given knowledge of three variables: the expected future...

1. INTRODUCTION

1 Introduction

• In the last chapter, uncovered interest parity (UIP) provided us with a theory of how the spot exchange rateis determined, given knowledge of three variables: the expected future exchange rate, the home interest rate,and the foreign interest rate.

— In this chapter we look at the "long run" to see how the expected future exchange rate is determined,and then, in the next chapter, we turn to the "short run" and discuss how (home and foreign) interestrates are determined in each country.

∗ When all the pieces are put together, we will have a complete theory of how exchange rates aredetermined in the short run and the long run.

• In this chapter, we study a theory of how exchange rates are determined "in the long run." Thetheory we will develop has two parts:

1. The first part involves the theory of purchasing power which links the exchange rate to price levelsin two countries in the long run.

— The foundation of this theory is the fundamental arbitrage principle known as the law of one price(LOOP).

2. In the second part, we explore how price levels in the long run are related to monetary conditionsin each country.

Thus, combining the purchasing power theory of exchange rate determination with the monetary theory of pricelevel determination, we emerge with a long-run theory known as "the monetary approach to exchangerates."

— Like I said, such a long-run theory is useful to see how the expected future exchange rate is determined.

∗ Note again that in the last chapter we learned how the spot exchange rate is determined, where theexpected future exchange rate is one of exogenous variables that determines the spot exchange rate.

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2. EXCHANGE RATES AND PRICES IN THE LONG RUN: PURCHASING POWER PARITY AND GOODS MARKET EQUILIBRIUM

2 Exchange Rates and Prices in the Long Run: Purchasing Power Parity and Goods Market Equilibrium

• Just as arbitrage occurs in the international markets for financial assets (the resulting no-arbitrage conditionsare covered and uncovered interest parity), it also occurs in the international markets for "goods."

— The result of international goods market arbitrage (i.e., a no-arbitrage condition for the internationalgoods market) is that the prices of goods in different countries expressed in a common currencytend to be equalized.

∗ Intuitively, if the price of a good were not the same in two locations, buyers would rush to buy at thecheap location (forcing prices up there) and shy away from the expensive location (forcing prices downthere). This process continues until the prices in two locations are equalized.

1. Applied to a single good, this idea is referred to as the law of one price (LOOP).

2. Applied to an entire basket of goods (a measure of the price level in each country; e.g., CPI), it iscalled the theory of purchasing power parity (PPP).

• Our goal is to develop a simple yet useful theory, based on an idealized world of frictionless trade wheretransaction costs can be neglected.

— We first start at the microeconomic level with single goods, which leads to LOOP.

— We then move to the macroeconomic level to consider baskets of goods, which leads to PPP.

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2.1 The Law of One Price

• The law of one price (LOOP) states that in the absence of trade frictions (such as transport costs and tariffs),and under conditions of free competition and price flexibility (where no individual sellers or buyers have powerto manipulate prices and prices can freely adjust), identical goods sold in different locations must sell forthe same price when prices are expressed in a common currency.

— This is a no-arbitrage condition: a good market is in equilibrium.

— For example, if diamonds can be freely moved between New York and Amsterdam, both markets mustoffer the same price (economists refer to this situation in the two locations as an integrated market).

∗ If diamonds were more expensive in New York, arbitragers would buy at a low price in Holland and sellat a high price in Manhattan, forcing prices up in Holland and down in Manhattan.

• We can algebraically state LOOP as follows:

1. For any good g sold in two countries, the relative price of good g in a common currency is:

qgUS/EUR︸︷︷︸

Relative price of good g in Europe versus U.S.

= E$/€PgEUR︸︷︷︸

European price of good g in $

/P gUS︸︷︷︸

U.S. price of good g in $

— qgUS/EUR

is the rate at which goods can be exchanged:

∗ It tells us how many units of the U.S. good are needed to purchase one unit of the same good inEurope (hence, the subscript in qg

US/EURuses the notation US/EUR).

