# Non-separable Models with High-dimensional Data

arXiv: https://arxiv.org/abs/1702.04625 · HTML: https://mlsanity.com/paper/1702.04625/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2017.

## Built on by (most cited first, 3 of 3)

- [Automatic Double Machine Learning for Continuous Treatment Effects](https://mlsanity.com/paper/2104.10334/) (2021)
- [Multiply Robust Causal Mediation Analysis with Continuous Treatments](https://mlsanity.com/paper/2105.09254/) (2021)
- [Stable Probability Weighting: Large-Sample and Finite-Sample Estimation and Inference Methods for Heterogeneous Causal Effects of Multivalued Treatments Under Limited Overlap](https://mlsanity.com/paper/2301.05703/) (2023)

## Abstract (arXiv)

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.