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Artificial Regressions

  • Davidson, R.
  • MacKinnon
  • J.G.

Associated with every popular nonlinear estimationmethod is at least ont "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 paremeter 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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Paper provided by Universite Aix-Marseille III in its series G.R.E.Q.A.M. with number 99a04.

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Length: 22 pages
Date of creation: 1999
Date of revision:
Handle: RePEc:fth:aixmeq:99a04
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G.R.E.Q.A.M., (GROUPE DE RECHERCHE EN ECONOMIE QUANTITATIVE D'AIX MARSEILLE), CENTRE DE VIEILLE CHARITE, 2 RUE DE LA CHARITE, 13002 MARSEILLE.

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  1. 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.
  2. Murphy, Anthony, 1996. "Simple LM tests of mis-specification for ordered logit models," Economics Letters, Elsevier, vol. 52(2), pages 137-141, August.
  3. Russell Davidson & James G. MacKinnon, 1982. "Convenient Specification Tests for Logit and Probit Models," Working Papers 514, Queen's University, Department of Economics.
  4. 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.
  5. Russell Davidson & James G. MacKinnon, 1980. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Working Papers 378, Queen's University, Department of Economics.
  6. 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.
  7. Davidson, Russell & MacKinnon, James G, 1992. "A New Form of the Information Matrix Test," Econometrica, Econometric Society, vol. 60(1), pages 145-57, January.
  8. repec:cup:etheor:v:6:y:1990:i:1:p:17-43 is not listed on IDEAS
  9. L. G. Godfrey & M. R. Wickens, 1981. "Testing Linear and Log-Linear Regressions for Functional Form," Review of Economic Studies, Oxford University Press, vol. 48(3), pages 487-496.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. Russell Davidson & James G. MacKinnon, 1985. "Heteroskedasticity-Robust Tests in Regression Directions," Working Papers 616, Queen's University, Department of Economics.
  15. 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.
  16. Chesher, Andrew, 1983. "The information matrix test : Simplified calculation via a score test interpretation," Economics Letters, Elsevier, vol. 13(1), pages 45-48.
  17. 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.
  18. Chesher, Andrew & Spady, Richard, 1991. "Asymptotic Expansions of the Information Matrix Test Statistic," Econometrica, Econometric Society, vol. 59(3), pages 787-815, May.
  19. Thomas, Jonathan M, 1993. "On Testing the Logistic Assumption in Binary Dependent Variable Models," Empirical Economics, Springer, vol. 18(2), pages 381-92.
  20. 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.
  21. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-53, July.
  22. Miguel A. Delgado & Thanasis Stengos, 1990. "Semiparametric Specification Testing," Working Papers 778, Queen's University, Department of Economics.
  23. 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.
  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. 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.
  26. Miguel A. Delgado & Thanasis Stengos, 1994. "Semiparametric Specification Testing of Non-nested Econometric Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 291-303.
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