Improving Risk Equalization with Constrained Regression

Several countries rely on regulated health plan competition to combine affordability of health plans with incentives for cost containment and quality improvement. Typically, these policies include premium regulation supplemented with risk equalization to compensate health plans for predictable variation in medical spending. An extensive empirical literature shows, however, that even the state-of-the-art risk equalization models undercompensate some risk groups and overcompensate others, leaving systematic incentives for risk selection. A natural approach to reducing under or overcompensation for a group is to include membership in that group as an indicator in the risk equalization model. For several types of indicators, however, inclusion can be problematic or infeasible. This paper introduces and illustrates an alternative approach to reducing over or undercompensation in such cases: constraining the estimated coefficients of the risk equalization model so as to limit over or undercompensation. Our empirical illustration is based on administrative data on medical spending and risk characteristics of nearly all individuals with basic health insurance in the Netherlands. We evaluate empirically the benefits of constraints in terms of reduced under or overcompensation on indicators omitted from the Dutch risk equalization model and their costs in terms of increased under or overcompensation on indicators included in the model. Our findings imply that the benefits of introducing constraints can be worth the costs. Constrained regression adds a tool for developing risk equalization models that can improve the overall economic performance of health plan payment schemes.