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Double-Length Artificial Regressions

  • Russell Davidson
  • James G. MacKinnon

Artificial linear regressions often provide a convenient way to calculate test statistics and estimate covariance matrices. This paper discusses one family of these regressions, called "double-length" because the number of observations in the artificial regression is twice the actual number of observations. These double-length regressions can be useful in a wide variety of situations. They are easy to calculate, and seem to have good properties when applied to samples of modest size. We first discuss how they are related to Gauss-Newton and squared-residuals regressions for nonlinear models, and then show how they may be used to test for functional form and other applications.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_691.pdf
File Function: First version 1987
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Paper provided by Queen's University, Department of Economics in its series Working Papers with number 691.

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Length: 20 pages
Date of creation: 1987
Date of revision:
Publication status: Published in Oxford Bulletin of Economics and Statistics, 50, 1988
Handle: RePEc:qed:wpaper:691
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  1. Russell Davidson & James G. MacKinnon, 1981. "Small Sample Properties of Alternative Forms of the Lagrange Multiplier Test," Working Papers 439, Queen's University, Department of Economics.
  2. Russell Davidson & James G. MacKinnon, 1981. "Model Specification Tests Based on Artificial Linear Regressions," Working Papers 426, Queen's University, Department of Economics.
  3. Durbin, J, 1970. "Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables," Econometrica, Econometric Society, vol. 38(3), pages 410-21, May.
  4. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-94, September.
  5. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  6. 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.
  7. Engle, Robert F., 1982. "A general approach to lagrange multiplier model diagnostics," Journal of Econometrics, Elsevier, vol. 20(1), pages 83-104, October.
  8. Russell Davidson & James G. MacKinnon, 1987. "Testing for Consistency using Artificial Regressions," Working Papers 687, Queen's University, Department of Economics.
  9. 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.
  10. Koenker, Roger, 1981. "A note on studentizing a test for heteroscedasticity," Journal of Econometrics, Elsevier, vol. 17(1), pages 107-112, September.
  11. 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.
  12. 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.
  13. 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.
  14. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-53, July.
  15. Chesher, Andrew, 1983. "The information matrix test : Simplified calculation via a score test interpretation," Economics Letters, Elsevier, vol. 13(1), pages 45-48.
  16. Russell Davidson & James G. MacKinnon, 1982. "Convenient Specification Tests for Logit and Probit Models," Working Papers 514, Queen's University, Department of Economics.
  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. 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.
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