Monetary-Policy-Asset-Prices | Macro Paper Warehouse

Estimating the Interest Rate Trend in a Shadow Rate Term Structure Model

Wed, 01 Jan 2025 00:00:00 +0000

This paper proposes a shadow rate no-arbitrage dynamic term structure model (SDTSM) with drifting trends to estimate the long-run trend of the real interest rate using yield curve data from the U.S., U.K., and Germany from January 1972 to April/March 2022. The model combines the shadow rate approach of Wu and Xia (2016) to handle the zero lower bound with the shifting endpoint of Bauer and Rudebusch (2020) to capture low-frequency movements. Interest rate trends in all three countries have declined since the 1990s, with strong co-movement among them. The model provides better yield forecasts than existing models. Term premium estimates from the model are stationary and positively correlated with inflation uncertainty measures, corroborating Wright (2011). Under the convention that all permanent shocks to real interest rates are derived from real shocks, the model’s trend estimate also serves as a measure of the natural rate of real interest.

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

In depth

Q1. What are the two key modeling innovations?

The model combines two innovations: (1) a shadow rate approach following Wu and Xia (2016) to handle the zero lower bound (ZLB)—defining the policy rate as max(shadow rate, lower bound) so that the model remains valid when rates are near zero; and (2) a drifting trend (shifting endpoint) following Bauer and Rudebusch (2020) to capture the slow downward movement of the interest rate trend since the 1990s. Combining these two features is the paper’s key contribution: existing shadow rate models (Wu-Xia) do not model the low-frequency trend; existing shifting-endpoint models (Bauer-Rudebusch) do not account for the ZLB. The combination produces better-identified trend estimates because the shadow rate summarizes financial conditions including the effects of unconventional monetary policy.

Q2. Why use the full yield curve rather than a few selected maturities?

Using the full yield curve with no-arbitrage restrictions allows the model to exploit all information in the Treasury bond market and impose internally consistent restrictions on how maturities are related, improving estimation efficiency relative to models that select a few yields and do not impose no-arbitrage restrictions (e.g., Del Negro et al. 2017; Johannsen and Mertens 2021). The failure of the pure expectations hypothesis implies that a model handling term premiums coherently and flexibly is necessary to correctly extract interest rate trends from long-term yields; the no-arbitrage DTSM provides this structure while also being free of the liquidity premium complications in TIPS-based models.

Q3. What are the main empirical findings about the interest rate trend?

Interest rate trends in the U.S., U.K., and Germany have all declined since the 1990s, with strong co-movement among them; under the convention that all permanent shocks to real interest rates are derived from real shocks, the paper’s trend estimate can be interpreted as a trend estimate of the natural rate of real interest. The strong international co-movement is consistent with global factors—such as declining trend output growth, rising savings, and global safe asset demand—driving the secular decline in real interest rates rather than purely country-specific factors.

Q4. What is the relationship between term premiums and inflation uncertainty?

Term premium estimates from the model are stationary (rather than trending downward as in some models where the trend and the term premium are not well separated) and are positively correlated with inflation uncertainty measures, corroborating Wright (2011)’s finding that term premiums are driven partly by inflation risk. The stationarity of term premiums is a desirable property that results from properly separating the trend component (modeled via the shifting endpoint) from the cyclical component; models that do not include a shifting endpoint may attribute some of the trend to the term premium, producing non-stationary term premium estimates.

Key concepts

shadow rate dynamic term structure model (SDTSM) : a term structure model in which the policy rate is defined as the maximum of a latent shadow rate and the effective lower bound, following Wu and Xia (2016); allows the model to be estimated without modification when short-term rates are near zero. drifting trend (shifting endpoint) : a slow-moving unconditional mean of interest rates that evolves over time, following Bauer and Rudebusch (2020); captures the secular decline in interest rates since the 1990s and separates trend from cyclical variation and term premiums. natural rate of real interest : the long-run equilibrium real interest rate consistent with stable inflation and output at potential; under the assumption that all permanent shocks to real rates are real shocks, the paper’s trend estimate provides a measure of this rate. Beveridge-Nelson trend : the long-run forecast of the shadow rate derived from the model; used here as the operational definition of the interest rate trend; transforms the information in the entire yield curve into a single macroeconomic equilibrium measure.

