This paper describes a method for testing a parametric model of the me
an of a random variable Y conditional on a vector of explanatory varia
bles X against a semiparametric alternative. The test is motivated by
a conditional moment test against a parametric alternative and amounts
to replacing the parametric alternative model with a semiparametric m
odel. The resulting semiparametric test is consistent against a larger
set of alternatives than are parametric conditional moments tests bas
ed on finitely many moment conditions. The results of Monte Carlo expe
riments and an application illustrate the usefulness of the new test.