Exchange rates depend on agents' expectations as well as `fundamental' variables. If a currency whose rate is pegged reaches the limit of its band and a discrete devaluation appears very likely, then the exchange rate may react sharply even to minor `news' as forward-looking agents bid down that currency. Conversely, expectations of intervention to defend a given band should have a stabilizing effect by reducing the exchange rate's responsiveness to movements in fundamentals. The perceived likelihood of realignment vis-à-vis defence of the parity should depend inversely on the size of available reserves.

In Discussion Paper No. 504, Research Fellow Giuseppe Bertola and Ricardo Caballero present a model in which the exchange rate depends on the rate of change of its expected value and on `fundamentals' of two types: the first vary smoothly over time, and the second are subject to discrete jumps. If the probabilities of such jumps are constant or independent of the exchange rate and the fundamentals, the relationship between fundamentals and the exchange rate remains linear; but if their size or probability is related to the fundamentals or the exchange rate, then the fundamentals and the exchange rate will exhibit a non-linear relationship, as found in the `target zone' literature.

The smoothly varying component of the fundamentals represents money velocity shocks or the monetization of government deficits beyond the authorities' control; the `jump' component represents non-sterilized intervention in foreign exchange markets, which is assumed to be related to the exchange rate's behaviour in a target zone. The jumps and hence reserves follow a random walk, and reserves reach arbitrarily large or small levels with certainty. Bertola and Caballero model the probability of a realignment at the upper edge of the band as a decreasing function of cumulative intervention to date. They show that cumulative intervention is bounded and study the joint behaviour of the fundamentals, the central parity and cumulative interventions in a sustainable target zone regime over time. In particular, they examine how the level of reserves affects the short-run relationship between the exchange rate and the fundamentals. For a probability of intervention that is a linear function of cumulative interventions, they show that intervention is more likely to increase than to reduce reserves as they become scarce.

They also show that when the expectation over all values of cumulative interventions (or reserves) has a well-defined probability distribution, the unconditional relationship between the exchange rate and the fundamentals is linear, as with a free float. Hence if no information on reserves is available, the exchange rate can be expected to behave as if under a free float. Bertola and Caballero conclude by outlining some possible generalizations of their simple model. If intra-marginal intervention is permitted, realignments and interventions should be modelled as functions of not only reserves but also the fundamentals.

Sustainable Intervention Policies and Exchange Rate Dynamics
Giuseppe Bertola and Ricardo J Caballero

Discussion Paper No. 504, January 1991 (IM)