Incorporating Model Uncertainty in Market Response Models with Multiple Endogenous Variables by Bayesian Model Averaging

We develop a method to incorporate model uncertainty by model averaging in generalized linear models subject to multiple endogeneity and instrumentation. Our approach builds on a Gibbs sampler for the instrumental variable framework that incorporates model uncertainty in both outcome and instrumentation stages. Direct evaluation of model probabilities is intractable in this setting. However, we show that by nesting model moves inside the Gibbs sampler, a model comparison can be performed via conditional Bayes factors, leading to straightforward calculations. This new Gibbs sampler is slightly more involved than the original algorithm and exhibits no evidence of mixing difficulties. We further show how the same principle may be employed to evaluate the validity of instrumentation choices. We conclude with an empirical marketing study: estimating opening box office by three endogenous regressors (prerelease advertising, opening screens, and production budget).