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,
Zt = Ct + It, (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,
Btt0 , Kt0 , Ktt0 , and Mt0-1, Mtt0-1, a rational expectations equilibrium is a set of sequences
{Ct, Ctt , Mt, Mtt , Lt, Ltt , Kt, Ktt , Bt, Bt, Rt, Rtt , MCt, MCtt , wt, wtt , rrt, rrtt , Yt, Ytt ,
- —` —`
et, Qt, Pt, Pt PHt, PHt, PF,t, PH,t, PF,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