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Specification Tests Based on Artificial Regressions

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Author Info

  • Russell Davidson
  • James G. MacKinnon

Abstract

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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Bibliographic Info

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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Related research

Keywords: Durbin-Wu-Hausman test; conditional moment test; Lagrange Multiplier test; LM test; artificial regression;

References

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  1. 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.
  2. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  3. 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.
  4. Russell Davidson & James G. MacKinnon, 1980. "Model Specification Tests Based on Artificial Linear Regressions," Working Papers 390, Queen's University, Department of Economics.
  5. 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.
  6. 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.
  7. J. A. Hausman, 1976. "Specification Tests in Econometrics," Working papers 185, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. DAVIDSON, Russel & MACKINNON, James G., . "Heteroskedastcity-robust tests in regressions directions," CORE Discussion Papers RP -678, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Wooldridge, Jeffrey M., 1991. "Specification testing and quasi-maximum- likelihood estimation," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 29-55.
  10. 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.
  11. Russell Davidson & James G. MacKinnon, 1984. "Implicit Alternatives and the Local Power of Test Statistics," Working Papers 556, Queen's University, Department of Economics.
  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. 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.
  14. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
  15. Davidson, Russell & MacKinnon, James G., 1989. "Testing for Consistency using Artificial Regressions," Econometric Theory, Cambridge University Press, vol. 5(03), pages 363-384, December.
  16. Engle, Robert F., 1982. "A general approach to lagrange multiplier model diagnostics," Journal of Econometrics, Elsevier, vol. 20(1), pages 83-104, October.
  17. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-50, July.
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Cited by:
  1. C. A. Olson & D. Ackerman, . "High School Inputs and Labor Market Outcomes for Male Workers in Their Mid-Thirties: New Data and New Estimates from Wisconsin," Institute for Research on Poverty Discussion Papers 1205-00, University of Wisconsin Institute for Research on Poverty.
  2. Kenneth G. Stewart, 1998. "Gauss-Newton, Milliken-Graybill, and Exact Misspecification Testing Using Artificial Regressions," Econometrics Working Papers 9811, Department of Economics, University of Victoria.
  3. José Ignacio Sémbler & Patricio Meller & Joaquín Vial, 2006. "Un Análisis Econométrico del Consumo Mundial de Celulosa," Documentos de Trabajo 227, Centro de Economía Aplicada, Universidad de Chile.

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