Emerging Markets & Open-Economy Macroeconomics
Calvo Sudden-Stop Absorption Cut & RER Jump Formula
Calculate Guillermo Calvo’s (1998, 2004) sudden-stop Tradable Absorption Contraction CAD / omega_T and required Real Exchange Rate Depreciation (1 - CAD / omega_T)^(-1 / xi) - 1.
See why a 6% current-account deficit forces a 77.8% real currency crash in closed economies!
Guillermo Calvo, Alejandro Izquierdo, and Luis-Fernando Mejia (2004) explained why Sudden Stops in external capital inflows devastate semi-closed emerging markets far worse than trade-open economies! Suppose an economy runs a pre-crisis Current_Account_Deficit_to_GDP CAD_gdp financed by external borrowing that abruptly stops (requiring CAD -> 0), while Tradable_Absorption_Share_of_GDP is only omega_T (e.g., 24%) and short-run Tradable & Non-Tradable outputs are fixed. Closing the external gap requires Tradable Absorption to contract by fraction Cut_T = CAD_gdp / omega_T! Under homothetic CES demand with Tradable/Non-Tradable Substitution Elasticity xi > 0, clearing the non-tradable market requires Relative Price of Tradables P_T / P_N (the Real Exchange Rate) to jump by RER_Jump = ((1 - CAD_gdp / omega_T) ^ (-1 / xi)) - 1!
Verify on Pre_Stop_CAD_GDP = 0.06 (6.0% of GDP, B2), Tradable_Absorption_Share omega_T = 0.24 (24.0% of GDP, B3), and Short_Run_Substitution_Elasticity xi = 0.50 (B4): Required Tradable Absorption Collapse is 0.06 / 0.24 = 0.2500 (25.00% plunge!), Calvo Leverage Multiplier (1 / omega_T) is 4.1667x, and Required Real Exchange Rate Depreciation is (1 - 0.2500)^(-1 / 0.50) - 1 = (0.75)^(-2) - 1 = 1.7778 - 1 = +0.7778 (+77.78% real depreciation)! Open the economy to trade (omega_T = 0.60 in B3): Tradable Cut shrinks to 10.00% and RER Jump drops from +77.78% to (0.90)^(-2) - 1 = +0.2346 (+23.46%)!
| Calvo Sudden-Stop Metric (CAD=6% GDP, omega_T=24% GDP, xi=0.50) | Formula | Verified Output |
|---|---|---|
| Tradable Absorption Collapse (Cut_T) | CAD_gdp / omega_T | 0.2500 (25.00% Drop) |
| Calvo Openness Leverage Factor | 1 / omega_T | 4.1667x |
| Required RER Depreciation (Delta P_T/P_N) | ((1 - CAD_gdp / omega_T) ^ (-1 / xi)) - 1 | +0.7778 (+77.78% Jump) |
| Open-Economy Comparison (omega_T = 0.60) | Cut_T = 10.0%; (0.90)^(-2) - 1 | +0.2346 (+23.46% Jump) |
Calvo-Izquierdo-Mejia (2004) Required Real Exchange Rate Jump Formula
Enforce 0 <= CAD_gdp < omega_T <= 1 and xi > 0: if CAD_gdp >= omega_T, even eliminating 100% of domestic tradable consumption cannot close the external gap without immediate default or export jump!
=LET(cd_gd, B2, om_tr, B3, xi_sb, B4, IF(OR(cd_gd < 0, om_tr <= 0, om_tr > 1, cd_gd >= om_tr, xi_sb <= 0), "Invalid Sudden-Stop Input", ROUND(((1 - cd_gd / om_tr) ^ (-1 / xi_sb)) - 1, 4)))Tradable Absorption Cut & Cobb-Douglas (xi = 1) Check Formula
Test B4 = 1.00 (unit Cobb-Douglas substitution elasticity): RER depreciation drops from +77.78% to (0.75)^(-1) - 1 = +0.3333 (+33.33%)!
=IF(ISTEXT(E3), E3, ROUND(B2 / B3, 4))Try the example
Use the original values or change them to test your understanding.