Relative efficiency measurement in the public sector with data envelopment analysis

Abstract

Traditional efficiency measures have two significant drawbacks. Firstly, they fail to recognise that output is the result of all inputs operating in combination; thus output per head is a misleading indicator of intrinsic labour productivity. Secondly, they have often been defined in terms of average levels of performance in least squares production functions. In practice, average performance norms may institutionalise some level of inefficiency. The first of these problems may be overcome in a total-factor view of efficiency. This implies the extension of traditional ratio measures to include all inputs and outputs simultaneously. The second requires the comparison of performance with frontier possibilities. Both of these improvements are embodied in Data Envelopment Analysis (DEA). Two applications of DEA are undertaken on U. K. public sector data. The first of these defines frontier efficiency in local education authorities (LEAs). It develops an 8 variable model with 3 outputs (based on exam pass rates) and 5 inputs. Four of the inputs are uncontrollable background variables allowing for differences in student catchment area; the fifth, teaching expenditure, is under LEA control and can be targeted. The results suggest that 44 authorities are best-practice and at the remainder spending per pupil could have been reduced by an average of 6.8%. These results are replicated on smaller clusters of LEAs to examine the sensitivity of DEA to the size of the performance comparison. The clustering procedure produces marked effects on targets, peer groups and the efficiency status of certain authorities. A second case study investigates the performance of a sample of 33 prisons with a high remand population. The model separately identifies the effects of remand prisoners on costs, and includes separate variables to reflect the levels of overcrowding and offences. In 1984/85 the combined budget of these prisons was overspent by 4.6% vis a vis best-practice costs. Using an alternative constant returns technology this overspend rises to 13.1%. Two aspects of DEA targets are explored. A model of Leibenstein's inert area suggests reasons for the persistence of inefficiency and hence that targets may be unattainable without coercion. Secondly, the literature has justified the recommendation of DEA targets in their being Pareto efficient. This interpretation is disputed and an alternative DEA-Dominance criterion is proposed as a more appropriate basis for targeting.