not only in applications in which the relationship between the de-
pendent variable and its lagged values is of direct interest, but also
in applications in which the lagged dependent variable is an im-
portant control variable. For an overview of dynamic panel mod-
els, see Baltagi (2008). While parametric dynamic panel models
are increasingly popular, until very recently few, if any, estimators
for dynamic panel models allowed the lagged dependent variable
to enter the regression function nonparametrically. A recent pa-
per by Su and Lu (2013) addresses this gap in the literature. The
authors introduce a recursive local polynomial estimation method
for fixed effects dynamic panel models. They use methods devel-
oped in Mammen et al. (2009) to derive the uniform consistency
and asymptotic normality of the estimators under the assumption
of zero serial correlation in the idiosyncratic errors.
We propose a test for the null hypothesis zero serial correla-
tion. As argued in Li and Hsiao (1998), testing for serial correlation
has long been a standard practice in applied econometric analy-
sis because if the errors are serially correlated, not only an esti-
mator ignoring serial correlation is generally inefficient, it can be
inconsistent if the regressors contain lagged dependent variables.
Moreover, strong serial correlation is often an indication of omit-
ting important explanatory variables. Hence, testing autocorrela-
tion is important because the choice of an appropriate estimation
procedure for a given panel data model crucially depends on the
error structure assumed by the model. Often the estimation meth-
ods could be considerably simplified if the errors are not autocor-
related. In this paper, we will generalize Li and Hsiao’s test for zero