Considering endogeneity and heterogeneit: a hierarchical random parameters approach to measuring efficiency

Modelling efficiency in healthcare with stochastic production frontiers (SPF) is complicated because of the immeasurable elements, quality of care and casemix as well as complex data structures. This analysis considers a SPF approach to estimating efficiencies for organizations in the Republic of Ireland that supply GP services outside of normal working hours. These organizations are run out of a number of primary care centres. The daily payroll for the centre is the output in the SPF and the services offered by these centres enter the production function as inputs. It is argued that these services are exogenous variables and are determined by patient characteristics and reported conditions and not the staff within the centre. A characteristic of the data used is a two-tier structure emanating from a centre lying within a co-op. To account for this tier structure the analysis considers a random parameters approach. The analysis also considers proxies for quality of care and casemix and incorporates them into the SPF. The sensitivity of efficiency values to the excluding the random parameters, quality of care and casemix variables is examined by estimating three reduced forms of the model which ignore each of these elements