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Inverse probability weighted estimation for general missing data problems

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  • Wooldridge, Jeffrey M.

Abstract

I study inverse probability weighted M-estimation under a general missing data scheme. The cases covered that do not previously appear in the literature include M-estimation with missing data due to a censored survival time, propensity score estimation of the average treatment effect for linear exponential family quasi-log-likelihood functions, and variable probability sampling with observed retainment frequencies. I extend an important result known to hold in special cases: estimating the selection probabilities is generally more efficient than if the known selection probabilities could be used in estimation. For the treatment effect case, the setup allows for a simple characterization of a “double robustness” result due to Scharfstein, Rotnitzky, and Robins (1999): given appropriate choices for the conditional mean function and quasi-log-likelihood function, only one of the conditional mean or selection probability needs to be correctly specified in order to consistently estimate the average treatment effect.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 141 (2007)
Issue (Month): 2 (December)
Pages: 1281-1301

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Handle: RePEc:eee:econom:v:141:y:2007:i:2:p:1281-1301

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Web page: http://www.elsevier.com/locate/jeconom

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  1. Wooldridge, Jeffrey M., 2001. "Asymptotic Properties Of Weighted M-Estimators For Standard Stratified Samples," Econometric Theory, Cambridge University Press, vol. 17(02), pages 451-470, April.
  2. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," NBER Technical Working Papers 0251, National Bureau of Economic Research, Inc.
  3. Imbens, G., 1990. "An Efficient Method of Moments Estimator for Discrete Choice Models with Choice-Based Sampling," Discussion Paper 1990-9, Tilburg University, Center for Economic Research.
  4. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
  5. Honore, Bo & Khan, Shakeeb & Powell, James L., 2002. "Quantile regression under random censoring," Journal of Econometrics, Elsevier, vol. 109(1), pages 67-105, July.
  6. Murphy, Kevin M & Topel, Robert H, 1985. "Estimation and Inference in Two-Step Econometric Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(4), pages 370-79, October.
  7. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  8. Newey, Whitney K., 1984. "A method of moments interpretation of sequential estimators," Economics Letters, Elsevier, vol. 14(2-3), pages 201-206.
  9. Jeffrey M. Wooldridge, 1999. "Asymptotic Properties of Weighted M-Estimators for Variable Probability Samples," Econometrica, Econometric Society, vol. 67(6), pages 1385-1406, November.
  10. Jeffrey M. Wooldridge, 2002. "Inverse probability weighted M-estimators for sample selection, attrition and stratification," CeMMAP working papers CWP11/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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