A Dynamic and static study of capital, labour, and energy substitutability : eleven Canadian industrial sectors
Date
1994
Authors
Campbell, Kevin Francis
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Abstract
Recent studies on factor substitution have concentrated on the use of flexible functional forms such as the translog cost function. These functions allow the elasticities of substitution to assume arbitrary but theoretically consistent values. By theoretically consistent I mean that the cost function is capable of taking on all the desirable properties of a cost function. I make use of the translog function first to estimate an energy submodel, which consists of gasoline, fuel oil, electricity, coal and coke, natural gas, and liquid petroleum gas. This is used to derive a price index for energy which along with price series for labour and capital for eleven Canadian industrial sectors, is used in a dynamic and a static study of capital, labour, energy (KLE) substitutability. By substitutability I mean the degree to which the producer is able to replace one factor of production with another as their relative prices change.
In both studies tests are performed to determine whether the model has Hicks neutral technological change, homotheticity, homogeneity, homogeneity and symmetry and whether the underlying cost function is concave. To test for the concavity of the cost function the characteristic roots are examined, for the other properties a likelihood ratio test is performed. Furthermore the static, partial adjustment, and autoregressive models are nested within the dynamic model, so tests are performed to determine the correct structure of the model. Once this has been accomplished both the Allen elasticities of substitution and the price elasticities of substitution are derived. This is done for the energy submodel, the static model, and the dynamic model.