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Specification Tests Based on Artificial Regressions

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Author Info
Russell Davidson
James G. MacKinnon

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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://www.econ.queensu.ca/working_papers/papers/qed_wp_707.pdf
File Format: application/pdf
File Function: First version 1988
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Publisher 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
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Publication status: Published in Journal of the American Statistical Association, 85, 1990
Handle: RePEc:qed:wpaper:707

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

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-50, July. [Downloadable!] (restricted)
  2. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443. [Downloadable!] (restricted)
  3. Godfrey, Lesley G & Wickens, Michael R, 1981. "Testing Linear and Log-Linear Regressions for Functional Form," Review of Economic Studies, Blackwell Publishing, vol. 48(3), pages 487-96, July. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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  5. Davidson, Russell & MacKinnon, James G, 1987. "Implicit Alternatives and the Local Power of Test Statistics," Econometrica, Econometric Society, vol. 55(6), pages 1305-29, November. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
  7. Russell Davidson & James G. MacKinnon, 1985. "Heteroskedasticity-Robust Tests in Regression Directions," Working Papers 616, Queen's University, Department of Economics. [Downloadable!]
  8. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, vol. 46(6), pages 1251-71, November. [Downloadable!] (restricted)
  9. 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. [Downloadable!] (restricted)
  10. Russell Davidson & James G. MacKinnon, 1987. "Testing for Consistency using Artificial Regressions," Working Papers 687, Queen's University, Department of Economics. [Downloadable!]
  11. Wooldridge, Jeffrey M., 1991. "Specification testing and quasi-maximum- likelihood estimation," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 29-55. [Downloadable!] (restricted)
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  12. Engle, Robert F., 1982. "A general approach to lagrange multiplier model diagnostics," Journal of Econometrics, Elsevier, vol. 20(1), pages 83-104, October. [Downloadable!] (restricted)
  13. 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. [Downloadable!] (restricted)
    Other versions:
  14. 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. [Downloadable!] (restricted)
  15. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
  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. [Downloadable!]
  3. 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. [Downloadable!]
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