Tests of exogeneity in duration models with censored data

TL;DR

This paper develops nonparametric tests for exogeneity in duration models with censored data, using instrumental variables and conditional rank independence, with proven asymptotic properties and empirical validation.

Contribution

It introduces novel nonparametric tests for exogeneity in censored duration models leveraging instrumental variables and conditional rank independence, with theoretical and empirical validation.

Findings

Test statistics have a known limiting distribution.

Estimator converges faster than the usual parametric rate.

Finite sample performance is good in Monte Carlo simulations.

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 $U\sim \mathcal{U}[0,1]$. 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 $\varphi$, 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.