Lagrange multiplier type tests for slope homogeneity in panel data models

In this paper, we employ the Lagrange multiplier (LM) principle to test parameter homogeneity across cross‐section units in panel data models. The test can be seen as a generalization of the Breusch–Pagan test against random individual effects to all regression coefficients. While the original test procedure assumes a likelihood framework under normality, several useful variants of the LM test are presented to allow for non‐normality, heteroscedasticity and serially correlated errors. Moreover, the tests can be conveniently computed via simple artificial regressions. We derive the limiting distribution of the LM test and show that if the errors are not normally distributed, the original LM test is asymptotically valid if the number of time periods tends to infinity. A simple modification of the score statistic yields an LM test that is robust to non‐normality if the number of time periods is fixed. Further adjustments provide versions of the LM test that are robust to heteroscedasticity and serial correlation. We compare the local power of our tests and the statistic proposed by Pesaran and Yamagata. The results of the Monte Carlo experiments suggest that the LM‐type test can be substantially more powerful, in particular, when the number of time periods is small.