Tests for structural break in quantile regressions

The paper compares the existing tests for parameter instability in quantile regression. One is based on the estimated objective function and the other on the gradient. Their definition determines their characteristics and helpfulness. The former allows to check if the impact of a break on the entire equation changes across quantiles while a modified version of the latter verifies if the break affects only some coefficients or all of them and helps locating the break point. In addition the paper presents a Lagrange multiplier test for structural break. The advantage of the LM test is in the ease of implementation, since it simply requires the estimation of an auxiliary regression. An example shows the characteristics of each test. A Monte Carlo study concludes the analysis.