∗ It contrasts with the nominal exchange rate E$/€ which expresses the rate at which currencies canbe exchanged ($/€).

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2. When good g is more or less expensive in Europe than in the U.S. (i.e., qgUS/EUR

> 1⇔ E$/€PgEUR > P g

US

or qgUS/EUR

< 1 ⇔ E$/€PgEUR < P g

US), there are arbitrage opportunities. Hence, in a goods marketequilibrium (i.e., no arbitrage), LOOP holds:

qgUS/EUR

= 1⇔ E$/€PgEUR = P g

US

• LOOP furthers our understanding of exchange rates.

— Rearranging the equation for price equality E$/€PgEUR = P g

US gives:

E$/€ =P gUS

P gEUR︸︷︷︸

Ratio of goods’prices

— That is, if LOOP holds, then the exchange rate must equal the ratio of the goods’prices expressed in thetwo currencies.

∗ Note that the left-hand side for the exchange rate is expressed in dollars per euro and the right-handside for the price ratio is also a ratio of dollars to euros ($ per unit of goods divided by € per unit ofgoods).

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2.2 Purchasing Power Parity

• Purchasing power parity (PPP) is the macroeconomic counterpart to the microeconomic LOOP.

— LOOP relates exchange rates to the relative price of an individual goods, while PPP relates exchangerates to the relative price of a basket of goods that measures the relative price level of two countries.Thus, in studying international macroeconomics, PPP is the more relevant concept.

• Let’s define a price level denoted by P in each country (e.g., CPI) as a weighted average of the prices of allgoods g in a basket, using the same goods and weights in two countries, Home (U.S.) and Foreign (Europe):PUS and PEUR.

— If LOOP holds for every good in a basket of goods, it will aslo hold for the price of the basket as a whole.

— To express PPP algebraically, we can compute the relative price of the two baskets of goods in a commoncurrency:

qUS/EUR︸︷︷︸Relative price of basket of goods in Europe versus U.S.

= E$/€PEUR︸︷︷︸European price of basket of goods in $

/PUS︸︷︷︸

U.S. price of basket of goods in $

∗ Note that in the above, we don’t use a superscript g for any single good in the case of LOOP.

Then, there are no arbitrage opportunities when the basket is the same price in both countries. Hence,PPP holds when price levels in two countries are equal when expressed in a common currency:

qUS/EUR = 1⇔ E$/€PEUR = PUS

∗ This statement about equality of price levels is also called absolute PPP (these "overall" price levelsin each country must be the same).

∗ For example, suppose the European basket costs €100, and the exchange rate is $1.20 per euro. ForPPP to hold, the U.S. basket would have to cost 1.20× 100 = $120.

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• In the above, the relative price of the baskets of two countries q is one of the most important concept ininternational macroeconomics, and has a special name: it is known as the real exchange rate.

— The U.S.-Europe real exchange rate, qUS/EUR =E$/€PEURPUS

, tells us how many U.S. (Home) basketsare needed to purchase one European (Foreign) basket (i.e., how many U.S. baskets can beexchanged for one European basket).

∗ It is the price of the European (Foreign) basket in terms of the U.S. (Home) basket —the real exchangerate is a real concept, while the exchange rate for currencies is a nominal concept.

— The real exchange rate has some terminology similar to that used with the nominal exchange rate:

∗ If the real exchange rate rises (falls), i.e., more (fewer) Home goods are needed in exchange forForeign goods, we say the Home country has experienced a real depreciation (appreciation).

— The real exchange rate measures deviations from absolute PPP:

∗ Absolute PPP states that the real exchange rate is equal to one: q = 1. Thus, it is common practiceto use the absolute PPP-implied level of 1 as a benchmark or reference level for the real exchange rate.

