F — Pension transition simulator

Appendice F

PENSION TRANSITION SIMULATOR — METHODOLOGY AND LIMITS

Reference: Chapter VII (Protecting Oneself Without the Welfare State), Appendix E (Pension Transition)

F.1 — Simulator Objective

The pension transition simulator is a macro-economic modeling tool designed to answer a precise question: is it financially feasible to transition from a pay-as-you-go pension system to a funded system, without abandoning current retirees’ acquired rights?

It is not an economic forecasting tool. It does not claim to predict the future. Its purpose is to demonstrate the technical feasibility of a transition, by showing how both debts—public and implicit—can converge to zero within an explicit and adjustable framework of assumptions.

What the simulator demonstrates:

• The transition is technically achievable
• It takes 2 to 3 generations (70 to 90 years depending on country)
• The transition effort (differential) is temporary and decreasing
• All salaries win from day one

F.2 — The Macro-Economic Logic

The model rests on simple but rigorous logic.

The Central Problem: The Double Debt

At the start of transition, two debts must be absorbed:

1. Official public debt — the one everyone knows (80-120% of GDP depending on country).

2. Implicit pension debt — unfunded pension promises accumulated by the pay-as-you-go system. This “hidden” debt typically represents 200 to 300% of GDP. It appears in no balance sheet, but it is very real: these are the pensions the State will have to pay to current and future retirees.

The Transition Mechanism

The transition works in three simultaneous phases:

Phase 1: Honor acquired rights. Current retirees continue receiving their pensions (possibly reduced by 10% through “solidarity contribution”). They contributed their whole lives with this promise—we don’t abandon them.

Phase 2: Switch new workers. From day one of transition, new labor market entrants contribute to their own capitalization. They owe nothing to anyone.

Phase 3: Manage mid-career workers. Those who have already contributed retain proportional rights to their seniority. A worker with 20 years’ career has 50% rights in the old system (paid by the differential) and capitalizes for the remaining 50%.

The Differential: A Temporary and Decreasing Tax

During transition, a temporary tax (the “differential”) finances payment of old-system pensions. This differential:

• Starts at about 8-12% of GDP (depending on country)
• Decreases progressively over 40 years
• Reaches zero when all old-system beneficiaries have passed away

The decrease can follow several profiles: linear (simplest), quadratic (slower at start, faster at end), or in steps.

F.3 — Model Assumptions

The simulator rests on explicit assumptions, all modifiable by the user.

Demographic Assumptions

Note on mortality: The model uses progressive mortality that increases with age. It is not a complete actuarial mortality table—it is a sufficient approximation for macro-economic simulation.

Economic Assumptions

Note on growth: The model assumes declining but positive growth. With flat tax and reduced contributions, a positive Laffer effect is expected—real growth could exceed projections.

Financing Assumptions

Interest Rate Assumptions

Debt interest rate is a function of debt/GDP ratio:

This tiered structure reflects market reality: the more indebted a country, the more it pays to borrow.

F.4 — Simulation Engine Operation

The simulator proceeds in two passes.

Pass 1: Calibration (the multiplier)

The first pass calculates a “multiplier” that ensures consistency between pension flows and implicit debt. This multiplier guarantees that the sum of pensions paid over the entire transition exactly equals the initial implicit debt (after solidarity reduction).

Why this calibration? Official data on average pensions and retiree numbers don’t exactly match the implicit debt calculated by economists. The multiplier corrects this gap.

Pass 2: Year-by-Year Simulation

For each simulation year, the engine executes in order:

1. GDP growth — Application of appropriate growth rate for the period.

2. Adding a new retiree cohort — New retirees enter with rights proportional to their seniority in the old system.

3. Pension flow calculation — Sum of pensions for all living cohorts, weighted by their rights.

4. Mortality application — Each cohort loses a percentage of members, according to a rate increasing with age.

5. Differential calculation — Comparison between pension flow to pay and theoretical differential ceiling. If flow exceeds ceiling, difference is borrowed (transition debt).

6. Debt repayment — Differential surplus (if flow is below ceiling) first repays transition debt, then public debt.

7. Interest — Calculation and capitalization of interest on all real debts.

8. Implicit debt update — Reduction of implicit debt by amount of pensions paid.

9. End verification — Simulation stops when all three debts (public, transition, implicit) are at zero.

The Cohort System

The model manages retirees by cohorts. Each cohort represents people who retired in a given year. It has:

• A number of living members (decreasing)
• An average pension
• An old-system rights rate (decreasing from one cohort to the next)

This cohort approach allows modeling progressive extinction of the old system without tracking millions of individuals.

F.5 — Graphical Interface User Guide

The simulator has a complete graphical interface for visualizing the transition and exploring different scenarios.

