Bayesian model averaging andweighted-average least squares: equivariance, stability, and numerical issues

In this article, we describe the estimation of linear regression modelswith uncertainty about the choice of the explanatory variables. We introducethe Stata commands bma and wals, which implement, respectively, the exactBayesian model-averaging estimator and the weighted-average least-squares estimatordeveloped by Magnus, Powell, and Prufer (2010, Journal of Econometrics154: 139–153). Unlike standard pretest estimators that are based on some preliminarydiagnostic test, these model-averaging estimators provide a coherent way ofmaking inference on the regression parameters of interest by taking into accountthe uncertainty due to both the estimation and the model selection steps. Specialemphasis is given to several practical issues that users are likely to face in appliedwork: equivariance to certain transformations of the explanatory variables, stability,accuracy, computing speed, and out-of-memory problems. Performances ofour bma and wals commands are illustrated using simulated data and empiricalapplications from the literature on model-averaging estimation.