(Case III) a < -
2-δ
1-δ-
< 0.5,
Λ > 2Л2(1 + β)[1 + 2μ(1 - a)]
1 (1+ μ)[α(1 - 2a)(2 - Λ2) - Λ2]
Л <f min / 2α(1 - 2a) Л1а(1 - 2a) 1.
Л2 < mm{1 + α(1 - 2a), 2(1 - a) ∫ ;
and
and
(36)
(37)
where Λ1 = (1 ψ)ψ1 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 2α(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)________
Ihis IOllOws since ʌ > (1+μ)[α(i-2α)(2-Λ2)-Λ2] > (l+μ)[α(l-2a)(2-Λ2)-Λ2] ∙
18