Main reference: B&W Chapter 13
Models of inflation and the macroeconomy.
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Introduction
Slides for 9 September 2003 lecture
Previous lecture (wage-price dynmaics) showed that economists may have accepted the Phillips curve natural rate model to readily.
Ragnar Nymoen
University of Oslo, Department of Economics
September 4, 2003
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.
This is important since the view taken on the “right” model of wage-price
formation has overriding implications:
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• If Phillips curve, then there is little reason for targeting unemployment
using the instrument of economic policy.
Aggregate demand (AD) and aggregate supply
(AS)
The AD-AS framework dates back to the 1970s, the “neo-classical synthesis”.
• 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.
AD schedule from IS-LM analysis.
AS from the assumptions:
— 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 B&Ws exposition,
which is based on the conventional Phillips curve.
1. Short-run analysis. So capital stock is given and exogenous.
2. 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,
3. N is determined by the condition
W
= F 0(N ),
P
W denotes the wage level and P denote the GDP deflator (price index)
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4. There is nominal wage rigidity, thus W is exogenous.
Aggregate demand and the current account
This implies:
Y = Y (P/W ), Y 0 > 0, Y 00 < 0
from the supply side.
In B&W, the main chapter on this 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.
B&W adds twist to this framework:
1. Different interpretation of the AS schedule. From Ch. 12: based on the
expectations augmented Phillips-cuve and Okuns-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)
This represents a subtle but important distinction from the case where there
is one identical commodity which is produced both home and abroad, which
would entail an extremely open (Big Mac?) economy.
In particular, the natural assumption to make is that the GDP deflators, P and
P ∗ are different, also when turned into a common currency.
3. Most important: open economy.
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Ch 11.3.2 defines the trade balance, or primary current account PCA, as
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=
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
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)
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
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.
We next define two distinct macro models, one corresponding to the regime
with a fixed exchange rate, and the other for the case of a floating exchange
rate.
For each regime we distinguish between the a short-run and long-run versions.
The short-run model can be used to illustrate graphically (and if we want to
calculate mathematically) the impact multipliers. The long-run model defines
the long-run multipliers.
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Fixed exchange rates
Endogenous: Y, i, M , and π.
a) Short-run version of the model:
Predeterminded and/or exogenous: Ω̄, T̄ , q̄, Ḡ, Y ∗, π ∗, i∗, π̄, se, s, Ȳ , P, σ−1.
From definition of real exchange rate, obtain the relative change of σ
b) Long-run version of the model
∆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 wage as
σ = (s + π − π ∗ + 1)σ−1
where s is the rate of change of the nominal exchange rate.
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 )
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The equilibrium is defined by
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)
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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 .
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 % , M %, π %.
B&W also consider monetary policy with captial controls, by supressing the
FI-line. Technically, M is then exogenous and i is determined on the domestic
money market, as they show.
Strictly speaking there is an inconsistency here, since cannot simply abstract
from the market for foreign exchange, by invoking capital controls. The relevant
chapters in OEM corrects this.
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.
The impact effects: Y % , M %, π %.
The long-run effects: σ % , P %, M %.
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b) Long-run version of the model
Floating exchange rates
The equilibrium is defined by
New assumption:
se = s ≡
i.e., perfect expectations:
∆S
S−1
a) Short-run model
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∗ − s
π = π̄ + a(Y − Ȳ )
Endogenous: Y, i, s, and π.
Predetermined and/or exogenous: Ω̄, T̄ , q̄, Ḡ, Y ∗, π ∗, i∗, π̄, M, Ȳ , P, σ−1.
Y = Ȳ , and π = π̄, 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
s = π∗ − π
M
= L(Ȳ , i)
P
i = i∗ − s,
(FI- line in the graphs)
Endogenous: i, σ, s, π, S, and P .
Predetermined and/or exogenous: Ω̄, T̄ , q̄, Ḡ, Y ∗, π ∗, i∗, π̄, Ȳ
Hence, the model is not determined after all! It lacks a monetary anchor.
Remember that S was exogenous in the fixed exchange rate case, which gave
us the anchor there.
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Example of analysis (float)
Differentiate
M
∗
σ PS
= L(Ȳ , i∗ − s)
with respect to time. Let µ and gy denote the exogenous rates of money and
GDP growth. Then
Y
η = LY
L(Ȳ , i)
gives us the extra condition we need. Note that the model on more compact
form becomes
s = π ∗ − µ + ηgy ,
Ȳ = C(Ω̄, Ȳ − T̄ ) + I(q̄, i∗ − π ∗) + Ḡ + P CA(Ȳ , Y ∗, σ)
M
= L(Ȳ , i∗ − π ∗ + µ − ηgy )
P
with 2 endogenous variables, σ, and P .
i) Expansive fiscal policy: Ḡ increases permanently.
impact effects: Y % , i %, s < 0, π %.
long-run effects (compared to initial equilibrium): σ % and thus S % .
ii) Monetary policy : One-off increase in M , but µ constant.
Impact effects: i &, s > 0, Y %, π %.
appendix)
(lots of simultaneity here, see
Long-run effects: P % proportionally.
ii) Monetary policy : Permanent increase in µ
Impact effects: i &, s > 0, Y %, π %.
Note that
π = µ − ηgy
in the long run equilibirum.
Long-run effects: s &, P increases more than M !?
Several other case-studies in the last pars of Ch 13!
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Is inflation a monetary phenomenon?
Popular view among economist, especially for “the long-run”. But
• Even in the simple models here, π is influenced by product market disequilibria and shocks, expectations etc.
• Regime dependent. With fixed exch. rate π = π ∗, in the long run. Money
growth does not in any way determine inflation.
• With a float regime, it follows from s = π ∗ − π and s = π ∗ − µ + ηgy that
π = µ − ηgy steady-state.
• Moreover, a hypothetical steady-state may have have limited practical relevance. Countries which have attempted controlling the money supply have
often been frustrated (new financial instruments, money demand function
is subject to regime shifts). Example: UK under Thatcherism.
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Inflation targeting
In this framework inflation targeting can be interpreted as
π̄ = (π ∗ − s)
i.e., expected inflation is brought in line with the inflation target (here: the
foreign rate of inflation - appreciation). Short-run model:
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∗ − s
π = π̄ + a(Y − Ȳ )
π̄ = π ∗
thus: π̄ is moved to list of endogenous variable.
thus exogenous. M therefore endogenous.
i is the instrument and is
What should the inflation target be?
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Appendix: Algebra for impact of increase in M in a float regime (check it!)
(1 − CY − P CAY − P CAσ a)
dY = CY dY + Ir di + P CAY dY + P CAσ (ds + dπ)
dM = LY dY + Lidi
di = −ds
dπ = adY
dY
ds
dY
di
dY
dπ
= CY
+ Ir
+ P CAY
+ P CAσ (
+
)
dM
dM
dM
dM
dM
dM
dY
di
+ Li
1 = LY
dM
dM
di
ds
=−
dM
dM
dπ
dY
=a
dM
dM
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dY
di
− (Ir + P CAσ )
=0
dM
dM
dY
di
+ Li
=1
LY
dM
dM
dY
(Ir + P CAσ )
=
>0
dM
Li(1 − CY − P CAY − P CAσ a) + LY (Ir + P CAσ )
(1 − CY − P CAY − P CAσ a)
di
=
<0
dM
Li(1 − CY − P CAY − P CAσ a) + LY (Ir + P CAσ )
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