Threshold Regression with Endogeneity

By Ping Yu, Peter C. B. Phillips. 2017

69 citations recorded by the source corpus.

This paper studies estimation and specification testing in threshold regression with endogeneity. Three key results differ from those in regular models. First, both the threshold point and the threshold effect parameters are shown to be identified without the need for instrumentation. Second, in partially linear threshold models, both parametric and nonparametric components rely on the same data, which prima facie suggests identification failure. But, as shown here, the discontinuity structure of the threshold itself supplies identifying information for the parametric coefficients without the need for extra randomness in the regressors. Third, instrumentation plays different roles in the estimation of the system parameters, delivering identification for the structural coefficients in the usual way, but raising convergence rates for the threshold effect parameters and improving efficiency for the threshold point. Specification tests are developed to test for the presence of endogeneity and threshold effects without relying on instrumentation of the covariates. 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. Simulation studies corroborate the theory and the asymptotics. An empirical application is conducted to explore the effects of 401(k) retirement programs on savings, illustrating the relevance of threshold models in treatment effects evaluation in the presence of endogeneity.

View Paper: https://www.semanticscholar.org/paper/b122288252c929e20784299ff2b4d98907295b27

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Xiaodong Fan
2. J. Shiu
3. Yingyao Hu
4. Ping Yu
5. X. d'Haultfoeuille
6. Susanne M. Schennach
7. S. Bonhomme
8. Dong Li

Citations in the corpus

• NONPARAMETRIC IDENTIFICATION USING INSTRUMENTAL VARIABLES: SUFFICIENT CONDITIONS FOR COMPLETENESS (2011, background): “Finally, in threshold regression cases thresholding parameters are identifiable and consistently estimable in spite of endogeneity of the regressor (see Yu and Phillips (2017)).”
• Threshold Regression With a Threshold Boundary (2020, methodology): “Second, combining with the analysis in Porter and Yu (2015), Yu and Phillips (2018a), and Yu, Liao, and Phillips (2018), we can estimate the nonparametric threshold regression with a nonparametric threshold boundary, y = { m1(x, q) + ε1, m2(x, q) + ε2, q ≤ g(z), q > g(z).”