6.3 Research 6.3.1 Smoothing the time series The latest fitted values from the historical time series (see a) to d) in the previous paragraph) are the starting point for the estimations of the European trend and the Dutch deviation from it. A change in the starting point for the European trend is particularly determinative for the projections table. For insurers and pension funds the impact of an update to the projections table can be significant. The purpose of smoothing is to prevent unnecessary fluctuations in the provisions year on year. Smoothing time series makes sense if adjustments in the projections can be seen to have alternating signs year on year. This would imply that a rise in one year is often followed by a drop in the next year and vice versa. A risk of smoothing is that a potential trend break is detected at a later stage. We have investigated the benefit of smoothing the time series by adding a term to the specification of the European trend. This so-called moving average term allows for shock in the time series for a particular year to be correlated with a shock in the previous year. This can prevent positive shocks in one year being followed by negative shocks in the next and vice versa. The parameters of this moving average effect turned out to be very close to zero. Consequently, we elected not to complicate the model unnecessarily. Other smoothing mechanisms are statistically less tenable. Moreover, additional subjective choices would need to be made. CSO has elected not to implement this in Projections Life Table AG2018. 6.3.2 Sensitivities of the model to changes in the input The sensitivities of the model have been plotted by calculating the consequences of potential changes in the input, such as the impact of new mortality data, the country selection and the length of the data set used. These analyses do not give rise to changes in the choices made before. Sensitivity of the model to changes in the input – country selection It turns out that the results of the model are dominated by the three large countries: Germany, France and the United Kingdom. Removing or adding other countries has only a limited effect on the results. Sensitivity of the model to changes in the input – starting year 1970 The starting year 1970 was kept. The reasons are: 1. Mortality data from all countries included in the modelling are available as of 1970; 2. For males, there appears to be a trend break around 1970; mortality drops quicker because men stop smoking. For women this effect only becomes apparent at a later moment; 3. Males and females are estimated jointly, including correlations between the two. Therefore the same observation period must be used for both men and women; 4. With starting year 1970, 47 observation years are available. Postponing the starting year reduces the volume of available data. Projection Table AG2018 Mortality data and model assumptions 17
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