Journal Article

PROGRAM EVALUATION AND CAUSAL INFERENCE WITH HIGH-DIMENSIONAL DATA

Hansen, C., Belloni, A., Fernández-Val, I., Chernozhukov, V.

2017

Overview

In this paper, we provide efficient estimators and honest confidence bands for a variety of treatment effects including local average (LATE) and local quantile treatment effects (LQTE) in data-rich environments. We can handle very many control variables, endogenous receipt of treatment, heterogeneous treatment effects, and function-valued outcomes. Our framework covers the special case of exogenous receipt of treatment, either conditional on controls or unconditionally as in randomized control trials. In the latter case, our approach produces efficient estimators and honest bands for (functional) average treatment effects (ATE) and quantile treatment effects (QTE). To make informative inference possible, we assume that key reduced-form predictive relationships are approximately sparse. This assumption allows the use of regularization and selection methods to estimate those relations, and we provide methods for postregularization and post-selection inference that are uniformly valid (honest) across a wide range of models. We show that a key ingredient enabling honest inference is the use of orthogonal or doubly robust moment conditions in estimating certain reducedform functional parameters. We illustrate the use of the proposed methods with an application to estimating the effect of 401(k) eligibility and participation on accumulated assets. The results on program evaluation are obtained as a consequence of more general results on honest inference in a general moment-condition framework, which arises from structural equation models in econometrics. Here, too, the crucial ingredient is the use of orthogonal moment conditions, which can be constructed from the initial moment conditions. We provide results on honest inference for (function-valued) parameters within this general framework where any high-quality, machine learning methods (e.g., boosted trees, deep neural networks, random forest, and their aggregated and hybrid versions) can be used to learn the nonparametric/high-dimensional components of the model. These include a number of supporting auxiliary results that are of major independent interest: namely, we (1) prove uniform validity of a multiplier bootstrap, (2) offer a uniformly valid functional delta method, and (3) provide results for sparsitybased estimation of regression functions for function-valued outcomes.

• Publisher: Econometric Society,Blackwell Publishing Ltd
• Subject: Approximation / Causality / Clinical trials / Decision making models / Deferred compensation / Econometrics / Economic models / endogeneity / Endogenous / Entropy / Estimating techniques / Estimation methods / Estimators / Frame analysis / Function / heterogenous treatment effects / Inference / inference after model selection / Instrumental variables estimation / instruments / Internet / Lasso / Lasso and Post‐Lasso with functional response data / local average and quantile treatment effects / local effects of treatment on the treated / Logistics / Machine learning / Mathematical functions / moment‐condition models / moment‐condition models with a continuum of target parameters / Neural networks / Neyman orthogonality / Orthogonality / Parameter estimation / Program evaluation / propensity score / randomized control trials / Retirement benefits / Structural equation modeling / Structural models / Trees / Validation studies