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Introduction
Main reference: B&W Chapter 13
Part 3:
Models of inflation and the macroeconomy.
Previous topic (wage-price dynamics) showed that economists may have accepted the Phillips curve natural rate model to readily.
For example, there are both logical and empirical reasons for doubting the
doctrine that unemployment has to be brought in line with a Phillips curve
natural rate in order to stabilize inflation.
Ragnar Nymoen
University of Oslo, Department of Economics
February 25, 2005
This is important since the view taken on (what is) the “right” model of wageprice formation has overriding implications:
• If Phillips curve, then there is little reason for targeting unemployment
using the instrument of economic policy.
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Plan of this part of the lectures:
• Conversely: if the main-course model, or other model which allows for
direct influence of profitability on wages is the “right model”, then there is
no natural rate of unemployment which is determined from the wage-price
system alone.
— Thus, no inconsistencies arise from choosing unemployment as the target (or at least provoke a discussion about the lexicographic ordering
of targets).
However, with that background in mind, we will now follow convention and use
a Phillips curve to represent the supply side of the economy
• The AD-AS framework
— Earlier version of AD-AS framework: The “neoclassical synthesis”.
— Relationship to the AD-AS version in B&W
• Aggregate demand and the current account
• AD-AS model for the case of a fixed exchange rate.
— The equations
— Short-run and long-run versions of the model
— Example: Currency devaluation and fiscal policy
• March 7: AD-AS model with flexible exchange rates. Fiscal policy
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The AS-schedule was derived in the following 3 steps
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Aggregate demand (AD) and aggregate supply
(AS)
1. There is a (short-run) macro production function Y = F (N ), F 0 > 0,
F 00 < 0, where Y is GDP and N is total employment,
2. N is determined by the condition
The AD-AS framework dates back to the 1970s, was the “neoclassical synthesis” since it combined unemployment ( a Keynesian feature) with a flexible
price level (a classical feature)
The AD schedule was derived from IS-LM analysis. Aggregate demand (Y D )
depends positively on the real money stock. If the nominal stock is exogenous
then there is a negative relationship between Y D and the price level P . This
is the AD-schedule.
W
= F 0(N ),
P
W denotes the wage level and P denote the GDP deflator (price index)
3. There is nominal wage rigidity, thus W is exogenous.
This implies:
Y S = Y (P/W ), Y 0 > 0, Y 00 < 0,
from the supply side. The AS-schedule
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Aggregate demand and the current account
B&W modernizes this framework in a New-Keynesian model:
1. Different interpretation of the AS schedule. From Ch. 12: based on the
expectations augmented Phillips curve and Okun’s-law (refer to Ch 11.2)
. Means that AS part of model gives GDP output above/below trend as
a function of the rate of inflation (rather than the price level).
2. AD is also in terms of the rate of inflation (not the price level)
3. Most important: open economy.
In B&W, the main chapter on this is Ch 11. Some comments:
We need to be clearer (than B&W) about the degree of openness of the economy. The convention for this type of model is to assume that the “GDP
commodity” of the home country is differentiated from the foreign commodity.
This represents an important distinction from the case where there is one identical commodity which is produced both home and abroad, which would entail
an extremely open ( one commodity (Big Mac?)) economy.
In particular, the GDP deflators, P and P ∗ are likely to be different, also when
they are converted into a common currency. Hence, purchasing power parity,
PPP, is not a realistic assumption to make for short-run analysis.
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Hence in each period (quarter, year, 5-year) we expect that:
P 6= EP ∗
where E is the kroner/EURO exchange rate, if P ∗ is the price (index) of EURO
GDP. Equivalently, using the notation by B&W
P 6=
1 ∗
P
S
where S denotes EURO/Krone.
Ch 11.3.2 defines the trade balance, or primary current account PCA, as
P CA = X − Z
where X is “exports” and Z is “imports”.
Unsatisfactory, since presumably, if we want to add P CA together with domestic demand, X is in units of domestic output, and then Z must also be in
units of the home GDP.
Need to be more careful. Better to start with
Of course, this means that we expect that the real exchange rate
SP
P
=
∗
P
EP ∗
is fluctuating and to be susceptible to long lasting effects of shocks. Example:
Swedish real exchange rate.
