On the Production Function For Agriculture - Research Paper Example

On the Production Function For Agriculture Among the production functions, the Cobb-Douglas production function is the most widely used in theoretical and empirical analyses of growth and productivity (Felipe and Adams 2005, p. 428). According to Felipe and Adams (2005, p. 428), the Cobb-Douglas production function is “central to much of today’s work on growth, technological change, productivity, and labour”. Further, the empirical estimates on the Cobb-Douglas aggregate production function are essential in macroeconomics and important theoretical constructs (Felipe and Adams 2005, p. 428). The origin of the Cobb-Douglas production function can be traced to the 1928 seminal work of Paul Douglas and Charles Cobb in studying the United States manufacturing sector using the data set of 1899-1922 (Felipe and Adams 2005, p. 428). However, Felipe and Adams (2005, p. 428) also pointed out that several authors like Paul Samuelson have argued that Knut Wicksell should have taken the credit as well for its discovery. Nevertheless, the Cobb and Douglas’s econometric or empirical estimation of an aggregate production function was the first in the profession of economics (Felipe and Adams 2005, p. 428). The production function is discussed in Gujarati (2004, p. 224). In its Cobb-Douglas form, it is possible to know or estimate whether we have an increasing, constant, or decreasing returns to scale (Gujarat 2004, p. 244). In a way, the production function reflects the technological constraints or the production feasibility set (Varian 2006, pp. 322-327). Meanwhile, we can see in the literature that the production function estimation has been supplemented by several techniques to improve precision or correct perceived weaknesses. Mittlehammer et al. (1980) employed mixed estimation and principal component regression to mitigate the effects of severe multicollinearity that was preventing accurate through ordinary least squares. The methods improved precision as well as the theoretical reasonableness of estimated parameters. Just et al. (1983, p. 770) developed a technique for the estimation of multicrop production functions. Their method employed all available information and they claim that their empirical results show that their approach is practical and inexpensive. Mittlehammer and Conway (1988, p. 859) developed a mixed estimation procedure of the production frontier that departs from the Theil-Goldberger model that had been questioned in the literature. Mittlehammer and Conway (1988, p. 865) introduced instead a prior integrated mixed estimator or the PIME that are based on generally accepted principles. Taking a different tact, Banker and Maindiratta (1992, p. 401) proposed a composed error model for maximum likelihood estimation of production frontiers. According to them, the approach avoids an untestable restriction of parameters and provides nonparametric frontier estimation. Coyle (1992, p. 850) developed a duality model of production function to factor in risk aversion and uncertainty. In particular, Coyle developed the model within the context of a mean-variance model of utility maximization (1992, p. 849). Coyle argued that the model is more general while retaining simplicity (1992, p 849). Echevarria (1998) used a three-factor agricultural production to estimate the agricultural production function for Canada. Through the said three-factor production function, Echevarria (1998) was able to compare select areas in Canada on factor shares in agricultural production across areas of Canada. Bera and Sharma (1999) used uncertainty and stochastic frontier production function models to estimate inefficiency. Some of the more important and fundamental stochastic models are in the Bera and Sharma (1999) material. Mundlak (1999) used within and between regression analysis to assess the significance of various inputs to output. The work has not much significance except in illustrating that useful insights can be obtained from within and between regression analysis. Kudaligama and Yanagida (2000, p. 57) compared country differences in agricultural production using deterministic and stochastic production frontiers for 43 countries in 1960, 1970, and 1980. They found that not all countries are technically efficient while a number of developing countries perform better in the agricultural sector than some of the developed countries (p. 57). They found that there a potential to improve the productivity of developing countries through the capital stock and education as indicated through the high output elasticities of the production frontiers they have estimated (p. 57). In the process of