Monetary Approach to Exchange Rates

Rajesh Singh

Feb 6, 2018

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 1 / 20

Absolute and relative PPP

Absolute

E$/euro =PUSPEU

Relative PPP4E$/euro

E$/euro= πUS − πEU

The question is: How are price levels determined?

We need a theory of price level

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 2 / 20

Absolute and relative PPP

Absolute

E$/euro =PUSPEU

Relative PPP4E$/euro

E$/euro= πUS − πEU

The question is: How are price levels determined?

We need a theory of price level

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 2 / 20

Absolute and relative PPP

Absolute

E$/euro =PUSPEU

Relative PPP4E$/euro

E$/euro= πUS − πEU

The question is: How are price levels determined?

We need a theory of price level

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 2 / 20

Absolute and relative PPP

Absolute

E$/euro =PUSPEU

Relative PPP4E$/euro

E$/euro= πUS − πEU

The question is: How are price levels determined?

We need a theory of price level

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 2 / 20

Money, output, and inflation

The need to conduct transactions is in proportion to an individual’sincome.

Assume that the aggregate money demand will behave similarly.A rise in national dollar income (nominal income)

will cause a proportional increase in transactions andin aggregate money demand.

A simple model in which the demand for money is proportional todollar income is known as the quantity theory of money

Md = L PY

Supply of Money —by the central bank (Federal reserve system): MMoney market equilibrium Md = M determines price level

P =ML Y

In the long run, we assume prices are flexible and will adjust to putthe money market in equilibrium.

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 3 / 20

Money, output, and inflation

The need to conduct transactions is in proportion to an individual’sincome.Assume that the aggregate money demand will behave similarly.

A rise in national dollar income (nominal income)

will cause a proportional increase in transactions andin aggregate money demand.

A simple model in which the demand for money is proportional todollar income is known as the quantity theory of money

Md = L PY

Supply of Money —by the central bank (Federal reserve system): MMoney market equilibrium Md = M determines price level

P =ML Y

In the long run, we assume prices are flexible and will adjust to putthe money market in equilibrium.

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 3 / 20

Money, output, and inflation

The need to conduct transactions is in proportion to an individual’sincome.Assume that the aggregate money demand will behave similarly.A rise in national dollar income (nominal income)

will cause a proportional increase in transactions andin aggregate money demand.

A simple model in which the demand for money is proportional todollar income is known as the quantity theory of money

Md = L PY

Supply of Money —by the central bank (Federal reserve system): MMoney market equilibrium Md = M determines price level

P =ML Y

In the long run, we assume prices are flexible and will adjust to putthe money market in equilibrium.

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 3 / 20

Money, output, and inflation

The need to conduct transactions is in proportion to an individual’sincome.Assume that the aggregate money demand will behave similarly.A rise in national dollar income (nominal income)

will cause a proportional increase in transactions and

in aggregate money demand.

A simple model in which the demand for money is proportional todollar income is known as the quantity theory of money

Md = L PY

Supply of Money —by the central bank (Federal reserve system): MMoney market equilibrium Md = M determines price level

P =ML Y

In the long run, we assume prices are flexible and will adjust to putthe money market in equilibrium.

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 3 / 20

Money, output, and inflation

The need to conduct transactions is in proportion to an individual’sincome.Assume that the aggregate money demand will behave similarly.A rise in national dollar income (nominal income)

will cause a proportional increase in transactions andin aggregate money demand.

A simple model in which the demand for money is proportional todollar income is known as the quantity theory of money

Md = L PY

Supply of Money —by the central bank (Federal reserve system): MMoney market equilibrium Md = M determines price level

P =ML Y

In the long run, we assume prices are flexible and will adjust to putthe money market in equilibrium.

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 3 / 20

Money, output, and inflation

The need to conduct transactions is in proportion to an individual’sincome.Assume that the aggregate money demand will behave similarly.A rise in national dollar income (nominal income)

will cause a proportional increase in transactions andin aggregate money demand.

A simple model in which the demand for money is proportional todollar income is known as the quantity theory of money

Md = L PY

Supply of Money —by the central bank (Federal reserve system): MMoney market equilibrium Md = M determines price level

P =ML Y

In the long run, we assume prices are flexible and will adjust to putthe money market in equilibrium.

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 3 / 20

Money, output, and inflation

The need to conduct transactions is in proportion to an individual’sincome.Assume that the aggregate money demand will behave similarly.A rise in national dollar income (nominal income)

will cause a proportional increase in transactions andin aggregate money demand.

A simple model in which the demand for money is proportional todollar income is known as the quantity theory of money

Md = L PY

Supply of Money —by the central bank (Federal reserve system): M

Money market equilibrium Md = M determines price level

P =ML Y

In the long run, we assume prices are flexible and will adjust to putthe money market in equilibrium.

