Over the last two decades, dynamic equilibrium models have become a standard instrument to study a variety of issues in economics, from Business Cycles and Growth Theory to Public Finance, International Trade, Industrial Organization and Labor Economics. Since a dynamic equilibrium economy is an artificial construction, these models will always be false. This fact presents two main challenges for econometric practice: first, how to select appropriate values for the “deep” parameters of the model (i.e. those describing technology, preferences, and so on) and, second, how to compare two or more misspecified models that might be nonnested.
Bayesian econometrics addresses these two challenges by suggesting both a procedure to select parameters and a criterion for model comparison. Parameter choice is undertaken by the computation of posteriors while model comparison is performed through the use of posterior odds ratios. The bayesian approach is, of course, well known. Inference about parameter values follows directly from Bayes’ Theorem while model comparison through posterior odds was introduced by Je reys (1961) (in the form of hypothesis testing) and recently revived by Gelfand and Dey (1994), Geweke (1998), Landon-Lane (1999), and Schorfheide (2000), among others.
Our work follows this tradition. In particular, this paper makes two contributions. First, we show that the Bayesian approach to model estimation and comparison has a classical interpretation: asymptotically, the parameter point estimates converge to their pseudotrue values, and the best model under the Kullback-Leibler measure will have the highest posterior probability, both results holding even for misspecified and/or nonnested models. Second, we illustrate the strong small sample behavior of Bayesian methods using a well-known application: the U.S. cattle cycle. Bayesian estimates outperform Maximum Likelihood results, and the proposed model is compared with a set of Bayesian Vector Autoregressions.
These contributions are important for two reasons. Our first point helps to remove one of the main criticism of bayesian methods, the possible impact of priors in our reading of the data, since they imply that, as the sample grows, the priors disappear. The convergence of the posterior odds ratio toward the Kullback-Leibler preferred model is attractive because there is a complete axiomatic foundation that justifies why this measure is precisely the criterion a rational agent should use to choose between models. Details of this axiomatic foundation are presented in Shore and Johnson (1980) and Csiszar (1990). Our second point shows how, in real life applications, a bayesian approach delivers a very strong performance when applied to dynamic equilibrium models.
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Comparing Dynamic Equilibrium Models to Data: A Bayesian Approach
