Tests of exogeneity in duration models with censored data

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Main Authors: Crommen, Gilles, Florens, Jean-Pierre, Van Keilegom, Ingrid
Format: Preprint
Published: 2025
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author Crommen, Gilles
Florens, Jean-Pierre
Van Keilegom, Ingrid
author_facet Crommen, Gilles
Florens, Jean-Pierre
Van Keilegom, Ingrid
contents 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 $T=φ(X,Z,U)$, where $X$ is a vector of baseline covariates, $φ(X,Z,U)$ is strictly increasing in the error term $U$ for each $(X,Z)$ and $U\sim \mathcal{U}[0,1]$. 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 $φ$, 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.
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id arxiv_https___arxiv_org_abs_2510_26613
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Tests of exogeneity in duration models with censored data
Crommen, Gilles
Florens, Jean-Pierre
Van Keilegom, Ingrid
Econometrics
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 $T=φ(X,Z,U)$, where $X$ is a vector of baseline covariates, $φ(X,Z,U)$ is strictly increasing in the error term $U$ for each $(X,Z)$ and $U\sim \mathcal{U}[0,1]$. 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 $φ$, 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.
title Tests of exogeneity in duration models with censored data
topic Econometrics
url https://arxiv.org/abs/2510.26613