∗ This leads naturally to some new terminology: If the real exchange rate qUS/EUR is above (below)1 by x%, then Foreign [European] goods are relatively expensive (cheap), x% more expensive(cheaper) than Home [U.S.] goods. In this case, the Home currency [the dollar] is said to be weak(strong), the Foreign currency [the euro] is strong (weak), and we say the Foreign currency [theeuro] is said to be overvalued (undervalued) by x%.

· This is because the Foreign currency [the euro] is x% more expensive (cheaper) than it would haveto be to satisfy absolute PPP (i.e., qUS/EUR = 1).

· For example, if a European basket costs E$/€PEUR = $550 in dollar terms, and a U.S. basket costsonly PUS = $500, then qUS/EUR = 1.10, the euro is strong, and the euro is 10% overvalued againstthe dollar.

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2.3 Absolute PPP, Prices, and the Nominal Exchange Rate

• Now, we can see that absolute PPP supplies a reference level for what the nominal exchange rate isin the long run.

— Rearranging the PPP equation gives:

Absolute PPP implies E$/€ = PUSPEUR

∗ PPP implies that the exchange rate at which two currencies trade equals the relative price levels ofthe two countries.

∗ The PPP theory can be used to predict exchange rate movements "in the long run" - thesesimply reflect relative price levels, so all we need to forecast the expected future exchangerate is to predict future price levels.

— In this model, the price levels are treated as known exogenous variables (in the green boxes), and themodel uses these variables to predict the unknown endogenous variable (in the red box), which is theexchange rate.

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2.4 Relative PPP, Inflation, and Exchange Rate Depreciation

• Recall how to calculate the growth rate of a variable X : letting xt ≡ logXt, the growth rate of X is as follows:

∆xt = xt − xt−1 = logXt − logXt−1 = log

(Xt

Xt−1

)= log

(1 +

Xt −Xt−1

Xt−1

)≈ Xt−Xt−1

Xt−1

— When X represents the price level P , its growth rate ∆pt = logPt − logPt−1 ≡ πt is known as inflation.

• We now examine the implications of absolute PPP. Taking logarithms of both sides of the absolute PPPequation yields:

log(E$/€,t

)︸︷︷︸ = log

(PUS,t

PEUR,t

)= log (PUS,t)− log (PEUR,t)︸︷︷︸

which gives us:[log(E$/€,t

)− log

(E$/€,t−1

)]= [log (PUS,t)− log (PUS,t−1)]− [log (PEUR,t)− log (PEUR,t)]

which is re-expressed as:

E$/€,t − E$/€,t−1

E$/€,t−1︸︷︷︸Rate of depreciation of the nominal exchange rate

=

[PUS,t − PUS,t−1

PUS,t−1

]︸︷︷︸Home inflation rate

−[PEUR,t − PEUR,t−1

PEUR,t−1

]︸︷︷︸

Foreign inflation rate

= πUS,t − πEUR,t︸︷︷︸Inflation differential

— This is known as relative PPP that states that the rate of depreciation of the nominal exchange rate(the depreciation rate) equals the difference between the inflation rates of two countries (the inflationdifferential).

∗ For example, over 20 years, Canadian prices rose 16% (by 0.75% per year) more than U.S. prices (theinflation differential), and the Canadian dollar depreciated 16% against the U.S. dollar. In this case,relative PPP held.

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— Relative PPP is derived from absolute PPP, so the latter always implies the former: if absolute PPP holdsfor levels of the exchange rate and prices, then it must also hold for rates of change in these variables.But, the converse need not be true: relative PPP does not necessarily imply absolute PPP (if relativePPP holds, absolute PPP can hold or fail).

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2.5 Evidence on PPP in the Long Run and Short Run

• This scatterplot shows the relationship betweenthe rate of exchange rate depreciation againstthe U.S. dollar (the vertical axis) and the in-flation differential against the United States(horizontal axis) over "the long run (1975 to2005)," based on data for a sample of 82 coun-tries.

— The correlation between the two variables isstrong and bears a close resemblance to thetheoretical prediction of PPP that all datapoints would appear on the 45-degree line.

