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International Monetary Economics

Lecture 5: Exchange Rates and Prices in the Long Run

Master d’Affaires Publiques SciencesPo Spring 2013

Pierre-Olivier Gourinchas

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§  Introduction •  The Law of One Price •  Purchasing Power Parity

§  A Long-Run Exchange Rate Model Based on PPP §  Empirical Evidence on the Law of One Price and PPP §  Explaining Problems with PPP §  Beyond Purchasing Power Parity: A General Model of Long-

Run Exchange Rates §  International Interest Rate Differences and the Real Exchange

Rate: Real Interest Rate Parity §  Summary

Roadmap

3

Introduction

§  The model of long-run exchange rate behavior provides the framework that actors in asset markets use to forecast future exchange rates.

§  Predictions about long-run movements in exchange rates are

important even in the short run. §  In the long run, national price levels play a key role in determining

both interest rates and the relative prices at which countries’ products are traded.

§  The theory of purchasing power parity (PPP) explains movements

in the exchange rate between two countries’ currencies by changes in the countries’ price levels.

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The Law of One Price §  Law of one price

•  Identical goods sold in different countries must sell for the same price when their prices are expressed in terms of the same currency.

•  It implies that the dollar price of good i is the same wherever it is sold: PiUS = E$/€ x PiE

where: PiUS is the dollar price of good i when sold in the U.S. PiE is the corresponding euro price in Europe E$/€ is the dollar/euro exchange rate

•  Equivalently, we can solve for the dollar/euro exchange rate: E$/€ = PiUS / PiE

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Purchasing Power Parity §  Theory of (Absolute) Purchasing Power Parity (PPP)

•  The exchange rate between two countries’ currencies equals the ratio of the countries’ price levels.

•  It compares average prices across countries. •  It predicts a dollar/euro exchange rate of:

E$/€ = PUS/PE where:

PUS is the dollar price of a reference commodity basket sold in the United States

PE is the euro price of the same basket in Europe

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§  The Relationship Between PPP and the Law of One Price •  The law of one price applies to individual commodities, while PPP

applies to the general price level. •  If the law of one price holds true for every commodity, PPP must hold

automatically for the same reference baskets across countries. •  Validity of PPP does not require the law of one price to hold exactly.

Purchasing Power Parity

7

Empirical Evidence on PPP and the Law of One Price

Figure 5-1: The Yen/Dollar Exchange Rate and Relative Japan/US Price Levels, 1980-2006

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§ Absolute PPP and Relative PPP •  Absolute PPP

–  It states that exchange rates equal relative price levels. •  Relative PPP

–  It states that the percentage change in the exchange rate between two currencies over any period equals the difference between the percentage changes in national price levels.

– Relative PPP between the United States and Europe would be:

(E$/€,t - E$/€,t-1)/E$/€,t-1 = πUS,t - πE,t Where πt is the inflation rate.

Purchasing Power Parity

9

§ Monetary approach to the exchange rate •  A theory of how exchange rates and monetary factors

interact in the long run. •  Factors that do not influence money supply or money

demand play no explicit role. •  This is a long run theory of the exchange rate, since it does

not allow for price rigidity.

A Long-Run Exchange Rate Model Based on PPP

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§  The Quantity Theory of Money and exchange rates •  Recall that real liquidity demand depends only upon output

–  In the United States: PUS = MsUS/ (kYUS)

–  In Europe: PE = MsE/ (k YE)

•  Combining:


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•  Use PPP to solve for the exchange rate:

E$/€ = (MsUS/ MsE) . (YE/ YUS) •  The monetary approach makes a number of specific

predictions about the long-run effects on the exchange rate of changes in:

– Money supplies

– Output levels


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Figure 5-2(a): Relative Money Growth and Depreciation (against USD), OECD, 1970-1998

Money, the Price Level, and the Exchange Rate in the Long Run

USA

DEU

SWE

DNKBELAUTJPN

NORCAN

CHENTL

FINAUSIRLGBR

NZL ESP

PRTGRE

ISL

-.1

-.05

0

.05

.1

.15

.2

depr

ecia

tion

rate

, 197

0-98

0 .05 .1 .15 .2relative money growth, 1970-98

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Figure 5-2(b): Relative Output Growth and Depreciation (against USD), OECD, 1970-1998

