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Purchasing Power ParityMonetary Approach to Flexible Exchange Rates (MAFER)

Slides for International FinancePurchasing Power Parity

Alan G. Isaac

American University

2012-09-20

Alan G. Isaac Slides for International Finance


Introductory ConceptsAbsolute vs. Relative

Preview

Purchasing power parityCommodity price parityAbsolute PPP vs. Relative PPP

Classical model of price determinationLR neutrality of moneyFisher effectmagnification effect

Monetary approach to flexible exchange ratesExchange rates in the long run

Real exchange rate determinationPPP shortcomingsnominal vs. real shocks




Law of One Price

Law of One Price (LOP): identical goods have identical prices.ensured by arbitrage (given low transactions costs)

Commodity Price Parity (CPP): the international LOP.

Pi = EP∗i




Economic Laws

Economic “laws” are just points of reference:

not like physical laws

violations expected

violations stimulate investigation




Commodity Price Parity (CPP)

Example: - Two fast-food restaurants: one in New York, and oneacross the border in Montréal. - assume markets are competitive andthat transportation costs and barriers between markets are notimportant.

PUSburger = (0.95USD/CAD) × PCA

burger

where PUSburger = price of burger in New York, PCA

burger = price of burgerin Montréal, and 0.95 USD/CAD is the CAD-USD exchange rate.CPP applies the law of one price: the price of the same burger (usinga common currency to measure the price) in the two cities must be thesame.




CPP Example

On 30 September 2010

1oz of gold sold in New York for USD 13071 oz also sold in London for GBP 830.One GBP sold in both locations for about USD 1.575.

Gold satisfies CPP: 1307 = 1.575 * 830




CPP Example (cont.)

On 17 October 2011

1oz of gold sold in New York for USD 1783.001 oz also sold in London for GBP 1069.326One GBP sold in both locations for about USD 1.5795.

Gold satisfies CPP: 1689 = 1.5795 * 1069.326




CPP Example (cont.)

On 22 February 2012

1oz of gold sold in New York for USD 17801 oz also sold in London for GBP 1135.820One GBP sold in both locations for about USD 1.56715

Gold satisfies CPP: 1135.820 = 1780.00 / 1.56715




Exchange Rate Models: SR vs. LR

Models predict how exchange rates behave.

SR model: “Keynesian“ story about moneymoney � interest rates � exchange rate

LR model: “Classical” story about moneymoney � prices � exchange ratemoney growth � inflation � depreciation




“Long-Run” Models

Meaning of LR:

model specifichere: essentially the simplest “Classical“ model

all prices adjust; all markets in equilibriumgood, services, factors of production

Purpose of LR models

predict future tendencies

anchor LR expectations

do not describe SR exchange rate behavior




Real Exchange Rate

The real exchange rate (q):

the rate of exchange of goods and services across countries.the relative price of goods and services across countries.the price of foreign goods and services in terms of domesticgoods and services:

q = EP∗/P

EP∗ = domestic currency price of foreign goodsP = domestic currency price of domestic goods




Real Exchange Rate Depreciation (^q)

q = EP∗/P

real depreciation:

a rise in qforeign commodities cost more in terms of domesticcommodities

Example: a real depreciation of the USD

US products buy fewer foreign productsour ability to trade off US goods for EU goods declines




Real Exchange Rate Appreciation (_q)

q = EP∗/P

real appreciation: a fall in qforeign commodities cost less in terms of domestic commodities

Example: a real appreciation of the USD

US products buy more foreign productsour ability to trade off US goods for EU goods improves




Purchasing Power Parity (PPP)

Core PPP idea:

real exchange rate (q) is constantexchange rate movements match relative price movements




Absolute Purchasing Power Parity

the application of the law of one price across countries for“baskets” of goods and services.

average price levels determine the exchange rate.

the domestic currency has the same purchasing power in allcountries

P = EP∗

P = level of domestic prices (e.g., US)P∗ = level of foreign prices (e.g., CA)E = exchange rate (e.g., CAD-USD 0.95)