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 3 / 20

Money, output, and inflation

The need to conduct transactions is in proportion to an individual’sincome.Assume that the aggregate money demand will behave similarly.A rise in national dollar income (nominal income)

will cause a proportional increase in transactions andin aggregate money demand.

A simple model in which the demand for money is proportional todollar income is known as the quantity theory of money

Md = L PY

Supply of Money —by the central bank (Federal reserve system): MMoney market equilibrium Md = M determines price level

P =ML Y

In the long run, we assume prices are flexible and will adjust to putthe money market in equilibrium.

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 3 / 20

Money, output, and inflation

The need to conduct transactions is in proportion to an individual’sincome.Assume that the aggregate money demand will behave similarly.A rise in national dollar income (nominal income)

will cause a proportional increase in transactions andin aggregate money demand.

A simple model in which the demand for money is proportional todollar income is known as the quantity theory of money

Md = L PY

Supply of Money —by the central bank (Federal reserve system): MMoney market equilibrium Md = M determines price level

P =ML Y

In the long run, we assume prices are flexible and will adjust to putthe money market in equilibrium.Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 3 / 20

Exchange rate

US price level

PUS =MUS

LUS Y US

EU price level

PEU =MEU

LUS Y EU

Exchange rate

E$/euro =PUSPEU

=MUS

LUS Y US

MEU

LUS Y EU

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 4 / 20

Exchange rate

US price level

PUS =MUS

LUS Y US

EU price level

PEU =MEU

LUS Y EU

Exchange rate

E$/euro =PUSPEU

=MUS

LUS Y US

MEU

LUS Y EU

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 4 / 20

Exchange rate

US price level

PUS =MUS

LUS Y US

EU price level

PEU =MEU

LUS Y EU

Exchange rate

E$/euro =PUSPEU

=MUS

LUS Y US

MEU

LUS Y EU

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 4 / 20

Money, output, and inflation

In the equation P = ML Y , L is a constant.

If M Changes by µ% and Y changes by g%, by how much % does Pchange?

Inflation

π =4PP

=4MM︸ ︷︷ ︸µ

− 4YY︸︷︷︸g

− 4LL︸︷︷︸0

Thus,π = µ− g

Question 1:5− 3 = 2%

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 5 / 20

Money, output, and inflation

In the equation P = ML Y , L is a constant.

If M Changes by µ% and Y changes by g%, by how much % does Pchange?

Inflation

π =4PP

=4MM︸ ︷︷ ︸µ

− 4YY︸︷︷︸g

− 4LL︸︷︷︸0

Thus,π = µ− g

Question 1:5− 3 = 2%

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 5 / 20

Money, output, and inflation

In the equation P = ML Y , L is a constant.

If M Changes by µ% and Y changes by g%, by how much % does Pchange?

Inflation

π =4PP

=4MM︸ ︷︷ ︸µ

− 4YY︸︷︷︸g

− 4LL︸︷︷︸0

Thus,π = µ− g

Question 1:5− 3 = 2%

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 5 / 20

Money, output, and inflation

In the equation P = ML Y , L is a constant.

If M Changes by µ% and Y changes by g%, by how much % does Pchange?

Inflation

π =4PP

=4MM︸ ︷︷ ︸µ

− 4YY︸︷︷︸g

− 4LL︸︷︷︸0

Thus,π = µ− g

Question 1:5− 3 = 2%

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 5 / 20

Money, output, and inflation

In the equation P = ML Y , L is a constant.

If M Changes by µ% and Y changes by g%, by how much % does Pchange?

Inflation

π =4PP

=4MM︸ ︷︷ ︸µ

− 4YY︸︷︷︸g

− 4LL︸︷︷︸0

Thus,π = µ− g

Question 1:5− 3 = 2%

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 5 / 20

Money, output, and inflation, and exchange rates

We already showed that

π =4PP

= µ− g

Exchange rate from PPP

E$/euro =PUSPEU

In PUS changes by x% and PEU changes by y%, we say that E$/eurochanges by (x − y)%. Using their symbolic notation, it means

4E$/euro

E$/euro=4PUSPUS

− 4PEUPEU

= πUS − πEU

= (µUS − gUS )− (µEU − gEU )All else equal, if the United States runs a looser monetary policymeasured by a faster money growth rate, the dollar will depreciatemore rapidlyIf the U.S. economy grows faster in the long run, the dollar willappreciate more rapidlyQuestion 2:µUS = 1.5; µEU = 1; gUS = 3; gEU = 1

(1.5− 1)− (3− 1) = −1.5%

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 6 / 20

Money, output, and inflation, and exchange rates

We already showed that

π =4PP

= µ− g

Exchange rate from PPP

E$/euro =PUSPEU

In PUS changes by x% and PEU changes by y%, we say that E$/eurochanges by (x − y)%. Using their symbolic notation, it means

