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

CentER Working Paper Series No. 2011-082

31 Pages Posted: 25 Jul 2011

See all articles by Giuseppe De Luca

Giuseppe De Luca

University of Palermo - d/SEAS

J.R. Magnus

Vrije Universiteit Amsterdam, School of Business and Economics

Date Written: July 21, 2011

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.

Keywords: model uncertainty, model averaging, Bayesian analysis, exact computation

JEL Classification: C11, C51, C52

Suggested Citation

De Luca, Giuseppe and Magnus, Jan R., Bayesian Model Averaging and Weighted Average Least Squares: Equivariance, Stability, and Numerical Issues (July 21, 2011). CentER Working Paper Series No. 2011-082. Available at SSRN: https://ssrn.com/abstract=1894610 or http://dx.doi.org/10.2139/ssrn.1894610

Giuseppe De Luca

University of Palermo - d/SEAS

Viale delle Scienze, edificio 13
Palermo, 90124
Italy

Jan R. Magnus (Contact Author)

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

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