Inference on locally ordered breaks in multiple regressions

We consider issues related to inference about locally ordered breaks in a system of equations, as originally proposed by Qu and Perron (2007). These apply when break dates in different equations within the system are not separated by a positive fraction of the sample size. This allows constructing joint confidence intervals of all such locally ordered break dates. We extend the results of Qu and Perron (2007) in several directions. First, we allow the covariates to be any mix of trends and stationary or integrated regressors. Second, we allow for breaks in the variance-covariance matrix of the errors. Third, we allow for multiple locally ordered breaks, each occurring in a different equation within a subset of equations in the system. Via some simulation experiments, we show first that the limit distributions derived provide good approximations to the finite sample distributions. Second, we show that forming confidence intervals in such a joint fashion allows more precision (tighter intervals) compared to the standard approach of forming confidence intervals using the method of Bai and Perron (1998) applied to a single equation. Simulations also indicate that using the locally ordered break confidence intervals yields better coverage rates than using the framework for globally distinct breaks when the break dates are separated by roughly 10% of the total sample size.