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Monetary Approach to Exchange Rates

Rajesh Singh

Feb 13, 2018

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 1 / 17

Forecasting exchange rates — in levels

Money market equilibrium

PUS =MUS

LUS YUS

PPP

E$/euro =PUSPEU

Relative PPP∆E$/euro

E$/euro= πUS − πEU

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 2 / 17

Forecasting exchange rates — in levels

Money market equilibrium

PUS =MUS

LUS YUS

PPP

E$/euro =PUSPEU

Relative PPP∆E$/euro

E$/euro= πUS − πEU

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 2 / 17

Forecasting exchange rates — in levels

Money market equilibrium

PUS =MUS

LUS YUS

PPP

E$/euro =PUSPEU

Relative PPP∆E$/euro

E$/euro= πUS − πEU

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 2 / 17

Forecasting exchange rates — in levels

Feb 4 exercise —MUS rises by 5% all else equal. PUS rises

⇒ E$/euro rises by 5%, i.e., dollar depreciates.More US money chasing the same amount of goods, prices riseFor foreigners US goods become expensive if US dollar also does notbecome cheaperPPP forces the dollar to depreciate

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 3 / 17

Forecasting exchange rates — in levels

Feb 4 exercise —MUS rises by 5% all else equal. PUS rises

⇒ E$/euro rises by 5%, i.e., dollar depreciates.

More US money chasing the same amount of goods, prices riseFor foreigners US goods become expensive if US dollar also does notbecome cheaperPPP forces the dollar to depreciate

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 3 / 17

Forecasting exchange rates — in levels

Feb 4 exercise —MUS rises by 5% all else equal. PUS rises

⇒ E$/euro rises by 5%, i.e., dollar depreciates.More US money chasing the same amount of goods, prices rise

For foreigners US goods become expensive if US dollar also does notbecome cheaperPPP forces the dollar to depreciate

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 3 / 17

Forecasting exchange rates — in levels

Feb 4 exercise —MUS rises by 5% all else equal. PUS rises

⇒ E$/euro rises by 5%, i.e., dollar depreciates.More US money chasing the same amount of goods, prices riseFor foreigners US goods become expensive if US dollar also does notbecome cheaper

PPP forces the dollar to depreciate

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 3 / 17

Forecasting exchange rates — in levels

Feb 4 exercise —MUS rises by 5% all else equal. PUS rises

⇒ E$/euro rises by 5%, i.e., dollar depreciates.More US money chasing the same amount of goods, prices riseFor foreigners US goods become expensive if US dollar also does notbecome cheaperPPP forces the dollar to depreciate

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 3 / 17

Forecasting exchange rates — in growth rates

The U.S. money supply grows at a steady fixed rate 2%. Then, attime T Fed announces that a new rate 5%

Money supply M is growing at a constant rate:

MP= LY

Real money balances M/P remain constant, as before.

The price level P and money supply M must move in the sameproportion:

πUS = µUS

Then∆E$/euro

E$/euro= πUS − πEU = πUS

Note here that M grows over time, but does not jump at any time.Therefore, prices and exchange rates are also not supposed to jump.

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 4 / 17

Forecasting exchange rates — in growth rates

The U.S. money supply grows at a steady fixed rate 2%. Then, attime T Fed announces that a new rate 5%

Money supply M is growing at a constant rate:

MP= LY

Real money balances M/P remain constant, as before.

The price level P and money supply M must move in the sameproportion:

πUS = µUS

Then∆E$/euro

E$/euro= πUS − πEU = πUS

Note here that M grows over time, but does not jump at any time.Therefore, prices and exchange rates are also not supposed to jump.

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 4 / 17

Forecasting exchange rates — in growth rates

The U.S. money supply grows at a steady fixed rate 2%. Then, attime T Fed announces that a new rate 5%

Money supply M is growing at a constant rate:

MP= LY

Real money balances M/P remain constant, as before.

The price level P and money supply M must move in the sameproportion:

πUS = µUS

Then∆E$/euro

E$/euro= πUS − πEU = πUS

Note here that M grows over time, but does not jump at any time.Therefore, prices and exchange rates are also not supposed to jump.

