A New and Efficient Debiased Estimation of General Treatment Models by Balanced Neural Networks Weighting

TL;DR

This paper introduces a balanced neural networks weighting method for general treatment models that improves debiased estimation of treatment effects, especially in small samples, by leveraging deep learning for covariate balance and robustness.

Contribution

It proposes a novel neural network-based weighting approach that handles various treatment types, achieves rate double robustness, and simplifies inference without estimating influence functions.

Findings

Outperforms existing methods in simulations, especially with small samples.

Achieves $\,\sqrt{N}$-asymptotic normality and semiparametric efficiency.

Effectively estimates average and quantile treatment effects in real datasets.

Abstract

Estimation and inference of treatment effects under unconfounded treatment assignments often suffer from bias and the `curse of dimensionality' due to the nonparametric estimation of nuisance parameters for high-dimensional confounders. Although debiased state-of-the-art methods have been proposed for binary treatments under particular treatment models, they can be unstable for small sample sizes. Moreover, directly extending them to general treatment models can lead to computational complexity. We propose a balanced neural networks weighting method for general treatment models, which leverages deep neural networks to alleviate the curse of dimensionality while retaining optimal covariate balance through calibration, thereby achieving debiased and robust estimation. Our method accommodates a wide range of treatment models, including average, quantile, distributional, and asymmetric least squares treatment effects, for discrete, continuous, and mixed treatments. Under regularity conditions, we show that our estimator achieves rate double robustness and $\sqrt{N}$-asymptotic normality, and its asymptotic variance achieves the semiparametric efficiency bound. We further develop a statistical inference procedure based on weighted bootstrap, which avoids estimating the efficient influence/score functions. Simulation results reveal that the proposed method consistently outperforms existing alternatives, especially when the sample size is small. Applications to the 401(k) dataset and the Mother's Significant Features dataset further illustrate the practical value of the method for estimating both average and quantile treatment effects under binary and continuous treatments, respectively.