title: Improving risk equalization with constrained regression.
abstract: 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 the under- or overcompensation for a particular group is enriching the risk equalization model with risk adjustor variables that indicate membership in that group. For some groups, however, appropriate risk adjustor variables may not (yet) be available. For these situations, this paper proposes an alternative approach to reducing under- or overcompensation: constraining the estimated coefficients of the risk equalization model such that the under- or overcompensation for a group of interest equals a fixed amount. We show that, compared to ordinary least-squares, constrained regressions can reduce under/overcompensation for some groups but increase under/overcompensation for others. In order to quantify this trade-off two fundamental questions need to be answered: "Which groups are relevant in terms of risk selection actions?" and "What is the relative importance of under- and overcompensation for these groups?" By making assumptions on these aspects we empirically evaluate a particular set of constraints using individual-level data from the Netherlands (N = 16.5 million). We find that the benefits of introducing constraints in terms of reduced under/overcompensations for some groups can be worth the costs in terms of increased under/overcompensations for others. Constrained regressions add a tool for developing risk equalization models that can improve the overall economic performance of health plan payment schemes.
authors.affiliation: Institute of Health Policy and Management, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands. vankleef@bmg.eur.nl.
authors.forename: Richard C
authors.initials: RC
authors.lastname: van Kleef
authors.affiliation: Department of Health Care Policy, Harvard Medical School, 180 Longwood Avenue, Boston, MA, 02115, USA.|National Bureau of Economic Research, 1050 Massachusetts Avenue, Cambridge, MA, 02138, USA.
authors.forename: Thomas G
authors.initials: TG
authors.lastname: McGuire
authors.affiliation: Institute of Health Policy and Management, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands.
authors.forename: René C J A
authors.initials: RCJA
authors.lastname: van Vliet
authors.affiliation: Institute of Health Policy and Management, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands.
authors.forename: Wynand P P M
authors.initials: WPPM
authors.lastname: van de Ven
mesh_terms: D005102:Health Expenditures; D007348:Insurance, Health; D009426:Netherlands; D020379:Risk Adjustment; D012307:Risk Factors
keywords: Capitation; Constrained regression; Health insurance; Risk equalization; Risk selection