  We establish oracle inequalities for a version of the Lasso in
high-dimensional fixed effects dynamic panel data models. The inequalities are
valid for the coefficients of the dynamic and exogenous regressors. Separate
oracle inequalities are derived for the fixed effects. Next, we show how one
can conduct uniformly valid simultaneous inference on the parameters of the
model and construct a uniformly valid estimator of the asymptotic covariance
matrix which is robust to conditional heteroskedasticity in the error terms.
Allowing for conditional heteroskedasticity is important in dynamic models as
the conditional error variance may be non-constant over time and depend on the
covariates. Furthermore, our procedure allows for inference on high-dimensional
subsets of the parameter vector of an increasing cardinality. We show that the
confidence bands resulting from our procedure are asymptotically honest and
contract at the optimal rate. This rate is different for the fixed effects than
for the remaining parts of the parameter vector.
