Resolving the Spanning Puzzle in Macro-Finance Term Structure Models

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.