Default Priors and Predictive Performance in Bayesian Model Averaging, with Application to Growth Determinants

Abstract

Economic growth has been a showcase of model uncertainty, given the many competing theories and candidate regressors that have been proposed to explain growth. Bayesian Model Averaging (BMA) addresses model uncertainty as part of the empirical strategy, but its implementation is subject to the choice of priors: the priors for the parameters in each model, and the prior over the model space. For a well-known growth dataset, we show that model choice can be sensitive to the prior specification, but that economic significance (model-averaged inference about regression coefficients) is quite robust to the choice of prior. We provide a procedure to assess priors in terms of their predictive performance. The Unit Information Prior, combined with a uniform model prior outperformed other popular priors in the growth dataset and in simulated data. It also identified the richest set of growth determinants, supporting several new growth theories. We also show that there is a tradeoff between model and parameter priors, so that the results of reducing prior expected model size and increasing prior parameter variance are similar. Our branch-and-bound algorithm for implementing BMA was faster than the alternative coin flip importance sampling and MC3 algorithms, and was also more successful in identifying the best model.