Limitations of the Approximation Capabilities of the Translog Model: Implications for Energy Demand and Technical Change Analysis

In this paper, we evaluate the capacity of the Translog cost share model to approximate the producer’s true demand system and introduces two non-linear functional forms, which have been achieved by altering and extending the standard quadratic logarithmic Translog model. The extensions have additional desirable approximation properties with respect to output and time variables, and thus allow more flexible treatments of non-homothetic technologies and non-neutral technical change than those provided by the standard Translog. The performances of the three models are assessed (1) on theoretical ground, by the size of the domain of regularity, (2) on their ability to provide plausible estimates of the economic and technological indicators being measured and finally (3) on their reliability in fitting input shares, input-output ratios and unit cost. The most important finding is that the standard model exhibits some weakness in fitting. We show via a series of experiments that those shortcomings are due to a lack of flexibility of the logarithmic model. The estimation results obtained with the new extended model are more satisfactory and promising.