Do long-term yields help to estimate short-term risk premia?

We identify a new and important property of affine term structure models: at long maturities, the slope of the term structure of risk premia becomes “almost observable”. Exploiting this property by fitting models to long-maturity data dramatically improves the precision of estimates of risk premia and expected short rates across the term structure. In a Monte Carlo experiment we show that using rates with maturities up to 25 years, rather than 10 years as is standard in the literature, reduces the standard deviation of estimation errors in risk premia, expected short rates and term premia by over 70%. Applying this approach to US Treasury data, we find that variation in expected short rates accounts for a much larger share of variation in yields (and variation in term premia a correspondingly smaller fraction) than in the widely used estimates reported by the Federal Reserve. Accounting for time-variation in yield volatility is key to successful extraction of the risk premium information in long rates. Our approach therefore departs from much of the empirical literature in two important respects: it incorporates long-maturity yields and allows for time-varying yield volatility, whereas most existing studies ignore long-term yields and rely on constant volatility models.