  This paper develops a consistent series-based specification test for
semiparametric panel data models with fixed effects. The test statistic
resembles the Lagrange Multiplier (LM) test statistic in parametric models and
is based on a quadratic form in the restricted model residuals. The use of
series methods facilitates both estimation of the null model and computation of
the test statistic. The asymptotic distribution of the test statistic is
standard normal, so that appropriate critical values can easily be computed.
The projection property of series estimators allows me to develop a degrees of
freedom correction. This correction makes it possible to account for the
estimation variance and obtain refined asymptotic results. It also
substantially improves the finite sample performance of the test.
