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The classical model of the SMALL OPEN
economy
Open Economy Macroeconomics
Dr hab. Joanna Siwińska-Gorzelak
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Overview
• This lecture is based on the chapter „The Open Economy” from G. Mankiw „Macroeconomics”
• This lecture reviews
– accounting identities for the open economy
– the small open economy model
• what makes it “small”
• how the trade balance and exchange rate are determined
• how policies affect trade balance & exchange rate
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Why learn this?
• To understand:
– what trade surpluses and trade deficits are.
– the link between the trade balance and net capital outflow or net lending to/borrowing from abroad
– why countries have huge trade deficits?
– what can the government do about this?
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In an open economy,
• spending need not equal output
• saving need not equal investment
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Preliminaries: spending in open economy
EX = exports = foreign spending on domestic goods
IM = imports = C f + I f + G f = spending on foreign goods
NX = net exports (a.k.a. the “trade balance”) = EX – IM
d fC C C
d fI I I
d fG G G
superscripts:
d = spending on domestic
goods
f = spending on foreign
goods
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The national income identity in an open economy
d d dY C I G EX
( ) ( ) ( )f f fC C I I G G EX
( )f f fC I G EX C I G
C I G EX IM
C I G NX
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The national income identity in an open economy
Y = C + I + G + NX
or, NX = Y – (C + I + G )
net exports
domestic
spending
output
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Trade surpluses and deficits
• trade surplus: output > spending and exports > imports Size of the trade surplus = NX
• trade deficit: spending > output and imports > exports Size of the trade deficit = –NX
NX = EX – IM = Y – (C + I + G )
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International capital flows
• Net capital outflow
= S – I
= net (out)flow of “loanable funds”
= net purchases of foreign assets the country’s purchases of foreign assets
minus foreign purchases of domestic assets
• When S > I, country is a net lender (funds flow out)
• When S < I, country is a net borrower (funds flow in)
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The link between trade & cap. flows
NX = Y – (C + I + G )
implies
NX = (Y – C – G ) – I
= S – I
trade balance = net capital outflow
Thus,
a country with a trade deficit (NX < 0)
is a net borrower (S < I ).
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Classical model of small open economy
• An open-economy version of the classical model of the closed economy:
• Includes many of the same elements:
– production function
– consumption function
– investment function
– exogenous policy variables
– assume fully flexible prices (!)
Y Y F K L ( , )
C C Y T ( )
I I r ( )
G G T T ,
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Classical model of SOP
• Assumptions: fully flexible prices; production always equal to potential output, economy is small, capital is perfectly mobile across countries
• This is a long run model (!), not suitable to analyse short-term shocks and fluctuations
• But it is also NOT a very long run growth model
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National saving: The supply of loanable funds
r
S, I
Assumption made here:
national saving does
not depend on the
interest rate
( )S Y C Y T G
S
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Recall: types of saving
• private saving = (Y –T ) – C
• public saving = T – G
• national saving, S
= private saving + public saving
= (Y –T ) – C + T – G
= Y – C – G
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Investment
• Recall from your macro course:
• Profit max. implies MPK = user cost
• User cost in its simplest form is:
• uc=(r+d)
• Hence, ceteris paribus, as r falls, the DESIRED level of capital stock increases, hence investment increases
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Investment: The demand for loanable funds
Investment is still a
downward-sloping function
of the interest rate,
r *
but the exogenous
world interest rate…
…is one of the
several factors that
determines the
country’s level of
investment.
