Random Coefficients in Unbalanced Panels: An Application on Data from Chemical Plants

A framework for analyzing substitution and scale properties from plant-level panel data is presented. Focus is on comparing the constant and random coefficient specification of the substitution and scale parameters and investigating the variation of the parameters across plants. Characteristics of the model framework are (i) an equation system consisting of a three-factor translog cost function and the corresponding cost-share equations, (ii) random plant specific heterogeneity in coefficients, and (iii) a Maximum Likelihood procedure allowing for unbalanced panel data. The empirical results, based on data from Norwegian chemical plants, indicate pronounced plant specific heterogeneity in substitution and scale properties. Substantial parts of the variances of the cost and the cost shares can be ascribed to variation in the coefficient vector. The estimated mean scale properties are considerably influenced by the choice of model specification, while conclusions regarding price effects are more robust.