Small Sample Properties of Alternative Forms of the Lagrange Multiplier Test

This paper investigates the small-sample properties of several forms of the Lagrange Multiplier test. We find that alternative variants of the LM test, which can be easily computed from artificial linear regressions, perform very differently in small samples. One variant appears to be acceptably close to its asymptotic distribution; the other can yield quite misleading inferences. These results suggest that care should be taken when choosing which form of LM test to use in applied work.