# Inverse probability weighted M-estimators for sample selection, attrition, and stratification

## Author

Listed:
• Jeffrey M. Wooldridge

(Michigan State University)

## Abstract

. I provide an overview of inverse probability weighted (IPW) M-estimators for cross section and two-period panel data applications. Under an ignorability assumption, I show that population parameters are identified, and provide straightforward $\sqrt{N}$ -consistent and asymptotically normal estimation methods. I show that estimating a binary response selection model by conditional maximum likelihood leads to a more efficient estimator than using known probabilities, a result that unifies several disparate results in the literature. But IPW estimation is not a panacea: in some important cases of nonresponse, unweighted estimators will be consistent under weaker ignorability assumptions.

## Suggested Citation

• 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.
• Handle: RePEc:spr:portec:v:1:y:2002:i:2:d:10.1007_s10258-002-0008-x
DOI: 10.1007/s10258-002-0008-x
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## References listed on IDEAS

as
1. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
2. James J. Heckman, 1976. "The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 475-492, National Bureau of Economic Research, Inc.
3. Richard Blundell & Monica Costa Dias, 2009. "Alternative Approaches to Evaluation in Empirical Microeconomics," Journal of Human Resources, University of Wisconsin Press, vol. 44(3).
4. Robert Moffitt & John Fitzgerald & Peter Gottschalk, 1999. "Sample Attrition in Panel Data: The Role of Selection on Observables," Annals of Economics and Statistics, GENES, issue 55-56, pages 129-152.
5. John Fitzgerald & Peter Gottschalk & Robert Moffitt, 1998. "An Analysis of Sample Attrition in Panel Data: The Michigan Panel Study of Income Dynamics," Journal of Human Resources, University of Wisconsin Press, vol. 33(2), pages 251-299.
6. 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.
7. Horowitz, Joel L. & Manski, Charles F., 1998. "Censoring of outcomes and regressors due to survey nonresponse: Identification and estimation using weights and imputations," Journal of Econometrics, Elsevier, vol. 84(1), pages 37-58, May.
8. 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.
9. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245, Elsevier.
10. Papke, Leslie E & Wooldridge, Jeffrey M, 1996. "Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 619-632, Nov.-Dec..
11. repec:adr:anecst:y:1999:i:55-56:p:05 is not listed on IDEAS
12. John Fitzgerald & Peter Gottschalk & Robert Moffitt, 1998. "An Analysis of the Impact of Sample Attrition on the Second Generation of Respondents in the Michigan Panel Study of Income Dynamics," Journal of Human Resources, University of Wisconsin Press, vol. 33(2), pages 300-344.
13. Jeffrey M. Wooldridge, 1999. "Asymptotic Properties of Weighted M-Estimators for Variable Probability Samples," Econometrica, Econometric Society, vol. 67(6), pages 1385-1406, November.
14. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
Full references (including those not matched with items on IDEAS)

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### Keywords

Attrition; Inverse probability weighting; M-estimator; Nonresponse; Sample selection; Treatment effect;
All these keywords.

### 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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