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The Inconsistency of the Breusch-Pagan Test

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  • Asad Zaman

    (Lahore University of Management Sciences)

Abstract

The Breusch-Pagan Lagrange Multiplier test for heteroskedascity is supposedly able to detect heteroskedasticity which is an arbitrary function of some set of regressors. We will show that in fact it detects only linear functions. The test is inconsistent for general alternatives, in the sense that its power does not go to 1 as the sample size increases (and in fact, can be arbitrarily low). Since in fact the Breusch-Pagan test is essentially an F test in a special model, we also give necessary and sufficient conditions for the consistency of the F test under misspecification.

Suggested Citation

  • Asad Zaman, 2002. "The Inconsistency of the Breusch-Pagan Test," Econometrics 0205001, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:0205001
    Note: Type of Document - pdf; prepared on ibm-pc; pages: 10 ; figures: none. preprint of article subsequently published in Journal of Economic and Social Research vol 2 number 1 p1-11
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    References listed on IDEAS

    as
    1. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-872, July.
    2. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    3. Dutta, J. & Zaman, A., 1989. "What Do Heteroskedasticity Tests Detect?," Papers fb-89-10, Columbia - Graduate School of Business.
    4. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-1294, September.
    5. Koenker, Roger, 1981. "A note on studentizing a test for heteroscedasticity," Journal of Econometrics, Elsevier, vol. 17(1), pages 107-112, September.
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    Cited by:

    1. Azimi, Mohammad Naim, 2016. "An economic growth model: Evaluating the interaction of market consumption with GDP growth rate in Afghanistan," MPRA Paper 69517, University Library of Munich, Germany, revised 11 Jan 2016.

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    More about this item

    Keywords

    Breusch-Pagan test; heteroskedasticity; Lagrange Multiplier Test; Test consistency; F-test; necessary and sufficient conditions for consistency of F test;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables

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