Beliefs About the Economy are Excessively Sensitive to Household-Level Shocks: Evidence from Linked Survey and Administrative Data

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

Business, Liquidity, and Information Cycles

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

The paper studies how the two roles of stock markets — revealing information about firms’ fundamentals (which guides capital allocation) and providing liquidity — interact, arguing that when stocks are used more intensively for liquidity, their prices reveal less information about fundamentals. The authors build a Grossman-Stiglitz-style trading model with two types of rational traders (‘day’ traders who value liquidity and ’night’ traders who value fundamentals) that generates endogenous noise in prices, derive an analytical measure of price informativeness (PI), and structurally estimate PI from firm-level panel data for 16 countries over 1984-2022, finding that PI declines in periods of insufficient funding liquidity (such as the Great Recession and the COVID-19 pandemic) and that these fluctuations are explained mostly by changes in trading activity rather than information quality. Integrating the trading module into a real business cycle model with heterogeneous firms calibrated to the United States, they simulate recessions: a stand-alone recession is ‘cleansing’ — prices become more informative and allocation improves, mitigating output losses by 4.4% — whereas a recession coinciding with banking distress is ‘sullying’ — agents rely more on stocks for liquidity, prices become less informative, and worsened misallocation magnifies output losses by 22%. A counterfactual with exogenous (rather than endogenous) information implies output would fall about 43% more than in the benchmark, which the authors read as evidence that endogenous information acquisition lets stock markets ’lean against the wind’ in recessions. All magnitudes are model-based and specific to the U.S. calibration.

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 interaction between stock-market roles does the paper study?

The paper studies how the liquidity role of stock markets affects their information role: if stocks are used more intensively for liquidity, prices reveal less information about firms’ fundamentals. While the information and liquidity roles of stock markets are each well studied, their interaction is less understood; the authors ask whether using stocks for liquidity enhances or weakens their information role, how distress in other liquidity sources (such as banks) affects price informativeness, and how this contributes to the depth of recessions.

Q2. How does the trading model generate the information-liquidity tradeoff?

The authors extend Grossman and Stiglitz (1980) by replacing noise traders with two types of rational traders — ‘day’ traders interested in liquidity and ’night’ traders interested in fundamentals — so that each type’s trades act as endogenous noise for the other. In equilibrium a linear pricing function exists in which price informativeness depends on the relative weights of fundamental versus liquidity information in prices, and those weights are determined by how many day and night traders operate, their information choices, and how aggressively they trade. When funding markets malfunction, the economy relies more on stocks for liquidity, there are more day traders, and price informativeness declines.

Q3. What is Price Informativeness (PI), and how is it estimated?

Price Informativeness (PI) is defined analytically as a function of the dispersion of firm productivity, the dispersion of stock-price fluctuations, and their respective price loadings; in a high-PI market, a firm’s high relative stock price is a strong signal of positive information about its fundamentals. The authors estimate PI structurally using firm-level panel data from 16 countries spanning 1984 to 2022. The linear relationship among stock prices, earnings, and stock liquidity holds independently of general-equilibrium considerations, which is what makes the structural estimation tractable.

Q4. What are the empirical cyclical properties of PI?

PI exhibits cyclicality and, more importantly, declines in periods of insufficient funding liquidity, such as the Great Recession and the COVID-19 pandemic. Decomposing PI into its four components, the authors show its fluctuations are mostly explained by changes in trading activity rather than by changes in information quality or the amount of information acquired.

Q5. How is the trading module embedded in a general-equilibrium model and disciplined?

The trading module is integrated into a real business cycle model with heterogeneous firms in which stock prices guide capital allocation, calibrated to the United States with two possibly correlated aggregate shocks — one to aggregate productivity and one to funding liquidity — to capture recessions with and without banking distress. The calibrated model replicates the cyclical properties of the empirical PI measure without targeting them. The authors also discipline how much new information prices convey using price-investment correlations across firms and over time, concluding that new stock-price information is roughly as important as what decision makers already know.

Q6. What are the quantitative real effects in recessions?

