  This paper develops a consistent heteroskedasticity robust Lagrange
Multiplier (LM) type specification test for semiparametric conditional mean
models. Consistency is achieved by turning a conditional moment restriction
into a growing number of unconditional moment restrictions using series
methods. The proposed test statistic is straightforward to compute and is
asymptotically standard normal under the null. Compared with the earlier
literature on series-based specification tests in parametric models, I rely on
the projection property of series estimators and derive a different
normalization of the test statistic. Compared with the recent test in Gupta
(2018), I use a different way of accounting for heteroskedasticity. I
demonstrate using Monte Carlo studies that my test has superior finite sample
performance compared with the existing tests. I apply the test to one of the
semiparametric gasoline demand specifications from Yatchew and No (2001) and
find no evidence against it.
