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Artificial Regressions

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Author Info
Russell Davidson () (McGill University)
James G. MacKinnon () (Queen's University)

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Abstract

Associated with every popular nonlinear estimation method is at least one "artificial" linear regression. We define an artificial regression in terms of three conditions that it must satisfy. Then we show how artificial regressions can be useful for numerical optimization, testing hypotheses, and computing parameter estimates. Several existing artificial regressions are discussed and are shown to satisfy the defining conditions, and a new artificail regression for regression models with heteroskedasticity of unknown form is introduced.

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File URL: http://www.econ.queensu.ca/working_papers/papers/qed_wp_978.pdf
File Format: application/pdf
File Function: First version 1999
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Publisher Info
Paper provided by Queen's University, Department of Economics in its series Working Papers with number 978.

Download reference. The following formats are available: HTML, plain text, BibTeX, RIS (EndNote), ReDIF
Length: 23 pages
Date of creation: Jan 1999
Date of revision:
Publication status: Published in B. Baltagi, Companion to Theoretical Econometrics, Blackwell, 2001
Handle: RePEc:qed:wpaper:978

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Related research
Keywords: Gauss-Newton Regression Specification Test Heteroskedasticity

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing

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. MacKinnon, James G & Magee, Lonnie, 1990. "Transforming the Dependent Variable in Regression Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(2), pages 315-39, May. [Downloadable!] (restricted)
  2. 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)
  3. 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)
    Other versions:
  4. Miguel A. Delgado & Thanasis Stengos, 1990. "Semiparametric Specification Testing," Working Papers 778, Queen's University, Department of Economics.
  5. Murphy, Anthony, 1996. "Simple LM tests of mis-specification for ordered logit models," Economics Letters, Elsevier, vol. 52(2), pages 137-141, August. [Downloadable!] (restricted)
  6. repec:cup:etheor:v:6:y:1990:i:1:p:17-43 is not listed on IDEAS
  7. Delgado, Miguel A & Stengos, Thanasis, 1994. "Semiparametric Specification Testing of Non-nested Econometric Models," Review of Economic Studies, Blackwell Publishing, vol. 61(2), pages 291-303, April. [Downloadable!] (restricted)
  8. Godfrey, Leslie G & McAleer, Michael & McKenzie, Colin R, 1988. "Variable Addition and LaGrange Multiplier Tests for Linear and Logarithmic Regression Models," The Review of Economics and Statistics, MIT Press, vol. 70(3), pages 492-503, August. [Downloadable!] (restricted)
  9. Russell Davidson & James G. MacKinnon, 1985. "Heteroskedasticity-Robust Tests in Regression Directions," Working Papers 616, Queen's University, Department of Economics. [Downloadable!]
  10. 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)
  11. Davidson, Russell & MacKinnon, James G, 1981. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Econometrica, Econometric Society, vol. 49(3), pages 781-93, May. [Downloadable!] (restricted)
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  12. Thomas, Jonathan M, 1993. "On Testing the Logistic Assumption in Binary Dependent Variable Models," Empirical Economics, Springer, vol. 18(2), pages 381-92.
  13. Davidson, Russell & MacKinnon, James G, 1999. "Bootstrap Testing in Nonlinear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 487-508, May.
    Other versions:
  14. Godfrey, Leslie G, 1978. "Testing against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1293-1301, November. [Downloadable!] (restricted)
  15. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-53, July. [Downloadable!] (restricted)
  16. 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)
    Other versions:
  17. 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)
  18. Davidson, Russell & MacKinnon, James G, 1992. "A New Form of the Information Matrix Test," Econometrica, Econometric Society, vol. 60(1), pages 145-57, January. [Downloadable!] (restricted)
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  19. 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. [Downloadable!] (restricted)
  20. Messer, Karen & White, Halbert, 1984. "A Note on Computing the Heteroskedasticity Consistent Covariance Matrix Using Instrumental Variable Techniques," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 46(2), pages 181-84, May.
  21. 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)
  22. Chesher, Andrew, 1983. "The information matrix test : Simplified calculation via a score test interpretation," Economics Letters, Elsevier, vol. 13(1), pages 45-48. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, 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.)

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  8. Kenneth G. Stewart, 1998. "Gauss-Newton, Milliken-Graybill, and Exact Misspecification Testing Using Artificial Regressions," Econometrics Working Papers 9811, Department of Economics, University of Victoria. [Downloadable!]
  9. Russell Davidson & James G. MacKinnon, 1987. "Testing for Consistency using Artificial Regressions," Working Papers 687, Queen's University, Department of Economics. [Downloadable!]
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