Estimating elasticities of substitution and price elasticities of industrial demand using different levels of aggregation for energy inputs

Elasticities are key parameters in economic models to evaluate climate or energy policies, but estimates for disaggregated energy inputs are lacking in the empirical literature. This research estimates elasticities of substitution and price elasticities of demand for energy inputs in Chile through an industrial demand system based on the translog cost function. Additionally, the effect of aggregation levels on the values of elasticities is explicitly analyzed, a comparison that has typically been made in previous literature through sensitivity analysis. For the above, data from the National Annual Industrial Survey and econometric methods for nonlinear regression systems (NLS) are used. The demand system estimates are sensitized through regression with or without theoretical restrictions on the coefficients and four specifications that differ in the number of explanatory variables to determine the most precise and robust elasticities. The results show that the model with the greatest disaggregation of energy inputs (electricity, coal, coke, fuel oil No. 6, diesel, gasoline, kerosene, liquefied propane gas, natural gas, liquefied natural gas, and biomass) is the one that provides the most reasonable estimations for price elasticities, but elasticities of substitution do not necessarily improve with the finest level of detail. Finally, the usefulness of the elasticities obtained is exemplified by simulating the change in consumption and emissions at the firm level if a carbon tax of 50 USD/tCO2 is applied.