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Consistent Sets of Estimates for Restricted Regressions with Errors in All Variables


  • Klepper, Steven
  • Stapleton, David C


In the errors-in-variables model, positive semidefinite conditions on covariance matrices, together with sufficiently small prior limits on the severity of measurement error, imply that the set of feasible values for population coefficients is bounded. The authors show how maintained restrictions can be used to reduce further the set of feasible values for the coefficients. If the restrictions are incorrect, the restricted feasible set will be empty for sufficiently small limits on the severity of measurement error. Hence the restrictions are testable even though the coefficients are not identified. Copyright 1987 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Suggested Citation

  • Klepper, Steven & Stapleton, David C, 1987. "Consistent Sets of Estimates for Restricted Regressions with Errors in All Variables," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(2), pages 445-457, June.
  • Handle: RePEc:ier:iecrev:v:28:y:1987:i:2:p:445-57

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    References listed on IDEAS

    1. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    2. K. R. W. Brewer, 1963. "Decisions Under Uncertainty: Comment," The Quarterly Journal of Economics, Oxford University Press, vol. 77(1), pages 159-161.
    3. Uzi Segal, 1984. "Nonlinear Decision Weights with the Independence Axiom," UCLA Economics Working Papers 353, UCLA Department of Economics.
    4. Roger Sherman, 1974. "The Psychological Difference Between Ambiguity and Risk," The Quarterly Journal of Economics, Oxford University Press, vol. 88(1), pages 166-169.
    5. Schoemaker, Paul J H, 1982. "The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations," Journal of Economic Literature, American Economic Association, vol. 20(2), pages 529-563, June.
    6. Robert A. Jones & Joseph M. Ostroy, 1984. "Flexibility and Uncertainty," Review of Economic Studies, Oxford University Press, vol. 51(1), pages 13-32.
    7. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    8. Mossin, Jan, 1969. "A Note on Uncertainty and Preferences in a Temporal Context," American Economic Review, American Economic Association, vol. 59(1), pages 172-174, March.
    9. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    10. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    11. Vernon L. Smith, 1969. "Measuring Nonmonetary Utilities in Uncertain Choices: The Ellsberg Urn," The Quarterly Journal of Economics, Oxford University Press, vol. 83(2), pages 324-329.
    12. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    13. Hogarth, Robin M & Kunreuther, Howard, 1989. "Risk, Ambiguity, and Insurance," Journal of Risk and Uncertainty, Springer, vol. 2(1), pages 5-35, April.
    14. repec:bla:joares:v:9:y:1971:i:2:p:307-332 is not listed on IDEAS
    15. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
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    Cited by:

    1. Jonathan Temple, 1995. "Testing the augmented Solow Model," Economics Papers 18 & 106., Economics Group, Nuffield College, University of Oxford.

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