  We develop a method to perform model averaging in two-stage linear regression
systems subject to endogeneity. Our method extends an existing Gibbs sampler
for instrumental variables to incorporate a component of model uncertainty.
Direct evaluation of model probabilities is intractable in this setting. We
show that by nesting model moves inside the Gibbs sampler, model comparison can
be performed via conditional Bayes factors, leading to straightforward
calculations. This new Gibbs sampler is only slightly more involved than the
original algorithm and exhibits no evidence of mixing difficulties. We conclude
with a study of two different modeling challenges: incorporating uncertainty
into the determinants of macroeconomic growth, and estimating a demand function
by instrumenting wholesale on retail prices.