I (r* )
r
S, I
I (r )
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If the economy were closed…
r
S, I
I (r )
S
rc
cI
S
r
( )
…the interest
rate would
adjust to
equate
investment
and saving:
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Assumptions: Capital flows
a. domestic & foreign bonds are perfect substitutes (same risk, maturity, etc.);
b. perfect capital mobility: no restrictions on international trade in assets
c. economy is small: cannot affect the world interest rate, denoted r*
a & b imply r = r*
c implies r* is exogenous
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But in a small open economy…
r
S, I
I (r )
S
rc
r*
I 1
the exogenous
world interest
rate determines
investment…
…and the
difference
between saving
and investment
determines net
capital (out)flow
and net exports
NX
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A small open economy that lends abroad, with saving dependent on the interest rate
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A small open economy that borrows from abroad, with saving that depends on the interest rate
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Saving and Investment in a Small Open Economy
• Result: rw may be such that Sd > Id, Sd = Id, or Sd < Id
– If Sd > Id, the excess of desired saving over desired investment is lent internationally (net foreign lending is positive) and NX > 0
– If Sd = Id, there is no net foreign lending and NX = 0
– If Sd < Id, the excess of desired investment over desired saving is financed by borrowing internationally (net foreign lending is negative) and NX < 0
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Next, three experiments:
1. Fiscal policy at home
2. Fiscal policy abroad
3. An increase in investment demand
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1. Fiscal policy at home
r
S, I
I (r )
1S
I 1
An increase in G
or decrease in T
reduces saving. 1
*r
NX1
2S
NX2
Results:
0I
0NX S
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1. Fiscal policy at home
• Recall that national saving is a sum of government saving and private saving
• The previous slide assumed that the change in fiscal policy will not affect private savings
• However, recall Ricardian Equivalence that holds that a change in public saving will be offset by the change in private saving
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The Ricardian view
• due to David Ricardo (1820), more recently advanced by Robert Barro
• According to Ricardian equivalence,
a debt-financed tax cut has no effect on
consumption, national saving, net exports, or real
GDP, even in the short run.
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The logic of Ricardian Equivalence
• Consumers are forward-looking, know that a debt-financed tax cut today implies an increase in future taxes that is equal – in present value – to the tax cut.
• The tax cut does not make consumers better off, so they do not increase consumption spending.
Instead, they save the full tax cut in order to repay the future tax liability.
• Result: Private saving rises by the amount public saving falls, leaving national saving unchanged.
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2. Fiscal policy abroad
r
S, I
I (r )
1SExpansionary
fiscal policy
abroad raises
the world
interest rate. 1
*rNX1
NX2
Results:
0I
0NX I
2
*r
1( )*I r2( )*I r
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3. An increase in investment demand
r
S, I
I (r )1
EXERCISE:
Use the model to
determine the impact
of an increase in
investment demand
on NX, S, I, and
net capital outflow.
NX1
*r
I 1
S
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3. An increase in investment demand
r
S, I
I (r )1
ANSWERS:
I > 0,
S = 0,
net capital
outflow and
NX fall by the
amount I
NX2
NX1
*r
I 1 I 2
S
I (r )2
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The nominal exchange rate
e = nominal exchange rate, the relative price of foreign currency in terms of domestic currency OR domestic currency in terms of foreign currency
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The real exchange rate is the price level adjusted exchange rate.
Its meant to capture the relative value of goods and services
across countries
P
PeRER
*
Nominal Exchange Rate
(DOMESTIC currency to
FOREIGN currency) Domestic price
Foreign price
The real exchange rate
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~ McZample ~
• one good: Big Mac
• price in PL: P = 10 PLN
• price in USA: P* = $4.00
• nominal exchange rate e = 4 PLN/$ To buy a U.S. Big Mac,
someone from PL
would have to pay an
amount that could buy
1.6 Polish Big Mac.
slide 32
6,110
16
10
4*4*
PLN
PLN
PLN
USDUSD
PLN
P
eP
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ε in the real world & our model
• In the real world: We can think of ε as the relative price of a basket of domestic goods in terms of a basket of foreign goods
• In our macro model: There’s just one good, “output.” So ε is the relative price of one country’s output in terms of the other country’s output
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How NX depends on ε
ε Home goods become LESS expensive relative
to foreign goods
IM, EX
NX INCREASES
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The net exports function
• The net exports function reflects this positive
relationship between NX and ε :
NX = NX(ε )
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The NX curve for Home.
0 NX
ε
NX (ε)
ε1
When ε is
relatively high,
Home goods are
relatively
inexpensive
NX(ε1)
so Home
net exports
will
be high
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How ε is determined
• The accounting identity says NX = S – I
• We saw earlier how S – I is determined:
– S depends on domestic factors (output, fiscal policy variables, etc)
– I is determined by the world interest rate r *
• So, ε must adjust to ensure
( ) ( )*NX ε S I r
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How ε is determined
Neither S nor I depend on ε, so the net capital outflow curve is vertical.
