DATA ENVELOPMENT ANALYSIS AND APPROACHES FOR MEASURING THE EFFICIENCY OF DECISION-MAKING UNITS WITH AN APPLICATION TO PROGRAM FOLLOW-THROUGH IN UNITED STATES EDUCATION

In this study we develop a scalar measure of efficiency which is especially suitable for use by decision-makers as a basis for evaluating and/or controlling public sector activities. We further demonstrate how this scalar "technical efficiency" (TEF) measure makes it possible to distinguish between efficiency associated with "program possibilities" and efficiency due to subsequent managerial utilization of such possibilities. In any case, the orientation is toward decision-making units (DMU's) and their utilization of resources as an extension of the traditional concept of the business firm model in economics.; Enroute to these results we introduce a new type of production function along with new methods for effecting empirical estimates. This new type of production function is based on optimality principles formulated with respect to observational data that bypasses the usual problems of aggregation--while continuing to take account of each and every DMU simultaneously. The new types of estimation methods are specifically directed to estimating extremal relations (i.e., relations based on optimization principles) and in doing so bypass the mismatch between economic theory where such relations are posited and ordinary statistical estimation methods (such as least squares) which focus on average relationships.; The thesis begins with a review of classical approaches to production functions. These are then extended by means of linear programming formulations and algorithms for the TEF values. Theoretical characteristics of this measure and conceptual linkages to traditional economic theory are explored. This is followed by extensions of these production function concepts to multiple input/multiple output cases. A new formal definition of efficiency is then provided which unifies economics, engineering, and management science definitions and methods of computation.; A new empirical approach which we have called Data Envelopment Analysis (DEA) is then introduced to adjust the data to meet the requirements of the previously exposited theory. This approach uses the TEF measure to locate and analyze various performance "frontiers" or "efficiency envelopes". These envelopes represent an "efficiency frontier" germane only to "firms" or production units sharing the same conditions. Other envelopes encompassing these "program specific" frontiers are also calculated. Via a comparison and adjustment of observations associated with these different types of frontiers the DEA approach is then used to distinguish between program and managerial types of efficiency. Suitable types of statistical measures are then introduced to allow for these adjusted differences in the resulting tests of hypotheses.; To provide a practical illustration, the DEA approach is then applied to the evaluation of data from a public sector education experiment entitled "Program Follow Through," proposed as a primary school performance enrichment program in the early 1970's. Applying the DEA approach to three outputs and five inputs from the available collection of eleven outputs and twenty-six inputs utilized in the Follow Through Experiment, an evaluation of its "program efficiency" is effected relative to the Non Follow Through members in this same experimental study. Although the example is only illustrative, the results are a-1 negative so that even this illustrative application of DEA raises serious questions as to the advisability of funding any such program.