Restrictions on the risk-pricing in dynamic term structure models (DTSMs) tighten the link between cross-sectional and time-series variation of interest rates, and make absence of arbitrage useful for inference about expectations. This article presents a new econometric framework for estimation of affine Gaussian DTSMs under restrictions on risk prices, which addresses the issues of a large model space and of model uncertainty using a Bayesian approach. A simulation study demonstrates the good performance of the proposed method. Data for U.S. Treasury yields calls for tight restrictions on risk pricing: only level risk is priced, and only changes in the slope affect term premia. Incorporating the restrictions changes the model-implied short-rate expectations and term premia. Interest rate persistence is higher than in a maximally flexible model, hence expectations of future short rates are more variable—restrictions on risk prices help resolve the puzzle of implausibly stable short-rate expectations in this literature. Consistent with survey evidence and conventional macro wisdom, restricted models attribute a large share of the secular decline in long-term interest rates to expectations of future nominal short rates.

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.