Investment and Interest Rate Policy in the Open Economy

where J₁ = (^μ-1) [1 + ^а(1-Лл2^(2а-1)] and J₂ = О^-1)<^1-Л2^)(2а-1) under domestic inflation
t_arp'etinp'∙ wħe_reαs J₁ = (^μ-1)(2a^-1)[a(1-л2⁾⁺ (2a^-1)^] and j = (^μ-1⁾⁽1^-λ2 ⁾⁽²a^-1) under cpι
targeting; whereas J¹ = βΛ2[i-2(i-a)μ]       ^and J² = βΛ2[i-2(l-a)μ] ^undercPI

inflation targeting. Finally J₃ = Ca ^α) KZ [1 + α4θa(1 — a)] + σα(2a — 1)KC. Analogous
to the aggregate system, one eigenvalue of the system is zero. Therefore determinacy
requires the eigenvalue 1 + (₂a-₁) [C + δ2(1 — a)] to have a modulus greater than one,
and the two remaining eigenvalues of B^R are also outside the unit circle. By Proposition

C.1 of Woodford (2003) the following results are obtained:

Proposition 5 Suppose that monetary policy reacts to forward-looking domestic price
inflation. Then for an active monetary policy (μ > 1), the necessary and sufficient con-
ditions for determinacy of the difference system are

(Case I) a > 0.5 and

₁ <U< _{1 +} m_in∫_rB ≡ (1 — в^)Л2 _ГА ≡    2(1+ в)^Л2 V

<^μ< ⁺ t¹ ≡ αΛι(2a — 1)² ≡ Λια(2 — Λ2)(2a — 1) ∫ ;

0.5 > a > - - 1 — ^δ — =-

2 — δ        K 2
where Λ₁ = ^{(1 ψ})(^{1 βψ}) and Λ₂ = 1 — β(1 — δ).

Proposition 6 Suppose that monetary policy reacts to forward-looking consumer price
inflation. Then for an active monetary policy (μ > 1), the necessary and sufficient con-

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