Download Open Economy IS/LM Model

Open Economy IS/LM Model
Prof. Lutz Hendricks
Econ520
April 6, 2017
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Objectives
In this section you will learn
1. how to extend the IS-LM model to an open economy
2. how to analyze monetary and fiscal policy in an open economy
3. why the Central Bank loses control over the money supply
under fixed exchange rates
Note: All this is for the short run.
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Equilibrium with open economy
We need to clear
1. the goods market: IS
2. the money market: LM
3. the foreign exchange market
Four cases:
1. exchange rate: fixed or floating
2. capital mobility: perfect or none
determines FX market clearing conditions
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Open Economy IS Curve
We return to the short-run model where output is determined by
aggregate demand
Start from the definition of aggregate demand in dollar terms
PZ = P(C + I + G + X) − EP∗ IM
(1)
P: domestic price level (dollars)
P∗ : foreign price level (pesos)
E: exchange rate (dollars/pesos)
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Open Economy IS Curve
Divide by P:
Z = C(Y − T ) + I(Y , r ) + G + X − IM/ε
+
+ −
(2)
IM/ε: dollar value of imports
ε = P/EP∗ is the relative price of foreign goods (the real exchange
rate)
I
ε ↑ means: foreign goods get cheaper
r: real interest rate
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Determinants of Imports
Income effect: Y ↑ =⇒ IM ↑
I
richer countries import more
Substitution effect: ε =
P
EP∗
↑ =⇒ IM ↑
I
dollar appreciates =⇒ imports rise
I
but note that the value of imports, IM/ε, may ↑ or ↓
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Determinants of Exports
Income effect: Y ∗ ↑ =⇒ X ↑
Substitution effect: ε ↑ =⇒ X ↓
I
domestic goods are more expensive
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Net Exports
The contribution of international trade to demand:
NX = X(Y ∗ , ε ) − IM(Y , ε )/ε
+ −
+ +
(3)
Y ↑ =⇒ trade balance ↓
I
richer countries import more
ε ↑ =⇒ trade balance ambiguous
I
so we use evidence to sign this effect (below).
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IS Curve
Assume that output is determined by demand: Y = Z
Y = C(Y − T ) + I(Y , r ) + G + X(Y ∗ , ε) − IM(Y, ε)/ε
+
+ −
(4)
Linear example:
Y = {C0 + c1 (Y − T)} + {I0 + i1 Y − i2 r} + G
im1 Y + im2 ε
+ {x1 Y ∗ − x2 ε} −
ε
[C0 − c1 T + I0 + G + x1 Y ∗ − im2 ] − x2 ε − i2 r
=
1 − c1 − i1 + im1 /ε
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IS Curve
Slope is negative: r ↑ =⇒ Y ↓
I
same reason as in closed economy (investment falls)
Shifters are
I
autonomous demands: C0 , I0 , G, Y ∗ (positive)
I
taxes T (negative)
I
real exchange rate ε
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r
IS Curve
IS
Y
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Currency Depreciation
I
Whether a depreciation increases or decreases demand is
ambiguous
I
Substitution effect:
I
I
I
I
Value effect:
I
I
dollar depreciates
foreign good become more expensive
IM ↓ and X ↑
the dollar value of a given IM quantity rises
We will assume that a depreciation increases demand (and
improves the trade balance):
ε ↓ =⇒ X − IM/ε ↑
(5)
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J-Curve
!
Net exports, NX
Depreciation
0
After depreciation: trade
balance typically
deteriorates initially
I
Quantities take time to
adjust
I
In the short run the rise in
import prices dominates
0
A
"
I
Time
C
B
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Foreign exchange market clearing
Exchange rates in the short run
Short-run exchange rates are asset prices.
I
Almost all FX trade is due to short-term (often intra-day)
asset trading.
I
Trade in goods is too small to play a role.
Daily FX trading volume, billions of dollars (Source: BIS)
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Exchange rates in the short run
I
Asset prices (in liquid markets) tend to fluctuate a lot.
I
The reasons for the fluctuations are not well understood.
I
Modern asset pricing theory predicts that prices should be
much smoother than the data.
I
Therefore:
I
I
We don’t know how short-run exchange rates are determined.
Much of the fluctuations are probably random noise.
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What Determines Capital Flows?
Most of the demand for dollars comes from international capital
flows (not from trade).
We can get an idea about what moves exchange rates, if we
understand what moves capital.
Capital flows into the U.S., if the risk adjusted rate of return of
investing in dollars is higher than abroad.
Factors that cause capital to flow into the U.S.:
1. high U.S. interest rate;
2. expected appreciation of the dollar;
3. increasing risk of investing abroad: political instability, external
debt, ...
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Uncovered Interest Parity (UIP)
UIP is one theory of short-run exchange rate determination.
