Industry-level Econometric Estimates of Energy-capital-labour Substitution with a Nested CES Production Function

Despite substantial interest in the role of energy in the economy, the degree of substitutability between energy and other production inputs, and the way energy should be included in the production function remain unresolved issues. Our study provides industry-level parameter estimates of two-level constant elasticity of substitution (CES) functions that include capital, labour and energy inputs and allow for technological change for Canada. In contrast to many existing studies, we do not impose prior restrictions on the order of input nesting, and we report the estimates for three possible specifications. We find that a nested production structure which first combines labour and energy into a composite good that is then combined with capital, fits the Canadian data best, in terms of respecting the restrictions imposed by cost minimization. We also find rather low elasticities of substitution between capital and labour, and limited evidence of exogenous technological change.