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Efficient Estimation of Data Combination Models by the Method of Auxiliary-to-Study Tilting (AST)

2015; Taylor & Francis; Volume: 34; Issue: 2 Linguagem: Inglês

10.1080/07350015.2015.1038544

1537-2707

Bryan S. Graham, Cristine Campos de Xavier Pinto, Daniel Egel,

Statistical Methods and Bayesian Inference

AbstractWe propose a locally efficient estimator for a class of semiparametric data combination problems. A leading estimand in this class is the average treatment effect on the treated (ATT). Data combination problems are related to, but distinct from, the class of missing data problems with data missing at random (of which the average treatment effect (ATE) estimand is a special case). Our estimator also possesses a double robustness property. Our procedure may be used to efficiently estimate, among other objects, the ATT, the two-sample instrumental variables model (TSIV), counterfactual distributions, poverty maps, and semiparametric difference-in-differences. In an empirical application, we use our procedure to characterize residual Black–White wage inequality after flexibly controlling for "premarket" differences in measured cognitive achievement. Supplementary materials for this article are available online.KEY WORDS: Average treatment effect on the treated (ATT)Double robustnessEarnings decompositionsPropensity scoreSemiparametric difference-in-differencesTwo-sample instrumental variables (TSIV) ACKNOWLEDGMENTSThe authors thank David Card, Stephen Cosslett, Jinyong Hahn, Michael Jansson, Patrick Kline, Richard Smith, Tom Rothenberg, and members of the Berkeley Econometrics Reading Group for helpful discussions. We are particularly grateful to Gary Chamberlain, Guido Imbens, Justin McCrary, Geert Ridder, Enrique Sentana, and Leonard Stefanski for detailed comments on earlier drafts. This article has benefited from comments by the co-editor, associate editor, and three anonymous referees. The authors thank Jing Qin and Biao Zhang for assistance in replicating the Monte Carlo designs in Qin and Zhang (Citation2008). The authors also acknowledge feedback and suggestions from participants in seminars at the University of Pittsburgh, Ohio State University, University of Southern California, University of California - Riverside, University of California - Davis, University of Maryland, Georgetown University, Duke University, University of California - Berkeley, CEMFI (Madrid), Pontif ícia Universidade Católica do Rio de Janeiro, and the 2013 North American Summer Meeting of the Econometric Society. Preliminary portions of the current article previously appeared in Section 4 of an early draft of the NBER Working Paper "Inverse probability tilting and missing data problems." The published version of that article excludes the material reported here. A supplemental appendix with proofs and additional details regarding computation may be found on the first author's web page. All the usual disclaimers apply.