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Artificial Regressions

Author

Listed:
  • James G. MacKinnon

    (Queen's University)

  • Russell Davidson

    (McGill University)

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 artificialregressions 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.

Suggested Citation

  • James G. MacKinnon & Russell Davidson, 2001. "Artificial Regressions," Working Paper 1038, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1038
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    References listed on IDEAS

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    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 315-339, May.
    2. Davidson, Russell & MacKinnon, James G, 1981. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Econometrica, Econometric Society, vol. 49(3), pages 781-793, May.
    3. DAVIDSON, Russel & MACKINNON, James G., 1985. "Heteroskedastcity-robust tests in regressions directions," LIDAM Reprints CORE 678, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Orme, Chris, 1995. "On the Use of Artificial Regressions in Certain Microeconometric Models," Econometric Theory, Cambridge University Press, vol. 11(2), pages 290-305, February.
    5. 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.
    6. 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.
    7. Thomas, Jonathan M, 1993. "On Testing the Logistic Assumption in Binary Dependent Variable Models," Empirical Economics, Springer, vol. 18(2), pages 381-392.
    8. Chesher, Andrew, 1983. "The information matrix test : Simplified calculation via a score test interpretation," Economics Letters, Elsevier, vol. 13(1), pages 45-48.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Davidson, Russell & MacKinnon, James G, 1992. "A New Form of the Information Matrix Test," Econometrica, Econometric Society, vol. 60(1), pages 145-157, January.
    14. Miguel A. Delgado & Thanasis Stengos, 1994. "Semiparametric Specification Testing of Non-nested Econometric Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 291-303.
    15. 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.
    16. 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.
    17. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May.
    18. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-1053, July.
    19. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    20. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    21. Miguel A. Delgado & Thanasis Stengos, 1990. "Semiparametric Specification Testing," Working Paper 778, Economics Department, Queen's University.
    22. Murphy, Anthony, 1996. "Simple LM tests of mis-specification for ordered logit models," Economics Letters, Elsevier, vol. 52(2), pages 137-141, August.
    23. Wooldridge, Jeffrey M., 1990. "A Unified Approach to Robust, Regression-Based Specification Tests," Econometric Theory, Cambridge University Press, vol. 6(1), pages 17-43, March.
    24. 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.
    25. L. G. Godfrey & M. R. Wickens, 1981. "Testing Linear and Log-Linear Regressions for Functional Form," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(3), pages 487-496.
    26. repec:cup:etheor:v:6:y:1990:i:1:p:17-43 is not listed on IDEAS
    27. 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 181-184, May.
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    More about this item

    Keywords

    artificial regression; LM test; specification test; Gauss-Newton regression; one-step estimation; OPG regression; double-length regression; binary response model;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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