The variance of the length of stay and the optimal DRG outlier payments

Abstract

Prospective payment schemes in health care often include supply-side insurance for cost outliers. In the early US Medicare and the current German DRG systems, the outlier scheme fixes a length of stay (LOS) threshold, constraining the loss risk for the provider. This threshold is to increase with the standard deviation of the LOS distribution. The present paper addresses the adequacy of the DRG threshold rule of risk-averse hospitals with preferences depending on expected profits and its variance. It first shows that the optimal threshold solves the hospital`s tradeoff between higher profit risk and lower premium loading payments. It then demonstrates for normally distributes LOS that the optimal threshold generally decreases with in increase of the standard deviation. The intuition for this results is that a higher variance increases the profit risk, which in turn leads hospitals to insure a larger part of the LOS distribution.