Data envelopment analysis, endogeneity and the quality frontier for public services

Applying Data Envelopment Analysis (DEA) to real-world public policy issues can raise many interesting complications beyond those considered in standard models of DEA. One of these complications arises if the funding levels of public service providers, and their ability to attract and retain clients and able staff, depend upon the quality of the output which they produce. This dependency introduces additional inter-relationships between inputs and outputs beyond the uni-directional Production Possibility Frontier (PPF) relationship considered by standard DEA models. The paper therefore analyses the multiplier effects which can be generated by these additional relationships, in which key resource inputs become endogenous variables subject to the external environmental variables which the public service provider faces across these different relationships. The magnitude of these multiplier effects can be captured by focusing DEA on the estimation of an Achievement Possibility Frontier, which reveals the wider set of opportunities which are available to a public service provider to improve its own output quality than that revealed by the estimation of the PPF associated with standard models of DEA. In doing so, the paper enables DEA to be still applied, but in modified form, to the estimation of the scope for improved output of any given public service provider in the presence of such resource endogeneity.