A Comparison of DEA, DFA and SFA Methods using Data from Caspian Cattle Feedlot Farms

INTRODUCTION

For all agricultural sectors, achieving a high level of efficiency is an important task. Cattle raising has been proven as a main resource to supply meat in Iranian agricultural industry. The meat consumption in Iran is evaluated to be about 12 kg per person and approximately, 65244 tons were imported in 2007. One of the most important ways to become free of need of meat in developing countries is the development of an efficient farm and the improvement of an inefficient farm (IRICA, 2009).

In the last two decades, several agricultural policies in Iran have attempted to improve the performance of this industry, but none of these policies were scientific.

Due to the arguments presented above, it is important to assess the efficiency of Iranian Caspian cattle feedlot farms.

As we know, the technical efficiency of a farm measures its success in producing maximum outputs from a given set of input. As is well established in the literature, productivity growth can be decomposed into Technological Change (TC) and Technical Efficiency (TE). This decomposition makes it possible to study the sources of productivity growth from different points of view. Specifically, TE can be interpreted as a relative measure of managerial ability for a given technology, while TC evaluates the effect in productivity from the adoption of new production practices. In other words, gains in TE are derived from improvements in decision-making, which in turn are related to a host of variables including knowledge, experience and education. By contrast, TC relates to investments in research and technology.

The purpose of this study is to analysis the technical efficiency in Caspian cattle feedlot farms in Iran by using parametric and nonparametric techniques such as DEA, Data Frontier Analysis (DFA) and Stochastic Frontier Analysis (SFA).

Data envelopment analysis (DEA) is a nonparametric technique for measuring and evaluating the relative efficiencies of decision making units (DMUs). Since the pioneering research of Charnes et al. (1979), DEA has demonstrated to be an effective technique for measuring the relative efficiency of a set of DMUs which utilize the same inputs to produce the same outputs.

The aims of this study is thus to evaluate the technical efficiency in Caspian cattle feedlot farms In Iran. A comparison of DEA, DFA and SFA results is put forwarded.

Data Envelopment Analysis (DEA), introduced by Charnes et al. (1979), provides a nonparametric methodology for evaluation the relative efficiency of each of a set of comparable decision making units (DMUs), relative to one another. The definition of a DMU is generic and DMUs can be in business firms and others.

In measuring TE, different methodologies and strategies have been proposed and considerable controversy has surrounded the choice and merits of a specific methodology and the impact of such choice on the ensuing analysis. Wadud and White (2000) indicate that in most empirical studies the selection of the methodology used to measure of TE is arbitrary and mainly based on the objective of the study, the data variable and the personal preference of the researcher.

In Cook and Green (2005), the DEA technique was used to evaluate the operational efficiency of a set of electric power plants and of the individual power units that make up those plants.

Lin et al. (2009) have used the DEA technique to evaluate the operating efficiency of each branches of the case bank in 2006 in an attempt to have more objective and impartial measuring indices for appraising the operating performances of branches and proposed the suggestions for each management DMUs while providing for head quarter management unit to allocate internal objectives to branches, branches operating advantages and disadvantages can be known.

Erbetta and Rappuoli (2008) applied the DEA technique to determine the optimal scale in the Italian gas distribution industry. Stochastic Frontier Analysis (SFA) and Data Envelope Analysis (DEA) are introduced to measure and compare the technical efficiency scores for 79 forest and paper companies by Lee (2005). They suggested that using only one of these methods to improve efficiency may cause incorrect measurement of increase output or reduce input since each of these approaches has some inherent limitations. Before any correctional improvements are taken, the stability of the technical efficiency estimates from a parametric (or nonparametric) method should be evaluated by comparing them against those found using the nonparametric (or parametric) method.

This type of study can be found in the sectors of public education by Chakraborty et al. (2001), banks by Kohers et al. (2000) and public schools by Ruggiero and Vitaliano (1999) and Hjalmarsson et al. (1996).

AN INTRODUCTION TO DEA, DFA AND SFA DEA efficiency analysis: To describe the DEA efficiency measurement, let there are n DUMs and the performance of each DMU is characterized by a production process of m inputs (x_ij : i = 1,...,m) to yields s outputs (y_ri : r = l,...,s). The ratio DEA model also known as the CCR model, measures the efficiency of DMU_o as the maximum of the ratio of its weighted outputs to its weighted inputs as:

where, the maximum is sought subject to the conditions that this ratio does not exceed one for any DMU_j and all the input and output weights are positive. To estimate the DEA efficiency of DMU_o, we solve the following DEA model (Charnes et al., 1979):

(1)

where, ε>0 is a non-archimedean construct. This linear fractional programming problem can be reduced to a non-ratio format in the usual manner of Charnes and Cooper (1962). Specifically, make the transformation

and let

Then Eq. 1 can be expressed in the form:

(2)

This model is a Constant Returns to Scale (CRS) program and assumes that all input/output data are known exactly and all produced outputs are perfect and complete. The efficiency ratio θ_o ranges between zero and one, with DMU_o being considered relatively efficient if it receives a score of one. From a managerial perspective, this model delivers assessments and targets with an output maximization orientation.

