IDEAS home Printed from https://ideas.repec.org/p/nbr/nberte/0155.html
   My bibliography  Save this paper

Small Sample Properties of Generalized Method of Moments Based Wald Tests

Author

Listed:
  • 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.

Suggested Citation

  • Craig Burnside & Martin Eichenbaum, 1994. "Small Sample Properties of Generalized Method of Moments Based Wald Tests," NBER Technical Working Papers 0155, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberte:0155 Note: EFG
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/t0155.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Edward C. Prescott, 1986. "Theory ahead of business cycle measurement," Quarterly Review, Federal Reserve Bank of Minneapolis, pages 9-22.
    2. Backus, David K & Kehoe, Patrick J & Kydland, Finn E, 1992. "International Real Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 100(4), pages 745-775, August.
    3. 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.
    4. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    5. 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.
    6. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, pages 309-327.
    7. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 631-653.
    8. Hansen, Gary D., 1985. "Indivisible labor and the business cycle," Journal of Monetary Economics, Elsevier, pages 309-327.
    9. Burnside, Craig & Eichenbaum, Martin, 1996. "Factor-Hoarding and the Propagation of Business-Cycle Shocks," American Economic Review, American Economic Association, pages 1154-1174.
    10. Kocherlakota, Narayana R., 1990. "On tests of representative consumer asset pricing models," Journal of Monetary Economics, Elsevier, pages 285-304.
    11. Chirinko, Robert S, 1982. "An Empirical Investigation of the Returns to Job Search," American Economic Review, American Economic Association, pages 498-501.
    12. 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, pages 115-157.
    13. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    14. 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.).
    15. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, pages 817-858.
    16. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", pages 125-132.
    17. 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.
    18. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, pages 953-966.
    19. Prescott, Edward C., 1986. "Theory ahead of business-cycle measurement," Carnegie-Rochester Conference Series on Public Policy, Elsevier, pages 11-44.
    20. Christiano, Lawrence J & Eichenbaum, Martin, 1992. "Current Real-Business-Cycle Theories and Aggregate Labor-Market Fluctuations," American Economic Review, American Economic Association, pages 430-450.
    21. Kenneth D. West, 1993. "Inventory Models," NBER Technical Working Papers 0143, National Bureau of Economic Research, Inc.
    22. Backus, David K. & Kehoe, Patrick J., 1989. "On the denomination of government debt : A critique of the portfolio balance approach," Journal of Monetary Economics, Elsevier, pages 359-376.
    23. 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, vol. 30(4), pages 889-920, November.
    24. 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, pages 115-157.
    25. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-1468, November.
    26. Christiano, Lawrence J., 1988. "Why does inventory investment fluctuate so much?," Journal of Monetary Economics, Elsevier, pages 247-280.
    27. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-1286, September.
    28. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christiano, Lawrence J & Eichenbaum, Martin & Marshall, David, 1991. "The Permanent Income Hypothesis Revisited," Econometrica, Econometric Society, pages 397-423.
    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. West, Kenneth D & Wilcox, David W, 1996. "A Comparison of Alternative Instrumental Variables Estimators of a Dynamic Linear Model," Journal of Business & Economic Statistics, American Statistical Association, pages 281-293.
    4. Dufour, Jean-Marie & Khalaf, Lynda, 2002. "Exact tests for contemporaneous correlation of disturbances in seemingly unrelated regressions," Journal of Econometrics, Elsevier, pages 143-170.
    5. Uribe, Martin, 1997. "Exchange-rate-based inflation stabilization: The initial real effects of credible plans," Journal of Monetary Economics, Elsevier, pages 197-221.
    6. 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, pages 255-289.
    7. 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.
    8. Wagenvoort, Rien & Waldmann, Robert, 2002. "On B-robust instrumental variable estimation of the linear model with panel data," Journal of Econometrics, Elsevier, pages 297-324.
    9. 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.
    10. Francesco Bravo, "undated". "Empirical likelihood inference with applications to some econometric models," Discussion Papers 00/05, Department of Economics, University of York.
    11. 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.
    12. repec:cdl:ucsdec:96-17 is not listed on IDEAS
    13. Nevo, Aviv, 2002. "Sample selection and information-theoretic alternatives to GMM," Journal of Econometrics, Elsevier, pages 149-157.
    14. 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.
    15. repec:wop:calsdi:96-17 is not listed on IDEAS
    16. Wouter J. Den Haan & Andrew Levin, 1996. "Inferences from Parametric and Non-Parametric Covariance Matrix Estimation Procedures," NBER Technical Working Papers 0195, National Bureau of Economic Research, Inc.

    More about this item

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nbr:nberte:0155. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://edirc.repec.org/data/nberrus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.