their discussion, Kudaligama and Yanagida (2000, p. 60) differentiated deterministic from stochastic production frontiers. Deterministic production function considers deviation from the frontiers as arising from inefficiency or statistical noise arising from inefficiency, measurement error, or incomplete specification (Kudaligama and Yanagida 2000, p. 60). In contrast, stochastic production frontier account for the said deviation via a composed error term (Kudaligama and Yanagida 2000, p. 60). Tzouvelekas (2000, p. 33) provided a theoretical and methodological framework for estimating a translog production function using generalized least square. Antle and Capalbo (2001, p. 391) pointed out that empirical production functions that do not incorporate site specific variables can lead to biased and inconsistent parameter estimates and highlighted the need for country, locality, and circumstance specific production functions. Mundlak (2001) surveyed the literature and discussed how the production function has been used to explain economic growth and describe technology. Taking off from Arrow and Debreau that production under uncertainty can be represented by states of nature and in turn the states of nature can be represented as finite or continuous, Chambers and Quiggin (2002, p. 514) argued that the production function can be modelled in the same manner. In addition, a risk premium variable can be introduced into the production function (Chambers and Quiggin 2002, p. 515). The risk premium can represent the cost of removing uncertainty in the production function (Chambers and Quiggin 2000, p. 515). A risk premium can be additive or multiplicative. A production function with additive uncertainty has constant absolute riskiness (Chambers and Quiggin 2000, p. 517). On the other hand, a stochastic production function with multiplicative uncertainty has constant relative riskiness (Chambers and Quiggin 2000, p. 518). However, an alternative is to use the Just and Pope production function that has become the model of choice for many agricultural economists studying production decision-making under uncertainty (Chamber and Quiggin 2002, p. 519). A Just-Pope production function or technology is an additive combination of nonstochastic technology with a multiplicative technology (Chambers and Quiggin 2000, p. 519). However, the work of Chambers and Quiggin (2000) did not specify how the additive, multiplicative, and the Just-Pope production function may be estimated. The work merely described the three stochastic production functions. Following the suggestion of Paul Samuelson and claiming empirical evidence, Felipe and Adams (2005, p. 441) argued that the Cobb-Douglas production function simply reproduce the income identity in which value added equals the sum of wage and total profits. Based on this, Felipe and Adams argued (2005, p. 442) that “if the correct form of the identity, written as a production function, were fitted, one should always conclude that the aggregate production function exhibits constant returns to scale, and that the factor markets are competitive”. For Felipe and Adams (2005, p. 442), this implies that essentially the production function can never be empirically tested because they cannot be refuted. Arguing that ignoring risk considerations can cause inefficient estimates while selectivity can lead to biased estimate, Koundouri and Nauges (2005, p. 597) showed that correcting for risks without correcting for selectivity can lead to incorrect inferences. In addressing this problem, Koundouri and Nauges (2005, p. 606) recommended the use of Heckman’s correction to a Just-Pope production function. The work of Koundouri and Nauges (2005, p. 606) illustrated the bias that can result from selectivity and the benefits that can be realized if correction for selectivity is employed using the Heckman’s correction. In assessing the determinants of agricultural production and profitability, Olujenyo (2008, p. 37) employed ordinary least squares estimation techniques and found that age, education, labour and labour and non-labour inputs significantly affect and positively output while farm size and years of experience were negatively affecting output. Arguing that exceptional crop yield observations or outliers can cause misleading results if ordinary least square regression is used, Felipe and Hediger (2008, p. 2) employed robust regression. According to Felipe and Hediger (2008, p. 2), the results of their regression showed that robust regression reduces the potential cost of misspecification. According to Felipe and Heidiger (2008, p. 16), robust regression is better compared to quadratic and square root regression. Baten et al. (2009, p. 