Inference on individual treatment effects in nonseparable triangular models

Jun Ma, Vadim Marmer () and Zhengfei Yu

Journal of Econometrics, 2023, vol. 235, issue 2, 2096-2124

Abstract: In nonseparable triangular models with a binary endogenous treatment and a binary instrumental variable, Vuong and Xu (2017) established identification results for individual treatment effects (ITEs) under the rank invariance assumption. Using their approach, Feng et al. (2019) proposed a uniformly consistent kernel estimator for the density of the ITE that utilizes estimated ITEs. In this paper, we establish the asymptotic normality of the density estimator of Feng et al. (2019) and show that the ITE estimation errors have a non-negligible effect on the asymptotic distribution of the estimator. We propose asymptotically valid standard errors that account for ITEs estimation, as well as a bias correction. Furthermore, we develop uniform confidence bands for the density of the ITE using the jackknife multiplier or nonparametric bootstrap critical values.

Keywords: Individual treatment effects; Nonparametric triangular models; Two-step nonparametric estimation; Bootstrap; Uniform confidence bands; Labor supply and family size (search for similar items in EconPapers)
JEL-codes: C12 C14 C31 C36 (search for similar items in EconPapers)
Date: 2023
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Working Paper: Inference on Individual Treatment Effects in Nonseparable Triangular Models (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:235:y:2023:i:2:p:2096-2124

DOI: 10.1016/j.jeconom.2023.02.011

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