Structural Threshold Regression
66 Pages Posted: 15 Jun 2009 Last revised: 2 May 2016
Date Written: July 21, 2014
This paper introduces the structural threshold regression model that allows for an endogenous 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 fi nance. 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 speci fic 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 fi nite samples.
Keywords: Threshold regression, nonlinear regression, instrumental variables
JEL Classification: C13, C51
Suggested Citation: Suggested Citation