Estimation of a demand system to obtain the price elasticities of water and elasticities of substitution in the Chilean industrial sector

A system of demand for inputs and productive factors is estimated to calculate the elasticities of substitution and the own-price elasticity of industrial water demand in Chile. A previous study used the Annual National Industrial Survey (ENIA) panel (1995-2014) to estimate the value of water and own-price elasticity through a translog production function. However, that database does not report the industrial firms' location to protect the informants' statistical secrecy. In contrast, in this study, the survey ENIA 2018 is chosen since it includes the region where each firm is located, which allows for evaluating the endogeneity of the water price variable and using three instrumental variables related to the water supply. In addition, the performance of nonlinear regression methods with constraints is evaluated to ensure that the estimated coefficients meet the conditions imposed by economic theory. The results show that the elasticity of industrial water demand is unitary but not statistically significant in most subsectors. The water demand in the wood and paper industry subsector is elastic (-2.2) and statistically significant. On the other hand, the elasticities of substitution obtained adopt values very low, indicating that water is an essential resource that is difficult to replace by other inputs or productive factors.