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

  • Daniel G. Sullivan

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.

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Paper provided by Federal Reserve Bank of Chicago in its series Working Paper Series with number WP-01-23.

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Date of creation: 2001
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Handle: RePEc:fip:fedhwp:wp-01-23
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  1. David Card & Dean Hyslop, 1995. "Does Inflation 'Grease the Wheels of the Labor Market'?," Working Papers 735, Princeton University, Department of Economics, Industrial Relations Section..
  2. Christina D. Romer & David H. Romer, 1997. "Reducing Inflation: Motivation and Strategy," NBER Books, National Bureau of Economic Research, Inc, number rome97-1.
  3. David G. Blanchflower & Andrew J. Oswald, 1989. "The Wage Curve," NBER Working Papers 3181, National Bureau of Economic Research, Inc.
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  4. Blanchard, O & Katz, L, 1996. "What We Know and Do Not Know about the Natural Rate of Unemployment," Working papers 96-29, Massachusetts Institute of Technology (MIT), Department of Economics.
  5. Danial Aaronson & Daniel G. Sullivan, 1999. "Worker insecurity and aggregate wage growth," Working Paper Series WP-99-30, Federal Reserve Bank of Chicago.
  6. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
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