RDP 9307: Explaining Forward Discount Bias: Is it Anchoring? Appendix F: Real Exchange Rate Shocks are AR(1)

The empirical results reported by (for example) Frankel and Meese (1987) suggest modelling real exchange rate shocks as a stationary AR(1) process rather than a random walk and hence replacing equation (7) by

For the special case of the model when the supply of domestic and foreign interest-bearing assets managed by the traders matches their minimum-variance portfolio, the ‘no-bubble’ solution for the exchange rate change Δs_t+1 becomes

where χ = (αβ)/(αβ + (1 − α) (1 − ρ)). There are two things of note about equation (11′). Firstly, real exchange rate shocks are uncorrelated with the forward discount by assumption. Hence, for given a, since the coefficient on the forward discount is the same in equations (11) and (11′), the bias of the forward discount is also the same. In this respect, modelling real exchange rate shocks as a stationary AR(1) process makes no difference to the results.

Secondly, and by contrast, note that in the absence of anchored traders, the real exchange rate shocks have no impact on the exchange rate (α = 0 ⇒ χ = 0). In setting the spot exchange rate, rational agents in the foreign exchange market simply ignore stationary shocks to the long-run real exchange rate. Given our empirical estimates of σ_m, this implies (counterfactually) very little exchange rate volatility when α = 0. Thus, to explain the observed volatility of exchange rates within the framework of the model assuming (7′) rather than (7), it would be necessary to invoke some auxiliary assumption (like, perhaps, imposing some myopia on the rational foreign exchange traders).