Analysing the effectiveness of public service producers with endogenous resourcing

Abstract

Public services, such as education and health care, are important forms of economic activity whose performance is of wide public interest and whose assessment raises interesting issues. The paper extends the existing focus of stochastic frontier analysis (SFA) on production and cost functions by considering additional inter-relationships which may exist between a public service provider’s funding level, input prices, clientele characteristics and the level and quality of the output they achieve in different relevant directions. The potentially large multiplier effects which these additional relationships generate from efficiency and effectiveness improvements are incorporated into the analysis and the estimation process by extending the standard notion of a production possibility frontier to the more general concept of an achievement possibility frontier. The paper also generalises SFA’s use of a univariate half-normal density function by deploying a multivariate skew-normal density function in the stochastic structure of these multiple inter-relationships, thereby permitting correlations to exist between the efficiency and effectiveness deviations for individual producers across these different inter-relationships, while including a half-normal marginal distribution for production efficiency deviations as a special limiting case. This approach also generates point estimates for the cumulative effectiveness coefficient of each individual public service producer that generalise the earlier results based on a half-normal distribution. In doing so, the paper extends the analysis of SFA of feasible increases in an individual producer’s output to important contexts in which the endogeneity of key variables needs to be taken into account.