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Errors in Variables in Linear Systems

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  • Leamer, Edward E

Abstract

This paper extends the simple errors-in-variable bound to the setting of systems of equations. Both diagonal and nondiagonal measurement error covariance matrices are considered. In the nondiagonal case, the analogue of the simple errors-in-variable interval of estimates is an ellipsoid with diagonal equal to the line segment connecting t he direct least squares with a two-stage least-squares estimate. For the diagonal case, the set of estimates under some conditions must li e within the convex hull of 2k points. Copyright 1987 by The Econometric Society.

Suggested Citation

  • Leamer, Edward E, 1987. "Errors in Variables in Linear Systems," Econometrica, Econometric Society, vol. 55(4), pages 893-909, July.
    • Handle: RePEc:ecm:emetrp:v:55:y:1987:i:4:p:893-909
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    Cited by:

    1. Jeremy J. Nalewaik, 2014. "Missing Variation in the Great Moderation: Lack of Signal Error and OLS Regression," Finance and Economics Discussion Series 2014-27, Board of Governors of the Federal Reserve System (U.S.).
    2. Hu, Yingyao, 2006. "Bounding parameters in a linear regression model with a mismeasured regressor using additional information," Journal of Econometrics, Elsevier, vol. 133(1), pages 51-70, July.
    3. Christian Bontemps & Thierry Magnac & Eric Maurin, 2012. "Set Identified Linear Models," Econometrica, Econometric Society, vol. 80(3), pages 1129-1155, May.
    4. Paris, Quirino & Caputo, Michael R., 2004. "Efficient Estimates Of A Model Of Production And Cost," 2004 Annual meeting, August 1-4, Denver, CO 20358, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    5. Chalak, Karim & Kim, Daniel, 2020. "Measurement error in multiple equations: Tobin’s q and corporate investment, saving, and debt," Journal of Econometrics, Elsevier, vol. 214(2), pages 413-432.
    6. Rachida Hennani & Michel Terraza, 2012. "Value-at-Risk stressée chaotique d’un portefeuille bancaire," Working Papers 12-23, LAMETA, Universtiy of Montpellier, revised Sep 2012.
    7. Molinari, Francesca, 2020. "Microeconometrics with partial identification," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 355-486, Elsevier.
    8. Carmichael, Benoît & Coën, Alain, 2008. "Asset pricing models with errors-in-variables," Journal of Empirical Finance, Elsevier, vol. 15(4), pages 778-788, September.
    9. Thierry Magnac, 2013. "Identification partielle : méthodes et conséquences pour les applications empiriques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 89(4), pages 233-258.
    10. Paris, Quirino & Caputo, Michael R., 2004. "A Nonlinear Generalized Additive Error Model of Production and Cost," Working Papers 93743, University of California, Davis, Department of Agricultural and Resource Economics.
    11. Coën, Alain & Hübner, Georges, 2009. "Risk and performance estimation in hedge funds revisited: Evidence from errors in variables," Journal of Empirical Finance, Elsevier, vol. 16(1), pages 112-125, January.
    12. Hyslop, Dean R & Imbens, Guido W, 2001. "Bias from Classical and Other Forms of Measurement Error," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 475-481, October.
    13. Chalak, Karim, 2024. "Nonparametric Gini-Frisch bounds," Journal of Econometrics, Elsevier, vol. 238(1).
    14. Wegge, Leon L., 1996. "Local identifiability of the factor analysis and measurement error model parameter," Journal of Econometrics, Elsevier, vol. 70(2), pages 351-382, February.
    15. Thierry Magnac & Eric Maurin, 2008. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 835-864.
    16. Sadefo Kamdem, J. & Mbairadjim Moussa, A. & Terraza, M., 2012. "Fuzzy risk adjusted performance measures: Application to hedge funds," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 702-712.
    17. Francesca Molinari, 2019. "Econometrics with Partial Identification," CeMMAP working papers CWP25/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Francis J. DiTraglia & Camilo García-Jimeno, 2021. "A Framework for Eliciting, Incorporating, and Disciplining Identification Beliefs in Linear Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 1038-1053, October.
    19. Hong, Han & Tamer, Elie, 2003. "A simple estimator for nonlinear error in variable models," Journal of Econometrics, Elsevier, vol. 117(1), pages 1-19, November.
    20. Erickson, Timothy & Whited, Toni M., 2005. "Proxy-quality thresholds: Theory and applications," Finance Research Letters, Elsevier, vol. 2(3), pages 131-151, September.
    21. Heij, C. & Scherrer, W. & Destler, M., 1996. "System Identification by Dynamic Factor Models," Econometric Institute Research Papers EI 9501-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    22. Bent Christensen & Jesper Bagger, 2014. "Wage and Productivity Dispersion: The Roles of Rent Sharing, Labor Quality and Capital Intensity," 2014 Meeting Papers 473, Society for Economic Dynamics.

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