Model Comparison Using the Hansen-Jagannathan Distance

摘要

Although it is of interest to test whether a particular asset pricing model is literally true or not, a more useful task for empirical researchers is to determine how wrong a model is and to compare the performance of competing asset pricing models. In this paper, we propose a new methodology to test whether two competing linear asset pricing models have the same Hansen-Jagannathan distance or not. We show that the asymptotic distribution of the test statistic depends on whether the competing models are correctly specified or misspecified, and on whether the competing models are nested or non-nested. In addition, given the increasing interest in misspecified models, we propose a simple methodology for computing the standard errors of the estimated stochastic discount factor parameters that are robust to model misspecification. Using the same data as in Hodrick and Zhang (2001), we show that the commonly used returns and factors are, for the most part, too noisy to conclude that one model is superior to the other models in terms of Hansen-Jagannathan distance. In addition, we show that many of the macroeconomic factors commonly used in the literature are no longer priced once potential model misspecification is taken into account.