Thus, the data offer some support for relativePPP most clearly over the long run, suggestingthat relative PPP is an approximate, use-ful guide to the relationship between pricesand exchange rates in the long run, overhorizons of many years or decades.

• Data for the United States and United Kingdomfor 1975 to 2009 show that the exchange rateand relative price levels do not always movetogether in the short run.

— Relative price levels tend to change slowly andhave a small range of movement.

Exchange rates move more abruptly and expe-rience large fluctuations.

∗ For example, from 1980 to 1985, the pounddepreciated by 45% (from $2.32 to $1.28)against the dollar, but the cumulative in-flation differential over these five years wasonly 9%.

Hence, relative PPP does not hold "in theshort run."

— However, it is a better guide to "the long run,"and we can see that the two series do tend todrift together over the decades.

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2.6 How Slow is Convergence to PPP?

• As we have seen before, the evidence suggests that PPP works better in the long run. But how long is thelong run?

— Research shows that deviations from PPP (measured by the real exchange rate) can be quite persistent.

∗ Note that deviations from PPP are measured by the real exchange rate: when the real exchange rateis not equal to one (i.e., above or below one), there is the deviations from PPP.

1. Estimates suggest that these deviations may die out at a rate of about 15% per year. This kindof measure is often called a speed of convergence of 15% per year: how quickly deviations fromPPP disappear over time.

∗ A speed of convergence of 15% per year means that 85% of an initial deviation from PPP stillpersists after one year.

2. Given the estimate of a speed of convergence of 15% per year, it takes four years for approximatelyhalf of an initial deviation from PPP to disappear. Economists would refer to this as a four-yearhalf-life.

∗ The half-life measures how long it takes for half of an initial deviation from PPP to disappear: afterfour year, 52% (0.52 = 0.854) of the initial deviation still persists, which means that it takes fouryears for approximately half of any PPP deviation to disappear.

• Such estimates provide a rule of thumb that is useful as a guide to forecasting "real" exchange rates.

— Suppose the home basket costs $100 and the foreign basket $90 in home currency. Then, Home’s realexchange rate is 0.9 (= 90/100), so the deviation of the real exchange rate from PPP-implied level of 1is −10% (or −0.1) — the home currency is overvalued. Our rule of thum tells us:

∗ Next year 15% of this deviation will have disapppered (i.e., 0.015 = 0.1× 0.15), so the new deivationwill be only −0.085 (= −0.1 + 0.015), meaning that Home’s real exchange rate would be forecast to

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be 0.915 (= 1− 0.085) after one year after a small depreciation (i.e., the increase from 0.9 to 0.915).

∗ Similary, after four years, all else being equal, 52% of the devation (or 0.052 = 0.1× 0.52) would havebeen erased, and the real exchange rate would by then be 0.952 (= 0.9 + 0.052), only −5% from thePPP-implied level of one.

• Knowing the real exchange rate and the speed of convergence also allows us to forceast "nominal" exchangerates. From the definition of the real exchange rate as a measure of deviations from PPP (i.e., qUS/EUR =E$/€PEURPUS

), it follows:—

∆E$/€,t

E$/€,t−1=

∆qUS/EUR,tqUS/EUR,t−1

+ (πUS,t − πEUR,t)

1. When PPP holds at all times (i.e., qUS/EUR,t is constant over time), the first term on the righthand side is zero.

∗ Forecasting nominal exchange rate changes is simple to compute the inflation differential.

2. When PPP doesn’t hold (i.e., qUS/EUR,t deviates from one), the rate of change of the nominalexchange rate equals the rate of change of the real exchange rate plus the inflation differential.

∗ In this case, knowing the real exchange rate and its convergence speed in addition to theinflation differential may still allow us to construct a forecast of nominal exchange ratechanges.

