Causal Effect Identification and Inference with Endogenous Exposures and a Light-tailed Error

2024-08-12

AI Summary

Endogeneity in exposures impedes causal identification, and conventional approaches rely either on strong functional-form assumptions or valid instrumental variables (IVs). This paper proposes an extremal conditional quantile contrast method grounded in a light-tailed error assumption. We establish, for the first time, that extreme quantile regression is inherently robust to endogeneity under light-tailed errors—enabling causal identification without IVs or additional parametric restrictions. Theoretically, we prove strong consistency of the estimator and asymptotic normality in linear models. Simulation studies and empirical analysis using automobile sales data demonstrate that the method maintains high estimation accuracy and reliable confidence interval coverage even when invalid IVs are present. By circumventing reliance on external instruments or stringent modeling assumptions, our approach substantially broadens the scope of applicable settings for endogeneity-robust inference.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Causality

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

Endogeneity poses significant challenges in causal inference across various research domains. This paper proposes a novel approach to identify and estimate causal effects in the presence of endogeneity. We consider a structural equation with endogenous exposures and an additive error term. Assuming the light-tailedness of the error term, we show that the causal effect can be identified by contrasting extreme conditional quantiles of the outcome given the exposures. Unlike many existing results, our identification approach does not rely on additional parametric assumptions or auxiliary variables. Building on the identification result, we develop a new method that estimates the causal effect using extreme quantile regression. We establish the consistency of the proposed extreme-based estimator under a general additive structural equation and demonstrate its asymptotic normality in the linear model setting. These results reveal that extreme quantile regression is invulnerable to endogeneity when the error term is light-tailed, which is not appreciated in the literature to our knowledge. The proposed extreme-based method can be applied to causal inference problems with invalid auxiliary variables, e.g., invalid instruments or invalid negative controls, for the selection of auxiliary variables and construction of valid confidence sets for the causal effect. Simulations and data analysis of an automobile sale dataset show the effectiveness of our method in addressing endogeneity.

Problem

• Identify causal effects with endogenous exposures and light-tailed errors
• Estimate causal effects using extreme quantile regression without auxiliary variables
• Address endogeneity in causal inference with invalid auxiliary variables

Innovation

• Uses extreme quantile regression for causal effect
• Identifies effects via extreme conditional quantiles
• Assumes light-tailed error term for estimation