Working Paper: NBER ID: w14284
Authors: Han Hong; Bruce Preston
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.
Keywords: model selection; criteria; nonnested; posterior odds; BIC
JEL Codes: C14; C52
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Bayesian model averaging (C11) | frequentist post-selection predictions (C52) |
| Bayesian posterior odds (C11) | best model with most parsimonious parameterization (C52) |
| Bayesian posterior odds (C11) | predictive accuracy (C52) |
| Bayesian posterior odds (C11) | inconsistency for selecting among nonnested models (C52) |