∗ Suppose (a) U.S. inflation is 3% and Eurozone inflation is 2%, (b) the US dollar is 10% overvaluedagainst the euro (i.e., qUS/EUR,t = 0.9 = $90

$100) relative to a PPP-implied value of one, and (c) the

estimate of the speed of convergence of qUS/EUR,t is 15% per year.

Then, (a) the inflation differential (πUS,t − πEUR,t) is equal to 1%; (b) it is expected that 15% ofthat deviation of −0.1 (= 0.9 − 1) vanishes in one year (i.e., the real exchange rate is expected tochange toward one from 0.9 observed today, which means that qUS/EUR is expected to rise by 1.5%;(c) therefore, we expect E$/€ to rise by 2.5% (= 1.5% + 1%).

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2.7 What Explains Deviations from PPP?

• As research indicates, it takes four years for even half of any given price difference to dissipate. So we need toexplain how arbitrage takes so long to eliminate price differences.

• Economists have found a variety of reasons why PPP fails in the short run.

1. Transaction costs:

— Trade is not frictionless as we have asumed thus far.

∗ Ttransaction costs are signficant for most goods and some goods also bear additional costs, such astariffs and duties. On average, they are more than 20% of the price of goods traded internationally.

∗ Other costs arise due to shipping and delays associated with developing distribution networks andsatisfying legal and regulatory requirements in foreign markets.

2. Nontraded goods:

— Some goods are inherently nontradable, and thus they can be thought of as having infinitely hightransaction costs. Most goods and services fall somewhere between tradable and nontradable. As aresult, PPP may not hold.

3. Imperfect competition and legal obstacles:

— Many goods are not simple undifferentiated commodities, as LOOP and PPP assume, but are differen-tiated products with brand names, copyrights, and legal protection. Such differentiated goods createconditions of imperfect competition because firms have some power to set the prices of their goods.With this kind of market power, firms can charge different prices not just across brands but also acrosscountries.

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4. Price stickiness:

— One of the most common assumptions of macroeconomics is that prices are sticky in the short run —that is, they do not or cannot adjust quickly and flexibly to changes in market conditions. PPP assumesthat arbitrage can force prices to adjust. But adjustment will be slowed down by price stickiness, whichis supported by the data — in one of figures provided before, the nominal exchange rate moves up anddown in a very dramatic fashion but price levels are mush more sluggish in their movements and donot fully match exchange rate changes.

• Despite these problems, the evidence suggests that as a long-run theory of exchange rates, PPP is stll a usefulapproach.

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2.8 PPP as a Theory of the Exchange Rate

• The PPP theory in the absolute or relative form suggests that price levels in different countries and exchangerates are tightly linked either in levels or in rates of change:

1. In levels, we have absolute PPP:

E$/€︸︷︷︸Exchange rate

=PUS

PEUR︸︷︷︸Ratio of price levels

2. In rates of change, we have relative PPP:

∆E$/€,t

E$/€,t−1︸︷︷︸Rate of depreciation of the exchange rate


• According to the PPP theory, we can predict exchange rate movements by using movements of prices.

— Then, we need to ask "where do price levels (and inflation rates) come from?" which is whatwe study in the next.

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3. MONEY, PRICES, AND EXCHANGE RATES IN THE LONG RUN: MONEY MARKET EQUILIBRIUM IN A SIMPLE MODEL

3 Money, Prices, and Exchange Rates in the Long Run: Money Market Equilibrium in a Simple Model

• The theory of PPP says that in the long run the exchange rate is determined by the ratio of the price levelsin two countries.

— This prompts a question: What determines those price levels?

• Monetary theory supplies an answer to this question:

— In the long run, price levels are determined in each country by the relative demand and supply ofmoney (i.e., monetary conditions).

• Thus, this section recaps the essential elements of monetary theory and shows how they fit into our theory ofexchange rates in the long run.

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3.1 What Is Money? and The Measurement of Money

• Economists think of money as performing three key functions in an economy:

1. Money is a store of value because money held from today until tomorrow can still be used to buy goodsand services in the future.