In a stand-alone recession, increased uncertainty induces all traders to acquire more information, raising price informativeness and improving allocation, which mitigates output losses by 4.4% (‘cleansing’); when a recession coincides with funding-market distress, heightened liquidity-driven trading makes prices less informative and worsens allocation, magnifying output losses by 22% (‘sullying’). The authors interpret the 22% figure as a sizable real effect of banking problems operating through a novel channel: the weakening of the information and allocative role of stock markets.

Q7. What do the information-structure counterfactuals show?

If information were exogenous rather than endogenously acquired, liquidity distress would reduce PI by more and output would decline about 43% more than in the benchmark — implying endogenous information acquisition lets stock markets ’lean against the wind’ during recessions. The authors further find that halving the cost of information about fundamentals would make output declines about 5% smaller, whereas halving the cost of information about a stock’s liquidity would make declines about 2% larger, leading them to conclude that the welfare effect of transparency is nuanced — easier access to one type of information can make it harder to infer another.

Q8. What are the main limitations and scope conditions?

The authors flag two limitations: the framework assumes no feedback from the real economy back to financial markets (prices affect investment, but investment does not affect prices), and the counterfactuals focus on how the information environment affects price informativeness, abstracting from other channels through which information affects production. Adding two-way feedback would sacrifice the tractability of linear pricing but could introduce additional magnification forces. All quantitative magnitudes are specific to the U.S. calibration.

Key concepts

price informativeness (PI) : the extent to which stock prices reveal to an outside observer the information that informed traders hold about firms’ fundamentals; defined in the paper as an analytical function of productivity dispersion, price-fluctuation dispersion, and their price loadings, and estimated structurally.

day traders vs. night traders : the paper’s two types of rational traders — day traders trade to satisfy liquidity needs, night traders trade on information about fundamentals — whose trades act as endogenous noise for one another, replacing the exogenous noise traders of Grossman-Stiglitz.

funding liquidity vs. market liquidity : funding liquidity is liquidity provided by intermediaries through credit; market liquidity is the ability to trade stocks to meet liquidity needs; when funding liquidity is scarce, agents substitute toward market liquidity, raising liquidity-driven trading.

cleansing vs. sullying recessions : in the paper’s usage, a cleansing recession improves allocation (here via more informative prices), while a sullying recession worsens it; a recession is cleansing without banking distress and sullying when it coincides with funding-market distress.

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

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

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

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

In depth

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

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

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

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

Q3. When does QE affect credit spreads?

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

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

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

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

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

Key concepts

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

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

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

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

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

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

Dynamics of the Long-Term Housing Yield: Evidence from Natural Experiments

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

Each month a fraction of UK property leases are extended by 90 years or more, creating thousands of natural experiments in which the same property’s rent and capital value are revealed simultaneously. This paper uses these lease extensions — and Massachusetts and Cambridge rent-control removals as a second identification strategy — to estimate the expected long-term housing yield (annual rent-to-price ratio) and decompose its dynamics into rent-growth expectations and discount-rate components. The central finding is that housing yield movements are dominated by discount-rate shocks: variation in required returns on housing explains the overwhelming majority of yield variance, while expected rent growth contributes less than 10 percent. Housing booms are therefore primarily driven by falling required returns, not by rational expectations of higher future rents. The yield responds to real long-term interest rates with a slope significantly below one, consistent with a non-pecuniary convenience yield on housing that is not fully displaced by interest rate changes.

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 do the natural experiments identify?

Lease extensions reveal the market’s valuation of the same physical dwelling at two points — just before and just after the 90-year extension — with the extension itself creating a clean variation in the remaining lease term (and hence in the present value of ownership) without changing the property’s rent-generating characteristics. This design separates the rent and price components of the yield at the property level, allowing identification of discount-rate and rent-growth contributions free of compositional differences across properties.

Q2. Why do discount rates dominate yield variation?

A present-value decomposition of the housing yield into expected rent growth and the discount rate assigns more than 90 percent of variance to the discount rate component, implying that periods of low housing yields (high prices relative to rent) reflect primarily that investors demand a lower return on housing — not that they expect rents to rise faster. This result mirrors Campbell-Shiller findings for equity markets but is especially striking for housing, where naive narratives often attribute booms to expected rent appreciation.

