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Gauss-Newton, Milliken-Graybill, and Exact Misspecification Testing Using Artificial Regressions

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Abstract

The Gauss-Newton regression (GNR) is widely used to compute Lagrange multiplier statistics. A regression described by Milliken and Graybill yields an exact F test in a certain class of nonlinear models which are linear under the null. This paper shows that the Milliken- Graybill regression is a GNR. Hence one interpretation of Milliken- Graybill is that they identi ed a class of nonlinear models for which the GNR yields an exact test.

Suggested Citation

  • 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.
    • Handle: RePEc:vic:vicewp:9811
    Note: ISSN 1485-6441
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    References listed on IDEAS

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    1. James G. MacKinnon & Russell Davidson, 1999. "Artificial Regressions," Working Paper 978, Economics Department, Queen's University.
    2. Michael McAleer, 1981. "Exact Tests of a Model Against Non-Nested Alternatives," Working Paper 431, Economics Department, Queen's University.
    3. 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.
    4. Fisher, Gordon R. & McAleer, Michael, 1981. "Alternative procedures and associated tests of significance for non-nested hypotheses," Journal of Econometrics, Elsevier, vol. 16(1), pages 103-119, May.
    5. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, Decembrie.
    6. L. G. Godfrey & M. R. Wickens, 1981. "Testing Linear and Log-Linear Regressions for Functional Form," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(3), pages 487-496.
    7. Russell Davidson & James G. MacKinnon, 1988. "Specification Tests Based on Artificial Regressions," Working Paper 707, Economics Department, Queen's University.
    8. Bera, Anvil K & McAleer, Michael, 1983. "Some Exact Tests for Model Specification," The Review of Economics and Statistics, MIT Press, vol. 65(2), pages 351-354, May.
    9. Fisher, Gordon R., 1983. "Tests for two separate regressions," Journal of Econometrics, Elsevier, vol. 21(1), pages 117-132, January.
    10. Jan F. Kiviet, 1986. "On the Rigour of Some Misspecification Tests for Modelling Dynamic Relationships," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 241-261.
    11. Davidson, Russel & MacKinnon, James G., 1983. "Small sample properties of alternative forms of the Lagrange Multiplier test," Economics Letters, Elsevier, vol. 12(3-4), pages 269-275.
    12. Godfrey, Leslie G, 1983. "Testing Non-Nested Models after Estimation by Instrumental Variables or Least Squares," Econometrica, Econometric Society, vol. 51(2), pages 355-365, March.
    13. MacKinnon, James G, 1992. "Model Specification Tests and Artificial Regressions," Journal of Economic Literature, American Economic Association, vol. 30(1), pages 102-146, March.
    14. Godfrey, L. G., 1998. "Tests of non-nested regression models some results on small sample behaviour and the bootstrap," Journal of Econometrics, Elsevier, vol. 84(1), pages 59-74, May.
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. The Milliken-Graybill Theorem
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-07-06 20:08:00

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    More about this item

    Keywords

    Specification testing; Milliken-Graybill Theorem; Gauss- Newton regression;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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