In this paper we develop a rational expectations exchange-rate model which is capable of confronting explicitly agents' beliefs about a future switch in exogenous driving processes. In our set-up the agents know with certainty both the initial exogenous process and the new process to be adopted when the switch occurs. However, they do not know with certainty the timing of future switch as it depends on the path followed by the (stochastic) exchange rate. The model is discussed in terms of the British return to pre-war parity, in 1925. However, our results are applicable to a variety of situations where process switching depends on the motion of a key endogenous variable. OFTEN, A POLICY AUTHORITY such as a central bank operates by establishing a policy rule to set the variables under its control. Such a rule is allowed to operate freely as long as certain endogenous variables of interest to the authority remain within particular bounds; however, when those endogenous variables cross their bounds, the authority switches to a new policy rule which it had prepared to meet this contingency. Since variables such as prices are determined partly by agents' beliefs about future events, agents' behavior injects the probabilities that policy switches will occur at particular future times into current price determination. In this paper we explore in a formal model the determination of a current exchange rate when future policy regime switches are possible. In order to do this we develop a new aspect of an otherwise standard exchange-rate model; this key component is the probability density function (p.d.f.) for the first passage through a barrier of the endogenous variable (the exchange rate) which interests the policy authority.2 Since analytical solutions for first passage p.d.f.'s are available for only a limited number of stochastic processes, we are restricted to these processes in formulating our example. However, within this class of processes, our results are generally applicable to many different kinds of macroeconomic problems. We present our ideas in the context of a model of exchange rate determination. Our choice of a specific example is intended to add concreteness to the analysis but should not be interpreted as setting limits on the applicability of the analysis. Indeed, the structure of the problem at hand virtually duplicates the structures
Stored only when both papers are in the corpus — 80 citations exist upstream.
Imported from OpenAlex (CC0) — nothing here is generated.