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

Mishra, SK (2007): Least squares estimation of joint production functions by the Differential Evolution method of global optimization.

Abstract

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.

• Item Type: MPRA Paper
• Institution: North-Eastern Hill University, Shillong (India)
• Language: English
• Keywords: Joint production; multiple output; allocation parameters; nonlinear least squares; Differential Evolution; Nerlove-Ringstad; Transcendental; CES; macro; implicit; composite production function; transformation function; canonical correlation; multiple dependent variables
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; D - Microeconomics > D2 - Production and Organizations > D24 - Production ; Cost ; Capital ; Capital, Total Factor, and Multifactor Productivity ; Capacity

References

· Chetty, VK (1969) “Econometrics of Joint Production: A Comment”, Econometrica, 37(4), p. 731. · Chizmar, JF and Zak, TA (1983) “Modeling Multiple Outputs in Educational Production Functions” , The American Economic Review, 73(2), pp. 18-22. · Dhrymes, PJ and Mitchell, BM (1969) “Estimation of Joint Production Functions”, Econometrica, 37(4), pp. 732-736. · Diewert, W.E. (1971) “An Application of the Shepherd Duality Theorem: A Generalized Leontief Production Function”, The Journal of Political Economy, 79(3), pp. 481-507. · Efron, B and Tibshirani, R (1993) An Introduction to the Bootstrap, Chapman and Hall, New York. · Griffin, JM (1977) “The Economics of Joint Production: Another Approach”, The Review of Economics and Statistics, 59(4), pp. 389-397. · Halter, AN, Carter, HO and Hocking, JG (1957) “A Note on the Transcendental Production Function”, Journal of Farm Economics, 29, pp. 966-974. · Hotelling, H (1936) “Relations Between Two Sets of Variates”, Biometrica, 28, pp. 321-377. · Just, RE, Zilberman, D and Hochman, E (1983) “Estimation of Multicrop Production Functions”, American Journal of Agricultural Economics, 65(4), pp. 770-780. · Kendall, MG and Stuart, A (1968) The Advanced Theory of Statistics, Vol. 3, Charles Griffin & Co. London. · Klein, LR (1947) The Use of Cross-Section Data in Econometrics with Application to a Study of Production of Railroad Services in the United States, (Mimeographed) National Bureau of Economic Research, Washington, DC. · Manne, AS (1958) “A Linear Programming Model of the U.S. Petroleum Refinery Industry”, Econometrica, 26, pp. 67-106. · Mishra, SK (2007) “Performance of Differential Evolution Method in Least Squares Fitting of Some Typical Nonlinear Curves”, SSRN http://ssrn.com/abstract=1010508 · Mundlak, Y (1963) “Specification and Estimation of Multiproduct Production Functions” (mimeographed), paper read at the meetings of the Econometric Society and the American Farm Economic Association, Pittsburgh, USA (Dec. 1962), summarized in the Journal of Farm Economics, 45 pp. 433-443. · Mundlak, Y (1964) “Transcendental Multiproduct Production Functions”, International Economic Review, 5(3), pp. 273-284. · Mundlak, Y and Razin, A (1971) “On Multistage Multiproduct Production functions”, American Journal of Agricultural Economics, 53(3), pp. 491-499. · Nerlove, M (1963) “Returns to Scale in Electricity Supply”, in Christ, CF et al. (Eds) Measurement in Econometrics: Studies in Mathematical Economics and Econometrics in Memory of Yehuda Grunfeld, Stanford Univ. Press, Stanford. · Pfouts, RW (1961) “The Theory of Cost and Production in the Multiproduct Firm”, Econometrica, 39, pp. 65-68. · Rao, P (1969) “A Note on Econometrics of Joint Production” , Econometrica, 37(4), pp. 737-38. · Ringstad, V (1967) “Econometric Analysis based on a Production Function with Neutrally Variable Scale Elasticity”, Swedish Journal of Economics, 69, pp. 115-133. · Sato, K. (1967) “A Two-Level Constant-Elasticity-of-Substitution Production Function”, Review of Economic Studies, 43, pp. 201-218. · Vinod, HD (1968) “Econometrics of Joint Production”, Econometrica, 36(2), pp. 322-336. · Vinod, HD (1969) “Econometrics of Joint Production – A Reply”, Econometrica, 37(4), pp. 739-740. · Vinod, HD (1976) “Canonical Ridge and Econometrics of Joint Production”, Journal of Econometrics, 4(2), pp. 147-166. · Weaver, RD (1983) “Multiple Input, Multiple Output Production Choices and Technology in the U.S. Wheat Region”, American Journal of Agricultural Economics, 65(1), pp. 45-56.