  This study considers tests for coefficient randomness in predictive
regressions. Our focus is on how tests for coefficient randomness are
influenced by the persistence of random coefficient. We show that when the
random coefficient is stationary, or I(0), Nyblom's (1989) LM test loses its
optimality (in terms of power), which is established against the alternative of
integrated, or I(1), random coefficient. We demonstrate this by constructing a
test that is more powerful than the LM test when the random coefficient is
stationary, although the test is dominated in terms of power by the LM test
when the random coefficient is integrated. The power comparison is made under
the sequence of local alternatives that approaches the null hypothesis at
different rates depending on the persistence of the random coefficient and
which test is considered. We revisit an earlier empirical research and apply
the tests considered in this study to the U.S. stock returns data. The result
mostly reverses the earlier finding.
