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An Introduction to the Augmented Inverse Propensity Weighted Estimator

Published online by Cambridge University Press:  04 January 2017

Adam N. Glynn  and
Kevin M. Quinn
Adam N. Glynn*
Affiliation:
Department of Government, Harvard University, 1737 Cambridge Street, Cambridge, MA 02138
Kevin M. Quinn
Affiliation:
UC Berkeley School of Law, 490 Simon Hall, Berkeley, CA 94720-7200. e-mail: [email protected]
*
e-mail: [email protected] (corresponding author)
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Abstract

In this paper, we discuss an estimator for average treatment effects (ATEs) known as the augmented inverse propensity weighted (AIPW) estimator. This estimator has attractive theoretical properties and only requires practitioners to do two things they are already comfortable with: (1) specify a binary regression model for the propensity score, and (2) specify a regression model for the outcome variable. Perhaps the most interesting property of this estimator is its so-called “double robustness.” Put simply, the estimator remains consistent for the ATE if either the propensity score model or the outcome regression is misspecified but the other is properly specified. After explaining the AIPW estimator, we conduct a Monte Carlo experiment that compares the finite sample performance of the AIPW estimator to three common competitors: a regression estimator, an inverse propensity weighted (IPW) estimator, and a propensity score matching estimator. The Monte Carlo results show that the AIPW estimator has comparable or lower mean square error than the competing estimators when the propensity score and outcome models are both properly specified and, when one of the models is misspecified, the AIPW estimator is superior.

Type
Research Article
Information
Political Analysis , Volume 18 , Issue 1 , Winter 2010 , pp. 36 - 56
Copyright
Copyright © The Author 2009. Published by Oxford University Press on behalf of the Society for Political Methodology 

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Footnotes

Authors's note: We thank the editors and three anonymous referees for helpful comments on an earlier draft of this paper. An R package that implements the estimators discussed in this paper is available at http://cran.r-project.org/as a contributed package with the name CausalGAM.

References

Angrist, Joshua D., Imbens, Guido W., and Rubin, Donald B. 1996. Identification of causal effects using instrumental variables. Journal of the American Statistical Association 91: 444–55.Google Scholar
Busso, Matias, DiNardo, John, and McCrary, Justin. 2009a. Finite sample properties of semiparametric estimators of average treatment effects. Berkeley: University of California, Working paper.Google Scholar
Busso, Matias, DiNardo, John, and McCrary, Justin. 2009b. New evidence on the finite sample properties of propensity score matching and reweighting estimators. Working paper, University of California Berkeley.CrossRefGoogle Scholar
Cochran, William G. 1968. The effectiveness of adjustment by subclassification in removing bias in observational studies. Biometrics 24: 295–313.CrossRefGoogle ScholarPubMed
Diamond, A., and Sekhon, J. S. 2005. Genetic matching for estimating causal effects: A general multivariate matching method for achieving balance in observational studies. http://sekhon.berkeley.edu/papers/GenMatch.Google Scholar
Glynn, Adam, and Quinn, Kevin. 2009. Estimation of causal effects with generalized additive models. Vienna, Austria: R Foundation for Statistical Computing.Google Scholar
Hastie, Trevor. 2009. Generalized additive models. Vienna, Austria: R Foundation for Statistical Computing.Google Scholar
Ho, D. E., Imai, K., King, G., and Stuart, E. A. 2007. Matching as nonparametric preprocessing for reducing model dependence in parametric causal inference. Political Analysis 15: 199.CrossRefGoogle Scholar
Imbens, Guido W. 2004. Nonparametric estimation of average treatment effects under exogeneity: A review. The Review of Economics and Statistics 86: 4–29.CrossRefGoogle Scholar
Kang, Joseph D.Y., and Schafer, Joseph L. 2007a. Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data.” Statistical Science 22: 523–39.Google Scholar
Kang, Joseph D.Y., and Schafer, Joseph L. 2007b. Rejoinder: Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science 22: 574–80.Google Scholar
King, Gary, and Zeng, Langche. 2006. The dangers of extreme counterfactuals. Political Analysis 14: 131–59.CrossRefGoogle Scholar
Lunceford, Jared K., and Davidian, Marie. 2004. Stratification and weighting via the propensity score in estimation of causal treatment effects: A comparative study. Statistics in Medicine 23: 2937–60.CrossRefGoogle ScholarPubMed
Morgan, Stephen L., and Winship, Christopher. 2007. Counterfactuals and causal inference: Methods and principles for social research. New York: Cambridge University Press.CrossRefGoogle Scholar
Pearl, Judea. 1995. Causal diagrams for empirical research. Biometrika 82: 669–710.CrossRefGoogle Scholar
Pearl, Judea. 2000. Causality: Models, reasoning, and inference. New York: Cambridge University Press.Google Scholar
R Development Core Team. 2007. R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.Google Scholar
Ridgeway, Greg, and McCaffrey, Daniel F. 2007. Comment: Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science 22(4): 540–3.CrossRefGoogle Scholar
Robins, J. M. 1986. A new approach to causal inference in mortality studies with a sustained exposure period-application to control of the healthy worker survivor effect. Mathematical Modeling 7: 1393–512.CrossRefGoogle Scholar
Robins, James M. 1999. Robust estimation in sequentially ignorable missing data and causal inference models. Proceedings of the American Statistical Association Section on Bayesian Statistical Science 6–10.Google Scholar
Robins, James M., Rotnitzky, Andrea, and Zhao, Lue Ping. 1994. Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association 89: 846–66.CrossRefGoogle Scholar
Robins, James, Sued, Mariela, Lei-Gomez, Quanhong, and Rotnitzky, Andrea. 2007. Comment: performance of double-robust estimators when “inverse probability” weights are highly variable. Statistical Science 22: 544–59.CrossRefGoogle Scholar
Robins, J. M., and Wang, N. 2000. Inference for imputation estimators. Biometrika 87(1): 113–24.CrossRefGoogle Scholar
Rosenbaum, Paul R., and Rubin, Donald B. 1983. The central role of the propensity score in observational studies for causal effects. Biometrika 70: 41–55.CrossRefGoogle Scholar
Rubin, D. B. 2006. Matched sampling for causal effects. New York: Cambridge University Press.CrossRefGoogle Scholar
Scharfstein, Daniel O., Rotnitzky, Andrea, and Robins, James M. 1999. Rejoinder to adjusting for nonignorable drop-out using semiparametric nonresponse models. Journal of the American Statistical Association 94: 1135–46.Google Scholar
Sekhon, Jasjeet S. 2009. Multivariate and propensity score matching with balance optimization. Vienna, Austria: R Foundation for Statistical Computing.Google Scholar
Tan, Zhiqiang. 2007. Comment: Understanding OR, PS, and DR. Statistical Science 22(4): 560–68.CrossRefGoogle Scholar
Tsiatis, Anastasios A. 2006. Semiparametric theory and missing data. New York: Springer.Google Scholar
Tsiatis, Anastasios A., and Davidian, Marie. 2007. Comment: Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data.” Statistical Science 22(4): 569–73.CrossRefGoogle ScholarPubMed