This paper provide an initial empirical application of Lee and Pitt's approach to the problem of corner solutions with panel data. This approach deals with zero expenditure in a manner consistent with behavioral theory. In this model energy demand, at industrial plant level, is the result of a discrete/continuous choice. The econometric model is essentially an endogenous switching regime model which require the evaluation of multivariate probability integrals. We estimate the random effect model by maximum likelihood using a panel of French plants and we do simulations of the effects of prices variations and a CO2 tax on energy demand.