Econ 141 Fall 2013

Econ 141 Fall 2013Slide Set 4Simple and general models of the monetary approach to the exchange rate.

Money and Exchange Rates – Simple Model

• We first use a simple theory of household money demand that assumes that the transactions demand for money is proportional to an household’s income.• Summing up, aggregate money demand is proportional to national

nominal income. A rise in national nominal income leads to a proportional increase in transactions and, hence, in aggregate money demand.• This is the quantity theory of money:

($) income

NominalconstantA ($)money for

Demand

PYLM d

Demand for money• Dividing the previous equation by P, the price level, we derive the

demand for real money balances:

• Real money balances measure of the purchasing power of the stock of money in terms of goods and services. The demand for real money balances is strictly proportional to real income.

YL

PM d

demandmoney Real

Money Market Equilibrium

• Just set the demand for money equal to the supply of money, M (assumed determined by the central bank). • Nominal money supply equals nominal money demand:

or, equivalently, the real money supply equals real money demand:

M L PY

MP

L Y

A Simple Monetary Model of Prices

• We use money market equilibrium to write expressions for the price levels in the U.S. and Europe as:

• These equations exemplify the monetary model of the price level.

• In the long run, we assume nominal prices are flexible and adjust to maintain money market equilibrium.

PUS MUS

L USYUS

PEUR M EUR

L EURYEUR

A Simple Monetary Model of the Exchange Rate• We substitute the two price equations into the absolute PPP equation

to get an expression for the exchange rate:

• This is the fundamental equation of the monetary approach to exchange rates.

demandsmoney real relativeby divided

suppliesmoney nominal Relativelevels price of Ratiorate Exchange

€/$ //

EUREURUSUS

EURUS

EUREUR

EUR

USUS

US

EUR

US

YLYLMM

YLM

YLM

PPE

Implications of this equation

• Suppose the U.S. money supply increases, all else equal. The right-hand side increases (the U.S. nominal money supply increases relative to Europe), causing the exchange rate to increase (the U.S. dollar depreciates against the euro).

• Now suppose the U.S. real income level increases, all else equal. Then the right-hand side decreases (the U.S. real money demand increases relative to Europe), causing the exchange rate to decrease (the U.S. dollar appreciates against the euro).

EUREURUSUS

EURUS

YLYLMME

//

€/$

Money Growth, Inflation, and Depreciation

• The growth rate of the U.S. money supply is MUS, is μUS

• The growth rate of real income in the U.S. is gUS:

in U.S.growth supply money of Rate

,

,1,,

tUS

tUStUStUS M

MM

in U.S.growth income real of Rate

,

,1,,

tUS

tUStUStUS Y

YYg

• The growth rate of PUS =MUS/LUSYUS equals the money supply growth rate μUS minus the real income growth rate gUS. The growth rate of PUS is the inflation rate πUS. The quantity theory of money in terms of rates is

• European inflation is calculated similarly:

• When money growth is higher than income growth, we have “more money chasing fewer goods” and this leads to inflation.

EUR ,t EUR ,t gEUR ,t

US ,t US ,t gUS ,t


• We can rewrite the fundamental equation of the monetary approach to exchange rates,

in rates of change

and then use our equations for inflation to substitute and get


EUREURUSUS

EURUS

YLYLMME

//

€/$

ratesgrowth

output realin alDifferenti

,,

ratesgrowth supplymoney nominalin alDifferenti

,,

rate exchange nominal theofondepreciati of Rate

,€/$

€/$tEURtUStEURtUS

t

t ggEE

tEURtUStEURtEURtUStUSt

t ggEE

,,,,,,,€/$

€/$

Intuition behind the fundamental equation,

• If the United States runs a looser monetary policy in the long run (measured by a faster money growth rate), the dollar will depreciate more rapidly, all else equal. • If the U.S. economy grows faster in the long run, the dollar will

appreciate more rapidly, all else equal (because inflation will be lower for any given money growth rate).


tEURtUSt

t

EE

,,,€/$

€/$

Applying the Simple Monetary Model

• The monetary model assumes that all prices are flexible and purchasing power parity holds. • It gives us a theory of how exchange rates behave in the long run. • The exchange rate is a nominal concept. If all prices are flexible and

goods markets are integrated (no trade frictions), the exchange will be determined by relative money supplies.• The fundamental equation of the monetary model tells us that the

rate of depreciation equals relative inflation. • If we use the model to predict future exchange rates then we assume

that all prices are flexible and relative PPP holds.

