Model Documentation

Global Digital Currency Simulation — methodology, equations, and calibration


Abstract

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.

Country Groups

Eight groups calibrated to 2023 IMF World Economic Outlook data.

GroupGDP SharePop. ShareNAIRUTrend GrowthInitial Gini
United States25.4%4.3%4.5%2.5%0.41
Eurozone17.2%4.5%6.5%1.6%0.31
China18.1%17.8%5.0%4.5%0.46
Japan6.5%1.6%3.0%1.0%0.33
United Kingdom4.3%0.9%5.0%1.8%0.35
Other Advanced8.2%3.8%5.5%2.0%0.30
Emerging Asia12.1%31.5%6.0%5.5%0.38
Other Emerging & Frontier8.2%35.6%7.0%3.5%0.45

Model Equations

IS Curve

Output is a decreasing function of the real interest rate gap. b is the interest-rate sensitivity of aggregate demand.

Phillips Curve

Inflation equals expected inflation minus the disinflation from slack labor markets, plus a cost-push shock.

Adaptive Expectations

Agents update inflation expectations as a weighted average of last period's realized inflation and prior expectation.

Taylor Rule

The central bank sets the nominal rate to stabilize inflation around target and output around potential.

Okun's Law

Unemployment deviates from the natural rate in proportion to the output gap.

Uncovered Interest Parity

The exchange rate adjusts so that returns on domestic and foreign assets are equalized (no arbitrage).

Armington Trade Shares

Country i's import share from j depends on cost-adjusted prices and iceberg trade costs τ. θ is the elasticity of substitution.

Velocity with Reflexivity

Money velocity falls when agents expect rising prices under fixed supply — a deflationary-hoarding mechanism.

Fisher Debt-Deflation

Unexpected deflation erodes the real value of debt, damaging banking sector net worth and triggering crises.

Log-Normal Income Distribution

Income within each country is log-normally distributed. The Gini coefficient has a closed form in terms of σ.

Theil Decomposition

Global inequality decomposes into between-group (T_B, cross-country income gaps) and within-group (T_W) components.

Atkinson Index

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.

Quantity Theory

Money growth in excess of real GDP growth and velocity changes translates into inflation. Key channel for fixed-supply architecture.

CES Production Function

Constant elasticity of substitution production with TFP factor A. Elasticity σ = 1/(1−ρ), with ρ=0.5 giving σ=2.

Monetary Architecture Definitions

Fiat Baseline. Each country group retains an independent central bank following a Taylor rule with φπ = 1.5 and φy = 0.5. Money supply growth is endogenous to the Taylor rule. Exchange rates float freely under UIP. This is the counterfactual benchmark.
Fixed Supply. Total digital currency supply is held constant (μ = 0). Under quantity theory, MV = PY, any real growth in Y combined with fixed M and potentially falling V produces deflation. This creates a Fisher debt-deflation channel: unexpected price declines erode bank net worth, potentially triggering crises. Currency holders (wealthier households) benefit; debtors lose. Countries that adopted the currency early hold larger shares (empirical distribution).
Programmatic. Supply grows at 4% per year (≈ trend NGDP growth) with a feedback rule that contracts growth when world NGDP exceeds target. This eliminates central bank discretion while providing a stable nominal anchor. The rule reduces, but does not eliminate, inflation volatility — supply shocks still pass through.
Reserve-Backed. Digital currency supply is backed by a portfolio of fiat reserves (ρ = 30% baseline). Supply expands endogenously as reserves accumulate. Exchange rates are managed in a partial float. Trade cost reductions are smaller than the fixed-supply case because counterparty risk in the backing portfolio limits adoption.

Shocks and Calibration

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.

Assumption Inventory

Inflation Targetπ*
2%
Taylor (1993); Bernanke & Mishkin (1997)
World Neutral Real Rater*
2%
Laubach & Williams (2003); Holston et al. (2017)
Expectations Adaptationλ
0.4
Sargent (1971); Fuhrer (1997)
Taylor Inflation Coefficientφπ
1.5
Taylor (1993)
Taylor Output Gap Coefficientφy
0.5
Taylor (1993); Orphanides (2003)
Inflation Shock Std. Dev.σε
0.4%
Smets & Wouters (2007)
Trade Elasticityθ
4
Anderson & van Wincoop (2003); Head & Mayer (2014)
Crisis Leverage Thresholdλ̄
12x
Minsky (1986); Reinhart & Rogoff (2009)
Net Worth Recovery SpeedνNW
0.05
Bernanke, Gertler & Gilchrist (1999)
Velocity Sensitivityβv
0.15
Bordo & Jonung (1990); Carstens (2019)
Reserve Backing Ratioρ
0.3
Diem Association (2019); IMF (2022)
TFP Growth (Annual)g_A
2%
Fernald (2015); Gordon (2016)

Bibliography

Taylor, J.B. (1993). Discretion versus policy rules in practice. Carnegie-Rochester Conference Series on Public Policy, 39, 195–214.
Bernanke, B. & Mishkin, F.S. (1997). Inflation targeting: A new framework for monetary policy?. Journal of Economic Perspectives, 11(2), 97–116.
Laubach, T. & Williams, J.C. (2003). Measuring the natural rate of interest. Review of Economics and Statistics, 85(4), 1063–1070.
Holston, K., Laubach, T. & Williams, J.C. (2017). Measuring the natural rate of interest: International trends and determinants. Journal of International Economics, 108, S59–S75.
Sargent, T.J. (1971). A note on the accelerationist controversy. Journal of Money, Credit and Banking, 3(3), 721–725.
Fuhrer, J.C. (1997). The (un)importance of forward-looking behavior in price specifications. Journal of Money, Credit and Banking, 29(3), 338–350.
Smets, F. & Wouters, R. (2007). Shocks and frictions in US business cycles: A Bayesian DSGE approach. American Economic Review, 97(3), 586–606.
Anderson, J.E. & van Wincoop, E. (2003). Gravity with gravitas: A solution to the border puzzle. American Economic Review, 93(1), 170–192.
Head, K. & Mayer, T. (2014). Gravity equations: Workhorse, toolkit, and cookbook. Handbook of International Economics, Vol. 4, 131–195.
Minsky, H.P. (1986). Stabilizing an Unstable Economy. Yale University Press.
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Nakamoto, S. (2008). Bitcoin: A peer-to-peer electronic cash system. Bitcoin.org white paper.
Mundell, R.A. (1963). Capital mobility and stabilization policy under fixed and flexible exchange rates. Canadian Journal of Economics and Political Science, 29(4), 475–485.
Fleming, J.M. (1962). Domestic financial policies under fixed and under floating exchange rates. IMF Staff Papers, 9(3), 369–380.
Friedman, M. (1968). The role of monetary policy. American Economic Review, 58(1), 1–17.
Phelps, E.S. (1968). Money-wage dynamics and labor-market equilibrium. Journal of Political Economy, 76(4), 678–711.
Okun, A.M. (1962). Potential GNP: Its measurement and significance. Proceedings of the Business and Economics Statistics Section, ASA, 98–104.
Fisher, I. (1933). The debt-deflation theory of great depressions. Econometrica, 1(4), 337–357.
Atkinson, A.B. (1970). On the measurement of inequality. Journal of Economic Theory, 2(3), 244–263.
Theil, H. (1967). Economics and Information Theory. North-Holland Publishing Company.
IMF (2022). Global Financial Stability Report: Navigating the High-Inflation Environment. International Monetary Fund.

Limitations and Caveats

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.

Parameters are illustrative; this model is for educational use only.