Paul Krugman has recently argued that there is a paradox in the literature on the gold standard and fixed exchange rates. On reasonable assumptions about the fundamentals that drive the shadow floating exchange rate and the stock of international reserves, a speculative attack can only occur after the country has already `naturally' run out of reserves, i.e. without a sudden run on its currency. And when a country runs out of gold reserves its currency will immediately appreciate.
In Discussion Paper No. 361, Research Fellows Willem Buiter and Vittorio Grilli re-examine Krugman's paradox in two different two-country models. In the first, the only assets are the two currencies, held by private agents, and gold, held only by the central banks. The second model adds two fixed-price, single-period bonds, one denominated in each currency. Buiter and Grilli define two concepts of a fixed exchange rate system's viability: that the system should not suffer a speculative attack (`S-viability') and that the system should not suffer a reserve collapse (`R-viability'). The fixed exchange rate system is viable when both are satisfied simultaneously.
These concepts provide a general criterion for determining whether there is a paradox. If a low value of the currency is associated with expectations of appreciation following a collapse, there will not be a correct speculative attack; and similarly if a high currency value is associated with expectations of depreciation.
Buiter and Grilli show that Krugman's paradox is a very general phenomenon, which can be present in discrete and continuous time models. They establish a necessary and sufficient condition for a system to be `paradox-free', i.e. to have speculative attacks only in the right direction. When this condition is satisfied, there will never be any trouble when the movement of the actual shadow exchange rate is always in the same direction as the change in the expected rate of change of the exchange rate at the moment a collapse occurs. If we start above (below) the lower (upper) boundary, the system will never descend (rise) towards it.
Krugman conjectures that there can be no non-paradoxical fixed exchange rate regime, and so replaces this assumption with a `target zone' that has hard boundaries as long as reserve thresholds are not broken. The transformation of the gold standard into a band delivers a proper equilibrium, but Buiter and Grilli show that it is not necessary to abandon the assumption of perfectly fixed exchange rates in order to recover a well-defined equilibrium

The `Gold Standard Paradox' and its Resolution
Willem H Buiter and Vittorio U Grilli

Discussion Paper No. 361, December 1989 (IM)