Advantages of the DEA Approach
A key advantage of DEA, over other approaches of measuring efficiency, is that it can easily accommodate both multiple inputs and multiple outputs. As a result, it is particularly useful for analysing farm efficiency, because prior aggregation of the outputs is not necessary. Furthermore, unlike the Stochastic Frontier Analysis (SFA) approach, with DEA a specific functional form, for the production process, does not need to be imposed on the model. Moreover, it is possible to determine the input reduction needed for a given farm to achieve technical efficiency (Cooper; Seiford and Tone, 2000).
Disadvantages of the DEA Approach
Despite its several strengths, the major weakness of DEA, for use in measuring farm performance, is that it does not take into account the effects of weather variations, disease incidences and/or measurement errors. To take care of this weakness, studies have to be based at a regional level (small geographical area), where potential variations in weather conditions, pests and disease incidences are likely to be minimal. Notwithstanding this weakness of DEA, the method is still suited to the present study, as the detailed economic analysis of the performance of the producers of potential feedstocks for biofuels production (which focussed on sugarcane) covers a small geographical area, with minimal variations in weather, common pests and diseases.
Moreover, the difficulties involved in imposing various constraints to the distance functions framework when using the stochastic frontier analysis approach to estimate farm performance undermine its perceived superiority over DEA. The estimated parameters of output distance functions frequently violate the monotonicity, quasiconvexity and convexity constraints implied by economic theory (Färe and Primont, 1995; Reinhard and Thijssen (1998); O’Donnell and Coelli, 2003). This, inevitably, causes the estimated elasticities and shadow prices to have incorrect signs, and ultimately leads to perverse conclusions concerning the effects of input and output changes on relative efficiency levels. This emphasises the credibility of the decision to make use of DEA in assessing efficiency among the producers of potential feedstocks for producing biofuels.
Advantages of the SFA Approach
The main advantage of the SFA approach is that it accounts for data noise, i.e. data errors and omitted variables. Moreover, with this approach, standard statistical tests can be used to test hypotheses on model specification and significance of the variables included in the model. It is also more amenable to modelling effects of other variables, like land quality and variations in weather conditions.
Disadvantages of the SFA Approach
The main disadvantage of the SFA approach is that it requires the specification of a functional form (to represent the production technology). Also, the separation of noise and inefficiency relies on strong assumptions on the distribution of the error term which might not be true in certain circumstances.
Furthermore, in most cases the stochastic frontier approach is used to determine the maximum output given a set of inputs. A long standing major criticism of this method is that it cannot adequately handle multiple outputs. Although there are two frameworks which have been developed in an attempt to make the stochastic frontier approach suitable for multiple outputs situations, they (the frameworks) have several drawbacks. The first framework is the stochastic distance function approach and the second is the polar coordinates approach (Ray, 2003).
Fare et al., (1994) introduced the concept of using distance functions to express the output bundle of a multiple-products technology. In their approach, the distance function is specified as a function of variable and fixed inputs and output levels. The technology is specified as a translog function, and subsequently estimated by linear programming procedures. Unfortunately however, multi-products stochastic distance functions suffer from input-output separability and linear homogeneity in outputs (Ray, 2003).
Despite the drawbacks of the multi - products stochastic distance functions, there are several studies which have managed to extract information on the shadow prices of inputs and/or outputs from the estimated distance functions by exploiting various duality theorems. The duality results rely on particular theoretical properties of distance functions, i.e. they rely on the fact that the output distance function is non-decreasing, convex and homogenous of degree one in outputs, and non-increasing and quasi-convex in inputs. The input distance function is non-increasing, concave and homogenous of degree one in inputs, and non-decreasing and quasiconcave in outputs. This (the need to use duality theorems which depend on theoretical properties of distance functions to extract information, such as shadow prices for inputs) emphasises the importance of ensuring that the distance function does not violate the monotonicity, quasiconvexity and convexity constraints implied by economic theory. Unfortunately, however, there are very few empirical studies (if any) in which all these properties, i.e. monotonicity, quasiconvexity and convexity have been imposed on parametric (input or output) distance functions. In addition, there are only few studies which have bothered to report the degree to which their estimated functions satisfy these properties. And for those few studies which report the degree to which their estimated functions satisfies the theoretical conditions, their functions violate significantly the theoretical conditions (O’Donnell and Coelli, 2003).
O’Donnell and Coelli (2003) reported that in their survey of distance function applications, they found that all papers had imposed homogeneity and monotonicity (i.e. the non-increasing/decreasing properties), but they did not find any paper which had attempted to impose the curvature conditions (i.e. the convexity/quasi-convexity and concavity/quasi-concavity properties). They attributed the large proportion of studies which managed to impose the homogeneity and monotonicity constraints to the relative
ease with which they can be imposed. The homogeneity constraints can be written as linear equality constraints on the parameters and can be easily imposed using either linear programming or econometric methods. Likewise, the monotonicity constraints are linear inequality constraints which are easy to impose using linear programming, but difficult to impose using traditional econometric approaches, especially since they need to be imposed at each data point. On the other hand, they attributed the lack of studies which attempted to impose the curvature constraints to the difficulties involved in imposing them. For a distance function to satisfy the curvature conditions, one has to impose non-linear inequality constraints at each data point. Unfortunately, this is very difficult when using traditional sampling theory econometric methods. While sampling theorists have developed methods for imposing convexity and concavity constraints, extension of the methods to deal with quasi-convexity and quasi-concavity is not straightforward (Gallant and Golub's, (1984); O’Donnell and Coelli, 2003).
As a result of the difficulties involved in imposing various constraints to the distance functions which have been described in the previous paragraphs, the estimated parameters of output distance functions frequently violate the monotonicity, quasiconvexity and convexity constraints implied by economic theory. This, inevitably, causes the estimated elasticities and shadow prices to have incorrect signs, and ultimately leads to perverse conclusions concerning the effects of input and output changes on productivity growth and relative efficiency levels.
The second framework developed in an attempt to make the SFA approach suitable for multi-products (production) technologies is the polar coordinate framework. The polar coordinate framework specifies a translog flexible functional form of a multiple product technology. The dependent variable is specified as a distance function relative to the distances of all outputs from the origin. The independent variables are the usual factors of production but include polar coordinate values obtained relative to the various outputs. Estimation is accomplished by conventional maximum likelihood procedures with two error terms, as in the single product stochastic frontier approach. The main drawback of the polar coordinate framework is that there is likely to be a problem of implicit simultaneous equation bias. This is because functions of the dependent variable appear on both sides of the equation (Ray, 2003).