An individual choice model of energy mix

Usually firms operate with a restricted number of energy sources. In the dairy industry, most firms have multi-energy systems allowing them to shift from one energy source to another at almost no cost. Zero expenditures are observed because firms minimize costs and non-negativity constraints on the demand functions are binding. Estimation of demand systems when the probability of observing zero expenditures is not nil has already received attention from econometricians. However, most surveys generally report prices only for the subset of goods actually purchased. The econometrician faces a problem of missing price observations when zero expenditures occur. The originality of our approach is to propose a combined and coherent treatment of both the zero expenditures and missing data. Price equations are added to the demand system and the cost-minimizing mix of energy inputs leads to a simultaneous equation/limited dependent variable model. A general framework is provided in which it is possible to formulate parameter restrictions which guarantee consistency of the cost minimizing model and its relationship to a generalized tobit model with errors in variables. An application to a sample drawn from a survey on firms of the French dairy industry shows the strength of a model which decomposes the choice of energy mix in two parts: a qualitative preference and a quantitative decision. A micro-simulation model gives evidence of the practical use of this study. Nonetheless some theoretical points remain unsolved and should motivate further research.