Inference and Specification Testing in Threshold Regression with Endogeneity

We propose three new methods of inference for the threshold point in endogenous threshold regression and two specification tests designed to assess the presence of endogeneity and threshold effects without necessarily relying on instrumentation of the covariates. The first inferential method is a parametric two-stage least squares method and is suitable when instruments are available. The second and third methods are based on smoothing the objective function of the integrated difference kernel estimator in different ways and these methods do not require instrumentation. All three methods are applicable irrespective of endogeneity of the threshold variable. The two specification tests are constructed using a score-type principle. 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. Simulations show good finite sample performance of these procedures and the methods provide flexibility in testing and inference for practitioners working with threshold models.