# Data Envelopment Analysis Research Paper

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Data Envelopment Analysis (DEA) is a technique relying on mathematical programming methods for estimating various types of efficiency in production. First applied by Michael Farrell in 1957, the technique was popularized and named by Abraham Charnes, William W. Cooper, and Eduardo Rhodes in the late 1970s. As of 2004, more than 1,800 articles using DEA had been published (see Gattoufi et al. 2004).

Standard microeconomic theory of the firm describes a production set containing all feasible combinations of input quantities and output quantities for a given industry. Firms operating on the upper boundary of this set are technically efficient, while firms operating below the upper boundary are technically inefficient. Technically efficient firms may be allocatively inefficient if they do not use the optimal mix of inputs (determined by input prices) to produce the optimal mix of outputs (determined by output prices). Technically inefficient firms can feasibly reduce the quantities of inputs used without reducing output quantities, increase output quantities without increasing input quantities, or simultaneously reduce input quantities while increasing output quantities.

Various measures of efficiency have been defined, and, in each case, efficiency depends on the firm’s location within the production set. Given observations on pairs of input and output quantities, DEA estimates the unknown production set using a convex set determined by the data. As a practical matter, DEA efficiency estimates are usually computed by solving a linear program.

The usefulness of DEA lies in its ability to estimate efficiency when multiple inputs are used to produce multiple outputs, without the need to specify distributions or functional forms. DEA is a fully nonparametric estimation method. For estimating technical efficiency, DEA does not require information about prices, making it especially useful in many public-policy applications, where economically meaningful prices often do not exist. These features contrast with parametric approaches, where distributions for random variables reflecting noise and inefficiency, as well as a functional form (e.g., translog) for the response function, must be specified. The nonparametric nature of DEA means that it is very flexible and can potentially be used to describe a wide variety of situations.

Unlike parametric approaches, however, DEA makes no allowance for noise or measurement error, which can severely distort DEA efficiency estimates. A number of outlier-detection techniques have been developed for use with DEA estimators (e.g., Wilson 1993; Simar 2003; Porembski et al. 2005). In addition, researchers have recently introduced new estimators that retain the nonparametric feature of DEA but are resistant to the effects of outliers and related problems.

Until recently, the statistical properties of DEA estimators remained unknown, and methods for making inferences about efficiency using DEA estimators were unavailable. In 2000, Léopold Simar and Paul Wilson provided a survey of new developments. In particular, the convergence rates of DEA estimators depend on the numbers of inputs and outputs, or the dimensionality of the production set. These rates worsen with increasing dimensionality. Consequently, to retain the same order of magnitude in estimation error, sample sizes must increase exponentially as dimensionality increases. Computationally intensive bootstrap methods provide the only practical approach to inference with DEA estimators. Due to the boundary of the production set, standard bootstrap methods must be modified by smoothing procedures to yield consistent inference.

Bibliography:

1. Charnes, Abraham, William W. Cooper, and Eduardo Rhodes. Measuring the Efficiency of Decision Making Units. European Journal of Operational Research 2: 429–444.
2. Charnes, Abraham, William W. Cooper, and Eduardo Rhodes. 1981. Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through. Management Science 27: 668–697.
3. Farrell, Michael J. 1957. The Measurement of Productive Efficiency. Journal of the Royal Statistical Society 120 (A): 253–281.
4. Gattoufi, Said, Muhittin Oral, and Arnold Reisman. 2004. Data Envelopment Analysis Literature: A Bibliography : Update (1951–2001). Socio-Economic Planning Sciences 38: 159–229.
5. Porembski, Marcus, Kristina Breitenstein, and Paul Alpar. 2005. Visualizing Efficiency and Reference Relations in Data Envelopment Analysis with an Application to the Branches of a German Bank. Journal of Productivity Analysis 23: 203–221.
6. Simar, Léopold. 2003. Detecting Outliers in Frontier Models: A Simple Approach. Journal of Productivity Analysis 20 (3): 391–424.
7. Simar, Léopold, and Paul W. Wilson. 1998. Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models. Management Science 44 (1): 49–61.
8. Simar, Léopold, and Paul W. Wilson. 2000a. A General Methodology for Bootstrapping in Non-parametric Frontier Models. Journal of Applied Statistics 27 (6): 779–802.
9. Simar, Léopold, and Paul W. Wilson. 2000b. Statistical Inference in Nonparametric Frontier Models: The State of the Art. Journal of Productivity Analysis 13 (1): 49–78.
10. Wilson, Paul W. 1993. Detecting Outliers in Deterministic Nonparametric Frontier Models with Multiple Outputs. Journal of Business and Economic Statistics 11 (3): 319–323.