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Testing for Consistency using Artificial Regressions

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Author Info
Russell Davidson
James G. MacKinnon

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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://www.econ.queensu.ca/working_papers/papers/qed_wp_687.pdf
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File Function: First version 1987
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Publisher 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
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Publication status: Published in Econometric Theory, 5, 1989
Handle: RePEc:qed:wpaper:687

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

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Russell Davidson & James G. MacKinnon, 1987. "Double-Length Artificial Regressions," Working Papers 691, Queen's University, Department of Economics. [Downloadable!]
    Other versions:
  2. Orme, Christopher, 1988. "The Calculation of the Information Matrix Test for Binary Data Models," The Manchester School of Economic & Social Studies, Blackwell Publishing, vol. 56(4), pages 370-76, December.
  3. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-72, July. [Downloadable!] (restricted)
  4. Davidson, R. & MacKinnon & J.G., 1999. "Artificial Regressions," G.R.E.Q.A.M. 99a04, Universite Aix-Marseille III.
    Other versions:
  5. Godfrey, Lesley G & Wickens, Michael R, 1981. "Testing Linear and Log-Linear Regressions for Functional Form," Review of Economic Studies, Blackwell Publishing, vol. 48(3), pages 487-96, July. [Downloadable!] (restricted)
  6. Davidson, Russell & MacKinnon, James G., 1984. "Convenient specification tests for logit and probit models," Journal of Econometrics, Elsevier, vol. 25(3), pages 241-262, July. [Downloadable!] (restricted)
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  7. 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. [Downloadable!] (restricted)
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  8. 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. [Downloadable!] (restricted)
  9. Orme, Chris, 1990. "The small-sample performance of the information-matrix test," Journal of Econometrics, Elsevier, vol. 46(3), pages 309-331, December. [Downloadable!] (restricted)
  10. Hall, Alastair, 1987. "The Information Matrix Test for the Linear Model," Review of Economic Studies, Blackwell Publishing, vol. 54(2), pages 257-63, April. [Downloadable!] (restricted)
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  11. Davidson, Russel & MacKinnon, James G., 1983. "Small sample properties of alternative forms of the Lagrange Multiplier test," Economics Letters, Elsevier, vol. 12(3-4), pages 269-275. [Downloadable!] (restricted)
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  12. Russell Davidson & James G. MacKinnon, 1985. "Heteroskedasticity-Robust Tests in Regression Directions," Working Papers 616, Queen's University, Department of Economics. [Downloadable!]
  13. Gordon Fisher & Richard J. Smith, 1985. "Least Squares Theory and the Hausman Specification Test," Working Papers 641, Queen's University, Department of Economics.
  14. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, vol. 46(6), pages 1251-71, November. [Downloadable!] (restricted)
  15. 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. [Downloadable!] (restricted)
  16. 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. [Downloadable!] (restricted)
  17. Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-59, May. [Downloadable!] (restricted)
  18. 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. [Downloadable!] (restricted)
  19. Engle, Robert F., 1982. "A general approach to lagrange multiplier model diagnostics," Journal of Econometrics, Elsevier, vol. 20(1), pages 83-104, October. [Downloadable!] (restricted)
  20. 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. [Downloadable!] (restricted)
  21. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-53, July. [Downloadable!] (restricted)
  22. Davidson, Russell & MacKinnon, James G, 1984. "Model Specification Tests Based on Artificial Linear Regressions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(2), pages 485-502, June. [Downloadable!] (restricted)
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  23. 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. [Downloadable!] (restricted)
  24. Breusch, T S & Godfrey, L G, 1986. "Data Transformation Tests," Economic Journal, Royal Economic Society, vol. 96(380a), pages 47-58, Supplemen. [Downloadable!] (restricted)
  25. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September. [Downloadable!] (restricted)
  26. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January. [Downloadable!] (restricted)
  27. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May. [Downloadable!] (restricted)
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  16. Russell Davidson & James G. MacKinnon, 1987. "Double-Length Artificial Regressions," Working Papers 691, Queen's University, Department of Economics. [Downloadable!]
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  17. D. Fabbri & C. Monfardini & R. Radice, 2004. "Testing exogeneity in the bivariate probit model: Monte Carlo evidence and an application to health economics," Working Papers 514, Dipartimento Scienze Economiche, Università di Bologna. [Downloadable!]
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