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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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Publication status: published as Hyslop, Dean R. and Guido W. Imbens. "Bias From Classical And Other Forms Of Measurement Error," Journal of Business and Economic Statistics, 2001, v19(4,Oct), 475-481.
Handle: RePEc:nbr:nberte:0257

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  1. Joshua Angrist & Alan Krueger, 1998. "Empirical Strategies in Labor Economics," Working Papers 780, Princeton University, Department of Economics, Industrial Relations Section..
  2. Das, J.W.M. & Dominitz, J. & Soest, A.H.O. van, 1997. "Comparing Predictions and Outcomes: Theory and Application to Income Changes," Discussion Paper 1997-45, Tilburg University, Center for Economic Research.
  3. repec:att:wimass:8905 is not listed on IDEAS
  4. 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.
  5. Bound, John & Krueger, Alan B, 1991. "The Extent of Measurement Error in Longitudinal Earnings Data: Do Two Wrongs Make a Right?," Journal of Labor Economics, University of Chicago Press, vol. 9(1), pages 1-24, January.
  6. Pischke, Jorn-Steffen, 1995. "Measurement Error and Earnings Dynamics: Some Estimates from the PSID Validation Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 305-14, July.
  7. 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.
  8. 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..
  9. 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.
  10. David Card & Dean Hyslop, 1997. "Does Inflation “Grease the Wheels of the Labor Market”?," NBER Chapters, in: Reducing Inflation: Motivation and Strategy, pages 71-122 National Bureau of Economic Research, Inc.
  11. 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.
  12. Leamer, Edward E, 1987. "Errors in Variables in Linear Systems," Econometrica, Econometric Society, vol. 55(4), pages 893-909, July.
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