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Partial Identification of Probability Distributions with Misclassified Data

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Author Info
Molinari, Francesca (Cornell U)

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Abstract

This paper addresses the problem of data errors in discrete variables. When data errors occur, the observed variable is a misclassified version of the variable of interest, whose distribution is not identified. Inferential problems caused by data errors have been conceptualized through convolution and mixture models. This paper introduces the direct misclassification approach. The approach is based on the observation that in the presence of classification errors, the relation between the distribution of the "true" but unobservable variable and its misclassified representation is given by a linear system of simultaneous equations, in which the coefficient matrix is the matrix of misclassification probabilities. Formalizing the problem in these terms allows one to incorporate any prior information--e.g., validation studies, economic theory, social and cognitive psychology--into the analysis through sets of restrictions on the matrix of misclassification probabilities. Such information can have strong identifying power; the direct misclassification approach fully exploits it to derive identification regions for any real functional of the distribution of interest. A method for estimating the identification regions and construct their confidence sets is given, and illustrated with an empirical analysis of the distribution of pension plan types using data from the Health and Retirement Study.

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Paper provided by Cornell University, Center for Analytic Economics in its series Working Papers with number 05-10.

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Date of creation: Apr 2005
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Handle: RePEc:ecl:corcae:05-10

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Find related papers by JEL classification:
C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
J26 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Retirement; Retirement Policies

References listed on IDEAS
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  1. John Pepper & Brent Kreider, 2001. "Inferring Disability Status from Corrupt Data," Virginia Economics Online Papers 354, University of Virginia, Department of Economics. [Downloadable!]
    Other versions:
  2. Klepper, Steven & Leamer, Edward E, 1984. "Consistent Sets of Estimates for Regressions with Errors in All Variables," Econometrica, Econometric Society, vol. 52(1), pages 163-83, January. [Downloadable!] (restricted)
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    Other versions:
  6. Robert P. Sherman & Jeff Dominitz, 2006. "Identification and estimation of bounds on school performance measures: a nonparametric analysis of a mixture model with verification," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(8), pages 1295-1326. [Downloadable!]
  7. Jason Abrevaya & Jerry A. Hausman, 1999. "Semiparametric Estimation with Mismeasured Dependent Variables: An Application to Duration Models for Unemployment Spells," Annales d'Economie et de Statistique, ADRES, issue 55-56, pages 10, Juillet-D. [Downloadable!]
  8. Alan L. Gustman & Olivia S. Mitchell & Andrew A. Samwick & Thomas L. Steinmeier, . "Evaluating Pension Entitlements," Pension Research Council Working Papers 98-20, Wharton School Pension Research Council, University of Pennsylvania.
  9. Ramalho, Esmeralda A., 2002. "Regression models for choice-based samples with misclassification in the response variable," Journal of Econometrics, Elsevier, vol. 106(1), pages 171-201, January. [Downloadable!] (restricted)
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  13. 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.. [Downloadable!]
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  15. Card, David, 1996. "The Effect of Unions on the Structure of Wages: A Longitudinal Analysis," Econometrica, Econometric Society, vol. 64(4), pages 957-79, July. [Downloadable!] (restricted)
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  17. Blundell, Richard William & Gosling, Amanda & Ichimura, Hidehiko & Meghir, Costas, 2004. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," CEPR Discussion Papers 4705, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  18. repec:att:wimass:199525 is not listed on IDEAS
  19. Bo E. Honoré & Elie Tamer, 2002. "Bounds on Parameters in Dynamic Discrete Choice Models," CAM Working Papers 2004-23, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics, revised Aug 2004. [Downloadable!]
  20. Lewbel, Arthur, 2000. "Identification Of The Binary Choice Model With Misclassification," Econometric Theory, Cambridge University Press, vol. 16(04), pages 603-609, August. [Downloadable!]
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  21. Hausman, J. A. & Abrevaya, Jason & Scott-Morton, F. M., 1998. "Misclassification of the dependent variable in a discrete-response setting," Journal of Econometrics, Elsevier, vol. 87(2), pages 239-269, September. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. Bo E. Honore & Adriana Lleras Muney, 2004. "Bounds in Competing Risks Models and the War on Cancer," NBER Working Papers 10963, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  2. Gundersen, Craig & Kreider, Brent, 2008. "Bounding the Effects of Food Insecurity on Children's Health Outcomes," Staff General Research Papers 13008, Iowa State University, Department of Economics. [Downloadable!]
  3. 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, Yale University. [Downloadable!]
  4. Kreider, Brent, 2006. "Partially Identifying the Prevalence of Health Insurance Given Contaminated Sampling Response Error," Staff General Research Papers 12588, Iowa State University, Department of Economics. [Downloadable!]
  5. Arthur Lewbel, 2003. "Estimation of Average Treatment Effects With Misclassification," Boston College Working Papers in Economics 556, Boston College Department of Economics, revised 04 Sep 2006. [Downloadable!]
    Other versions:
  6. Fitzenberger, Bernd & Osikominu, Aderonke & Völter, Robert, 2005. "Imputation Rules to Improve the Education Variable in the IAB Employment Subsample," ZEW Discussion Papers 05-10, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research. [Downloadable!]
    Other versions:
  7. Gundersen, Craig & Kreider, Brent, 2006. "Food Stamps and Food Insecurity: What Can Be Learned in the Presence of Non-classical Measurement Error?," Staff General Research Papers 12690, Iowa State University, Department of Economics.
    Other versions:
  8. Cheti Nicoletti & Franco Peracchi & Francesca Foliano, 2009. "Estimating Income Poverty in the Presence of Missing Data and Measurement Error," CEIS Research Paper 145, Tor Vergata University, CEIS, revised 30 Sep 2009. [Downloadable!]
  9. Arie Beresteanu & Francesca Molinari, 2006. "Asymptotic properties for a class of partially identified models," CeMMAP working papers CWP10/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  10. Guido Imbens & Charles F. Manski, 2003. "Confidence intervals for partially identified parameters," CeMMAP working papers CWP09/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  11. Kreider, Brent & Pepper, John V., 2006. "Identification of Expected Outcomes in a Data Error Mixing Model with Multiplicative Mean Independence," Staff General Research Papers 12496, Iowa State University, Department of Economics. [Downloadable!]
  12. repec:ese:iserwp: is not listed on IDEAS
  13. Brent Kreider & John Pepper, 2008. "Inferring disability status from corrupt data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(3), pages 329-349. [Downloadable!]
    Other versions:
  14. Erich Battistin & Barbara Sianesi, 2006. "Misreported schooling and returns to education: evidence from the UK," CeMMAP working papers CWP07/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
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