Investment and Interest Rate Policy in the Open Economy

	1 — α(2a — 1)	— ΛiJi	Etbt^R+i = B^Rbt^R , α (2a — 1) — α Ji		R bt = ∖mc_t	xR πR(^h^-^f*) KK_tR] 0
_BR _≡	— (2a — 1) —	ΛiJ2	α(2a — 1)	J2		0
	Λι β		0	1 β		0
	— ∣^σ(²a — 1) KC +	4θa(1-a) Z "I ^(2a^-1) K J	J3	0	1 +__¹____ ^{1 +} (2a-1)	[ KC^{+ δ2}(¹^—^a)]

where J₁ = (^μ-1) [1 + ^а⁽¹^-^Лл2⁽²^а-¹⁾] and J₂ = О^-¹⁾<¹^-Л2⁾⁽²^а-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

(40)

(41)

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

(Case II)

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-

CorPapers

Investment and Interest Rate Policy in the Open Economy

More intriguing information