Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-12T10:46:29.794Z Has data issue: false hasContentIssue false
  • English
  • Français

A GENERAL DOUBLE ROBUSTNESS RESULT FOR ESTIMATING AVERAGE TREATMENT EFFECTS

Published online by Cambridge University Press:  16 February 2017

Tymon Słoczyński and
Jeffrey M. Wooldridge
Tymon Słoczyński
Affiliation:
Brandeis University
Jeffrey M. Wooldridge*
Affiliation:
Michigan State University
*
*Address correspondence to Jeffrey M. Wooldridge, Department of Economics, Michigan State University, East Lansing, MI 48824-1038, USA; e-mail: wooldri1@msu.edu.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In this paper we study doubly robust estimators of various average and quantile treatment effects under unconfoundedness; we also consider an application to a setting with an instrumental variable. We unify and extend much of the recent literature by providing a very general identification result which covers binary and multi-valued treatments; unnormalized and normalized weighting; and both inverse-probability weighted (IPW) and doubly robust estimators. We also allow for subpopulation-specific average treatment effects where subpopulations can be based on covariate values in an arbitrary way. Similar to Wooldridge (2007), we then discuss estimation of the conditional mean using quasi-log likelihoods (QLL) from the linear exponential family.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 34 , Issue 1 , February 2018, pp. 112 - 133
Copyright
Copyright © Cambridge University Press 2017 

Footnotes

We thank Peter Phillips (Editor), Arthur Lewbel (Co-Editor), and three anonymous referees for helpful comments. Tymon Słoczyński also acknowledges financial support from the National Science Centre (grant DEC-2012/05/N/HS4/00395) and the Foundation for Polish Science (a START scholarship).

