  A new statistical procedure, based on a modified spline basis, is proposed to
identify the linear components in the panel data model with fixed effects.
Under some mild assumptions, the proposed procedure is shown to consistently
estimate the underlying regression function, correctly select the linear
components, and effectively conduct the statistical inference. When compared to
existing methods for detection of linearity in the panel model, our approach is
demonstrated to be theoretically justified as well as practically convenient.
We provide a computational algorithm that implements the proposed procedure
along with a path-based solution method for linearity detection, which avoids
the burden of selecting the tuning parameter for the penalty term. Monte Carlo
simulations are conducted to examine the finite sample performance of our
proposed procedure with detailed findings that confirm our theoretical results
in the paper. Applications to Aggregate Production and Environmental Kuznets
Curve data also illustrate the necessity for detecting linearity in the
partially linear panel model.
