Econometrica: Jul 1954, Volume 22, Issue 3
Stability of the Exchange Rate Mechanism in a Multi-Country System
J. J. Polak, Ta-Chung LiuThe conditions under which a devaluation will improve a country's balance of payments--stability conditions of exchange rate adjustments--have been extensively dealt with in literature for a two-country system under static conditions. This paper represents an attempt to analyze the complications arising from the introduction of more countries into the system under dynamic conditions. The dynamic stability conditions for an n-counutry model have been derived in mathematical terms through a system of difference equations under quite general conditions in the Appendix. Special pain has been taken in the text to interpret these mathematical conditions in economic terms for a more restricted three-country model. Three cases of exchange rate adjustments have been analyzed. It has been found that, provided that each country taken by itself is stable (i.e., that a depreciation of its currency will improve its balance of payments, all other countries' par values remaining unchanged), a sufficient condition for the stability of a three-country system is that, for any pair of countries, the absolute value of the product of the effects on each others' balances, each acting alone, is smaller than the product of the effects on their own balances.
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