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.

It is common in efficiency studies which analyse the environment for pollution to form part of the production technology. Pollution therefore affects efficiency and the TFP growth decomposition. As an alternative approach we draw on theoretical studies from the environmental economics literature, which demonstrate that TFP affects environmental quality. Along these lines we adopt a two-stage empirical methodology. Firstly, we obtain two estimates of productive performance (efficiency and TFP growth) using a stochastic production frontier framework in Stage 1 for European countries (1995–2008), from which we omit emissions. Secondly, in Stage 2 these measures of productive performance are used as regressors in spatial models of per capita nitrogen and sulphur emissions for European countries. From our preferred Stage 2 spatial models we find that a country’s TFP growth must fall to reduce its per capita nitrogen and sulphur emissions. This is likely to be because nitrogen and sulphur emissions in the EU have been tightly regulated for a long period of time via air quality standards and consequently, substantial reductions in emissions from cleaner and more productive technology were achieved some time ago.