Money, the Price Level, and the Exchange Rate in the Long Run

CHE

SWE

DNK

NZLGBR

FRA

GRE

BEL

ITL

DEUNTLAUT

FINESP

USACANAUS

JPN

PRT

NOR

ISL

LUX

IRL

-.1

-.05

0

.05

.1

.15

.2

depr

ecia

tion

rate

, 197

0-98

-.02 -.01 0 .01 .02relative output growth, 1970-98

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§ Ongoing Inflation, Interest Parity, and PPP •  Money supply growth at a constant rate eventually results in

ongoing inflation (i.e., continuing rise in the price level) at the same rate.

•  The nominal interest rate is not independent of the money

supply growth rate in the long run. •  The Fisher Effect:

it = rt + πe


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Figure 5-3: Inflation and Interest Rates in Switzerland, the United States, and Italy, 1970-2000


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•  Combine (relative) PPP with UIP: (ETe

- Et)/Et = πe - πe*

it = it* + (ETe

- Et)/Et

•  To obtain: it - it* = πe

- πe* The international interest rate difference is the difference between expected national inflation rates.


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§ Comparing the effect of a permanent increase in the level and growth rate of the money supply: •  A permanent increase in the money supply (level):

•  A permanent increase in the growth rate of money supply when prices are flexible

•  One needs to be careful about the underlying factors that cause interest rates to move.


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§ Slope = π + Δπ

§ t0

§ MUS, t0

§ Slope = π

§ (a) U.S. money supply, MUS

§ Time

§ Slope = π § Slope = π

§ R$1

Figure 5-4: Long-Run Time Paths of U.S. Economic Variables after a Permanent Increase in the Growth Rate of the U.S. Money Supply

§ (d) Dollar/euro exchange rate, E$/€

§ Time

§ (b) Dollar interest rate, i$

§ Time § (c) U.S. price level, PUS

§ Time


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§  The empirical support for the law of one price is weak in recent data. •  The prices of identical goods, when converted to a single

currency, differ substantially across countries.

Empirical Evidence on the Law of One Price

regular 25oz sparkling water, Perrier

Slide 5-24

Figure 5-5: The Border Effect; Gopinath, Gourinchas, Hsieh (11)

Canada

US

Oregon Washington

Median price, cost and markup border discontinuity And exchange rate

Empirical Evidence on the Law of One Price

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§  The Big-Mac index. •  Compiles the price of a “well-known item” •  Evidence of large deviations from LOP, even for a

relatively homogenous consumer good.



Figure 5-6: Mc Currencies (January 2013)

The Big Mac IndexActual dollar Under(-)/over(+)

Implied PPP exchange rate valuation againstCountry in local currency in dollars of the dollar Jan-13 the dollar (%)Argentina 19.00 3.82 4.35 4.98 -12.58Australia 4.70 4.90 1.08 0.96 12.21Brazil 11.25 5.64 2.58 1.99 29.22Britain 2.69 4.25 0.62 0.63 -2.73Canada 5.41 5.39 1.24 1.00 23.51Chile 2,050 4.35 469 472 -0.50China 16.00 2.57 3.66 6.22 -41.10

