Lecture 13: Macro dynamics of the open
economy (cont)
Ragnar Nymoen
Department of Economics, University of Oslo
Corrected version (2. May)
1
Recapitulation from lecture 12
From Lecture 11 and 12 we have the following system of equations:
f
yt = β0 + β1ert − β2rt + β3gt + β4yt
e
rt = it − πt+1
f
ert = ∆et + πt − πt + ert−1
πt = πte + γ(yt − ȳ) + st
f
it = it + ee + αe(∆et + et−1)
mt − pt = m0 − m1it + m2yt, mi > 0, i = 1, 2
(1)
(2)
(3)
(4)
(5)
(6)
We analyzed the short-run and long-run effects of a permanent change in gt
in two exchange rate regimes: Float with money supply as exogenous target
variable, and fixed with Et as exogenous target variable and i as instrument.
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Main conclusions:
1. The regimes can be graphically represented in one graph: the slopes of the
AD lines are different. Steeper in the floating ex-rate regime
2. Short-run effect of fiscal policy expansion largest in case of fixed ex-rate
regime
3. No long-run effects on y in either regime. The new long run equilibrium
level of ert is lower than before the shock. Nominal appreciation in the case
of float. Increased P in the fixed exchange rate regime.
3
More on fiscal policy in the fixed exchange rate regime
The above is based on fixed and exogenous inflation and a permanent policy
change. We now relax these assumptions, and we also want to say something
about dynamics.
a. Change in gt is permanent and πte and πte are constant
Short-run: AD curve shifts. Dynamics: AD curve shift gradually back again.
e
= πte = π f
The economy is “gliding” back to initial equilibrium point (πt+1
and yt = ȳ). Gradually ert is reduced.
e
=
b. As in case a) but inflation expectations are rational in the sense of πt+1
πte = π f , see page 739 in IAM.
Same analysis!
4
Formal analysis of dynamics and stability
See 739-741 in ch 24.3 of IAM.
So far we have implitely assumed that the dynamic process which is triggered
by the raise in gt is stable, so that a new long-run equilibrium is reached.
Intuitively, the dynamics are in fact stable, since a process of real currency
appreciation is begins as a result of the shock. As an exercise, this can be
shown formally.
Fixed ex-rate sssumptions:
e
πt+1
= πte = π f
eet+1 − et = 0
∆et = 0
5
The model can be written in somewhat more compact form as
f
yt − ȳ = β̂0 − β1(πt − πt ) + β1ert−1 + β3gt + dt,
f
f
f
dt = −β2(it − πt ) + β4yt − ȳ
f
πt − πt = γ(yt − ȳ) + st
f
ert = −(πt − πt ) + ert−1
(7)
(8)
(9)
f
Use (7) and (8) to express for ert−1 by yt − ȳ (e.g. by substitution for (πt −πt )):
1
β3
dt
β̂0
r
−
et−1 = (1 + β1γ)(yt − ȳ) + st − gt −
β1
β1
β1 β1
which is equation (17) page 739. We also have:
1
β3
dt+1 β̂0
r
et = (1 + β1γ)(yt+1 − ȳ) + st+1 − gt+1 −
−
β1
β1
β1
β1
Using these two expressions in (9), together with (8), gives the following ADL
model for (yt+1 − ȳ):
1
β3
(yt+1 − ȳ) =
(yt − ȳ) +
∆gt+1 + ....
1 + β1γ
(1 + β1γ)
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or, for yt :
(yt − ȳ) =
1
β3
(yt−1 − ȳ) +
∆gt + ....
1 + β1γ
(1 + β1γ)
(10)
We can now apply what we have learnt about stability earlier, namely that
(yt − ȳ) is dynamically stable if
1
<1
1 + β1γ
which holds since β1γ > 0.
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Temporary versus permanent fiscal policy shocks (IAM p 24.3)
We can also use (10) to analyze the different responses to permanent and
temporary fiscal policy shocks.
A permanent shock amounts to ∆g1 > 0, for example ∆g1 = 1, and ∆g2 =
∆g3 = ... = 0.
A temporary shock amounts to ∆g1 = 1, ∆g2 = −1, for example, and ∆g3 =
8
∆g4 = ... = 0.
perm
temp
impact
β3
(1+β1γ)
β3
(1+β1γ)
2nd
β3
(1+β1γ)2
−β1γβ3
(1+β1γ)2
3rd
β3
(1+β1γ)3
−β1γβ3
(1+β1γ)3
...
0
...
0
Hence the temporary leads to a short expansion, and then a longer period where
yt − ȳ < 0.
So far we have considered unsystematic fiscal policy, An example of systematic
fiscal policy is:
gt − ḡ = a(ȳ − yt),
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a > 0.
(11)
Intuitively, in this model, systematic fiscal policy leads to a steeper short-run
AD schedule. A real appreciation leads to less reduction in y in the case of
a > 0, than a = 0, see fig 24.4.
Effects of negative demand shocks are smothered.
The speed of adjustment is reduced.
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