[Paper Review] De-biased Machine Learning for Compliers

Rahul Singh, Liyang Sun|arXiv (Cornell University)|Sep 10, 2019

Economic Policies and Impacts4 citations

TL;DR

This paper introduces a de-biased machine learning method, DML-RRR, for estimating complier parameters—such as the local average treatment effect and counterfactual outcome distributions—in high-dimensional settings using instrumental variables. The approach ensures consistency, asymptotic normality, and semi-parametric efficiency, outperforming existing methods in simulations and real-world analysis of 401(k) participation effects on net financial assets.

ABSTRACT

Instrumental variable identification is a concept in causal statistics for estimating the counterfactual effect of treatment D on output Y controlling for covariates X using observational data. Even when measurements of (Y,D) are confounded, the treatment effect on the subpopulation of compliers can nonetheless be identified if an instrumental variable Z is available, which is independent of (Y,D) conditional on X and the unmeasured confounder. We introduce a de-biased machine learning (DML) approach to estimating complier parameters with high-dimensional data. Complier parameters include local average treatment effect, average complier characteristics, and complier counterfactual outcome distributions. In our approach, the de-biasing is itself performed by machine learning, a variant called de-biased machine learning via regularized Riesz representers (DML-RRR). We prove our estimator is consistent, asymptotically normal, and semi-parametrically efficient. In experiments, our estimator outperforms state of the art alternatives. We use it to estimate the effect of 401(k) participation on the distribution of net financial assets.

Motivation & Objective

• To address the challenge of estimating treatment effects on compliers in high-dimensional observational data where confounding is present.
• To develop a method that ensures consistent, asymptotically normal, and semi-parametrically efficient estimation of complier parameters despite high-dimensional covariates.
• To extend machine learning techniques to instrumental variable settings by incorporating de-biasing via regularized Riesz representers.
• To provide a robust framework for estimating local average treatment effects and counterfactual outcome distributions under unconfoundedness and exclusion restrictions.

Proposed method

• Proposes a de-biased machine learning framework, DML-RRR, that uses regularized Riesz representers to estimate nuisance parameters in instrumental variable models.
• Employs machine learning to estimate the conditional mean functions of potential outcomes and treatment propensity, reducing bias in the final estimator.
• Applies a Neyman-orthogonal estimating equation to ensure robustness to estimation errors in nuisance functions.
• Uses cross-fitting to improve finite-sample performance and maintain asymptotic validity.
• Implements a double-robustness structure where the estimator remains consistent if either the outcome or treatment model is correctly specified.
• Derives asymptotic normality and semi-parametric efficiency bounds for the estimator under regularity conditions.

Experimental results

Research questions

• RQ1 Can de-biased machine learning be effectively adapted to estimate complier parameters in high-dimensional settings with instrumental variables?
• RQ2 Does the proposed DML-RRR method achieve asymptotic normality and semi-parametric efficiency in estimating local average treatment effects?
• RQ3 How does DML-RRR compare to existing state-of-the-art methods in finite-sample performance and robustness?
• RQ4 What is the impact of 401(k) participation on the distribution of net financial assets, as estimated using the complier-specific treatment effect?

Key findings

• The DML-RRR estimator is consistent, asymptotically normal, and achieves semi-parametric efficiency under regularity conditions.
• Empirical experiments show that DML-RRR outperforms state-of-the-art alternatives in terms of bias, variance, and coverage probability.
• The method successfully estimates the local average treatment effect of 401(k) participation on net financial assets, revealing a significant positive effect on compliers.
• The estimator provides reliable inference on complier counterfactual outcome distributions, even with high-dimensional covariates.
• The use of regularized Riesz representers enables accurate and stable estimation of nuisance functions in high-dimensional settings.
• Cross-fitting and Neyman-orthogonal estimating equations improve finite-sample performance and robustness to model misspecification.