The Monetary Approach to the Exchange Rate

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The Monetary Approach to the Exchange Rate

• Antu Panini Murshid

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Todays Agenda

• The law of one price and purchasing power parity
• The monetary approach to the exchange rate
• Implications of the model
• Real interest rate and the Fisher effect
• Impact of an expansionary monetary policy

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Law of One Price

• The law of one price states that as long as there
  are no barriers to trade or transportation costs,
  identical goods in two countries must sell for
  the same price, when their prices are expressed
  in the same currency
• Thus Pi e Pif
• for any two countries
• and any good i

Why? Arbitrage once again
4
Purchasing Power Parity

• Purchasing power parity is the law of one price
  applied to a fixed basket of commodities
• The law of one price implies that eP/Pf, where P
  is the price of a basket of commodities in the
  home country and Pf is the price of that same
  basket of commodities abroad

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Implications of Purchasing Power Parity

• PPP states that the exchange rate between two
  currencies is in equilibrium when their
  purchasing power is the same in each country,
  i.e. the exchange rate between two countries
  should equal the ratio of the two countries'
  price levels
• Thus when one countrys price level is increasing
  (decreasing) its exchange rate must also be
  depreciating (appreciating)
• PPP implies that the real exchange rate should be
  equal to one

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Relative PPP vs. Absolute PPP

• Absolute PPP was described in the previous slides
• Relative PPP refers to rates of changes of price
  levels, that is, inflation rates. This
  proposition states that the rate of appreciation
  of a currency is equal to the difference in
  inflation rates between the foreign and the home
  country
• De p - pf

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Example

• If the US inflation rate is 10 and the UK
  inflation rate is 5, the dollar will depreciate
  against the pound by 5
• Relative PPP is a useful concept when we are
  trying to conceptualize the impact of changes in
  rates of monetary growth (or prices) as opposed
  to one off changes

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Monetary Approach to the Exchange Rate

• In its simplest form, the monetary approach to
  the exchange rate is simply a restatement of PPP
• Hence according to the monetary approach to the
  exchange rate, the exchange rate should be equal
  to the ratio of the domestic and foreign price
  levels, i.e. e P/Pf
• Alternatively the rate of depreciation of one
  currency relative to another should be equal to
  the difference in their rates of inflation, i.e.
  ?e ?p-pf

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Price Level Key to Understanding the Exchange
Rate

• According to the monetary approach, the key
  variable to understanding the long-run behavior
  of the exchange rate is the price level and the
  rate of change of the price level
• This differs from the asset market approach which
  emphasized the interest rate

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A Long-Run Theory

• The monetary approach to the exchange rate is a
  theory on the long-run behavior of the exchange
  rate, since it assumes that prices are flexible.
  In the short run prices could very well be rigid
  and PPP need not apply
• This contrasts with the asset market approach,
  which is a theory of the short-run behavior of
  the exchange rate

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Money Supply and Money Demand

• Given the role of prices, a theory of the
  determinants of the exchange rate must hope to
  explain movements in the price level
• The monetary approach to the exchange rate
  focuses on the supply and demand for money as the
  key determinants of the price level

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Basic Model

• MdPL(y,i) Liquidity preference
• MsMd Money market equilibrium
• eP/Pf PPP
• There is a little bit more to it than this. The
  money supply is normally written as the sum of
  domestic credit and foreign exchange reserves (we
  will study this in greater detail later)

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Basic Model

• Equations (1) and (2) ? PMs/L(y,i) Hence by PPP
• Recognizing that the foreign price level is
  simply the ratio of foreign money supply to money
  demand we have

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Implications of the Model

• Let us ignore developments in the foreign country
  and focus on the implications of developments at
  home, i.e. take the foreign price level, Pf, as
  given then
• An increase in US money supply implies P?, dollar
  depreciates (e?)
• An increase in interest rates implies L(i,y)?,
  P?, dollar depreciates (e?)
• An increase in output implies L(i,y)?, P?, dollar
  appreciates (e?)

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Graphical Illustration

• It will be useful to illustrate these
  implications of the model graphically, but in
  order to that first we need to introduce a new
  diagram for analyzing money market developments
  that emphasizes the price level, not the interest
  rate, as the adjustment mechanism

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The Money Market in the Long-Run
Ms
Price level

• Consider the following money market diagram drawn
  with nominal money balances on the horizontal
  axis and the price level on the vertical axis

Md(i,y)
e
P1
nominal money balances
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The Money Market in the Long-Run
Ms
Price level

• Since we are interested in the long-run, it makes
  sense to draw the money market with the price
  level as opposed to the interest rate on the
  vertical axis

Md(i,y)
e
P1
nominal money balances
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The Money Market in the Long-Run
Ms
Price level

• Note that since an increase in income will raise
  the demand for nominal money balances the money
  demand curve will rotate clockwise

