International Macroeconomics & Sovereign Risk
Original Sin & Currency Mismatch Debt Shock Formula
Calculate post-depreciation sovereign Debt-to-GDP valuation jump d_1 = d_0*(1 + alpha_fx * Delta_S)/(1 + g_y) under Eichengreen-Hausmann "Original Sin" and Goldstein-Turner Net FX Debt / Exports mismatch.
Quantify instant balance-sheet debt explosions when sovereign debt is in foreign currency!
Barry Eichengreen, Ricardo Hausmann, and Ugo Panizza (2003) coined "Original Sin" for emerging economies unable to borrow abroad in domestic currency! When share alpha_fx in [0, 1] of Initial Sovereign Debt-to-GDP d_0 is denominated in USD/EUR while tax revenues are in local currency, a Real Exchange Rate Depreciation Shock Delta_S > 0 (percentage increase in local-currency units per USD) combined with Real GDP Growth g_y instantly inflates Debt-to-GDP to d_1 = (d_0 * ((1 - alpha_fx) + (1 + Delta_S) * alpha_fx)) / (1 + g_y) = (d_0 * (1 + alpha_fx * Delta_S)) / (1 + g_y) — even at a ZERO fiscal deficit! Morris Goldstein and Philip Turner (2004) paired this with the Net FX Debt-to-Exports Currency Mismatch Ratio (alpha_fx * d_0 - FX_Reserves_GDP) / Exports_GDP!
Verify on Initial_Debt_GDP d_0 = 0.60 (60.0%, B2), Foreign_Currency_Share alpha_fx = 0.50 (50.0% FX debt, B3), Exports_to_GDP = 0.20 (20.0%, B4), FX_Reserves_to_GDP = 0.10 (10.0%, B5), Real_FX_Depreciation_Shock Delta_S = 0.40 (+40.0% LCU/USD jump, B6), and Recession_GDP_Growth g_y = -0.04 (-4.0%, B7): Post-Shock Debt-to-GDP jumps from 0.6000 to (0.60 * (1 + 0.50 * 0.40)) / (1 - 0.04) = 0.72 / 0.96 = 0.7500 (75.00% of GDP — an instant +15.00 percentage-point balance-sheet shock!), and Net FX Debt-to-Exports Mismatch is (0.30 - 0.10) / 0.20 = 1.0000 (100% of annual exports)! Eliminate Original Sin (alpha_fx = 0): d_1 rises only to 0.60 / 0.96 = 0.6250 (+2.50 pp)!
| Currency Mismatch Sovereign Metric (d_0=60%, fx=50%, dS=+40%, g=-4%) | Formula | Verified Output |
|---|---|---|
| Post-Shock Debt-to-GDP Ratio (d_1) | d_0 * (1 + alpha_fx * Delta_S) / (1 + g_y) | 0.7500 (75.00% of GDP) |
| Balance-Sheet Valuation Debt Jump | d_1 - d_0 | +0.1500 (+15.00% of GDP) |
| Net FX Debt-to-Exports Mismatch | (alpha_fx * d_0 - Reserves_GDP) / Exports_GDP | 1.0000 (100% of Exports) |
| Local-Currency Debt Benchmark (alpha_fx = 0) | d_0 / (1 + g_y) | 0.6250 (+2.50% vs +15.00%) |
Original-Sin Balance-Sheet Debt-to-GDP Valuation Formula
Validate d_0 >= 0, 0 <= alpha_fx <= 1, Exports_GDP > 0, Reserves_GDP >= 0, Delta_S > -1, and g_y > -1!
=LET(d_in, B2, fx_s, B3, x_gd, B4, rs_g, B5, ds_sh, B6, gy_r, B7, IF(OR(d_in < 0, fx_s < 0, fx_s > 1, x_gd <= 0, rs_g < 0, ds_sh <= -1, gy_r <= -1), "Invalid Mismatch Input", ROUND((d_in * (1 + fx_s * ds_sh)) / (1 + gy_r), 4)))Goldstein-Turner Net FX Debt-to-Exports Mismatch Ratio Formula
Notice that when FX Reserves exceed FX Debt (Reserves_GDP > alpha_fx * d_0), Net FX Mismatch turns negative — meaning depreciation strengthens the sovereign balance sheet in local currency!
=IF(ISTEXT(E2), E2, ROUND((B3 * B2 - B5) / B4, 4))Try the example
Use the original values or change them to test your understanding.