hazard problem, the inverse of the marginal utility process is a positive supermartingale, leading to immiseration (consumption converging to zero) when the borrower is impatient. In this model with two-sided LE and MH, the inverse Euler equation (Lemma 4, equation 21) has the form: E_s[{1/u′(c(x′,s′))} · {(1+ν_l)/(1+ν_b)}] = η · {1/u′(c(x,s))}. The LE multipliers truncate the supermartingale whenever borrower or lender constraints bind, recurrently preventing both immiseration and permanent lender losses. The MH constraint introduces state-contingent perturbations to the path of consumption (via likelihood ratios) even between binding episodes.

Q6: What is the novel decentralization result, and why is it theoretically significant?

A: The paper provides two welfare theorems (Propositions 1 and 2). The Second Welfare Theorem shows that any constrained-efficient Fund contract can be decentralized as a recursive competitive equilibrium with: (a) long-term state-contingent (Arrow security) assets, (b) Pigouvian state-contingent taxes τ^a(s′) on Arrow securities — which are budget-neutral in equilibrium — where 1/(1+τ^a(s′)) = 1 + χ(x,s)·u′(c(x,s))·[∂_e π(s′|s,e)/π(s′|s,e)], and (c) endogenous borrowing limits “not too tight” relative to outside options. The First Welfare Theorem shows the reverse. This decentralization is novel because it handles both limited commitment and dynamic moral hazard simultaneously — prior work handled each in isolation. The taxes internalize the full social value of effort by creating a wedge between the borrower’s and lender’s intertemporal rates of substitution, removing the need to impose the ICC directly as a constraint in the competitive equilibrium.

Q7: What drives the negative spreads in the Fund economy, and how do they differ from the positive spreads in the IMD economy?

A: In the IMD economy, positive spreads reflect the probability of default: the bond price embeds an expected default discount. In the Fund economy, default is eliminated by construction. Negative spreads arise when the lender’s LE constraint is binding in some future state s′ (i.e., ν_l(x′,s′) > 0): this means the borrower’s Pareto weight is so high that the Fund risks permanent losses by continuing to lend. The asset price equation (45) shows the Arrow security price equals the maximum of the borrower’s discounted marginal utility valuation and the risk-free discounted return — so when the lender’s constraint binds, the price is driven by the risk-free return (q(s′|s) = π(s′|s,e)·A(s′)/(1+r)), which generates a negative implicit spread. The negative spread acts as a DSA-like signal: the Fund is better off restraining lending in those states.

Q8: How does the calibration match the GIPS data, and what is the main misfit?

A: The IMD economy is calibrated to average GIPS moments over 1980–2015 using a panel Markov regime-switching AR(1) for productivity (three regimes: crisis, intermediate, normal) and a three-state government expenditure process. The model matches well: average debt/GDP of 78.57 percent (data: 78.33), average spread of 4.17 percent (data: 4.15), labor moments, relative volatility of spreads (1.74 vs. 1.67 in data), government-output correlation (0.38 matches data), and relative volatility of the primary surplus (0.97 vs. 1.00 in data). The main misfit is the average primary surplus/GDP: the model generates a positive value (consistent with stationarity and debt servicing), while the data shows a slight deficit over the sample, plausibly reflecting growth expectations. The paper notes this level misfit does not compromise its core welfare-comparison results, since what matters is the relative time-series behavior.

Q9: How does the Fund compare to the IMD economy in the crisis simulation initialized at pre-2008 GIPS conditions?

A: The economy is initialized at 70 percent debt-to-GDP and 0.8 percent spread (consistent with 2005–2007 GIPS averages), then hit with a negative productivity and high government expenditure shock. In the IMD economy, this shock generates a wave of defaults (Figure 6), sharp spread increases (spreads spike, consistent with GIPS experience of 2009–2010 where spreads reached 4.04 percent on average), and a required increase in labor supply despite low productivity. Under the Fund, no defaults occur: instead, the country runs a large primary deficit financed by the state-contingent component of the Fund contract (debt actually falls under the Fund while rising in the IMD), consumption is higher than in the IMD for approximately the first 10 periods of the crisis, and labor supply is allowed to fall (consistent with efficiency). The welfare gain in this counterfactual is approximately 10.59 percent in consumption-equivalent terms, exceeding the zero-debt-initial-condition gain of 8.57 percent for the same shock state, demonstrating that welfare gains are amplified when the Fund takes over pre-existing debt.

Q10: How does the Fund affect effort incentives differently in normal times versus crisis times?

A: In normal times, the Fund provides better incentives for effort: long-run average effort is 17 percent higher under the Fund than in the IMD economy. The Fund’s long-term contract links future government expenditure outcomes directly to future lifetime utility via the law of motion for x (equation 5): low g realizations shift x upward (reward the borrower), creating forward-looking incentives. In crisis times, the Fund allows effort to fall relative to the IMD economy; the IMD imposes higher effort in bad states through spread increases and effective borrowing constraints that make budget relief through effort more valuable. The paper interprets this as the efficient outcome: “austerity” (high effort during a crisis) is not part of the constrained-efficient Fund allocation.

Q11: What is the welfare decomposition methodology, and what does it reveal about channels of welfare gain?

