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Small sample properties of generalized method of moments based Wald tests

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Author Info

  • 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 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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Keywords: Statistics ; Business cycles;

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References

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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 95-3, Federal Reserve Bank of Chicago.
  2. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  3. 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.
  4. 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.
  5. Sumru Altug, 1986. "Time to build and aggregate fluctuations: some new evidence," Working Papers 277, Federal Reserve Bank of Minneapolis.
  6. Ellen McGrattan & Richard Rogerson & Randall Wright, 1993. "Household production and taxation in the stochastic growth model," Staff Report 166, Federal Reserve Bank of Minneapolis.
  7. Edward C. Prescott, 1986. "Theory ahead of business cycle measurement," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 9-22.
  8. Christiano, Lawrence J., 1988. "Why does inventory investment fluctuate so much?," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 247-280.
  9. 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.
  10. Gary Hansen, 2010. "Indivisible Labor and the Business Cycle," Levine's Working Paper Archive 233, David K. Levine.
  11. Kenneth D. West & David W. Wilcox, 1993. "Some evidence on finite sample behavior of an instrumental variables estimator of the linear quadratic inventory model," Finance and Economics Discussion Series 93-29, Board of Governors of the Federal Reserve System (U.S.).
  12. 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.
  13. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  14. 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.
  15. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  16. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-68, November.
  17. 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.
  18. Kenneth D. West & Whitney K. Newey, 1995. "Automatic Lag Selection in Covariance Matrix Estimation," NBER Technical Working Papers 0144, National Bureau of Economic Research, Inc.
  19. Craig Burnside & Martin Eichenbaum, 1994. "Factor Hoarding and the Propagation of Business Cycles Shocks," NBER Working Papers 4675, National Bureau of Economic Research, Inc.
  20. Christiano, Lawrence J & Eichenbaum, Martin, 1992. "Current Real-Business-Cycle Theories and Aggregate Labor-Market Fluctuations," American Economic Review, American Economic Association, vol. 82(3), pages 430-50, June.
  21. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
  22. Kenneth D. West, 1993. "Inventory Models," NBER Technical Working Papers 0143, National Bureau of Economic Research, Inc.
  23. Kocherlakota, Narayana R., 1990. "On tests of representative consumer asset pricing models," Journal of Monetary Economics, Elsevier, vol. 26(2), pages 285-304, October.
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Citations

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Cited by:
  1. Lawrence J. Christiano & Wouter den Haan, 1995. "Small sample properties of GMM for business cycle analysis," Working Paper Series, Macroeconomic Issues 95-3, Federal Reserve Bank of Chicago.
  2. Wouter J. den Haan & Andrew T. Levin, 1995. "Inferences from parametric and non-parametric covariance matrix estimation procedures," International Finance Discussion Papers 504, Board of Governors of the Federal Reserve System (U.S.).
  3. Peter R. Hartley & Joseph A. Whitt, Jr., 1997. "Macroeconomic fluctuations in Europe: demand or supply, permanent or temporary?," Working Paper 97-14, Federal Reserve Bank of Atlanta.
  4. Wagenvoort, Rien & Waldmann, Robert, 2002. "On B-robust instrumental variable estimation of the linear model with panel data," Journal of Econometrics, Elsevier, vol. 106(2), pages 297-324, February.
  5. Wouter J. Den Haan & Andrew T. Levin, 1996. "A Practitioner's Guide to Robust Covariance Matrix Estimation," NBER Technical Working Papers 0197, National Bureau of Economic Research, Inc.
  6. Dufour, J.M. & Torres, O., 2000. "Markovian Progresses, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes," Cahiers de recherche 2000-12, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  7. 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.
  8. Francesco Bravo, . "Empirical likelihood inference with applications to some econometric models," Discussion Papers 00/05, Department of Economics, University of York.
  9. Nevo, Aviv, 2002. "Sample selection and information-theoretic alternatives to GMM," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 149-157, March.

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