Risk adjustment and the trade-off between efficiency and risk selection: an application of the theory of fair compensation

Abstract

We exploit the similarity between the problem of risk adjustment with prospective reimbursement schemes in the health care sector and the problem of fair compensation analysed in the social choice literature. The starting point is the distinction between two sets of variables in the explanation of medical expenditures: those for which the insurers (or the providers) can be held responsible, and those for which they have to be compensated. Using this partitioning the objectives of cost-efficiency and no risk selection can be expressed in terms of two simple axioms. If the medical expenditure function is additively separable in the two sets of variables, there exists a natural division rule which is analogous to the standard linear risk adjustment schemes. We show how this rule should be applied if the total level of actual medical expenditures is different from the budget to be divided over the insurers (or providers) and how information from the disturbances in the regression equation can be used in an optimal way. We discuss the analogy with mixed reimbursement systems. If the medical expenditure function is not additively separable in the two sets of variables, the conflict between efficiency and risk selection is unavoidable, even if one has perfect information about that function. The theoretical results are illustrated with empirical results derived from the Belgian setting where the move towards prospective reimbursement of the mutualities has necessitated the introduction of a risk adjustment formula.

Capitation and Risk Adjustment in Health Care Financing: An International Progress Report

“…"Supplier-induced demand" has been the subject of some concern in England, and has played a central role in determining the selection of needs factors there (Carr-Hill et al 1994). Although other countries have raised similar concerns, they have done little to address the issueexcept Belgium, where there has been considerable debate over whether to retain physician supply in the regression equations used to distribute funds to health plans (Schokkaert, Dhaene, and Van de Voorde 1998). The outcome has been that supplier-induced demand has been excluded from the calculations, meaning that health plans are not compensated for variations in the physician supply available to their beneficiaries, even though the plans may have no control over the consequent variation in utilization.…”

Giving equality of opportunity a fair innings

“…The matter of responsibility was highlighted by Schokkaert et al (1998) who, in the context of risk adjustment, show that failure to account for responsibility (effort) variables significantly biases the estimate of fair compensation. A related argument was made by Gravelle (2003) who proposed a partial concentration index which is standardised for need, controlling for non-need variables in the process.…”

School accountability: can we reward schools and avoid pupil selection?

“…To answer this question, we do not start from an overall social objective function, but we model the requirements to be imposed on the school …nancing scheme directly in terms of two basic principles. These principles, and some of the results later on, are inspired by the theory of fair allocation (see, e.g., Fleurbaey, 2008, for an overview) and its application to health insurance (Schokkaert et al, 1998;Schokkaert and Van de Voorde, 2004). We …rst formulate the basic principles, then show that they are incompatible in general, and …nally introduce some possible compromise solutions.…”