Structural Threshold Regression

This paper extends the simple threshold regression framework of Hansen (2000) and Caner and Hansen (2004) to allow for endogeneity of the threshold variable. We develop a concentrated least squares estimator of the threshold parameter based on an inverse Mills ratio bias correction. We show that our estimator is consistent and investigate its performance using a Monte Carlo simulation that indicates the applicability of the method in finite samples.

Structural Threshold Regression

This paper introduces the structural threshold regression model that allows for an endogeneous threshold variable as well as for endogenous regressors. This model provides a parsimonious way of modeling nonlinearities and has many potential applications in economics and finance. Our framework can be viewed as a generalization of the simple threshold regression framework of Hansen (2000) and Caner and Hansen (2004) to allow for the endogeneity of the threshold variable and regime specific heteroskedasticity. Our estimation of the threshold parameter is based on a concentrated least squares method that involves an inverse Mills ratio bias correction term in each regime. We derive its asymptotic distribution and propose a method to construct bootstrap confidence intervals. We also provide inference for the slope parameters based on GMM. Finally, we investigate the performance of the asymptotic approximations and the bootstrap using a Monte Carlo simulation that indicates the applicability of the method in finite samples.

Structural Threshold Regression

This paper extends the simple threshold regression framework of Hansen (2000) and Caner and Hansen (2004) to allow for endogeneity of the threshold variable. We develop a concentrated least squares estimator of the threshold parameter based on an inverse Mills ratio bias correction. We show that our estimator is consistent and investigate its performance using a Monte Carlo simulation that indicates the applicability of the method in …nite samples Classification-JEL: C13, C51

Structural Threshold Regression

This paper extends the simple threshold regression framework of Hansen (2000) and Caner and Hansen (2004) to allow for endogeneity of the threshold variable. We develop a concentrated least squares estimator of the threshold parameter based on an inverse Mills ratio bias correction. We show that our estimator is consistent and investigate its performance using a Monte Carlo simulation that indicates the applicability of the method in finite samples.

Structural Threshold Regression

This paper introduces the structural threshold regression model that allows for an endogeneous threshold variable as well as for endogenous regressors. This model provides a parsimonious way of modeling nonlinearities and has many potential applications in economics and .finance. Our framework can be viewed as a generalization of the simple threshold regression framework of Hansen (2000) and Caner and Hansen (2004) to allow for the endogeneity of the threshold variable and regime specific heteroskedasticity. Our estimation of the threshold parameter is based on a concentrated least squares method that involves an inverse Mills ratio bias correction term in each regime. We derive its asymptotic distribution and propose a method to construct bootstrap confidence intervals. We also provide inference for the slope parameters based on GMM. Finally, we investigate the performance of the asymptotic approximations and the bootstrap using a Monte Carlo simulation that indicates the applicability of the method in finite samples.nonlinear regression, endogenous threshold, sample split, regime shifts, inverse Mills ratio

THRET: Threshold Regression with Endogenous Threshold Variables

This paper extends the simple threshold regression framework of Hansen (2000) and Caner and Hansen (2004) to allow for endogeneity of the threshold variable. We develop a concentrated two-stage least squares (C2SLS) estimator of the threshold parameter that is based on an inverse Mills ratio bias correction. Our method also allows for the endogeneity of the slope variables. We show that our estimator is consistent and investigate its performance using a Monte Carlo simulation that indicates the applicability of the method is finite samples. We also illustrate its usefulness with an empirical example from economic growth.

Threshold Regression with Endogeneity

This paper studies estimation in threshold regression with endogeneity in the regressors and thresholding variable. 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. 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.preprin

A smoothed least squares estimator for threshold regression models

We propose a smoothed least squares estimator of the parameters of a threshold regression model. Our model generalizes that considered in Hansen (2000) to allow the thresholding to depend on a linear index of observed regressors, thus allowing discrete variables to enter. We also do not assume that the threshold e¤ect is vanishingly small. Our estimator is shown to be consistent and asymptotically normal thus facilitating standard inference techniques based on estimated standard errors or standard bootstrap for the threshold parameters themselves. We compare our con dence intervals with those of Hansen (2000) in a simulation study and show that our methods outperform his for large values of the threshold. We also include an application to cross-country growth regressions

Threshold Regression with Endogeneity

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

The bootstrap in threshold regression

This paper develops a general procedure to check the bootstrap validity in M-estimation. We apply the procedure in discontinuous threshold regression to show the inconsistency of the nonparametric bootstrap for inference on the threshold point. Especially, the conditional weak limit of the nonparametric bootstrap is shown not to exist. By comparing with two other boundaries in the literature, we show the fact that the threshold point is a boundary of the covariate that makes its bootstrap inference so different. The remedies to the bootstrap failure in the literature are summarized, and the nonparametric posterior interval is suggested by some simulation studies. Copyright © Cambridge University Press 2014.published_or_final_versio