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A note on the estimation of linear regression models with Heteroskedastic measurement errors

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  • Daniel G. Sullivan

Abstract

I consider the estimation of linear regression models when the independent variables are measured with errors whose variances differ across observations, a situation that arises, for example, when the explanatory variables in a regression model are estimates of population parameters based on samples of varying sizes. Replacing the error variance that is assumed common to all observations in the standard errors-in-variables estimator by the mean measurement error variance yields a consistent estimator in the case of measurement error heteroskedasticity. However, another estimator, which I call the Heteroskedastic Errors in Variables Estimator (HEIV), is, under standard assumptions, asymptotically more efficient. Simulations show that the efficiency gains are likely to appreciable in practice. In addition, the HEIV estimator, which is equal to the ordinary least squares regression of the dependent variable on the best linear predictor of the true independent variables, is simple to compute with standard regression software.

Suggested Citation

  • Daniel G. Sullivan, 2001. "A note on the estimation of linear regression models with Heteroskedastic measurement errors," Working Paper Series WP-01-23, Federal Reserve Bank of Chicago.
  • Handle: RePEc:fip:fedhwp:wp-01-23
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    File URL: http://www.chicagofed.org/digital_assets/publications/working_papers/2001/Wp2001-23.pdf
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    References listed on IDEAS

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    1. Christina D. Romer & David H. Romer, 1997. "Reducing Inflation: Motivation and Strategy," NBER Books, National Bureau of Economic Research, Inc, number rome97-1, June.
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    3. Olivier Blanchard & Lawrence F. Katz, 1997. "What We Know and Do Not Know about the Natural Rate of Unemployment," Journal of Economic Perspectives, American Economic Association, vol. 11(1), pages 51-72, Winter.
    4. 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.
    5. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    6. Daniel Aaronson & Daniel G. Sullivan, 1999. "Worker insecurity and aggregate wage growth," Working Paper Series WP-99-30, Federal Reserve Bank of Chicago.
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    Cited by:

    1. Tahir Andrabi & Jishnu Das & Asim Ijaz Khwaja & Tristan Zajonc, 2011. "Do Value-Added Estimates Add Value? Accounting for Learning Dynamics," American Economic Journal: Applied Economics, American Economic Association, vol. 3(3), pages 29-54, July.
    2. Andrabi, Tahir & Das, Jishnu & Khwaja, Asim Ijaz & Zajonc, Tristan, 2009. "Here Today, Gone Tomorrow? Examining the Extent and Implications of Low Persistence in Child Learning," Scholarly Articles 4412571, Harvard Kennedy School of Government.
    3. Bhashkar Mazumder & Sarah Miller, 2016. "The Effects of the Massachusetts Health Reform on Household Financial Distress," American Economic Journal: Economic Policy, American Economic Association, vol. 8(3), pages 284-313, August.
    4. Brian A. Jacob & Lars Lefgren, 2005. "Principals as Agents: Subjective Performance Measurement in Education," NBER Working Papers 11463, National Bureau of Economic Research, Inc.
    5. Brian A. Jacob & Lars Lefgren, 2005. "What Do Parents Value in Education? An Empirical Investigation of Parents' Revealed Preferences for Teachers," NBER Working Papers 11494, National Bureau of Economic Research, Inc.

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    Regression analysis;

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