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 4 / 17

Forecasting exchange rates — in growth rates

The U.S. money supply grows at a steady fixed rate 2%. Then, attime T Fed announces that a new rate 5%

Money supply M is growing at a constant rate:

MP= LY

Real money balances M/P remain constant, as before.

The price level P and money supply M must move in the sameproportion:

πUS = µUS

Then∆E$/euro

E$/euro= πUS − πEU = πUS

Note here that M grows over time, but does not jump at any time.Therefore, prices and exchange rates are also not supposed to jump.

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 4 / 17

Forecasting exchange rates — in growth rates

The U.S. money supply grows at a steady fixed rate 2%. Then, attime T Fed announces that a new rate 5%

Money supply M is growing at a constant rate:

MP= LY

Real money balances M/P remain constant, as before.

The price level P and money supply M must move in the sameproportion:

πUS = µUS

Then∆E$/euro

E$/euro= πUS − πEU = πUS

Note here that M grows over time, but does not jump at any time.Therefore, prices and exchange rates are also not supposed to jump.

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 4 / 17

Forecasting exchange rates — in growth rates

The U.S. money supply grows at a steady fixed rate 2%. Then, attime T Fed announces that a new rate 5%

Money supply M is growing at a constant rate:

MP= LY

Real money balances M/P remain constant, as before.

The price level P and money supply M must move in the sameproportion:

πUS = µUS

Then∆E$/euro

E$/euro= πUS − πEU = πUS

Note here that M grows over time, but does not jump at any time.Therefore, prices and exchange rates are also not supposed to jump.

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 4 / 17

Interest-elastic money demand

MP = LY assumes that the demand for money is independent ofinterest rates in the economy.

This is problematic

A general model allows for money demand to vary with the nominalinterest rate.

Let i be the nominal interest rate.

MP= L (i)Y

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 5 / 17

Interest-elastic money demand

MP = LY assumes that the demand for money is independent ofinterest rates in the economy.

This is problematic

A general model allows for money demand to vary with the nominalinterest rate.

Let i be the nominal interest rate.

MP= L (i)Y

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 5 / 17

Interest-elastic money demand

MP = LY assumes that the demand for money is independent ofinterest rates in the economy.

This is problematic

A general model allows for money demand to vary with the nominalinterest rate.

Let i be the nominal interest rate.

MP= L (i)Y

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 5 / 17

Interest-elastic money demand

MP = LY assumes that the demand for money is independent ofinterest rates in the economy.

This is problematic

A general model allows for money demand to vary with the nominalinterest rate.

Let i be the nominal interest rate.

MP= L (i)Y

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 5 / 17

UIP, PPP, and Fisher effect

UIP

i$ = iEU +E e$/eu − E$/eu

E$/eu, or

E e$/eu − E$/eu

E$/eu= i$ − iEU

Relative PPP — in expectations

E e$/eu − E$/eu

E$/eu= πeUS − πeEU

If both holdi$ − iEU = πeUS − πeEU

Fisher effect: a country with relatively higher expected inflation willhave a higher nominal interest rate

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 6 / 17

UIP, PPP, and Fisher effect

UIP

i$ = iEU +E e$/eu − E$/eu

E$/eu, or

E e$/eu − E$/eu

E$/eu= i$ − iEU

Relative PPP — in expectations

E e$/eu − E$/eu

E$/eu= πeUS − πeEU

If both holdi$ − iEU = πeUS − πeEU

Fisher effect: a country with relatively higher expected inflation willhave a higher nominal interest rate

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 6 / 17

UIP, PPP, and Fisher effect

UIP

i$ = iEU +E e$/eu − E$/eu

E$/eu, or

E e$/eu − E$/eu

E$/eu= i$ − iEU

Relative PPP — in expectations

E e$/eu − E$/eu

E$/eu= πeUS − πeEU

If both holdi$ − iEU = πeUS − πeEU

Fisher effect: a country with relatively higher expected inflation willhave a higher nominal interest rate

