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Inference on the Distribution of Individual Treatment Effects in Nonseparable Triangular Models

Jun Ma, Vadim Marmer, Zhengfei Yu

arXiv 18 Sep 2025 · Econometrics · publishedJournal of Econometrics (2023) · 1 citations (OpenAlex)

arXiv:2509.15401 · PDF · DOI · OpenAlex · Extracted main text

Abstract

In this paper, we develop inference methods for the distribution of heterogeneous individual treatment effects (ITEs) in the nonseparable triangular model with a binary endogenous treatment and a binary instrument of Vuong and Xu (2017) and Feng, Vuong, and Xu (2019). We focus on the estimation of the cumulative distribution function (CDF) of the ITE, which can be used to address a wide range of practically important questions such as inference on the proportion of individuals with positive ITEs, the quantiles of the distribution of ITEs, and the interquartile range as a measure of the spread of the ITEs, as well as comparison of the ITE distributions across sub-populations. Moreover, our CDF-based approach can deliver more precise results than density-based approach previously considered in the literature. We establish weak convergence to tight Gaussian processes for the empirical CDF and quantile function computed from nonparametric ITE estimates of Feng, Vuong, and Xu (2019). Using those results, we develop bootstrap-based nonparametric inferential methods, including uniform confidence bands for the CDF and quantile function of the ITE distribution.

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38
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Feng, Q., Q. Vuong, and H. Xu (2019) Estimation of heterogeneous individual treatment effects with endogenous treatments1.000285100%
2Ma, J., V. Marmer, and Z. Yu (2023) Inference on individual treatment effects in nonseparable triangular models self1.000154100%
3Vuong, Q. and H. Xu (2017) Counterfactual mapping and individual treatment effects in nonseparable models with binary endogeneity1.000153100%
4Van der Vaart, A. W (2000) Asymptotic Statistics1.00073100%
5Kosorok, M. R (2007) Introduction to Empirical Processes and Semiparametric Inference0.87452100%
6Chernozhukov, V., I. Fernández-Val, and Y. Luo (2018) The sorted effects method: Discovering heterogeneous effects beyond their averages0.64422100%
7Heckman, J. J., S. Urzua, and E. Vytlacil (2006) Understanding instrumental variables in models with essential heterogeneity0.64422100%
8Vytlacil, E. and N. Yildiz (2007) Dummy endogenous variables in weakly separable models0.64422100%
9Abrevaya, J. and H. Xu (2023) Estimation of treatment effects under endogenous heteroskedasticity0.64422100%
10Van Der Vaart, A. W. and J. A. Wellner (2007) Empirical processes indexed by estimated functions0.64422100%

Showing the top 10 of 38 scored citations.