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Small Sample Properties of Generalized Method of Moments Based Wald Tests

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  • Craig Burnside
  • Martin Eichenbaum

Abstract

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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Bibliographic Info

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

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  1. Lawrence J. Christiano & Wouter den Haan, 1995. "Small sample properties of GMM for business cycle analysis," Working Paper Series, Macroeconomic Issues, Federal Reserve Bank of Chicago 95-3, Federal Reserve Bank of Chicago.
  2. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, Elsevier, vol. 16(3), pages 309-327, November.
  3. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, Econometric Society, vol. 50(6), pages 1345-70, November.
  4. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, Econometric Society, vol. 55(3), pages 703-08, May.
  5. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, Econometric Society, vol. 60(4), pages 953-66, July.
  6. Jeffrey Fuhrer & George Moore & Scott Schuh, 1993. "Estimating the linear-quadratic inventory model: maximum likelihood versus generalized method of moments," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 93-11, Board of Governors of the Federal Reserve System (U.S.).
  7. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 817-58, May.
  8. Burnside, Craig & Eichenbaum, Martin, 1996. "Factor-Hoarding and the Propagation of Business-Cycle Shocks," American Economic Review, American Economic Association, American Economic Association, vol. 86(5), pages 1154-74, December.
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  12. Kenneth D. West, 1993. "Inventory Models," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0143, National Bureau of Economic Research, Inc.
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  14. Robert J. Hodrick & Edward Prescott, 1981. "Post-War U.S. Business Cycles: An Empirical Investigation," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  15. Altug, Sumru, 1989. "Time-to-Build and Aggregate Fluctuations: Some New Evidence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(4), pages 889-920, November.
  16. 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, National Bureau of Economic Research, Inc 0139, National Bureau of Economic Research, Inc.
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  19. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 1029-54, July.
  20. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, Econometric Society, vol. 50(5), pages 1269-86, September.
  21. Kenneth D. West & Whitney K. Newey, 1995. "Automatic Lag Selection in Covariance Matrix Estimation," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0144, National Bureau of Economic Research, Inc.
  22. Eichenbaum, Martin & Hansen, Lars Peter, 1990. "Estimating Models with Intertemporal Substitution Using Aggregate Time Series Data," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 8(1), pages 53-69, January.
  23. 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, American Statistical Association, vol. 4(4), pages 397-416, October.
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Cited by:
  1. Wouter J. Den Haan & Andrew T. Levin, 1996. "A Practitioner's Guide to Robust Covariance Matrix Estimation," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0197, National Bureau of Economic Research, Inc.
  2. Dufour, J.M. & Torres, O., 2000. "Markovian Progresses, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 2000-12, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Lawrence J. Christiano & Wouter den Haan, 1995. "Small sample properties of GMM for business cycle analysis," Working Paper Series, Macroeconomic Issues, Federal Reserve Bank of Chicago 95-3, Federal Reserve Bank of Chicago.
  4. Andersen, Torben G & Sorensen, Bent E, 1996. "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 14(3), pages 328-52, July.
  5. Francesco Bravo, . "Empirical likelihood inference with applications to some econometric models," Discussion Papers, Department of Economics, University of York 00/05, Department of Economics, University of York.
  6. Christopher R. Knittel & Konstantinos Metaxoglou, 2008. "Estimation of Random Coefficient Demand Models: Challenges, Difficulties and Warnings," NBER Working Papers 14080, National Bureau of Economic Research, Inc.
  7. Wouter J. Den Haan & Andrew Levin, 1996. "Inferences from Parametric and Non-Parametric Covariance Matrix Estimation Procedures," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0195, National Bureau of Economic Research, Inc.
  8. Nevo, Aviv, 2002. "Sample selection and information-theoretic alternatives to GMM," Journal of Econometrics, Elsevier, Elsevier, vol. 107(1-2), pages 149-157, March.
  9. Peter R. Hartley & Joseph A. Whitt, Jr., 1997. "Macroeconomic fluctuations in Europe: demand or supply, permanent or temporary?," Working Paper, Federal Reserve Bank of Atlanta 97-14, Federal Reserve Bank of Atlanta.
  10. Wagenvoort, Rien & Waldmann, Robert, 2002. "On B-robust instrumental variable estimation of the linear model with panel data," Journal of Econometrics, Elsevier, Elsevier, vol. 106(2), pages 297-324, February.

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