and women is close to the critical threshold for stability7. This begs the question if a more stable model would be found if we allow the expected values of these time series to converge to non-zero values. How much history should be included in the creation of the projections? If convergence to other values is allowed, the question is raised whether these values are constant over time and, more specifically, if they are unchanged since 1970. This question touches upon the choice of historical dataset used for the calibration and that is a subject that the actuarial field has had questions about at earlier projections publications. The choice to start the datasets in 1970 was driven by the relatively stable pattern in the European mortality characteristics since that year. The effects of negative factors such as smoking, aids and the rise of obesity on the one hand and positive developments such as the successful battle against cancer and cardiovascular diseases on the other have yielded an all but constant trend in the logarithmic hazard rates within the selected group of European countries. The observed fluctuations in the Dutch deviation from this trend since 1970 are more ambiguous. Periods of increase and decrease emerge that make convergence (in expected value) to zero less likely if we only look at recent data. It may therefore make sense to exclude some data after 1970 from the estimation of the expected value of the long-term difference between the Netherlands and other European countries. 6.2.2 Adjustments made In light of the above considerations the Committee has decided to implement two adjustments. 7 – The autoregressive parameter values for men and women were 0.975 and 0.993 respectively. The critical threshold for these parameters is 1. 8 – The Akaike Information criterion (AIC) and the Bayesian Information Criterion (BIC) are quantities that measure the plausibility of a fitted model with a loglikelyhood term, but seek to avoid unnecessary complexity by introducing a “penalty term” that increases as more parameters get used in the model. Projections Life Table AG2020 The projection model 20 The European dataset starts in 1970, the Dutch deviation dataset starts in 1983. The choice of 1983 as the starting point for the Dutch calibration data and leaving the starting point for the European data unchanged, is the result of an extensive analysis of the time series involved. The Working Group also analysed several alternatives, including specifications that also adjusted the calibration period for Europe, specifications with different calibration periods for men and women, excluding any dependencies between European changes and the Dutch deviation. The Committee’s deliberations around the model choice included statistical model selection criteria such as log-likelihood, AIC and BIC values8 and the long-term robustness and stability of fitted models and plausibility of the projections. As a matter of fact, entering the start of the calibration period as a free parameter in the model selection procedures almost invariably led to 1983 as preferred option, based on the time series for women. That made the case for this choice. The time series describing the differences between the Netherlands and the other countries converge to values no longer assumed to be zero. These limits are now new parameters included in the calibration, because new constant terms are added to the autoregressive processes describing the Dutch deviation. This leads to a change in the expected value of the difference in the longer term. Because the variance of the time series does not move to zero over time, there will always be fluctuations around this expected value. Dutch mortality probabilities will continue to fall in terms of expected value, as the Dutch deviation is added to the falling European trend.
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