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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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Suggested Citation

  • Craig Burnside & Martin Eichenbaum, 1994. "Small sample properties of generalized method of moments based Wald tests," Working Paper Series, Macroeconomic Issues 94-12, Federal Reserve Bank of Chicago.
  • Handle: RePEc:fip:fedhma:94-12
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    References listed on IDEAS

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    1. 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.
    2. Chistiano, Lawrence J & den Haan, Wouter J, 1996. "Small-Sample Properties of GMM for Business-Cycle Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 309-327, July.
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    Citations

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    Cited by:

    1. Chistiano, Lawrence J & den Haan, Wouter J, 1996. "Small-Sample Properties of GMM for Business-Cycle Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 309-327, July.
    2. 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, vol. 14(3), pages 328-352, July.
    3. Dufour, Jean-Marie & Torres, Olivier, 2000. "Markovian processes, two-sided autoregressions and finite-sample inference for stationary and nonstationary autoregressive processes," Journal of Econometrics, Elsevier, vol. 99(2), pages 255-289, December.
    4. 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.).
    5. Peter R. Hartley & Joseph A. Whitt, 1997. "Macroeconomic fluctuations in Europe: demand or supply, permanent or temporary?," FRB Atlanta Working Paper 97-14, Federal Reserve Bank of Atlanta.
    6. 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.
    7. Francesco Bravo, "undated". "Empirical likelihood inference with applications to some econometric models," Discussion Papers 00/05, Department of Economics, University of York.
    8. Wouter Denhaan & Andrew T. Levin, 1996. "VARHAC Covariance Matrix Estimator (GAUSS)," QM&RBC Codes 64, Quantitative Macroeconomics & Real Business Cycles.
    9. repec:cdl:ucsdec:96-17 is not listed on IDEAS
    10. Nevo, Aviv, 2002. "Sample selection and information-theoretic alternatives to GMM," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 149-157, March.
    11. 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.

    More about this item

    Keywords

    Statistics ; Business cycles;

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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