Investment and Interest Rate Policy in the Open Economy

where Λ1 = ^{(1 ψ})ψ^{1 βψ}), Λ2 = 1 - β(1 - δ) and Λ4 = Λ1α(2a - 1).

Proof. See Appendix A.2. □

Comparison of Propositions 2 and 3 highlight important qualitative differences between
reacting to consumer and domestic price inflation. First, the range of second-order in-
determinacy is relatively lower if consumer price inflation is targeted. This follows from
direct comparison of conditions (29) and (33):

(2β - 1)Λ2 < Γ1 < 2βΛ2(1 - a)μ + Γι,

where Γ1 = Λ1 [1 - β(1 - δ)(1 - (2a - 1)α)]. Secondly, the range of first-order indeter-
minacy is relatively greater under consumer price inflation targeting. By comparing the
Case III conditions of Propositions 2 and 3, it is straightforward to show that (36) is a
stronger requirement for determinacy than condition (i) of (32).¹⁷ Furthermore by com-
paring condition (ii) of (32) with (37), reacting to consumer price inflation introduces an
additional determinacy condition given by Λ₂ < ^Л ₂^α(1^-2)a). Figure 2 depicts the regions
in the parameter space (a, μ) that are associated with determinacy (D) and (first-order)
indeterminacy (I) around the neighborhood of the steady state given α = 0.36, β = 0.99,
δ = 0.025, λ = 7.66 and ψ = 0.75. First observe that second-order indeterminacy does
not arise under these parameter values. Furthermore determinacy exists only if the de-
gree of trade openness is sufficiently large a ≥ 0.4716, otherwise first-order indeterminacy
prevails for any value of μ > 1.

3.3 Discussion

In the absence of capital the Taylor principle holds under a current-looking rule regardless
of whether the economy is open or closed. However as shown in the previous section,
This follows since ʌ I > ²M⁽¹ + e)[1 + ^⁽¹-a)] > ________^2Λ2(¹ + β)________

Ih^is IOllO^{ws s}i^nce ʌ > (1+μ)[α(i-2_α)(2-Λ2)-Λ2] > (l+μ)[α(l-2a)(2-Λ2)-Λ2] ∙

18

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