References

REFERENCES

Abadie, A. (2002) Bootstrap tests for distributional treatment effects in instrumental variable models. Journal of the American Statistical Association 97, 284–292.CrossRefGoogle Scholar
Abadie, A., Angrist, J., & Imbens, G. (2002) Instrumental variables estimates of the effect of subsidized training on the quantiles of trainee earnings. Econometrica 70, 91–117.CrossRefGoogle Scholar
Bang, H. & Robins, J.M. (2005) Doubly robust estimation in missing data and causal inference models. Biometrics 61, 962–972.CrossRefGoogle ScholarPubMed
Belloni, A., Chernozhukov, V., Fernández-Val, I., & Hansen, C. (2017) Program evaluation and causal inference with high-dimensional data. Econometrica 85, 233–298.CrossRefGoogle Scholar
Belloni, A., Chernozhukov, V., & Hansen, C. (2014) Inference on treatment effects after selection among high-dimensional controls. Review of Economic Studies 81, 608–650.CrossRefGoogle Scholar
Cao, W., Tsiatis, A.A., & Davidian, M. (2009) Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data. Biometrika 96, 723–734.CrossRefGoogle ScholarPubMed
Cassel, C.M., Särndal, C.E., & Wretman, J.H. (1976) Some results on generalized difference estimation and generalized regression estimation for finite populations. Biometrika 63, 615–620.Google Scholar
Cattaneo, M.D. (2010) Efficient semiparametric estimation of multi-valued treatment effects under ignorability. Journal of Econometrics 155, 138–154.CrossRefGoogle Scholar
Cattaneo, M.D., Drukker, D.M., & Holland, A.D. (2013) Estimation of multivalued treatment effects under conditional independence. Stata Journal 13, 407–450.Google Scholar
Chernozhukov, V., Fernández-Val, I., & Melly, B. (2013) Inference on counterfactual distributions. Econometrica 81, 2205–2268.Google Scholar
Donald, S.G. & Hsu, Y.C. (2014) Estimation and inference for distribution functions and quantile functions in treatment effect models. Journal of Econometrics 178, 383–397.CrossRefGoogle Scholar
Emsley, R., Lunt, M., Pickles, A., & Dunn, G. (2008) Implementing double-robust estimators of causal effects. Stata Journal 8, 334–353.CrossRefGoogle Scholar
Farrell, M.H. (2015) Robust inference on average treatment effects with possibly more covariates than observations. Journal of Econometrics 189, 1–23.CrossRefGoogle Scholar
Firpo, S. & Pinto, C. (2016) Identification and estimation of distributional impacts of interventions using changes in inequality measures. Journal of Applied Econometrics 31, 457–486.CrossRefGoogle Scholar
Foresi, S. & Peracchi, F. (1995) The conditional distribution of excess returns: An empirical analysis. Journal of the American Statistical Association 90, 451–466.CrossRefGoogle Scholar
Frandsen, B.R., Frölich, M., & Melly, B. (2012) Quantile treatment effects in the regression discontinuity design. Journal of Econometrics 168, 382–395.CrossRefGoogle Scholar
Frölich, M. & Melly, B. (2013) Unconditional quantile treatment effects under endogeneity. Journal of Business & Economic Statistics 31, 346–357.CrossRefGoogle Scholar
Glynn, A.N. & Quinn, K.M. (2010) An introduction to the augmented inverse propensity weighted estimator. Political Analysis 18, 36–56.CrossRefGoogle Scholar
Gourieroux, C., Monfort, A., & Trognon, A. (1984) Pseudo maximum likelihood methods: Theory. Econometrica 52, 681–700.Google Scholar
Graham, B.S., de Xavier Pinto, C. Campos, & Egel, D. (2012) Inverse probability tilting for moment condition models with missing data. Review of Economic Studies 79, 1053–1079.CrossRefGoogle Scholar
Heckman, J. & Pinto, R. (2015) Causal analysis after Haavelmo. Econometric Theory 31, 115–151.Google ScholarPubMed
Hirano, K. & Imbens, G.W. (2001) Estimation of causal effects using propensity score weighting: An application to data on right heart catheterization. Health Services & Outcomes Research Methodology 2, 259–278.Google Scholar
Horvitz, D.G. & Thompson, D.J. (1952) A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association 47, 663–685.CrossRefGoogle Scholar
Hu, Z., Follmann, D.A., & Qin, J. (2012) Semiparametric double balancing score estimation for incomplete data with ignorable missingness. Journal of the American Statistical Association 107, 247–257.Google Scholar
Imbens, G.W. (2000) The role of the propensity score in estimating dose-response functions. Biometrika 87, 706–710.Google Scholar
Imbens, G.W. & Angrist, J.D. (1994) Identification and estimation of local average treatment effects. Econometrica 62, 467–475.Google Scholar
Kaiser, B. (2016) Decomposing differences in arithmetic means: A doubly robust estimation approach. Empirical Economics 50, 873–899.Google Scholar
Kang, J.D.Y. & Schafer, J.L. (2007) Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science 22, 523–539.CrossRefGoogle Scholar
Kiefer, N.M. (1989) The ET interview: Arthur S. Goldberger. Econometric Theory 5, 133–160.Google Scholar
