On the Effect of Prior Assumptions in Bayesian Model Averaging With Applications to Growth Regression

Abstract

Abstract. We consider the problem of variable selection in linear regression models. Bayesian model averaging has become an important tool in empirical settings with large numbers of potential regressors and relatively limited numbers of observations. We examine the effect of a variety of prior assumptions on the inference concerning model size, posterior inclusion probabilities of regressors and on predictive performance. We illustrate these issues in the context of cross-country growth regressions using three datasets with 41 to 67 potential drivers of growth and 72 to 93 observations. Finally, we recommend priors for use in this and related contexts.

Unveiling covariate inclusion structures in economic growth regressions using latent class analysis

“…5 We have carried out several robustness checks changing the elicitation of the priors which did not lead to any significant differences in the inference results as long as the prior setting implies a preference for a relatively small number of clusters. 6 It should be noted that, in contrast to Fernandez et al (2001) and Ley and Steel (2007), we employ a hyperprior for prior inclusion probabilities and model-specific parameters, following Ley and Steel (2009b) and Liang et al (2008), respectively.…”

“…Such a mixture model implies, that given assignment to a cluster, the inclusion of covariate k resembles the probabilistic process proposed, for example, in Ley and Steel (2009b). The inclusion probability of covariate k in a given cluster c is thus governed by a Bernoulli distribution whose parameter follows a Beta distribution.…”

“…We use a Beta-Binomial prior for covariate inclusion (Ley and Steel, 2009b) and a unit information prior for the parameters in the BMA application. For this small example with K = 10 a complete enumeration of all models is performed.…”

“…The use of techniques that explicitly assess model uncertainty (mostly within the class of linear regression models) has thus become widespread in econometric research dealing with the empirical determinants of income growth differences across countries (for some seminal contributions to this literature, see e.g. Fernandez et al, 2001;Sala-i Martin et al, 2004;Masanjala and Papageorgiou, 2008;Durlauf et al, 2008;Ley and Steel, 2009b).…”

Bayesian Variable Selection in Spatial Autoregressive Models

“…A natural choice would be to use a uniform prior such that p(M m ) = 2 −q , which treats each candidate model as equally likely a priori. Alternative choices for p(M m ) which allow for more flexible prior settings across model sizes are discussed in Ley and Steel (2009). The marginal likelihood, p(D|M m ), in turn, is given by…”