It does not hold all that well, but it has the right idea...
Definition
Uncovered interest parity holds, if the dollar returns of investing at
home and abroad the same
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The return of investing abroad
I
Example: Invest $100 in Euro
I
Today’s exchange rate is 2 $/Euro [E(t) = 12 ]
I
I
Buy 50 Euro
The Euro interest rate is iEuro = 0.05
I
Earn 0.05 × 50Euro = 2.50Euro
I
Next year the exchange rate is 2.2 $/Euro [E(t + 1) = 1/2.2]
I
Sell 52.50 Euro and buy $2.2 × 52.50 = $115.5
I
Rate of return: 15.5%
I
5% interest + 10% Euro appreciation.
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The dollar return of investing in Euro
Start with
Convert into Euro
Earn interest
Convert back into $
E (t) is in $/Euro.
$1
Euro 1/E(t)
Euro (1 + iEuro ) /E (t)
$ (1 + iEuro ) E (t + 1) /E (t)
Total return:
1 + rEuro = (1 + iEuro ) E (t + 1) /E (t)
{z
}
| {z } |
interest
capital gain
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Uncovered interest parity
1 + i$ = (1 + iEuro ) E (t + 1) /E (t)
(6)
i$ = iEuro + x
(7)
or approximately
where:
I
E is the exchange rate in $/Euro (E ↑ means the Euro
appreciates)
I
x = E (t + 1) /E (t) − 1 is the Euro rate of appreciation.
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Risk Premiums
If currencies differ in risk, UIP subtracts a risk premium from the
foreign currency return.
1 + i$ = (1 + iEuro − RPEuro ) E (t + 1) /E (t)
(8)
The same from the European perspective
1 + iEuro = (1 + i$ − RP$ ) E (t) /E (t + 1)
(9)
The risk premium must be negative for one country.
Why?
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How shocks affect the exchange rate
Solve the UIP condition for today’s spot rate:
E (t) = E (t + 1)
1 + iEuro − RPEuro
1 + i$
(10)
The exchange rate responds to 3 types of shocks:
1. The Euro becomes less risky: RPEuro ↓. Then E (t) ↑ (Euro
appreciates)
2. The Euro interest rate rises or the dollar interest rate falls:
iEuro ↑=⇒ E (t) ↑.
3. The Euro is expected to be more valuable in the future:
E (t + 1) ↑=⇒ E (t) ↑
Intuition: Good news such as lower risk or a higher interest rate
make the Euro attractive to investors. Its value rises.
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Is the Euro strong when the interest rate is high?
Today: i$ = iEuro = 10%; E (t) = 1 [$/Euro]
UIP: Investors must expect E to remain constant
Shock: Euro interest rate rises to 15%
Key assumption: No change in E(t + 1)!
Result:
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e [$/Euro]
Is the Euro strong when the interest rate is high?
x
t
t+1
Time
x is the expected depreciation of the Euro
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Is the Euro strong when the interest rate is high?
Key point
A rise in the Euro interest rate leads to Euro appreciation.
A high Euro interest rates means that investors expect a Euro
depreciation in the future.
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Expectations Matter
Fact
UIP determines E(t) only relative to the future E(t + 1).
Changes in expectations about E(t + 1) are reflected immediately in
the spot rate.
.
Example
Start from i$ = iEuro .
Investors view the Euro as riskier: RP ↑
Violation of UIP: i$ > iEuro − RP.
Traders sell Euros until UIP is restored. That requires
i$ = iEuro − RP + x.
To compensate for the risk, investors need expected Euro
appreciation.
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Possibility of self-fulfilling prophecies
I
Without an anchor to pin down the long-run exchange rate,
any E can be an equilibrium
I
Mean-reversion to PPP (purchasing power parity) provides an
anchor, but it is weak.
I
This is generally true for asset prices.
I
This is one reason why asset prices are so volatile.
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Summary
We now have the pieces required to figure out equilibrium in the
open economy:
1. good market clearing: IS
Y = C(Y − T ) + I(Y , r ) + G + X(Y ∗ , ε) − IM(Y, ε)/ε
+
+ −
(11)
2. money / bond market clearing: LM
M/P = YL (i)
(12)
3. FX market clearing
3.1 perfect / high capital mobility: UIP
E=
1 + i∗ e
E
1+i
(13)
3.2 no capital mobility:
NX = X − IM = 0
(14)
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Some Comments
1. LM is unchanged: we assume that only locals hold currency
2. Since we take prices as given, we can use the nominal interest
rate i instead of the real one (r)
3. We assume that a depreciation improves the trade balance
4. We rewrote UIP:
1 + i = (1 + i∗ )E/Ee
(15)
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Reading
Blanchard / Johnson, Macroeconomics, 6th ed., ch. 18-20
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