Comparing neural networks and efficiency techniques in non-linear production functions

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Facultad de Ciencias Económicas y Empresariales. Decanato
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Non-linear production functions are common in economic theory and in real life, especially in cases with increasing and diminishing returns to scale but there are also contexts where an increase in one input implies a decrease in one output. The aim of this paper is to test how non-linearity affect estimations of technical efficiency obtained by ordinary and corrected least squares (OLS, COLS), data envelopment analysis with constant and variables returns to scale (DEAcrs, DEAvrs), stochastic frontier analysis (SFA) and by multilayer perceptron neural networks with backpropagation (MLP). To do this we will construct a very simple non-linear one input-one output production function and we will obtain different synthetic data with 50, 100, 200 and 300 decision-making units (DMUs). Afterwards we will add up different quantities of noise to the data and finally we will compare real efficiency with estimated values for all techniques named before among the different scenarios. Our results suggest that MLP is a flexible tool to fit production functions and a possible alternative to traditional techniques under non-linear contexts.
Álvarez, A. (2001): “La Medición de la Eficiencia y la Productividad”. Ed. Pirámide. Baker, B. D. (2001): “Can flexible non-linear modelling tell us anything new about educational productivity?”. Economics of Education Review 20 (2001) 81-92. Bishop, C. M. (1995): “Neural Networks for Pattern Recognition”. Oxford University Press. Coelli, T. (1996a): “A Guide to DEAP Version 2.1: A Data Envelopment Analysis Program”. Centre for Efficiency and Productivity Analysis (CEPA), Working Paper 96/08. Coelli, T. (1996b): “A Guide to FRONTIER Version 4.1: A Computer Program for Stochastic Frontier Production and Cost Function Estimation”. Centre for Efficiency and Productivity Analysis (CEPA), Working Paper 96/07. Costa, A y Markellos, R (1997): “Evaluating public transport efficiency with neural networks models”. Transportation Research. Part C. Vol. 5C, Nº5. October. Cybenko, G. (1988): “Continuous valued neural networks with two hidden layers are sufficient”. Technical Report, Dept. of Computer Science, Tufts University. Eide, E. y Showalter, M. H. (1998): “The effect of school quality on student performance: A quantile regression approach”. Economics Letters 58, pp. 345-350. Figlio, D. N. (1999): “Functional form and the estimated effects of school resources”. Economics of Education Review Vol.18. Pp. 241-252. Fried, H. O., Lovell, C. A. K. and Schmidt, S. S. (1993): “The Measurement of Productive Efficiency”. Oxford University Press, Oxford. Funahashi, K. (1989): “On the approximate realization of continuous mappings by neural networks 2: 183. Guermat, C. y Hadri, K. (1999): “Backpropagation Neural Network Versus Translog Model in Stochastic Frontiers: A Monte Carlo Comparison”. Discussion Paper in Economics Nº 99/16, University of Exeter. Hanushek, E. (1986): “The economics of Schooling”. Journal of Economic Literature. Vol 24, nº3, pp. 1141-1171. Hashem, S. (1993): “Optimal linear combinations of neural networks”. Doctoral dissertation. University of Purdue. Hornik, K., Stinchcombe, M. y White, H. (1989): “Multilayer Feed-forward Networks are Universal Approximators”. Neural networks 2, pp. 359-66. Hornik, K., Stinchcombe, M. and White, H. (1990). “Universal Approximation of an Unknown Mapping and its Derivatives using Multilayer Feed-forward Networks”. Neural Networks 3, pp. 551-60. Kuan, C. and White, H. (1994): “Artificial neural networks: an econometrics perspective”. Econometrics Review, 13 (1): 1-91. Lee, T., White, H. and Granger, C. W. J. (1993): “Testing for neglected nonlinearity in time series models: a comparison of neural networks methods and alternative tests”. Journal of Econometrics, 56 (3): 269-91. Ripley, B. D. (1996): “Pattern Recognition and Neural Networks”. Cambridge. Cambridge University Press. Rumelhart, D. E.; McClelland, J.L.; and the PDP Research Group (Eds.) (1986): “Parallel Distributed Processing: Explorations on the Microstructure of Cognition, vol.I. Foundations”, MIT Press, Cambridge, MA Zhang, Y. and Bartels, R. (1998): “The Effect of Sample Size on the Mean Efficiency in DEA with an Application to Electricity Distribution in Australia, Sweden and New Zealand”. Journal of Productivity Analysis, 9, 187-204.