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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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    1. Leamer, Edward E, 1982. "Sets of Posterior Means with Bounded Variance Priors," Econometrica, Econometric Society, vol. 50(3), pages 725-736, May.
    2. Bekker, Paul & Kapteyn, Arie & Wansbeek, Tom, 1987. "Consistent Sets of Estimates for Regressions with Correlated or Uncorrelated Measurement Errors in Arbitrary Subsets of All Variables," Econometrica, Econometric Society, vol. 55(5), pages 1223-1230, September.
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    Cited by:

    1. Christian Bontemps & Thierry Magnac & Eric Maurin, 2012. "Set Identified Linear Models," Econometrica, Econometric Society, vol. 80(3), pages 1129-1155, May.
    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. 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.
    4. Thierry Magnac & Eric Maurin, 2008. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 835-864.
    5. 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.
    6. Rachida Hennani & Michel Terraza, 2012. "Value-at-Risk stressée chaotique d’un portefeuille bancaire," Working Papers 12-23, LAMETA, Universitiy of Montpellier, revised Sep 2012.
    7. Magnac, Thierry, 2013. "Identification partielle : méthodes et conséquences pour les applications empiriques," L'Actualité Economique, Société Canadienne de Science Economique, vol. 89(4), pages 233-258, Décembre.
    8. 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.
    9. Carmichael, Benoît & Coën, Alain, 2008. "Asset pricing models with errors-in-variables," Journal of Empirical Finance, Elsevier, vol. 15(4), pages 778-788, September.
    10. Erickson, Timothy & Whited, Toni M., 2005. "Proxy-quality thresholds: Theory and applications," Finance Research Letters, Elsevier, vol. 2(3), pages 131-151, September.
    11. 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.
    12. 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.
    13. 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.

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