IDEAS home Printed from https://ideas.repec.org/p/ecm/nasm04/21.html
   My bibliography  Save this paper

Estimation of Nonlinear Models with Measurement Error Using Marginal Information

Author

Listed:
  • Geert Ridder
  • Yingyao Hu

Abstract

We consider the problem of consistent estimation of nonlinear models with mismeasured explanatory variables, when marginal information on the true values of these variables is available. The marginal distribution of the true variables is used to identify the distribution of the measurement error, and the distribution of the true variables conditional on the mismeasured and the other explanatory variables. The estimator is shown to be root-n consistent and normally distributed. The simulation results are in line with the asymptotic results. The semi-parametric MLE is applied to a duration model for AFDC welfare spells with misreported welfare benefits. The marginal distribution of welfare benefits is obtained from an administrative source

Suggested Citation

  • Geert Ridder & Yingyao Hu, 2004. "Estimation of Nonlinear Models with Measurement Error Using Marginal Information," Econometric Society 2004 North American Summer Meetings 21, Econometric Society.
    • Handle: RePEc:ecm:nasm04:21
    as

    Download full text from publisher

    File URL: http://www.eco.utexas.edu/~hu/EIV-marg-final.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Moffitt, Robert, 1992. "Incentive Effects of the U.S. Welfare System: A Review," Journal of Economic Literature, American Economic Association, vol. 30(1), pages 1-61, March.
    2. Meyer, Bruce D, 1990. "Unemployment Insurance and Unemployment Spells," Econometrica, Econometric Society, vol. 58(4), pages 757-782, July.
    3. 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.
    4. Angrist, Joshua D. & Krueger, Alan B., 1999. "Empirical strategies in labor economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 23, pages 1277-1366, Elsevier.
    5. 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 221-229, April.
    6. 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.
    7. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
    8. repec:mpr:mprres:2734 is not listed on IDEAS
    9. Ridder, Geert & Moffitt, Robert, 2007. "The Econometrics of Data Combination," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 75, Elsevier.
    10. 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.
    11. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    12. 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.
    13. Bound, John & Krueger, Alan B, 1991. "The Extent of Measurement Error in Longitudinal Earnings Data: Do Two Wrongs Make a Right?," Journal of Labor Economics, University of Chicago Press, vol. 9(1), pages 1-24, January.
    14. 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.
    15. 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.
    16. 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.
    17. Cheng Hsiao, 1991. "Identification and Estimation of Dichotomous Latent Variables Models Using Panel Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(4), pages 717-731.
    18. 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 523-542, May.
    19. 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.
    20. Hsiao, Cheng, 1989. "Consistent estimation for some nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 41(1), pages 159-185, May.
    21. David T. Ellwood, 1986. "Targeting Would-Be Long-Term Recipients of AFDC," Mathematica Policy Research Reports 35f03eda0fa0455aa0dc255fb, Mathematica Policy Research.
    22. 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.
    23. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    24. 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.
    25. 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.
    26. Joel L. Horowitz & Marianthi Markatou, 1996. "Semiparametric Estimation of Regression Models for Panel Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(1), pages 145-168.
    27. Wang, Liqun, 1998. "Estimation of censored linear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 84(2), pages 383-400, June.
    28. repec:mpr:mprres:652 is not listed on IDEAS
    29. Whitney K. Newey, 2001. "Flexible Simulated Moment Estimation Of Nonlinear Errors-In-Variables Models," The Review of Economics and Statistics, MIT Press, vol. 83(4), pages 616-627, November.
    30. 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.
    31. 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, December.
    32. Blank, Rebecca M., 1989. "Analyzing the length of welfare spells," Journal of Public Economics, Elsevier, vol. 39(3), pages 245-273, August.
    33. Joel L. Horowitz & Marianthi Markatou, 1993. "Semiparametric Estimation Of Regression Models For Panel Data," Econometrics 9309001, University Library of Munich, Germany.
    34. Thomas J. Kane & Cecilia Rouse & Douglas Staiger, 1999. "Estimating Returns to Schooling When Schooling is Misreported," Working Papers 798, Princeton University, Department of Economics, Industrial Relations Section..
    35. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
    36. Bound, John & Brown, Charles & Duncan, Greg J & Rodgers, Willard L, 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 345-368, July.
    37. Bekker, Paul A, 1986. "Identification in the Linear Errors in Variables Model: Comment," Econometrica, Econometric Society, vol. 54(1), pages 215-217, January.
    38. 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.
    39. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    2. Aprajit Mahajan, 2009. "Estimating Price Elasticities with Nonlinear Errors in Variables," The Review of Economics and Statistics, MIT Press, vol. 91(4), pages 793-805, November.
    3. Chen, Xiaohong & Hu, Yingyao & Lewbel, Arthur, 2008. "Nonparametric identification of regression models containing a misclassified dichotomous regressor without instruments," Economics Letters, Elsevier, vol. 100(3), pages 381-384, September.
    4. Yingyao Hu & Arthur Lewbel & Susanne M. Schennach, 2007. "Nonparametric identification of the classical errors-in-variables model without side information," CeMMAP working papers CWP14/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Devereux, Paul J. & Tripathi, Gautam, 2009. "Optimally combining censored and uncensored datasets," Journal of Econometrics, Elsevier, vol. 151(1), pages 17-32, July.
    6. Xiaohong Chen & Yingyao Hu, 2006. "Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors," Cowles Foundation Discussion Papers 1590, Cowles Foundation for Research in Economics, Yale University.
    7. Xiaohong Chen & Yingyao Hu & Arthur Lewbel, 2007. "Nonparametric identification and estimation of nonclassical errors-in-variables models without additional information," CeMMAP working papers CWP18/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Shiu, Ji-Liang, 2016. "Identification and estimation of endogenous selection models in the presence of misclassification errors," Economic Modelling, Elsevier, vol. 52(PB), pages 507-518.
    9. Natalia, Khorunzhina & Wayne Roy, Gayle, 2011. "Heterogenous intertemporal elasticity of substitution and relative risk aversion: estimation of optimal consumption choice with habit formation and measurement errors," MPRA Paper 34329, University Library of Munich, Germany.

