Energy-Extended CES Aggregate Production: Current Aspects of Their Specification and Econometric Estimation

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.

From Theory to Econometrics to Energy Policy: Cautionary Tales for Policymaking Using Aggregate Production Functions

“…Mishra [18] provides an excellent history of production functions and a detailed discussion of the key controversies surrounding their use. Brockway et al [19] is a "sister" paper to this and provides a general, non-empirical discussion of the landscape around CES APFs, summarizing several notable critics and their arguments [5,6,[20][21][22] and providing guidance for the application of the CES APF to economic growth modeling. Recent application of cointegration analysis by Santos et al [23] suggests that APFs can provide statistically significant long-run relationships among economic output, capital, labor, and energy, thereby avoiding the critique of APFs in Felipe and Fisher [7].…”

“…Brockway et al [19] found that the two most common APFs are C-D (Equation (1)) and CES (Equation (3)), with the more flexible CES function overtaking Cobb-Douglas recently [12,24,[30][31][32]. (Brockway et al [19] suggest several reasons for the change: (a) critique of the C-D APF [7]; (b) empirical studies suggesting CES APFs give improved results versus the C-D APF [33]; (c) interest in elasticity of substitution (σ 1 ) which cannot be assessed by C-D APFs which assume σ 1 = 1 [34]; (d) increasing use of the CES APF in government economic models [10,35]; and (e) increasing computing capability to estimate parameters of CES APFs [28].)…”

“…(Brockway et al [19] suggest several reasons for the change: (a) critique of the C-D APF [7]; (b) empirical studies suggesting CES APFs give improved results versus the C-D APF [33]; (c) interest in elasticity of substitution (σ 1 ) which cannot be assessed by C-D APFs which assume σ 1 = 1 [34]; (d) increasing use of the CES APF in government economic models [10,35]; and (e) increasing computing capability to estimate parameters of CES APFs [28].) Other functions are also in use and worth noting here, including the translog production function [36,37] and cost functions that use factor prices as inputs instead of aggregated production factors [38].…”

“…Other functions are also in use and worth noting here, including the translog production function [36,37] and cost functions that use factor prices as inputs instead of aggregated production factors [38]. Notably, the CES APF is cited more than twice as often as the translog APF over the last five decades ( [19] (Figure 1)). Trade-offs exist: Kander and Stern [39] (p. 58) considered both CES and translog functions, deciding "that it was better to model some of the main features more reliably or believably [via CES] than to attempt to model many features of the data less reliably [via translog]".…”

Developing an Input-Output Based Method to Estimate a National-Level Energy Return on Investment (EROI)

“…Assuming that firms are profit maximizing, markets are perfectly competitive and the economy is in equilibrium (as in neoclassical economic growth models), it is a mathematical result from the Cobb-Douglas production function that the partial output elasticity of the factors of production equal their respective cost shares of aggregate output [30]. However, the cost share principle does not apply when using other production functions (e.g., CES function) [31], and perhaps more importantly, it is theoretically contested by insights from ecological economics that highlight the vital importance of energy for economic growth compared to its historically low cost [32,33]. This is because if the physical cost of energy production rises then this might severely impact the productive resources available to the rest of the economy (in terms of labour, physical infrastructure and investment capital, for instance).…”