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Artificial Regressions

  • Russell Davidson

    ()

    (McGill University)

  • James G. MacKinnon

    ()

    (Queen's University)

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 artificial regression for regression models with heteroskedasticity of unknown form is introduced.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1038.pdf
File Function: First version 2001
Download Restriction: no

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1038.

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Length: 24 pages
Date of creation: Jan 2001
Date of revision:
Publication status: Published in B. Baltagi, Companion to Theoretical Econometrics, Blackwell, 2001
Handle: RePEc:qed:wpaper:1038
Contact details of provider: Postal: Kingston, Ontario, K7L 3N6
Phone: (613) 533-2250
Fax: (613) 533-6668
Web page: http://qed.econ.queensu.ca/
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  1. Miguel A. Delgado & Thanasis Stengos, 1990. "Semiparametric Specification Testing," Working Papers 778, Queen's University, Department of Economics.
  2. 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.
  3. Ernst R. Berndt & Bronwyn H. Hall & Robert E. Hall & Jerry A. Hausman, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 653-665 National Bureau of Economic Research, Inc.
  4. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-53, July.
  5. 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.
  6. Russell Davidson & James G. MacKinnon, 1982. "Convenient Specification Tests for Logit and Probit Models," Working Papers 514, Queen's University, Department of Economics.
  7. 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.
  8. Thomas, Jonathan M, 1993. "On Testing the Logistic Assumption in Binary Dependent Variable Models," Empirical Economics, Springer, vol. 18(2), pages 381-92.
  9. Orme, Chris, 1995. "On the Use of Artificial Regressions in Certain Microeconometric Models," Econometric Theory, Cambridge University Press, vol. 11(02), pages 290-305, February.
  10. Chesher, Andrew, 1983. "The information matrix test : Simplified calculation via a score test interpretation," Economics Letters, Elsevier, vol. 13(1), pages 45-48.
  11. 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.
  12. Wooldridge, Jeffrey M., 1990. "A Unified Approach to Robust, Regression-Based Specification Tests," Econometric Theory, Cambridge University Press, vol. 6(01), pages 17-43, March.
  13. 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.
  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.
  15. Russell Davidson & James G. MacKinnon, 1988. "A New Form of the Information Matrix Test," Working Papers 724, Queen's University, Department of Economics.
  16. 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.
  17. 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.
  18. Delgado, Miguel A & Stengos, Thanasis, 1994. "Semiparametric Specification Testing of Non-nested Econometric Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 291-303, April.
  19. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May.
  20. 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.
  21. 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.
  22. 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.
  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.
  24. repec:cup:etheor:v:6:y:1990:i:1:p:17-43 is not listed on IDEAS
  25. Murphy, Anthony, 1996. "Simple LM tests of mis-specification for ordered logit models," Economics Letters, Elsevier, vol. 52(2), pages 137-141, August.
  26. Russell Davidson & James G. MacKinnon, 1985. "Heteroskedasticity-Robust Tests in Regression Directions," Working Papers 616, Queen's University, Department of Economics.
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