— Compared with many other assets, money bears no interest so that there is an opportunity cost toholding money. If this cost is low, we will hold money more willingly than we hold other assets (stocks,bonds, etc.).

2. Money also gives us a unit of account in which all prices in the economy are quoted.

— When we enter a store in France, we expect to see all prices of goods to read something like "100euros."

3. Money is a medium of exchange that allows us to buy and sell goods and services without the need toengage in ineffi cient barter (direct swaps of goods).

— Money is the most liquid asset of all.

• What counts as money?

1. M0 (base money) = currency in circulation (i.e., cash in the hands of the nonbank public) + the reservesof commerical banks (i.e., cash held in their vaults or on deposit at their central bank like the Fed)

— It is the narrowest definition of money (also called "base money").

2. M1 (narrow Money) = currency in circulation + highly liquid instruments such as demand deposits inchecking accounts and traveler’s checks

— It excludes banks’reserves, and thus may be a better gauge of money available for transaction purposes.

— Note that demand deposits are checking accounts payable on demand by the bank customer.

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3. M2 (broad Money) = M1 + other less liquid assets

— Other less liquid assets include savings accounts, small time deposits, and money market mutual funds.

For our purpose, money is defined as the stock of liquid assets that are routinely used to finance transactions,in the sense implied by the "medium of exchange" function of money. Thus, when we speak of money(denoted by M), we will generally mean M1.

• This figure shows the major kinds of monetary aggregates (currency, M0, M1, and M2) for the United Statesfrom 2004 to 2010.

— Normally, bank reserves are very close to zero, so M0 and currency in circulation are virtually identical.But reserves (and thus M0) spiked up during the financial crisis in 2008, as private banks sold securitiesto the Fed and stored up the cash proceeds in their Fed reserve accounts as a precautionary hoard ofliquidity.

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3.2 The Supply of Money, The Demand for Money: A Simple Model, and Equilibrium in the MoneyMarket

• How is the supply of money determined?

— In practice, a country’s central bank controls the money supply. Thus, we assume that the nominalmoney supply M (= M1) is controlled by the central bank.

∗ In fact, by issuing notes and coins, the central bank directly controls the level of M0, the amountof currency in the economy. However, it can indirectly control the level of M1 by using interest ratepolicies and other monetary policy tools (such as reserve requirements) to influence the behavior ofthe private banks that are responsible for checking deposits.

∗ Thus, our assumption here means that the central bank’s policy tools are suffi cient to allow it tocontrol indirectly, but accurately, the level of M1.

• A simple theory of household money demand is motivated by the assumption that the need to use money forconducting transactions is in proportion to an individual’s income.

— The aggregate money demand will behave similarly: All else equal, a rise in national dollar income (nominalincome) will cause a proportional increase in transactions and thus, in aggregate money demand.

— A "simple" model in which the demand for money is proportional to nominal income is knownas the "quantity theory of money:"

Md︸︷︷︸Demand for money ($)

= L︸︷︷︸A constant

× (PY )︸︷︷︸Nominal income ($)

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

Md

P︸︷︷︸Demand for real money

= L︸︷︷︸A constant

× Y︸︷︷︸Real income

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∗ The demand for real money balances is a constant multiple of the real income level: The more realincome we have, the more real transactions we have to perform, so the more real money we need.

• The condition for equilibrium in the money market is simple to state that the demand for money Md

must equal the supply of money M : Md = M , which gives us:

M︸︷︷︸Supply of nominal money

= LPY︸︷︷︸Demand for nominal money

, equivalentlyM

P︸︷︷︸Supply of real money

= LY︸︷︷︸Demand for real money

— In the long run, we assume that "prices" are flexible and will adjust to put the money market inequilibrium.

∗ This means that we can solve for the price level, given the supply of nominal money and real incomelevel.

