COBB-DOUGLAS, TRANSLOG STOCHASTIC PRODUCTION FUNCTION AND DATA ENVELOPMENT ANALYSIS IN TOTAL FACTOR PRODUCTIVITY OF MAIN BRAZILIAN GRAIN CROPS Estimation of Factor Employment and Inefficiencies through Time

Edward Bernard Bastiaan Rivera Rivera, Paulo Dutra Costantin, Diogenes Manoel Leiva Martin
DOI: https://doi.org/10.5329/RECADM.20080701001

Abstract

The objective of this paper is to apply a Cobb-Douglas, Translog Stochastic Production Function and Data Envelopment Analysis – particularly the Malmquist index - in order to estimate increases or decreases of inefficiencies over time as well as the sources of TFP changes for the main Brazilian grain crops - namely, rice, beans, maize, soybeans and wheat - throughout the most recent data available comprising the period 2001-2006. According to the Cobb Douglas model, the greatest elasticity presented is that of harvested area, followed by agricultural credit and limestone. The Translog production function presents an amelioration of aggregate productivity over time and, in a decreasing order, the Brazilian regions that have presented the greatest relative degree of efficiency are the Northeast, North, Southeast, South and Center-West regions. The results indicate that, although there have been positive changes in TFP for the sample analyzed, a decline in the use of technology has been evidenced for all the principal Brazilian grain crops between 2005/2007 – period in which we observe a remarkable downfall in the use of inputs in Brazilian agriculture.

Keywords

Total Factor Productivity; Stochastic Frontier Analysis; Data Envelopment Analysis

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References


AFRIAT, S. N. Efficiency Estimation of Production Functions. International Economic Review, XI11, 568-98, 1972.

AIGNER, D.J.; CHU, S. F. Estimating the Industry Production Function. American Economic Review, 58, 826-39, 1968.

AIGNER, D.; LOVELL, C. A. K.; SCHMIDT, P. Formulation and Estimation of Stochastic Frontier Production Function Models. Journal of Econometrics, 6, 21–37, 1977.

ALAM, I. M. S. A Non-Parametric Approach for Assessing Productivity Dynamics of Large Banks. Journal of Money, Credit and Banking, 33, 121 – 139, 2001.

BATTESE, G.; COELLI, T. Frontier production functions, technical efficiency and panel data with application to paddy farmers in India. Journal of Productivity Analysis, v. 3, pp. 153-169, 1992.

BATTESE, G.; COELLI, T. A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data. Empirical Economics, v. 20, pp. 325-332, 1995.

BOLES, J. N. Efficiency Squared-Efficient Computation of Efficiency Indexes. Proc. Thirty-ninth Ann. Meeting, Western Farm Econ. Assoc., 1966.

BRESSLER, R. G. "The Measurement of Productive Efficiency. Proc. Thirty-ninth Ann. Meeting, Western Farm Econ. Assoc., 1966.

CAVES, D. W.; CHRISTENSEN, L. R.; DIEWERT, W. E. The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity, Econometrica 50: 1393-1414, 1982.

CHARNES, A.; COOPER, W. W.; RHODES, E. Measuring the efficiency of decision making units. European Journal of Operational Research, v. 2, n. 6, p. 429-444, 1978.

COELLI, T. J.; RAO, D. S. P. Total Factor Productivity Growth in Agriculture: A Malmquist Index Analysis of 93 Countries, 1980-2000. Working Paper no. 02/2003, Centre for Efficiency and Productivity Analysis, School of Economics, The University of Queensland, 2003

CORNWELL, C.; SCHMIDT, P. SICKLES, R. Production Frontiers with Cross-Sectional and TimeSeries Variation in Efficiency Levels. Journal of Econometrics 46, 185–200, 1990.

DEBREU, G. The coefficient of resource utilization. Econometrica, 19, p. 273-292, 1951.

DUFFY , J.; PAPAGEORGIOU, C. A cross-country empirical investigation of the aggregate production function specification. Journal of Economic Growth, 5, p. 87-120, 2000.

FARE, R.; GROSSKOPF, S.; NORRIS, M; ZHANG, Z. Productivity Growth, Technical Progress and Efficiency Changes in Industrialized Countries. American Economic Review, 84, 66-83, 1994.

FARRELL, M. J. The measurement of productive efficiency. Journal of the Royal Statistical Society, Series A, Part 3, p. 253-290, 1957.

