Assignments WS 2024/2025

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Please, put here your assignments. Do not forget to sign them. You can use ~~~~ (four tildas) for an automatic signature. Use Show preview in order to check the result before your final sumbition.

Please, strive to formulate your assignment carefully. We expect an adequate effort to formulate the assignment as it is your semestral paper. Do not forget that your main goal is a research paper. It means your simulation model must generate the results that are specific, measurable and verifiable. Think twice how you will develop your model, which entities you will use, draw a model diagram, consider what you will measure. No sooner than when you have a good idea about the model, submit your assignment. And of course, read How to deal with the simulation assignment.

Topics on gambling, cards, etc. are not welcome.

In order to avoid possible confusion, please, check if you have added approved in bold somewhere in our comment under your submission. If there is no approved, it means the assignment was not approved yet.

Criteria for evaluation of the simulation proposal

The proposal must contain:

  • What you will simulate
  • The goal of the simulation (what you analyze - i.e. not "to simulate balloon factory", but what problem should the simulation solve).
  • Who would actually use such simulation (example of such user) and how would it help him
  • What method and simulation environment you plan to use. Choose only from the development environments that we have used in the course.
  • What variables will be incorporated
  • What variables will be random
  • What exact data you will base values of your variables on
  • (In case of Monte Carlo) What exact data you will base your determination of probability distribution of your random variables on
  • What exact data you will base your formulas in the simulation (simulation behavior) on

If any of the above points are missing from the simulation proposal, the proposal is considered incomplete. Unless the proposal contains all of the above points it will not be evaluated at all (and therefore cannot be approved).

  1. Is it clear from the proposed assignment how the simulation will work?
  2. Does the simulation make sense?
  3. Is the simulation model complex enough to simulate credibly the real-world phenomenon that the simulation tries to simulate?
  4. Is the data used real and relevant for the real-world phenomenon that the simulation tries to simulate?
  5. Is the simulation feasible? (in given time by the course)

If the answer to any of the above points is no, you need to improve your proposal. Don't wait for us to tell you so - you're wasting your time.

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)
    • Life expectancy (affects number of years in retirement)
  • 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)

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