SFA (stochastic frontier approach): The stochastic frontier production function was independently proposed by Aigner et al. (1977) and Meeusen and Van den Broeck (1977). The original specification involves a production function specified for cross-sectional data which has an error term which is comprised of two components, one to account for random effects and another to account for technical inefficiency. This model can be expressed in the following form:

where, Y_i is the production (or the logarithm of the production) of the i-th firm, X_i is a kx1 vector of (transformations of the) input quantities of t he i-th firm, β is an vector of unknown parameters, ε_i s are random errors with N(0, σ²V), which are associated with random factors such as measurement errors in production and independent of the U_i, which are non-negative random variables which are assumed to account for technical inefficiency in production and are often assumed to be symmetric independently distributed as N(0, σ²,U) random variables and independent of U_i. This original specification has been used in a vast number of empirical applications over the past two decades. A number of comprehensive reviews of this literature are available, such as Forsund et al. (1980), Schmidt (1986), Bauer (1990) and Greene (1993).

DFA (deterministic frontier approach): For DFA analysis, we estimated Cobb-Douglas production function by the Ordinary Least Square (OLS) method. In this method, the differences between actual production and Frontier Production Attributed to management factors. The Deterministic Frontier Production function was expressed in the following forms:

where, y_i is output of farm j; j; X_ij is input i that farm j be used. β_i is the OLS estimated coefficient of input i (the elasticity of input i). ε_j is representation of technical efficiency of farm j.

In is estimated production of farm j that is greater than or equal to its actual production (ln y_j). Only in farms that having 100% technical efficiency, In = In y_i. So we solve the following:

Then technical efficiency is determined as:

METHODOLOGY AND DATA DESCRIPTION

This study utilizes DEA as it is an approach that can easily model slacks, even though there exists some literature on the separate estimation of technical and allocative inefficiencies using stochastic frontiers Kumbhakar and Lovell (2000), Kumbhakar and Tsionas (2004). DEA studies, however, do not explicitly account for slack variables in the relative efficiency analysis. As Fried et al. (1993) point out," The solution to DEA problem yields the Farrell (1957) radial measure of technical efficiency plus additional non-radial input slacks and output surpluses. In typical DEA studies, slacks and surpluses are neglected at worst and relegated to the background at best. Such input and output slacks are essentially associated with the violation of neoclassical assumption. If we take the standard input-oriented DEA approach, for example, input slacks would be associated with the assumption of strong or free disposability of inputs. Hence, units with extensive usage of some inputs would be deemed to be efficient according to standard Banker et al. (1984). If slacks were incorporated into the relative efficiency analysis, however, such units could actually be found to be inefficient.

For the reasons outlined above, therefore, we feel it is appropriate to use the Slack-Based Measure (SBM) of Tone (2001). This SBM approach specifically incorporates slacks in the objective function. To describe the SBM model of Tone, let there are n DMUs and the performance of each DMU is characterized by a production process of m inputs(x_ij : i = 1,...,m) to yields s outputs (x_ij : i = 1,...,s):

The optimal solution is when e₀ = 1 and hence a DMU will have zero input and output slacks and be fully efficient on the frontier. We also have used Stochastic Frontier Analysis (SFA) and frontier analysis to evaluate the cattle feedlot farms. The sample consisted of around 70 Iranian Caspian cattle feedlot farms. The data for this analysis are derived from operations during 2007 and 2008.

The raw data are reported in Table 1. We use six variables from the data set as inputs and outputs. Inputs include number of calve per farm (x₁), number of labors/ days/hours (x₂), total metabolizable energy intake (Mcal) (x₃), total crude protein intake (kg) (x₄) and total cost of hygiene- treatment of calve (Rials) (x₅).

The unique output is total live weigh gain of calve per farm (kg) (y).

Details of inputs and outputs are defined below:

EMPIRICAL RESULTS

Table 2 presents the estimation results of the cost and technical frontiers, as the table indicates, 11 farms are efficient in DEA. However, we note that except for farm 3, all of the other farms are inefficient in DEA and DFA approaches.

We also have calculated the correlation between the mean of technical efficiencies calculated in different methods. The results are listed in Table 3, as we can see there is a significant correlation in different methods. The maximum correlation is DFA and SFA, while the minimum one is in DEA and DFA. It is to be noted that DEA is a nonparametric approach, while DFA is a parametric approach. Efficiency intervals in three methods DFA, DEA and SFA are, respectively (0.15 , 1), (0.2 , 1) and (0.183 , 1). As we can see, farm 3 is the top-ranked farm and farm 13 is the low-ranked in three methods.

Table 4 presents Descriptive Statistics of technical efficiency, means of technical efficiency in DFA(0. 6910) is the least and significantly different with SFA(0. 6910) and DEA(0. 7221) Methods(p<0.01).

Table 1:	Variables and raw data get as inputs(x1…x5) and output(y)

Table 2:	Technical efficiency estimated by DFA, SFA and DEA methods

Table 3:	Pearson correlations
**Correlation is significant at the 0.01 level (2-tailed)

Table 4:	Descriptive statistics of technical efficiency
*Difference is significant (p<0.01), (cal F = 6.166), (N = 59)

Efficiency scores in this study were estimated using the computer programs, DEAP Version 2.1 (Coelli, 1996), FRONTIER Version 4.1 and SPSS Statistics 17.0.