Resolving the Spanning Puzzle in Macro-Finance Term Structure Models

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. 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. Terms of use: Documents in EconStor mayJEL-Code: E430, E440, E520.

Estimating Inflation Risk Premia Using Inflation‐linked Bonds: A Review

“…13. See Bauer and Rudebusch (2017) for an excellent review of macro-finance term structure models. 14.…”

Robust Bond Risk Premia

“…In particular, Duffee (2011b) demonstrated that if the effects of some elements of z t on yields nearly offset each other, those components will be very difficult to infer from current observed yields alone. Cieslak and Povala (2015) and Bauer and Rudebusch (2017) noted that in affine yield-curve models, even small measurement errors can make it impossible to recover z t from observed yields. Third, statistical expectations may differ from subjective expectations due to learning (as in, for example, Piazzesi et al, 2015).…”

Monetary Policy Expectations at the Zero Lower Bound

“…This specification is consistent with the expressed view of the Federal Open Market Committee (FOMC) that the short rate will be based on the unemployment and inflation rates. For further discussion of this issue and a defense of spanned macro-finance DTSMs see Bauer and Rudebusch (2015).…”

“…A natural application of our framework would be the recent period of near-zero interest rates in euro countries and the United Kingdom, as well as the long period of low interest rates in Japan over the past 20 years. Regarding our modeling framework, one could evaluate and impose restrictions on the risk pricing, which would tighten the link between the cross-sectional and time series dynamics of the risk factors (Joslin et al, 2014;Bauer, 2015). Such restrictions would improve model parsimony, alleviate some of the statistical issues related to the highly persistent nature of interest rates, and lead to more precise inference about short-rate expectations and policy liftoff under the real-world P-measure.…”

“…On December 16, 2008, the FOMC lowered the target for the federal funds rate to a range from 0 to 25 basis points, hence we choose December 2008 as the first month of the ZLB subsample.17 One possibility would be to go to a model with three yield factors and two macro factors (as inBauer and Rudebusch, 2015).18 Throughout this paper, for simplicity we refer to Q-measure expectations of future short rates as forward rates. These differ from the actual forward rates, which can be contracted by simultaneously buying and selling bonds of different maturities, by a convexity term.…”