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.

Examining unpriced risk heterogeneity in the Dutch health insurance market

“…When new or better risk adjusters are not available (in the short run), another option to reduce undercompensation for specific groups is overpaying individuals on the basis of their predicted spending from the risk equalization model. Such overpayment can be realized by, for instance, the use of constrained least squares regression [8,25].…”

“…Finally, risk selection may reduce cross-subsidization from low-risk to high-risk individuals when these risk types are concentrated in different health plans (e.g., high-versus lower-quality plans, see previous example). Incomplete cross-subsidization might lead to compromised accessibility and affordability and violates the level playing field for insurers [19,25,26,29].…”

Introducing risk adjustment and free health plan choice in employer-based health insurance: Evidence from Germany

“…Another set of papers studies how different regulator objectives, such as reducing adverse selection, would theoretically translate into differently designed risk adjustment schemes (Glazer and McGuire, 2002;Breyer et al, 2011;McGuire et al, 2013;, while yet another deals with optimizing risk adjustment by incorporating new risk adjusters or innovative statistical methods 6 (van de Ven and Ellis, 2000;Manning et al, 2005;Breyer et al, 2011;Buchner et al, 2013;Lorenz, 2014;van Kleef et al, 2015;Buchner et al, 2017;Geruso and McGuire, 2016 and (iv) whether and how insurers pay for capital costs of hospitals. In contrast to the first German RAS evaluated in this paper, more sophisticated RAS' are based on regression models, high-cost diagnoses, and sometimes detailed pharmaceutical information (Juhnke et al, 2016).…”

Risk equalization in competitive health insurance markets: Identifying healthy individuals on the basis of multiple‐year low spending

“…If incorporating this information in the RE model is nonetheless considered desirable, other estimation methods, such as constrained least squares regression, may be required (A. A. Withagen‐Koster, R. C. van Kleef, & F. Eijkenaar, To be submitted for publication) …”

“…An interesting direction for further research is to investigate the extent to which remaining risk‐selection potential in these countries can be meaningfully mitigated further by introducing new risk adjusters or that the focus should shift to other potential solutions such as alternative estimation methods (A. A. Withagen‐Koster, R. C. van Kleef, & F. Eijkenaar, To be submitted for publication), sophisticated forms of ex post risk‐sharing, and relaxing premium regulation.…”