The Money Supply, Interest Rates, and the Exchange Rate

1
The Money Supply, Interest Rates, and the
Exchange Rate

• Antu Panini Murshid

2
Todays Agenda

• The money market
• The money market, interest rates and exchange
  rates in the short run
• Exchange rate expectations given
• Changing expectations

3
Demand For Money

• What are the motives for holding money?
• In his General Theory Keynes identified three
  motives for holding money
• Transactions motive
• Precautionary motive
• Speculative motive

4
Transactions Motive

• The transactions motive is the primary motive for
  holding cash, which is the most liquid of all
  assets
• Households would hold all of their money as
  interest bearing securities if they could.
  However securities are illiquid. There are costs
  associated with liquidating portfolios, both in
  terms of money and time

5
Tobin-Baumol Model of Money Demand

• James Tobin and William Baumol developed a theory
  of money demand based on the transactions motive
  for holding money
• According to the Baumol-Tobin model, households
  face a tradeoff between the benefits provided by
  holding money, i.e. liquidity services, and the
  costs of holding money, i.e. lost
  interest-earnings

6
Square-Root Formula

• The Baumol-Tobin model predicts that the demand
  for money will be positively related to a
  households income, positively related to the
  transactions costs associated with liquidating
  securities, and negatively related to the
  interest rate
• Specifically the model predicts that the optimal
  quantity of money demanded will be given by the
  following function

income
fixed cost of liquidating securities
money demand
interest rate
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Precautionary Motive

• The precautionary motive for money arises as a
  precaution against an unforeseen need for
  liquidity
• It is reasonable to suppose that the
  precautionary motive for holding money will also
  be positively related to income
• Moreover the precautionary motive for holding
  money should also be negatively related to the
  interest rate

8
Speculative Motive

• Keynes also identified the speculative motive for
  holding money
• This is often misinterpreted
• People also hold money for speculative purposes,
  so they can respond to financially attractive
  opportunities
• This is wrongKeynes was actually referring to
  shifts in households liquidity preferences in
  response to shifts in expectations regarding
  future developments in financial markets

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A Digression Into Bonds

• What determines the price of bonds?
• The price of bonds is inversely related to the
  interest rate. An example will make this clear
• Consider a 100 bond w/coupon payment of 5
• That is the current interest rate or the yield of
  the bond is 5
• Suppose the price of bond decreases to 50
• Now that same bond pays a yield of 10

10
Interest-Elasticity of Money Demand

• For Keynes the speculative motive was a means of
  making money demand interest-elastic
• Keynes argued that there should be a negative
  relationship between money demand and the
  interest rate. Why?
• If interest rates are high (above normal), you
  would expect rates to fall and the price of bonds
  to rise. Hence you shift your portfolio into
  bonds and out of money. Conversely if rates are
  low you would expect to make a capital loss by
  holding bonds, so you shift into money

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Money Demand Function

• In summary we expect money demand to be
• A positive function of income
• Positively related to real incomes
• Proportional to prices
• A negative function of interest rates
• Hence our money demand function

Demand for nominal money balances
Demand for real money balance
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Money Supply

• Money serves at least three roles. It is a unit
  of account, a medium of exchange and a store of
  value
• Which financial assets satisfy this role? Two
  accepted measures of money are
• M1 (narrow money) currency in circulation
  demand deposits travelers checks
• M2 (broad money) M1 savings deposits small
  time deposits

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Control of Money Supply

• The Federal Reserve controls the supply of money
  balances by
• Conducting open market operations (sale and
  purchase of government securities)
• Changing the reserve requirement
• Adjusting the discount rate
• The Fed rarely changes reserve requirements or
  the discount rate, and almost never uses other
  tools for discretionary monetary policy such as
  regulation W

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Exogenous Money Supply

• Throughout we will assume that money supply is
  exogenous
• In fact we will assume that the Fed has perfect
  control over the money supply and that the money
  supply function is not interest-elastic

