Estimation and Inference for Multi-Threshold Regression with Endogeneity
提出一种基于工具变量的两阶段估计方法，用于处理存在内生解释变量的多阈值回归，并开发了数据自适应的阈值选择准则和检验统计量，通过401(k)计划对财富的阈值效应示例验证了方法的有效性。
Heterogeneity and endogeneity become increasingly common in statistical modeling and econometric practice. Threshold regression provides a simple yet flexible modeling strategy to account for heterogeneity. This paper studies estimation and inference for multi-threshold regression with endogenous regressors. We exploit a novel two-stage estimation procedure based on instrumental variables, which first identifies a set of possible threshold locations using the group LASSO estimation, and then refines the candidate set by a predetermined selection criterion. Given that the performance of the conventional information criteria is sensitive to the choice of the penalization factor, we develop a data-adaptive threshold-based cross-validation criterion incorporating an order-preserved sample-splitting strategy to determine the number of thresholds. Regarding inference, we develop test statistics to test for the presence of threshold effects and the existence of endogeneity, respectively. Numerical simulations and an application analyzing the threshold effects of 401(k) plans on wealth demonstrate the excellent finite sample performance of our methods. Finally, we develop a user-friendly R package MultiThreshold to implement the methodologies.