Big Mac Prices

Euro area 3.59 4.88 0.82 0.74 11.69Hong Kong 17.00 2.19 3.89 7.76 -49.83Hungary 830 3.82 190 217 -12.61India 89.00 1.67 20.38 53.40 -61.83Indonesia 27,939 2.86 6,397 9,768 -34.51Israel 14.90 4.00 3.41 3.72 -8.40Japan 320 3.51 73.27 91.07 -19.54Mexico 37.00 2.90 8.47 12.74 -33.49New Zealand 5.20 4.32 1.19 1.20 -0.98Norway 43.00 7.84 9.85 5.48 79.56Pakistan 290 2.97 66.40 97.67 -32.01Peru 10.00 3.91 2.29 2.56 -10.54Philippines 118 2.91 27.02 40.60 -33.45Poland 9.10 2.94 2.08 3.09 -32.61Russia 72.88 2.43 16.69 30.05 -44.46Saudi Arabia 11.00 2.93 2.52 3.75 -32.84Singapore 4.50 3.64 1.03 1.23 -16.56South Africa 18.33 2.03 4.20 9.05 -53.61South Korea 3,700 3.41 847 1,085 -21.95Sri Lanka 350 2.77 80.14 126 -36.62Sweden 48.40 7.62 11.08 6.35 74.54Switzerland 6.50 7.12 1.49 0.91 63.14United States 4.37 4.37 1.00 1.00 0.00

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§  PPP in the Short Run and in the Long Run •  Departures from PPP are greater in the short- run than in the

long run. •  Over time, arbitrage mechanism kicks in. •  But it takes a good deal of time (between 2 and 5 years) for

PPP deviations to disappear.

Explaining the Problems with PPP

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§  The failure of the empirical evidence to support the PPP and the law of one price is related to:

Explaining the Problems with PPP

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§  How to compare income levels in different countries? •  If price levels differ, a given nominal income does not buy the same

amount of goods. •  Suppose:

PPP and Income Comparisons

Cars Food Income

P Q P Q

US $10,000 1 $10,000 1 $20,000

Russia R60,000 1/15 R8,000 1 R12,000

•  E = R4/USD. At current exchange rate, YR =

•  Alternative: use PPP numbers. Use the US prices to compute the $ budget necessary to achieve the Russian basket of goods. YRPPP =

Gross national income per capita 2010, Atlas method and PPPPurchasing

Atlas power paritymethodology (international

Ranking Economy (US dollars) Ranking Economy dollars)

1 Monaco 197,460 a 4 Luxembourg 63,8502 Liechtenstein 136,540 a 6 Macao SAR, China 57,120 a

3 Bermuda .. a 8 Norway 57,1304 Norway 85,380 10 Singapore 54,7005 Qatar .. a 14 Switzerland 49,1806 Luxembourg 79,510 15 Brunei Darussalam 48,760 a

7 Switzerland 70,350 17 Hong Kong SAR, China 47,3008 Cayman Islands .. a 18 United States 47,0209 Isle of Man .. a 23 Netherlands 42,590

10 Denmark 58,980 25 Denmark 40,14011 Channel Islands .. a 26 Sweden 39,60012 United Arab Emirates .. a 27 Austria 39,41013 Kuwait .. a 28 Australia 38,510 a

14 Sweden 49,930 29 Germany 38,17015 Netherlands 49,720 30 Belgium 37,84016 San Marino 50,670 a 31 Canada 37,280 a

17 Finland 47,170 32 Finland 37,18018 United States 47,140 33 United Kingdom 36,58019 Austria 46,710 35 Japan 34,79020 Faeroe Islands .. a 36 Bahrain 33,530 a

21 Belgium 45,420 37 France 34,44022 Andorra 41,130 a 39 Ireland 32,74023 Australia 43,740 a 41 Spain 31,55024 Germany 43,330 43 Italy 31,09026 France 42,390 44 Cyprus 30,160 a, b

27 Canada 41,950 a 48 Korea, Rep. 29,01028 Japan 42,150 52 Iceland 28,63029 Ireland 40,990 53 New Zealand 28,050 a

30 Singapore 40,920 54 Israel 27,80031 Macao SAR, China 39,520 a 55 Greece 27,36032 United Kingdom 38,540 56 Slovenia 26,97035 Italy 35,090 57 Oman 24,410 a

36 Iceland 33,870 58 Portugal 24,71037 Hong Kong SAR, China 32,900 59 Saudi Arabia 23,900 a

38 Spain 31,650 60 Trinidad and Tobago 24,000 c

39 Brunei Darussalam 31,180 a 61 Equatorial Guinea 23,81040 Cyprus 30,460 a, b 62 Czech Republic 23,62041 New Zealand 29,050 a 63 Malta 23,070 a

