This paper introduces a new estimation method for
arbitrary temporal heterogeneity in panel data
models. The paper provides a semiparametric method
for estimating general patterns of cross-sectional
specific time trends. The methods proposed in the
paper are related to principal component analysis
and estimate the time-varying trend effects using a
small number of common functions calculated from the
data. An important application for the new estimator
is in the estimation of time-varying technical
efficiency considered in the stochastic frontier
literature. Finite sample performance of the
estimators is examined via Monte Carlo simulations.
We apply our methods to the analysis of productivity
trends in the U.S. banking industry.