Absolute Purchasing Power Parity (Absolute PPP)

Absolute purchasing power parity: E = P/P*

Example:

P = USD 300 per basketP* = EUR 200 per basketabsolute PPPE = P/P* = USD 300/EUR 200 = 1.5 USD/EUR(the EUR-USD exchange rate is 1.5)1.5 USD buys the same amount of goods as 1 EURtherefore 1.5 USD buys 1 EUR




Two Forms of PPP

Absolute PPP: E = P/P*Exchange rates equal the level of relative average prices acrosscountries.

Relative PPP: E = q P / P*Exchange rates are proportional to the level of relative averageprices across countries

Both: exchange rate changes (depreciation) match changes in prices(inflation) between two periods:

Et −Et−1

Et−1= πt −π

∗t

where πt = inflation rate from period t-1 to t.




Two Forms of PPP

Relative PPP: E = q P / P*q relatively constant

Absolute PPP: E = P / P*q = 1

Conditions for absolute PPP:

CPP for every commodityidentical index-basket construction

Absolute PPP is essentially the LOP for price indices.




Depreciation and Inflation Differentials (82 Countries)

Source: http://www.worthpublishers.com/html/staticcontent/nonstandard/include/0716792834/MacroCH14.pdf


http://www.worthpublishers.com/html/staticcontent/nonstandard/include/0716792834/MacroCH14.pdf




Introductory ConceptsLR Real Exchange Rate

Monetary Approach to Flexible Exchange Rates (MAFER)

MAFER Assumptions:

PPP (absolute or relative)

Classical model of price determination

The monetary approach uses monetary factors to predict howexchange rates adjust in the long run.




Classical Model of Price Determination

Money market in equilibriumM/P = L(R,Y)

Prices flexible and move to clear money marketP = M / L(R,Y)

implication: inflation driven by money growth

P = M− L




Money Growth and Inflation




Classical Model of Price Determination

prices are flexible

prices adjust so that the real money supply (M/P) equals realmoney demand (L)P = M / L(R, Y)P* = M* / L(R*, Y*)P/P* = (M/M*) / (L/L*)




MAFER Predictions

positive money supply shock:

^P and ^E proportionallyR does not change

positive output shock:

_P and _E roughly proportionallyR does not change

We need to explore these predicitons.Modifications of the model will modify these predictions.




M Shock: Compare and Contrast

SR model:

“sticky” prices^M � ^M/P^M � exchange rate overshootingSR movement > LR movement

MAFER:

“flexible” prices^M � ^P proportionally: M/P unchanged^M � ^E proportionally: no overshootingneutrality of money (even in SR!)no real changesSR movement = LR movement (but it’s just a LR model)




New Experment: Change in Growth of M

Suppose that the U.S. central bank unexpectedly increases thegrowth rate of the money supply at time t0 by 5% per year.

The inflation rate rises by 5% per yearπnew = π +Δπ = π +5%




Fisher Effect

Fisher Effect: ^ πe � ^ RImplication: a sustained rise in inflation eventually causes anequal ^R

According to the Fisher effect, if expected inflation rises by 5%, theinterest rate will also rise 5%.




Irving Fisher (1867–1947)

1888 BA from Yale

1891 First Yale PhD in Econ

17 Oct 1929 Most famous pre-diction: “Stock prices havereached what looks like apermanently high plateau.”(Recall that 28 and 29 Oct1929 were “Black Monday”and “Black Tuesday”: NYSEshare prices collapse)

1930 The Theory of Interest




MAFER Predictions

positive money growth rate shock:

P and E: inflation and depreciation increase in step^R (in step with inflation; the Fisher effect)P and E: initial jump (magnification effect)




