Assignments WS 2024/2025

Assignment Proposal (Draft) Title:

• Simulation of pension reform in the Czech Republic: Analysis of long-term sustainability

What will be simulated:

• A system dynamics model of the Czech pension system that simulates the long-term financial sustainability under varying demographic, economic, and policy scenarios. The simulation will project future balances of the pension system, incorporating the flows of revenues (social insurance contributions) and expenditures (pension payouts)

Goal of the simulation (What problem should the simulation solve):

• The main goal is to analyze how different pension reform strategies (e.g., adjusting retirement age, altering contribution rates, changing the indexation formula of pensions) will affect the long-term stability of the Czech pension system. The simulation aims to identify specific policy levers and thresholds that ensure the pension system’s financial equilibrium over a multi-decade horizon, despite changing demographic and economic conditions.

Who would use the simulation and how it helps them:

• The potential users include not only the Ministry of Finance, the Ministry of Labour and Social Affairs, but also the general public and the media. Although the model does not simulate the pension system in complete detail, it provides a general overview and helps users understand the basic mechanisms and trends that will shape the future of the pension system. In this way, users can:
  • Gain a preliminary orientation and inspiration: By experimenting with simple scenarios (e.g., raising the retirement age or altering contribution rates), users can gain a clearer picture of how different reform steps could influence the stability of the pension system.
  • Provide context for public debate: The model can assist citizens, journalists, and non-profit organizations in better understanding the issues surrounding pension reform. This allows them to critically evaluate political proposals or expert recommendations.
  • Lead to more informed decision-making: While this is not a tool for detailed macroeconomic forecasting, the simulation provides a general insight into potential long-term trends. This can contribute to a broader understanding of the necessity for reforms and their impact on future generations.

Method and simulation environment:

• Method: System Dynamics
• Simulation environment: Vensim PLE (freely available for academic use)

Variables in the model (deterministic and random):

• Core Population Variables:
  • Number of children (new entrants to future workforce)
  • Number of working-age population (workers contributing to the system)
  • Number of pensioners (beneficiaries)

• Policy Variables:
  • Statutory retirement age
  • Contribution rate to social insurance (percentage of wage)
  • Pension benefit formula and indexation mechanism

• Economic Variables:
  • Average wage (influences contributions)
  • Inflation rate (influences indexation of pensions and wage growth)

• Fiscal Variables:
  • Total contributions collected (based on number of workers, contribution rate, and average wage)
  • Total pension expenditure (based on number of pensioners and average pension)
  • Pension system reserve fund (if applicable) and its depletion or accumulation

• Random Variables:
  • The model will incorporate stochastic elements through probability distributions derived from historical data and OECD/EUROSTAT projections to reflect uncertainty in:
    • Fertility rate (affects future workforce size; random from projected distribution)
    • Mortality rate / Life expectancy changes (stochastic variation around central OECD forecasts)
    • Inflation rate (stochastic variation around central forecast from CNB/OECD data)
    • Retirement rate (number of people retire each year +-)

Data sources (for deterministic baseline and to derive distributions):

• Czech Statistical Office (ČSÚ) for historical demographic data
• OECD demographic and economic projections for Czech Republic
• Eurostat long-term demographic projections for EU countries

Formulas in the simulation (examples):

• Pension Expenditure: Total Pension Expenditure = Number of Pensioners * Average Pension
• Average Pension Calculation: Average Pension(t+1) = Average Pension(t) * (1 + InflationIndex)
• Contribution Revenue: Total Contributions = Number of Workers * Average Wage * Contribution Rate
• System Balance: Annual Balance = Total Contributions - Total Pension Expenditure
• Accumulation or depletion of the pension reserve fund is then modeled as a stock: Reserve(t+1) = Reserve(t) + Annual Balance.

Model complexity and data linking:

• Causal loop diagrams (CLD): Will illustrate feedback loops such as how employment and wage growth influence contributions, and how demographic changes influence the ratio of workers to retirees.
• Stock and Flow Diagrams: Will detail population stocks (children, workers, retirees), and financial stocks (pension fund reserves), along with flows (entrants to workforce, retirees, death rates, pension contributions, and payouts).

Specific, measurable, and verifiable results:

• Specificity: The model will project the pension system’s financial status from year X to year X+50 under various reform scenarios, providing exact quantitative outcomes (e.g., fund balance in billions CZK, pension-to-wage ratio).

• Measurable metrics:
  • Dependency ratio (number of pensioners per 100 workers)
  • Pension system annual balance (CZK) and cumulative reserves over time
  • Average replacement rate (pension/average wage ratio)
  • Sensitivity of sustainability gap to changes in retirement age or contribution rate

• Verifiability: The initial model run will be calibrated against historical data for the past decade. Adjustments to parameters and comparison with known OECD and ČSÚ forecasts will verify the model’s credibility.

Omaj01 (talk) / NOT APPROVED

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Simulation concept – Invasive Plant Species vs. Native Plants vs. Herbivores Jan César (cesj05)

Objectives:

Understand the dynamics of competition between invasive plant species and native plants in a shared environment

Explore the conditions under which either the invasive species dominates, coexists, or fails to establish.

Environment:

Each patch represents a piece of land that can grow either a natrive or invasive plant (or remain empty)

Plants compete for resources on each path

Agents:

Native Plants: Slower growth but more resistant to herbivores or harsh conditions.

Invasive Plants: Faster growth and higher seed dispersal rate but less resistant to herbivores.

Herbivores: Agents that eat plants, with a preference for invasive or native species (modifiable by the user).

Methods

Initialization:

Randomly populate the grid with a mix of invasive and native plants.

Set up resource levels for each patch.

Place herbivores randomly across the grid.

Simulation Steps (Turtles/Agents):

Each plant (agent) checks:

Whether it has resources to grow or reproduce.

If conditions are favorable, it spreads seeds to nearby patches.

Herbivores move and consume plants on the patches they visit.

Competition between plants on shared patches determines which survives.

Interaction Dynamics: Modify the probability of herbivory or the effectiveness of seed dispersal as sliders to explore different scenarios.

The simulation will be done in NetLogo, as for the data, it will not be used from real world, but it will be set up, so the behaviour of agents will be as close as it can to real life (this will be based on real life data, or on information for example how fast does some X Y invasive plant grow in comparison to native plant etc...)

This simulation can be used by gardeners trying to maintain their garden. Cesj05 (talk) 16:19, 6 December 2024 (CET)