Simple monetary approach: example 1 Suppose that U.S. and European real income growth rates both equal

zero (gUS = gEUR = 0), and that the European price level is constant, so that European inflation is zero. Example 1: Consider a one-time 10% increase in the U.S. money supply. 1. Because prices are flexible and GDP, YUS, is constant, the price level rises by 10% and real money balances MUS/PUS are constant.

2. PPP implies that the exchange rate E rises by 10% because the price level for the U.S. rises relative to the price level for Europe. The dollar depreciates by 10%.

USUSUS

US YLP

M

E

US

PPE €/$

Example 2: Assume the U.S. money supply grows at a fixed rate μ.

1. GDP growth is zero, so the growth rate of real balances M/P is zero.2. The price level P and money supply M must grow at the same rate, μ. Inflation in the U.S. equals μ .

3. The rate of depreciation of the exchange rate is determined by relative PPP as

4. If the European inflation rate is zero, the dollar depreciates at a rate of μ against the euro:

Simple monetary approach: example 2

USUS g

EURUSEE

€/$

€/$

EUR

€/$

€/$

EE

At time T, the United States will raise the rate of money supply growth to a higher rate, μ + Δμ

At T, real balances must continue to stay constant (U.S. and European GDP growth rates are zero). U.S. inflation rises at time T from to

The rate of depreciation of the dollar against the euro also rises from to

US US

€/$

€/$

EE

€/$

€/$

EE

Example 2 continued

The monetary approach: example 2

Evidence for the Monetary Approach

EURUSEE

€/$

€/$

The monetary approach to prices and exchange rates suggests that, all else equal:Increases in the relative rate of inflation should correspond to equal increases in the rate of depreciation for the home currency,

EUREURUSUS ggEE

€/$

€/$

Increases in the relative money supply growth rates should correspond to equal increases in relative inflation and, hence, the rate of exchange rate depreciation for the home country.



Hyperinflations of the Twentieth Century

Hyperinflation and redenomination

• In hyperinflations, currency lose value rapidly and are often replaced by foreign currency (usually, US$). Ecuador is a recent example.• A central bank may redenominate by introducing a new currency unit

equal to 10N old units.• In the 1980s, Argentina suffered hyperinflation. • On June 1, 1983, the peso argentino replaced the peso at a rate of 1 new

per 10,000 old. • On June 14, 1985, the austral replaced the peso argentino again at a rate

of 1 per 1,000 old. • On January 1, 1992, the convertible peso replaced the austral at 1 peso

per 10,000 austral (this was equivalent to 10,000,000,000 of the 1982 pesos).

Redenomination in Brazil

• 1942: The cruzeiro replaced the reis at a rate of 1 per 1000• 1962: The cruzeiro novo replaced the cruzeiro at 1 per 1000• 1986 (March 1): The cruzado replaced the cruzeiro novo at 1 per 1000• In 1990, it was renamed the cruzeiro again, at par.• 1993 (August 1): The cruzeiro real replaced the cruzeiro at 1 per 1000• 1994 (June 30): The real was introduced at 1 real per 2750 cruzeiro

reals.

In Zimbabwe• In 1980, the ZW$ replaced the Rhodesian$ at par• On August 1, 2006, a new dollar was introduced at 1 per 1000 old.• In September 2007, the official exchange rate was ZW$30,000 per 1

US$, but the black market rate was ZW$600,000 per 1 US$.• On August 1, 2008, another new dollar was introduced at 1 per 10

billion old.• On February 2, 2009, a new ZW$ was introduced for 1 trillion old,but Zimbabwe legalized foreign currency use and dollarized.

