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
Dickey-Fuller test statistics results for random walk and random walk with a drift
Source: Author’s calculations. Table 2
Dickey-Fuller statistics and confidence intervals for the data of 16 observations
Source: Author’s calculations Table 3
Parameters in the Lee-Carter model
Source: Author’s calculations Table 4
Dickey-Fuller statistics for newborns per person index
Source: Author’s calculations. 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
Source: Author’s calculations. 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: 15-19 Source: Author’s calculations.Figure 9
Stochastic simulation results for newborns per person rates, age group: 30-34 Source: Author’s calculations. 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
Source: Author’s calculations. Table 7
Dickey-Fuller statistics for mortality index
Source: Author’s calculations. 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
Source: Author’s calculations. Table 9
Estimated parameters for mortality index
Source: Author’s calculations. 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
Source: Author’s calculations. Table 11
Analysis of new pensioners
Source: Eurostat; HZMO; Author’s calculations 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
Source: Author’s calculations 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
Source: Author’s calculations 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
Source: Narodne novine, author’s calculations Figure 34
PACF of growth rates in wages Source: Author’s calculations.Table 15
AR (1) process for growth rates in wages
Source: Author’s calculations. 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
Source: HZMO; Author’s calculations 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.Figure 1 Total population in Croatia (in millions) DISPLAY Figure Figure 2 Total population in Croatia in two different age groups (in millions) DISPLAY Figure Figure 3 Total population in Croatia in two different age groups (in millions) DISPLAY Figure Figure 4 Net migration in Croatia (in thousands) DISPLAY Figure Table 1 Dickey-Fuller test statistics results for random walk and random walk with a drift DISPLAY Table Table 2 Dickey-Fuller statistics and confidence intervals for the data of 16 observations DISPLAY Table Table 3 Parameters in the Lee-Carter model DISPLAY Table Table 4 Dickey-Fuller statistics for newborns per person index DISPLAY Table Figure 5 Autocorrelation function (ACF) for newborns per person index DISPLAY Figure Figure 6 Partial autocorrelation function (PACF) for newborns per person index DISPLAY Figure Table 5 AR (1) process of newborns per person index DISPLAY Table Figure 7 Stochastic simulation results for newborns per person index DISPLAY Figure Figure 8 Stochastic simulation results for newborns per person rates, age group: 15-19 DISPLAY Figure Figure 9 Stochastic simulation results for newborns per person rates, age group: 30-34 DISPLAY Figure Figure 10 Stochastic simulation of total newborns per person rates, time horizon: 2017-2060 DISPLAY Figure Table 6 Parameters for mortality index in the Lee-Carter model DISPLAY Table Table 7 Dickey-Fuller statistics for mortality index DISPLAY Table Figure 11 Mortality index over time DISPLAY Figure Figure 12 Mortality rates in the USA for the period of 1930-2017 DISPLAY Figure Table 8 Dickey-Fuller statistics for mortality index set as a model with linear trend DISPLAY Table Table 9 Estimated parameters for mortality index DISPLAY Table Figure 13 Mortality index simulations DISPLAY Figure Figure 14 Simulated results for mortality rates for the first cohort: newborns DISPLAY Figure Figure 15 Simulated results for the mortality index for group aged 45-49 DISPLAY Figure Figure 16 Stochastic forecast of the Croatian population from 2018 to 2060 DISPLAY Figure Figure 17 Histogram of the Croatian population in 2060 forecast by using the stochastic method on the Leslie model DISPLAY Figure Figure 18 Stochastic forecast of the population aged 65+ from 2018 to 2060 DISPLAY Figure Figure 19 Stochastic forecast of the population aged 15-65 from 2018 to 2060 DISPLAY Figure Table 10 Proportion of specific age population in cohorts 60-64 and 65-69 DISPLAY Table Table 11 Analysis of new pensioners DISPLAY Table Figure 20 PACF for the ratio of new male pensioners to male population aged 65 DISPLAY Figure Figure 21 PACF for new female pensioners to female population aged 62 DISPLAY Figure Table 12 AR (1) process for ratio of new female/male pensioners to female/male population aged 62/65 DISPLAY Table Figure 22 Stochastic forecast of new male pensioners ratio from 2018 to 2060 DISPLAY Figure Figure 23 Stochastic forecast of new female pensioners ratio from 2018 to 2060 DISPLAY Figure Figure 24 Stochastic forecast of the number of pensioners from 2018 to 2060 DISPLAY Figure Figure 25 Distribution histogram for the number of pensioners in 2060 DISPLAY Figure Figure 26 Labour force to working age population DISPLAY Figure Figure 27 PACF of labour force to working age population ratio DISPLAY Figure Table 13 AR (1) process of labour force to working age population ratio DISPLAY Table Figure 28 Stochastic forecast of labour force ratio from 2018 to 2060 DISPLAY Figure Figure 29 Historical unemployment rate in Croatia DISPLAY Figure Figure 30 Forecast of the future unemployment rate: Scenario 1 DISPLAY Figure Figure 31 Stochastic forecast of the employed population: Scenario 1 DISPLAY Figure Figure 32 Stochastic forecast of the employed population: Scenario 2 DISPLAY Figure Figure 33 Stochastic forecast of the employed population: Scenario 3 DISPLAY Figure Table 14 Average gross salary and growth rates DISPLAY Table Figure 34 PACF of growth rates in wages DISPLAY Figure Table 15 AR (1) process for growth rates in wages DISPLAY Table Figure 35 Stochastic forecast for growth rates in wages DISPLAY Figure Figure 36 Stochastic forecast of future wages DISPLAY Figure Figure 37 Histogram of wage distribution in 2060 DISPLAY Figure Table 16 Average pension by year and percentage in gross salary DISPLAY Table Figure 38 Stochastic forecast of government net cash flow from the pension system: Scenario 1 DISPLAY Figure Figure 39 Stochastic forecast of government net cash flow from the pension system: Scenario 2 DISPLAY Figure Figure 40 Stochastic forecast of government net cash flow from the pension system: Scenario 3 DISPLAY Figure Figure 41 Expected present value of government future cash flow generated from the pension system: Scenario 3 DISPLAY Figure 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 DISPLAY Figure 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 DISPLAY Figure 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 DISPLAY Figure 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 DISPLAY Figure |
June, 2020I/2020 |