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 6 / 17

UIP, PPP, and Fisher effect

UIP

i$ = iEU +E e$/eu − E$/eu

E$/eu, or

E e$/eu − E$/eu

E$/eu= i$ − iEU

Relative PPP — in expectations

E e$/eu − E$/eu

E$/eu= πeUS − πeEU

If both holdi$ − iEU = πeUS − πeEU

Fisher effect: a country with relatively higher expected inflation willhave a higher nominal interest rate

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 6 / 17

Fisher effect and real interest rate

Fisher effecti$ − iEU = πeUS − πeEU

Question 1:iEU = i$ − (πeUS − πeEU )

Rearrangei$ − πeUS = iEU − πeEU = r

e

Real interest rate must be the same across countries

Question 2:r e = 1%

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 7 / 17

Fisher effect and real interest rate

Fisher effecti$ − iEU = πeUS − πeEU

Question 1:iEU = i$ − (πeUS − πeEU )

Rearrangei$ − πeUS = iEU − πeEU = r

e

Real interest rate must be the same across countries

Question 2:r e = 1%

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 7 / 17

Fisher effect and real interest rate

Fisher effecti$ − iEU = πeUS − πeEU

Question 1:iEU = i$ − (πeUS − πeEU )

Rearrangei$ − πeUS = iEU − πeEU = r

e

Real interest rate must be the same across countries

Question 2:r e = 1%

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 7 / 17

Fisher effect and real interest rate

Fisher effecti$ − iEU = πeUS − πeEU

Question 1:iEU = i$ − (πeUS − πeEU )

Rearrangei$ − πeUS = iEU − πeEU = r

e

Real interest rate must be the same across countries

Question 2:r e = 1%

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 7 / 17

Fisher effect and real interest rate

Fisher effecti$ − iEU = πeUS − πeEU

Question 1:iEU = i$ − (πeUS − πeEU )

Rearrangei$ − πeUS = iEU − πeEU = r

e

Real interest rate must be the same across countries

Question 2:r e = 1%

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 7 / 17

Money growth and exchange rates

Question 3πeUS = µUS = 5%

Question 4:iUS − πUS = r

e

US interest rate rises by 5%

Question 5MP= L (i)Y

Higher i (by 5%)

⇒ MP must drop, i.e., people want to hold less money since interest

rate has risenBut money supply M has not changed at all, only µ has changed.Fall in the money demand in equilibrium raises price levelExchange rate jumps on impact

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 8 / 17

Money growth and exchange rates

Question 3πeUS = µUS = 5%

Question 4:iUS − πUS = r

e

US interest rate rises by 5%

Question 5MP= L (i)Y

Higher i (by 5%)

⇒ MP must drop, i.e., people want to hold less money since interest

rate has risenBut money supply M has not changed at all, only µ has changed.Fall in the money demand in equilibrium raises price levelExchange rate jumps on impact

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 8 / 17

Money growth and exchange rates

Question 3πeUS = µUS = 5%

Question 4:iUS − πUS = r

e

US interest rate rises by 5%

Question 5MP= L (i)Y

Higher i (by 5%)

⇒ MP must drop, i.e., people want to hold less money since interest

rate has risenBut money supply M has not changed at all, only µ has changed.Fall in the money demand in equilibrium raises price levelExchange rate jumps on impact

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 8 / 17

Money growth and exchange rates

Question 3πeUS = µUS = 5%

Question 4:iUS − πUS = r

e

US interest rate rises by 5%

Question 5MP= L (i)Y

Higher i (by 5%)

⇒ MP must drop, i.e., people want to hold less money since interest

rate has risenBut money supply M has not changed at all, only µ has changed.Fall in the money demand in equilibrium raises price levelExchange rate jumps on impact

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 8 / 17

Money growth and exchange rates

Question 3πeUS = µUS = 5%

Question 4:iUS − πUS = r

e

US interest rate rises by 5%

Question 5MP= L (i)Y

Higher i (by 5%)

⇒ MP must drop, i.e., people want to hold less money since interest

rate has risenBut money supply M has not changed at all, only µ has changed.Fall in the money demand in equilibrium raises price levelExchange rate jumps on impact

