The impossible trinity and Krugman׳s balance of payments crisis model

The “impossible trinity” refers to the impossibility of the simultaneous presence of a fixed exchange rate regime, uncovered interest parity and the Central Bank׳s control over the money supply. I apply this to Krugman׳s (1979) balance of payments crisis model, where he argued that there is a unique date on which a crisis occurs. I show that the crisis can occur on any date. The Central Bank may be left with reserves in excess of the level that they wish to defend, which seems consistent with the data. But for the attack to be successful the amount of foreign exchange reserves that the Central Bank will lose on any date is uniquely determined, and is the same as in Krugman (1979).