43 Israel 27,340 65 Slovak Republic 23,14044 Greece 27,240 67 Seychelles 20,470 c

45 Greenland 26,150 a 68 Estonia 19,50047 Slovenia 23,860 69 Hungary 19,28048 Bahrain 25,420 a 70 Russian Federation 19,19049 Portugal 21,860 71 Poland 19,02056 Korea, Rep. 19,890 72 Croatia 18,71058 Oman 17,890 a 73 Lithuania 17,88059 Malta 18,350 a 74 Libya 16,330 a, c

60 Czech Republic 17,870 75 Latvia 16,36061 Saudi Arabia 17,200 a 76 Antigua and Barbuda 15,380 c

62 Slovak Republic 16,220 77 Argentina 15,15064 Trinidad and Tobago 15,380 78 Mexico 15,01065 Equatorial Guinea 14,680 79 Turkey 14,58066 Estonia 14,360 80 Malaysia 14,36067 Croatia 13,760 81 Lebanon 14,17069 Hungary 12,990 82 Romania 14,05070 Poland 12,420 83 Belarus 14,02071 Libya 12,020 a 84 Botswana 13,91072 Latvia 11,620 85 Chile 13,89073 Venezuela, RB 11,590 85 Uruguay 13,89074 Lithuania 11,400 87 Mauritius 13,67075 Antigua and Barbuda 10,610 88 Bulgaria 13,21076 Uruguay 10,590 89 Gabon 13,19077 St. Kitts and Nevis 9,980 90 St. Kitts and Nevis 13,170 c

78 Chile 9,940 91 Panama 12,940 c

World Development Indicators database, World Bank, 1 July 2011 1

Slide 5-35

PPP and Income Comparisons Figure 5-7: PPP adjusted incomes (World Bank), 2010

Gross national income per capita 2010, Atlas method and PPPPurchasing

Atlas power paritymethodology (international

Ranking Economy (US dollars) Ranking Economy dollars)

79 Russian Federation 9,910 92 Montenegro 12,71080 Turkey 9,500 93 Venezuela, RB 11,95081 Seychelles 9,490 94 Iran, Islamic Rep. 11,420 a

82 Brazil 9,390 95 Serbia 11,23083 Mexico 9,330 96 Brazil 10,92084 Lebanon 9,020 97 Costa Rica 10,880 c

85 Argentina 8,450 98 Macedonia, FYR 10,83086 Malaysia 7,900 99 Palau 10,760 c

87 Romania 7,840 101 Kazakhstan 10,61088 Gabon 7,760 102 South Africa 10,28089 Mauritius 7,740 104 Ecuador 9,27090 Kazakhstan 7,440 105 Azerbaijan 9,22092 Panama 6,990 106 Colombia 9,00093 Botswana 6,890 107 Bosnia and Herzegovina 8,97094 Montenegro 6,690 108 Peru 8,94095 Costa Rica 6,580 109 Albania 8,84096 Palau 6,460 110 Dominican Republic 8,700 c

97 Bulgaria 6,240 111 Dominica 8,580 c

98 South Africa 6,100 112 St. Lucia 8,520 c

99 Belarus 6,030 113 St. Vincent and the Grenadines 8,260 c

100 Suriname 5,920 a 114 Thailand 8,240101 Serbia 5,820 115 Tunisia 8,140102 Cuba 5,550 a 116 Algeria 8,130 c

103 Grenada 5,560 117 Suriname 7,610 a, c

104 Colombia 5,510 118 China 7,570105 Azerbaijan 5,180 119 Grenada 7,560 c

106 St. Lucia 4,970 120 Jamaica 7,430 c

107 Dominica 4,960 121 Turkmenistan 7,160 c

108 Dominican Republic 4,860 123 Namibia 6,580109 St. Vincent and the Grenadines 4,850 123 Ukraine 6,580110 Bosnia and Herzegovina 4,790 125 El Salvador 6,390 c

