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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 Federal Reserve Bank of Chicago in its series Working Paper Series, Macroeconomic Issues with number 94-12.

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Date of creation: 1994
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Handle: RePEc:fip:fedhma:94-12
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  1. 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.
  2. Craig Burnside & Martin Eichenbaum, 1994. "Factor Hoarding and the Propagation of Business Cycles Shocks," NBER Working Papers 4675, National Bureau of Economic Research, Inc.
  3. 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.
  4. repec:att:wimass:9220 is not listed on IDEAS
  5. Robert J. Hodrick & Edward Prescott, 1981. "Post-War U.S. Business Cycles: An Empirical Investigation," Discussion Papers 451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-68, November.
  7. Prescott, Edward C., 1986. "Theory ahead of business-cycle measurement," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 25(1), pages 11-44, January.
  8. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  9. Ellen McGrattan & Richard Rogerson & Randall Wright, 1993. "Household production and taxation in the stochastic growth model," Staff Report 166, Federal Reserve Bank of Minneapolis.
  10. Christiano, Lawrence J., 1988. "Why does inventory investment fluctuate so much?," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 247-280.
  11. Lawrence J. Christiano & Martin Eichenbaum, 1990. "Current real business cycle theories and aggregate labor market fluctuations," Working Paper Series, Macroeconomic Issues 90, Federal Reserve Bank of Chicago.
  12. 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.
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  14. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
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  17. 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.
  18. Kocherlakota, Narayana R., 1990. "On tests of representative consumer asset pricing models," Journal of Monetary Economics, Elsevier, vol. 26(2), pages 285-304, October.
  19. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  20. Gary Hansen, 2010. "Indivisible Labor and the Business Cycle," Levine's Working Paper Archive 233, David K. Levine.
  21. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  22. 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.
  23. 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.
  24. Kenneth D. West, 1993. "Inventory Models," NBER Technical Working Papers 0143, National Bureau of Economic Research, Inc.
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