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Specification Tests Based on Artificial Regressions

  • Russell Davidson
  • James G. MacKinnon

Many specification tests can be computed by means of artificial linear regressions. These are linear regressions designed to be used as calculating devices to obtain test statistics and other quantities of interest. In this paper, we discuss the general principles which underlie all artificial regressions, and the use of such regressions to compute Lagrange Multiplier and other specification tests based on estimates under the null hypothesis. We demonstrate the generality and power of artificial regressions as a means of computing test statistics, show how Durbin-Wu-Hausman, conditional moment, and other tests which are not explicitly Lagrange Multiplier tests may be computed, and discuss a number of special cases which serve to illustrate the general results and can also be very useful in practice. These include tests of parameter restrictions in nonlinear regression models and tests of binary choice models such as the logit and probit models.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_707.pdf
File Function: First version 1988
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Paper provided by Queen's University, Department of Economics in its series Working Papers with number 707.

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Length: 19 pages
Date of creation: 1988
Date of revision:
Publication status: Published in Journal of the American Statistical Association, 85, 1990
Handle: RePEc:qed:wpaper:707
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  1. 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.
  2. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
  3. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-50, July.
  4. Davidson, Russell & MacKinnon, James G., 1989. "Testing for Consistency using Artificial Regressions," Econometric Theory, Cambridge University Press, vol. 5(03), pages 363-384, December.
  5. Jeffrey M. Wooldridge, 1987. "Specification Testing and Quasi-Maximum Likelihood Estimation," Working papers 479, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Russell Davidson & James G. MacKinnon, 1984. "Implicit Alternatives and the Local Power of Test Statistics," Working Papers 556, Queen's University, Department of Economics.
  7. Russell Davidson & James G. MacKinnon, 1982. "Convenient Specification Tests for Logit and Probit Models," Working Papers 514, Queen's University, Department of Economics.
  8. 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.
  9. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 38(2), pages 112-134.
  10. Ruud, Paul A., 1984. "Tests of Specification in Econometrics," Department of Economics, Working Paper Series qt4kq8m0hf, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  11. 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.
  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. 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.
  14. Engle, Robert F., 1982. "A general approach to lagrange multiplier model diagnostics," Journal of Econometrics, Elsevier, vol. 20(1), pages 83-104, October.
  15. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  16. 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.
  17. 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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