Least squares estimation of joint production functions by the Differential Evolution method of global optimization

In the economics of joint production one often distinguishes between the two cases: the one in which a firm produces multiple products each produced under separate production process, and the other “true joint production” where a number of outputs are produced from a single production process, where each product shares common inputs. In the econometric practice the first case has often been dealt with by aggregation of individual production functions into a macro production function. The second case has often called for estimation of an implicit aggregate production function. Most of the studies relating to estimation of joint production functions have noted two difficulties: first that allocation of inputs to different outputs are not known, and the second that a method of estimation (such as the Least Squares) cannot have more than one dependent variable. Construction of a composite (macro) output function is at least partly motivated by the inability of the estimation methods to deal with multiple dependent variables and different forms of production function for different outputs. This study has conducted some simulation experiments on joint estimation of the CES, the Transcendental and the Nerlove-Ringstad functions. Allocation parameters (of inputs) across the products have been introduced. Estimation has been done jointly, but without constructing a composite macro production function or an output transformation function. We use nonlinear least squares based on the Differential Evolution method of global optimization that permits fitting multiple production functions simultaneously.