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EC201 Intermediate Macroeconomics
EC201 Intermediate Macroeconomics

Lecture 23-24: Introduction to Open Economy
Macro
Lecture Outline:
- National Income identity in an open economy;
- Balance of Payments;
- The Nominal and Real Exchange Rates;
- Uncovered Interest Parity condition;
Essential reading:
Mankiw: Ch
...
Here we consider the
case where an economy can have transactions with foreign economies, therefore, an
economy can spend more than it produces domestically, by importing from abroad or
it can spend less than it produces and sell the difference to foreign countries
(exporting goods)
...
In this case
our economy is spending less than it produces and so it LENDS to the rest of the
world
...
Our economy is spending
more than it produces and so it BORROWS from the rest of the world
...
This is case b) described above
...
If the trade balance is zero, then we have the case
of a closed economy
...
Firms
borrowing to finance their investment could only borrow from domestic savers
...
But in an open economy, S needs not to be equal I
...
g
...
Similarly, domestic firms can finance their investment
projects by borrowing from domestic savers or by borrowing them from foreign
savers
...
Rather, what can flow
internationally is financial capital, which of course is used to finance the purchase of
physical capital
...
In either case, a person in one country ends up owning part of
the capital stock of another country
...

Alternatively, if firms wish to borrow more than domestic savers wish to lend, then
the firms borrow the excess on international financial markets
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Y − (C + G ) = I + NX

1)

We know that Y − (C + G ) is the national saving = real national income less what is
consumed domestically
...
This identity says that a
country (such as the U
...
) with persistent, large trade deficits (NX < 0) also has low
saving, relative to its investment, and is a net borrower of assets
...
Net saving is just

S−I
...

The Balance of Payments is divided into two main parts:
a) The Current Account: it records exports and imports of goods and services,
receipts and payments of investment income and transfer payments
...

b) The Financial Account (it used to be called Capital Account): it records
mainly purchases and sales of foreign assets and purchases and sales of
domestic assets by foreign residents (for example, a British resident that buys
a US bond for $100 will enter with a minus into the capital account (-$100
converted into pounds according to the exchange rate)
...

We are mainly interested in the Trade Balance that is part of the current account, since
the trade balance directly influences the real output
...


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Overall the UK current account is in deficit, meaning that UK is a net borrower
...
There two ways to quote an exchange rate:
a) The relative price of domestic currency in terms of foreign currency
...
55 = £1
...
55 euros
...
For
example, UK pounds per Euros
...
645 = €1
...
645 pounds
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Define the exchange rate €1
...
55 , that is the price of a pound in
terms of Euros
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645 = €1 as e£,€ = 0
...

Then, it is clear that: e€,£ =

1

...
The reason is: suppose that e€,£ increases, for example, from 1
...
This means that it is more expensive to buy British pounds using Euros
...
On the other hand if e€,£ decreases, then it is cheaper to buy the same
amount of pounds using euros, and therefore the British pound is DEPRECIATING
against the Euro
...
This means that an increase in e will mean an appreciation of
the home currency and a decrease in e will mean a depreciation in home currency
...
If e£,€ increases, for example from 0
...
This case is considered in the following graph
...
On the vertical axis you have the pound value for 1 Euro
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67350 Pounds
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The Real Exchange Rate
The real exchange rate is defined as the relative price of
domestic goods in terms of foreign goods (for example, the Big Mac in Japan
compared to the Big Mac in US)
...
The real exchange rate measures the amount of purchasing power in the

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Foreign country that must be sacrificed for each unit of purchasing power in the
Domestic country
...
Assume that
in UK the price of a Big Mac is £2, while in the US the price is $2
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The real exchange rate is:

ε=

eP 2 × £2 $4
=
=
=2
P*
$2
$2

In order to buy a Big Mac in UK someone in US should pay an amount that could buy
2 Big Macs in US
...
In all the macro models we have seen
there is normally only one good, real output
...

