Endogeneity in Semiparametric Threshold Regression

In this paper, we investigate semiparametric threshold regression models with endogenous threshold variables based on a nonparametric control function approach. Using a series approximation, we propose a two-step estimation method for the threshold parameter. For the regression coefficients, we consider least-squares estimation in the case of exogenous regressors and two-stage least-squares estimation in the case of endogenous regressors. We show that our estimators are consistent and derive their asymptotic distribution for weakly dependent data. Furthermore, we propose a test for the endogeneity of the threshold variable, which is valid regardless of whether the threshold effect is zero or not. Finally, we assess the performance of our methods using a Monte Carlo simulation.