A: The authors construct a sequence of counterfactual IMD economies. Channel (i) removes the output penalty upon default, isolating its welfare cost: contributes 6.58 percent (θl, gh) and 5.31 percent (θl, gl) of total gain. Channel (ii) additionally removes market exclusion after default (immediate return): contributes 1.67 percent and 1.38 percent respectively. Channel (iii) solves counterfactual economies with the Fund’s state-specific endogenous borrowing limits but no default allowed, quantifying the value of greater debt capacity: contributes 63.65 percent and 51.92 percent. Channel (iv) is the residual attributable to state-contingent insurance payments: contributes 28.10 percent and 41.39 percent. The decomposition reveals that in the worst state (θl, gh), debt capacity dominates (63.65 percent), while in (θl, gl) — where the low government expenditure partially offsets low productivity — state-contingent insurance is relatively more important (41.39 percent). Together, channels (iii) and (iv) exceed 90 percent of total gains in both cases examined.

Q12: Why is the Fund’s decentralization unlikely to emerge from private international capital markets?

A: Two reasons are given. First, private international lenders typically lack the legal authority to impose state-contingent taxes (τ^a(s′)) on domestic economies; these taxes are a necessary component of the decentralization to internalize the social value of effort. Second, even if such taxes were optimal from the joint perspective of borrower and lender, the borrower has no unilateral incentive to impose them given market conditions — the taxes are only individually rational within the Fund’s constrained-efficient contract. This provides a rationale for an institutional implementation of the Fund rather than reliance on decentralized sovereign debt markets.

Key Concepts

Financial Stability Fund (Fund): A long-term partnership contract between a risk-neutral lender (the Fund) and a risk-averse sovereign borrower, designed to provide risk-sharing and consumption smoothing through state-contingent transfers subject to two-sided limited enforcement and moral hazard constraints, without ever incurring expected permanent losses. Distinguished from standard lending by its long-term contingent structure and dual role as risk-sharing mechanism and crisis-resolution tool.

Two-sided limited enforcement (LE) constraints: Forward-looking constraints in the Fund contract that prevent either party from reneging. The borrower’s LE constraint ensures the contract always delivers at least as much lifetime utility as defaulting and entering incomplete debt markets. The lender’s LE constraint (with Z = 0 in the benchmark) ensures the Fund never accumulates a negative expected net present value from its contractual obligations — i.e., no permanent transfers occur. Both constraints are binding recurrently in the long-run ergodic set.

Moral hazard (MH) / incentive compatibility constraint (ICC): The constraint arising from the fact that government policy reform effort e is non-contractable (sovereign right). The ICC requires that the marginal cost of effort v′(e) equals the marginal lifetime benefit, which depends on the likelihood ratio of future shocks with respect to effort. The Fund contract provides long-horizon performance-based rewards and punishments (via the law of motion of the relative Pareto weight x) to induce efficient effort, without imposing ex-ante austerity conditions.

Discounted relative Pareto weight (x): The key co-state variable in the recursive formulation, defined as x_t = [β(1+r)]^t · (µ_b,t / µ_l,t), where µ_b and µ_l are the time-varying Pareto weights of borrower and lender. It captures the entire history of binding constraints and serves as the state variable summarizing the borrower’s “entitlement” in the contract. Declines over time due to borrower impatience (η = β(1+r) < 1), but is upward-adjusted when the borrower’s LE constraint binds, and shifts state-contingently due to MH likelihood ratios.

Saddle-Point Functional Equation (SPFE): The recursive formulation of the Fund contracting problem (equation 6), analogous to Bellman’s equation but for saddle-point (min-max) problems. Required because standard dynamic programming fails when constraints are forward-looking; solved by the Marcet–Marimon recursive contract approach. The SPFE characterizes the constrained-efficient Fund allocation as a function of the co-state x and exogenous state s.

Incomplete markets with default (IMD) economy: The benchmark comparison economy in which the sovereign borrows via non-contingent long-term defaultable bonds (parameterized by maturity δ and coupon κ), with asymmetric output penalties upon default and probabilistic market re-entry. Calibrated to GIPS countries 1980–2015. Generates positive spreads that reflect default risk; serves as both the status quo and the source of the borrower’s outside option V°(s) in the Fund contract.

Pigouvian Arrow security taxes: State-contingent taxes τ^a(s′) on Arrow security holdings, defined by 1/(1+τ^a(s′)) = 1 + χ(x,s)·u′(c)·[∂_e π/π], introduced in the decentralization of the Fund contract. These taxes create a wedge between the borrower’s and lender’s intertemporal rates of substitution to internalize the full social value of non-contractable effort. Budget-neutral in equilibrium: the government’s lump-sum transfer τ(s) exactly offsets expected tax revenue.

Debt Sustainability Analysis (DSA) interpretation: The paper interprets the lender’s LE constraint (Z = 0) as a Fund-level DSA: it sets the boundary beyond which the contract would embed permanent transfers. A negative spread in the Fund economy signals that the lender’s LE constraint is binding in some future state — a DSA warning that the Fund is better off investing at the risk-free rate rather than extending more credit.

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.

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.