On the inconsistency of the Breusch-Pagan test
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.
|Date of creation:||Apr 1995|
|Date of revision:|
|Publication status:||Published in Journal of Economic and Social Research 2.1(2000): pp. 1-11|
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- Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-72, July.
- Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-94, September.
- Jayasri Dutta & Asad Zaman, 1989. "What Do tests for Heteroskedasticity Detect?," Discussion Paper Serie A 248, University of Bonn, Germany.
- White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
- 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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