Substitution Elasticities in a CES Production Framework. An Empirical Analysis on the Basis of Non-Linear Least Squares Estimations

Many of today’s challenges require regulative interventions by policymakers. From an economic perspective, effectiveness, cost-efficiency and distribution issues are crucial for any form of future regulation. Ultimately, this results in the need for capable and above all reliable instruments to assess environmentally motivated regulations ex ante, for example Computable General Equilibrium (CGE) models. Elasticities are key parameters for such analyses. But despite the central role of elasticities, the experience regarding of elasticities is rather unsatisfying and there exist only few estimates of the required elasticities. As a consequence, modellers frequently feel impelled to employ in their models elasticities from various originally unrelated sources or to use elasticities derived from different conceptual frameworks, thereby exposing themselves to criticism with respect to the usage of potentially inconsistent parameters estimates.

In this paper we seek to contribute to the solution of this problem and aim at overcoming the lack of adequate estimates. To this end, we consistently estimate substitution elasticities for CES production functions on the basis of different nonlinear least squares estimation procedures. Thereby, we focus on the well-established nested CES KLEM production structure. Thus on three level production functions, in which capital and labour are combined in the bottom nest, energy is added in the middle nest and finally intermediates enter the production in the top nest. In the process we take advantage of the World Input-Output Database (WIOD). The new WIOD database allows for the first time to use one consistent dataset for the estimation process and gives us the opportunity to derive elasticities from the same data which researchers can also use to calibrate their simulations.

Our results show that compared to standard linear estimations using Kmenta approximations, non-linear estimation techniques perform significantly better in this context. Moreover, no significant change in input substitutability takes place during the time period we consider. Hence for most sectors we do not observe technological change through this channel. Although technological progress in the form of changing substitution elasticities may potentially be an issue when studying longer time periods. On the basis of our estimations, we demonstrate that the common practice of using Cobb-Douglas or Leontief production functions in economic models must be rejected for the majority of sectors. As a consequence we object a simplified approach to the choice of substitution elasticities in the framework of policy oriented economic modelling. In particular in response to this result, we provide a comprehensive set of consistently estimated substitution elasticities covering 35 sectors. Therewith we hope to make a valuable contribution to making instruments designed to evaluate policy measures ex-ante more reliable and support policy makers in their efforts to cope with global environmental problems such as climate change.

Koesler, Simon and Michael Schymura (2012), Substitution Elasticities in a CES Production Framework. An Empirical Analysis on the Basis of Non-Linear Least Squares Estimations, ZEW Discussion Paper No. 12-007, Mannheim.