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Summary of week 3 of the course International Money and Finance
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Summary of week 3 of the course International Money and Finance. Including Chapter 7.
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Summary of week 7 of the course International Money and Finance
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Chapter 7: Modern Models Of Exchange Rate DeterminationThe PPP theory outlined in Chapter 6 is far from a satisfactory explanation of observed exchange rate
behavior. In particular, it is very much concerned with goods arbitrage and has nothing to say about
capital movements internationally. The common thread to the models that we will analyse in this
chapter is that they all emphasize the important role of relative money supplies in explaining the
exchange rate. These models make an assumption that domestic and foreign bonds are perfect
substitutes; and there has developed a brand of models known as portfolio balance models that
allow for differences in riskiness between domestic and foreign bonds.
Uncovered Interest Rate Parity
Since international investors can quickly and easily switch out of domestic bonds into foreign bonds
and vice versa, the exchange rate can be viewed as a relative asset price. The fundamental
characteristic of an asset price is that its present value will be largely influenced by its expected rate
of return. There will be two factors that international investors will bear in mind when considering
which to purchase: the rates of interest on UK bonds and US bonds, and what they expect to happen
to the pound-dollar exchange rate. The international bond market is in equilibrium if
E ś=r uk −r us
Where E ś is the expected rate of depreciation of the exchange rate of the pound, defined as pounds
per dollar, r uk is the UK interest rate and r us is the US interest rate. The equation is known as the
uncovered interest parity condition (UIP). UIP states that the expected rate of depreciation of the
pound against the dollar is equal to the interest rate differential between UK and US bonds.
With an exchange rate of £0.50/$1, investing £1,000 in UK bonds will yield the investor £100 return
(10%) at the end of the year. If he expects the pound to depreciate by 6% during the year, he expects
the pound-dollar exchange rate to be £0.53/$1. Hence, he could purchase £1,000 worth of dollars
today at £0.50/$1, which gives him $2,000 and which will earn the UA interest rate of 4%, meaning
he will have $2,080 which he expects to convert back into pounds at £0.53/$1, giving him £1,102.4.
This expected return of £102.4 (approximately 10%) from investing in UA bonds, which is
approximately equal to the expected return on UK bonds. Hence, the UIP condition implies that the
expected rate of return on domestic and foreign bonds are equal.
When there is both perfect capital mobility and equal riskiness of domestic and foreign bonds, UK
and US bonds are said to be perfect substitutes. Perfect substitutability implies that the UIP
condition will hold on a continuous basis.
The Monetary Models Of Exchange Rate Determination
Having provided the basic background to the monetary models of exchange rate determination we
now proceed to examine the specific characteristics and predictions of three of the major monetarist
models of exchange rate determination: ‘flexible-price’, ‘sticky-price’ and ‘real-interest-rate-
differential’ monetary models. A common characteristic of these models is that the supply and
demand for money are the key determinants of exchange rates. Another common starting point is
that all the models employ the UIP condition; that is, they assume that domestic and foreign bonds
are equally risky so that their expected rates of returns are equalized.
The Flexible-Price Monetary Model
The model assumes that PPP holds continuously. It represents a valuable addition to exchange rate
theory because it explicitly introduces relative money stocks into the picture as determinants of the
relative prices which in turn determine the exchange rate.
, We start by assuming that there is a conventional money demand function so that money market
equilibrium is given by:
m− p=ηyy−σrr
Where m is the log of the domestic money stock, p is the log of the domestic price level, y is the log
of domestic real income and r is the nominal domestic interest rate. The equation says that the
demand to hold real money balances is positively related to real domestic income, due to increased
transactions demand, and inversely related to the domestic interest rate. A similar relationship holds
for the foreign money demand function so that
m¿ −p ¿=ηyy ¿−σr r ¿
It is assumed that PPP holds continuously, expressed as:
s= p− p¿
Where s is the log of the exchange rate defined as domestic currency units per unit of foreign
currency. The monetarist models make a crucial assumption that domestic and foreign bonds aare
perfects substitutes. This being the case, the UIP condition holds:
E ś=r−r ¿
The equation says that the expected rate of depreciation of the home currency is equal to the
interest rate differential between domestic and foreign bonds. We can rearrange the equations to
give solutions for the domestic and foreign price levels:
p=m−ηyy +σrr
p¿ =m ¿−ηy y¿ +σr r ¿
We then obtain:
s= ( m−m ¿ ) −ηy ( y− y ¿ ) + σr (r −r ¿ )
This equation is what is known as a ‘reduced-form’ exchange rate equation. The spot exchange rate
(the dependent variable) on the left-hand side is determined by the variables (explanatory variables)
listed on the right-hand side of the equation. The equation predicts the following concerning the
effect of a change in one of the right-hand variables on the exchange rate:
1. Relative money supplies affect exchange rates: a given percentage increase in the home
money supply leads to an exactly equivalent depreciation of the currency, while a given
percentage increase in the foreign money supply leads to an exactly equivalent percentage
appreciation of the domestic currency.
2. Relative levels of national income influence exchange rates: if domestic income were to
rise, this increases the transactions demand for money, and the increased demand for
money means that if the money stock and interest rates are held constant the increased
demand for real balances can only come about through a fall in domestic prices. The fall in
domestic prices then requires an appreciation of the currency to maintain PPP.
3. Relative interest rates affect exchange rates: an increase in the domestic interest rate leads
to an depreciation of the domestic currency. The rationable behind this is that a rise in the
domestic interest rate leads to a fall in demand for money and hence a depreciation of the
domestic currency. Another rationalization for this effect can be made by expressing the
nominal interest rate as made up of two components, the real interest rate and the expected
inflation rate; that is:
r =i+ P é
Where i is the real rate of interest and P é is the expected rate of price inflation. Similarly the
foreign nominal interest rate is given by:
r ¿ =i ¿ + P é ¿
¿
Assuming that the real rate of interest is constant and identical in both countries ( i=i ), an
increase in the domestic nominal interest rate is due to an increase in domestic price
inflation expectations. Such increased inflation expectations lead to a decreased demand for
money and an increased expenditure on goods., which in turn leads to a rise in domestic
prices. The rise in domestic prices then requires a depreciation of the currency to maintain
PPP.
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