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The Information Matrix Test for the Linear Model

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  • Alastair Hall

Abstract

We derive the information matrix test, suggested by White, for the normal fixed regressor linear model, and show that the statistic decomposes asymptotically into the sum of three independent quadratic forms. One of these is White's general test for heteroscedasticity and the remaining two components are quadratic forms in the third and fourth powers of the residuals respectively. Our results show that the test will fail to detect serial correlation and never be asymptotically optimal against heteroscedasticity, skewness and non-normal kurtosis.

Suggested Citation

  • Alastair Hall, 1987. "The Information Matrix Test for the Linear Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(2), pages 257-263.
    • Handle: RePEc:oup:restud:v:54:y:1987:i:2:p:257-263.
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    File URL: http://hdl.handle.net/10.2307/2297515
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    1. Maxwell L. King & Xibin Zhang & Muhammad Akram, 2011. "A New Procedure For Multiple Testing Of Econometric Models," Monash Econometrics and Business Statistics Working Papers 7/11, Monash University, Department of Econometrics and Business Statistics.
    2. Davidson, Russell & MacKinnon, James G., 1989. "Testing for Consistency using Artificial Regressions," Econometric Theory, Cambridge University Press, vol. 5(3), pages 363-384, December.
    3. Joachim Zietz, 2006. "Detecting neglected parameter heterogeneity with Chow tests," Applied Economics Letters, Taylor & Francis Journals, vol. 13(6), pages 369-374.
    4. Andreas Georgiadis & Christos N. Pitelis, 2008. "HRM Practices and Knowledge Processes Outcomes: Empirical Evidence from a Quasi-Experiment on UK SMEs in the Tourism Hospitality and Leisure Sector," CEP Discussion Papers dp0850, Centre for Economic Performance, LSE.
    5. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
    6. Jin Seo Cho & Halbert White, 2014. "Testing the Equality of Two Positive-Definite Matrices with Application to Information Matrix Testing," Working papers 2014rwp-67, Yonsei University, Yonsei Economics Research Institute.
    7. Wooldridge, Jeffrey M., 1991. "On the application of robust, regression- based diagnostics to models of conditional means and conditional variances," Journal of Econometrics, Elsevier, vol. 47(1), pages 5-46, January.
    8. Cho, Jin Seo & Phillips, Peter C.B., 2018. "Pythagorean generalization of testing the equality of two symmetric positive definite matrices," Journal of Econometrics, Elsevier, vol. 202(1), pages 45-56.
    9. 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.
    10. Joachim Zietz & Bobby Newsome, 2001. "A Note on Buyer's Agent Commision and Sales Price," Journal of Real Estate Research, American Real Estate Society, vol. 21(3), pages 245-254.
    11. Astrid Molenveld & Koen Verhoest & Jan Wynen, 2021. "Why public organizations contribute to crosscutting policy programs: the role of structure, culture, and ministerial control," Policy Sciences, Springer;Society of Policy Sciences, vol. 54(1), pages 123-154, March.
    12. Jin Seo Cho & Peter C.B. Phillips, "undated". "Testing Equality of Covariance Matrices via Pythagorean Means," Cowles Foundation Discussion Papers 1970, Cowles Foundation for Research in Economics, Yale University.
    13. Dhaene, Geert & Hoorelbeke, Dirk, 2004. "The information matrix test with bootstrap-based covariance matrix estimation," Economics Letters, Elsevier, vol. 82(3), pages 341-347, March.
    14. MacKinnon, James G, 1992. "Model Specification Tests and Artificial Regressions," Journal of Economic Literature, American Economic Association, vol. 30(1), pages 102-146, March.
    15. Nadeem A. Burney & Mohammad Alenezi & Nadia Al-Musallam & Ahmed Al-Khayat, 2016. "The demand for medical care services: evidence from Kuwait based on households’ out-of-pocket expenses," Applied Economics, Taylor & Francis Journals, vol. 48(28), pages 2636-2650, June.
    16. Riccardo LUCCHETTI & Claudia PIGINI, 2011. "Conditional Moment Tests for Normality in Bivariate Limited Dependent Variable Models: a Monte Carlo Study," Working Papers 357, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    17. Riccardo Lucchetti & Claudia Pigini, 2013. "A test for bivariate normality with applications in microeconometric models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 535-572, November.
    18. Dirk Hoorelbeke, 2004. "Bootstrap correcting the score test," Econometric Society 2004 North American Summer Meetings 228, Econometric Society.
    19. J. Scott Long & Pravin K. Trivedi, 1992. "Some Specification Tests for the Linear Regression Model," Sociological Methods & Research, , vol. 21(2), pages 161-204, November.

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