A critical review of the use of R2 in risk equalization research

Nearly all empirical studies that estimate the coefficients of a risk equalization formula present the value of the statistical measure R-2. The R-2-value is often (implicitly) interpreted as a measure of the extent to which the risk equalization payments remove the regulation-induced predictable profits and losses on the insured, with a higher R-2-value indicating a better performance. In many cases, however, we do not know whether a model with R-2 = 0.30 reduces the predictable profits and losses more than a model with R-2 = 0.20. In this paper we argue that in the context of risk equalization R-2 is hard to interpret as a measure of selection incentives, can lead to wrong and misleading conclusions when used as a measure of selection incentives, and is therefore not useful for measuring selection incentives. The same is true for related statistical measures such as the Mean Absolute Prediction Error (MAPE), Cumming's Prediction Measure (CPM) and the Payment System Fit (PSF). There are some exceptions where the R-2 can be useful. Our recommendation is to either present the R-2 with a clear, valid, and relevant interpretation or not to present the R-2. The same holds for the related statistical measures MAPE, CPM and PSF.