# 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
as

File Function: Abstract
---><---

As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

## References listed on IDEAS

as
1. 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.
2. Richard Blundell & Monica Costa Dias, 2009. "Alternative Approaches to Evaluation in Empirical Microeconomics," Journal of Human Resources, University of Wisconsin Press, vol. 44(3).
3. 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.
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. 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.
6. 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.
7. 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.
8. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
9. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
10. 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.
11. 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..
12. repec:adr:anecst:y:1999:i:55-56:p:05 is not listed on IDEAS
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.
Full references (including those not matched with items on IDEAS)

## Most related items

These are the items that most often cite the same works as this one and are cited by the same works as this one.
1. Esmeralda A. Ramalho & Richard J. Smith, 2013. "Discrete Choice Non-Response," Review of Economic Studies, Oxford University Press, vol. 80(1), pages 343-364.
2. Wooldridge, Jeffrey M., 2007. "Inverse probability weighted estimation for general missing data problems," Journal of Econometrics, Elsevier, vol. 141(2), pages 1281-1301, December.
3. Giovanni Forchini & Grant Hillier, 2005. "Ill-conditioned problems, Fisher information and weak instruments," CeMMAP working papers CWP04/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
4. Onur Başer & Joseph C. Gardiner & Cathy J. Bradley & Hüseyin Yüce & Charles Given, 2006. "Longitudinal analysis of censored medical cost data," Health Economics, John Wiley & Sons, Ltd., vol. 15(5), pages 513-525, May.
5. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
6. Wooldridge, Jeffrey M., 2020. "On the consistency of the logistic quasi-MLE under conditional symmetry," Economics Letters, Elsevier, vol. 194(C).
7. Prokhorov, Artem & Schmidt, Peter, 2009. "GMM redundancy results for general missing data problems," Journal of Econometrics, Elsevier, vol. 151(1), pages 47-55, July.
8. Schwiebert, Jörg & Wagner, Joachim, 2015. "A Generalized Two-Part Model for Fractional Response Variables with Excess Zeros," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113059, Verein für Socialpolitik / German Economic Association.
9. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
10. José M. R. Murteira & Joaquim J. S. Ramalho, 2016. "Regression Analysis of Multivariate Fractional Data," Econometric Reviews, Taylor & Francis Journals, vol. 35(4), pages 515-552, April.
11. Kyungchul Song, 2009. "Efficient Estimation of Average Treatment Effects under Treatment-Based Sampling," PIER Working Paper Archive 09-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
12. Wooldridge, Jeffrey M., 2014. "Quasi-maximum likelihood estimation and testing for nonlinear models with endogenous explanatory variables," Journal of Econometrics, Elsevier, vol. 182(1), pages 226-234.
13. John Mullahy, 2010. "Multivariate Fractional Regression Estimation of Econometric Share Models," NBER Working Papers 16354, National Bureau of Economic Research, Inc.
14. Huber, Martin & Lechner, Michael & Wunsch, Conny, 2013. "The performance of estimators based on the propensity score," Journal of Econometrics, Elsevier, vol. 175(1), pages 1-21.
15. Nour Meddahi & Eric Renault, 1998. "Quadratic M-Estimators for ARCH-Type Processes," CIRANO Working Papers 98s-29, CIRANO.
16. Bryan S. Graham & Cristine Campos De Xavier Pinto & Daniel Egel, 2012. "Inverse Probability Tilting for Moment Condition Models with Missing Data," Review of Economic Studies, Oxford University Press, vol. 79(3), pages 1053-1079.
17. Hitomi, Kohtaro & Nishiyama, Yoshihiko & Okui, Ryo, 2008. "A Puzzling Phenomenon In Semiparametric Estimation Problems With Infinite-Dimensional Nuisance Parameters," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1717-1728, December.
18. Huber, Martin & Lechner, Michael & Wunsch, Conny, 2010. "How to Control for Many Covariates? Reliable Estimators Based on the Propensity Score," IZA Discussion Papers 5268, Institute of Labor Economics (IZA).
19. Arvid Raknerud, 2002. "Identification, Estimation and Testing in Panel Data Models with Attrition: The Role of the Missing at Random Assumption," Discussion Papers 330, Statistics Norway, Research Department.
20. Giuliani, Elisa & Martinelli, Arianna & Rabellotti, Roberta, 2016. "Is Co-Invention Expediting Technological Catch Up? A Study of Collaboration between Emerging Country Firms and EU Inventors," World Development, Elsevier, vol. 77(C), pages 192-205.

### 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

## Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:portec:v:1:y:2002:i:2:d:10.1007_s10258-002-0008-x. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Springer Nature Abstracting and Indexing). General contact details of provider: http://www.springer.com .

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.