EXTENSION TO MEASURES OF RELATIVE EFFICIENCY WITH AN APPLICATION TO EDUCATIONAL PRODUCTIVITY (DATA ENVELOPMENT ANALYSIS, STATISTICS, ECONOMIC EFFICIENCY)

The dissertation is based on one central notion: the measurement of relative efficiency and productivity. It is in two parts. The applied section is devoted to program evaluation where an approach to discussing policy issues pertaining implementation of compensatory education programs in elementary schools is developed. The methodological section focuses on some of the theoretical issues that have arisen through the use and application of Data Envelopment Analysis (DEA) to the measurement of relative efficiency.; We use DEA to develop indices of relative effectiveness and resource efficiency of compensatory programs in reading and mathematics implemented in elementary schools of the School District of Philadelphia. We show how the DEA index may be used to overcome problems, resulting from regression to the mean, in the measurement of change, in particular, the effect of intervention of a compensatory education program. We use the index, free of the regression effect, to study the effects of program design, student and school characteristics on the improvement due to compensatory education. Given the present data, the analysis suggests that differences in the programs and other characteristics do not account for the variability in the effectiveness of the programs.; The empirical analysis uses DEA in its present form. The dissertation includes a number of extensions to the existing methodology. The first methodological contribution is in the development of non-radial measures of relative efficiency. A second methodological contribution is in the development of tests for correct partitioning of data. The literature suggests a procedure for partitioning the data into homogeneous groups. We develop tests based on the Khinchin-Kullback Information Statistic to determine whether the partitioning is appropriate. The third methodological contribution is a reformulation of the DEA mathematical program to allow for random variations in data. In order to obtain the stochastic formulation of the problem we first need the data distribution. We show that the lognormal distribution provides a good approximation to the distribution of the ratio of two normal variates. We use this approximation to obtain the mathematical program for stochastic data and derive its deterministic equivalent.