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Money Market Equilibrium

• Suppose we are at point a, i.e. the interest rate
  is i1
• Clearly the demand for money exceeds the supply
  of money
• As individuals shift out of bonds and into money,
  the price of bonds falls and interest rates rise
  choking of the excess money demand

Ms
interest rate
e
i
excess demand for money
a
i1
Md
real money balances
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Money Market Equilibrium

• Now suppose we are at point b, i.e. the interest
  rate is i2
• Clearly the supply of money exceeds the demand
  for money
• As individuals shift out of money and into bonds,
  the price of bonds rises and interest rates fall
  restoring equilibrium

Ms
interest rate
excess supply of money
b
i2
e
i
excess demand for money
a
i1
Md
real money balances
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Money Market Equilibrium

• Thus the equilibrium interest rate is determined
  in the money market in accordance to the demand
  for and supply of liquidity

Ms
interest rate
excess supply of money
b
i2
e
i
Md
real money balances
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Expansionary Monetary Policy in the Short Run

• In the short-run we can take prices as given
• Suppose the Fed increases money supply from M1 to
  M2
• This will lead to a decrease in the equilibrium
  interest rate

M1s
M2s
interest rate
e1
i
e2
i2
Md
real money balances
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Expansionary Monetary Policy in the Short Run

• The reduction in interest rates stimulates
  investment and raises income
• This shifts the money demand function to the
  right
• Thus the increase in output is partially crowded
  out and the interest rate settles at i2

M1s
M1s
interest rate
e1
i1
e2
i2
e2
i2
M2d
M1d
real money balances
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Contractionary Monetary Policy in the Short Run

• In the short-run we can take prices as given
• Suppose the Fed decreases money supply from M1 to
  M2
• This will lead to an increase in the equilibrium
  interest rate

M1s
M2s
interest rate
e2
i2
e1
i
Md
real money balances
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Contractionary Monetary Policy in the Short Run

• The increase in interest rates reduces investment
  and lowers income
• This shifts the money demand function to the left
• This will lead to an increase in the equilibrium
  interest rate

M1s
M2s
interest rate
e2
i2
e2
i2
e1
i
M1d
real money balances
M2d
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Monetary Policy, Interest Rates and Exchange Rates

• So far we have ignored the consequences of
  monetary policy for the exchange rate
• However it should be clear that an expansionary
  monetary policy, which lowers the interest rate
  will also lead to a depreciation of the domestic
  currency (recall uncovered interest rate parity)

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An Expansionary Monetary Policy in the Short Run

• An increase in money will cause interest rates to
  fall in the short-run
• If exchange rate expectations are given, then
  UCIP no longer holds
• Domestic interest rates are lower. Thus
  investors will shift to foreign assets
• This will cause an increase in the demand for
  foreign currency and a decrease in the demand for
  dollars. The dollar will immediately depreciate
  (e?), such that UCIP is again restored

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Example

• Suppose i10, if5, et1 and E(et)1.05
• Note that UCIP holds, i.e. iifE(De)
• Now if i? to 5, i?ifE(De)
• However if et? to 1.05 then E(De)0, hence UCIP
  is restored

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Graphical Illustration
Money supply M1s/P

• First lets draw the money market graph
• The equilibrium interest rate is 10

Interest rate
Equilibrium interest rate
i110
Money demand L(i,y)
real money balances
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Graphical Illustration
Money supply M1s/P

• Now lets make everything disappear.

Interest rate
Equilibrium interest rate
i110
Money demand L(i,y)
real money balances
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Graphical Illustration

• and reappear but rotated clockwise by 90 degrees

i110
Interest rate
Money supply M1s/P
Equilibrium interest rate
real money balances
Money demand L(i,y)
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Graphical Illustration
return on assets
/

• Now lets add the foreign exchange market graph

Expected return on assets
e11.00
i110
Interest rate
Money supply M1s/P
Equilibrium interest rate
real money balances
Money demand L(i,y)
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Graphical Illustration
Equilibrium exchange rate?
return on assets
/

• Now suppose the government raises money supply

Expected return on assets
e21.05
e11.00
i110
i25
Interest rate
Money supply M1s/P
Money supply M2s/P
Equilibrium interest rate
Equilibrium interest rate ?
real money balances
Money demand L(i,y)
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Are Our Assumptions Reasonable?

