arXiv 18 Sep 2013 · Mathematics — Statistics Theory · publishedJournal of Econometrics (2015) · 340 citations (OpenAlex)
arXiv:1309.4686 · PDF · DOI · OpenAlex · Extracted main text
This paper concerns robust inference on average treatment effects following model selection. In the selection on observables framework, we show how to construct confidence intervals based on a doubly-robust estimator that are robust to model selection errors and prove that they are valid uniformly over a large class of treatment effect models. The class allows for multivalued treatments with heterogeneous effects (in observables), general heteroskedasticity, and selection amongst (possibly) more covariates than observations. Our estimator attains the semiparametric efficiency bound under appropriate conditions. Precise conditions are given for any model selector to yield these results, and we show how to combine data-driven selection with economic theory. For implementation, we give a specific proposal for selection based on the group lasso, which is particularly well-suited to treatment effects data, and derive new results for high-dimensional, sparse multinomial logistic regression. A simulation study shows our estimator performs very well in finite samples over a wide range of models. Revisiting the National Supported Work demonstration data, our method yields accurate estimates and tight confidence intervals.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Belloni, Chernozhukov, and Hansen (2014) Inference on Treatment Effects after Selection Amongst High-Dimensional Controls | 1.000 | 6 | 4 | 100% |
| 2 | Belloni, Chen, Chernozhukov, and Hansen (2012) Sparse models and methods for optimal instruments with an application to eminent domain | 0.855 | 8 | 5 | 62% |
| 3 | Cattaneo (2010) Efficient Semiparametric Estimation of Multi-valued Treatment Effects under Ignorability | 0.843 | 3 | 3 | 100% |
| 4 | Wooldridge (2010) Econometric Analysis of Cross Section and Panel Data | 0.843 | 3 | 3 | 100% |
| 5 | Lounici, Pontil, van de Geer, and Tsybakov (2011) Oracle Inequalities and Optimal Inference under Group Sparsity | 0.794 | 12 | 4 | 50% |
| 6 | Belloni and Chernozhukov (2013) Least Squares After Model Selection in High-dimensional Sparse Models | 0.737 | 5 | 4 | 40% |
| 7 | de la Peña, Lai, and Shao (2009) Self-Normalized Processes: Limit Theory and Statistical Applications, Probability and Its Applications | 0.737 | 5 | 4 | 40% |
| 8 | Belloni and Chernozhukov (2011) $_1$-Penalized quantile regression in high-dimensional sparse models | 0.737 | 4 | 3 | 50% |
| 9 | Belloni, Chernozhukov, Fernandez-Val, and Hansen (2014) Program Evaluation with High-Dimensional Data | 0.737 | 3 | 2 | 100% |
| 10 | Obozinski, Wainwright, and Jordan (2011) Support Union Recovery in High-Dimensional Multivariate Regression | 0.737 | 3 | 2 | 100% |
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