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Identification and estimation of nonlinear models with misclassification error using instrumental variables: A general solution

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  • Hu, Yingyao

Abstract

This paper provides a general solution to the problem of identification and estimation of nonlinear models with misclassification error in a general discrete explanatory variable using instrumental variables. The misclassification error is allowed to be correlated with all the explanatory variables in the model. It is not enough to identify the model by simply generalizing the identification in the binary case with a claim that the number of restrictions is no less than that of the unknowns. Such a claim requires solving a complicated nonlinear system of equations. This paper introduces a matrix diagonalization technique which allows one to easily find the unique solution of the system. The solution shows that the latent model can be expressed as an explicit function of directly observed distribution functions. Therefore, the latent model is nonparametrically identifiable and directly estimable using instrumental variables. The results show that certain monotonicity restrictions on the latent model may lead to its identification with virtually no restrictions on the misclassification probabilities. An alternative identification condition suggests that the nonparametric identification may rely on the belief that people always have a higher probability of telling the truth than of misreporting. The nonparametric identification in this paper directly leads to a -consistent semiparametric estimator. The Monte Carlo simulation and empirical illustration show that the estimator performs well with a finite sample and real data.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 144 (2008)
Issue (Month): 1 (May)
Pages: 27-61

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Handle: RePEc:eee:econom:v:144:y:2008:i:1:p:27-61

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Web page: http://www.elsevier.com/locate/jeconom

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References

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Citations

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Cited by:
  1. Yonghong An & Michael R. Baye & Yingyao Hu & John Morgan & Matt Shum, 2010. "Horizontal Mergers of Online Firms: Structural Estimation and Competitive Effects," Economics Working Paper Archive 564, The Johns Hopkins University,Department of Economics.
  2. Erich Battistin & Andrew Chesher, 2009. "Treatment effect estimation with covariate measurement error," CeMMAP working papers CWP25/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  3. Yingyao Hu & Matthew Shum, 2008. "Nonparametric identification of dynamic models with unobserved state variables," CeMMAP working papers CWP13/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Yingyao Hu & Yutaka Kayaba & Matt Shum, 2010. "Nonparametric Learning Rules from Bandit Experiments: The Eyes have it!," Economics Working Paper Archive 560, The Johns Hopkins University,Department of Economics.
  5. Deng, Ping & Hu, Yingyao, 2009. "Bounding the effect of a dichotomous regressor with arbitrary measurement errors," Economics Letters, Elsevier, vol. 105(3), pages 256-260, December.
  6. Yingyao Hu & Matthew Shum & Wei Tan, 2010. "A Simple Estimator for Dynamic Models with Serially Correlated Unobservables," Economics Working Paper Archive 558, The Johns Hopkins University,Department of Economics.
  7. Lamy, Laurent, 2012. "The econometrics of auctions with asymmetric anonymous bidders," Journal of Econometrics, Elsevier, vol. 167(1), pages 113-132.
  8. Shuaizhang Feng & Yingyao Hu, 2012. "Misclassification Errors and the Underestimation of the U.S. Unemployment Rate," Economics Working Paper Archive 595, The Johns Hopkins University,Department of Economics.
  9. El-Attar, Mayssun, 2009. "Could Education Promote the Israeli-Palestinian Peace Process?," IZA Discussion Papers 4447, Institute for the Study of Labor (IZA).
  10. Yonghong An & Michael R Baye & Yingyao Hu & John Morgan & Matt Shum, 2010. "Identification and Estimation of Online Price Competition with an Unknown Number of Firms," Working Papers 2010-17, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy, revised Nov 2012.
  11. Hu, Yingyao & McAdams, David & Shum, Matthew, 2013. "Identification of first-price auctions with non-separable unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 174(2), pages 186-193.
  12. Cameron McIntosh, 2014. "The presence of an error term does not preclude causal inference in regression: a comment on Krause (2012)," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(1), pages 243-250, January.
  13. Yingying Dong, 2012. "Regression Discontinuity Applications with Rounding Errors in the Running Variable," Working Papers 111206, University of California-Irvine, Department of Economics.
  14. An, Yonghong & Hu, Yingyao & Shum, Matthew, 2010. "Estimating first-price auctions with an unknown number of bidders: A misclassification approach," Journal of Econometrics, Elsevier, vol. 157(2), pages 328-341, August.
  15. Xavier d'Haultfoeuille & Philippe Fevrier, 2010. "Identification of Mixture Models Using Support Variations," Working Papers 2010-12, Centre de Recherche en Economie et Statistique.
  16. Fu, Lianyan & Gao, Wei & Shi, Ning-Zhong, 2011. "Estimation of relative average treatment effects with misclassification," Economics Letters, Elsevier, vol. 111(1), pages 95-98, April.
  17. Stephane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Nonparametric spectral-based estimation of latent structures," CeMMAP working papers CWP18/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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