Data Envelopment Analysis Models for Identifying Bottlenecks in Hospital Operations Through Partial Productivity Measures

Productivity measures the performance of decision-making units - firms, organizations, industries, or the overall economy - as the ratio of outputs to inputs. This article discusses an improved approach for estimating partial productivity - the additional amount of output that can be produced by increasing a specific input by one unit. The measure is given by the ratio of the shadow price of an input to the shadow price of an output. The proposed model provides a robust estimate while avoiding zero-valued shadow prices that commonly arise due to 1) the specification of multiple inputs and multiple outputs (which may result in slack) and 2) the multiple optimal solutions that may occur in linear programing. We illustrate our model using data on Chinese provincial hospitals, offering evidence on the evolution of hospitals' partial productivities over the period 2009-2022. The results reveal significant disparities of the partial productivities of each input across provinces and regions. The new insights available from our model have clear policy implications for decision makers, guiding them on how to improve resource allocation that would reduce costs and allow health care to be expanded.