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 $\gamma$ in linear regression models with structural break. In contrast the conventional that does not take into account uncertainty unknown break location $\tau$, we consider incorporates such uncertainty. Our main theoretical contribution is Bernstein-von Mises type theorem (Bayesian asymptotic normality) for under wide class priors, which essentially indicates an equivalence between frequentist and inference. Consequently, researcher could look at credible intervals check robustness respect $\tau$. Simulation show confidence tend undercover finite samples whereas offer more reasonable coverages general. As size increases, two methods coincide, as predicted from our conclusion. Using data Paye Timmermann (2006) on stock return prediction, illustrate traditional might underrepresent true sampling