σ=
This makes the imposition of PPP unrealistic, at least in model of the short-run.
EP ∗ ∗
Z
P
where Z ∗ (home imports) is in units of foreign GDP-output. Next, as in B&W,
postulate
P CA = X −
X = X(Y ∗, σ), XA∗ > 0, Xσ < 0
but replace B&W’s (11.7) with
Z ∗ = Z(Y, σ), ZY > 0, Zσ > 0
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to obtain the correct definition of the PCA function
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P CA = X(Y ∗, σ) − Z(Y, σ) ≡ P CA(Y, Y ∗, σ)
σ
since
1
σ = EP ∗
However subject to the Marshall-Lerner condition, we have P CAσ < 0, as
postulated by B&W.
The two first partial derivatives are trivial: P CAY < 0 and P CAY ∗ > 0 .
where (B&W notation)
However P CAσ cannot be signed without making assumptions about the joint
strength of the two quantity effects (via X(Y ∗, σ) and Z(Y, σ)) relative to the
terms-of-trade effect (in terms of the domestic GDP the volume of imports is
reduced when σ rises).
C = private consumption.
The needed condition is known as the Marshall-Lerner condition. We leave
out the derivation, but note instead that while the terms-of-trade effect is
effective from “day-one” after a devaluation for example, both X and Z ∗
are somewhat slower to react. Hence, in models with explicit dynamics, the
dynamic multipliers of P CA with respect to a permanent change in σ often
exhibits a sign change.
Ω = household wealth.
P
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GDP demand is then defined by
Y = C(Ω̄, Y − T̄ ) + I(q̄, r) + Ḡ + P CA(Y, Y ∗, σ)
I = private investments
G = government expenditure
q = Tobin’s-q
r = the real interest rate.
¯ denotes an exogenous variable
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Make sure that you are comfortable with the (partial) derivatives of the consumption and investment function!
If necessary, look up the definition of Tobin’s-qIn the following both Ω̄ and q̄ will be regarded as constants, hence we might
have dropped them from the model, but we keep them to maintain correspondence with the book’s notation
The equations of the AD-AS models
Y = C(Ω̄, Y − T̄ ) + I(q̄, r) + Ḡ + P CA(Y, Y ∗, σ)
product market
SP
σ = ∗ , definition of real ex rate
P
r = i − π̄, real interest rate
M
= L(Y, i), money-market
P
i = i∗ − se(S), financial market arbitrage condition
π = π̄ + a(Y − Ȳ ), a > 0 AS
The arbitrage condition is the equilibrium condition on the foreign exchange
market (which is the only financial market in the model). It is often referred to
as the uncovered interest rate parity condition, UIP. It requires perfect capital
mobility, which will be discussed later in the course (in Ch 1 and 3 of OEM).
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se denotes the expected rate of appreciation of the domestic currency, it is a
function of S:
se = se(S), s0e ≷ 0
There is a small conflict of notation, since B&W later use s to represent a
supply-side shock, Ch 13.4.1.
Using these equations as building block we can define different macro models,
corresponding to a regime with a fixed exchange rate, and to the case of a
floating exchange rate.
We distinguish between the a short-run and long-run versions.
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THE MODELS
Short-run, fixed exchange rate Short-run, floating exchange rate
Long-run, fixed exchange rate Long-run, floating exchange rate
A characteristic of the models we will set up is that purchasing power parity,
PPP, is not imposed in the short-run models, only in the long-run versions of
the model. UIP is imposed in both the short-run and in the long-run.
The short-run model can be used to find the impact multipliers. The long-run
model let us derive the long-run multipliers, given that the dynamic process
leading from an initial steady state to a new one is stable. Conditions for
stability will not be considered.
