Estimating international adverse selection in annuities

North American Actuarial Journal, Oct 2002 by Mitchell, Olivia S, McCarthy, David

A graphical comparison of the U.S. and the Japanese voluntary annuitant table is provided in Figure 4. Apparently large differences are evident across the two countries in the distributions of ages at death for men, but in an unexpected direction. The Japanese voluntary annuitant table indicates far higher expected mortality than for U.S. annuitants, particularly for men, despite the fact that Japanese population mortality rates are lower than in the U.S.

To test whether these patterns are statistically distinguishable, Table 3 extends the empirical model described above by adding the Japanese mortality data, a Japan effect indicator, and three new variables specific to Japan. One is an indicator of whether the mortality table refers to Japanese annuitants, the second represents the EPF annuitant pool, and the third represents the TQPP annuitant table. We test the hypothesis that the coefficients on these additional variables are zero-in other words, that the patterns of mortality differences between the different Japanese tables are statistically indistinguishable from those our model would predict.

The results indicate that there is higher mortality than the model would predict in both the voluntary annuitant and TQPP tables. The magnitudes of these unexpected differences are quantitatively substantial; TQPP and voluntary annuitants in Japan would be seen to face a 29-35% higher mortality and live 3 to 4 years less than what our model predicts based on international norms. In fact, the excess mortality assumed in the TQPP tables results in these tables being heavier than Japanese population tables, implying negative adverse selection. We confirm that Japanese mortality is low relative to the U.S. because the Japan indicator variable is statistically significant for all measures. Also the Japanese pension indicator variables are highly significantly different from zero in most cases.16 All other coefficients in the baseline model are robust to the inclusion of additional data and variables.

A further illustration of the excess mortality contained in these tables appears in Figure 5, which provides confidence intervals for the predicted values of the A/E metric for Japanese compulsory and voluntary male and female annuitants, together with the actual values of this metric. The vertical axis represents the A/E mortality measure and the four types of non-population mortality tables considered for Japan (compulsory selection, represented by TQPP and EPF mortality tables, and the voluntary annuitant table, for males and females). The vertical bars represent confidence intervals for predicted levels of the A/E metric, while the points show where we calculated these tables actually lie.17 As the hypothesis tests imply, the TQPP and voluntary annuitant mortality patterns are well outside the confidence intervals for both males and females, while the EPF tables are very close to the lower limit of the confidence interval. The fact that the two compulsory annuitant tables behave so differently from each other underscores the point that Japanese annuitant tables embody mortality patterns that are unusual in an international context.