A consensus has recently emerged that variables beyond the level, slope, and curvature of the yield curve can help predict bond returns. This paper shows that the statistical tests underlying this evidence are subject to serious small-sample distortions. We propose more robust tests, including a novel bootstrap procedure specifically designed to test the spanning hypothesis. We revisit the analysis in six published studies and find that the evidence against the spanning hypothesis is much weaker than it originally appeared. Our results pose a serious challenge to the prevailing consensus.

Most existing macro-finance term structure models (MTSMs) appear incompatible with regression evidence of unspanned macro risk. This “spanning puzzle” appears to invalidate those models in favor of new unspanned MTSMs. However, our empirical analysis supports the previous spanned models. Using simulations to investigate the spanning implications of MTSMs, we show that a canonical spanned model is consistent with the regression evidence; thus, we resolve the spanning puzzle. In addition, direct likelihood-ratio tests find that the knife-edge restrictions of unspanned models are rejected with high statistical significance, though these restrictions have only small effects on cross-sectional fit and estimated term premia.

Social discount rates (SDRs) are crucial for evaluating the costs of climate change. We show that the fundamental anchor for market-based SDRs is the equilibrium or steady-state real interest rate. Empirical interest rate models that allow for shifts in this equilibrium real rate find that it has declined notably since the 1990s, and this decline implies that the entire term structure of SDRs has shifted lower as well. Accounting for this new normal of persistently lower interest rates substantially boosts estimates of the social cost of carbon and supports a climate policy with stronger carbon mitigation strategies.

Regressions of private-sector macroeconomic forecast revisions on monetary policy surprises often produce coefficients with signs opposite to standard macroeconomic models. The “Fed information effect” argues these puzzling results are due to monetary policy surprises revealing Fed private information. We show they are also consistent with a “Fed response to news” channel, where both the Fed and professional forecasters respond to incoming economic news. We present new evidence challenging the Fed information effect and supporting the Fed response to news channel, including: regressions that control for economic news, our own survey of professional forecasters, and financial market responses to FOMC announcements. (JEL D82, E23, E27, E43, E44, E52, E58)

Macro-finance theory implies that trend inflation and the equilibrium real interest rate are fundamental determinants of the yield curve. However, empirical models of the term structure of interest rates generally assume that these fundamentals are constant. We show that accounting for time variation in these underlying long-run trends is crucial for understanding the dynamics of Treasury yields and predicting excess bond returns. We introduce a new arbitrage-free model that captures the key role that long-run trends play in determining interest rates. The model also provides new, more plausible estimates of the term premium and accurate out-of-sample yield forecasts. (JEL E31, E43, E47)

We estimate perceptions about the Federal Reserve’s monetary policy rule from panel data on professional forecasts of interest rates and macroeconomic conditions. The perceived dependence of the federal funds rate on economic conditions varies substantially over time, in particular over the monetary policy cycle. Forecasters update their perceptions about the Fed’s policy rule in response to monetary policy actions, measured by high-frequency interest rate surprises, suggesting that they have imperfect information about the rule. Monetary policy perceptions matter for monetary transmission, as they affect the sensitivity of interest rates to macroeconomic news, term premia in long-term bonds, and the response of the stock market to monetary policy surprises. A simple learning model with forecaster heterogeneity and incomplete information about the policy rule motivates and explains our empirical findings.

Term premia implied by maximum likelihood estimates of affine term structure models are misleading because of small-sample bias. We show that accounting for this bias alters the conclusions about the trend, cycle, and macroeconomic determinants of the term premia estimated in Wright (2011). His term premium estimates are essentially acyclical, and often just parallel the secular trend in longterm interest rates. In contrast, bias-corrected term premia show pronounced countercyclical behavior, consistent with theoretical and empirical arguments about movements in risk premia. (JEL E31, E43, E52, G12, H63)