The GMM Parameter Normalization Puzzle

30 Pages Posted: 26 Oct 1999

See all articles by Charles A. Fleischman

Charles A. Fleischman

Federal Reserve Board - Macroeconomic Analysis Section

Date Written: August 20, 1997


A feature of GMM estimation--the use of a consistent estimate of the optimal weighting matrix rather than the joint estimation of the model parameters and the weighting matrix--can lead to the sensitivity of GMM estimation to the choice of parameter normalization. In many applications, including Euler equation estimation, a model parameter multiplies the equation error in some, but not all, normalizations. But, conventional GMM estimators that either hold the estimate of the weighting matrix fixed or allow some limited iteration on the weighting matrix fail to account for the dependence of the weighting matrix on the parameter vector implied by the multiplication of the error by the parameter. In finite samples, GMM effectively minimizes the square of the parameter times the objective function that obtains from an alternative normalization where no parameter multiplies the equation error, resulting in estimates that are smaller (in absolute value) than those from the alternative normalization. Of course, normalization is irrelevant asymptotically.

JEL Classification: C13, C51, E24, C81

Suggested Citation

Fleischman, Charles A., The GMM Parameter Normalization Puzzle (August 20, 1997). FEDS Working Paper No. 97-43. Available at SSRN: or

Charles A. Fleischman (Contact Author)

Federal Reserve Board - Macroeconomic Analysis Section ( email )

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