From equation 2) we have:
a)

For a given nominal exchange rate, when prices increases in the domestic
countries compared to the foreign country, meaning

P
> 1 , the real
P*

exchange rate increases, meaning that goods in the domestic country are
becoming relatively expensive compared to the goods in the foreign country
...

b)

When prices in the foreign country increases compared to domestic prices
we have

P
< 1 , then
P*

ε ↓,

and we say that there is a REAL

DEPRECIATION of domestic currency
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Nominal Exchange Rate and Inflation Differential
From the definition of the real exchange rate we can see that the nominal exchange
rate is given by:
e=ε

P*
P

Rewrite that expression in terms of growth rates:
∆ e ∆ε ∆ P * ∆ P
=
+ * −
e
ε
P
P

However, π * =

∆P
∆P *
is the inflation rate in the foreign country, while π =
is the
*
P
P

domestic rate of inflation
...
The growth rate of nominal exchange rate is zero if we are in a
regime with fixed exchange rate
...
This property of fixed exchange rates has been used by some developing
countries in order to reduce domestic inflation
...
In particular the

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exchange rate was fixed as 1 peso = 1 US dollar
...

The Law of One Price and the Purchasing Power Parity (PPP)
Suppose that in a given market there are no transportation costs (obviously this is
normally unrealistic) and there are no barriers to trade, then, the same good sold in
different locations must have the same price
...
If this is not the case then there is an arbitrage opportunity
...
If it is not costly moving from Colchester to London, we can go to
London, buy some amount of good A for £10 and sell it in Colchester by £15 and
make a £5 profit for each unit of the good sold
...
However, this arbitrage opportunity will
restore the equality in the price of good A in those two locations
...
On the other hand the demand for good A in Colchester will decrease
...
This movement in prices will stop when there will not be any arbitrage
opportunity and therefore, when the price of good A is the same in both locations
...
Suppose that two countries produce
similar baskets of goods, then the law of one price can be written as:
eP = P *

3)

where eP is the price level in the domestic country expressed in foreign currency
...
Obviously the price levels must be calculated on similar basket
of goods for equation 4) to make sense
...

P*

If PPP holds, then the real exchange rate must be equal to 1
...

Does the PPP hold in real world data?
No, for two reasons:
1
...

nontraded goods
transportation costs

2
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Nonetheless, PPP is a useful theory
...
In the real world,
nominal exchange rates tend toward their PPP values over the long run
...
If P increases compared to
P*

P*, then ε ↑
...

Therefore, there is an incentive to buy goods from abroad and therefore imports
should increase
...
With
this reasoning we can say that:
X (ε ) : Exports are a function of the real exchange rate (among other possible
variables) with the property that

dX
<0
dε

M (ε ) : Imports are a function of the real exchange rate with the property that

dM
> 0
...

A real appreciation will worsen the trade balance, while a real depreciation will
improve the trade balance
...
We should expect the Greek current
account to run deficits
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The Covered Interest Parity (CIP) condition is the result of arbitrage between
domestic and foreign currency returns in the absence of risk-taking
...
Suppose that a UK citizen buys a UK
government bond that costs £1 at time t
...
Suppose that there is no uncertainty about the interest rate, so the
return is known with certainty
...
First, you convert
your pound into dollars
...
Let’s call this exchange rate et that is the Spot Exchange rate
...
After
one period say at t+1 you get some money (expressed in dollars) from that investment
that you need to convert into pounds
...
This represents a
risk for the investor
...
The price Ft is the Forward
*

exchange rate that is known and agreed upon in period t for period t+1
...

Ft

In this case the two investments faced by the investor (investing in the UK bond or in
the US bond) are equally riskless (the only risk was the movement in the exchange
rate, but by signing the forward contract you eliminate that risk)
...

F
Log  t
e
 t

 Ft − et
≅
(remember the relationship between logs and the growth rate of a

et


variable)
Using those facts into equation 7) and re-arrange it:
it = i t −
*

Ft − et
et

8)

Equation 8) is called the Covered Interest Parity condition
...

et

A positive forward premium means that the forward value of the pounds in terms of
dollars is higher than its spot value
...
Now investing in the US
bond is risky for our investor because at time t, when he makes the investment
decision, he does not know what it will be the exchange rate at t+1
...
We make a
strong assumption: the investor is Risk Neutral, meaning that he does not worry about

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risk
...
Call this expectation as Et (et +1 )
...
1
It is called uncovered because now you cannot cover yourself against the exchange
rate risk (before you could by using forward contracts)
...
The expected change in exchange

 ∆e 
*
rate depends on the interest rate differential
...
When it < it , Et   < 0 and the
 e 
nominal exchange rate is expected to depreciate
...
This is because the

t
t
t
 e 

exchange rate is defined in terms of domestic currency (definition b) in this lecture note
...


t
 e 

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