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Approximate Bias Correction in Econometrics

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  • James G. MacKinnon
  • Anthony A. Smith Jr.

Abstract

This paper discusses ways to reduce the bias of consistent estimators that are biased in finite samples. It is necessary that the bias function, which relates parameter values to bias, should be estimable by computer simulation or by some other method. If so, bias can be reduced or, in some cases that may not be unrealistic, even eliminated. In general, several evaluations of the bias function will be required to do this. Unfortunately, reducing bias may increase the variance, or even the mean squared error, of an estimator. Whether or not it does so depends on the shape of the bias functions. The techniques of the paper are illustrated by applying them to two problems: estimating the autoregressive parameter in an AR(1) model with a constant term, and estimation of a logit model.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_919.pdf
File Function: First version 1995
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 919.

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Length: 28 pages
Date of creation: Jan 1995
Date of revision:
Handle: RePEc:qed:wpaper:919

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Keywords: bias function; mean squared error; simulation; finite samples;

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References

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  1. Phillips, Peter C. B., 1988. "The ET Interview: Professor James Durbin," Econometric Theory, Cambridge University Press, vol. 4(01), pages 125-157, April.
  2. Mackinnon, J.G. & Smith, A.A., 1996. "Approximate Bias Correction in Econometrics," G.R.E.Q.A.M. 96a14, Universite Aix-Marseille III.
  3. Chesher, Andrew & Peters, Simon, 1994. "Symmetry, Regression Design, and Sampling Distributions," Econometric Theory, Cambridge University Press, vol. 10(01), pages 116-129, March.
  4. Smith, Anthony A, Jr & Sowell, Fallaw & Zin, Stanley E, 1997. "Fractional Integration with Drift: Estimation in Small Samples," Empirical Economics, Springer, vol. 22(1), pages 103-16.
  5. Orcutt, Guy H & Winokur, Herbert S, Jr, 1969. "First Order Autoregression: Inference, Estimation, and Prediction," Econometrica, Econometric Society, vol. 37(1), pages 1-14, January.
  6. Russell Davidson & James G. Mackinnon, 1990. "Regression-Based Methods for Using Control and Antithetic Variates in Monte Carlo Experiments," Working Papers 781, Queen's University, Department of Economics.
  7. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S85-118, Suppl. De.
  8. Smith, A A, Jr, 1993. "Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S63-84, Suppl. De.
  9. Kiviet, Jan F. & Phillips, Garry D.A., 1993. "Alternative Bias Approximations in Regressions with a Lagged-Dependent Variable," Econometric Theory, Cambridge University Press, vol. 9(01), pages 62-80, January.
  10. repec:cup:etheor:v:10:y:1994:i:1:p:116-29 is not listed on IDEAS
  11. Davidson, Russell & MacKinnon, James G., 1992. "Regression-based methods for using control variates in Monte Carlo experiments," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 203-222.
  12. Kiviet, Jan F. & Phillips, Garry D. A., 1994. "Bias assessment and reduction in linear error-correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 215-243, July.
  13. repec:cup:etheor:v:9:y:1993:i:1:p:62-80 is not listed on IDEAS
  14. Sawa, Takamitsu, 1978. "The exact moments of the least squares estimator for the autoregressive model," Journal of Econometrics, Elsevier, vol. 8(2), pages 159-172, October.
  15. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-65, January.
  16. Chesher, Andrew, 1995. "A Mirror Image Invariance for M-Estimators," Econometrica, Econometric Society, vol. 63(1), pages 207-11, January.
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