Table 1: Linearized system of equations
|
Cross-Country Differences | |||
|
Et {CR+1} = CCR + σRCR - σEt {∏R+ι} |
ISr | ||
|
RCR = Et {∆⅞+ι} |
UIP | ||
|
rRI—-/*) ʌ r !i i (^R(f-f*CI Ct =Λιmct + βEt ∣∏t+ι 1 ½ |
ASr | ||
|
mcR = Ct- + axR + 2(1 — a)Tt |
Marginal cost | ||
|
CCR+1 = Ccr + σΛ2 [≡⅛+ι + (1 - α)xR+ι - Kt+1 = (2θ-Γ) Kκx xt - (4kJ Ct - -(20- |
2(1 |
— a)τt+i] |
Investment |
|
-a) -i) |
( к ) Tt+Λ3KR |
Resource constraint | |
|
CR ..77 RR 1 C CR llC R^f-f~f* Rt = μEt χπt⅛vj or Rt = μEt ∣πt+v |
)} |
Taylor rule | |
|
CR = (2a — 1)CR(f-f *) + 2(1 — a)∆Ct |
Inflation | ||
|
^ -1 ^ -ɪ-, . ^ (Ct = 1 (CR = (2a — 1)Tt |
RER | ||
|
World Aggregates | |||
|
Et {CCW1} = CCtW + σRCtW — σEt {∏W1} |
ISW | ||
|
CW = Λ1fCcW + βEt {πWι} |
ASW | ||
|
WW CtW l WV mct = —t—+ αxt |
Marginal cost | ||
|
CCWi = CCW + σΛ2 [mcWi + (1 — a)CWi] |
Investment | ||
|
KCWi = (1 — α) (Z) CW — ⅛) CW + [Z + |
— δ] KtW |
Resource constraint | |
|
JCW-Z-MEdCWJ______________ |
Taylor rule —- | ||
R
Notes: The index R refers to the difference between home and foreign variables e.g. CtR ≡
(ct — cR) , "RRh f ) ≡ (Ch — Ct*f). The index W refers to world aggregates where πw =
π+2∏ = π +2π f and ∆et ≡ Ct — Ct-1. The parameters are defined as: Λ1 ≡ (1-ψ)ψ1-βψ),
λ2 ≡ 1 - β(1 - δ) and λ3 = [KK (2α1-i) + 1 - δ]
where the steady state levels are given by
KZ = C + δ and C = α [β - (1 - δ)] λ-1 - δ
3 Equilibrium Determinacy
We start by examining the conditions for equilibrium determinacy when monetary policy
is characterized by a current-looking rule. First note that for a labor-only version of this
open economy model, in which production is linear in labor (α = 0), under a current-
looking rule the Taylor principle (μ > 1) prevents the emergence of real indeterminacy
for both the aggregate and difference systems.12 As this section shows the conditions for
reduces to the relative PPP condition for consumer price inflation i.e. ΠR = ∆Ct∙
12For example, as shown by McKnight (2007), the Taylor principle is both a necessary and sufficient
condition for local determinacy of the aggregate system and the difference system when domestic inflation
is targeted. If CPI inflation is targeted then the Taylor principle is a necessary condition for determinacy
12