Data envelopment analysis (DEA): a method for benchmarking

The literature reviewed has shown that most performance measures are system-specific and that there is no consensus on the best set of benchmarks to concisely describe a dairy farming system. However, efficiency can fulfil the role of being a simple, comprehensive, and versatile indicator that naturally stands out as a benchmark because it is always a relative measure. Efficiency measures the ability of a certain business to use the existing technology or set of resources in the best possible way. Using an output-oriented perspective, it is the observed output of a particular farm compared to the maximum attainable output that can be produced under the current production frontier or technology set (Farrel, 1957). Villano et al. (2010) defined efficiency as the ratio of the observed output to the corresponding technological frontier or benchmarking peer, conditional on the level of inputs used. Although it is debatable whether technical efficiency is the ultimate measure of performance as claimed by Diewert and Lawrence (1999), it is undoubtedly important because if a firm does not attain technical efficiency, it means that resources are being wasted.

It is important to distinguish between efficiency and productivity. Jiang (2011) highlighted the differences and similarities between both terms, and claimed that these were not interchangeable since productivity is an absolute measure. DairyNZ (2012) defined productivity as the ratio, aggregated inputs to aggregated outputs. However, Bravo-Ureta (1986) warned that the aggregation of inputs and outputs is subjective and can affect the conclusions. Despite differences in methodology, warnings, and acknowledged limitations, modern benchmarking analyses increasingly use best practice or frontier analysis methods. Table 7 presents a taxonomy of frontier methods adapted from Bogetoft and Otto (2011).

Table 7

Frontier Methods Taxonomy

In the choice of deterministic or stochastic methods, the key question is whether the analysis requires flexibility in the mean structure or precision in the noise separation. Data Envelopment Analysis (DEA) is a deterministic, non-parametric method that responds to flexibility, without the need to know the underlying production functions or to have price information. Gattoufi, Oral, and Reisman (2002) reported that top DEA article journals include the European Journal of Operations Research, Management Science, Journal of Productivity Analysis, Applied Economics, Journal of Econometrics, and Journal of Banking and Finance. In the last decade, DEA has increasingly gained popularity among more diverse areas of research because of its simplicity, versatility, and relevance.

Farrell (1957) first envisioned the use of the production frontier in terms of efficiency, observing that there existed an efficient function from which all the observed points deviate randomly but in the same direction. Later, Charnes, Cooper and Rhodes (1978) introduced DEA as a technique based on mathematical optimisation, which had the ability to evaluate relative efficiency and to set individual firm efficiency targets. More recently, Coelli (1997) pointed out that a firm was only efficient if it operated on the frontier, and further, if all associated ‘input excesses’ were zero. A distinct advantage of DEA is that it provides explicit, real peer units for benchmarking. Rouse et al. (2010) described DEA as a formal method, either for efficiency measurement, benchmarking, or both.

DEA owes its name to the way the frontier envelops observations, which are typically represented by a performance score that ranges between zero and one and an expected skewed to the right distribution for the efficiency scores with most scores falling above 0.5 (Cooper, Seiford, & Tone, 2006). The production frontier has several important properties, such as non- negativity, non-decreasing values, concavity, and weak essentiality. The first to third conditions

Deterministic Stochastic

Parametric Corrected Ordinary Least Squares (COLS) Stochastic Frontier Analysis (SFA)

Aigner and Chu (1968), Lovell (1993), Greene (1990, 2008) Agner et al. (1977), Battese and Coelli (1992), Coelli et al (1998a)

Non-parametric Data Envelopment Analysis (DEA) Stochastic Data Envelopment Analysis (SDEA)

are obvious in their meanings, while the weak essentiality property means that the production of positive output is impossible without the use of at least one input (Coelli, Prasada Rao, O’Donnell, & Battese, 2005).

DEA models separate the data variables into input or output types such that input variables are causal factors to the outputs. The proper treatment of inputs and outputs in efficiency studies has been regarded as being very important; the variables have to be consistent with the phenomena they are supposed to capture. According to Coelli et al. (2005), inputs may be classified into five categories: capital (K); labour (L); energy (E); material inputs (M); and services (S). Often E, M and S categories are aggregated into a single category ‘EMS’. Capital, unlike the other variables which are consumed in the production process, is a durable input which may be measured from the various assets of a particular Decision Making Unit (DMU) or farm. In farming, K is typically composed of land, livestock, buildings, and plant. Labour constitutes another primary input, normally measured using a single variable which aggregates paid and unpaid labour and management. It may be expressed in physical full-time-equivalent units, hours of work, or in monetary terms. None of these measures take into account the composition and quality of the labour force such as skills, age, gender, and education levels (Coelli et al., 2005).

