Investment and Interest Rate Policy in the Open Economy

where R > 1 and the timing-index v represents the inflation-targeting behavior of the
monetary authority. If v = 0, the monetary authority targets current inflation. If v =
-1 the policy rule is backward-looking, whereas v = 1 corresponds to forward-looking
inflation targeting. The parameter μ determines whether monetary policy is active or
passive. An active monetary policy corresponds to μ > 1, where the real interest rate
rises in response to higher inflation, as the monetary authority increases the nominal
interest rate by more than the increase in inflation. A passive monetary policy on the
other hand corresponds to 0 ≤ μ < 1, where the real interest rate falls in response to
higher inflation.

2.5 Market Clearing and Equilibrium

Market clearing for the home goods market requires

ZHt + ZH ,t = Yt.                            (24)

Total home demand must equal the supply of the final good,

Z_t = C_t + I_t,                                  (25)

and the labor, capital, money and bond markets all clear:

Υt = Mt - Mt—ι     Bt + Bt =0.                   (26)

Definition 1 (Rational Expectations Equilibrium): Given an initial allocation of Bt₀,
B_t^t₀ , K_t0 , K_t^t₀ , and M_t0-1, M_t^t_0-1, a rational expectations equilibrium is a set of sequences
{Ct, Ct^t , Mt, Mt^t , Lt, Lt^t , Kt, Kt^t , Bt, Bt, Rt, Rt^t , MCt, MCt^t , wt, wt^t , rrt, rrt^t , Yt, Yt^t ,
-   —`     —`

et, Qt, Pt, Pt PHt, PHt, PF,t, PH,t, P_F,t, P∏_v Zt, Zt, ZHt, ZF,t, ZH₁,t, ZF,t} for all
t ≥ t0 characterized by: (i) the optimality conditions of the representative agent, (16) to
(19), and the capital accumulation equation (15); (ii) the intermediate firms’ first-order
conditions (8) and (9), price-setting rules, (11) and (12), and the aggregate version of the
production function (7); (iii) the final good producer’s optimality conditions, (2), and
(4); (iv) all markets clear, (24) to (26); (v) the representative agent’s budget constraint

10

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