IDEAS home Printed from https://ideas.repec.org/p/esx/essedp/2887.html
   My bibliography  Save this paper

Invariance and the Wald Test

Author

Listed:
  • Kemp, GCR

Abstract

Many models and hypotheses of interest in econometrics are invariant to certain types of data transformations such as measurement unit changes. Dagenais and Dufour (1991, 1992) and Dufour and Dagenais (1992) have shown that Wald test are not invariant in general to such data transformations. In this paper, I provide a simple set of sufficient conditions to ensure that a Wald test for a null hypothesis is invariant to such a data transformation. I then use this set of conditions to help account for certain features of the Monte Carlo results from Gregory and Veall (1986) on the properties of a variety of Wald tests for Sargan's COMFAC restriction (Sargan 1980) in the first-order autoregressive distributed-lag model.

Suggested Citation

  • Kemp, GCR, 2000. "Invariance and the Wald Test," Economics Discussion Papers 2887, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:2887
    as

    Download full text from publisher

    File URL: https://repository.essex.ac.uk/2887/
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dagenais, Marcel G & Dufour, Jean-Marie, 1991. "Invariance, Nonlinear Models, and Asymptotic Tests," Econometrica, Econometric Society, vol. 59(6), pages 1601-1615, November.
    2. Gregory, Allan W. & Veall, Michael R., 1986. "Wald tests of common factor restrictions," Economics Letters, Elsevier, vol. 22(2-3), pages 203-208.
    3. Phillips, Peter C B & Park, Joon Y, 1988. "On the Formulation of Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 56(5), pages 1065-1083, September.
    4. Dagenais, Marcel G. & Dufour, Jean-Marie, 1992. "On the lack of invariance of some asymptotic tests to rescaling," Economics Letters, Elsevier, vol. 38(3), pages 251-257, March.
    5. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    6. Gregory, Allan W & Veall, Michael R, 1985. "Formulating Wald Tests of Nonlinear Restrictions," Econometrica, Econometric Society, vol. 53(6), pages 1465-1468, November.
    7. Sargan, J D, 1980. "Some Tests of Dynamic Specification for a Single Equation," Econometrica, Econometric Society, vol. 48(4), pages 879-897, May.
    8. Lafontaine, Francine & White, Kenneth J., 1986. "Obtaining any Wald statistic you want," Economics Letters, Elsevier, vol. 21(1), pages 35-40.
    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. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Axioms of invariance for TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 891-902, November.
    2. repec:ebl:ecbull:v:3:y:2008:i:62:p:1-10 is not listed on IDEAS
    3. Peter Huber & Michael Pfaffermayr, 2010. "Testing for Conditional Convergence in Variance and Skewness: The Firm Size Distribution Revisited," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(5), pages 648-668, October.
    4. Naorayex K Dastoor, 2008. "A simple explanation for the non-invariance of a Wald statistic to a reformulation of a null hypothesis," Economics Bulletin, AccessEcon, vol. 3(62), pages 1-10.
    5. Dastoor, Naorayex, 2009. "The perceived framework of a classical statistic: Is the non-invariance of a Wald statistic much ado about null thing?," Working Papers 2009-25, University of Alberta, Department of Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jean-Marie Dufour & Alain Trognon & Purevdorj Tuvaandorj, 2017. "Invariant tests based on M -estimators, estimating functions, and the generalized method of moments," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 182-204, March.
    2. Brown, Kenneth & Cribari-Neto, Francisco, 1992. "On Hypothesis Testing: A Selective Look at the Lagrange Multiplier, Likelihood Ratio and Wald Tests," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 12(2), November.
    3. Goh, Kim-Leng & King, Maxwell L., 1996. "Modified Wald tests for non-linear restrictions: A cautionary tale," Economics Letters, Elsevier, vol. 53(2), pages 133-138, November.
    4. Naorayex K Dastoor, 2008. "A simple explanation for the non-invariance of a Wald statistic to a reformulation of a null hypothesis," Economics Bulletin, AccessEcon, vol. 3(62), pages 1-10.
    5. Dastoor, Naorayex, 2009. "The perceived framework of a classical statistic: Is the non-invariance of a Wald statistic much ado about null thing?," Working Papers 2009-25, University of Alberta, Department of Economics.
    6. repec:ebl:ecbull:v:3:y:2008:i:62:p:1-10 is not listed on IDEAS
    7. Francisco J. Goerlich Gisbert, 1992. "Un test alternativo de la hipótesis de sustitución intertemporal del trabajo," Investigaciones Economicas, Fundación SEPI, vol. 16(2), pages 259-280, May.
    8. Lung-fei Lee & Jihai Yu, 2012. "The C(α)-type gradient test for spatial dependence in spatial autoregressive models," Letters in Spatial and Resource Sciences, Springer, vol. 5(3), pages 119-135, October.
    9. Crudu, Federico & Osorio, Felipe, 2020. "Bilinear form test statistics for extremum estimation," Economics Letters, Elsevier, vol. 187(C).
    10. Helen Popper, 1995. "Term premia comovement in German, Japanese, and U.S. domestic markets," Open Economies Review, Springer, vol. 6(1), pages 49-62, January.
    11. Lu, Zeng-Hua & King, Maxwell L., 2004. "A Wald-type test of quadratic parametric restrictions," Economics Letters, Elsevier, vol. 83(3), pages 359-364, June.
    12. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, University Library of Munich, Germany, revised 05 Mar 1996.
    13. Paul Hansen, 1997. "Inference on “earnings dynamics over the life cycle: New evidence for New Zealand”," New Zealand Economic Papers, Taylor & Francis Journals, vol. 31(2), pages 221-227.
    14. Peter Huber & Michael Pfaffermayr, 2010. "Testing for Conditional Convergence in Variance and Skewness: The Firm Size Distribution Revisited," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 72(5), pages 648-668, October.
    15. King, Maxwell L. & Zhang, Xibin & Akram, Muhammad, 2020. "Hypothesis testing based on a vector of statistics," Journal of Econometrics, Elsevier, vol. 219(2), pages 425-455.
    16. Albers, C.J. & Critchley, F. & Gower, J.C., 2011. "Applications of quadratic minimisation problems in statistics," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 714-722, March.
    17. Alessandra Canepa & Raymond O'Brien, 2000. "The Size and Power of Bootstrap Tests for Linear Restrictions in Misspecified Cointegrating Relationships," Econometric Society World Congress 2000 Contributed Papers 1807, Econometric Society.
    18. Alexander, W. Robert J. & Hansen, Paul & Owen, P. Dorian, 1996. "Inference on productivity differentials in multi-sector models of economic growth," Journal of Development Economics, Elsevier, vol. 51(2), pages 315-325, December.
    19. Stanislav Kolenikov & Kenneth A. Bollen, 2012. "Testing Negative Error Variances," Sociological Methods & Research, , vol. 41(1), pages 124-167, February.
    20. Zaka Ratsimalahelo, 2017. "Generalised Wald type Test of nonlinear restrictions," Working Papers 2017-13, CRESE.
    21. Marcel G. Dagenais, 1992. "Pièges et limitations de l'analyse micro-économétrique," Économie et Prévision, Programme National Persée, vol. 102(1), pages 1-9.

    More about this item

    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:esx:essedp:2887. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Essex Economics Web Manager (email available below). General contact details of provider: https://edirc.repec.org/data/edessuk.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.