Moreover, the number of efficient DMUs relies on the number of inputs plus outputs (Cinca & Molinero, 2004). The greater the dimensionality of the production function the more constraints the model has and the less discerning the analysis (Jenkins & Anderson, 2003). The analysis ought only to include inputs and outputs that are definitely relevant to the proposed study. According to Rouse et al (2010) there are some other rules about their proportion:

1. The number of farms (firms or decision-making units) must exceed a minimum of three times the number of inputs plus outputs; or

2. The number of farms must be higher than the product of inputs and outputs.

One important point to note is that inputs need to represent a production function or technology set such that the proposed output is achievable (Coelli et al., 2005). Another rule is that input variables should be controllable variables. The transformation of multiple inputs into outputs is affected by controllable and non-controllable variables, as well as observable and non- observable managerial characteristics. Therefore, there is a lack of information about the true underlying technology that needs to be acknowledged. This, in turn, leads to an efficiency estimate that is always higher than the real value of efficiency. The efficient DMUs (peers) resulting from a DEA provide concrete evidence of performance improvement targets for both inputs and outputs. As peer units are usually interpreted as those demonstrating how a firm can

improve, it is relevant that changes are actually feasible, which is only possible if inputs are fully controllable. The analysis of the DEA peers is out of the scope of this study; exploring the explicit, real peer units would be a field for further research.

Economic or ‘overall’ efficiency (EE) is one of the major factors explaining differences in firm survival and growth (Olson & Vu, 2009). It has two components: price or ‘Allocative’ Efficiency (AE) and technical efficiency (E), such that

EE = E x AE (Farrel, 1957; Olson & Vu, 2009).

AE reflects the ability of a business to use inputs and produce outputs in optimal proportions to maximise profit, given their respective prices (Farrell, 1957). In turn, E is a measure of how a business transforms inputs into physical outputs and includes two components: pure technical efficiency (TE) and scale efficiency (SE) (Moreira & Bravo-Ureta, 2010). According to Barnard and Boehlje (1998), economic efficiency is determined to a large extent by pure technical efficiency because it reflects managerial ability especially in smaller firms. Allocative, scale, and pure technical efficiencies all impact profit, but the first is always related to changes in input and/or output prices, neither of which are controlled by farmers. In contrast, technical efficiency refers only to discretionary variables or those variables that can be influenced by someone’s discretion, judgement, or preference (Harrison, Rouse & Amstrong, 2012). According to Latruffe (2010), in most circumstances an improvement in technical efficiency can result from a more competent use of the existing technology: that is by producing the same output by using less inputs or more output with the same level of inputs. A second way to improve efficiency is through economies of scale. Figure 6 shows a graphical representation of both constant (CRS) and variable returns to scale (VRS) DEA envelopes for one output and one input condition.

Figure 6. CRS and VRS DEA envelopes. Adapted from: Coelli (1997)

Scale refers to a firm’s size; scale efficient firms have a scale elasticity of one and work under Constant Returns to Scale (CRS), while scale inefficient firms could exploit either scale economies or diseconomies, which imply Variable Returns to Scale (VRS), including both decreasing (DRS) and increasing returns to scale (IRS) (Coelli, 1997). DRS takes place when a proportionate increase in all inputs results in a less than proportional increase in output; the latter conversely happens when increased inputs lead to a more than proportionate increase in output. ‘Scale’ interacts with technical efficiency in predictable ways: in larger scale operations, managerial input can be spread too widely and this might generate inefficiencies, while excessively small scale operations can result in high costs, because the fixed investment is spread over relatively low output levels (Barnard & Boehlje, 1998). TE, when measured under the assumption of CRS, only represents the true technical efficiency if the firm has an optimal scale of operation (Rouse, Harrison, & Chen, 2010). Otherwise, the pure TE component, which refers solely to management practices rather than the firm’s operating scale, must be calculated under the VRS assumption. SE may also be of interest, and can be calculated as the ratio CRS:VRS. Different DEA assumptions define diverse DEA methods that differ in the ex-ante assumptions involved. A major DEA assumption is that data is measured without error, and thus, differences in efficiency scores are due to inefficient transformation of input into outputs, not allowing for noise or error. The free disposability assumption stipulates that unnecessary inputs and unwanted outputs can be freely discarded.