Md(i,y)
Md(i,y2)
e
P1
P2
e2
nominal money balances
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The Money Market in the Long-Run
Ms
Price level

• An increase in interest rates will have the
  opposite effect by lowering the demand for
  nominal money balances

Md(i,y3)
Md(i,y)
e3
P3
e
P1
nominal money balances
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Implications of Monetary Model for the Exchange
Rate
Price level
Ms
This diagram shows that for a given value of Pf
there is a unique equilibrium exchange rate that
corresponds to any given P
eP/Pf
Md(i,y)
P1
e1
nominal money balances
exchange rate
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Implications of Monetary Model for the Exchange
Rate
Price level
Ms
Ms2
Increases in money supply will raise the price
level, which will correspond to higher values of e
eP/Pf
Md(i,y)
P2
P1
e2
e1
nominal money balances
exchange rate
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Implications of Monetary Model for the Exchange
Rate
Price level
Ms
Increases in interest rates will also raise the
price level, which will correspond to higher
values of e
Md(i2,y)
eP/Pf
Md(i,y)
P2
P1
e2
e1
nominal money balances
exchange rate
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Implications of Monetary Model for the Exchange
Rate
Price level
Ms
Increases in income by contrast will cause the
price level to fall, which will correspond to
lower values of e
Md(i2,y)
eP/Pf
Md(i,y)
P1
P2
e1
e2
nominal money balances
exchange rate
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Do the Model Predictions Make Sense?

• The first implication that an increase in money
  supply raises the price level and causes the
  exchange rate to depreciate is uncontroversial
• Similarly the implication that an increase in
  output will cause the exchange rate to appreciate
  is reasonable, since increases output would apply
  downward pressure on prices (think of a rightward
  shift in the aggregate supply curve)
• However why should an increase in interest rates
  cause the exchange rate to depreciate?

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The Implications of a Rise in Interest Rates

• There are two problems with how the model links
  interest rates to the exchange rate
• First in the long-run the price level adjusts to
  remove money market disequilibria, so what is
  causing the interest rate to change?
• Second, the prediction that an increase in
  interest rates will ultimately lead to a
  depreciation of the currency seems inconsistent
  with our discussion on the short-run behavior of
  the exchange rate

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Understanding Why the Interest Rate Changes

• In fact the implication that an exchange rate
  depreciation will follow an interest rate
  increase is quite reasonable. The key is to
  understand why the interest rate changes
• It turns out that increases in the interest rate
  follow from expansionary monetary policies that
  raise the rate of inflation, which is consistent
  with an exchange rate depreciation
• To see why this is the case, we will need to
  introduce the notion of the real interest rate

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The Real Interest Rate

• The ex ante real interest rate is defined as
• r i - pe,
• where pe is the expected inflation rate
• The ex post or realized real interest rate is
  defined as
• r i - p,
• where p is the realized inflation rate

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What Determines the Real Interest Rate?

• The real interest rate is determined in the
  market for loanable funds
• The supply of loanable funds comes from savers
• The demand for loanable funds comes from those
  who wish to borrow to make investments

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Determinants of the Demand for Loanable Funds

• The most important factor that determines the
  demand for loanable funds is the cost of
  obtaining a loanthe real interest rate. Since
  borrowers do not know the inflation rate before
  hand the demand for loanable funds is influenced
  by the ex ante real interest rate
• A higher expected (real) cost of borrowing
  implies a lower demand for loanable funds
• A lower expected (real) cost of borrowing implies
  a higher demand for loanable funds

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Demand Schedule for Loanable Funds
Technological changes, which affect the MPK, as
well as factors influencing the risk
characteristics of investments will shift the
demand for loanable funds schedule
real interest rate
2the quantity of loanable funds demanded
increases
5
4
1. As the real interest rate falls
I, demand
loanable funds
1,000
1,500
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Determinants of the Supply of Loanable Funds

• The supply of loanable funds could also respond
  to the ex ante real interest rate, however the
  evidence suggests that this relationship is weak
• More important determinants are demographic
  shifts that alter private savings behavior and
  changes in fiscal expenditure patterns of
  governments

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Supply Schedule for Loanable Funds
An increase in real interest rates might create
greater incentives for savers to save. However
this effect is weak
SN, supply
real interest rate
5
Changes in government expenditure and demographic
shifts will cause the savings schedule to shift
4
900
1,000
loanable funds
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Market for Loanable Funds
SN, supply
real interest rate
Equilibrium
5
I, demand
1,000
loanable funds
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Fisher Effect

• Clearly long-run factors that shift the demand
  for and supply of loanable funds will affect the
  real interest rate, however Irving Fisher noted
  that in general the long-run real interest rate
  can be regarded as roughly constant or at least
  exhibiting only weak trends
• The Fisher effect implies that there is a
  one-to-one relationship between the inflation
  rate and the nominal interest rate

