The Impact of Sectoral Aggregation on Elasticities of Substitution Using Translog Cost Function

Abstract

Economic models are widely used to simulate policy scenarios, in which elasticities are used as measures of substitutability between production inputs. These models need appropriate levels of sector aggregation to produce policy-relevant results and to capture the variations of input substitutability among different sectors, while still adhering to the monotonicity and concavity requirements of aggregate production function. The purposes of this study are (i) to assess the cost (production) functions that fulfill these requirements appropriately, (ii) to analyze the impact of sector aggregation on the elasticities, and (iii) to determine the optimum resolution level for modelling cost function. This study utilized two databases to construct an industry-level panel dataset for 1995–2016, EU-KLEMS to obtain the price indices of the capital and labor inputs, and time-series monetary EXIOBASE v3.6, in both current and constant prices, to obtain the monetary inputs and price indices of intermediate inputs. Dynamic translog in GMM estimation is selected to derive the elasticities of substitution on different levels of sector aggregation since it performs better in reducing concavity violations, compared to pooled and fixed-effect estimation method. Selecting a higher resolution level is preferred to produce better model fittings, but it occasionally results in more concavity violations. Modelling cost functions at a more aggregated level leads to a larger estimate of the elasticity of substitution. The optimized level of sector aggregation for modelling cost function obtained in this study is at 86 industry sectors, capturing the different elasticities of substitution in various mining and manufacturing sectors of basic materials and electricity production.