Most economic models employ forward-looking variables that are driven by forcing processes whose form is fixed for all time, but in the real world the forcing process may be subject to change following the occurrence of a random event, for example when a country's currency appreciates to such an extent the policy-maker has to begin targeting the exchange rate to deter further deterioration of the current account balance. When variables such as interest rates, current accounts, inflation or exchange rates reach extreme values, the authorities may change not only their policies but also their policy-reaction functions.

In Discussion Paper No. 522, Kenneth Froot and Research Fellow Maurice Obstfeld analyse the behaviour of exchange rates under a variety of stochastically-triggered regime shifts. They consider recent models of two types. The first applies the technique of regulated Brownian motion to the processes whereby otherwise passive policy-makers intervene to prevent forward-looking variables from moving out of a predetermined range. This includes a variety of stochastic models of the effects of hiring and firing costs in the labour market, exchange rate target zones and the intersectoral allocation of capital with costly installation. The second studies the effects on forward-looking asset prices of once-and-for-all changes in regime, such as the UK's 1925 return to the gold standard or the unification of a system of dual exchange rates.
Froot and Obstfeld apply techniques of regulated Brownian motion to derive intuitive closed-form solutions that allow a precise description and calibration of the statistical estimation problems that possible future regime shifts may cause. They examine exchange rate dynamics in three cases, when the authorities promise: to confine a floating rate within a predetermined range; to peg the currency once it reaches a predetermined future level; and to unify a system of dual exchange rates. They stress the similarities between these and several related examples of regime switching and discuss the implications of stochastic regime shifts for the statistical distributions of asset prices and for econometric work. They find that prospective policy shifts induce non-linearities which imply both that standard linear econometric models are misspecified and also perhaps more importantly that the events that probably cause such non-linearities may occur only infrequently in time-series samples of the usual size.

Exchange Rate Dynamics Under Stochastic Regime Shifts: A Unified Approach
Kenneth Froot and Maurice Obstfeld

Discussion Paper No. 522, March 1991 (IM)