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)
Source: Eurostat.
Table 1
DickeyFuller test statistics results for random walk and random walk with a drift
Table 2
DickeyFuller statistics and confidence intervals for the data of 16 observations
Table 3
Parameters in the LeeCarter model
Table 4
DickeyFuller statistics for newborns per person index
Figure 5
Autocorrelation function (ACF) for newborns per person index
Note: The dotted line is used as a boundary for statistical significance. Everything that is above the dotted line is statistically significant.
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
Source: Author’s calculations.
Figure 8
Stochastic simulation results for newborns per person rates, age group: 1519 Source: Author’s calculations. Figure 9
Stochastic simulation results for newborns per person rates, age group: 3034
Source: Author’s calculations.
Figure 10
Stochastic simulation of total newborns per person rates, time horizon: 20172060 Source: Author’s calculations. Table 6
Parameters for mortality index in the LeeCarter model
Table 7
DickeyFuller 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 19302017 Source: Mortality.org (2019). Table 8
DickeyFuller 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 4549 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 1565 from 2018 to 2060 Source: Author’s calculations. Table 10
Proportion of specific age population in cohorts 6064 and 6569
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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