Abstract
Uncertainty about the choice of identifying assumptions is common in causal studies,
but is often ignored in empirical practice. This paper considers uncertainty over models
that impose different identifying assumptions, which can lead to a mix of point- and set-identified models. We propose performing inference in the presence of such uncertainty
by generalizing Bayesian model averaging. The method considers multiple posteriors for
the set-identified models and combines them with a single posterior for models that are
either point-identified or that impose non-dogmatic assumptions. The output is a set of
posteriors (post-averaging ambiguous belief ), which can be summarized by reporting the
set of posterior means and the associated credible region. We clarify when the prior model
probabilities are updated and characterize the asymptotic behavior of the posterior model
probabilities. The method provides a formal framework for conducting sensitivity analysis
of empirical findings to the choice of identifying assumptions. For example, we find that in
a standard monetary model one would need to attach a prior probability greater than 0:28
to the validity of the assumption that prices do not react contemporaneously to a monetary
policy shock, in order to obtain a negative response of output to the shock.