How wrong could it be?

We have written previously about the importance of the independence assumption when modelling mortality for annuities and pensions. In a recent presentation to the Royal Statistical Society I showed the audience how life insurers deduplicate their annuity data and how they use postcodes to identify socio-economic status.

When I pointed out the strong link between income, status and multiple policies, a member of the audience asked about the impact of failing to deduplicate. This is an interesting question, since getting mortality assumptions correct for annuity pricing is particularly important due to the great sensitivity of profitability on reserve levels.

We therefore fitted a simple Perks model of mortality with age, gender and Mosaic group to an annuity portfolio. We fitted the same model once with deduplication (the correct method) and once without deduplication (the wrong method). How wrong could the non-deduplicated parameters be? Table 1 shows the percentage errors in the parameter estimates from not deduplicating.

Table 1. Percentage errors in parameter values from not deduplicating an annuity portfolio.

Table 1 shows a few Mosaic groups where the failure to deduplicate has made little difference: D, G and H, for example. However, there are numerous other Mosaic groups where the error is too large to be acceptable: B, C, E, J and K for this portfolio. Deduplication is clearly essential not just for the independence assumption, but also to avoid serious parameter bias.

In fact, the errors from not deduplicating properly are even worse than they seem. The Mosaic groups with the biggest errors from not deduplicating are also the groups where pensions are larger than average, as shown in Richards and Currie (2009). Thus, failure to deduplicate has an even bigger financial impact than Table 1 suggests.