# Non-separable Models with High-dimensional Data

## TL;DR

This paper introduces a three-step estimation method for non-separable models with high-dimensional control variables, enabling the estimation of various treatment effects with theoretical guarantees and practical validation.

## Contribution

It develops a novel three-step estimation procedure for high-dimensional non-separable models with continuous treatments, including inference methods and finite sample performance analysis.

## Key findings

- Estimators perform well in finite samples.
- The method effectively handles high-dimensional control variables.
- Asymptotic properties are established for the estimators.

## Abstract

This paper studies non-separable models with a continuous treatment when the dimension of the control variables is high and potentially larger than the effective sample size. We propose a three-step estimation procedure to estimate the average, quantile, and marginal treatment effects. In the first stage we estimate the conditional mean, distribution, and density objects by penalized local least squares, penalized local maximum likelihood estimation, and numerical differentiation, respectively, where control variables are selected via a localized method of L1-penalization at each value of the continuous treatment. In the second stage we estimate the average and marginal distribution of the potential outcome via the plug-in principle. In the third stage, we estimate the quantile and marginal treatment effects by inverting the estimated distribution function and using the local linear regression, respectively. We study the asymptotic properties of these estimators and propose a weighted-bootstrap method for inference. Using simulated and real datasets, we demonstrate that the proposed estimators perform well in finite samples.