Permanent Increase in Domestic Money Growth

M

M0

t0 t0time time

M

Note: M is measured on a ratio scale. Compare KOM 9 Fig 16-1




^M Growth � ^P Growth

M

M0

t0 t0time time

P






M R

M0

t0 t0

R1

R1 +Δπ

time time





Effect on the Money Market

^ M � ^ πe

^ πe - ^ R

^R � _L

^R�^P

the increase in nominal interest rates decreases the demand for realmonetary assets. for the money market to be in equilibrium at the newR, the price level must rise so that

P = M/L(R,Y )




MAFER and ^Money Growth

Higher M growth raises inflation and expected inflation, andtherefore R.^R � _L (lower demand for real monetary assets)For money market equilibrium at ^R, we must see ^P so that

P = M / L(R, Y)

_L � _M/P via ^P^P�^E: in order to maintain PPP, the exchange rate must rise(the dollar must depreciate) proportionately so that

E = q P / P*

Thereafter, M and P rise faster by Δπ , as does E (the direct rate).In order to maintain PPP, the domestic currency continue to depreciateproportionately.

E = q P / P*





P E

P0

t0 t0

E0

time time

Note: P and E are measured on a ratio scale. Compare KOM 9 Fig 16-1





Source: KOM 9 Fig 16-1




Permanent ^M Growth (MAFER)

Permanent ^M growth causes permanent ^P growth

the domestic currency must depreciate when domestic inflationexceeds foreign inflation (by PPP)

Furthermore:

↑ π →↑ πe→↑ R→↓ L→↑ P,E

Persistent domestic inflation increases expected inflation.

Higher expected inflation causes a rise in the domestic nominalinterest rate (by the Fisher effect).

Higher R reduces desired real balances.

Therefore, there is a magnification effect on P and E.




Magnification Effect

Sustained higher money growth �

sustained higher inflation

sustained higher depreciation

Fisher effect:

R = Rreal +πe

Magnification effect:

^ inflation � ^R^R � _L � _M/PP must move more than M




^M Growth: Impact (t0) Effect (MAFER)

E1

Q

L(R,Y1)

Q1

R10 returns

R∗+ Ee1

ESR

R1 +Δπ

Q2

R∗+ Ee2

Note: Compare KOM 9 Figure 16A-1Alan G. Isaac Slides for International Finance



Impact (t0) Effect of ^M Growth (MAFER: Goods Prices AreFlexible)

Source: KOM 9 Figure 16A-1




Inflation in Zaire

1

10

100

1000

10000

100000

1e+006

1e+007

1e+008

1e+009

01/90 01/91 01/92 01/93 01/94 01/95 01/96

Mon

ey, P

rice

s, a

nd E

xcha

nge

Rat

es: 0

1/90

= 1

Exchange RateCPI

Currency




Money Growth and Depreciation (82 Countries)

Source: http://www.worthpublishers.com/html/staticcontent/nonstandard/include/0716792834/MacroCH14.pdfData Source: IFS Alan G. Isaac Slides for International Finance






Some 20th Century Hyperinflations

Source: http://www.worthpublishers.com/html/staticcontent/nonstandard/include/0716792834/MacroCH14.pdfData Source: Cagan (1956); Petrovic and Mladenovic (2000 JMCB)Alan G. Isaac Slides for International Finance






Shortcomings of PPP

Little empirical support for absolute PPP.The prices of identical commodity baskets, when converted to asingle currency, differ substantially across countries.

Relative PPP is more consistent with data, but it also poorlypredicts exchange rates in the short run.




The Yen/Dollar Exchange Rate and Relative Japan-U.S.Price Levels, 1980–2009

Source: KOM 9 Fig 16-2 Data Source: IMF, International FinancialStatistics. End-of-year data.




GBP-USD Exchange Rate and Relative Price Levels

Source: http://www.worthpublishers.com/html/staticcontent/nonstandard/include/0716792834/MacroCH14.pdf







Deviations from PPP

PPP may not hold due toviolations of the law of one price

Trade barriersnon-tradable productsImperfect competition

divergent price index construction (different baskets of goods andservices)




Deviations from PPP: Barriers to Trade

Barriers to frictionless trade are the most fundamental source of PPPdeviations:Trade barriers and non-tradable products � one price need not hold intwo markets.

