Asymptotic properties of Bayesian inference in linear regression with a structural break

This paper studies large sample properties of a Bayesian approach to inference about slope parameters in linear regression models with a structural break. In contrast to the conventional approach to inference about the slope parameters that does not take into account the uncertainty of the unknown break location, the Bayesian approach that we consider incorporates such uncertainty. Our main theoretical contribution is a Bernstein-von Mises type theorem (Bayesian asymptotic normality) for the slope parameters under a wide class of priors, which essentially indicates an asymptotic equivalence between the conventional frequentist and Bayesian inference. Consequently, a frequentist researcher could look at credible intervals of the slope parameters to check robustness with respect to the uncertainty of the break location. Simulation studies show that the conventional confidence intervals of the slope parameters tend to undercover in finite samples whereas the credible intervals offer more reasonable coverages in general. As the sample size increases, the two methods coincide, as predicted from our theoretical conclusion