A Model for Estimating Productivity in Service Systems

In this paper, we introduce a new model of a technology function that describes the input–output relations of service systems. Key features of the model reflect distinguishing features of service systems and differentiate the model from the conventional modelling of input–output relations of production systems. We also derive mathematical expressions for productivity changes for service systems with this model. The model incorporates multiple input factors and output variables. The output variables are discrete as opposed to the continuous outputs of conventional production functions. The values of each output variable represent states that a service system creates as opposed to representing volumes of resources produced as in conventional models of production systems. Furthermore, to admit such categorical output variables, the model does not require the utility of output states to be monotonic in the values of the output variables. The model includes a stochastic response of the service system; this response is represented by the logit of probabilities of the output states as opposed to the inclusion of a random deviation variable. No distribution assumptions are required by the model. We derive new measures of productivity change with the model and demonstrate the application of the model to productivity estimation with a sample of data from a healthcare service system.