Q3. What does the convenience yield interpretation imply?

Housing yields respond less than one-for-one to real interest rate movements — a slope well below one in the yield-rate regression — implying that housing carries a non-pecuniary convenience yield (liquidity, collateral value, direct utility of ownership) that buffers the required return on housing against interest rate changes. When real rates rise, housing yields rise by less, so price-to-rent ratios decline by less than a frictionless model would predict.

Key concepts

housing yield : the annual rent-to-price ratio on residential property; the paper’s central object, decomposed into discount-rate and rent-growth components.

discount-rate channel : the dominant source of housing yield variation in this paper; movements in investors’ required return on housing, not expected rent growth, drive the observed yield dynamics.

convenience yield : the non-pecuniary value of housing ownership (liquidity, collateral, direct utility) that drives a wedge between the housing yield and the risk-free real interest rate; explains the less-than-one slope in the yield-rate relationship.

EU ETS Market Expectations and Rational Bubbles

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

This paper tests whether the sharp rise in EU Emissions Trading System (EU ETS) allowance prices from 2018 onward was driven by a rational bubble. The methodological contribution is to modify the Fama (1984) Predictive Regression (FPR) approach to remain valid for rational bubble testing when the risk premium is time-varying — potentially stationary, integrated of order one, or even explosive — and when the fundamental price process exhibits a unit root or mildly explosive behavior. Standard bubble tests (including the KPSS applied to the price-expectations differential, and the Phillips-Shi-Yu SADF/GSADF tests applied to price levels) lose size control when the risk premium follows a nonstationary process; the paper’s FPR approach combined with the IVX estimator of Kostakis, Magdalinos, and Stamatogiannis (2015) retains correct size under all risk premium specifications. Using weekly EU ETS spot and futures data from 2013 to 2023 (T = 563), the paper finds: (1) explosive behavior in both spot and futures price levels during the third and fourth trading phases (2018–2023), confirming a necessary condition for a bubble; (2) no evidence of a rational bubble in the FPR test — the IVX-AR Wald statistic fails to reject the null of no bubble (β₂,ₙ = 0) in full-sample and sub-sample analyses across delivery horizons of 4, 8, 12, and 16 weeks; (3) no evidence of explosiveness in the differential between future spot rates and futures rates; (4) no evidence of co-explosiveness between spot and futures prices within either the third or fourth trading period separately. The paper concludes that the EU ETS price surge reflects a shift in market expectations about future allowance scarcity — driven by policy tightening of the cap trajectory and reform of the Market Stability Reserve — rather than speculative excess.

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 Fama Predictive Regression approach to testing rational bubbles, and what is its key limitation with a dynamic risk premium?

The Fama (1984) decomposition splits the futures price F_{n,t} into expected future spot price E_t[P_{t+n}] and a risk premium RP_{n,t}; from this, two predictive regressions (FPR 1 and FPR 2) have slope coefficients β₁,ₙ and β₂,ₙ that equal 1 and 0, respectively, in the absence of a rational bubble, and deviate from these values (β₁,ₙ < 1, β₂,ₙ > 0) when a bubble is present. The paper shows analytically (equations 27–33) that when a rational bubble is present, β₁,ₙ decreases monotonically as Var(B_t) increases and β₂,ₙ increases monotonically, with the direction of the bias confirmed under both zero and nonzero covariance between the bubble and the risk premium. The key limitation of standard OLS inference in this regression is that when the regressor (F_{n,t} − P_t) is highly persistent or mildly explosive, the OLS t-statistic has a non-standard distribution, and Stambaugh (1999) bias can lead to over-rejection of the no-bubble null. The paper addresses this by applying the IVX estimator, which replaces the persistent regressor with an instrument of controllable lower persistence, yielding a Wald statistic that converges to a standard chi-squared distribution regardless of the persistence or trending behavior of the risk premium.

Q2. Why does the KPSS test applied to the price-expectations differential fail in the presence of a nonstationary risk premium?