    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. Yingyao Hu & Geert Ridder, 2012. "Estimation of nonlinear models with mismeasured regressors using marginal information," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(3), pages 347-385, April.
    2. Xiaohong Chen & Yingyao Hu, 2006. "Identification and Inference of Nonlinear Models Using Two Samples with Arbitrary Measurement Errors," Cowles Foundation Discussion Papers 1590, Cowles Foundation for Research in Economics, Yale University.
    3. Susanne M. Schennach, 2012. "Measurement error in nonlinear models - a review," CeMMAP working papers 41/12, Institute for Fiscal Studies.
    4. Xiaohong Chen & Han Hong & Denis Nekipelov, 2011. "Nonlinear Models of Measurement Errors," Journal of Economic Literature, American Economic Association, vol. 49(4), pages 901-937, December.
    5. Song, Suyong, 2015. "Semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors," Journal of Econometrics, Elsevier, vol. 185(1), pages 95-109.
    6. Hu, Yingyao, 2008. "Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution," Journal of Econometrics, Elsevier, vol. 144(1), pages 27-61, May.
    7. Chen, Xiaohong & Hu, Yingyao & Lewbel, Arthur, 2008. "Nonparametric identification of regression models containing a misclassified dichotomous regressor without instruments," Economics Letters, Elsevier, vol. 100(3), pages 381-384, September.
    8. Xiaohong Chen & Yingyao Hu & Arthur Lewbel, 2007. "Nonparametric Identification and Estimation of Nonclassical Errors-in-Variables Models Without Additional Information," Boston College Working Papers in Economics 676, Boston College Department of Economics.
    9. Daniel Wilhelm, 2018. "Testing for the presence of measurement error," CeMMAP working papers CWP45/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Xiaohong Chen & Han Hong & Alessandro Tarozzi, 2008. "Semiparametric Efficiency in GMM Models of Nonclassical Measurement Errors, Missing Data and Treatment Effects," Cowles Foundation Discussion Papers 1644, Cowles Foundation for Research in Economics, Yale University.
    11. Takahide Yanagi, 2019. "Inference on local average treatment effects for misclassified treatment," Econometric Reviews, Taylor & Francis Journals, vol. 38(8), pages 938-960, September.
    12. Han Hong, 2010. "Comment for identification and estimation of nonlinear models using two samples with nonclassical measurement errors, by Carroll, Chen and Hu," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 405-408.
    13. Anish Agarwal & Rahul Singh, 2021. "Causal Inference with Corrupted Data: Measurement Error, Missing Values, Discretization, and Differential Privacy," Papers 2107.02780, arXiv.org, revised Feb 2024.
    14. van der Klaauw, Wilbert, 2005. "Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 154-157, April.
    15. Qing Li, 2014. "Identifiability of mean-reverting measurement error with instrumental variable," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(2), pages 118-129, May.
    16. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, January.
    17. de Nicola, Francesca & Giné, Xavier, 2014. "How accurate are recall data? Evidence from coastal India," Journal of Development Economics, Elsevier, vol. 106(C), pages 52-65.
    18. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
    19. Hu, Yingyao & Schennach, Susanne & Shiu, Ji-Liang, 2022. "Identification of nonparametric monotonic regression models with continuous nonclassical measurement errors," Journal of Econometrics, Elsevier, vol. 226(2), pages 269-294.
    20. Jeremy J. Nalewaik, 2014. "Missing Variation in the Great Moderation: Lack of Signal Error and OLS Regression," Finance and Economics Discussion Series 2014-27, Board of Governors of the Federal Reserve System (U.S.).

    More about this item

    Keywords

    measurement error model; marginal information; deconvolution;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • I38 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Government Programs; Provision and Effects of Welfare Programs

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:ecm:nasm04:21. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.