Econometric Risk Adjustment, Endogeneity, and Extrapolation Bias

In econometric risk-adjustment exercises, models estimated with one or more included endogenous explanatory variables ("risk adjusters") will generally result in biased predictions of outcomes of interest, e.g. unconditional mean healthcare expenditures. This paper shows that a first-order contributor to this prediction bias is the difference between the distribution of explanatory variables in the estimation sample and the prediction sample -- a form of "extrapolation bias." In the linear model context, a difference in the means of the respective joint marginal distributions of observed covariates suffices to produce bias when endogenous explanatory variables are used in estimation. If these means do not differ, then the "endogeneity-related" extrapolation bias disappears although a form of "standard" extrapolation bias may persist. These results are extended to some of the nonlinear models in common use in this literature with some provisionally-similar conclusions. In general the bias problem will be most acute where risk adjustment is most useful, i.e. when estimated risk-adjustment models are applied in populations whose characteristics differ from those from which the estimation data are drawn.