This paper quantifies how variation in real economic activity and inflation in the U.S. influenced the market prices of level, slope, and curvature risks in U.S. Treasury markets. To accomplish this we develop a novel arbitrage-free DT SM in which macroeconomic risks – in particular, real output and inflation risks – impact bond investment decisions separately from information about the shape of the yield curve. Estimates of our preferred macro-DT SM over the twenty-three year period from 1985 through 2007 reveal that unspanned macro risks explained a substantial proportion of the variation in forward terms premiums. Unspanned macro risks accounted for nearly 90 % of the conditional variation in short-dated forward term premiums, with unspanned real economic growth being the key driving factor. Over horizons beyond three years, these effects were entirely attributable to unspanned inflation. Using our model, we also reassess some of Chairman Bernanke’s remarks on the interplay between term premiums, the shape of the yield curve, and macroeconomic activity.

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Many equilibrium term structure models (ETSMs) in which the state of the economy follows an affine process imply that the variation in expected excess returns on bond portfolio positions is fully spanned by the conditional variances of the state variables. We show that these two assumptions alone – an affine state process with conditional variances that span expected excess returns – are sufficient to econometrically identify the factors determining risk premiums in these ETSMs from data on the term structure of bond yields. Using this result we derive maximum likelihood estimates of the conditional variances of the state – the “quantities of risk” – and evaluate the goodness-of-fit of a large family of affine ETSMs. These assessments of fit are fully robust to the values of the parameters governing preferences and the evolution of the state, and to whether or not the economy is arbitrage free. Our findings suggest that, to be consistent with U.S. macroeconomic and Treasury yield data, affine ETSMs should have the features that: (i) inflation risk, and not long-run risks or variation in risk premiums arising from habit-based preferences, is a significant (and perhaps the dominant) risk underlying risk premiums in U.S. Treasury markets; and (ii) risks that are unspanned by bond yields have substantial explanatory power for risk premiums consistent with time-varying market prices of risks.

This chapter reviews some of the academic literature that links nominal and real term structures with the macroeconomy. The main conclusion is that none of our models is consistent with basic properties of nominal yields. It is difficult to explain the average shape of the nominal yield curve, the variation of yields over time, and the predictability of excess bond returns. There are two overarching problems. First, much of the variation over time in economic activity is orthogonal to variation in nominal yields, and vice versa. Second, although mean excess returns to nominal Treasury bonds are positive, these returns do not appear to positively covary with risks that require compensation, at least according to standard asset-pricing models.

Identification problems arise naturally in forward-looking models when agents observe more than economists. We illustrate the problem in several macro-finance models with Taylor rules. When the shock to the rule is observed by agents but not economists, identification of the rule’s parameters requires restrictions on the form of the shock. We show how such restrictions work when we observe the state directly, indirectly, or infer it from observables. JEL Classification Codes: E43, E52, G12. Keywords: models. forward-looking models; information sets; monetary policy; exponential-affine Preliminary. We welcome comments, including references to related papers we inadvertently overlooked. The project started with our reading of John Cochrane’s paper on the same subject and subsequent emails and conversations with him and Mark Gertler. We thank them both. We also thank Patrick Feve and Gregor Smith for comments on an earlier draft, and participants in seminars at, and conference sponsored

This paper develops an affine model of the term structure of interest rates in which bond yields are driven by observable and unobservable macroeconomic factors. It imposes restrictions to identify the effects of monetary policy and other structural disturbances on output, inflation, and interest rates and to decompose movements in long-term rates into terms attributable to changing expected future short rates versus risk premia. The estimated model highlights a broad range of channels through which monetary policy affects risk premia and the economy, risk premia affect monetary policy and the economy, and the economy affects monetary policy and risk premia.

This paper characterizes the risk-return trade-off in the U.S. Treasury market through the lens of a discrete-time no-arbitrage term structure model, in which bond prices are solved in closed form and the conditional variances of bond yields feature a short-run component and a long-run component. Using Treasury yields data from January 1962 to August 2007, we find that for short-dated bonds, most of the variations in risk premiums are attributable to investors ’ changing attitudes toward risks. For longer-dated bonds, risk premiums reflect both the amount of risks bond investors face as well as their tolerance for risks over time. Furthermore, we find that the short-run volatility component of bond yields commands a positive risk premium whereas the long-run volatility component does not.

The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Federal Reserve Bank of San Francisco or the

This paper develops an affine model of the term structure of interest rates in which bond yields are driven by observable and unobservable macroeconomic factors. It imposes restrictions to identify the effects of monetary policy and other structural disturbances on output, inflation, and interest rates and to decompose movements in long-term rates into terms attributable to changing expected future short rates versus risk premia. The estimated model highlights a broad range of channels through which monetary policy affects risk premia and the economy, risk premia affect monetary policy and the economy, and the economy affects monetary policy and risk premia.