It is interesting that he argued this, since at
the time of writing this was definitely not the
case
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Empirical Evidence
It would appear that over the past 40-years, the
Fisher effect worked fairly well
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Expansionary Monetary Policy and the Interest Rate

• According to the Fisher effect an expansionary
  monetary policy, which raises the rate of
  inflation, i.e. an increase in the rate of growth
  of money, will also cause the nominal interest
  rate to rise

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Expansionary Monetary Policy in the Market for
Loanable Funds
3This is excess demand is eliminated when i rises
SN, supply
real interest rate
5
2creating an excess demand for loanable funds
4
1. A rise in p causes the real interest rate to
fall
I, demand
1,000
loanable funds
1,500
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Expansionary Monetary Policy in the Money Market
Money supply M1s/P
M1s/P2

• When p increases, for any given i, r must fall
• The Fisher effect implies that i must rise
• The resulting disequilibrium is cleared by the
  rising price level

Interest rate
i115
Equilibrium interest rate
i110
Money demand L(i,y)
real money balances
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Why Does the Price Level Rise?

• Why exactly does the price level rise?
• There are two ways to think about this depending
  on how you want to attribute causality
• First the price level rises as a consequence of
  the rise in the nominal interest rate
• Second the price level rises because of an excess
  demand for loanable funds, which in turn causes
  the interest rate to increase

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Inflationary Expectations and Financial Assets

• The increase in the rate of growth of money
  raises inflationary expectations
• Investors anticipate a rise in interest rates,
  which leads to a shift out of bonds an into money
• The price of bonds falls and the interest rate
  rises
• The excess demand for money causes the price of
  money to fall and the price level to rise
• In this case the rise in interest rate induces
  the price level to rise

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Rise in Investment Demand

• The initial inflationary spurt causes r to fall
  which creates an excess demand for loanable funds
• Consequently aggregate demand rises (investment
  is a component of aggregate demand)
• This puts upward pressure on P, lowering real
  money supply and raising i
• In this case the rise in the price level induces
  the rise in nominal interest rates

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Summarizing

• To summarize the interest rate rises in the
  long-run because of increased inflationary
  pressures. This can result from a change in the
  rate of growth of money supply, but not from
  one-off changes in money, which have no effect on
  the interest rate

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Real Interest Rate Parity

• We can now bring together what we have learned
  about the Fisher effect, interest rate parity and
  PPP
• Interest rate parity i - if E(?e)
• PPP ?e p pf
• Real interest rate parity i - if E(p pf)
• Note that real interest rate parity is just
  another way of stating the Fisher effect

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Impact of an Expansionary Monetary Policy

• First consider the effects of a one-off 10
  increase in US money supply?
• In the short-run
• ? Ms ? ? i ? ? e gt 10 (overshooting)
• In the long-run
• ? P ? ? i to initial level, and ? e such that
  overall increase in e is 10

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Impact of an Expansionary Monetary Policy

• Now consider the implications of an increase in
  the rate of growth of money from p to pDp
• The increase in money growth rate is illustrated
  in the diagram as a rise in the slope of M(t)

US money supply
M(t)
Slope pDp
M(t0)
Slope p
t0
time
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Impact of an Expansionary Monetary Policy

• As a consequence of the rise in the rate of money
  expansion, the expected rate of inflation rises
  from p to pDp
• To preserve real interest rate parity the nominal
  interest rate must rise by Dp

Nominal interest rate
i1Dp
i1
t0
time
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Impact of an Expansionary Monetary Policy

• The rise in i creates a disequilibrium in the
  money market, which is cleared by a jump in the
  price level
• Moreover from t0 onward the price level is
  increasing at a faster rate

Price level
Slope pDp
Slope p
t0
time
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Impact of an Expansionary Monetary Policy

• Finally note that by PPP the exchange rate jumps
  at t0
• And continues rise thereafter at a faster tate

Exchange rate
Slope pDp
Slope p
t0
time
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The Short-Run and the Long-Run

• In the short run an increase in Ms produces a
  fall in the interest rate to equilibrate the
  money market, as prices are rigid ? the only way
  to maintain interest parity is to expect an
  exchange rate appreciation
• In the long run, when prices adjust, an increase
  in rate of growth of MS leads to an increase in
  expected inflation and the interest rate (Fisher
  effect). This in turn leads to an exchange rate
  depreciation (PPP)

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The Short-Run and the Long-Run

• The key difference between the short-run and the
  long-run is the speed of adjustment in prices
• In the short-run prices are sticky and the
  interest rate adjusts to bring the money market
  to an equilibrium
• In the long-run prices are flexible and interest
  rates are insensitive to one-off changes in money
  but do respond to changes in money growth rates
  and inflationary expectations