In this article, we describe 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 estimator and the
weighted-average least-squares estimator developed by Magnus, Powell, and Prüfer
(2010, Journal of Econometrics 154: 139–153). Unlike standard
pretest estimators that 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
several 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.
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