The variance of length of stay and the optimal DRG outlier payments
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 profit risk for the hospital. This threshold increases with the standard deviation of the LOS distribution. The present paper addresses the adequacy of the DRG threshold rule for risk-averse hospitals with preferences depending on the expected value and the variance of profits. 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 distributed LOS that the optimal threshold generally decreases with an increase in the standard deviation.
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