# Estimation of Nonlinear Models with Mismeasured Regressors Using Marginal Information

• Yingyao Hu
• Geert Ridder

## Abstract

We consider the estimation of nonlinear models with mismeasured explanatory variables, when information on the marginal distribution of the true values of these variables is available. We derive a semi-parametric MLE that is shown to be $\sqrt{n}$ consistent and asymptotically normally distributed. In a simulation experiment we find that the finite sample distribution of the estimator is close to the asymptotic approximation. The semi-parametric MLE is applied to a duration model for AFDC welfare spells with misreported welfare benefits. The marginal distribution of the correctly measured welfare benefits is obtained from an administrative source.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

## Bibliographic Info

Paper provided by The Johns Hopkins University,Department of Economics in its series Economics Working Paper Archive with number 554.

as
in new window

 Length: Date of creation: Jun 2009 Date of revision: Handle: RePEc:jhu:papers:554 Contact details of provider: Postal: 3400 North Charles Street Baltimore, MD 21218Phone: 410-516-7601Fax: 410-516-7600Web page: http://www.econ.jhu.eduMore information through EDIRC

## References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
1. Meyer, Bruce D, 1990. "Unemployment Insurance and Unemployment Spells," Econometrica, Econometric Society, vol. 58(4), pages 757-82, July.
2. Robert A. Moffitt, 2003. "The Temporary Assistance for Needy Families Program," NBER Chapters, in: Means-Tested Transfer Programs in the United States, pages 291-364 National Bureau of Economic Research, Inc.
3. Hausman, J. A. & Newey, W. K. & Powell, J. L., 1995. "Nonlinear errors in variables Estimation of some Engel curves," Journal of Econometrics, Elsevier, vol. 65(1), pages 205-233, January.
4. Horowitz, Joel L & Markatou, Marianthi, 1996. "Semiparametric Estimation of Regression Models for Panel Data," Review of Economic Studies, Wiley Blackwell, vol. 63(1), pages 145-68, January.
5. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
6. repec:cup:cbooks:9780521496032 is not listed on IDEAS
7. Arthur Lewbel, 1997. "Constructing Instruments for Regressions with Measurement Error when no Additional Data are Available, with an Application to Patents and R&D," Econometrica, Econometric Society, vol. 65(5), pages 1201-1214, September.
8. Xiaohong Chen & Han Hong & Elie Tamer, 2005. "Measurement Error Models with Auxiliary Data," Review of Economic Studies, Oxford University Press, vol. 72(2), pages 343-366.
9. Hsiao, Cheng & Wang, Q Kevin, 2000. "Estimation of Structural Nonlinear Errors-in-Variables Models by Simulated Least-Squares Method," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(2), pages 523-42, May.
10. John M. Barron & Mark C. Berger & Dan A. Black, 1997. "On-the-Job Training," Books from Upjohn Press, W.E. Upjohn Institute for Employment Research, number ojt, June.
11. Mathiowetz, Nancy A & Duncan, Greg J, 1988. "Out of Work, Out of Mind: Response Errors in Retrospective Reports of Unemployment," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(2), pages 221-29, April.
12. John Bound & Alan B. Krueger, 1989. "The Extent of Measurement Error In Longitudinal Earnings Data: Do Two Wrongs Make A Right?," NBER Working Papers 2885, National Bureau of Economic Research, Inc.
13. Joshua Angrist & Alan Krueger, 1998. "Empirical Strategies in Labor Economics," Working papers 98-7, Massachusetts Institute of Technology (MIT), Department of Economics.
14. Whitney Newey, 1999. "Flexible Simulated Moment Estimation of Nonlinear Errors-in-Variables Models," Working papers 99-02, Massachusetts Institute of Technology (MIT), Department of Economics.
15. Bound, John & Brown, Charles & Mathiowetz, Nancy, 2001. "Measurement error in survey data," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 59, pages 3705-3843 Elsevier.
16. Blank, Rebecca M & Ruggles, Patricia, 1994. "Short-Term Recidivism among Public-Assistance Recipients," American Economic Review, American Economic Association, vol. 84(2), pages 49-53, May.
