Global Digital Currency Simulation — methodology, equations, and calibration
This simulation models the macroeconomic consequences of adopting a global digital currency across eight country groups over 240 monthly periods (20 years). Four monetary architectures are compared: a fiat baseline with discretionary central banks, a fixed-supply architecture (analogous to Bitcoin), a programmatic NGDP-targeting rule, and a reserve-backed stablecoin.
The model integrates an IS-LM framework for output and interest rates, an expectations-augmented Phillips Curve for inflation dynamics, Armington trade with iceberg costs for bilateral trade flows, a Fisher debt-deflation mechanism for banking crises, and log-normal distributions for within-country inequality tracking. Cross-country spillovers arise through correlated TFP shocks and the exchange rate channel.
Eight groups calibrated to 2023 IMF World Economic Outlook data.
| Group | GDP Share | Pop. Share | NAIRU | Trend Growth | Initial Gini |
|---|---|---|---|---|---|
| United States | 25.4% | 4.3% | 4.5% | 2.5% | 0.41 |
| Eurozone | 17.2% | 4.5% | 6.5% | 1.6% | 0.31 |
| China | 18.1% | 17.8% | 5.0% | 4.5% | 0.46 |
| Japan | 6.5% | 1.6% | 3.0% | 1.0% | 0.33 |
| United Kingdom | 4.3% | 0.9% | 5.0% | 1.8% | 0.35 |
| Other Advanced | 8.2% | 3.8% | 5.5% | 2.0% | 0.30 |
| Emerging Asia | 12.1% | 31.5% | 6.0% | 5.5% | 0.38 |
| Other Emerging & Frontier | 8.2% | 35.6% | 7.0% | 3.5% | 0.45 |
Output is a decreasing function of the real interest rate gap. b is the interest-rate sensitivity of aggregate demand.
Inflation equals expected inflation minus the disinflation from slack labor markets, plus a cost-push shock.
Agents update inflation expectations as a weighted average of last period's realized inflation and prior expectation.
The central bank sets the nominal rate to stabilize inflation around target and output around potential.
Unemployment deviates from the natural rate in proportion to the output gap.
The exchange rate adjusts so that returns on domestic and foreign assets are equalized (no arbitrage).
Country i's import share from j depends on cost-adjusted prices and iceberg trade costs τ. θ is the elasticity of substitution.
Money velocity falls when agents expect rising prices under fixed supply — a deflationary-hoarding mechanism.
Unexpected deflation erodes the real value of debt, damaging banking sector net worth and triggering crises.
Income within each country is log-normally distributed. The Gini coefficient has a closed form in terms of σ.
Global inequality decomposes into between-group (T_B, cross-country income gaps) and within-group (T_W) components.
The Atkinson index (ε=0.5) reflects the social welfare cost of inequality — the fraction of income that could be sacrificed without loss if distributed equally.
Money growth in excess of real GDP growth and velocity changes translates into inflation. Key channel for fixed-supply architecture.
Constant elasticity of substitution production with TFP factor A. Elasticity σ = 1/(1−ρ), with ρ=0.5 giving σ=2.
TFP shocks are drawn from a multivariate normal distribution using a factor model. Advanced economies (US, EZ, JP, UK, OA) share a common factor with correlation ρ = 0.6. China loads at ρ = 0.3 and emerging markets at ρ = 0.4 with each other and ρ = 0.25 with advanced economies.
Inflation shocks are independently drawn per country (after loading on the common factor at σε = 0.4% monthly, annualizing to ≈ 1.4%). The seeded LCG random number generator ensures exact reproducibility: changing the seed traces a different but deterministic path through the shock distribution.
Initial conditions are calibrated to 2023 actuals. Income distributions are parameterized as log-normal, with σ recovered from the initial Gini via the closed-form relationship Gini = 2Φ(σ/√2) − 1.
This model is a calibrated teaching instrument, not a structural policy tool. All parameters are set to illustrative values consistent with the empirical literature but are not estimated via GMM or Bayesian methods. Confidence intervals are not reported; the seeded RNG traces a single draw from the shock distribution.
The model abstracts from: sovereign debt dynamics, labor market heterogeneity, fiscal policy, capital account controls, and second-order network effects of digital currency adoption. The Armington trade structure imposes symmetric elasticities and ignores extensive margin responses (new firm entry, product variety).
Results should be interpreted as directional intuitions about the comparative statics of different monetary architectures, not as quantitative forecasts.