ε
NX
NX(ε )
1 ( *)S I r
ε adjusts to
equate NX
with net capital
outflow, S I.
ε 1
NX 1
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Interpretation: Supply and demand in the foreign exchange market
Demand (NX):
Demand for home currency to buy home’s net exports.
ε
NX
NX(ε )
1 ( *)S I r
Supply:
Net capital flow (S
I )
is the supply of
home currency
offered to buy
Foreign’s assets.
ε 1
NX 1
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Next, four experiments:
1. Fiscal policy at home
2. Fiscal policy abroad
3. An increase in investment demand
4. Trade policy to restrict imports
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1. Fiscal policy at home
A fiscal expansion reduces national saving, decreases net capital outflow, and the supply of home currency in the foreign exchange market…
…causing the real exchange rate
to appreciate and NX to decline
(i.e. trade DEFICT to increase)
ε
NX
NX(ε )
1 ( *)S I r
ε 2
NX 1 NX 2
2 ( *)S I r
ε 1
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2. Fiscal policy abroad
An increase in r* reduces investment, increasing net capital outflow and the supply of home currency in the foreign exchange market…
…causing the real
exchange rate to
depreciate and NX to rise.
ε
NX
NX(ε )
1 1( *)S I r
NX 1
ε 2
21 ( )*S I r
ε 1
NX 2
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3. Increase in investment demand
An increase in investment demand decreases net capital outflow and the supply of home currency in the foreign exchange market…
ε
NX
NX(ε )
…causing the real
exchange rate to
appreciate and NX
to fall.
ε 2
1 1S I
NX 1
21S I
NX 2
ε 1
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4. Trade policy to restrict imports
At any given value of ε,
an import quota
IM NX
increases the (net)
demand for
home currency
ε
NX
NX (ε )1
S I
NX1
ε 2
NX (ε )2
Trade policy doesn’t
affect S or I , so
capital flows and the
(S-I) or supply of
currency remains
fixed.
ε 1
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4. Trade policy to restrict imports
ε
NX
NX (ε )1 S I
NX1
ε 2
NX (ε )2
Results:
ε < 0
(demand
increase)
NX = 0
(supply fixed)
IM < 0
(policy)
EX < 0
(decrease in ε )
ε 1
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The determinants of the nominal exchange rate - intro
• Start with the expression for the real exchange rate:
Solve for the nominal exchange rate:
P
Pe
*
eP
P
*
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The determinants of the nominal exchange rate - intro
• So e depends on the real exchange rate and the price levels at home and abroad…
…and we know how each of them is determined:
( * , )M
L r YP
( ) ( )*NX ε S I r
** *
*( * *, )
ML r Y
P
*P
Pe
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Implications for growth
• Recall the Solow growth model, where the setady state level of capital per labour depends on the amount of savings
• This no longer holds, as the level of investment – at least in theory – is detached from savings
• The steady-state value of capital stock should depend on world interest rate and on country’s marginal product of capital
The Open Economy
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Chapter Summary
• Net exports--the difference between – exports and imports
– a country’s output (Y )
and its spending (C + I + G)
• Net capital outflow equals – purchases of foreign assets
minus foreign purchases of the country’s assets
– the difference between saving and investment
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Chapter Summary
• National income accounts identities: – Y = C + I + G + NX
– trade balance NX = S I net capital outflow
• Impact of policies on NX : – NX increases if policy causes S to rise
or I to fall
– NX does not change if policy affects neither S nor I. Example: trade policy
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Chapter Summary
• Exchange rates
– nominal: the price of a country’s currency in terms
of another country’s currency
– real: the price of a country’s goods in terms of
another country’s goods
– The real exchange rate equals the nominal rate
times the ratio of prices of the two countries.
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Chapter Summary
• How the real exchange rate is determined
– NX depends negatively on the real exchange rate,
other things equal
– The real exchange rate adjusts to equate
NX with net capital outflow
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