Technology Category
Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: CausalityCognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
Inference on the Distribution of Individual Treatment Effects in Nonseparable Triangular Models
🤖 AI Summary
This paper addresses statistical inference for the distribution of heterogeneous individual treatment effects (ITEs) in nonseparable triangular models. We propose a nonparametric inference framework based on the cumulative distribution function (CDF) of ITEs—distinct from conventional density estimation approaches. Our method establishes, for the first time, the weak convergence of the empirical ITE CDF and its quantile function, enabling consistent estimation and asymptotically efficient inference for key distributional features, including the proportion of positive ITEs, quantiles, and interquartile range. Leveraging empirical process theory and resampling techniques, we develop a bootstrap procedure that yields uniform confidence bands, facilitating rigorous comparison of ITE distributions across subpopulations. The resulting methodology provides the first statistically rigorous and practically implementable tool for distributional heterogeneity analysis in causal inference.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Infer distribution of heterogeneous individual treatment effects
Estimate cumulative distribution function for ITE analysis
Develop nonparametric inference methods with confidence bands
Innovation
Methods, ideas, or system contributions that make the work stand out.
Nonparametric inference for ITE distribution
Bootstrap-based confidence bands for CDF
Weak convergence to Gaussian processes analysis
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