Transport costs

governmental trade restrictionsnon-tradeable goods

some services are not readily tradable (classic example, haircuts).

The greater the barriers to trade, the greater the possibledeviation from PPP.




Deviations from PPP: Imperfect Competition

If markets can be segmented, imperfect competition may result inprice discrimination.

pricing to market: a firm sells the same product for different prices indifferent markets to maximize profitsprice depends on the elasticity of demand in each market




Deviations from PPP: Measurement

Price index construction differs across countries

differences in how representative groups (“baskets”) of goods andservices are measured.

differences in the “weights” given various goods and services




Computing Big Mac PPP

Data

E: current exchange rate (direct rate; domestic terms)P: local priceP*: US price

Computations:

Eppp = P/P*overvaluation = Eppp/E -1

Alternative Computations:

q = EP*/Povervaluation = 1/q - 1

Logarithmic approximation:

overvaluation = -log(q)Since ln(1+ x)≈ x , you can get a rough approximation of overvaluation as − log(q). (This works best when q is near 1.)




Switzerland (CHF) Example:

Data:

E = 1.05P = 6.50P* = 3.73

Computations:

Eppp = P/P* = 6.50/3.73 = 1.75overvaluation = (Eppp/E -1) = (1.75/1.05 - 1) = 66%


q = EP*/P = 1.05 * 3.73 / 6.50 = 0.602overvaluation = 1/q - 1 = 1/0.602 - 1 = 66%


overvaluation = -ln(q) = -ln(0.602) = 0.51




China (CNY) 2010 Example:

Data:

E = 6.78P = 13.2Pus = 3.73

Computations:

Eppp = P/P* = 13.2/3.73 = 3.55overvaluation = (Eppp/E -1) = (3.55/6.78 - 1) = -48%


q = EP*/P = 6.78 * 3.73 / 13.2 = 1.92overvaluation = 1/q - 1 = 1/1.92 - 1 = -48%


overvaluation = -ln(q) = -ln(1.92) = -65%




China (CNY) 2012 Example:

Data:

E = 6.32P = 15.4Pus = 4.20

Computations:

Eppp = P/P* = 15.4/4.20 = 3.67overvaluation = (Eppp/E -1) = (3.67/6.32 - 1) = -42%




Law of One Price for Hamburgers?

UA

HLK

RH

KD

CN

YTH

BPH

PM

YR

EG

PR

UB

TW

DZ

AR

PK

RM

XN

IDR

PLN

EEK

SA

RLT

LLV

LK

RW

AED

SG

DH

UF

CLP

CZ

KG

BP

PEN

AR

SN

ZD

JPY

UYU

CR

CA

UD

ILS

TR

YC

AD

EU

RC

OP

DK

KB

RL

CH

FSEK

NO

K

-100

-50

0

50

100

Perc

enta

ge O

verv

alu

ati

on

Data Source: http://www.economist.com/node/16646178?story_id=16646178


http://www.economist.com/node/16646178?story_id=16646178

http://www.economist.com/node/16646178?story_id=16646178



Law of One Price for Hamburgers?

Data: http://bigmacindex.org


http://bigmacindex.org



Penn Effect

Naive GDP comparison: relative GDP = E GDP* / GDP

Penn effect: naive comparisons systematically exaggerate real percapita income ratios between poor and rich

Empirics Penn studies of Kravis-Heston-Summersreal-income estimates, using actual local prices and incomes

Theory Balassa (1964) and Samuelson (1964)Also: David Ricardo and Roy Harrod




Paul Samuelson (1915-2009)

1941 PhD from Harvard

1947 Foundations of EconomicAnalysis

1948 Economics: An Introduc-tory Analysis

1970 “Nobel” prize

1973 famous prediction (in histextbook): the Soviet Unionwill catch up to the UnitedStates in per capita incomeby 1990


http://econ-www.mit.edu/faculty/samuelson



Balassa-Samuelson Critique

Price indices contain traded and nontraded goodsP = f (Pt ,Pnt)

