Entropy, Efficiency and the Index Numbers

Measuring productive efficiency of a set of decision making units (DMUs) basically involves the comparison of two sets of distribution of input-output data: one is the observed set and the other the optimal set. The technique of data envelopment analysis (DEA) defines the optimal set in terms of a Pareto criterion of efficiency and uses the positive distance between the two sets as a measure of inefficiency. The DEA approach however fails to incorporate any statistical aspect of the data distribution, e.g., skewness, asymmetry or heteroscedasticity. Farrell (1957) as the precursor of the DEA approach noted in his empirical analysis of the agricultural farms that the statistical distribution of the efficiency measure is highly skewed and also outlier sensitive. Since entropy provides a measure of diversity of the data distribution, it is useful to explore its application in comparing different output distributions.