Launching the Application

To launch the simulator, run the simulateur_gui.py file from the gui/ folder:

python simulateur_gui.py

The application starts with the Belgium scenario by default and automatically runs a first simulation.

Interface Layout

The interface is divided into three main areas:

Left area: Parameter panel

This panel displays all simulation parameters organized by category:

• Demographics — number of retirees, new retirees per year, life expectancy, mortality
• Economy — GDP, growth, privatizations, capitalization return
• Fiscal — flat tax rate, standard deduction, initial differential
• Pensions — average pension, solidarity reduction

By default, parameters are in read-only mode (gray background). To modify them:

1. Check the “Edit” box next to the parameter
2. Background becomes light pink to indicate the field is editable
3. Modify the value — simulation automatically reruns
4. Modified values display in green

Central area: Graph panel

This area displays simulation graphs. Use the dropdown menu at top to select which graph to display:

• GDP evolution
• Public debt (in billions or % of GDP)
• Implicit pension debt
• Transition differential
• Purchasing power evolution by salary level
• Year 0 combined effect (new system + abolished taxes)
• And many more…

Graph interactions:

• Mouse drag — pan (move the graph)
• Scroll wheel — zoom in/out
• Right double-click — reset view
• "⛶" button — open graph in enlarged window
• "📋" button — copy to clipboard as PNG
• "📄" button — copy to clipboard as SVG
• "💾" button — save graph (SVG or PNG)

Right area: Help panel

This panel displays contextual help and code legends used in graphs (SBRT = gross salary, ANEE = year, etc.).

Country Scenarios

The “Scenario” menu allows loading pre-configured configurations for different countries:

Each scenario uses realistic economic and demographic data for the country concerned.

Enlarged Window and “Live” Mode

Click “⛶” to open a graph in a separate window. This window offers:

• A larger and more detailed view
• “Live” mode (check the box) — graph updates automatically when you modify parameters in the main window
• Same copy and save functions

Results Table

The “View > Results Table” menu opens a window with raw year-by-year data:

• GDP, differential, debts
• Number of retirees by cohort
• Pension flows

This data can be copied or exported for external analysis.

Adjusting Font Size

The “View > Font Size” menu allows adjusting text size (from 10 to 24 points). Useful for high-resolution screens or presentations.

Language

The “Language” menu allows switching between French and English. The interface updates immediately.

F.6 — Model Limits

The simulator is a feasibility demonstration tool, not a forecasting tool. Its limits are acknowledged.

What the Model Does NOT Do

No micro-economic modeling. The simulator does not model individual behaviors (savings, consumption, investment). It works with macro-economic aggregates.

No economic cycles. The model assumes regular growth without recessions. In reality, there will be crises. But over 80 years, cycles balance out—the underlying trend remains valid.

No external shocks. Wars, pandemics, technological revolutions… The model does not anticipate them. It shows what happens “all else being equal.”

No financial market modeling. Capitalization returns are not simulated. The model simply assumes capitalization works—which 150 years of financial history largely confirms.

No inflation. All calculations are in constant currency. Inflation is neutralized.

Why These Simplifications Are Acceptable

A model is always a simplification of reality. The question is not “is it perfect?” but “is it useful?” As statistician George Box put it: “All models are wrong, but some are useful” [14]. Our cognitive capacities are limited [10]—a perfect model would be as complex as reality itself, therefore unusable.

The simulator answers a binary question: is the transition feasible? The answer is yes, and this answer is robust:

• Pessimistic scenarios also succeed
• Parameter variations change duration, not result
• Mathematical logic is unavoidable: old-system retirees pass away, their rights extinguish, so the differential can decrease

The error would be to model nothing. Without simulation, one often hears that “transition is impossible” or would “cost too much.” The simulator proves otherwise with verifiable numbers.

F.7 — Reproducibility and Transparency

The simulator’s source code is entirely available. All assumptions are explicit and modifiable. Results are reproducible.

Files provided:

• transition_pensions.py — Simulation engine
• simulateur_gui.py — Graphical interface
• configurations/*.ini — Country scenarios
• Complete documentation

What you can verify:

• Equations used
• Default parameters
• Logic of each step
• Results for any parameter set

Transparency is total. If you think an assumption is unrealistic, modify it and rerun the simulation. The model has nothing to hide.

F.8 — Conclusion: A Persuasion Tool, Not a Prediction Tool

The simulator does not predict the future. It demonstrates a possibility.

Faced with the mathematically collapsing pay-as-you-go system, many say there is “no alternative.” The simulator proves otherwise: a transition to capitalization is technically feasible, financially sustainable, and beneficial for all salaries from day one.

The choice remains political. But at least it can no longer be refused on grounds of supposed technical impossibility.

Return to Appendix E — Pension Transition