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This paper provides a broad range of various substitution elasticity values for sectoral nested constant elasticity of substitution (CES) production functions, estimated through panel data techniques and using the World Input-Output Database (WIOD) as the main data source. Although the related empirical literature has been growing over the recent years, there is still no single study focused on a large-scale estimation of various, both product- and industry-specific, elasticities with the use of an internally consistent database and a common methodology for all the production function nests. This paper constitutes an attempt to fill this gap. The obtained estimates may subsequently be used by computable general equilibrium (CGE) modellers in their applied research – covering fiscal, labour market, trade, energy or environmental topics. Significant heterogeneity in the estimated elasticity values is observed between various industries/products as well as between various nests of the production function. This constitutes a strong argument against the arbitrary use of Leontief and/or Cobb-Douglas specifications in multi-sector CGE models.

This paper presents the first year results of a three-year study that was designed to measure the impact of time-of-use rates in the Canadian province of Ontario. Unlike prior studies, which have analyzed such impacts in an experimental setting featuring the randomized allocation of customers to treatment and control groups, this study deals with a situation where the deployment of time-of-use rates was not experimental in nature. It was part of a full-scale program. By carefully drawing samples across four local distribution companies, we were able to interpret the study as a natural experiment and construct control groups and treatment groups. We used the Addilog model of consumer demand to estimate elasticities of substitution between peak, mid-peak and off-peak periods. The Addilog model includes as a special case the constant elasticity of substitution model that has been widely used in the literature on customer response to time-of-use rates. The estimated elasticities are well behaved and consistent with those found in the literature.

Top-down computable general equilibrium models of energy–economy interactions have a limited representation of the electricity sector, typically using constant elasticities of substitution between generation types. Detailed bottom-up electricity models generally have embedded load duration curves with the electricity price determined by the marginal cost of generation. This study incorporates a simple representation of electricity generation with these bottom-up features directly into the GTAP general equilibrium model. The motivation for this study is to help project generation adjustments and macroeconomic costs associated with policies and shocks affecting the electricity sector. Various scenarios are shown using a simple hypothetical model with Base, Mid and Peak generation types: introducing an incremental output tax on Base generation, assuming mobile capital and then fixed capital; flattening the load duration curve; and introducing an intermittent generation source. Key results are: different responses in electricity generation, price and GDP to a simple constant elasticity of substitution treatment; higher macroeconomic costs associated with a faster tax introduction due to merit order switching and capital decommissioning; an increase in GDP and a shift towards Base generation from flattening the load duration curve; and a displacement of Base generation from the introduction of an intermittent generation source, with variability leading to an increase in Peak generation and a cost to GDP. The model code is made available for replication of results and further application and development.

Top–down models usually include piecewise-smooth functions to describe marginal cost curves, while bottom–up models use step function curves. When a bottom–up cost curve is available, we can explicitly represent this curve with a top–down model in order to replicate its shape instead of using arbitrary assumptions. We propose several methods to approximate a piecewise function from a step function using constant elasticity of substitution technologies. Specifically, we consider a pollution abatement sector and calibrate the parameters of the abatement function in order to allow proper assessment of the economic effects of an environmental policy. Our methodology can be applied to any sector characterized by decreasing returns to scale technologies. We conclude that the elasticities of substitution need not be estimated only on the basis of historical data, but can be precisely calibrated on the basis of engineering estimates of technology potential.

Understanding fossil fuel supply behaviour is crucial for interpreting carbon leakage and assessing the potential effectiveness of border measures in climate policy. In most computable general equilibrium models, this fossil fuel supply is derived from a constant elasticity of substitution production function, in which a natural resource is treated as a fixed factor. We show that this leads to endogenously decreasing supply elasticities and sharply increasing marginal leakage rates for large coalitions that have ambitious emissions targets, particularly when fuel exporters participate in the coalition. We propose an alternative production function that has a constant elasticity of fuel supply, which results in more stable leakage rates and a different share of trade-related leakage. The role of this model variation for the assessment of border measures in climate policy turns out to be limited. In those cases where the model versions differ most (i.e. large coalition, ambitious targets), border measures have a small effect anyway.

This study estimates the elasticities of substitution for China from 1953 to 2006 by the two-level constant elasticity of substitution (CES) production function with three factor inputs: capital stock, labor and energy. A technological change rate and non-constant returns to scale are under considered. All possible combinations and two other subdivided periods are carried out respectively and their technological change rates, elasticities of substitution and returns to scale are found. This study also provides an analysis of production efficiency by using marginal productivity of specific factor input according to the estimated results and distinguishes the marginal productivities deriving from the three different combinations. It suggests that the decision-makers of China need to consider the effects of different factor inputs on GDP growth.

This paper demonstrates an econometric estimation of substitution elasticities of a nested constant elasticity of substitution production function (CES) between capital, energy and labour for the West German industry. In the last few years CES production functions have become more important in economic modelling, especially for applied general equilibrium models where CES production functions are an important building stone. In the literature, different results of estimated elasticities can be found. This paper investigates three different approaches for nested CES production functions and their estimated substitution elasticities. Capital, energy and labour are estimated as substitutes for the West German industry in the long run.

This paper uses the nested constant elasticity of substitution (CES) production function to estimate elasticities of substitution between capital, labour, energy and materials over the 1971–1976 period around the initial energy crisis. Elasticities are estimated for each of the two-digit SIC industries within US manufacturing, using more disaggregate four-digit SIC data. The nested CES function makes it possible to distinguish between engineering and economic elasticities of substitution. Capital and energy are estimated to be slight engineering substitutes and economic complements. Labour, energy and materials are estimated economic substitutes.