Modeling corner solutions with panel data: Application to the industrial energy demand in France

Abstract.

This paper provides an empirical application of Lee and Pitt’s (1986) approach to the problem of corner solutions in the case of panel data. This model deals with corner solutions in a manner consistent with the firm behavior theory while controlling for unobserved heterogeneity. In this model, energy demand at industrial plant level is the result of a discrete choice of the type of the energy to be consumed and a continuous choice that defines the level of demand. The econometric model is, essentially, an endogenous switching regime model which requires the evaluation of multivariate probability integrals. We estimate the random effect model by maximum likelihood using a panel of industrial French plants from the paper and pulp industry. We calculate empirical price elasticities of energy demand from the model. We also study the effects on energy demand of an environmental policy aimed at reducing CO₂ emissions.