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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 16, 2004
This is important since the view taken on the “right” model of wage-price
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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Organization of part 3 of 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 arises 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
— Previous version of AD-AS framework: The “neoclassical synthesis”.
— Relationship to AD-AS version in B&W
• Aggregate demand and the current account
• AD-AS model for the case of a fixed exchange rate.
— Short run and long run versions of the model
— Examples of policy analysis
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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, the “neoclassical synthesis”:
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:
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 natural assumption to make is that the GDP deflators, P and
P ∗ are different, also when they are converted into a common currency.
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Ch 11.3.2 defines the trade balance, or primary current account PCA, as
P CA = X − Z
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.
Of course, this means that we expect that the real exchange rate
SP
P
=
P∗
EP ∗
is fluctuating (possibly trending) over time.
σ=
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
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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The building blocks of the AD-AS model:
Y = C(Ω̄, Y − T̄ ) + I(q̄, r) + Ḡ + P CA(Y, Y ∗, σ)
Make sure that you are comfortable with the (partial) derivatives of the consumption and investment function!
product market
SP
σ = ∗ , definition
P
r = i − π̄, real interest rate
M
= L(Y, i), money-market
P
i = i∗ − se, financial market arbitrage condition
If necessary, look up the definition of Tobins-q.
In 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
π = π̄ − a(Y − Ȳ ), AS
Notation is as in B&W, except that we introduce se for the expected rate of
appreciation. We return to the interpretation of the arbitrage condition later
(when covering OEM).
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Note: 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 building block (Modules?) we can define different macro models,
corresponding to a regime with a fixed exchange rate, or to the case of a
floating exchange rate.
In this part of the lecture we only consider the fixed exchange rate.
We distinguish between the a short-run and long-run versions. 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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AD-AS analysis (fixed exchange rate)
a) Short-run version of the model:
From definition of real exchange rate, obtain the relative change of σ
∆σ = (s + π − π ∗)σ−1
where σ−1 is last periods real exchange rate. It is predetermined from history,
and is thus exogenous. Express the current real exchange rate as
σ = (s + π − π ∗ + 1)σ−1
where s is the rate of change of the nominal exchange rate.
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b) Long-run version of the model
The equilibrium is defined by
Y = C(Ω̄, Y − T̄ ) + I(q̄, i − π̄) + Ḡ + P CA(Y, Y ∗, (s + π − π ∗ + 1)σ−1)
M
= L(Y, i),
P
i = i∗ − se
π = π̄ + a(Y − Ȳ )
Endogenous: Y, i, M , and π.
Predetermined and/or exogenous: Ω̄, T̄ , q̄, Ḡ, Y ∗, π ∗, i∗, π̄, se, s, Ȳ , P, σ−1.
Y = Ȳ , π = π̄, and σ = σ−1
Moreover, since we consider the long-run, set s = se = 0.
Imposing all 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 ∗,
(PPP-line in the graphs)
M
= L(Ȳ , i)
P
i = i∗,
(FI- line in the graphs)
The third equation follows from the constancy of σ in equilibrium, and that
s = 0 in equilibrium.
Endogenous: M , i, σ, π and P .
Predetermined and/or exogenous: Ω̄, T̄ , q̄, Ḡ, Y ∗, π ∗, i∗, π̄, Ȳ .
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Example of analysis (fixed exchange rate)
i) Devaluation: Assume that the economy is initially in equilibrium. The one-off
devaluation means that s < 0 for one period, s = 0 thereafter.
The impact effects: Y % , , π %.
The long-run effects (i.e. compared to initial equilibrium): S & (since initial
increase was not reversed), P % (since σ unchanged) , M %.
ii) Expansive fiscal policy: Ḡ increases permanently.
B&W also consider monetary policy with capital controls, by suppressing the
FI-line. Technically, M is then exogenous and i is determined on the domestic
money market, as they show.
However there is an inconsistency here, since cannot simply abstract from the
market for foreign exchange, by invoking capital controls. The relevant chapters
in OEM shows how we should represent the market for foreign exchange when
there are capital controls.
The impact effects: Y % , M %, π %.
The long-run effects: σ % , P %, M %.
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