Gilles Crommen, Jean-Pierre Florens, Ingrid Van Keilegom
arXiv 30 Oct 2025 · Econometrics
arXiv:2510.26613 · PDF · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Fève, F., Florens, J.-P., and Van Keilegom, I (2018) Estimation of conditional ranks and tests of exogeneity in nonparametric nonseparable models self | 0.950 | 7 | 4 | 86% |
| 2 | Frandsen, B. R (2015) Treatment effects with censoring and endogeneity | 0.874 | 5 | 2 | 100% |
| 3 | Beyhum, J., Tedesco, L., and Van Keilegom, I (2024) Instrumental variable quantile regression under random right censoring | 0.811 | 4 | 2 | 100% |
| 4 | Chernozhukov, V. and Hansen, C (2005) An IV model of quantile treatment effects | 0.737 | 3 | 2 | 100% |
| 5 | Angrist, J. D., Imbens, G. W., and Rubin, D. B (1996) Identification of causal effects using instrumental variables | 0.644 | 2 | 2 | 100% |
| 6 | Beyhum, J., Florens, J.-P., and Van Keilegom, I (2022) Nonparametric instrumental regression with right censored duration outcomes self | 0.644 | 2 | 2 | 100% |
| 7 | Wüthrich, K (2020) A comparison of two quantile models with endogeneity | 0.644 | 2 | 2 | 100% |
| 8 | Akritas, M. G (1994) Nearest neighbor estimation of a bivariate distribution under random censoring | 0.511 | 2 | 1 | 100% |
| 9 | Crommen, G., Beyhum, J., and Van Keilegom, I (2024) An instrumental variable approach under dependent censoring self | 0.511 | 2 | 1 | 100% |
| 10 | Crommen, G., Beyhum, J., and Van Keilegom, I (2025) Estimation of the complier causal hazard ratio under dependent censoring self | 0.511 | 2 | 1 | 100% |
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