• We have assumed that
• Exchange rate expectations are given
• Prices are given
• It is perhaps reasonable to assume that prices
  are fixed in the short-run, but prices will most
  likely change in the long-run. In that case is
  it reasonable to assume that exchange rate
  expectations will be unchanged

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The Long-Run

• In the long-run money is neutral an x change in
  money supply will cause an x change in prices,
  but no change in output
• Thus in the long-run prices will adjust not the
  interest rate to bring the money market back into
  equilibrium
• To see this consider our money market equilibrium
  condition Ms PL(i,y). If Ms changes by x but
  so does P then money market equilibrium is
  restored

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Exchange Rate Expectations

• If in the long run prices adjust not the interest
  rate, what are the implications for the exchange
  rate?
• The implication would be that in the long-run
  monetary policy has no impact on the exchange
  rate
• However one thing that we have not considered is
  what happens to exchange rate expectations

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Purchasing Power Parity

• In order to understand how these expectations
  will change, we need some sort of understanding
  of what determines the exchange rate over a
  longer horizon
• Something we will study next lecture is called
  purchasing power parity. This says that the
  domestic price level, and therefore monetary
  policy, influences the long-run behavior of the
  exchange rate

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Implications of PPP

• PPP tells us that if the price level rises, the
  exchange rate will depreciate
• To see this consider the implications of a
  currency reform. Suppose the Argentine
  government replaced its current peso with new
  pesos, worth twice as much as the old peso, what
  will happen to the peso/ exchange rate?
• It will decrease by 50, that is the peso will
  appreciate by 100, while prices in Argentina, in
  terms of the new peso, will decline by 50

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Monetary Policy and Long-Run Expectations

• Hence an expansionary (contractionary) monetary
  policy that raises (lowers) the price level in
  the long-run will ultimately lead to a
  depreciation (appreciation) of the currency
• But this should mean that future expectations
  regarding the exchange rate will change
  accordingly. If an expansionary monetary policy
  is permanent we would expect e to be higher in
  the future and a contractionary policy means we
  will expect e to be lower

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Illustration of Long-Run Scenario
Hence the equilibrium exchange rate rises
/
But expectations change
e21.05
e11.00
i110
Interest rate
Money supply M1s/P
In the long-run the equilibrium interest rate
does not change
real money balances
Money demand L(i,y)
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Exchange Rate Overshooting in the Short-Run

• Our analysis of the short-run supposed that
  expectations were given. But this is not the
  case
• Once we allow for the fact that exchange rate
  expectations change, then it should be apparent
  that exchange rates will overshoot past there
  long-run positions. This is easy to see
  graphically

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Illustration of Exchange Rate Overshooting
Hence the exchange rate overshoots
e3
/
But the exchange rate does not rest here
e2
e4
expectations change
In the long-run the exch. rate falls
e1
i1
i2
Interest rate
Money supply M1s/P
Money supply M2s/P
In the short-run money supply increases and the
equilibrium interest rate falls
real money balances
Money demand L(i,y)
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Why Does the Exchange Rate Overshoot?

• Expansionary monetary policy implies US interest
  rates fall. The new equilibrium exchange rate
  consistent with interest rate parity is e2. This
  assumes that expectations are fixed
• But in the long run prices will increase
  (assuming that the shift in policy is permanent).
  Since higher prices imply that the dollar will
  depreciate in the long run, expectations must
  change

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Why Does the Exchange Rate Overshoot?

• As expectations change, the expected return on
  foreign assets rises (because of the expected
  appreciation in the foreign currency)
• Thus e2 can no longer be consistent with UCIP and
  the exchange rate must overshoot to e3
• In the long-run prices will increase (real money
  falls) and the equilibrium interest rate returns
  to i1. As this happens the economy moves to
  point e4