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The GMM parameter normalization puzzle

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Author Info
Charles A. Fleischman

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Abstract

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.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 1997-43.

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Date of creation: 1997
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Handle: RePEc:fip:fedgfe:1997-43

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Keywords: Econometrics

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References listed on IDEAS
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  1. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-80, July.
  2. Shapiro, Matthew D, 1986. "The Dynamic Demand for Capital and Labor," The Quarterly Journal of Economics, MIT Press, vol. 101(3), pages 513-42, August. [Downloadable!] (restricted)
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  3. Valerie A. Ramey & Kenneth D. West, 1997. "Inventories," NBER Working Papers 6315, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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    • Ramey, Valerie A. & West, Kenneth D., 1999. "Inventories," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 13, pages 863-923 Elsevier. [Downloadable!] (restricted)
  4. Sbordone, Argia M., 1996. "Cyclical productivity in a model of labor hoarding," Journal of Monetary Economics, Elsevier, vol. 38(2), pages 331-361, October. [Downloadable!] (restricted)
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  5. Bartelsman, Eric J., 1995. "Of empty boxes: Returns to scale revisited," Economics Letters, Elsevier, vol. 49(1), pages 59-67, July. [Downloadable!] (restricted)
  6. Burgess, Simon M & Dolado, Juan J, 1989. "Intertemporal Rules with Variable Speed of Adjustment: An Application to U.K. Manufacturing Employment," Economic Journal, Royal Economic Society, vol. 99(396), pages 347-65, June. [Downloadable!] (restricted)
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  8. Hall, Robert E, 1988. "The Relation between Price and Marginal Cost in U.S. Industry," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 921-47, October. [Downloadable!] (restricted)
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  10. Oliner, Stephen D. & Rudebusch, Glenn D. & Sichel, Daniel, 1996. "The Lucas critique revisited assessing the stability of empirical Euler equations for investment," Journal of Econometrics, Elsevier, vol. 70(1), pages 291-316, January. [Downloadable!] (restricted)
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  13. Kennan, John, 1988. "An Econometric Analysis of Fluctuations in Aggregate Labor Supply and Demand," Econometrica, Econometric Society, vol. 56(2), pages 317-33, March. [Downloadable!] (restricted)
  14. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-86, September. [Downloadable!] (restricted)
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  1. Joshua Hojvat Gallin, 1999. "Net migration and state labor market dynamics," Finance and Economics Discussion Series 1999-16, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
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