• Next, we consider a more general model of exchange rates in the long run that allows for money demand to vary with the nominal interest rate.

• The quantity theory of money assumes that the demand for money is stable: L (velocity) was constant.

• A more general theory (Keynesian) allows money demand to depend on the opportunity cost of holding money, the nominal interest rate.

• We first consider the links between inflation and the nominal interest rates in an open economy, and then apply this to how exchange rates are determined in the long run.

The Monetary Approach: Money, Interest Rates and Prices in the Long Run

The Demand for Money: The General Model• All else equal, a rise in national dollar income (nominal income) will

cause a proportional increase in transactions and, hence, in aggregate money demand.

• All else equal, a rise in the nominal interest rate will cause the aggregate demand for money to fall.

Dividing by P, we can derive the demand for real money balances

PYiLM d )(

YiLP

M d

The Demand for Money: The General Model

Long-Run Equilibrium in the Money Market

• We already derived two relationships for the exchange rate. The first is relative PPP which holds if all prices are flexible and goods markets are integrated.• The second is uncovered interest parity (UIP) which holds if there are

no unexploited arbitrage opportunities. In terms of the rate of depreciation of the home currency, these are

aldifferentiinflation Expected

ondepreciati dollar of rate Expected

€/$

€/$ eEUR

eUS

e

EE

rateinterest

euroNet

€

rateinterest dollarNet

$

ondepreciati dollar of rate Expected

€/$

€/$ iiEE e

The Fisher Effect• Putting PPP and UIP together, we get

• That is, the nominal interest differential equals the expected inflation differential:

• This says that, all else equal, a rise in the expected inflation rate in a country will lead to an equal rise in its nominal interest rate.

• This is the Fisher effect. • The Fisher effect predicts that the change in the opportunity cost of

money is equal to the change in the nominal interest rate and to the change in the inflation rate.

(expected)

aldifferenti rateinflation Nominalaldifferenti rateinterest Nominal

€$eEUR

eUSii

Real Interest Parity

• Rearranging the last equation, the Fisher effect is rewritten

• The difference between the nominal interest rate (i) and the expected inflation rate (πe) is the real interest rate (re) (the inflation-adjusted return on an interest-bearing asset).

• We have found that PPP and UIP together imply that

• This result states that if both PPP and UIP hold, then the expected real interest rates are equalized across countries.

• This is called real interest parity.

eEUR

eUS ii €$

rUSe rEUR

e

• This result can be stated as: • Arbitrage in goods and financial markets alone is sufficient to cause the equalization

of real interest rates across countries in the long run.• This implies that, in the long run, all countries will have the same expected real

interest rate. This is the long-run expected world real interest rate denoted r*, and

• We treat r* as a given, exogenous variable, something outside the control of a policy maker in any particular country.

• The Fisher effect tells us that

Real Interest Parity

rUSe rEUR

e r*

.*€

*$

eEUR

eEUR

eEUR

eUS

eUS

eUS rrirri

Evidence on the Fisher effect

Evidence for Real Interest Parity

1970197119721973197419751976197719781979198019811982198319841985198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

-15

-10

-5

0

5

10

15

Real Interest Differential (Annual % relative to US)

United Kingdom Germany Canada France

This graph shows the differences between the real interest rate and the U.S. real interest rate using monthly data for 1970 through 2012. These are calculated by subtracting average core CPI inflation for the past year from the current 3-month nominal rate.

Real interest rate convergence

1970197119721973197419751976197719781979198019811982198319841985198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012

-20

-15

-10

-5

0

5

10

15

Real Interest Rates, 1970-2012

United Kingdom Germany United States

These are the real interest rates for the U.S., U.K. and Germany used in the previous graph. (The differences between U.S. and U.K. rates reflects differences in inflation rates.)

The Fundamental Equation under the General Model

• This model differs from the simple model (the quantity theory) only by allowing L to vary as a function of the nominal interest rate i.

