##
Deriving Risk Adjustment Weights to Maximize Efficiency of Health Insurance Markets

*ad hoc*, with no explicit criteria for choice of relevant groups and no explicit criteria for deciding if one payment formula is better than another. The purpose of this paper is to combine the first and second stages so that risk adjustment weights (payments) are estimated to maximize the policy objective. In other words, we seek to replace the two-step “estimate-then-evaluate” approach with a one-step “estimate-to-maximize-the-objective” approach.

We propose an objective for risk adjustment in the form of minimizing the loss from service-level distortion due to adverse selection incentives. Our framework is general in that it covers a range of cases, including settings where health plans are able to distort allocations at the level of individuals, groups of individuals, particular sets of services, and combinations of groups and services. There are two classes of solutions to the loss-minimization problem. In one, where the number of groups and/or services potentially subject to distortion is less than the number of risk adjustment weights to be chosen, the welfare maximizing weights can be chosen via estimation of a constrained least-squares regression where the constraints are the conditions under which plan actions achieve efficiency. In the other class of solution, the number of groups and/or services exceeds the number of available risk adjustor weights. In this class of problem, which we consider to be the general case, we derive an expression for the welfare loss in terms of the risk adjustment weights, and specify a regression on transformed data that produces the welfare minimizing weights. We apply our methods to the actual data used to estimate risk adjustment weights in the Netherlands. It includes multiple years of information on medical spending, morbidity adjusters and some demographic information, including income and residence, on the full 16.5 million population of the Netherlands. We replicate the estimation of the Dutch risk adjustment formula in place for 2015, and compare this to our alternative approaches.