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

ABSTRACT

Nearly all empirical studies that estimate the coefficients of a risk equalization formula present the value of the statistical measure R2. The R2-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 R2-value indicating a better performance. In many cases, however, we do not know whether a model with R2 = 0.30 reduces the predictable profits and losses more than a model with R2 = 0.20. In this paper we argue that in the context of risk equalization R2 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 R2 can be useful. Our recommendation is to either present the R2 with a clear, valid, and relevant interpretation or not to present the R2. The same holds for the related statistical measures MAPE, CPM and PSF.