Insurer Standard Errors by Portfolio Size

Table 1 Row 1, shows insurer portfolio sizes in thousands (1,000s) of policyholders. Table 1 Row 2, shows portfolio size adjusted standard errors, $\sigma_{e_{N}}$ = $\sigma_{e_{PI}}$ * $\frac{\sqrt{1,000,000}}{\sqrt{N}}$. $NHI$'s standard error, $\sigma_{e_{NHI}}$, is 0.00285 while $\sigma_{e_{E}}$ = 0.50000, ten times larger than $\sigma_{e_{PI}}$ (0.05000), and 175 times larger than $\sigma_{e_{NHI}}$.

These insurers' normally distributed Population Loss Ratio Estimate Distribution Functions, are: $\Phi$(0.7500, 0.002849); $\Phi$(0.7500, 0.015811); $\Phi$(0.7500, 0.050000); $\Phi$(0.7500, 0.158114); and $\Phi$(0.7500, 0.500000), for $NHI$, $B$, $PI$, $D$ and $E$.

Capitation advocates must have failed to note these profound differences in PLRE Distribution Functions because all insurers larger than $PI$ have more probability below PLR + $\epsilon$ ($\epsilon > 0$) than $PI$, and all smaller insurers have more probability above PLR + $\epsilon$ than $PI$. When correctly analyzed, these subtle Distribution Functions result in dramatically different insurer operating results when insurance markets and health care (finance) systems are as efficient as possible, and policyholders are randomly selected.