The results for Europe in graph 6.1a show that for all ages shown the trend in the hazard rates is downward for both men and women. The Bx series Kt g values are positive while the time g are descending. The trend for lower ages is in general more severe (downward) than for higher ages, because the values in the middle graph are generally higher for lower ages. The results for the Dutch deviation in graph 6.1b show a more varied picture. For women we see in the third graph an upward timeseries until the year 2002 and a more or less flat development after that. The age specific effects for women in the second graph are positive for most ages. This means that for these ages the difference in logarithmic hazard rates between the Netherlands and Europe, or ln 冠 x v,NL (t) 冡 = ln 冠 x v (t) 冡 - ln 冠 x 冠 x v,EU (t) 冡, increases until 2002 and is more or less stationary after that. For men we see in the same graph a time series that goes up until 2002 and drops thereafter. For men too the age specific effects in the middle graph are positive for most ages. For these ages the difference in logarithmic hazard rates between the Netherlands and Europe, ln m,NL (t) 冡 = ln until 2002 and decreases after that. To estimate future hazard rates the time effects in Europe (Kt walk with drift. The time effects of the Dutch deviation (t g) are modelled as a random g) are modelled by a first order autoregressive AR(1) model (including the new constant terms cg). This leads to the following equations, with parameters g, ag and cg and noise terms ⑀t g and ␦t Kt g = Kt-1 g + g + ⑀t t g g = ag t-1 g + cg + ␦t g Table 6.1 shows the parameter estimates. The value of g is the estimated drift of the time effects in Europe. The values cg and ag are the estimated constant term and the estimated AR(1) term of the time effects in the Dutch deviation. Male a 0.1951 0.9347 Female -1.9639 -1.8603 c 0.4071 0.9484 Table 6.1 Time series parameter estimates The future time effects Kt g and t g: 冠 x m (t) 冡 - ln 冠 x m,EU (t) 冡, increases g can be estimated using these estimated models. Combined with the age dependent quantities Ax g, ␣x g, Bx g and x g (which are considered constant over time) these will produce estimates of both the future European hazard rates and the Dutch deviation from Europe. For Europe we find that the hazard rates continue to drop. For identical values of the age specific effects as shown in the middle graph of graph 6.1a the hazards rates for men decrease slightly more than those for women, the value for men being more negative than for women. For the Dutch deviation we observe that the logarithmic hazard rates of that deviation converge to limit values ␣x g + x g ∞ g . The limit values of the AR(1) processes ∞ g are positive for men and women. This leads to positive limit values for the logarithmic hazards rates of the Dutch deviation, for higher ages in particular. This means that, certainly in the longer term, the estimated mortality probabilities at higher ages for Dutch men and Projections Life Table AG2020 The projection model 23
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