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

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.