Abstract
Capital–labour–energy Constant Elasticity of Substitution (CES) production functions and their estimated parameters now form a key part of energy–economy models which inform energy and emissions policy. However, the collation and guidance as to the specification and estimation choices involved with such energy-extended CES functions is disparate. This risks poorly specified and estimated CES functions, with knock-on implications for downstream energy–economic models and climate policy. In response, as a first step, this paper assembles in one place the major considerations involved in the empirical estimation of these CES functions. Discussions of the choices and their implications lead to recommendations for CES empiricists. The extensive bibliography allows those interested to dig deeper into any aspect of the CES parameter estimation process.
Highlights
Elasticity of Substitution (CES) functions [6,7], as shown by the Google Scholar results illustrated in Figure 1. (Google Scholar was preferred to searching in Scopus or Web of Science, as it enabled access to wider “real-world” production function literature such as central bank reports)
Neo-classical capital–labour aggregate production functions ignore the possible role of energy as a factor of production, since it is viewed as an intermediate product, rather than a primary input
Spatial constraints mean we cannot empirically test the collated aspects. This is undertaken by Heun et al [35], which is an empirical complement to this landscape paper, where four key modelling choices are examined to establish the differences in resulting Constant Elasticity of Substitution (CES) parameter values, and the potential effects on downstream energy policy
Summary
Production functions seek to explain economic output arising from input factors of production, and are central to growth accounting (i.e., the study of the components of economic growth), empirical investigations versus economic theory, and macroeconomic modelling. An important parameter in economics is the elasticity of substitution (σ), a measure of the ease which one production factor (e.g., labour) may be substituted by another (e.g., capital). ( −(of δ)the factors of production and economic output) is added to the functional form (e.g., Equation (4)) to form an analytical model, whose. Historical time-series data (of the factors of production and economic output) is added to the functional form (e.g., Equation (4)) to form an analytical model, whose econometric estimation obtains values for the unknown CES function parameters. Whilst many studies follow this neo-classical C-D approach [4,15,16], many researchers—famously including Solow [3]—found that increases in capital and labour factors of production commonly explained only a minority of output growth, with the remainder ascribed to exogenous growth parameter λ. A focus on growth accounting (including the Solow residual) has remained a priority for researchers including Jorgenson [19], Denison [20] and Hulten [18,21]
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