Least squares estimation of joint production functions by the differential evolution method of global optimization

Most of the studies relating to estimation of joint production functions have noted two difficulties: first that allocation of inputs to different outputs is not known, and the second that a method of estimation cannot have more than one dependent variable, which necessitates construction of a composite output transformation function. 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. Citation: Mishra, Sudhanshu, (2007) "Least squares estimation of joint production functions by the differential evolution method of global optimization." Economics Bulletin, Vol. 3, No. 51 pp. 1-13 Submitted: September 12, 2007. Accepted: October 11, 2007. URL: http://economicsbulletin.vanderbilt.edu/2007/volume3/EB-07C10007A.pdf Least squares estimation of joint production functions by the Differential Evolution method of global optimization SK Mishra Department of Economics North-Eastern Hill University Shillong, Meghalaya (India) E-mail: [email protected] Introduction: Although only occasionally dealt with in economic analysis and empirical econometrics, enterprises producing multiple or joint output with some common inputs are the most frequent empirical reality (Pfouts, 1961). Beginning with farming wherein not only wheat but also straw and chaff (that may have some market value) partake of the same inputs, animal husbandry wherein sheep yield wool and meat, manufacturing and service establishments, more often than not, produce a range of commodities applying the inputs most shared by all the products in unknown proportions. Then, estimation of a single production function of the leading product (or some weighted combination of different products) is subject to unknown type of biases intractably affecting efficiency, substitution and scale parameters and the subsequent economic implications thereof. The economics of joint production often distinguishes between the two cases: the one in which a firm produces multiple products each produced under separate production process rarely using common variable inputs (but often using common fixed inputs or infrastructure), and the other “true joint production” where a number of outputs are produced from a single production process. In the second case all outputs of the process necessarily share all the common inputs without a clue to the share of any input allocated to different products. In the econometric practice the first case has often been dealt with by aggregation of individual production functions (for each product) into a gross or macro production function. The second case has often called for estimation of an implicit aggregate production function. A Brief Literature Review: Econometric analysis of joint production perhaps dates back to the work of Klein (1947). Since then a number of studies have been carried out that deal with this topic. In particular, studies in agricultural economics have addressed this problem more frequently (see Chizmar and Zak, 1983; Just et al., 1983; Mundlak, 1963; Mundlak and Razin, 1971; Weaver, 1983). Methodologically those studies may be classified under four heads: those formulating process analysis models; those formulating simultaneous equations systems; those formulating composite macro function; those formulating composite implicit macro function. Some important works are briefly reviewed as follows. Since the early work of Manne (1958) process analysis has amply exhibited its ability to deal with the economics of joint products. However, it requires a large database and solving large programming models. Further, it precludes the calculation of price and substitution elasticities that may have important policy implications. Griffin (1977) used a method similar to process analysis supplementing it with pseudo data to ascertain appropriate types of production frontier functions for different joint products of