Exploiting Incomplete Information in Risk Adjustment Using Constrained Regression

Abstract

Health insurance markets with regulated premiums typically include risk adjustment (RA) to mitigate selection incentives. Even the most sophisticated RA models, however, tend to undercompensate (overcompensate) insurers for people in poor (good) health. One reason RA models are imperfect is that some predictors cannot serve as risk adjustor because they are not available for the entire population. This paper applies an indirect method to exploit such predictive information: constrained regression. Our focus is on the Netherlands where morbidity data from general practitioners (GPs) are available for only around 10 percent of the population. We combine this incomplete sample with complete data (N=16.7 million) on spending and risk adjustors. In a first step, we find that GP morbidity data are predictive net of the Dutch RA model. In a second step, we use the GP morbidity data to impose constraints on the coefficients of the RA model. This results in more RA funds being sent to undercompensated groups. Using a split-sample approach, we simulate two constrained regression models and compare the outcomes to those of an unconstrained model. Our findings indicate that constrained regression can be a useful tool to exploit predictive information that is available for only a sample of the population.