1374), used a stochastic frontier production function for panel data to capture the inefficiency effects in agricultural production. The Baten et al. (2009) methodology is called as the Stochastic Frontier Analysis (SFA) methodology. The methodology found that a 49% technical inefficiency exists in tea production. Amarnath and Prasad (2009, p. 90) used not only a decomposition test but also a production function approach as well to assess the determinants of agricultural production from 1950 to 2006 in India. Through the production function approach, Amarnath and Prasad (2009, p. 90) found that land significantly affected agricultural output up to 1964 but became less significant in affecting agricultural output since that year. According to Amarnath and Prasad (2009, p. 90), the agricultural production function approach verified the results of the decomposition analysis. Meanwhile, it is interesting to note that although agriculture was theme of the World Bank World Development Report of 1997, not even one section was devoted to the discussion of the production function of the 386-page book. In summary, it can be said that the production continues to be an important topic in the economic literature but relatively but relatively recent discussion tends to neglect it. For instance, in doing this review of literature, not much on the production function was obtained from the recent literature. Further, modern discussion on the production has improved a lot. For instance, modern techniques on the production function can address multicollinearity and the risks in production. Reference List Amarnath, T. and Prasad, A., 2009. Agricultural development in India since independence: A study on progress, performance, and determinants. Journal of Markets, 1 (1), 63-92. Antle, J. and Capalbo, S., 2001. Econometric-process models for integrated assessment of agricultural production systems. Agricultural & Applied Economics Association, 83 (2), 389-401. Banker, R. and Maindiratta, A., 1992. Maximum likelihood estimation of monotone and concave production frontiers. Journal of Productivity Analysis, 3, 401-415. Bera, A. and Sharma, Subhash., 1999. Estimating production uncertainty in stochastic production function model. Journal of Productivity Analysis, 12, 187-210. Chambers, R. and Quiggin, J., 2002. The state-contingent properties of stochastic production functions. American Journal of Agricultural Economics, 84 (2), 513-526. Coyle, B., 1992. Risk aversion and price risk in duality models of production: A linear mean-variance approach. American Journal of Agricultural Economics, 74 (4), Echevarria, C., 1998. A three-factor agricultural production function: The case of Canada. International Economic Journal, 12 (3), 63-75. Felipe, J. and Adams, F., 2005. The estimation of the Cobb-Douglas function: A retrospective view. Eastern Economic Journal, 31 (3), 427-445. Finger, R. and Hediger, W., 2008. The application of robust regression to a production function comparison---the example of Swiss corn. Working Paper 2. Zurich: Institute for Environment Decisions. Gujarati, D., 2004. Basic econometrics. 4th ed. McGraw-Hill. Just, R., Zilberman, D., and Hochman, E. 1983. Estimation of multicrop production function. Agricultural and Applied Economics Association, 65 (4), 770-780. Koundouri, P. and Nauges, C., 2005. On production function estimation with selectivity and risk consideration. Journal of Agricultural and Resource Economics, 30 (3), 597-608. Kudaligama, V. and Yanagida, J., 2000. A comparison of intercountry agricultural production functions: A frontier function approach. Journal of Economic Development, 25 (1), 57-74. Mittlehammer, R., Young, D., Tasanasanta, D., and Donnely, J., 1980. Mitigating the effect of multicollinearity using exact and stochastic restrictions: The case of an aggregate production function in Thailand. Agricultural and Applied Economics Association, 62 (2), 199-210. Mittelhammer, R. and Conway, R. 1988. Applying mixed estimation in economic research. American Journal of Agricultural Economics, 70 (4), 859-866. Mundlak, Y., 1999. Rethinking within and between regressions: The case of agricultural production functions. Annales d’ Economie et de Statistique, 55/56, 475-501. Mundlak, Y., 2001. Explaining economic growth. Agricultural & Applied Economics Association, 83 (5), 1154-1167. Olujenyo, F., 2008. The determinants of agricultural production and profitability in Akoko Land, Ondo-State, Nigeria. Journal of Social Sciences, 4 (1), 37-41. World Bank, 2007. World development report 2008: Agriculture for Development. Washington: The World Bank. Varian, H., 2006. Intermediate microeconomics. New York: Norton & Company. Read More