α-returns to scale with quasi-fixed inputs: an application to Québec hospitals

This paper focuses on the determination and estimation of the optimal size of hospitals. To determine the optimal size of a production unit, we use the measurement of returns to scale (RTS) at the decision-making unit level. When the RTS are constant, the unit is deemed of optimal size as the average total cost is at its minimum. As we deal with public service in a non-market environment, we have to take into account the fact that hospitals may not operate efficiently. To estimate the required production frontier we adapt the α-returns to scale method (a DEA type algorithm compatible with non-convexity of the production set) to include quasi-fixed factors. This methodology is applied to Québec hospitals at different points in time in order to capture the effect of the restructuring of the public health system over the last three decades. We conclude that by relying more on larger institution the scale efficiency of the public system has increased. However, in spite of the large reduction in the number of small hospitals and their replacement by very large structures, the movement may have gone too far, as most of the large institutions tend to exhibits decreasing returns to scale.