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Small-Sample Bias in GMM Estimation of Covariance Structures

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  • Altonji, Joseph G
  • Segal, Lewis M

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

Article provided by American Statistical Association in its journal Journal of Business and Economic Statistics.

Volume (Year): 14 (1996)
Issue (Month): 3 (July)
Pages: 353-66

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Handle: RePEc:bes:jnlbes:v:14:y:1996:i:3:p:353-66

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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. Arellano, Manuel & Sargan, J D, 1990. "Imhof Approximations to Econometric Estimators," Review of Economic Studies, Wiley Blackwell, vol. 57(4), pages 627-46, October.
  3. Lehmann, Bruce N., 1990. "Residual risk revisited," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 71-97.
  4. Joshua Angrist & Alan Krueger, 1993. "Split Sample Instrumental Variables," Working Papers 699, Princeton University, Department of Economics, Industrial Relations Section..
  5. Bruce N. Lehmann, 1990. "Residual Risk Revisited," NBER Working Papers 1908, National Bureau of Economic Research, Inc.
  6. Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
  7. John M. Abowd & David Card, 1986. "Intertemporal Labor Supply and Long Term Employment Contracts," NBER Working Papers 1831, National Bureau of Economic Research, Inc.
  8. Shanken, Jay, 1990. "Intertemporal asset pricing : An Empirical Investigation," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 99-120.
  9. 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.
  10. repec:cup:etheor:v:10:y:1994:i:1:p:172-97 is not listed on IDEAS
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