Stochastic Frontier Models for Long Panel Data Sets: Measurement of the Underlying Energy Efficiency for the OECD Countries

Abstract

In this paper we propose a general approach for estimating stochastic frontier models, suitable when using long panel data sets. We measure efficiency as a linear combination of a finite number of unobservable common factors, having coefficients that vary across firms, plus a time-invariant component. We adopt recently developed econometric techniques for large, cross sectionally correlated, non-stationary panel data models to estimate the frontier function. Given the long time span of the panel, we investigate whether the variables, including the unobservable common factors, are non-stationary, and, if so, whether they are cointegrated. To empirically illustrate our approach, we estimate a stochastic frontier model for energy demand, and compute the level of the "underlying energy efficiency" for 24 OECD countries over the period 1980 to 2008. In our specification, we control for variables such as Gross Domestic Product, energy price, climate and technological progress, that are known to impact on energy consumption. We also allow for heterogeneity across countries in the impact of these factors on energy demand. Our panel unit root tests suggest that energy demand and its key determinants are integrated and that they exhibit a long-run relation. The estimation of efficiency scores points at European countries as the more efficient in consuming energy.