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Inverse probability weighted estimation for general missing data problems

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  • Jeffrey M. Wooldridge

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 scoreestimation 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 andquasi-log-likelihood function, only one of the conditional mean or selection probability needs to be correctly specified in order to consistently estimate the average treatmenteffect.

Suggested Citation

  • Jeffrey M. Wooldridge, 2004. "Inverse probability weighted estimation for general missing data problems," CeMMAP working papers 05/04, Institute for Fiscal Studies.
    • Handle: RePEc:azt:cemmap:05/04
    DOI: 10.1920/wp.cem.2004.0504
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    References listed on IDEAS

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    3. Honore, Bo & Khan, Shakeeb & Powell, James L., 2002. "Quantile regression under random censoring," Journal of Econometrics, Elsevier, vol. 109(1), pages 67-105, July.
    4. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    5. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    6. Jeffrey M. Wooldridge, 2002. "Inverse probability weighted M-estimators for sample selection, attrition, and stratification," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 1(2), pages 117-139, August.
    7. Wooldridge, Jeffrey M., 2001. "Asymptotic Properties Of Weighted M-Estimators For Standard Stratified Samples," Econometric Theory, Cambridge University Press, vol. 17(2), pages 451-470, April.
    8. Murphy, Kevin M & Topel, Robert H, 2002. "Estimation and Inference in Two-Step Econometric Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 88-97, January.
    9. Jeffrey M. Wooldridge, 2002. "Inverse probability weighted M-estimators for sample selection, attrition, and stratification," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 1(2), pages 117-139, August.
    10. Jeffrey M. Wooldridge, 1999. "Asymptotic Properties of Weighted M-Estimators for Variable Probability Samples," Econometrica, Econometric Society, vol. 67(6), pages 1385-1406, November.
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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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