The KPSS test applied to P_{t+n} − F_{n,t} tests whether this differential is stationary; under the no-bubble null (equation 16 in the paper), the differential equals the negative risk premium RP_{n,t}, so the KPSS test has correct size when RP is stationary but incorrectly rejects the no-bubble null when RP is integrated of order one or explosive — because non-stationarity in the risk premium is incorrectly attributed to a bubble. The paper’s Monte Carlo simulations (Table 1) confirm that the KPSS test maintains nominal size of 5 percent only when the risk premium is stationary (λ ∈ {0, 0.5} under RP 1); when λ = 1 or λ = 1.01, the KPSS test rejects far more often than 5 percent under the null. The FPR approach with IVX inference, by contrast, maintains size close to 5 percent across all risk premium specifications including explosive ones. This is the central methodological motivation: prior EU ETS bubble tests that relied on KPSS may have detected non-stationarity in the risk premium rather than a genuine bubble component.

Q3. What does the SADF/GSADF test find for EU ETS spot and futures prices, and what is its role in the paper’s empirical strategy?

The paper applies SADF and GSADF tests (Phillips, Shi, and Yu, 2015a,b) to weekly EU ETS spot and futures price levels from 2013 to 2023 and finds evidence of explosive behavior at the 5 percent significance level in both series, with consistent timing of explosive phases across spot and all four futures contracts. The explosive episodes are date-stamped using the BSADF sequence with wild-bootstrapped critical values (999 repetitions): explosive periods are identified during the end of the third trading period (2018–2022) and at the commencement of the fourth trading period (2021–2023). These results confirm that the necessary condition for a rational bubble — an explosive price component — is satisfied. However, the paper emphasizes that explosiveness in levels is not sufficient for a rational bubble: a mildly explosive fundamental or an explosive risk premium would produce the same SADF/GSADF result without any bubble component. The FPR-IVX test is designed to distinguish between these cases and constitutes the primary bubble test.

Q4. What do the FPR-IVX tests find for the presence of a rational bubble?

Across the full sample (January 2018 to October 2023, T = 302), the IVX-AR Wald statistic (denoted W̃_β, adjusting for serial correlation in FPR 2’s error term using the Yang, Long, Peng, and Cai (2020) procedure) fails to reject the null β₂,ₙ = 0 against β₂,ₙ ≠ 0 for all four delivery horizons n ∈ {4, 8, 12, 16} weeks. The Bayesian Information Criterion selects models with lagged error terms for both the full sample and sub-samples, confirming the need for the IVX-AR procedure over the standard IVX Wald statistic. The sub-sample analysis separates the third trading period (January 2018 to December 2020, T = 156) and the fourth trading period (January 2021 to October 2023, T = 146); in both sub-samples the null is not rejected for all delivery horizons. The conventional OLS t-statistic (|t_β|) sometimes provides marginal evidence against the null, but the paper interprets this as reflecting the Stambaugh bias problem and defers to the IVX-AR inference. These results contradict both the collapsing bubble hypothesis (which would require β₂,ₙ < 0) and the ongoing bubble hypothesis (which would require β₂,ₙ > 0).

Q5. What do the tests on the differential between future spot rates and futures rates find?

Applying the SADF/GSADF test to the differential P_{t+n} − F_{n,t} for n ∈ {4, 8, 12, 16} weeks reveals no evidence of explosiveness in this differential across all horizons (Table 9 in the paper). This is consistent with the absence of a rational bubble: under the FPR framework, a rational bubble would generate an explosive component in the futures basis (F_{n,t} − P_t), which would in turn produce explosiveness in the differential between actual future spot prices and futures prices. The absence of explosiveness in this differential therefore provides an additional check corroborating the FPR-IVX finding.

Q6. What does the co-explosiveness test find, and why does a structural break affect the full-sample result?

