Uncertain identification

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 nondogmatic 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.

Estimating the Effects of Monetary Policy in Australia Using Sign-restricted Structural Vector Autoregressions

“…When the sign restrictions constrain a single column of Q only, which is the case under Restrictions (1)-( 5), I use the algorithm proposed in Giacomini, Kitagawa and Volpicella (2022). This algorithm relies on the fact that any non-empty identified set for 1 q must contain a vertex on the Appendix B: Data…”

Estimating the Effects of Monetary Policy in Australia Using Sign‐restricted Structural Vector Autoregressions*

“…When the sign restrictions constrain a single column of Q only, which is the case under Restrictions (1)-( 5), I use the algorithm proposed in Giacomini et al (2022). This algorithm relies on the fact that any non-empty identified set for q 1 must contain a vertex on the unit sphere in R n where nÀ1 restrictions are active (i.e.…”

Advances in Using Vector Autoregressions to Estimate Structural Magnitudes

“…Giacomini, Kitagawa, and Uhlig (2019) explored the use of multiple priors in a neighborhood of a benchmark prior as a way to incorporate the useful information from the benchmark prior while allowing for the possibility that the benchmark prior could be misspecified in an unknown way. Giacomini, Kitagawa, and Volpicella (2022) extended the idea of Bayesian model averaging to applications that consider a range of possible identifying or set-identifying assumptions. They demonstrated that the robust Bayesian approach allows researchers to formalize the popular approach to sensitivity analysis of seeing how estimates vary under alternative identifying assumptions.…”