Why Gaussian Macro-Finance Term Structure Models are (Nearly) Unconstrained Factor-VARs
38 Pages Posted: 18 Mar 2011
Date Written: March 11, 2011
This paper explores the impact of simultaneously enforcing the no-arbitrage structure of a Gaussian macro-finance term structure model (MTSM) and accommodating measurement errors on bond yield through filtering on the maximum likelihood estimates of the model-implied conditional distributions of the macro risk factors and bond yields. For the typical yield curves and macro variables studied in this literature, the estimated joint distribution within a canonical MTSM is nearly identical to the estimate from an economic-model-free factor vector-autoregression (factor-VAR), even when measurement errors are large. It follows that a canonical MTSM does not offer any new insights into economic questions regarding the historical distribution of the macro risk factors and yields, over and above what is learned from a factor-VAR. In particular, the discipline of a canonical MTSM is empirically inconsequential for analyses of impulse response functions of bond yields and macro factors or empirical studies of term premiums. These results are rotation-invariant and, therefore, apply to many of the specifications of risk factors in the literature. In deriving these results we develop a new canonical form for MTSMs that is particularly revealing about the nature of the over-identifying restrictions implied by MTSMs relative to yield-based factor models.
Keywords: No-Arbitrage, Gaussian Macro-Finance Term Structure Models
JEL Classification: E43
Suggested Citation: Suggested Citation