Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations

By Max H. Farrell. 2013

366 citations recorded by the source corpus.

This paper concerns robust inference on average treatment effects following model selection. Under selection on observables, we construct confidence intervals using a doubly-robust estimator that are robust to model selection errors and prove their uniform validity over a large class of models that allows for multivalued treatments with heterogeneous effects and selection amongst (possibly) more covariates than observations. The semiparametric efficiency bound is attained under appropriate conditions. Precise conditions are given for any model selector to yield these results, and we specifically propose the group lasso, which is apt for treatment effects, and derive new results for high-dimensional, sparse multinomial logistic regression. Both a simulation study and revisiting the National Supported Work demonstration show our estimator performs well in finite samples.

Subfields: Statistics and Probability

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Citations in the corpus

FLAME: A Fast Large-scale Almost Matching Exactly Approach to Causal Inference (2017, background): “, Rubin, 1973a,b, 1976; Cochran and Rubin, 1973) with the extreme being work on propensity score matching, which was later extended to work on penalized regression approaches that leverage propensity (Schneeweiss et al., 2009; Rassen and Schneeweiss, 2012; Belloni et al., 2014; Farrell, 2015).”
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)).”
Approximate residual balancing: debiased inference of average treatment effects in high dimensions (2016, methodology): “…by either non-parametric inverse propensity weighting or non-parametric regression adjustments on their own (Chen et al., 2008; Hirano et al., 2003); doubly robust methods can then be used to relax the regularity conditions that are needed for efficiency (Farrell, 2015; Robins et al., 2017).”
Efficient Policy Learning (2017, background): “The weaker requirement (13) reflects the fact that doubly robust treatment effect estimators can trade-off accuracy of the μ-model with accuracy of the e-model, provided the product of the error rates is controlled (Farrell, 2015).”
Offline Multi-Action Policy Learning: Generalization and Optimization (2018, background): “In fact, Farrell (2015) has made clear the importance of Assumption 2 in achieving accurate treatment effect estimation (in binary treatment cases) for doubly robust/AIPW estimators.”
Targeted Undersmoothing. (2017, background): “Such inferential results have been extended to various settings, including panel data (see [11]), various nonparametric settings (see [12], [36]), settings with generalized linear models (see [31], [12]), and quantile regression (see [12]).”
A GENERAL DOUBLE ROBUSTNESS RESULT FOR ESTIMATING AVERAGE TREATMENT EFFECTS (2014, methodology): “These same moment conditions were also used in recent papers by Belloni, Chernozhukov, and Hansen (2014); Belloni, Chernozhukov, Fernández-Val, and Hansen (2017) and Farrell (2015) for treatment evaluation with high-dimensional data, including settings with more covariates than observations.”
Program evaluation with high-dimensional data (2013, methodology): “Belloni, Chernozhukov, and Hansen (2011) and Farrell (2013) also exploited this approach in the p ≫ n setting to develop a double-selection method that yields valid inference on the parameters of the linear part of the partially linear model and on average treatment effects when the treatment is exo”
Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data (2018, methodology): “E(Y |T = 1, X) = m(1)(X;α(1)) = αf(X), (9)”
Interpretable Almost-Exact Matching for Causal Inference (2019, methodology): “Early on, this led to techniques that reduce dimension using propensity score matching (Rubin, 1973b,a, 1976; Cochran and Rubin, 1973), which extend to penalized regression approaches (Schneeweiss et al., 2009; Rassen and Schneeweiss, 2012; Belloni et al., 2014; Farrell, 2015).”
Estimation of Conditional Average Treatment Effects With High-Dimensional Data (2019, methodology): “…and Robins (2003), Hirano, Imbens, and Ridder (2003), van der Laan and Rubin (2006), Firpo (2007), Tsiatis (2007), van der Laan and Rose (2011), Belloni et al. (2017), Farrell (2015), Kennedy et al. (2017), Robins et al. (2017), Wager and Athey (2018), and Su, Ura, and Zhang (2019), among others.”
Valid Post-Selection and Post-Regularization Inference: An Elementary, General Approach (2015, neutral): “This result is essentially due to Jing et al. (2003). The proof of this result, given in Belloni et al.”
Econometric Methods for Program Evaluation (2018, methodology): “…results have been extended to multi-valued treatments (Imbens, 2000; Lechner, 2001; Hirano and Imbens, 2004; Imai and van Dyk, 2004; Cattaneo, 2010; Farrell, 2015; Yang et al., 2016), to quantiles and related treatment effects (Firpo, 2007; Cattaneo, 2010), and to the analysis and interpretation…”
Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data (2017, methodology): “Similar results to those of Belloni et al. (2014) and Farrell (2015) were obtained.”