⁽¹⁾ Thus the uncovered interest parity condition may be written as ee _t = e_{t+ 1,t} + rd_t, where e_t is the log exchange rate at time t, e^e_{t +1,t} is the expectation, formed in period t, of the log exchange rate in period t + 1, and rd_t is the differential between domestic and foreign interest rates on one-period bills. (Here, as subsequently in the paper, the exchange rate is measured as the foreign currency price of domestic currency, so that an increase represents an appreciation.) Then successive substitution yields

$e_{\text{t}}=\sum _{i=0}^{\infty }r{d}_t^e+i,t+\overline{e}\text{w}\text{h}\text{e}\text{r}\text{e}\overline{e}(-e(\infty \left)\right)$

rate. Thus deviations of the exchange rate from equilibrium are driven by anticipated interest differentials cumulated into the future. Interest differentials may, in turn, be driven by a variety of variables, depending on the design of monetary policy.

⁽²⁾ See, for example, Dornbusch and Fischer (1980), and the impressive surveys provided by Branson and Henderson (1985) and Obstfeld and Stockman (1985).

⁽³⁾ See, for example, Currie (1985b) and Whittaker et al. (1986).

⁽¹⁾ Thus for the case where A ₁ + A ₂ = 1 and A ₃ = -A ₄ (both of which restrictions are acceptable by the data), if A ₆ ≠0, then in the long run with a constant real exchange rate and interest differential we must have In(X/M) = A ₆1 A ₀, so that the real trade position is pinned down in the long run. A permanent one percentage point rise in real interest rates permits a cumulative deficit (expressed as a proportion of imports) of A ₆1 A ₃.

⁽¹⁾ For a rather pessimistic view of the constraints on policy imposed by the current account in a world of imperfect capital mobility and a stock determination of the exchange rate, see Currie (1985b).

⁽¹⁾ The assumption of consistent expectations elsewhere in Model 8 is less stringent because the implied time horizon of expectations is much shorter in other markets.

⁽¹⁾ For a simple example of this forward solution, see the first footnote of this article. The solution in this case is more compli cated because of the presence of the lagged exchange rate in the exchange rate equation.

⁽²⁾ The lagged exchange rate term introduces an element of dis counting, so that the implied horizon is not infinite.

⁽³⁾ In technical terms, these paths represent unstable trajectories corresponding to the unstable roots of the system, which are usually ruled out by confining the system to the stable saddle-path.

⁽⁴⁾ See Blanchard and Watson (1982) for a discussion of rational stochastic bubbles in financial markets.

⁽⁵⁾ Barr and Currie (1986) show that, with any deviation from risk neutrality, sufficiently short-lived stochastic rational bubbles are necessarily chaotic in character.

⁽¹⁾ This may be relevant for the UK experience since 1979, since the point applies with equal force to the exchange rate consequences of fiscal contraction or expansion.

⁽²⁾ See Obstfeld (1984) for an analysis of the ‘peso problem’, where policy changes are forced by the self-fulfilling expectation of a change, despite policy being viable even in the long run.

⁽³⁾ Thus, for example, in terms of the model simulations reported here, suppose that the authorities implement a feedback rule of the form r_t - r*_t = -b(e_t - e*_t), where r is the interest rate and starred variables denote the values in the simulation run. Then the simulation results are unaffected, but the assumed degree of forward- looking behaviour required of the foreign exchange market declines as b is increased.