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The Money Supply, Interest Rates, and the Exchange Rate

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

Antu Panini Murshid

Today’s Agenda

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

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

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

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

Square-Root Formula

- The Baumol-Tobin model predicts that the demand for money will be positively related to a household’s 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

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

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 wrong…Keynes was actually referring to shifts in households’ liquidity preferences in response to shifts in expectations regarding future developments in financial markets

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%

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

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

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 + traveler’s checks
- M2 (broad money) = M1 + savings deposits + small time deposits + …

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

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

Money Market Equilibrium

Ms

interest

rate

- 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

e

i*

excess demand

for money

a

i1

Md

real money balances

Money Market Equilibrium

Ms

interest

rate

- 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

excess supply

of money

b

i2

e

i*

excess demand

for money

a

i1

Md

real money balances

Money Market Equilibrium

Ms

interest

rate

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

excess supply

of money

b

i2

e

i*

Md

real money balances

Expansionary Monetary Policy in the Short Run

M2s

M1s

interest

rate

- 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

e1

i*

e2

i2

Md

real money balances

Expansionary Monetary Policy in the Short Run

M1s

M1s

interest

rate

- 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*

e1

i1

e2*

i2*

e2

i2

M2d

M1d

real money balances

Contractionary Monetary Policy in the Short Run

M2s

M1s

interest

rate

- 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

e2

i2

e1

i*

Md

real money balances

Contractionary Monetary Policy in the Short Run

M2s

M1s

interest

rate

- 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

e2

i2

e2*

i2*

e1

i*

M1d

real money balances

M2d

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)

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

Example

- Suppose i=10%, if=5%, et=1 and E(et)=1.05
- Note that UCIP holds, i.e. i=if+E(%De)
- Now if i↓ to 5%, i≠if+E(%De)
- However if et↑ to 1.05 then E(%De)=0%, hence UCIP is restored

First lets draw the money market graph

The equilibrium interest rate is 10%

Graphical IllustrationMoney supply M1s/P

Interest rate

Equilibrium interest rate

i1=10%

Money demand L(i,y)

real money balances

Now lets make everything disappear….Graphical Illustration

Money supply M1s/P

Interest rate

Equilibrium interest rate

i1=10%

Money demand L(i,y)

real money balances

…and reappear but rotated clockwise by 90 degreesGraphical Illustration

i1=10%

Interest rate

Money supply M1s/P

Equilibrium interest rate

real money balances

Money demand L(i,y)

Now lets add the foreign exchange market graphGraphical Illustration

return on

$ assets

$/€

Expected return on € assets

e1=1.00

i1=10%

Interest rate

Money supply M1s/P

Equilibrium interest rate

real money balances

Money demand L(i,y)

Now suppose the government raises money supplyGraphical Illustration

Equilibrium exchange rate↑

return on

$ assets

$/€

Expected return on € assets

e2=1.05

e1=1.00

i2=5%

i1=10%

Interest rate

Money supply M1s/P

Money supply M2s/P

Equilibrium interest rate

Equilibrium interest rate ↓

real money balances

Money demand L(i,y)

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

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 Mschanges by x% but so does P then money market equilibrium is restored

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

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

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%

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

Illustration of Long-Run Scenario

Hence the equilibrium exchange rate rises

$/€

But expectations change

e2=1.05

e1=1.00

i1=10%

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)

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…

Illustration of Exchange Rate Overshooting

Hence the exchange rate overshoots

e3

$/€

But the exchange rate does not rest here

e2

e4

In the long-run the exch. rate falls

expectations change

e1

i2

i1

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)

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

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

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