Bayesian Model Averaging and Weighted-Average Least Squares: Equivariance, Stability, and Numerical Issues

Abstract

This article is concerned with the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals which implement, respectively, the exact Bayesian Model Averaging (BMA) estimator and the Weighted Average Least Squares (WALS) estimator developed by Magnus et al. (2010). Unlike standard pretest estimators which are based on some preliminary diagnostic test, these model averaging estimators provide a coherent way of making inference on the regression parameters of interest by taking into account the uncertainty due to both the estimation and the model selection steps. Special emphasis is given to a number practical issues that users are likely to face in applied work: equivariance to certain transformations of the explanatory variables, stability, accuracy, computing speed and out-of-memory problems. Performances of our bma and wals commands are illustrated using simulated data and empirical applications from the literature on model averaging estimation.