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Note that in line with OEM, but unlike B&W we will assume that expected
appreciation is linked to the level of the exchange rate:
se = se(S), s0e
The AD-AS model, fixed exchange rate
Short-run version:
From the log of the definition of real exchange rate,
≷0
s0e may depend both on regime (e.g., credibility of fixed exchange rate regime)
and on time-horizon. We will use the following assumptions:
short-run long-run
fixed s0e < 0
s0e = 0
0
float se < 0
s0e < 0
Hence we assume regressive or extrapolative expectations (we will return to
these terms in the OEM part of the lectures).
ln σ = ln S + ln P − ln P ∗
By differentiation, obtain the relative change in σ
∆σ
∆S ∆P
∆P ∗
=
+
−
σ
S
P
P
It will be convenient to instead express the changes with respect to last period’s
values of the (stock) variables σ, S, P and P ∗. Hence, we will use
∆σ
∆S
∆P
∆P ∗
=
+
− ∗
σ−1
S−1 P−1
P−1
Introducing notation for the 2 last right hand side variables:
∆σ
∆S
=(
+ π − π ∗),
σ−1
S−1
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Next, since ∆σ = σ − σ−1:
σ=(
∆S
+ π − π ∗ + 1)σ−1
S−1
where σ−1 is last period’s real exchange rate. It is predetermined from history,
and is exogenous in the short-run. Finally, since
we write
∆S
S
=
− 1,
S−1
S−1
σ=(
S
+ π − π ∗)σ−1
S−1
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In the product market equation, replace σ by ( SS + π − π ∗)σ−1, and r by
−1
i − π̄
Y = C(Ω̄, Y − T̄ ) + I(q̄, i − π̄) + Ḡ + P CA(Y, Y ∗, (
M
= L(Y, i),
P
i = i∗ − se(S)
S
+ π − π ∗)σ−1)
S−1
π = π̄ + a(Y − Ȳ )
Endogenous: Y, i, M , and π.
Predetermined and/or exogenous: Ω̄, T̄ , q̄, Ḡ, Y ∗, π ∗, i∗, π̄, S, S−1, Ȳ , σ−1.
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Long-run version
Example: A devaluation: Assume that the economy is initially in equilibrium.
The devaluation (e.g., dS = −1) means that s0e(−1) > 0.
The equilibrium is defined by
Y = Ȳ , π = π̄, and σ = σ−1
Imposing this gives the long run model
Ȳ = C(Ω̄, Ȳ − T̄ ) + I(q̄, i − π) + Ḡ + P CA(Ȳ , Y ∗, σ)
P∗
P =σ ,
S
π = π ∗,
M
= L(Ȳ , i)
P
i = i∗ − se(S).
The third equation follows from the assumption of long-run PPP, hence σ =
σ−1in equilibrium, and S/S−1 − 1 = 0 by assumption of a fixed exchange rate
regime.
Endogenous: M , i, σ, π and P .
Predetermined and/or exogenous: Ω̄, T̄ , q̄, Ḡ, Y ∗, π ∗, i∗, π̄, Ȳ , P ∗, S.
Y = C(Ω̄, Y − T̄ ) + I(q̄, i∗ − se(S) − π̄) + Ḡ + P CA(Y, Y ∗, (S/S−1 + π − π ∗)σ−1)
M
= L(Y, i∗ − se(S))
P
π = π̄ + a(Y − Ȳ )
The first equation defines an AD-curve in terms of Y and π. The slope of this
curve:
dπ ¯¯
1 − CY − P CAY
< 0.
¯AD,f ix,short =
dY
P CAσ σ−1
The slope of the short run AS curve:
dπ ¯¯
¯AS,short = a > 0
dY
The AD schedule is shifted horizontally by a change in S:
−Iρs0e + P CAσ σ−1/S−1
dY ¯¯
< 0,
¯AD,f ix,short =
dS
1 − CY − P CAY
so a devaluation shifts the AD curve to the right.
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Example: fiscal policy
Summary of short-run effects: Y % , π % , i & and M %.
There is no shift in the long-run AD-curve (since S/S−1 − 1 = 0 and s0e = 0
in the long run).
Summary: Long run effects (i.e., compared to initial equilibrium): S & (since
initial increase was not reversed), P % (since σ unchanged), M %. Y and i
unchanged relative to initial equilibrium.
Short-run
A change in Ḡ, lifts π for a given Y , graphically: a vertical shift in the short-run
AD curve:
dπ ¯¯
−1
¯AD,,f ix,short =
dḠ
P CAσ σ−1
while AS curve is unchanged. Y % , π % , M %
Long-run
AD and AS curves are unaffected. σ % , P % , M %.
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