Comments on: Reflections on the Probability Space Induced by Moment Conditions with Implications for Bayesian Inference

Abstract

The traditional Bayesian approach to inference is based on the combination of a fully specified density for the data conditional on the model parameters (the likelihood) with prior views on those parameters. Aside from other methodological considerations, the advantage of using prior information may be particularly important in low-frequency macro/finance time series contexts in which the number of observations is insufficient to precisely pin down the values of the unknown model parameters. Nevertheless, a potential drawback of the traditional Bayesian approach is that it is a full information procedure, which requires the correct specification of features of the distribution of the observed variables that the researcher might not be particularly interested in. In fact, many researchers prefer to use limited-information frequentist procedures, often with semi-parametric components, because under certain regularity conditions they reduce the potential for inconsistent estimation resulting from incorrect distributional assumptions. Whether those regularity conditions hold in any particular application (see Sims 2007 ), or whether the finite-sample performance of the limited-information, semi-parametric procedures agrees with the usual first-order asymptotic approximations even when they hold (see e.g., Cattaneo and Jansson 2014 ), is a different matter.