The fundamentals are unchanged for AG2020: The projections are based on publicly available mortality data in the Netherlands and a number of similar countries in Europe. Chapter 5 discussed the details of the dataset used. As in previous years, the Committee promotes that the parameter calibration can be replicated by everyone. To that end, Appendix A provides a comprehensive description of the estimation procedure. All required datasets can be found on the AG website. The model again builds on the fact that mortality developments in the selected group of European countries clearly shows a linear trend for hazard rates on a logarithmic scale, as we will show later in this chapter. This naturally leads to the use of a random walk with drift model. If we then compare the Dutch hazard rates to the European rates at the same logarithmic scale, we see annual fluctuations occurring, but there seems to be no divergence. Therefore, for the Dutch deviation a first-order autoregressive process was selected again. 3 – See Kannisto, V. (1992). Development of the oldest – old mortality, 1950-1980: evidence from 28 developed countries. Odense University Press. 4 – See Li, N and Lee, R. (2005). Coherent Mortality Forecasts for a Group of Populations: An Extension of the LeeCarter Method. Demography 42 (3), pp. 575 - 594 5 – See Brouhns, N., Denuit, M. and Vermunt, J.K. (2002). A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics & Economics 31(3), pp. 373-393. 6 – Please note that this does not imply that the deviation between the Netherlands and the other countries also converges to zero, because in addition to this time series the model includes a constant difference that does not vary over time (denoted as αx in the model specification). Projections Life Table AG2020 Males and females are modelled jointly, not separately. Dependencies between developments for men and women and between developments in the Netherlands and elsewhere in Europe are explicitly included in the modelling. There are four stochastic processes that describe the annual changes in mortality probabilities. Two pertain to the dynamics in Europe (one for men and the other for women) and the other two generate the Dutch deviation from the European trend for both sexes. Any dependencies between these four processes are allowed for by estimating all mutual correlations during the calibration. For high ages the common closing method of Kannisto is used. The relatively small numbers of observations available for higher aged persons make that data less reliable for estimating mortality probabilities. The difference between observed mortality frequencies and estimated mortality probabilities could be large here. Therefore, as with AG2018, mortality probabilities over age 90 are determined by extrapolation of mortality probabilities for lower ages, assuming that the development in higher ages corresponds to Kannisto’s parameterisation3. The measurement noise, the difference between observed mortality frequencies and the underlying mortality probabilities, has a Poisson distribution. As before, the basis for AG2020 is a Li-Lee4 model that combines linear specifications for hazard rates in the European countries and the Dutch deviation. Contrary to that model we model measurement noise explicitly5 and allow for dependencies between different stochastic drivers. 6.2 Adjusted model assumptions 6.2.1 Motivation for adjustments During the construction of the previous projections table in 2018 and in the subsequent discussions in the actuarial field a variety of pros and cons of the approach were brought forward. Below we discuss a number of items that were frequently mentioned. Are the time series for the difference between The Netherlands and other European countries expected to converge to zero? AG2018 explicitly assumes that the time series that describe the expected value of the difference between the logarithmic hazard rates in The Netherlands and in other selected European countries converges to zero6. The parameter driving the speed of convergence also drives the stability of the model. During the 2016 and 2018 calibrations it soon turned out that, although the model is stable, the values of this parameter for both men The projection model 19
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