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Testing for Consistency using Artificial Regressions

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Author Info

  • Russell Davidson
  • James G. MacKinnon

Abstract

We consider several issues related to what Hausman (1978) called "specification tests", namely tests designed to verify the consistency of parameter estimates. We first review a number of results about these tests in linear regression models, and present some new material on their distribution when the model being tested is false, and on a simple way to improve their power in certain cases. We then show how in a general nonlinear setting they may be computed as "score" tests by means of slightly modified versions of any artificial linear regression that can be used to calculate Lagrange multiplier tests, and explore some implications of this result. We show how to create a variant of the information matrix test to test for parameter consistency. We examine conventional tests and our new version in the context of binary choice models, and provide a simple way to compute both tests based on artificial regressions. Some Monte Carlo evidence suggests the most common form of information matrix test can be extremely badly behaved in samples of even quite large size.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_687.pdf
File Function: First version 1987
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 687.

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Length: 36 pages
Date of creation: 1987
Date of revision:
Publication status: Published in Econometric Theory, 5, 1989
Handle: RePEc:qed:wpaper:687

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Fax: (613) 533-6668
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Web page: http://qed.econ.queensu.ca/
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Related research

Keywords: Durbin-Hausman tests; information matrix tests; binary choice models; Lagrange multiplier tests;

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References

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  1. Russell Davidson & James G. MacKinnon, 1985. "Heteroskedasticity-Robust Tests in Regression Directions," Working Papers 616, Queen's University, Department of Economics.
  2. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May.
  3. Russell Davidson & James G. MacKinnon, 1987. "Double-Length Artificial Regressions," Working Papers 691, Queen's University, Department of Economics.
  4. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, vol. 46(6), pages 1251-71, November.
  5. Russell Davidson & James G. MacKinnon, 1980. "Model Specification Tests Based on Artificial Linear Regressions," Working Papers 390, Queen's University, Department of Economics.
  6. Engle, Robert F., 1984. "Wald, likelihood ratio, and Lagrange multiplier tests in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 13, pages 775-826 Elsevier.
  7. Godfrey, Lesley G & Wickens, Michael R, 1981. "Testing Linear and Log-Linear Regressions for Functional Form," Review of Economic Studies, Wiley Blackwell, vol. 48(3), pages 487-96, July.
  8. Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-59, May.
  9. Nakamura, Alice & Nakamura, Masao, 1981. "On the Relationships among Several Specification Error Tests Presented by Durbin, Wu, and Hausman," Econometrica, Econometric Society, vol. 49(6), pages 1583-88, November.
  10. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  11. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  12. Orme, Chris, 1990. "The small-sample performance of the information-matrix test," Journal of Econometrics, Elsevier, vol. 46(3), pages 309-331, December.
  13. Boothe, Paul & MacKinnon, James G, 1986. "A Specification Test for Models Estimated by GLS," The Review of Economics and Statistics, MIT Press, vol. 68(4), pages 711-14, November.
  14. Orme, Christopher, 1988. "The Calculation of the Information Matrix Test for Binary Data Models," The Manchester School of Economic & Social Studies, University of Manchester, vol. 56(4), pages 370-76, December.
  15. Russell Davidson & James G. MacKinnon, 1981. "Small Sample Properties of Alternative Forms of the Lagrange Multiplier Test," Working Papers 439, Queen's University, Department of Economics.
  16. Russell Davidson & James G. MacKinnon, 1985. "Testing Linear and Loglinear Regressions against Box-Cox Alternatives," Canadian Journal of Economics, Canadian Economics Association, vol. 18(3), pages 499-517, August.
  17. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-53, July.
  18. Davidson, Russell & Godfrey, Leslie & MacKinnon, James G, 1985. "A Simplified Version of the Differencing Test," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 639-47, October.
  19. Breusch, T S & Godfrey, L G, 1986. "Data Transformation Tests," Economic Journal, Royal Economic Society, vol. 96(380a), pages 47-58, Supplemen.
  20. Russell Davidson & James G. MacKinnon, 2001. "Artificial Regressions," Working Papers 1038, Queen's University, Department of Economics.
  21. Davidson, Russell & MacKinnon, James G, 1987. "Implicit Alternatives and the Local Power of Test Statistics," Econometrica, Econometric Society, vol. 55(6), pages 1305-29, November.
  22. Russell Davidson & James G. MacKinnon, 1982. "Convenient Specification Tests for Logit and Probit Models," Working Papers 514, Queen's University, Department of Economics.
  23. Engle, Robert F., 1982. "A general approach to lagrange multiplier model diagnostics," Journal of Econometrics, Elsevier, vol. 20(1), pages 83-104, October.
  24. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  25. Hall, A.R., 1984. "The Information Matrix Test for the Linear Model," The Warwick Economics Research Paper Series (TWERPS) 250, University of Warwick, Department of Economics.
  26. Plosser, Charles I & Schwert, G William & White, Halbert, 1982. "Differencing as a Test of Specification," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 535-52, October.
  27. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-72, July.
  28. Gordon Fisher & Richard J. Smith, 1985. "Least Squares Theory and the Hausman Specification Test," Working Papers 641, Queen's University, Department of Economics.
  29. Ruud, Paul A., 1984. "Tests of Specification in Econometrics," Department of Economics, Working Paper Series qt4kq8m0hf, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
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