111 Jamaica 4,750 126 Belize 5,970 c

112 Peru 4,710 127 Egypt, Arab Rep. 5,910113 Namibia 4,650 128 Jordan 5,770114 Iran, Islamic Rep. 4,530 a 130 Maldives 5,480116 Macedonia, FYR 4,520 131 Armenia 5,450117 Ecuador 4,510 132 Angola 5,430118 Algeria 4,460 132 Paraguay 5,430119 Jordan 4,350 134 Bhutan 5,070120 Maldives 4,270 134 Sri Lanka 5,070121 China 4,260 136 Georgia 4,980 d

122 Thailand 4,210 137 Swaziland 4,890123 Tunisia 4,070 138 Syrian Arab Republic 4,870124 Albania 4,000 140 Tonga 4,630 c

125 Angola 3,960 141 Guatemala 4,610 c

126 Belize 3,740 142 Bolivia 4,560127 Turkmenistan 3,700 142 Morocco 4,560 e

128 Fiji 3,610 144 Fiji 4,490129 Tonga 3,380 145 Vanuatu 4,450 c

130 El Salvador 3,360 147 Indonesia 4,300131 Kosovo 3,300 147 Samoa 4,300 c

132 Guyana 3,270 149 Philippines 3,930133 Cape Verde 3,160 150 Honduras 3,730 c

134 Armenia 3,090 151 Mongolia 3,700135 Ukraine 3,010 152 Cape Verde 3,670136 Marshall Islands 2,990 153 India 3,560137 Paraguay 2,940 154 Guyana 3,530 c

138 Samoa 2,930 155 Kiribati 3,510 c

140 Morocco 2,850 e 156 Micronesia, Fed. Sts. 3,420 c

141 Vanuatu 2,760 157 Moldova 3,340 f

142 Guatemala 2,740 158 Iraq 3,320143 Georgia 2,700 d 159 Congo, Rep. 3,280143 Micronesia, Fed. Sts. 2,700 160 Uzbekistan 3,090 c

145 Syrian Arab Republic 2,640 162 Vietnam 2,910

World Development Indicators database, World Bank, 1 July 2011 2

Slide 5-36

PPP and Income Comparisons, 2010

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§  International Differences in Price Levels •  Government measures of the price level differ from country

to country because people living in different countries spend their income in different ways.

•  Striking regularity: price levels are lower in poor countries

Why Price Levels are Lower in Poorer Countries

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Figure 5-8: Price Levels and Real Incomes, 2004

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§  The Samuelson and Balassa effect (1964) •  Poor countries are less productive in tradable goods than rich countries

(cars, computers…) •  Productivity differences are negligible in the nontradable sector

(services: haircuts, nanny…), •  If tradable goods satisfy the Law of One Price (LOP),

–  Lower productivity in tradable goods implies lower real wages in poor countries.

–  Lower real wages imply lower price of nontradable goods in poor countries

–  So the price level is lower in poor countries. •  Samuelson-Balassa effect implies that countries with rapid

productivity growth (in tradables) should experience an increase in their domestic price level relative to the rest of the world: a real appreciation.


41

§  The Samuelson and Balassa effect (1964) •  Technology in the traded and non-traded sectors:

YT = AT LT YN = LN

•  Labor is mobile between the two sectors: w= AT = pN

•  The price of non-traded goods increases with productivity in the traded sector.

•  The price index is: P = (1)α(pN)(1- α) = (AT)(1- α)

Increases with productivity in the traded sector •  Relative price level: P*/P = (A*T /AT)(1- α)

falls if domestic productivity growth in the traded sector exceeds foreign productivity growth in the traded sector.


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Figure 5-9: Sectoral Productivity Growth Differences and the Change in the Relative Price of Nontraded Goods, 1970-1985

§ Beyond Purchasing Power Parity: A General Model of Long-Run Exchange Rates

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§  The Real Exchange Rate •  It is a broad summary measure of the prices of one

country’s goods and services relative to the other's. •  It is defined in terms of nominal exchange rates and price

levels. •  The real dollar/euro exchange rate is the dollar price of the

European basket relative to that of the American: q$/€ = (E$/€ x PE)/PUS

Beyond Purchasing Power Parity: A General Model of Long-Run Exchange Rates

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•  When q = 1, PPP holds. •  Real depreciation of the dollar against the euro

– A rise in the real dollar/euro exchange rate q$/€

•  A real appreciation of the dollar against the euro is the opposite of a real depreciation.

