Approximate residual balancing: debiased inference of average treatment effects in high dimensions

By Susan Athey, Guido W. Imbens, Stefan Wager. 2016

426 citations recorded by the source corpus.

There are many settings where researchers are interested in estimating average treatment effects and are willing to rely on the unconfoundedness assumption, which requires that the treatment assignment be as good as random conditional on pretreatment variables. The unconfoundedness assumption is often more plausible if a large number of pretreatment variables are included in the analysis, but this can worsen the performance of standard approaches to treatment effect estimation. We develop a method for debiasing penalized regression adjustments to allow sparse regression methods like the lasso to be used for √n‐consistent inference of average treatment effects in high dimensional linear models. Given linearity, we do not need to assume that the treatment propensities are estimable, or that the average treatment effect is a sparse contrast of the outcome model parameters. Rather, in addition to standard assumptions used to make lasso regression on the outcome model consistent under 1‐norm error, we require only overlap, i.e. that the propensity score be uniformly bounded away from 0 and 1. Procedurally, our method combines balancing weights with a regularized regression adjustment.

Subfields: Management Science and Operations Research, Statistics and Probability, Causal Inference & Discovery

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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): “…common and important inference problems, and has often been used as a test case for theoretical study of inference following machine learning (e.g., Belloni, Chernozhukov, and Hansen (2014), Farrell (2015), Belloni, Cher-nozhukov, Fernández-Val, and Hansen (2017), Athey, Imbens, and Wager (2018)).”
Double/De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers (2018, methodology): “The Athey et al. (2018) estimator of the ATE is based on sparse linear regression and on approximate balancing weights when the regression is linear and strongly sparse.”
Generalized random forests (2016, background): “Recent contributions to the latter include Athey et al. (2016), Belloni et al. (2013), Chernozhukov et al. (2016), Robins et al. (1995), Robins et al. (2008), and van der Laan and Rubin (2006). In particular, Chernozhukov et al.”
Estimating individual treatment effect: generalization bounds and algorithms (2016, background): “However, most previous work on this subject focused on asymptotic consistency (Belloni et al., 2014; Athey et al., 2016; Chernozhukov et al., 2016), and so far there has not been much work on the generalization-error of such a procedure.”
Stable Prediction across Unknown Environments (2018, methodology): “They either employ propensity scores [10], [11], [12], [13], [14], or optimize balancing weights directly [15], [16], [17], [18].”
Offline Multi-Action Policy Learning: Generalization and Optimization (2018, methodology): “…assumptions are standard and commonly adopted in both the estimation literature (Rosenbaum and Rubin (1983), Imbens (2004), Imbens and Rubin (2015), Athey et al. (2016a)) and the existing offline policy learning literature (Zhang et al. (2012), Zhao et al. (2012), Kitagawa and Tetenov (2018),…”
Targeted Undersmoothing. (2017, methodology): “[4] perform residual rebalancing to estimate average treatment effects with high dimensional control variables when regression equations are given by sparse linear models under very”
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).”
Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data (2018, methodology): “Another related work is Athey et al. (2016), where valid confidence intervals are obtained for the sample treatment effects such as n 1 ∑ i:Ti=1 {m1(Xi) −m0(Xi)}, if a linear outcome model is correctly specified.”
Towards Out-Of-Distribution Generalization: A Survey (2021, methodology): “To solve such difﬁcult problem, motivated by the literature of variable balancing strategies [147], [148], [149], Shen et al. [118] propose to consider all the variables as the treat-ment and learn a set of global sample weights that could remove the confounding bias for all the potential…”
Using Wasserstein Generative Adversarial Networks for the design of Monte Carlo simulations (2019, positive): “[2014], Athey et al. [2018]). Using the LDW sample Abadie and Imbens [2011] estimate a model for the conditional means and the propensity score allowing for linear terms and second order terms.”
The Augmented Synthetic Control Method (2018, background): “See Athey, Imbens, and Wager (2018) for analogous results on balancing weights in high dimensional cross-sectional settings.”
Beyond prediction: Using big data for policy problems (2017, background): “Recent methodological advances focus on adjusting for observed confounders in big-data applications [e.g., ( 14 – 16 )].”
Locally Robust Semiparametric Estimation (2016, background): “…learning is useful for estimating economic and causal models where there are high dimensional covariates or state variables, e.g. as in Belloni et al. (2012), Robins et al. (2013), Belloni, Chernozhukov, and Hansen (2014), Farrell (2015), Belloni et al. (2017), and Athey, Imbens, and Wager (2018).”
Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap (2017, methodology): “, 2014, Athey et al., 2016, Chernozhukov et al., 2017). However, they all heavily rely on the NUC assumption. Robustness of the IPWtype estimators to unmeasured confounding bias are usually studied using pattern-mixture models (Birmingham et al., 2003) or selection models (Scharfstein et al., 1999),”