Program evaluation and causal inference with high-dimensional data

By Alexandre Belloni, Victor Chernozhukov, Iv'an Fern'andez-Val, Christian Hansen. 2013

380 citations recorded by the source corpus.

In this paper, we provide efficient estimators and honest con fidence bands for a variety of treatment eff ects including local average (LATE) and local quantile treatment eff ects (LQTE) in data-rich environments. We can handle very many control variables, endogenous receipt of treatment, heterogeneous treatment e ffects, 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 ecient estimators and honest bands for (functional) average treatment eff ects (ATE) and quantile treatment eff ects (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 eff ect 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, modern machine learning methods can be used to learn the nonparametric/high-dimensional components of the model. These include a number of supporting auxilliary results that are of major independent interest: namely, we (1) prove uniform validity of a multiplier bootstrap, (2) o er a uniformly valid functional delta method, and (3) provide results for sparsity-based estimation of regression functions for function-valued outcomes.

Subfields: Economics and Econometrics, Statistics and Probability

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Citations in the corpus

Deep Neural Networks for Estimation and Inference: Application to Causal Effects and Other Semiparametric Estimands (2018, methodology): “Our results for deep learning can be applied much more generally, see the longer version of this paper (Farrell, Liang, and Misra (2019a)) and other recent literature (Belloni et al. (2017), Chernozhukov et al. (2018)).”
Approximate residual balancing: debiased inference of average treatment effects in high dimensions (2016, methodology): “The starting point behind both our method and the doubly robust methods of Belloni et al. (2017), Chernozhukov et al. (2017), Farrell (2015), Van der Laan and Rose (2011), etc. is a recognition that high dimensional regression adjustments (such as the lasso) always shrink estimated effects, and…”
Quasi-oracle estimation of heterogeneous treatment effects (2017, methodology): “Chernozhukov et al. (2017) discusses how Robinson’s approach to the partially linear model generalizes naturally to this case, and Athey, Tibshirani, and Wager (2018) adapt their causal forest to work with instruments.”
Estimation and Inference about Heterogeneous Treatment Effects in High-Dimensional Dynamic Panels. (2017, background): “Further extensions of orthogonality for the functional parameter, such as distributional regression (Belloni et al. (2013), Belloni et al. (2019)) or support function in set-identified models (Semenova (2018)), do not nest our heterogeneous treatment effects framework.”
Double/debiased machine learning for treatment and structural parameters (2017, positive): “…we present results that complement this important classic work as well as the rapidly expanding body of work on estimation under unconfoundedness using ML methods; see, among others, Athey et al. (2016), Belloni et al. (2017), Belloni et al. (2014), Farrell (2015), and Imai and Ratkovic (2013).”
Inference in Linear Regression Models with Many Covariates and Heteroscedasticity (2015, background): “…concerns ultra-high-dimensional models where the number of covariates is much larger than the sample size, but some form of (approximate) sparsity is imposed in the model; see, for example, Belloni, Chernozhukov, and Hansen (2014), Farrell (2015), Belloni et al. (2017), and references therein.”
Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data (2018, methodology): “Obtaining model-assisted or doubly robust confidence intervals presents a considerable improvement over existing theory and methods in Belloni et al. (2014) and Farrell (2015). To illustrate main ideas, consider a logistic propensity score model (4) and a linear outcome regression model, E(Y |T = 1,”
Uniformity and the Delta Method (2015, methodology): “Uniformity of the delta method has also been studied recently by Belloni et al. (2013) with a focus on infinite dimensional parameters.”
Offline Multi-Action Policy Learning: Generalization and Optimization (2018, background): “…such conditions as well as the difference choices of estimators have been extensively studied in the estimation literature (see for instance Newey (1994), Robins and Rotnitzky (1995), Bickel et al. (1998), Farrell (2015), Belloni et al. (2017), Hirshberg and Wager (2018), Newey and Robins (2018)).”
High-dimensional econometrics and regularized GMM (2018, background): “This initial work has been expanded in many directions; see, for example, the textbook treatment of [32] as well as [36], [30], [8], [21], [7], [14], and [12] for results most closely related to the approach taken in this review.”