Research Interests
Research Interests
Theoretical and Applied Econometrics, Program Evaluation, Treatment Rules.
Theoretical and Applied Econometrics, Program Evaluation, Treatment Rules.
This paper proposes three inference methods for the threshold point in endogenous threshold regression and two specification tests for testing the presence of endogeneity and threshold effects without relying on instrumentation of the covariates. The first method is a parametric two-stage least squares method and is suitable when instruments are available. The second and third methods are non-parametric by smoothing the objective function of the integrated difference kernel estimator in different ways and do not require instrumentation. All three methods are applicable regardless of the endogeneity of the threshold variable. Both specification tests are score-type tests; especially, the threshold effect test extends conventional parametric structural change tests to the nonparametric case. A wild bootstrap procedure is suggested to deliver finite sample critical values for both tests.
This paper studies the control function approaches in endogenous threshold regression where the threshold variable can be endogenous. We first use a simple example to show that the structural threshold regression (STR) estimator of threshold point in Kourtellos, Stengos and Tan (2016, Econometric Theory 32, 827-860) is not consistent unless the endogeneity level of the threshold variable is small enough compared to the threshold effect. We then correct the control function in the STR estimator to generate a consistent estimator of the threshold point; this method can be treated as an extension of the two-stage least squares in Caner and Hansen (2004, Econometric Theory 20, 813-843). We also put forward a new control function approach which can be treated as an extension of the classical control function approach in endogenous linear regression. Both approaches explore some threshold effect information in conditional variance beyond that in conditional mean. Given the estimators of the threshold point, we further propose two types of estimators for slope parameters. The first type of estimator is a by-product of our control function approaches, and the second type of estimators are two generalized method of moments (GMM) estimators based on two new sets of moment conditions. Our simulation studies show that the second control function estimator and confidence interval for the threshold point and the associated second GMM estimator and confidence interval for slope parameters dominate the other methods.