17. Hsiao, Ch., 1989. "Identification and Estimation of Dichotomous Latent Variables Models using Panel Data," Discussion Paper 1989-44, Tilburg University, Center for Economic Research.
18. John Bound & Charles Brown & Greg J. Duncan & Willard L Rodgers, 1989. "Measurement Error In Cross-Sectional and Longitudinal Labor Market Surveys: Results From Two Validation Studies," NBER Working Papers 2884, National Bureau of Economic Research, Inc.
19. Bound, John, et al, 1994. "Evidence on the Validity of Cross-Sectional and Longitudinal Labor Market Data," Journal of Labor Economics, University of Chicago Press, vol. 12(3), pages 345-68, July.
20. Newey, W.K., 1991. "The Asymptotic Variance of Semiparametric Estimators," Working papers 583, Massachusetts Institute of Technology (MIT), Department of Economics.
21. Bound, John & Griliches, Zvi & Hall, Bronwyn H, 1986. "Wages, Schooling and IQ of Brothers and Sisters: Do the Family Factors Differ?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 77-105, February.
22. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
23. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, 01.
24. Hsiao, C., 1988. "Consistent Estimation For Some Nonlinear Errors-In- Variables Models," Papers m8810, Southern California - Department of Economics.
25. Wang, Liqun, 1998. "Estimation of censored linear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 84(2), pages 383-400, June.
26. Susanne M. Schennach, 2004. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometric Society 2004 North American Summer Meetings 602, Econometric Society.
27. Murphy, S. A. & Van Der Vaart, A. W., 1996. "Likelihood Inference in the Errors-in-Variables Model," Journal of Multivariate Analysis, Elsevier, vol. 59(1), pages 81-108, October.
28. Sepanski, J. H. & Carroll, R. J., 1993. "Semiparametric quasilikelihood and variance function estimation in measurement error models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 223-256, July.
29. Joel L. Horowitz & Marianthi Markatou, 1993. "Semiparametric Estimation Of Regression Models For Panel Data," Econometrics 9309001, EconWPA.
30. Hoynes, Hilary & MaCurdy, Thomas, 1994. "Has the Decline in Benefits Shortened Welfare Spells?," American Economic Review, American Economic Association, vol. 84(2), pages 43-48, May.
31. Hilary Williamson Hoynes, 2000. "Local Labor Markets And Welfare Spells: Do Demand Conditions Matter?," The Review of Economics and Statistics, MIT Press, vol. 82(3), pages 351-368, August.
32. Hausman, Jerry A. & Newey, Whitney K. & Ichimura, Hidehiko & Powell, James L., 1991. "Identification and estimation of polynomial errors-in-variables models," Journal of Econometrics, Elsevier, vol. 50(3), pages 273-295, December.
33. Thomas Augustin, 2004. "An Exact Corrected Log-Likelihood Function for Cox's Proportional Hazards Model under Measurement Error and Some Extensions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 43-50.
34. Yingyao Hu & Susanne Schennach, 2006. "Identification and estimation of nonclassical nonlinear errors-in-variables models with continuous distributions using instruments," CeMMAP working papers CWP17/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
35. Thomas J. Kane & Cecilia Elena Rouse & Douglas Staiger, 1999. "Estimating Returns to Schooling When Schooling is Misreported," NBER Working Papers 7235, National Bureau of Economic Research, Inc.
36. John M. Fitzgerald, 1995. "Local labor markets and local area effects on welfare duration," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 14(1), pages 43-67.
37. Blank, Rebecca M., 1989. "Analyzing the length of welfare spells," Journal of Public Economics, Elsevier, vol. 39(3), pages 245-273, August.
38. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
Full references (including those not matched with items on IDEAS)

## Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

## Corrections

When requesting a correction, please mention this item's handle: RePEc:jhu:papers:554. 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: (None)

The email address of this maintainer does not seem to be valid anymore. Please ask None to update the entry or send us the correct address

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.