Lifespan Disparity as an Additional Indicator for Evaluating Mortality Forecasts

Table 1 Mean of the absolute percentage errors (MAPE) for e ₀ and \( {e}_0^{\dagger } \) over the forecast years by country and method

Country and Measure	Method
Country and Measure	Lee-Carter	Lee-Carter, Rotated (Li et al.)	Bohk and Rau
Validation 1 (ref. years: 1965–1990; forecast years: 1991–2009)
Italy
e ₀	0.003	0.003	0.005
\( {e}_0^{\dagger } \)	0.019	0.015	0.014
Japan
e ₀	0.002	0.003	0.002
\( {e}_0^{\dagger } \)	0.087	0.080	0.034
Denmark
e ₀	0.008	0.007	0.006
\( {e}_0^{\dagger } \)	0.065	0.054	0.009
Validation 2 (ref. years: 1960–1985; forecast years: 1986–2009)
Italy
e ₀	0.010	0.010	0.002
\( {e}_0^{\dagger } \)	0.029	0.021	0.018
Japan
e ₀	0.002	0.002	0.004
\( {e}_0^{\dagger } \)	0.092	0.076	0.014
Denmark
e ₀	0.005	0.004	0.017
\( {e}_0^{\dagger } \)	0.094	0.077	0.021
Validation 3 (ref. years: 1955–1980; forecast years: 1981–2009)
Italy
e ₀	0.014	0.014	0.002
\( {e}_0^{\dagger } \)	0.027	0.019	0.012
Japan
e ₀	0.009	0.009	0.003
\( {e}_0^{\dagger } \)	0.118	0.092	0.022
Denmark
e ₀	0.007	0.008	0.029
\( {e}_0^{\dagger } \)	0.048	0.033	0.023
Validation 4 (ref. years: 1950–1975; forecast years: 1976–2009)
Italy
e ₀	0.018	0.018	0.008
\( {e}_0^{\dagger } \)	0.032	0.023	0.053
Japan
e ₀	0.018	0.018	0.012
\( {e}_0^{\dagger } \)	0.131	0.094	0.032
Denmark
e ₀	0.015	0.014	0.035
\( {e}_0^{\dagger } \)	0.020	0.018	0.043

Note: MAPEs are shown for four validating settings that all forecast mortality until 2009, but they use different historical periods.