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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