Kline, P. (2011) Oaxaca-Blinder as a reweighting estimator. American Economic Review: Papers & Proceedings 101, 532–537.Google Scholar
Lee, M.-J. (2009) Non-parametric tests for distributional treatment effect for randomly censored responses. Journal of the Royal Statistical Society: Series B 71, 243–264.CrossRefGoogle Scholar
Liu, L., Miao, W., Sun, B., Robins, J., & Tchetgen Tchetgen, E. (2015) Doubly robust estimation of a marginal average effect of treatment on the treated with an instrumental variable. Unpublished.Google Scholar
Long, Q., Hsu, C.H., & Li, Y. (2012) Doubly robust nonparametric multiple imputation for ignorable missing data. Statistica Sinica 22, 149–172.CrossRefGoogle ScholarPubMed
Lunceford, J.K. & Davidian, M. (2004) Stratification and weighting via the propensity score in estimation of causal treatment effects: A comparative study. Statistics in Medicine 23, 2937–2960.Google ScholarPubMed
Maier, M. (2011) Tests for distributional treatment effects under unconfoundedness. Economics Letters 110, 49–51.CrossRefGoogle Scholar
Newey, W.K. & McFadden, D. (1994) Large sample estimation and hypothesis testing. In Engle, R.F. & McFadden, D. (eds.), Handbook of Econometrics, vol. 4, pp. 2111–2245. North Holland.Google Scholar
Ogburn, E.L., Rotnitzky, A., & Robins, J.M. (2015) Doubly robust estimation of the local average treatment effect curve. Journal of the Royal Statistical Society: Series B 77, 373–396.CrossRefGoogle ScholarPubMed
Okui, R., Small, D.S., Tan, Z., & Robins, J.M. (2012) Doubly robust instrumental variable regression. Statistica Sinica 22, 173–205.CrossRefGoogle Scholar
Pearl, J. (2015) Trygve Haavelmo and the emergence of causal calculus. Econometric Theory 31, 152–179.CrossRefGoogle Scholar
Ridgeway, G. & McCaffrey, D.F. (2007) Comment: Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science 22, 540–543.CrossRefGoogle Scholar
Robins, J.M., Rotnitzky, A., & van der Laan, M. (2000) Comment. Journal of the American Statistical Association 95, 477–482.CrossRefGoogle Scholar
Robins, J.M., Rotnitzky, A., & Zhao, L.P. (1994) Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association 89, 846–866.CrossRefGoogle Scholar
Robins, J.M., Sued, M., Lei-Gomez, Q., & Rotnitzky, A. (2007) Comment: Performance of double-robust estimators when “inverse probability” weights are highly variable. Statistical Science 22, 544–559.CrossRefGoogle Scholar
Rothe, C. & Firpo, S. (2015) Semiparametric two-step estimation using doubly robust moment conditions. Unpublished.Google Scholar
Rotnitzky, A., Lei, Q., Sued, M., & Robins, J.M. (2012) Improved double-robust estimation in missing data and causal inference models. Biometrika 99, 439–456.Google ScholarPubMed
Sant’Anna, P.H.C. (2016) Program evaluation with right-censored data. Unpublished.CrossRefGoogle Scholar
Scharfstein, D.O., Rotnitzky, A., & Robins, J.M. (1999) Rejoinder. Journal of the American Statistical Association 94, 1135–1146.Google Scholar
Tan, Z. (2006a) A distributional approach for causal inference using propensity scores. Journal of the American Statistical Association 101, 1619–1637.CrossRefGoogle Scholar
Tan, Z. (2006b) Regression and weighting methods for causal inference using instrumental variables. Journal of the American Statistical Association 101, 1607–1618.CrossRefGoogle Scholar
Tan, Z. (2007) Comment: Understanding OR, PS and DR. Statistical Science 22, 560–568.Google Scholar
Tan, Z. (2010) Bounded, efficient and doubly robust estimation with inverse weighting. Biometrika 97, 661–682.CrossRefGoogle Scholar
Tchetgen Tchetgen, E.J. & Vansteelandt, S. (2013) Alternative identification and inference for the effect of treatment on the treated with an instrumental variable. Unpublished.Google Scholar
Tsiatis, A.A. & Davidian, M. (2007) Comment: Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science 22, 569–573.Google ScholarPubMed
Uysal, S.D. (2011) Doubly robust IV estimation of the local average treatment effect. Unpublished.Google Scholar
Uysal, S.D. (2015) Doubly robust estimation of causal effects with multivalued treatments: An application to the returns to schooling. Journal of Applied Econometrics 30, 763–786.CrossRefGoogle Scholar
Vermeulen, K. & Vansteelandt, S. (2015) Bias-reduced doubly robust estimation. Journal of the American Statistical Association 110, 1024–1036.Google Scholar
Wooldridge, J.M. (2005) Violating ignorability of treatment by controlling for too many factors. Econometric Theory 21, 1026–1028.CrossRefGoogle Scholar
Wooldridge, J.M. (2007) Inverse probability weighted estimation for general missing data problems. Journal of Econometrics 141, 1281–1301.CrossRefGoogle Scholar
Wooldridge, J.M. (2010) Econometric Analysis of Cross Section and Panel Data, 2nd ed. MIT Press.Google Scholar