Risk Adjustment of Health Plan Payments to Correct Inefficient Plan Choice from Adverse Selection

This paper develops and implements a statistical methodology to account for the equilibrium effects (aka adverse selection) in design of risk adjustment formula in health insurance markets. Our setting is modeled on the situation in Medicare and the new state Exchanges where individuals sort themselves between a discrete set of plan types (here, two). Our "Silver" and "Gold" plans have fixed characteristics, as in the well-known research on selection and efficiency by Einav and Finkelstein (EF). We build on the EF model in several respects, including by showing that risk adjustment can be used to achieve the premiums that will lead to efficient sorting. The target risk adjustment weights can be found by use of constrained regressions, where the constraints in the estimation are conditions on premiums that should be satisfied in equilibrium. We illustrate implementation of the method with data from seven years of the Medical Expenditure Panel Survey