•  Note that this is the same convention as for the nominal exchange rate


§ q$/€ = (E$/€ x PE)/PUS

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§ Demand, Supply, and the Long-Run Real Exchange Rate •  In a world where PPP does not hold, the long-run values of

real exchange rates depend on relative demand and supply conditions.


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•  There are two specific causes that explain why the long-run values of real exchange rates can change:

– A change in world relative demand for American products –  An increase (fall) in world relative demand for U.S. goods causes a

long-run real appreciation (depreciation) of the dollar against the euro.

– A change in relative output supply –  A relative expansion of U.S (European) output causes a long-run real

depreciation (appreciation) of the dollar against the euro.


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YUS/YE

Relative Supply

Figure 5-10: Determination of the Long-Run Real Exchange Rate

Ratio of U.S. to European real output (YUS/YE)

Real Exchange rate, q

1 q1

Relative Demand


48

YUS/YE

Relative Supply

Figure 5-11: An increase in the relative demand for US goods



1 q1

Relative Demand


50

YUS/YE

Relative Supply

Figure 5-12: An increase in the relative supply of US goods



1 q1

Relative Demand


52

§ Nominal and Real Exchange Rates in Long-Run Equilibrium •  Changes in national money supplies and demands give rise

to the proportional long-run movements in nominal exchange rates and international price level ratios predicted by the relative PPP theory.

•  From the definition of the real exchange rate, we solve for the nominal exchange rate: E$/€ = q$/€ (PUS/PE)


53

§  The most important determinants of long-run swings in nominal exchange rates (assuming that all variables start out at their long-run levels): •  A shift in relative money supply levels •  A shift in relative money supply growth rates •  A change in relative output demand •  A change in relative output supply


E$/€ = q$/€ x (PUS/PE)

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§ When all disturbances are monetary in nature, exchange rates obey relative PPP in the long run.

§ When disturbances occur in output markets, the exchange rate is unlikely to obey relative PPP, even in the long run.


55


Table 5-1: Effects of Money Market and Output Market Changes on the Long-Run Nominal Dollar/Euro Exchange Rate, E$/€

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§  Combining (qe$/€ - q$/€)/q$/€ = (Ee$/€ - E$/€)/E$/€ – (πeUS - πeE)

with the interest parity condition: i$ - i€ = (Ee$/€ - E$/€)/E$/€

§  To obtain: i$ - i€ = (qe$/€ - q$/€)/q$/€ + (πeUS - πeE)

§  Thus, the dollar-euro interest difference is the sum of two components:

–  The expected inflation difference between the U.S. and Europe –  The expected rate of real dollar depreciation against the euro

International Interest Rate Differences and the Real Exchange Rate

57

Summary

§ Absolute PPP states that the purchasing power of any currency is the same in any country and implies relative PPP.

§ Relative PPP predicts that percentage changes in exchange rates equal differences in national inflation rates.

§  The law of one price is a building block of the PPP theory. •  It states that under free competition and in the absence of

trade impediments, a good must sell for a single price regardless of where in the world it is sold.

58

Summary

§  The monetary approach to the exchange rate uses PPP to explain long-term exchange rate behavior exclusively in terms of money supply and demand. •  The Fisher effect predicts that long-run international interest

differentials result from different national rates of ongoing inflation.

§  There is weak empirical support for the law of one price.

59

Summary

§ Deviations from relative PPP can be viewed as changes in a country’s real exchange rate.

§ A stepwise increase in a country’s money stock leads to a proportional increase in its price level and a proportional fall in its currency’s foreign exchange value.

§  The (real) interest parity condition equates international differences in nominal (real) interest rates to the expected percentage change in the nominal (real) exchange rate.

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