RDP 9307: Explaining Forward Discount Bias: Is it Anchoring? Appendix A: Reduced Forms for the Stochastic Environment

We assume a standard domestic LM curve,

where is fixed real output and the other variables are defined in the text. As discussed, demand, D_t, is a simplified version of the Dornbusch (1976) form

and, following Dornbusch, goods prices adjust slowly to excess demand. Thus, the change in the log price of domestic goods, Δp_t+1, is

With no price stickiness, p_t = . In the special case of the model described in the text, the arbitrage condition in the foreign exchange market (equation (10)) implies that i = i^* in a long-run with the domestic money supply fixed. This condition implies that = m_t + λ i^* − ϕ , and hence

In this long-run, p_t = , Δp = 0, and hence from (A1),

Equation (A3) is the constraint imposed between exogenous variables described in the text. It implies that (A1) may be rewritten as

which is equation (5) in the text. Finally, combining (A2) with (4) and (5) gives (6).