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We develop a method to perform model averaging in two-stage linear regressionsystems subject to endogeneity. Our method extends an existing Gibbs samplerfor instrumental variables to incorporate a component of model uncertainty.Direct evaluation of model probabilities is intractable in this setting. Weshow that by nesting model moves inside the Gibbs sampler, model comparison canbe performed via conditional Bayes factors, leading to straightforwardcalculations. This new Gibbs sampler is only slightly more involved than theoriginal algorithm and exhibits no evidence of mixing difficulties. We concludewith a study of two different modeling challenges: incorporating uncertaintyinto the determinants of macroeconomic growth, and estimating a demand functionby instrumenting wholesale on retail prices.

Instrumental Variable Bayesian Model Averaging via Conditional Bayes Factors