The co-explosiveness test of Evripidou, Harvey, Leybourne, and Sollis (2022) tests whether spot and futures prices share a common explosive trend (null: co-explosive, no bubble) versus the alternative that they diverge by an explosive component (rational bubble or explosive risk premium). In the full sample from January 2018 to October 2023, the test rejects the null for all n ∈ {4, 8, 12, 16}, apparently indicating a non-stationary component separating spot and futures prices. However, sub-sample analysis dividing the sample at December 2021 reveals that neither the third trading period (January 2018 to December 2021) nor the fourth trading period (January 2022 to October 2023) sub-samples show rejection of the null — the co-explosive null cannot be rejected in either period alone. The paper interprets the full-sample rejection as reflecting a structural break in the risk premium at the boundary between the two trading periods (a mean shift in the risk premium) rather than a bubble, consistent with the KPSS size problem and with the lack of any significant positive serial correlation between the phases. The sub-sample co-explosiveness results align with the FPR-IVX findings.

Q7. What explains the EU ETS price surge if not a rational bubble, and what are the policy implications?

The paper interprets the consistent co-movement of spot and futures prices in an explosive common trend — without any divergence between them — as evidence that the fundamental value of allowances itself became explosive, driven by a regime shift in market expectations about future allowance scarcity. The scarcity shift is traced to two policy changes: (a) the progressive tightening of the EU ETS cap trajectory under the European Green Deal and the Fit-for-55 legislation, which reduced the total number of allowances available over time; and (b) reform of the Market Stability Reserve, which removed surplus allowances from circulation, making the cap effectively more binding than its nominal level. When market participants updated their expectations about how scarce allowances would become, the fundamental value — the present discounted value of allowance scarcity rents — rose along an explosive path without any bubble component. For policy, this distinction matters: if the price surge reflected a rational bubble, regulatory intervention to deflate it could be efficiency-improving (bubbles misallocate resources and their bursting creates financial instability); if the surge reflects genuine scarcity expectations, intervention would undermine the price signal that guides firms’ decarbonization investment decisions. The paper concludes there is no basis from historical data to justify bubble-prevention intervention in the EU ETS architecture.

Key concepts

rational bubble (in the EU ETS context): a component of the allowance price that exceeds the present discounted value of future allowance scarcity rents and grows at the discount rate; theoretically possible because allowances are storable and have positive returns from banking across periods; the paper finds no evidence of this component in EU ETS prices during 2018–2023.

Fama Predictive Regression (FPR): a regression of the basis (F_{n,t} − P_t) on itself or on subsequent spot-futures differentials, used here to test rational bubbles; FPR 2 (the regression of P_{t+n} − P_t on F_{n,t} − P_t) has slope β₂,ₙ = 0 under no bubble and β₂,ₙ > 0 under an ongoing bubble, with the direction of β₂,ₙ identifying both the presence and type (ongoing vs. collapsing) of the bubble.

IVX estimator: the instrumental-variable estimator of Kostakis, Magdalinos, and Stamatogiannis (2015) that instruments a mildly explosive or highly persistent regressor with an instrument of controllable lower persistence; produces a Wald statistic with a standard chi-squared limiting distribution regardless of the persistence or trending behavior of the risk premium, enabling valid inference on bubble hypotheses in the FPR when the risk premium is nonstationary.

IVX-AR procedure: the extension of the IVX estimator by Yang, Long, Peng, and Cai (2020) that additionally accounts for serial correlation in the error term of the predictive regression; the paper applies this as its primary inference procedure because BIC selects models with lagged errors in both full-sample and sub-sample analyses.

allowance scarcity expectations: market participants’ beliefs about the future tightness of the EU ETS cap relative to aggregate emissions; the paper finds that the price surge since 2018 is consistent with a shift in these expectations driven by cap trajectory tightening and Market Stability Reserve reform, rather than with a speculative bubble.

mildly explosive process: a time series with autoregressive root θ = 1 + c·T^{−α} for c > 0, α ∈ (0,1), converging to unity as T → ∞; used in the paper’s Monte Carlo and theoretical analysis to model the fundamental price process and the risk premium under the alternative hypothesis of ongoing rational bubble behavior, following Phillips and Magdalinos (2007).

