Risk selection and the specification of the conventional risk adjustment formula

We argue that a sharp distinction must be made between the empirical problem of finding the best equation for explaining medical expenditures and the normative question of deriving capitations which give health plans the appropriate incentives. We propose a procedure, taken from the social choice literature, to go from the estimated equations to the capitations. If the estimated equations are not additively separable in legitimate and illegitimate risk-adjusters, it is impossible to remove all incentives for risk selection while respecting at the same time a straightforward requirement of horizontal equity. This has immediate implications for the choice of the functional form. Moreover, in so far as the conventional risk adjustment literature only includes so-called "legitimate" risk-adjusters in the estimations, its results may suffer from omitted variables-bias. We illustrate our general methodological points with empirical results, obtained from a cross-section of 321,111 Belgian patients.