Incorporating self-reported health measures in risk equalization through constrained regression

Most health insurance markets with premium-rate restrictions include a risk equalization system to compensate insurers for predictable variation in spending. Recent research has shown, however, that even the most sophisticated risk equalization systems tend to undercompensate (overcompensate) groups of people with poor (good) self-reported health, confronting insurers with incentives for risk selection. Self-reported health measures are generally considered infeasible for use as an explicit 'risk adjuster' in risk equalization models. This study examines an alternative way to exploit this information, namely through 'constrained regression' (CR). To do so, we use administrative data (N = 17 m) and health survey information (N = 380 k) from the Netherlands. We estimate five CR models and compare these models with the actual Dutch risk equalization model of 2016 which was estimated by ordinary least squares (OLS). In the CR models, the estimated coefficients are restricted, such that the under-/overcompensation for groups based on self-reported general health is reduced by 20, 40, 60, 80, or 100%. Our results show that CR can improve outcomes for groups that are not explicitly flagged by risk adjuster variables, but worsens outcomes for groups that are explicitly flagged by risk adjuster variables. Using a new standardized metric that summarizes under-/overcompensation for both types of groups, we find that the lighter constraints can lead to better outcomes than OLS.