Investment and Interest Rate Policy in the Open Economy

EtbtR+1 =		ACRPIbtR,	R   RR bt = mcn xt	πR 1 πR K R1 , and ARPI ≡ t-1 t t ,            CPI
1 — α(2a — 1) + ʌ' 1 + J1 β	α2	(2a— 1) —	α J2 (1 + αJ1 )	J3 (1 + αJ1)		0
— (2a — 1) + J1J1		α(2a — 1)	J2 J1	J3J1		0
0		0	0	1		0
Λι(2α-1) β		0	2(1-a)μ β	1+2(1-a)βμ β		0
_ Γ σ(2a-1)C . 4θa(1-a) Z1 -    [    =    + (2a-1) =J		J4	0	0	1+	C+δ2(1-a) (2a-1)     .
where J1 = (1-Л2)22а-1), J2 =	2(1 (2a	-a)μ -1)β , J3 =	μ—β(2a-1)and J4	= ((21a-1)) KZ [1 + α4θa(1 — a)] +

σα(2a — 1) K=. Now there are two predetermined variables KR and ΠR-₁. Note that the
eigenvalue associated with the capital stock dynamics is the same regardless of the index

of inflation targeted. The Appendix proves the following:

Proposition 3 Suppose that monetary policy reacts to current-looking consumer 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 at least one of (33) and (34) is satisfied;

(2β — l)Λ2 — Λι [Λ2 + α(1 — Λ2)(2a — 1)]
Λ2β2(l — a)

(33)

2(1

ʌ ^λ4
^{a) +} Â2J

2(1 — a)(1 — β)μ + ^λ ^^{1   Л}2^)] — (1 + Λι)

Λ2

+ (1 — β) + μ [Λι — Λ4] + 2(1 — a)μβ + —— > 0;
Λ2

(34)

1 Γ . C 1

(Case II) 0.5 > a > 2—δ 1 — δ — = 2

and

Λ         2Λ-2(¹ + ^β)[¹ + ^2μ(^{1 — a)]}       .,.    ^2α(^{1 — 2}a)      ,

¹ < (1+ μ)[α(1 — 2a)(2 — Λ2) — Λ2] if 1 + α(1 — 2a) > ^2,

(35)

and at least one of (33) and (34) is satisfied;

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