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Small sample properties of alternative forms of the Lagrange Multiplier test


  • Davidson, Russel
  • MacKinnon, James G.


This paper investigates the small-sample properties of several forms of the Lagrange Multiplier test. We find that alternative variants of the LM test, which can be easily computed from artificial linear regressions, perform very differently in small samples. One variant appears to be acceptably close to its asymptotic distribution; the other can yield quite misleading inferences. These results suggest that care should be taken when choosing which form of LM test to use in applied work.
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  • 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.
  • Handle: RePEc:eee:ecolet:v:12:y:1983:i:3-4:p:269-275

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    1. von Ungern-Sternberg, Thomas, 1981. "Inflation and Savings: International Evidence on Inflation-Induced Income Losses," Economic Journal, Royal Economic Society, vol. 91(364), pages 961-976, December.
    2. Davidson, James E H, et al, 1978. "Econometric Modelling of the Aggregate Time-Series Relationship between Consumers' Expenditure and Income in the United Kingdom," Economic Journal, Royal Economic Society, vol. 88(352), pages 661-692, December.
    3. A. S. Deaton, 1972. "Wealth Effects on Consumption in a Modified Life-Cycle Model," Review of Economic Studies, Oxford University Press, vol. 39(4), pages 443-453.
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    Cited by:

    1. Y. K. Tse & Z. L. Yang, 2004. "Tests of Functional Form and Heteroscedasticity," Econometric Society 2004 Far Eastern Meetings 424, Econometric Society.
    2. Yang, Zhenlin & Chen, Gemai, 2004. "Tests of transformation in nonlinear regression," Economics Letters, Elsevier, vol. 84(3), pages 391-398, September.
    3. Mencia, Javier F. & Sentana, Enrique, 2004. "Estimation and testing of dynamic models with generalised hyperbolic innovations," LSE Research Online Documents on Economics 24742, London School of Economics and Political Science, LSE Library.
    4. Chesher, Andrew & Dumangane, Montezuma & Smith, Richard J., 2002. "Duration response measurement error," Journal of Econometrics, Elsevier, vol. 111(2), pages 169-194, December.
    5. Calzolari, Giorgio & Panattoni, Lorenzo, 1987. "Finite sample performance of the robust Wald test in simultaneous equation systems," MPRA Paper 22557, University Library of Munich, Germany.
    6. Murphy, Anthony, 1996. "Simple LM tests of mis-specification for ordered logit models," Economics Letters, Elsevier, vol. 52(2), pages 137-141, August.
    7. 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.
    8. Davidson, Russell & MacKinnon, James G, 1988. "Double Length Artificial Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 50(2), pages 203-217, May.
    9. Teresa Aparicio & Inmaculada Villanúa, 2007. "Some selection criteria for nested binary choice models: a comparative study," Computational Statistics, Springer, vol. 22(4), pages 635-660, December.
    10. Davidson, Russell & MacKinnon, James G., 1989. "Testing for Consistency using Artificial Regressions," Econometric Theory, Cambridge University Press, vol. 5(03), pages 363-384, December.
    11. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(01), pages 74-113, February.
    12. William H. Greene & David A. Hensher, 2008. "Modeling Ordered Choices: A Primer and Recent Developments," Working Papers 08-26, New York University, Leonard N. Stern School of Business, Department of Economics.
    13. Jouneau-Sion, Frederic & Torres, Olivier, 2006. "MMC techniques for limited dependent variables models: Implementation by the branch-and-bound algorithm," Journal of Econometrics, Elsevier, vol. 133(2), pages 479-512, August.
    14. Hamilton, James D., 1996. "Specification testing in Markov-switching time-series models," Journal of Econometrics, Elsevier, vol. 70(1), pages 127-157, January.
    15. Gabriele Fiorentini & Enrique Sentana & Giorgio Calzolari, 2000. "The Score Of Conditionally Heteroskedastic Dynamic Regression Models With Student T Innovations, An Lm Test For Multivariate Normality," Working Papers. Serie AD 2000-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    16. 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.
    17. Adrian C. Darnell, 1994. "A Dictionary Of Econometrics," Books, Edward Elgar Publishing, number 118.
    18. Javier Mencía & Enrique Sentana, 2012. "Distributional Tests in Multivariate Dynamic Models with Normal and Student-t Innovations," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 133-152, February.
    19. Wasel Shadat & Chris Orme, 2011. "An investigation of parametric tests of CCC assumption," The School of Economics Discussion Paper Series 1109, Economics, The University of Manchester.
    20. Dirk Hoorelbeke, 2004. "Bootstrap correcting the score test," Econometric Society 2004 North American Summer Meetings 228, Econometric Society.

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