The Productivity
Bond Model
Financing prosperity without promising infinite growth. Here's the alternative.
Abstract
Universal Basic Income (UBI) is coming as the inevitable dividend of an AI economy. We’ve built a financial system that needs the economy to grow forever — but the planet doesn’t work that way. Global debt has exploded while resources stay finite, and ordinary people eventually pay the price through higher taxes, service cuts, or inflation.
The Productivity Bond Model offers a better way: a government bond that pays investors when we get smarter with what we already have, not just bigger. When efficiency rises, a share of the gains goes to every citizen as a Productivity Dividend — your share of the prosperity you helped create. It’s a financial tool that works with reality, not against it.
The Productivity Bond Model proposes a sovereign debt instrument whose return is linked to measurable productivity gains (NPI) rather than fixed compounding. It addresses the fundamental contradiction between unlimited financial promises and a finite planet. The model is parameterised by θ_AI (government capture of AI gains), α_N (investor participation), and a cap/floor structure. Monte Carlo simulations (10,000 paths, 10‑year horizon) show a 3.1% cost reduction vs conventional bonds, with a feedback loop that can be mitigated via principal adjustment.
The model is designed for implementation by sovereign governments and includes a Productivity Dividend to share gains with citizens. This page is the canonical reference for the model, including formal definition, variable specification, simulation results, and implementation guide.
📉 The Infinite Debt Problem
The gap between financial promises and physical reality is the defining challenge of our time. Explore the divergence below – then see how the Productivity Bond bridges the gap.
Financial obligations (debt) rise steeply – compound interest fuels exponential growth. Resource extraction flattens as we hit planetary limits. The growing gap between them is the Infinite Debt Problem.
Financial promises grow exponentially. Resource extraction flattens. The gap is the debt we cannot repay with growth alone.
The Old Way
- 💸 Compound interest on debt – grows forever
- 📈 GDP growth is the only metric that matters
- 🏦 Debt stock expands exponentially
- 🌍 Planet pays the price
- ❌ No one wins in the long run
The New Way
- 📊 Productivity-linked bonds (NPI)
- 🔒 Capped returns + floor protection
- 💎 Shared gains – Productivity Dividend
- 🌱 Works within planetary boundaries
🏆 Who Wins with the Productivity Bond?
0% real floor protection
Sustainable debt service
50% of gains shared
infinite growth
📖 Quick Reference
▼Think of the economy like a machine. θ_AI measures what % of AI efficiency gains the government collects to fund public services. α_N is the % of those gains paid out to bondholders. C sets a hard cap to prevent the government from overpaying in a boom, while F acts as a safety net ensuring investors get 0% real return in bad years.
Model Parameters
Key Equations
Results
Formal Specification
This section defines the rules of our Productivity Bond. It explains what the model is, how wide it applies, the assumptions we make about the world, and the mathematical equation governing it.
Replace perpetual‑growth‑dependent sovereign debt with productivity‑linked financing that shares risks and rewards.
Sovereign debt issuance, fiscal policy, AI‑driven productivity, and public goods funding.
- Planet is finite (resources, ecological capacity).
- Compound interest is the core problem of debt.
- AI productivity gains are capturable by government.
- NPI can be measured transparently and independently.
NPI = GDP / (H^0.40 × E^0.25 × M^0.20 × K^0.15)
Variables & Components
📚 Glossary
Quick definitions of all key terms used in this model.
Government capture of AI‑driven productivity gains. Default 0.30.
Investor participation in NPI growth. Default 0.70.
Real return cap – protects government from overpaying in booms. Default 4.0%.
Real return floor – protects investors in bad years. Default 0%.
National Productivity Index – weighted geometric average of labour, energy, materials, and capital productivity.
Productivity Dividend share – percentage of productivity gains distributed to citizens. Default 50%.
Growth rate of the National Productivity Index.
Inflation rate (CPI). The coupon is CPI‑linked to protect purchasing power.
How It Works
This diagram shows the cycle of the Productivity Bond in action: The Government issues the bond, the economy grows, the return is calculated based on NPI, and the gains are shared with investors and citizens.
⚡ Live Monte Carlo Simulator
10,000 paths · 10-year horizonMove the sliders below to simulate the economy. θ_AI, α_N, and Cap control how the bond behaves. The graph will update to show you the expected financial cost and distress risk.
😌 Happiness Curve & Bond Strength
Here we show the relationship between economic productivity, societal happiness, and the strength of the financial bond. Move the slider to find the 'sweet spot' where the economy grows happily.
📊 Simulation Results
Here are the hard numbers. We compare our Productivity Bond against other types of bonds. A lower 'Cost' means it's cheaper for the government, and 'Distress' measures the chance of financial trouble.
