Multi-Threshold Structural Equation Model

In this article, we consider the instrumental variable estimation for causal regression parameters with multiple unknown structural changes across subpopulations. We propose a multiple change point detection method to determine the number of thresholds and estimate the threshold locations in the two-stage least square procedure. After identifying the estimated threshold locations, we use the Wald method to estimate the parameters of interest, that is, the regression coefficients of the endogenous variable. Based on some technical assumptions, we carefully establish the consistency of estimated parameters and the asymptotic normality of causal coefficients. Simulation studies are included to examine the performance of the proposed method. Finally, our method is illustrated via an application of the Philippine farm households data for which some new findings are discovered.