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Bias from Classical and Other Forms of Measurement Error

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  • Dean R. Hyslop
  • Guido W. Imbens

Abstract

We consider the implications of a specific alternative to the classical measurement error model, in which the data are optimal predictions based on some information set. One motivation for this model is that if respondents are aware of their ignorance they may interpret the question what is the value of this variable?' as what is your best estimate of this variable?', and provide optimal predictions of the variable of interest given their information set. In contrast to the classical measurement error model, this model implies that the measurement error is uncorrelated with the reported value and, by necessity, correlated with the true value of the variable. In the context of the linear regression framework, we show that measurement error can lead to over- as well as under-estimation of the coefficients of interest. Critical for determining the bias is the model for the individual reporting the mismeasured variables, the individual's information set, and the correlation structure of the errors. We also investigate the implications of instrumental variables methods in the presence of measurement error of the optimal prediction error form and show that such methods may in fact introduce bias. Finally, we present some calculations indicating that the range of estimates of the returns to education consistent with amounts of measurement error found in previous studies. This range can be quite wide, especially if one allows for correlation between the measurement errors.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0257.

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Date of creation: Aug 2000
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Handle: RePEc:nbr:nberte:0257

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  1. Orley Ashenfelter & Alan Krueger, 1992. "Estimates of the Economic Return to Schooling from a New Sample of Twins," Working Papers 683, Princeton University, Department of Economics, Industrial Relations Section..
  2. Klepper, Steven & Leamer, Edward E, 1984. "Consistent Sets of Estimates for Regressions with Errors in All Variables," Econometrica, Econometric Society, vol. 52(1), pages 163-83, January.
  3. Joshua Angrist & Alan Krueger, 1998. "Empirical Strategies in Labor Economics," Working papers 98-7, Massachusetts Institute of Technology (MIT), Department of Economics.
  4. Edward Leamer, 1906. "Errors in Variables in Linear Systems," UCLA Economics Working Papers 406, UCLA Department of Economics.
  5. Das, J.W.M. & Dominitz, J. & Soest, A.H.O. van, 1998. "Comparing predictions and outcomes: theory and application to income changes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-121742, Tilburg University.
  6. Horowitz, Joel L & Manski, Charles F, 1995. "Identification and Robustness with Contaminated and Corrupted Data," Econometrica, Econometric Society, vol. 63(2), pages 281-302, March.
  7. Pischke, J.S., 1994. "Measurement Error and Earnings Dynamics: Some Estimates from the PSID Validation Study," Working papers 94-01, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. John Bound & Alan B. Krueger, 1989. "The Extent of Measurement Error In Longitudinal Earnings Data: Do Two Wrongs Make A Right?," NBER Working Papers 2885, National Bureau of Economic Research, Inc.
  9. David Card & Dean Hyslop, 1996. "Does Inflation "Grease the Wheels of the Labor Market"?," NBER Working Papers 5538, National Bureau of Economic Research, Inc.
  10. repec:att:wimass:8905 is not listed on IDEAS
  11. Card, David, 1996. "The Effect of Unions on the Structure of Wages: A Longitudinal Analysis," Econometrica, Econometric Society, vol. 64(4), pages 957-79, July.
  12. N. Gregory Mankiw & Matthew D. Shapiro, 1986. "News or Noise? An Analysis of GNP Revisions," NBER Working Papers 1939, National Bureau of Economic Research, Inc.
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