Publication Date: December 2019
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.
Keywords: Threshold regression, Endogeneity, Identification, Confidence interval, 2SLS, IDKE, Secification testing, Bootstrap, U-statistic
JEL Classification Codes: C21, C24, C26