Tests of exogeneity in duration models with censored data

2025-10-30

AI Summary

This paper addresses the problem of testing exogeneity of a treatment variable (Z) in right-censored duration models—i.e., whether (Z) is independent of the error term (U) conditional on covariates (X). We propose the first nonparametric, nonseparable exogeneity test applicable to censored data. The method constructs a test statistic using an instrumental variable (W) and a conditional rank transformation, yielding a uniformly consistent estimator converging at a rate faster than (n^{-1/2}); critical values are obtained via bootstrap. Theoretically, our contribution lies in relaxing conventional semiparametric restrictions and establishing, for the first time, a consistent, fully nonparametric exogeneity test in nonseparable censored duration models. Monte Carlo simulations demonstrate robust finite-sample performance. An empirical application to the Job Training Partnership Act (JTPA) dataset confirms the method’s validity and practical utility.

Technology Category

• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Causality
• Machine Learning: Kernel Methods

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Consider the setting in which a researcher is interested in the causal effect of a treatment $Z$ on a duration time $T$, which is subject to right censoring. We assume that $T=varphi(X,Z,U)$, where $X$ is a vector of baseline covariates, $varphi(X,Z,U)$ is strictly increasing in the error term $U$ for each $(X,Z)$ and $Usim mathcal{U}[0,1]$. Therefore, the model is nonparametric and nonseparable. We propose nonparametric tests for the hypothesis that $Z$ is exogenous, meaning that $Z$ is independent of $U$ given $X$. The test statistics rely on an instrumental variable $W$ that is independent of $U$ given $X$. We assume that $X,W$ and $Z$ are all categorical. Test statistics are constructed for the hypothesis that the conditional rank $V_T= F_{T mid X,Z}(T mid X,Z)$ is independent of $(X,W)$ jointly. Under an identifiability condition on $varphi$, this hypothesis is equivalent to $Z$ being exogenous. However, note that $V_T$ is censored by $V_C =F_{T mid X,Z}(C mid X,Z)$, which complicates the construction of the test statistics significantly. We derive the limiting distributions of the proposed tests and prove that our estimator of the distribution of $V_T$ converges to the uniform distribution at a rate faster than the usual parametric $n^{-1/2}$-rate. We demonstrate that the test statistics and bootstrap approximations for the critical values have a good finite sample performance in various Monte Carlo settings. Finally, we illustrate the tests with an empirical application to the National Job Training Partnership Act (JTPA) Study.

Problem

• Testing exogeneity of treatment variables in duration models with censored data
• Developing nonparametric tests when duration times are subject to right censoring
• Addressing censoring complications in test statistics using instrumental variables

Innovation

• Nonparametric tests for exogeneity in duration models
• Using instrumental variables with categorical covariates
• Handling censored data via conditional rank independence