Panel kink threshold regression model with a covariate-dependent threshold

Abstract

This article extends the kink threshold regression model with a constant threshold to a panel data framework with a covariate-dependent threshold, where the threshold is modeled as a function of informative covariates. We suggest an estimator based on the within-group transformation and propose test statistics for kink threshold effect and threshold constancy. We establish the asymptotic joint normality of the slope and threshold estimators and derive the limiting distributions of the test statistics. Our asymptotic results show that the inclusion of a covariate-dependent threshold does not affect the asymptotic joint normality of the slope and threshold estimates in the kink threshold regression model. Monte Carlo simulations show that the finite-sample proprieties of the proposed estimator and test statistics are generally satisfactory.