4E$/euro

E$/euro=4PUSPUS

− 4PEUPEU

= πUS − πEU

= (µUS − gUS )− (µEU − gEU )All else equal, if the United States runs a looser monetary policymeasured by a faster money growth rate, the dollar will depreciatemore rapidlyIf the U.S. economy grows faster in the long run, the dollar willappreciate more rapidlyQuestion 2:µUS = 1.5; µEU = 1; gUS = 3; gEU = 1

(1.5− 1)− (3− 1) = −1.5%

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 6 / 20

Money, output, and inflation, and exchange rates

We already showed that

π =4PP

= µ− g

Exchange rate from PPP

E$/euro =PUSPEU

In PUS changes by x% and PEU changes by y%, we say that E$/eurochanges by (x − y)%. Using their symbolic notation, it means

4E$/euro

E$/euro=4PUSPUS

− 4PEUPEU

= πUS − πEU

= (µUS − gUS )− (µEU − gEU )

All else equal, if the United States runs a looser monetary policymeasured by a faster money growth rate, the dollar will depreciatemore rapidlyIf the U.S. economy grows faster in the long run, the dollar willappreciate more rapidlyQuestion 2:µUS = 1.5; µEU = 1; gUS = 3; gEU = 1

(1.5− 1)− (3− 1) = −1.5%

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 6 / 20

Money, output, and inflation, and exchange rates

We already showed that

π =4PP

= µ− g

Exchange rate from PPP

E$/euro =PUSPEU

In PUS changes by x% and PEU changes by y%, we say that E$/eurochanges by (x − y)%. Using their symbolic notation, it means

4E$/euro

E$/euro=4PUSPUS

− 4PEUPEU

= πUS − πEU

= (µUS − gUS )− (µEU − gEU )All else equal, if the United States runs a looser monetary policymeasured by a faster money growth rate, the dollar will depreciatemore rapidly

If the U.S. economy grows faster in the long run, the dollar willappreciate more rapidlyQuestion 2:µUS = 1.5; µEU = 1; gUS = 3; gEU = 1

(1.5− 1)− (3− 1) = −1.5%

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 6 / 20

Money, output, and inflation, and exchange rates

We already showed that

π =4PP

= µ− g

Exchange rate from PPP

E$/euro =PUSPEU

In PUS changes by x% and PEU changes by y%, we say that E$/eurochanges by (x − y)%. Using their symbolic notation, it means

4E$/euro

E$/euro=4PUSPUS

− 4PEUPEU

= πUS − πEU

= (µUS − gUS )− (µEU − gEU )All else equal, if the United States runs a looser monetary policymeasured by a faster money growth rate, the dollar will depreciatemore rapidlyIf the U.S. economy grows faster in the long run, the dollar willappreciate more rapidly

Question 2:µUS = 1.5; µEU = 1; gUS = 3; gEU = 1

(1.5− 1)− (3− 1) = −1.5%

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 6 / 20

Money, output, and inflation, and exchange rates

We already showed that

π =4PP

= µ− g

Exchange rate from PPP

E$/euro =PUSPEU

In PUS changes by x% and PEU changes by y%, we say that E$/eurochanges by (x − y)%. Using their symbolic notation, it means

4E$/euro

E$/euro=4PUSPUS

− 4PEUPEU

= πUS − πEU

= (µUS − gUS )− (µEU − gEU )All else equal, if the United States runs a looser monetary policymeasured by a faster money growth rate, the dollar will depreciatemore rapidlyIf the U.S. economy grows faster in the long run, the dollar willappreciate more rapidlyQuestion 2:µUS = 1.5; µEU = 1; gUS = 3; gEU = 1

(1.5− 1)− (3− 1) = −1.5%

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 6 / 20

Forecasting exchange rates — in levels

Money market equilibrium

PUS =MUS

LUS YUS

Question 3: PUS rises by 5%. No change in PEU . E$/euro =PUSPEU

alsorises by 5%

Question 4: PUS declines by a factor of 1.05. Falls from Pold toPold/1.05

11.05 − 11

= −0.048%

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 7 / 20

Forecasting exchange rates — in levels

Money market equilibrium

PUS =MUS

LUS YUS

Question 3: PUS rises by 5%. No change in PEU . E$/euro =PUSPEU

alsorises by 5%

Question 4: PUS declines by a factor of 1.05. Falls from Pold toPold/1.05

11.05 − 11

= −0.048%

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 7 / 20

Forecasting exchange rates — in levels

Money market equilibrium

PUS =MUS

LUS YUS

Question 3: PUS rises by 5%. No change in PEU . E$/euro =PUSPEU

alsorises by 5%

Question 4: PUS declines by a factor of 1.05. Falls from Pold toPold/1.05

11.05 − 11

= −0.048%

Rajesh Singh () Econ 457 — Spring 2018 Feb 6, 2018 7 / 20