Abstract
This work proposes a backtesting analysis that compares the Lee–Carter and the Cairns–Blake–Dowd mortality models, employing Italian data. The mortality data come from the Italian National Statistics Institute (ISTAT) database and span the period 1975–2014, over which we computed back-projections evaluating the performances of the models compared with real data. We propose three different backtest approaches, evaluating the goodness of short-run forecast versus medium-length ones. We find that neither model was able to capture the improving shock on mortality observed for the male population on the analysed period. Moreover, the results suggest that CBD forecasts are reliable prevalently for ages above 75, and that LC forecasts are basically more accurate for this data.
Highlights
Dowd et al (2010a) performed a backtesting analysis on seven different stochastic mortality models with results showing that the models performed adequately by most backtests
The observed male qx,t for individuals aged 57–59 in 1995 and 76–78 in 2014, respectively, are often under the lower extreme of the forecast confidence interval. It seems that models have replicated the cohort effect over an homologous cohort in 1995, but since the male mortality evolution has changed consistently from 1975–1994 to 1995–2014, the two homologous cohorts (i.e., 57–59 in 1975 and 57–59 in 1995) showed different trends that lead to forecast errors
The main aims of this paper are to scrutinize the forecast for both sexes proposed by the original formulation of the models, given the wide use of LC at the national level, and to analyse the long-term forecast with respect to the short term, observing qualitative differences in the estimation of the parameter to changes in the starting point of the database. Regarding the former, we find that, basically, neither model was able to capture the shock in terms of improvements on the male mortality trend, with greater biases for ages lower than x = 75, which were those more affected by the improvement
Summary
Dowd et al (2010a) performed a backtesting analysis on seven different stochastic mortality models with results showing that the models performed adequately by most backtests. The study of mortality risk, intended as the uncertainty in future mortality rates as well as longevity risk for the long-term trend in mortality rates (Cairns et al 2006), played a central role for both public and private annuity providers For these reasons, among all the principal stochastic mortality models , we chose to compare Lee–Carter (LC) and the Cairns–Blake–Dowd (CBD) ones. Chan et al (2014) have studied the new-data-invariant property on the quality of the CBD mortality index For this purpose, we introduced a new backtesting approach named the jumping fixed-length horizon, which makes short-run projections of five years,. For the sake of simplicity, we decided to adopt the same terminology used by Dowd et al (2010a)
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