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Covariate Measurement Error:Bias Reduction under Response-based Sampling

  • Esmeralda Ramalho

    ()

    (Universidade de Evora, Departamento de Economia, CEFAGE-UE)

In this paper we propose a general framework to deal with the presence of covariate measurement error (CME) in response-based (RB) samples. Using Chesher’s (1991) methodology, we obtain a small error variance approximation for the contaminated sampling distributions that characterise RB samples with CME. Then, following Chesher (2000), we develop generalised method of moments (GMM) estimators that reduce the bias of the most well known likelihood-based estimators for RB samples which ignore the existence of CME and derive a score test to detect the presence of this type of measurement error. Our approach only requires the specification of the conditional distribution of the response variable given the latent covariates and the classical additive measurement error model assumption, the availability of information on both the marginal probability of the strata in the population and the variance of the measurement error not being essential. Monte Carlo evidence is presented which suggests that, in RB samples of moderate sizes, the bias-reduced GMM estimators perform well.

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Paper provided by University of Evora, CEFAGE-UE (Portugal) in its series CEFAGE-UE Working Papers with number 2009_15.

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Length: 32 pages
Date of creation: 2009
Date of revision:
Handle: RePEc:cfe:wpcefa:2009_15
Contact details of provider: Postal: Colégio Espírito SANTO
Phone: (351) 266 740 869
Web page: http://www.cefage.uevora.pt
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  1. Andrew Chesher & Christian Schluter, 2002. "Welfare Measurement and Measurement Error," Review of Economic Studies, Oxford University Press, vol. 69(2), pages 357-378.
  2. Imbens, G.W. & Lancaster, T., 1991. "Efficient estimation and stratified sampling," Discussion Paper 1991-45, Tilburg University, Center for Economic Research.
  3. Esmeralda Ramalho & Joaquim Ramalho, 2006. "Bias-Corrected Moment-Based Estimators for Parametric Models Under Endogenous Stratified Sampling," Econometric Reviews, Taylor & Francis Journals, vol. 25(4), pages 475-496.
  4. Andrew Chesher & J. M. C. Santos Silva, 2002. "Taste Variation in Discrete Choice Models," Review of Economic Studies, Oxford University Press, vol. 69(1), pages 147-168.
  5. Schennach, Susanne M., 2004. "Nonparametric Regression In The Presence Of Measurement Error," Econometric Theory, Cambridge University Press, vol. 20(06), pages 1046-1093, December.
  6. Wang, C. Y. & Wang, Suojin & Carroll, R. J., 1997. "Estimation in choice-based sampling with measurement error and bootstrap analysis," Journal of Econometrics, Elsevier, vol. 77(1), pages 65-86, March.
  7. Wooldridge, Jeffrey M., 2001. "Asymptotic Properties Of Weighted M-Estimators For Standard Stratified Samples," Econometric Theory, Cambridge University Press, vol. 17(02), pages 451-470, April.
  8. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, 01.
  9. Andrew Chesher & Richard J. Smith, 1997. "Likelihood Ratio Specification Tests," Econometrica, Econometric Society, vol. 65(3), pages 627-646, May.
  10. Susanne M Schennach, 2007. "Instrumental Variable Estimation of Nonlinear Errors-in-Variables Models," Econometrica, Econometric Society, vol. 75(1), pages 201-239, 01.
  11. Imbens, G.W., 1990. "An Efficient Method Of Moments Estimator For Descrete Choice Models With Choice-Based Sampling," Papers 9009, Tilburg - Center for Economic Research.
  12. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, 01.
  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.
  14. Manski, Charles F & Lerman, Steven R, 1977. "The Estimation of Choice Probabilities from Choice Based Samples," Econometrica, Econometric Society, vol. 45(8), pages 1977-88, November.
  15. Cosslett, Stephen R, 1981. "Maximum Likelihood Estimator for Choice-Based Samples," Econometrica, Econometric Society, vol. 49(5), pages 1289-1316, September.
  16. 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.
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