GREENE, W. H. Maximum Likelihood Estimation of Econometric Frontier Functions. Journal of Econometrics, XI11, 27-56, 1980.

IBGE (Instituto Brasileiro de Geografia e Estatística). Levantamento Sistemático da Produção Agrícola. Rio de Janeiro, v.18, n.01, p.1-76, jan.2007.

IPEA (Instituto de Pesquisa Econômica Aplicada). Boletim de Conjuntura, n. 71, dez. 2005.

IPEA (Instituto de Pesquisa Econômica Aplicada).

Boletim de Conjuntura, n. 73, jun. 2006.

IPEA (Instituto de Pesquisa Econômica Aplicada). Boletim de Conjuntura, n. 74, set. 2006a.

IPEA (Instituto de Pesquisa Econômica Aplicada). Boletim de Conjuntura, n. 76, mar. 2007.

JONDROW, J.; LOVELL, C. A. K; SCHMIDT, P. On the Estimation of Technical Inefficiency in the Stochastic Frontier Production Model.” Journal of Econometrics 19, 233–238, 1982.

KOOPMANS, T. C. An analysis of production as an efficient combination of activities. In: Koopmans, T. C. (Ed.). Activity analysis of production and allocation. Wiley, New York: Cowles Commission for Research in Economics, Monograph, n. 13, 1951.

KNELLER, R.; STEVENS, P. A. The specification of the aggregate production function in the presence of inefficiency. Economic Letters, 81, p. 223-226, 2003.

KOOP, R. J.; DIEWERT, W. E. The decomposition of frontier cost function deviations into measures of technical and allocative efficiency. Journal of Econometrics, v. 19, p. 319 – 331, 1982.

KUMBHAKAR, S. C. Production Frontiers, Panel Data and Time-Varying Technical Inefficiency.” Journal of Econometrics 46, 201–211, 1990.

LEE, L. F. A test for Distributional Assumptions for the Stochastic Frontier Functions. Journal of Econometrics. 22:245-268, 1983.

MEEUSEN, W.; BROECK, J. Efficiency Estimation from Cobb–Douglas Production Functions with Composed Error.” International Economic Review 18, 435–444, 1997.

NICHOLSON, W. Microeconomic Theory: Basic Principles and Extensions. Canada: Thomson SouthWestern. Ninth Edition, 2006.

OLIVEIRA-MARTINS, J.; PILAT, D.; SCARPETTA, S. Mark-up ratios in manufacturing industries: Estimates for 14 OECD countries", OECD Economics Department Working Papers, No. 162.

PITT, M. M.; LEE, L. F. Measurement and Sources of Technical Inefficiency in the Indonesian Weaving Industry.” Journal of Development Economics 9, 43–64, 1981.

RICHMIND, J. Estimating the Efficiency of Production”, International Economic Review, XV (June), 515-21, 1974.

SCHMIDT, P.; LOVELL, C. A. K. Estimating Technical and Allocative Inefficiency Relative to Stochastic Production and Cost Frontiers. Journal of Econometrics, vol. 9, pp. 343-366. North-Holland,

SCHMIDT, P.; SICKLES, R. Production Frontiers and Panel Data.” Journal of Business & Economic Statistics 2(4), 367–74, 1984.

SEITZ, W. D. Efficiency Measures for Steam-Electric

Generating Plants. Proc. Thirty-ninth Ann. Meeting, Western Farm Econ. Assoc, 1966.

SEITZ, W. D. Productive Efficiency in the SteamElectric Generating Industry," Journal of Political Economy, LXXIX, 878-86, 1971.

SITORUS, B. L. Productive Efficiency and Redundant Factors of Production in Traditional Agriculture of Underdeveloped Countries. Proc. Thirty-ninth Ann. Meeting, Western Farm Econ. Assoc., 1966.

SUMANTH, D. Productivity, Engineering and Management, New York, McGraw-Hill, 1985.

SHEPARD, R. W. Cost and Production Functions, Princeton University Press, 1953.

STEVENSON, R. E. Likelihood Functions for Generalized Stochastic Frontier Estimation. Journal of Econometrics, vol. 13, pp. 57-66. North-Holland, 1980.

TIMMER, C. P. Using a Probabilistic Frontier Production Function to Measure Technical Efficiency, Journal of Political Economy, LXXIX, 776-94, 1971.




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