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Using Heteroskedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models

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  • Arthur Lewbel

    ()
    (Boston College)

Abstract

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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File URL: http://fmwww.bc.edu/EC-P/wp587.pdf
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Bibliographic Info

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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Keywords: simultaneous; endogenous; identification; heteroscedasticity; measurement error; partly linear models;

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References

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  1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  2. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
  3. 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.
  4. 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.
  5. 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..
  6. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
  7. 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.
  8. Roberto Rigobon, 2001. "The Curse of Non-Investment Grade Countries," NBER Working Papers 8636, National Bureau of Economic Research, Inc.
  9. Olivier Jean Blanchard & Danny Quah, 1988. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," NBER Working Papers 2737, National Bureau of Economic Research, Inc.
  10. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-94, July.
  11. 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.
  12. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
  13. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
  14. 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.
  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. 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.
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Cited by:
  1. M. Shahe Emran & Forhad Shilpi, . "The Extent of the Market and Stages of Agricultural Specialization," Working Papers 2008-11, The George Washington University, Institute for International Economic Policy.
  2. Inas Rashad Kelly & Dhaval M. Dave & Jody L. Sindelar & William T. Gallo, 2011. "The Impact of Early Occupational Choice On Health Behaviors," NBER Working Papers 16803, National Bureau of Economic Research, Inc.
  3. Todd, Prono, 2009. "GARCH-Based Identification and Estimation of Triangular Systems," MPRA Paper 20032, University Library of Munich, Germany.
  4. Clive R. Belfield & Inas Rashad Kelly, 2010. "The Benefits of Breastfeeding Across the Early Years of Childhood," NBER Working Papers 16496, National Bureau of Economic Research, Inc.
  5. Prono, Todd, 2011. "When A Factor Is Measured with Error: The Role of Conditional Heteroskedasticity in Identifying and Estimating Linear Factor Models," MPRA Paper 33593, University Library of Munich, Germany.
  6. Leandro M. Magnusson & Sophocles Mavroeidis, 2011. "Identification Using Stability Restrictions," Working Papers 1116, Tulane University, Department of Economics.
  7. Okumura, Tsunao, 2011. "Nonparametric Estimation of Labor Supply and Demand Factors," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 174-185.
  8. Claudia Buch & Iris Kesternich & Alexander Lipponer & Monika Schnitzer, 2014. "Financial constraints and foreign direct investment: firm-level evidence," Review of World Economics (Weltwirtschaftliches Archiv), Springer, vol. 150(2), pages 393-420, May.
  9. Todd Prono, 2008. "GARCH-based identification and estimation of triangular systems," Risk and Policy Analysis Unit Working Paper QAU08-4, Federal Reserve Bank of Boston.
  10. Brian Krauth, 2011. "Bounding a linear causal effect using relative correlation restrictions," Discussion Papers dp11-02, Department of Economics, Simon Fraser University.

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