• Only when nominal interest rates change does the general model have different implications than the simple model.

demandsmoney real Relativeby divided

suppliesmoney nominal Relative

€$

€

$

levels price of Ratiorate Exchange

€/$ )(/)(/

)(

)(

EUREURUSUS

EURUS

EUREUR

EUR

USUS

US

EUR

US

YiLYiLMM

YiLM

YiLM

PPE

Implications of the general model

• Reconsider what happens when the U.S. money supply growth increases from μ to a higher rate μ + Δμ.• For constant GDP growth rates, money supply growth and inflation

are related by

• The Fisher effect tells us that

• When the U.S. money growth rises, the U.S. inflation rate rises by Δμ and the U.S. nominal interest rate rises by Δμ.

EURUSEURUS

eEUR

eUS ii €$

• Real money demand declines when the nominal interest rate rises by Δμ:

vs• When the money growth rate rises, real money balances must fall

even though the money stock changes continuously. • The price level must immediately jump up because at the instant this

happens, M is given and M/P falls.


YiLP

M d

YiLP

M d

An increase in the money supply growth rate for the general model of money demand


• After the growth rate of money supply rises by Δμ at time T, the inflation rate is higher by Δμ. • Relative PPP

tells us that the rate of depreciation of the dollar also rises by Δμ.• The equation for the exchange rate

shows that E$/€ depreciates suddenly at T.


EURUSEE

€/$

€/$

EUREUR

EUR

USUS

US

EUR

US

YiLM

YiLM

PPE

)(

)(

€

$€/$

In this example, the growth rate of the U.S. money is raised from μ to μ+Δμ

The General Monetary Approach: Example 2 again

Exchange Rates and Monetary Policy RegimesThe nominal anchor • The central bank needs a long-run monetary policy objective. • In the long run, real interest rates, real GDP growth rates and real

exchange rates are independent of monetary policy.• The long-run relationship between the rate of depreciation of nominal

exchange rates, inflation rates and money supply growth rates is given by two equations:

• The exchange rate target, money supply target, and Inflation target are the three primary choices for a nominal target.

USBrazilUSBrazilUSBrazilReals

eReals gg

EE

$/

$/

Relative PPP says that home inflation equals the rate of depreciation plus foreign inflation.

A simple exchange rate rule is to set the rate of depreciation equal to a constant.

Choosing the desired long-run rate of depreciation implies that foreign (US) inflation rate anchors home (Brazilian) monetary policy.

Exchange rate target

USReals

eReals

Brazil EE

$/

$/

Money supply target

• A simple money supply rule is for the central bank to set the growth rate of the money supply equal to a constant, for example, 2% per year.

• The inflation rate will be given by

• A drawback of a money growth rate target is that real income growth fluctuates over the adjustment to the long run. With a fixed money supply growth rate, inflation and the rate of nominal exchange rate depreciation fluctuate with real income growth.

BrazilBrazilBrazil g

Inflation target under interest rate policy

Choosing a target rate of inflation sets the desired rate of depreciation given foreign (U.S.) inflation.

It allows the money supply growth rate to vary with real income growth.

The Fisher effect tells us how inflation depends on the international real rate of interest.

USBrazilReals

eReals

EE

$/

$/

BrazilBrazilBrazil g

eBrazilBrazil ri *

Exchange rate regimes and nominal anchorsCountries without a currency of their own

Fixed or Crawling Pegs or Bands

Managed Floating

Freely Floating

Freely falling (rapid depreciation)

Exchange Rate Target X X X

Money Supply Target X X

Inflation Target X X

No anchor X X

Nominal Anchors from Theory to Policy

• In the 1970s, inflation rates were high in most countries of the world. Inflations continued in the 1980s, even as the U.S. undertook aggressive disinflationary policies. • In the 1990s, central banks paid attention to the need to establish

working nominal anchors and designed policies to achieve more stable inflation. • Most, but not all, of those policies have turned out to be credible.

Some of this success is due to political acceptance of central-bank independence.

Monetary policy reform and outcomes

This chart shows the global disinflation

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Econ 141 Fall 2013