Estimating and Testing Quantile Regression with Structural Changes

This paper considers the issues related to the asymptotic properties of estimators and test statistics in linear quantile regression with structural changes. We first address the issue of estimating a single structural change and derive the asymptotic properties of the estimated break point. The rate of convergence of the estimated break point is derived. As a supplementary tool, a smoothed empirical likelihood ratio test is proposed for testing structural changes at the estimated break dates. Furthermore we propose a likelihood-ratio-type test for multiple structural changes in quantile regression. The number of break points can be consistently determined via the test procedure. Finally we construct an algorithm based on the principle of dynamic programming to estimate multiple structural changes occurring at unknown dates. Monte Carlo studies show that our method consistently estimates each break point