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On the inconsistency of the Breusch-Pagan test


  • Zaman, Asad


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

  • Zaman, Asad, 1995. "On the inconsistency of the Breusch-Pagan test," MPRA Paper 9904, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:9904

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    References listed on IDEAS

    1. Jayasri Dutta & Asad Zaman, 1989. "What Do tests for Heteroskedasticity Detect?," Discussion Paper Serie A 248, University of Bonn, Germany.
    2. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-872, July.
    3. 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.
    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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    More about this item


    heteroskedasticity; Breusch-Pagan test; test consistency; F test;

    JEL classification:

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


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