Political Pressure on the Fed

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

This paper combines a hand-collected archival data set of over 800 personal interactions between U.S. Presidents and Federal Reserve officials from 1933 to 2016 with a narrative structural VAR to identify shocks to political pressure on the Fed and quantify their macroeconomic effects. The identification strategy exploits the well-documented Nixon-Burns episode of 1971—corroborated by Nixon Tapes recordings and Burns’s personal diary—as a narrative restriction that the spike in personal interactions that year was driven primarily by a political pressure shock rather than by economic conditions. Political pressure shocks are found to (i) increase inflation strongly and persistently, (ii) lead to statistically weak negative effects on activity, (iii) contribute to inflationary episodes outside the Nixon era, and (iv) transmit differently from standard expansionary monetary policy shocks because political pressure can be publicly observed, generating a stronger direct effect on inflation expectations. Quantitatively, increasing political pressure by half as much as Nixon, sustained for six months, is estimated to raise the price level by more than 8%.

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 narrative identification strategy and how is the Nixon-Burns episode exploited?

The identification strategy imposes that the spike in President-Fed personal interactions in 1971 is mainly driven by a political pressure shock, exploiting the well-documented fact that Nixon pressured Burns to ease monetary policy in the run-up to his 1972 re-election. Recordings from the “Nixon Tapes” and Burns’s personal diary corroborate this interpretation: Burns wrote that “the President will do anything to be reelected” and that Nixon urged him to “start expanding the money supply.” Romer and Romer (2004) estimated large easing shocks to monetary policy prior to Nixon’s re-election, contrasting with a large systematic tightening after it, further supporting that Burns eased in response to the pressure. Narrative evidence from Johnson’s pressure in the 1960s is additionally used to strengthen the identification.

Q2. What does the new data on President-Fed personal interactions show?

The paper hand-collects over 800 personal interactions between U.S. Presidents and Fed officials from the historical daily schedules made available by the Presidential Libraries from Franklin D. Roosevelt (1933) through Barack Obama (2016). The average interaction lasts 53 minutes; 36% are one-on-one; 11% occur on weekends; 16% are in social settings such as dinners; 92% involve the Fed Chair and 8% other Fed officials. There is large variation across administrations: President Nixon interacted with Fed officials 160 times, while only 6 interactions occurred under Clinton. These interactions arise endogenously in response to economic conditions, which is why narrative identification is needed to isolate the political pressure component.

Q3. What are the estimated macroeconomic effects of political pressure shocks?

Political pressure shocks are found to increase inflation strongly and persistently, to have statistically weak negative effects on activity, and a pressure shock half as large as Nixon’s sustained over six months is estimated to raise the price level by more than 8%. The weak activity effect distinguishes these shocks from standard demand expansions; the mechanism operates more through expectations channels than through aggregate demand, consistent with the public observability of political pressure on the central bank. The evidence also suggests political pressure shocks contributed to inflationary episodes in periods beyond the Nixon era.

Q4. Why do political pressure shocks transmit differently from conventional monetary policy easing shocks?

Political pressure shocks transmit differently from standard expansionary monetary policy shocks primarily because political pressure on the Fed can be publicly observed, which generates a stronger direct effect on inflation expectations than a private Fed decision to ease. The paper finds a stronger effect of political pressure shocks on inflation expectations relative to the activity effect, consistent with this channel: when the public observes that the President is pressuring the central bank, expected inflation rises even before the Fed acts on that pressure.

Key concepts

President-Fed personal interactions : face-to-face or telephone contacts between U.S. Presidents and Federal Reserve officials recorded in historical presidential daily schedules 1933–2016; used as a noisy observable proxy for political attention to the Fed, from which a political pressure shock series is extracted via narrative restrictions.

political pressure shock : an exogenous, structurally identified shock to the intensity of political influence on Fed policy, isolated using a narrative SVAR restriction that the 1971 Nixon-Burns spike in interactions was driven by political pressure rather than economic conditions.

narrative identification : an approach that imposes sign or zero restrictions on a structural VAR at specific historical episodes known from external archival evidence to be driven predominantly by a particular structural shock; here used to exploit the Nixon-Burns and Johnson-Fed pressure episodes.

Stock market participation and macro-financial trends

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

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

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

In depth

Q1. What is the puzzle the paper addresses?

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

Q2. What is the novel risk-aversion channel?

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

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

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

Q4. What is the empirical evidence supporting the mechanism?

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

Key concepts

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