Investment and Interest Rate Policy in the Open Economy

of μ > 1 provided condition (28) is violated. However the region of indeterminacy is small.
For example if ψ = 0.8 then indeterminacy arises provided 1.1 < μ < 1.71, whereas if
ψ = 0.75 condition (28) is satisfied ∀μ > 1 and thus indeterminacy is not possible.

3.2 Difference System

3.2.1 Domestic Price Inflation

If domestic price inflation is the policy indicator, then the set of linearized conditions for
cross-country differences yields a system of the form:

		^Et^bt^R+1	⁼^AP^RP I ^bt^R^,	^bt^R	R = m^ncct	XR ∏R(^h^-^f*) KKR
	1 — α(2a — 1) + Λ1 J₁β	α²	(2a — 1) — α	(μ	^— β ) J¹	0
A^R ≡ ^APPI ^≡	^-(²^a^- 1) + ^λ1 J2		α(2a — 1)	(μ	^— β ) J²	0
	Λ1 β		0		1 β	0
	— [σ(2a — 1) C + '	) K ]	J3		0	1 ₊ C ⁺^δ²(^1-^a) ^{1 +} (2a-1) .

where Ji = [1 + ^a⁽¹^-^2⁽²^a-¹⁾] J2 = (1^-^Л2Х²^а-¹) and J3 = (⅛_-⅝ K [1 + α4θa(1 - a)] +
σα(2a — 1) C. As before, the capital stock dynamics can be decoupled from the rest of the

system. However, the eigenvalue associated with the capital stock dynamics now depends
on the degree of trade openness. Consequently this eigenvalue can be either inside or
outside the unit circle depending on the value of a. The Appendix proves the following:¹³

Proposition 2 Suppose that monetary policy reacts to current-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 either

(2β- 1)Λ2 < Λ1 [1 -β(1 - δ)(1 - (2a- 1)α)]

(29)

/'^λ∙i ΓΛ4(^{μ -} 1) . , . . .

Λ2β ` ^{+ λ}- ^- <^{1 + λ}∙ ⁺ ^'^e)

+ (1 — β) + Λιμ + —— > 0;

Λ2

(30)

¹³While determinacy of the difference system can also be achieved under a passive monetary policy (μ < 1),
such conditions are not reported since the aggregate system is always indeterminate (from Proposition
1).

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