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Using Heteroskedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models

  • Arthur Lewbel

    ()

    (Boston College)

This paper proposes a new method of obtaining identification in mismeasured regressor models, triangular systems, and simultaneous equation systems. The method may be used in applications where other sources of identification such as instrumental variables or repeated measurements are not available. Associated estimators take the form of two stage least squares or generalized method of moments. Identification comes from a heteroskedastic covariance restriction that is shown to be a feature of many models of endogeneity or mismeasurement. Identification is also obtained for semiparametric partly linear models, and associated estimators are provided. Set identification bounds are derived for cases where point identifying assumptions fail to hold. An empirical application estimating Engel curves is provided.

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Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 587.

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Date of creation: 19 Dec 2003
Date of revision: 15 Dec 2010
Publication status: published, Journal of Business and Economic Statistics, 2012, 30, 67-80
Handle: RePEc:boc:bocoec:587
Note: Previously circulated as "Identification of Heteroskedastic Endogenous or Mismeasured Regressor Models."
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  1. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-73, September.
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  3. Otsu, Taisuke, 2011. "Empirical Likelihood Estimation Of Conditional Moment Restriction Models With Unknown Functions," Econometric Theory, Cambridge University Press, vol. 27(01), pages 8-46, February.
  4. David Card, 1993. "Using Geographic Variation in College Proximity to Estimate the Return to Schooling," Working Papers 696, Princeton University, Department of Economics, Industrial Relations Section..
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  7. Erickson, Timothy & Whited, Toni M., 2002. "Two-Step Gmm Estimation Of The Errors-In-Variables Model Using High-Order Moments," Econometric Theory, Cambridge University Press, vol. 18(03), pages 776-799, June.
  8. 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.
  9. Dagenais, Marcel G. & Dagenais, Denyse L., 1997. "Higher moment estimators for linear regression models with errors in the variables," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 193-221.
  10. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
  11. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
  12. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
  13. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
  14. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-94, September.
  15. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  16. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-94, July.
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