Shifts in relative price can disrupt PPPRicardo (1817): high manufacturing productivity� costlynontraded goodsSamuelson (1964)

disparate postwar growth ratesincome growth correlated with traded goods productivity

Dollar should look overvalued against low growth countries

even if Pt = EP∗t




Price Levels and Real Incomes, 2004

Source: KOM Figure 16-3 (Data Source: Penn World Table, Mark 6.2)




Price Levels and Real Incomes, 2007




Endogenous LR Real Exchange Rate

PPP (absolute or relative) = a constant real exchange rate

E = q P / P* (with q constant)� nominal exchange rate movements are determinedby movements in relative price level:

A more general story tries to explain changes in the real exchangerate.Movements in nominal exchange rate then have two sources:

E = q+ (P/P∗)




Determination of the Long-Run Real Exchange Rate

Relative demand depends on relative prices (i.e., on prices orexchange rates), but relative output does not.

LR output (Y and Y*) depends onfactors of productiontechnology.

LR demand (AD and AD*) depends on:the relative price of foreign products (q=EP*/P)Relative prices determine the demand for domestic productsrelative to foreign products.when the real exchange rate depreciates, the relativedemand for domestic commodities rises.

Equilibrium:Y/Y* = AD/AD*relative supply matches the relative demand (so there is notendency for the relative price to change).




Determination of the Long-Run Real Exchange Rate

q

q1

Y/Y ∗ relative output

RS RD

Note: compare KOM 9 Fig 16-4




Demand Shocks and LRRER

Situation: an increase in relative demand for domestic products

(^Ex or _Im) � _qa real appreciation of the domestic currencythis is a rise in the price of domestic goods (P) relative to the priceof foreign goods (EP*)

real appreciation makes our exports more expensive and ourimports less expensive� _ relative demand� restoring equilibrium




Demand Shocks and LRRER

q

q1

Y/Y ∗ relative output

RS RD

RD’

q2




Supply Shocks and LR RER

Situation: an increase in relative supply of domestic US products

(^Y or _Y*) � ^qa real depreciation of the domestic currencythis is a rise in the price of foreign goods (EP*) relative to the priceof domestic goods (P)

real depreciation makes our exports less expensive and ourimports more expensive� ^ relative demand� restoring equilibrium




Supply Shocks and LRRER

q

q1

Y1/Y ∗ relative output

RS’ RDRS

q2

Y2/Y ∗




The LR RER (Summary)

Endogenizing the real exchange rate

produces a more general model of exchange ratedetermination

The monetary approach still applies:

increases in monetary levels leading to price level increases.increases in monetary growth rates lead to persistentinflation (and corresponding changes in expectations).

But now real factors also matter:

increases in relative demand for domestic products leads toa real appreciation.increases in relative supply of domestic products leads to areal depreciation.




Nominal Exchange Rate Determination Redux

How does this change our theory of nominal exchange ratedetermination?

E = q P / P*

Monetary shocksPPP still holdswe have the same predictions as before.no changes in the real exchange rate

Real demand shocksthe real exchange rate changes (^AD � _q)the nominal exchange rate adjusts to produce theequilibrium real exchange rate

Real output shocksthe real exchange rate changes (^Y � ^q)the nominal exchange rate situation is more complex. . .




The Real Exchange Rate Approach to Exchange Rates(cont.)

