A stochastic forecast for the Croatian pension system*
https://doi.org/10.3326/pse.44.1.2 | Published online: March 3, 2020 Figure 1
Total population in Croatia (in millions) Source: Eurostat. Figure 2
Total population in Croatia in two different age groups (in millions) Source: Eurostat. Figure 3
Total population in Croatia in two different age groups (in millions) Source: Eurostat. Figure 4
Net migration in Croatia (in thousands) Table 1
Dickey-Fuller test statistics results for random walk and random walk with a drift
Table 2
Dickey-Fuller statistics and confidence intervals for the data of 16 observations
Table 3
Parameters in the Lee-Carter model
Table 4
Dickey-Fuller statistics for newborns per person index
Figure 5
Autocorrelation function (ACF) for newborns per person index Source: Author’s calculations. Figure 6
Partial autocorrelation function (PACF) for newborns per person index Source: Author’s calculations. Table 5
AR (1) process of newborns per person index
Figure 7
Stochastic simulation results for newborns per person index Figure 8
Stochastic simulation results for newborns per person rates, age group: 15-19 Source: Author’s calculations. Figure 9
Stochastic simulation results for newborns per person rates, age group: 30-34 Figure 10
Stochastic simulation of total newborns per person rates, time horizon: 2017-2060 Source: Author’s calculations. Table 6
Parameters for mortality index in the Lee-Carter model
Table 7
Dickey-Fuller statistics for mortality index
Figure 11
Mortality index over time Source: Author’s calculations. Figure 12
Mortality rates in the USA for the period of 1930-2017 Source: Mortality.org (2019). Table 8
Dickey-Fuller statistics for mortality index set as a model with linear trend
Table 9
Estimated parameters for mortality index
Figure 13
Mortality index simulations Source: Author’s calculations. Figure 14
Simulated results for mortality rates for the first cohort: newborns Source: Author’s calculations. Figure 15
Simulated results for the mortality index for group aged 45-49 Source: Author’s calculations. Figure 16
Stochastic forecast of the Croatian population from 2018 to 2060 Note: Generated by the Leslie stochastic matrix. Source: Author’s calculations. Figure 17
Histogram of the Croatian population in 2060 forecast by using the stochastic method on the Leslie model Source: Author’s calculations. Figure 18
Stochastic forecast of the population aged 65+ from 2018 to 2060 Source: Author’s calculations. Figure 19
Stochastic forecast of the population aged 15-65 from 2018 to 2060 Source: Author’s calculations. Table 10
Proportion of specific age population in cohorts 60-64 and 65-69
Table 11
Analysis of new pensioners
Figure 20
PACF for the ratio of new male pensioners to male population aged 65 Source: Author’s calculations. Figure 21
PACF for new female pensioners to female population aged 62 Source: Author’s calculations. Table 12
AR (1) process for ratio of new female/male pensioners to female/male population aged 62/65
Figure 22
Stochastic forecast of new male pensioners ratio from 2018 to 2060 Source: Author’s calculations. Figure 23
Stochastic forecast of new female pensioners ratio from 2018 to 2060 Source: Author’s calculations. Figure 24
Stochastic forecast of the number of pensioners from 2018 to 2060 Source: Author’s calculations. Figure 25
Distribution histogram for the number of pensioners in 2060 Source: Author’s calculations. Figure 26
Labour force to working age population Source: CBS (2019); Eurostat; Author’s calculations. Figure 27
PACF of labour force to working age population ratio Source: Author’s calculations. Table 13
AR (1) process of labour force to working age population ratio
Figure 28
Stochastic forecast of labour force ratio from 2018 to 2060 Source: Author’s calculations. Figure 29
Historical unemployment rate in Croatia Source: CBS. Figure 30
Forecast of the future unemployment rate: Scenario 1 Source: Author’s calculations. Figure 31
Stochastic forecast of the employed population: Scenario 1 Source: Author’s calculations. Figure 32
Stochastic forecast of the employed population: Scenario 2 Source: Author’s calculations. Figure 33
Stochastic forecast of the employed population: Scenario 3 Source: Author’s calculations. Table 14
Average gross salary and growth rates
Figure 34
PACF of growth rates in wages Source: Author’s calculations. Table 15
AR (1) process for growth rates in wages
Figure 35
Stochastic forecast for growth rates in wages Source: Author’s calculations. Figure 36
Stochastic forecast of future wages Source: Author’s calculations. Figure 37
Histogram of wage distribution in 2060 Source: Author’s calculations. Table 16
Average pension by year and percentage in gross salary
Figure 38
Stochastic forecast of government net cash flow from the pension system: Scenario 1 Source: Author’s calculations. Figure 39
Stochastic forecast of government net cash flow from the pension system: Scenario 2 Source: Author’s calculations. Figure 40
Stochastic forecast of government net cash flow from the pension system: Scenario 3 Source: Author’s calculations. Figure 41
Expected present value of government future cash flow generated from the pension system: Scenario 3 Source: Author’s calculations. Figure 42
Stochastic forecast of government net cash flow with the assumption that pensioners decide to use a combined pension scheme after 2030. Unemployment rate from scenario 1 is used Source: Author’s calculations. Figure 43
Stochastic forecast of government net cash flow with the assumption that pensioners decide to use a combined pension scheme after 2030. Unemployment rate from scenario 3 is used Source: Author’s calculations. Figure 44
Stochastic forecast of government net cash flow with the assumption that the second pillar gains enough competitiveness to cover 50% of expenses after 2040. Scenario 1 unemployment rate is used Source: Author’s calculations. Figure 45
Stochastic forecast of government net cash flow with the assumption that the second pillar gain enough competitiveness to cover 50% of expenses and extra assumption that pension amounts to 35% of gross salary between 2030 and 2040 and 40% of gross salary after 2040. Scenario 1 of unemployment rate is used Source: Author’s calculations.
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March, 2020 I/2020 |
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