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Small Sample Properties of Generalized Method of Moments Based Wald Tests

  • Craig Burnside
  • Martin Eichenbaum

This paper assesses the small sample properties of Generalized Method of Moments (GMM) based Wald statistics. The analysis is conducted assuming that the data generating process corresponds to (i) a simple vector white noise process and (ii) an equilibrium business cycle model. Our key findings are that the small sample size of the Wald tests exceeds their asymptotic size, and that their size increases uniformly with the dimensionality of joint hypotheses. For tests involving even moderate numbers of moment restrictions, the small sample size of the tests greatly exceeds their asymptotic size. Relying on asymptotic distribution theory leads one to reject joint hypothesis tests far too often. We argue that the source of the problem is the difficulty of estimating the spectral density matrix of the GMM residuals, which is needed to conduct inference in a GMM environment. Imposing restrictions implied by the underlying economic model being investigated or the null hypothesis being tested on this spectral density matrix can lead to substantial improvements in the small sample properties of the Wald tests.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0155.

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Date of creation: May 1994
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Publication status: published as Burnside, Craig and Martin Eichenbaum. "Small-Sample Properties Of GMM-Based Wald Tests," Journal of Business and Economic Statistics, 1996, v14(3,Jul), 294-308.
Handle: RePEc:nbr:nberte:0155
Note: EFG
Contact details of provider: Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.
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  1. Burnside, Craig & Eichenbaum, Martin, 1996. "Factor-Hoarding and the Propagation of Business-Cycle Shocks," American Economic Review, American Economic Association, vol. 86(5), pages 1154-74, December.
  2. Tauchen, George, 1986. "Statistical Properties of Generalized Method-of-Moments Estimators of Structural Parameters Obtained from Financial Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(4), pages 397-416, October.
  3. Eichenbaum, Martin & Hansen, Lars Peter, 1990. "Estimating Models with Intertemporal Substitution Using Aggregate Time Series Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 53-69, January.
  4. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
  5. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July.
  6. Lawrence J. Christiano & Wouter J. Den Haan, 1995. "Small Sample Properties of GMM for Business Cycle Analysis," NBER Technical Working Papers 0177, National Bureau of Economic Research, Inc.
  7. Kenneth D. West & David W. Wilcox, 1993. "Some Evidence on Finite Sample Behavior of an Instrumental Variables Estimator of the Linear Quadtratic Inventory Model," NBER Technical Working Papers 0139, National Bureau of Economic Research, Inc.
  8. Edward C. Prescott, 1986. "Theory ahead of business cycle measurement," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 9-22.
  9. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  10. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  11. Sumru Altug, 1986. "Time to build and aggregate fluctuations: some new evidence," Working Papers 277, Federal Reserve Bank of Minneapolis.
  12. Lawrence J. Christiano & Martin Eichenbaum, 1990. "Current real business cycle theories and aggregate labor market fluctuations," Discussion Paper / Institute for Empirical Macroeconomics 24, Federal Reserve Bank of Minneapolis.
  13. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-68, November.
  14. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, vol. 16(3), pages 309-327, November.
  15. Newey, Whitney K & West, Kenneth D, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Wiley Blackwell, vol. 61(4), pages 631-53, October.
  16. Fuhrer, Jeffrey C. & Moore, George R. & Schuh, Scott D., 1995. "Estimating the linear-quadratic inventory model Maximum likelihood versus generalized method of moments," Journal of Monetary Economics, Elsevier, vol. 35(1), pages 115-157, February.
  17. Christiano, Lawrence J., 1988. "Why does inventory investment fluctuate so much?," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 247-280.
  18. Kenneth D. West, 1993. "Inventory Models," NBER Technical Working Papers 0143, National Bureau of Economic Research, Inc.
  19. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
  20. Ellen McGrattan & Richard Rogerson & Randall Wright, 1993. "Household production and taxation in the stochastic growth model," Staff Report 166, Federal Reserve Bank of Minneapolis.
  21. Kocherlakota, Narayana R., 1990. "On tests of representative consumer asset pricing models," Journal of Monetary Economics, Elsevier, vol. 26(2), pages 285-304, October.
  22. 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.
  23. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
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