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Threshold Regression with Endogeneity

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Abstract

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.

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  • Ping Yu & Peter C.B. Phillips, 2014. "Threshold Regression with Endogeneity," Cowles Foundation Discussion Papers 1966, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1966
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    More about this item

    Keywords

    Threshold regression; Endogeneity; Local shifter; Identification; Efficiency; Integrated difference kernel estimator; Regression discontinuity design; Optimal rate of convergence; Partial linear model; Specification test; U-statistic; Wild bootstrap; Threshold treatment model; 401(k) plan;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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