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3.3 A Simple Monetary Model of Prices

• The long-run price level in each of two countries, say, the U.S. and Europe, can now be expressed as:

PUS = MUS

LUSYUS; PEUR = MEUR

LEURYEUR

— This is the fundamental equation of the monetary model of the price level.

∗ The price level is determined by how much nominal money issued (M) relative to the demand for realmoney balances (LY ).

∗ For example, if the amount of money in circulation (the money supply) rises, say, by a factor of 100,and real income stays the same, then there will be "more money chasing the same quanity of goods.”This leads to inflation, and in the long run, the price level will rise by a factor of 100.

· In other words, we will be in the same economy as before except that all prices will have two zerosstacked on to them.

• The simple monetary model of prices treats the nominal money supply and real income as known exogenousvariables, predicting the unknown endogenous variable which is the price level in each country:

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3.4 A Simple Monetary Model of the Exchange Rate

• We are now in a position to develop a simple model of the exchange rate, using two building blocks:

1. The first building block is the quantity theory of money, a model that links prices to monetary conditions(PUS = MUS

LUSYUSand PEUR = MEUR

LEURYEUR).

2. The second building block is the PPP theory, a model that links exchange rates to prices (E$/€ = PUSPEUR

).

Thus, by substituting the price levels from the monetary model into absolute PPP, we put together the twobuilding blocks so as to solve for the exchange rate:

E$/€︸︷︷︸Exchange rate

=PUS

PEUR︸︷︷︸Ratio of price levels

=

(MUS

LUSYUS

)(

MEUR

LEURYEUR

) =(MUS/MEUR)(

LUSYUS/LEURYEUR)︸︷︷︸

Relative nominal money supplydivided by relative real money demand

— This is the fundamental equation of the monetary approach to the exchange rate. The implicationsof this equation are intuitive:

1. Suppose the U.S. money supply increases, all else equal. Then, the right-hand side increases (i.e., theU.S. nominal money supply increases relative to Europe), causing the exchange rate to increase (i.e.,the U.S. dollar depreciates against the euro). That is, a bigger U.S. supply of money leads to a weakerdollar. That makes sense—there are more dollars around, so you expect each dollar to be worth less.

2. Suppose the U.S. real income level increases, all else equal. Then, the right-hand side decreases (i.e.,the U.S. real money demand increases relative to Europe), causing the exchange rate to decrease (i.e.,the U.S. dollar appreciates against the euro). That is, a stronger U.S. economy (and thus a higherU.S. real income) leads to a stronger dollar. That makes sense—there is more demand for the samequantity of dollars, so you expect each dollar to be worth more.

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3.5 Money Growth, Inflation, and Depreciation

• The simple monetary model of the exchange rate can be expressed in terms of rates of change.

— Let µ and g denote the growth rates of money supply M and real income Y , respectively:

µUS,t ≡MUS,t −MUS,t−1

MUS,t−1and gUS,t ≡

YUS,t − YUS,t−1

YUS,t−1

Then, the fundamental equation of the monetary model of the price level (i.e., PUS = MUS

LUSYUS) can

be expressed in rates of change:

πUS,t = µUS,t − gUS,t

∗ Inflation equals the excess of nominal money supply growth rate over real income growth rate. In otherwords, when money growth is higher than real income growth, we have "more money chasing fewergoods" and this leads to inflation.

— Combining these expressions with relative PPP gives:

∆E$/€,t

E$/€,t−1︸︷︷︸Rate of depreciation of the exchange rate


=[µUS,t − gUS,t

]−[µEUR,t − gEUR,t

]

=(µUS,t − µEUR,t

)︸︷︷︸Differential in nominal money supply growth rates

− (gUS,t − gEUR,t)︸︷︷︸Differential in real income growth rates

1. If the U.S. runs a looser monetary policy in the long run measured by a faster money growth rate thanEurope, the dollar will depreciate more rapidly, all else equal.

2. If the U.S. economy grows faster in the long run, the dollar will appreciate more rapidly, all else equal.

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given knowledge of three variables: the expected future...

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