| An efficient organization produces the maximum combination of outputs from the inputs it utilizes. Over the years, researchers have studied ways to measure the efficiency of an organization. Many of the proposed solutions fail to incorporate multiple outputs and multiple inputs into the evaluation. Data envelopment analysis (DEA) provides an answer to this deficiency. To date, more than 1,000 articles in the literature deal with DEA and its application in banking (including use by the Federal Reserve system), software assessment, the military, supplier relations, agriculture, management, and government, among many others. The CCR (Charnes, Cooper, and Rhodes, 1978) data envelopment analysis model measures efficiency as a ratio of weighted outputs to weighted inputs with the weights chosen by the organization under evaluation. A major strength of this approach is its nonparametric nature; no mathematical model is specified for the optimal output for given input. A weakness of data envelopment analysis is the failure to incorporate stochastic aspects of the data into the measure of efficiency. To date, no consistent solutions has been proposed to incorporate statistical noise without imposing a functional form on the optimal frontier, assuming homoscedasticity of error, or considering only a single output.; This dissertation proposes a DEA solution that incorporates random error with standard deviation proportional to the level of output, a common form of heteroscedasticity in economic and production data. Simulating from various such distributions, DEA-assigned sample efficiency scores for truly efficient organizations are determined. Additionally, limiting distributions for sample efficiency scores for efficient organizations are constructed that are pertinent regardless of the number of outputs or inputs under consideration. These limiting distributions are surprisingly insensitive to sample size. All distributions are scale invariant and are relevant for any functional form of the efficient frontier, preserving the major structural advantage of data envelopment analysis. From the sample efficiency distributions, a statistically conservative hypothesis test is created that allows the testing of an individual organization's efficiency. |