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 8 / 17

Money growth and exchange rates

Question 3πeUS = µUS = 5%

Question 4:iUS − πUS = r

e

US interest rate rises by 5%

Question 5MP= L (i)Y

Higher i (by 5%)

⇒ MP must drop, i.e., people want to hold less money since interest

rate has risen

But money supply M has not changed at all, only µ has changed.Fall in the money demand in equilibrium raises price levelExchange rate jumps on impact

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 8 / 17

Money growth and exchange rates

Question 3πeUS = µUS = 5%

Question 4:iUS − πUS = r

e

US interest rate rises by 5%

Question 5MP= L (i)Y

Higher i (by 5%)

⇒ MP must drop, i.e., people want to hold less money since interest

rate has risenBut money supply M has not changed at all, only µ has changed.

Fall in the money demand in equilibrium raises price levelExchange rate jumps on impact

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 8 / 17

Money growth and exchange rates

Question 3πeUS = µUS = 5%

Question 4:iUS − πUS = r

e

US interest rate rises by 5%

Question 5MP= L (i)Y

Higher i (by 5%)

⇒ MP must drop, i.e., people want to hold less money since interest

rate has risenBut money supply M has not changed at all, only µ has changed.Fall in the money demand in equilibrium raises price level

Exchange rate jumps on impact

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 8 / 17

Money growth and exchange rates

Question 3πeUS = µUS = 5%

Question 4:iUS − πUS = r

e

US interest rate rises by 5%

Question 5MP= L (i)Y

Higher i (by 5%)

⇒ MP must drop, i.e., people want to hold less money since interest

rate has risenBut money supply M has not changed at all, only µ has changed.Fall in the money demand in equilibrium raises price levelExchange rate jumps on impact

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 8 / 17

A permanent rise in money supply

Consider a one time 5% increase in money supply —permanently

Long run Money market equilibrium

MP= L (i)Y

What happens to interest rate?

After everything settles down, there is no inflationinterest rate will remain the same

If output has not changed MP has to remain constant

Then in the long run P must rise by the same % as the money supply.

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 9 / 17

A permanent rise in money supply

Consider a one time 5% increase in money supply —permanently

Long run Money market equilibrium

MP= L (i)Y

What happens to interest rate?

After everything settles down, there is no inflationinterest rate will remain the same

If output has not changed MP has to remain constant

Then in the long run P must rise by the same % as the money supply.

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 9 / 17

A permanent rise in money supply

Consider a one time 5% increase in money supply —permanently

Long run Money market equilibrium

MP= L (i)Y

What happens to interest rate?

After everything settles down, there is no inflationinterest rate will remain the same

If output has not changed MP has to remain constant

Then in the long run P must rise by the same % as the money supply.

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 9 / 17

A permanent rise in money supply

Consider a one time 5% increase in money supply —permanently

Long run Money market equilibrium

MP= L (i)Y

What happens to interest rate?

After everything settles down, there is no inflation

interest rate will remain the same

If output has not changed MP has to remain constant

Then in the long run P must rise by the same % as the money supply.

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 9 / 17

A permanent rise in money supply

Consider a one time 5% increase in money supply —permanently

Long run Money market equilibrium

MP= L (i)Y

What happens to interest rate?

After everything settles down, there is no inflationinterest rate will remain the same

If output has not changed MP has to remain constant

Then in the long run P must rise by the same % as the money supply.

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 9 / 17

A permanent rise in money supply

Consider a one time 5% increase in money supply —permanently

Long run Money market equilibrium

MP= L (i)Y

What happens to interest rate?

After everything settles down, there is no inflationinterest rate will remain the same

If output has not changed MP has to remain constant

Then in the long run P must rise by the same % as the money supply.

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 9 / 17

A permanent rise in money supply

Consider a one time 5% increase in money supply —permanently

Long run Money market equilibrium

MP= L (i)Y

What happens to interest rate?

After everything settles down, there is no inflationinterest rate will remain the same

If output has not changed MP has to remain constant

Then in the long run P must rise by the same % as the money supply.

Rajesh Singh () Econ 457 — Spring 2018 Feb 13, 2018 9 / 17