Bayesian Averaging, Prediction and Nonnested Model Selection

Han Hong, Bruce Preston

    Research output: Contribution to journalArticle

    Abstract

    This paper studies the asymptotic relationship between Bayesian model averaging and post-selection frequentist predictors in both nested and nonnested models. We derive conditions under which their difference is of a smaller order of magnitude than the inverse of the square root of the sample size in large samples. This result depends crucially on the relation between posterior odds and frequentist model selection criteria. Weak conditions are given under which consistent model selection is feasible, regardless of whether models are nested or nonnested and regardless of whether models are correctly specified or not, in the sense that they select the best model with the least number of parameters with probability converging to 1. Under these conditions, Bayesian posterior odds and BICs are consistent for selecting among nested models, but are not consistent for selecting among nonnested models and possibly overlapping models. These findings have important bearing for applied researchers who are frequent users of model selection tools for empirical investigation of model predictions.
    Original languageEnglish
    Pages (from-to)358-369
    JournalJournal of Econometrics
    Volume167
    Issue number2
    DOIs
    Publication statusPublished - 2012

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