Inference for Nonlinear Endogenous Treatment Effects Accounting for High-Dimensional Covariate Complexity

TL;DR

This paper develops a novel inference method for nonlinear, endogenous treatment effects in high-dimensional settings, correcting biases and providing confidence bands, validated through simulations and empirical analysis.

Contribution

It introduces a double bias correction procedure for high-dimensional nonlinear endogenous treatment effect estimation, enabling valid inference with confidence bands.

Findings

Effective bias correction improves estimator accuracy.

Confidence bands reliably capture the true effect.

Method validated through simulations and empirical data.

Abstract

Nonlinearity and endogeneity are prevalent challenges in causal analysis using observational data. This paper proposes an inference procedure for a nonlinear and endogenous marginal effect function, defined as the derivative of the nonparametric treatment function, with a primary focus on an additive model that includes high-dimensional covariates. Using the control function approach for identification, we implement a regularized nonparametric estimation to obtain an initial estimator of the model. Such an initial estimator suffers from two biases: the bias in estimating the control function and the regularization bias for the high-dimensional outcome model. Our key innovation is to devise the double bias correction procedure that corrects these two biases simultaneously. Building on this debiased estimator, we further provide a confidence band of the marginal effect function. Simulations and an empirical study of air pollution and migration demonstrate the validity of our procedures.