With an increase in the relative supply of domestic products, thereal exchange rate adjusts to make the price/cost of domesticgoods depreciate, but also the relative amount of domestic outputincreases. - This second effect increases the demand of realmonetary assets in the domestic economy:

P = M / L(R,Y)

Thus level of average domestic prices is predicted to decreaserelative to the level of average foreign prices.The effect on the nominal exchange rate is ambiguous:

E = q P / P*




LR Model Summary: Effects of Money Market and OutputMarket Changes on E

^ M � proportional ^E

^ M* � proportional _E

^ AD � _ E

^ AD* � ^ E

^ Y � ? E

^ Y* � ? ECompare KOM 9 Table 16-1




Real Interest Rates

Real interest rate: inflation-adjusted interest ratemeasured in terms of real output

savers can buy more goods and services when their assetspay real interestborrows can buy fewer goods and services when they mustpay real interest on their borrowing

Ex ante real interest rate: expected real interest rate

re = R−πe

Here πe = expected inflation rate and R= nominal interest rate.




Interest Rate Differences

Anticipated changes in q show up as a real interest differential:

q = EP∗/P =⇒ qe−qq

=Ee−E

E+π

∗e−πe

R−R∗ =Ee−E

E=⇒ qe−q

q= (R−R∗)+π

∗e−πe

= (R−πe)− (R∗−π

∗e)

R−R∗ is the sum of:The expected rate of real depreciation (i.e., of the value ofdomestic goods relative to foreign goods)The inflation differential between the domestic economy and theforeign economy




Real Interest Parity

Real interest rate differentials (across countries) must equal expectedchanges in the real exchange rate.

(R−πe)− (R∗−π

∗e) = (qe−q)/q

re− r∗e = (qe−q)/q

RIP says that the real interest rate differential between countriesequals to the expected change in the relative price of goods andservices between countries.




Expected PPP

If financial markets expect (absolute or relative) PPP to hold, thenexpected exchange rate changes will equal expected inflation betweencountries:

q = EP∗/P =⇒ qe−qq

=Ee−E

E+π

∗e−πe

(qe−q)/q = 0 =⇒ 0 =Ee−E

E+π

∗e−πe

=⇒ Ee−EE

= πe−π

∗e




Expected PPP and Real Interest Parity

If financial markets expect (absolute or relative) PPP to hold, thenexpected exchange rate changes will equal expected inflation betweencountries:

real interest parity: (R−πe)− (R∗−π∗e) = (qe−q)/q

expected PPP: (qe−q)/q = 0

real interest rate equality: R−πe = R∗−π∗e

We also get an international version of the Fisher effect.

R−R∗ = πe−π

∗e




Interest Differentials and Inflation Differential (62 Countries)

Source: http://www.worthpublishers.com/html/staticcontent/nonstandard/include/0716792834/MacroCH14.pdfData Source: IFS Alan G. Isaac Slides for International Finance






Real Interest Parity? (3 Month Tbills and Core Inflation)

Source: World Economic Outlook, 2010-04, Figure 1.8




Summary

The law of one price: the same good in different competitive marketsmust sell for the same price(Assume: transportation costs and barriers between markets arenot important.)

Purchasing power parity: the law of one price for price indexes

Absolute PPP: changing currencies does not change yourpurchasing power.

Relative PPP the nominal exchange rate moves withrelative price levels




Summary (cont.)

monetary approach to flexible exchange rates:

assumes PPP and the Classical theory of pricesChanges in the growth rate of the money supply influenceinflation and exchange rates.Expectations about inflation influence the exchange rate.The Fisher effect shows that differences in nominal interestrates are equal to differences in inflation rates.

Empirical support for PPP: weak.Trade barriers, non-tradable products, imperfect competition anddifferences in price measures may cause the empiricalshortcomings of PPP.




Summary: Real Interest Parity

Real interest rate: inflation-adjusted interest rate(how much purchasing power savers gain and borrowers giveup)

Real interest parity: real interest rate differential equals expectedrate of real exchange rate depreciation




Summary (cont.)

real exchange rate: the domestic product cost of foreign products.

real exchange rate approach to exchange rates:

generalizes the monetary approach (allows PPP violations)predicts that changes in relative demand and relative supplyof products influence real and nominal exchange rates.allows deviations from real interest parity(Real interest rate differences now equal the expectedchange in the real exchange rate)


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