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Small sample bias in GMM estimation of covariance structures

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  • Joseph G. Altonji
  • Lewis M. Segal

Abstract

The authors examine the small sample properties of the generalized method of moments estimator applied to models of covariance structures, where it is commonly known as the optimal minimum distance (OMD) estimator. They find that OMD is almost always biased downward in absolute value. The bias arises because sampling errors in the second moments are correlated with sampling errors in the weighting matrix used by OMD. Furthermore, OMD is usually dominated by equally weighted minimum distance (EWMD). The authors also propose an alternative estimator that is unbiased and asymptotically equivalent to OMD. However, the Monte Carlo evidence indicates that it is usually dominated by EWMD.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Chicago in its series Working Paper Series, Macroeconomic Issues with number 94-8.

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Date of creation: 1994
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Handle: RePEc:fip:fedhma:94-8

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Keywords: Statistics;

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References

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  1. Altonji, Joseph G. & Martins, Ana Paula & Siow, Aloysius, 2002. "Dynamic factor models of consumption, hours and income," Research in Economics, Elsevier, vol. 56(1), pages 3-59, June.
  2. Lehmann, Bruce N., 1990. "Residual risk revisited," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 71-97.
  3. Joshua D. Angrist & Alan B. Krueger, 1995. "Split Sample Instrumental Variables," NBER Technical Working Papers 0150, National Bureau of Economic Research, Inc.
  4. Koenker, Roger & Machado, José A.F. & Skeels, Christopher L. & Welsh, Alan H., 1994. "Momentary Lapses: Moment Expansions and the Robustness of Minimum Distance Estimation," Econometric Theory, Cambridge University Press, vol. 10(01), pages 172-197, March.
  5. repec:cup:etheor:v:10:y:1994:i:1:p:172-97 is not listed on IDEAS
  6. Arellano, Manuel & Sargan, J D, 1990. "Imhof Approximations to Econometric Estimators," Review of Economic Studies, Wiley Blackwell, vol. 57(4), pages 627-46, October.
  7. Abowd, John M & Card, David, 1987. "Intertemporal Labor Supply and Long-term Employment Contracts," American Economic Review, American Economic Association, vol. 77(1), pages 50-68, March.
  8. Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
  9. Shanken, Jay, 1990. "Intertemporal asset pricing : An Empirical Investigation," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 99-120.
  10. Bruce N. Lehmann, 1986. "Residual Risk Revisited," NBER Working Papers 1908, National Bureau of Economic Research, Inc.
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