Resolving the Spanning Puzzle in Macro-Finance Term Structure Models

Previous macro-finance term structure models (MTSMs) imply that macroeconomic state variables are spanned by (i.e., perfectly correlated with) model-implied bond yields. However, this theoretical implication appears inconsistent with regressions showing that much macroeconomic variation is unspanned and that the unspanned variation helps forecast excess bond returns and future macroeconomic fluctuations. We resolve this contradiction—or “spanning puzzle”—by reconciling spanned MTSMs with the regression evidence, thus salvaging the previous macro-finance literature. Furthermore, we statistically reject “unspanned” MTSMs, which are an alternative resolution of the spanning puzzle, and show that their knife-edge restrictions are economically unimportant for determining term premia.