Nonparametric Regression with Multiple Thresholds: Estimation and Inference

Abstract

This paper examines nonparametric regression with an exogenous threshold variable, allowing for an unknown number of thresholds. Given the number of thresholds and corresponding threshold values, we first establish the asymptotic properties of the local constant estimator for a nonparametric regression with multiple thresholds. However, the number of thresholds and corresponding threshold values are typically unknown in practice. We then use our testing procedure to determine the unknown number of thresholds and derive the limiting distribution of the proposed test. The Monte Carlo simulation results indicate the adequacy of the modified test and accuracy of the sequential estimation of the threshold values. We apply our testing procedure to an empirical study of the 401(k) retirement savings plan with income thresholds.