Bond Type Comparison
| Bond Type | Expected Cost | Distress Prob. | Welfare | Effective Yield |
|---|---|---|---|---|
| Conventional | 0.5154 | 11.05% | 1.0687 | 4.00% |
| Inflation‑Linked | 0.4896 | 70.22% | 4.0044 | 3.55% |
| GDP‑Linked | 0.5114 | 90.32% | 5.0329 | 3.97% |
| Productivity | 0.4994 | 88.17% | 4.9134 | 3.74% |
| Hybrid | 0.5272 | 94.63% | 5.2647 | 4.25% |
| Share | Expected Cost | Distress Prob. | Welfare |
|---|---|---|---|
| 0% (Conv. only) | 0.5154 | 11.05% | 1.0687 |
| 10% | 0.5139 | 19.20% | 1.437 |
| 20% | 0.5112 | 35.40% | 2.320 |
| 30% | 0.5088 | 52.10% | 3.451 |
| 40% | 0.5061 | 67.80% | 4.501 |
| 50% | 0.5035 | 76.50% | 5.112 |
| 100% | 0.4994 | 88.17% | 4.9134 |
🎯 Sensitivity Analysis
How key parameters affect outcomes.
🌍 Adoption Scenarios
Click a preset to load optimal parameters for your country type.
🏛️ Advanced
Enablers: deep capital markets, strong stats.
🚀 Emerging
Enablers: World Bank/IMF support, capacity building.
🏝️ Small Open
Enablers: trusted stats, first‑mover advantage.
🧪 How to Implement the Model
Step‑by‑step guide to running the full simulation locally.
1. Clone the Repository
2. Install Dependencies
3. Run the Simulation
4. View Results
Key Files
- ROADMAP.md – Full mathematical specification
- run_simulation.py – Main simulation engine
- results/ – All CSV outputs from Appendix C
- CONTRIBUTING.md – How to help improve the model
🧐 Known Limitations
Every model has blind spots. Here are the most important ones to keep in mind.
In good years, higher coupons increase debt service, which can enlarge the debt stock. The principal‑adjustment mechanism mitigates this but is still under active research.
NPI relies on accurate, transparent data. In countries with weak statistical capacity, the bond could be gamed or mis‑priced. Legal locks and independent agencies are critical.
The model assumes the government acts in good faith. In practice, political capture could distort θ_AI or τ. Strong institutions and independent oversight are essential.
The model assumes the government can capture a significant share of AI‑driven productivity gains. If AI gains flow mostly to private actors, θ_AI will be lower and the bond less effective.
❓ Frequently Asked Questions
Quick answers to the most common questions about this model.
No. The Productivity Dividend is funded from productivity gains, not general taxation. It's a recognition of contribution, not a transfer payment.
The coupon is CPI‑linked, so purchasing power is fully protected. The real return is floored at 0%.
No – the NPI methodology is legally locked in the bond's trust indenture. The statistical agency is independent, and revisions don't affect past coupons.
The floor/cap structure prevents default. In bad years, the coupon drops to inflation (0% real). The principal‑adjustment mechanism can also reduce debt stock.
The feedback loop. In good years, higher coupons can increase debt service and enlarge the debt stock. This is fixed with a principal‑adjustment mechanism, which is under active research.
🔗 Canonical Reference
How to cite the Productivity Bond Model in academic work.
@misc{callan2026productivitybond,
author = {Ylia Callan},
title = {The Productivity Bond Model},
year = {2026},
publisher = {Traffic Torch},
url = {https://traffictorch.github.io/productivity-bond-model/},
version = {1.2.1},
isbn = {979-8-23578-956-2},
note = {Canonical reference for the Productivity Bond Model}
}
📄 Policy Brief
The Problem in One Sentence
We have built a financial system that assumes unlimited growth on a planet with limits.
The Contradiction
Global debt has grown from ~$50 trillion in 1980 to over $300 trillion today – an almost perfect exponential curve. Global resource extraction is flattening or declining in per‑capita terms. The gap between these two curves is the infinite debt problem.
The Solution: Productivity Bonds
- Inflation protection – CPI‑linked
- Productivity participation – α_N × NPI growth
- Downside protection – 0% real floor
- Upside limit – C (cap)
Key Results
- Cost Saving: −3.1% vs conventional debt
- Optimal Portfolio: 30% Productivity Bonds
- Critical Variable: θ_AI > 0.30
Read the Book
The concepts and models on this page are the foundation of a larger, comprehensive book exploring the infinite debt problem, the productivity bond solution, and a complete roadmap for citizens and policymakers. To truly understand the depth of this philosophy, reading the book is essential.
📚 ISBN: 979-8-23578-956-2