Parameter instability in quantile regression

The paper defines and analyzes the behavior of a test for structural break based on quantile regressions. The test compares the estimates of the model under the null and the alternative hypotheses, where the null imposes stability, while the alternative allows the regression coefficients to change in response to the break. Under the null the test considers only one equation over the entire sample. Under the alternative two different equations are estimated, one before and the other after the break. The objective functions under the null and the alternative are compared, and the test relies on the increase of the objective function and the worsening of the fit when unnecessary constraints are imposed. The extension of the test for structural break to quantile regressions provides a very flexible tool to investigate the behavior of the model not only at the center but also in the tails of the conditional distribution. Indeed the presence of a break at more than one point of the conditional distribution can be considered, thus verifying if the break has a constant impact across quantiles or if it changes according to the selected level of the dependent variable. It may be the case that the impact of the break at the center of the conditional distribution cancels due to the opposite impact of the break in the tails of the distribution and/or in the sub-samples of the unconstrained model. Two examples with serially correlated real data and a Monte Carlo study taking into account non-normal and non-i.i.d. errors analyze the behavior of the test.