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On the inconsistency of the Breusch-Pagan test

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  • Zaman, Asad

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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 9904.

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Date of creation: Apr 1995
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Publication status: Published in Journal of Economic and Social Research 2.1(2000): pp. 1-11
Handle: RePEc:pra:mprapa:9904

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

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  1. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, Econometric Society, vol. 48(4), pages 817-38, May.
  2. Koenker, Roger, 1981. "A note on studentizing a test for heteroscedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 17(1), pages 107-112, September.
  3. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, Econometric Society, vol. 52(4), pages 865-72, July.
  4. Jayasri Dutta & Asad Zaman, 1989. "What Do tests for Heteroskedasticity Detect?," Discussion Paper Serie A, University of Bonn, Germany 248, University of Bonn, Germany.
  5. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, Econometric Society, vol. 47(5), pages 1287-94, September.
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