Program Evaluation and Causal Inference with High-Dimensional Data (1311.2645v8)

Abstract: 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 post-regularization 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 reduced form 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 paper introduces a novel framework employing Lasso and Post-Lasso estimators to efficiently estimate treatment effects amidst high-dimensional control variables.
• It utilizes orthogonal moment conditions to ensure robust inference despite model selection errors and high-dimensional noise.
• An empirical application on 401(k) eligibility demonstrates the approach's capability to yield consistent and practical policy evaluations.

Overview of the Paper

The paper "Program Evaluation and Causal Inference with High-Dimensional Data" by Belloni, Chernozhukov, Fernandez-Val, and Hansen addresses the development and application of efficient estimation techniques within high-dimensional settings for evaluating treatment effects. The research presents a robust methodological framework allowing for precise inference of treatment effects by leveraging regularization and selection strategies. This work primarily focuses on efficiently handling numerous control variables, endogenous treatment conditions, and heterogeneous treatment effects, accommodating various estimands such as Local Average Treatment Effects (LATE) and Local Quantile Treatment Effects (LQTE).

Methodological Contributions

The methodology introduced revolves around estimating treatment effects when faced with a high-dimensional set of control variables. The paper enforces the assumption of approximate sparsity, where the true underlying relationships are present in sparse form, making them amenable to regularization techniques like Lasso and Post-Lasso estimation. This assumption facilitates the estimation and inferential processes by ensuring manageable computational complexity while maintaining accurate understating of the model's predictive capacity.

A critical highlight of the proposed approach is the employment of orthogonal or doubly robust moment conditions, underpinning the robustness and validity of the inference following the selection process. These conditions are instrumental in permitting honest inference even amidst high-dimensional noisy features and potential model selection mistakes. This framework is notably generalizable, extending its correctness to numerous machine learning tools such as boosted trees, deep neural networks, and random forests.

Empirical Application

An empirical illustration is provided, estimating the impact of 401(k) eligibility and participation on asset accumulation. The results underscore the practical applicability of the proposed framework, yielding consistent estimates that are robust against the inclusion of a vast array of possibly confounding variables through the high-dimensional specification.

Numerical and Theoretical Results

Numerically, the paper delivers strong results, documenting the effectiveness of their methodology in producing efficient estimators with valid inference using high-dimensional datasets. The usage of multipliers and functional delta-methods for bootstrapped confidence allows for flexible statistical application complemented by rigorous theoretical guarantees.

Implications for Future Research

The implications extend broadly within empirical economics and econometrics, paving new pathways for leveraging modern machine learning techniques in causal inference frameworks. This paper's contributions form a crucial basis for future exploration and refinement in high-dimensional econometric practices, with potential extensions applicable to various domains requiring sophisticated, precise treatment effect estimations.

Conclusion

This research makes substantial additions to the literature on program evaluation and causal inference under high-dimensional regimes. It provides vital methodological tools and frameworks for research requiring consideration of complex, multidimensional input variables and delivers both theoretical and empirical insights central to the discipline's advancement. The results underscore the need for a nuanced understanding of modern statistical tools, emphasizing their application within newly arising data-rich environments. This work is poised to influence applied econometric strategy significantly, especially concerning policy evaluation relying on intricate data architectures.