1 introduction in the data, however, substantial...

1. INTRODUCTION

1 Introduction

• The purchasing power parity (PPP) theory is one of building blocks of the monetary approach to exchangerates in the long run. In the data, however, substantial deviations from PPP occur "in the short run:"that is, the same basket of goods generally does not cost the same everywhere "at all times."

— These short-run failures of the monetary approach prompted economists to develop an alternative theoryto explain exchange rates in the short run: that is, the asset approach to exchange rates, which is thesubject of this chapter.

∗ The asset approach is based on the idea that currencies are assets: the price of the asset in this caseis the spot exchange rate, the price of one unit of foreign currency in terms of home currency.

— The asset approach differs from the monetary approach in its time frame and assumptions

∗ In the monetary approach, (a) we envisage a long run that takes several years; (b) we treat goodsprices as perfectly flexible, a plausible assumption in the long run, while in the asset approach (a) weare typically thinking of a short run of a matter of a few months, or a year or so at most; (b) weassume that goods prices are sticky, a more appropriate assumption in the short run.

— The asset approach complements the monetary approach, and provides us with the final building blocksnecessary to construct a complete theory of exchange rates (by unifying the monetary and asset ap-proaches).

• So far, we have assumed exchange rates are determined by market forces in the goods, money, and foreignexchange markets. Thus, our theory is relevant when the exchange rate floats: the authorities leave it to findits own market-determined level.

— We also see how the same theoretical framework can be applied to a fixed exchange rate regime at theend of the chapter.

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2. EXCHANGE RATES AND INTEREST RATES IN THE SHORT RUN: UIP AND FX MARKET EQUILIBRIUM

2 Exchange Rates and Interest Rates in the Short Run: UIP and FX Market Equilibrium

2.1 Risky Arbitrage

• As before, we assume the Home country is the U.S. and the Foreign country is Europe. We also consider aU.S. investor with two alternative investment strategies: a one-year investment in a U.S. dollar account withan interest rate i$, or a one-year investment in a euro account with an interest rate i€.

— For the case of risky arbitrage, the foreign exchange market is in equilibrium when there is no expecteddifference in the (dollar) rates of return on each type of currency investment — this is uncovered interestparity (UIP).

• The UIP equation is the fundamental equation of the asset approach to exchange rates:

i$︸︷︷︸Interest rate on dollar deposits

=Dollar rate of return on dollar deposits

= i€︸︷︷︸Interest rate on euro deposits

+Ee$/€ − E$/€E$/€︸︷︷︸

Expected rate of depreciation of dollar︸︷︷︸Expected dollar rate of return on euro deposits

— As we have seen, we can solve this equation for the spot exchange rate E$/€, provided we know all of theother variables, two nominal interest rates i$ and i€ and the expected future exchange rate Ee$/€.

— In other words, the asset approach to the exchange rate treats i$, i€, and Ee$/€ as known exogenousvariables, and then uses these variables to determine the unknown endogenous variable, E$/€:

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∗ Where does knowledge of short-term interest rates and the expected future exchange rate come from?

1. We can forecast the future level of the exchange rate rate Ee$/€, using the long-run monetary

approach to the exchange rate presented in the previous chapter.

2. We will see how short-term interest rates i$ and i€ are determined in the money market in eachcountry later.

2.2 Equilibrium in the FX Market Using the FX Market Diagram: An Example

• We now illustrate how equilibrium in the foreign exchange (FX) market is determined, using an FX marketdiagram that shows the relationship between the domestic and foreign returns in dollars.

— The fundamental equation of the asset approach is the equilibrium condition in the FX market.

• As for example, suppose we have made a forecast that the expected future (one year ahead) exchange rateEe$/€ is 1.224 dollars per euro. Suppose also that the current U.S. and European (annual) interest rates i$ and

i€ are 5% and 3%, respectively.

— This table reports the domestic rate of return (col-umn 1) and expected foreign rate of return (col-umn 6) in U.S. dollars for various values of thespot exchange rate E$/€, given Ee$/€ = 1.224,i$ = 0.05, i€ = 0.03.

∗ When the spot exchange rate is 1.20 dollarsper euro that yields both domestic and foreignreturns of 5% in annual dollar terms, the FXmarket is in equilibrium, which is highlightedin bold type.

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• The figure presents an FX market diagram, a graphical presentation of these returns in the forex market.

— In the diagram, the expected domestic and foreignreturns are on the vertical axis and today’s spotexchange rate is on the horizontal axis.

1. The domestic dollar return (DR) is indepen-dent of the spot exchange rate and is fixed at5%.

2. The expected foreign dollar return (FR) varieswith the spot exchange rate and is decreasingin it.

∗ If the dollar depreciates today (i.e., the spotexchange rate E$/€ rises), then $1 movedinto a European account is worth fewer eu-ros today (i.e., 1

E$/€falls), and these euros

today, in turn, leaves fewer euro proceeds ina year’s time after euro interest at a fixedlevel has accrued (i.e., 1

E$/€(1 + i€) falls).

Finally, given a fixed level of the expectedfuture exchange rate, those fewer future eu-ros will be worth fewer future dollars (i.e.,Ee$/€

E$/€(1 + i€) falls. Hence, the foreign return

in dollars goes down as E$/€ rises, all elseequal.

— Thus, we observe that:

∗ The FX market is in equilibrium at Point1, where the domestic return DR and the ex-

pected foreign return FR are equal at 5% andthe spot exchange rate E$/€ is 1.20.

∗ At Point 3, E$/€ is too high: FR < DR→arbitragers want to sell € and buy $ to investin dollar-denominated deposits. → E$/€ startsto fall (i.e., the dollar appreciates), moving upalong the FR line from Point 3 to Point 1.

∗ At Point 2, E$/€ is too low: FR > DR →arbitragers want to sell $ and buy € to invest ineuro-denominated deposits. → E$/€ starts torise (i.e., the dollar depreciates), moving downalong the FR line from Point 2 to Point 1.

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2.3 Changes in Domestic and Foreign Returns and FX Market Equilibrium

• To gain greater familiarity with the model, let’s see how the FX market considered in the previous exampleresponds to separate changes in three exogenous variables:

1. A higher domestic interest rate, i$ = 7% (from 5%)

2. A lower foreign interest rate, i€ = 1% (from 3%)

3. A lower expected future exchange rate, Ee$/€ = 1.2 (from 1.224)

1. A higher domestic interestrate

• DR shifts upward and thenE$/€ decreases (dollar ap-preciates), since dollar de-posits are more attractiveand thus traders buy dol-lars and sell euros.

2. A lower foreign interest rate

• FR shifts downward andthen E$/€ decreases (dol-lar appreciates), since eurodeposits are less attractiveand thus traders sell eurosand buy dollars.

3. A lower expected future ex-change rate

• FR shifts downward andthen E$/€ decreases (dollarappreciates), since a fall inEe$/€ lowers expected for-eign returns in dollar termsand thus euro deposits areless attractive.

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2.4 Summary

• The UIP equation (also called the fundamental equation of the asset approach to exchange rates) is animportant building block of the asset approach to exchange rates as a theory of how exchange rates aredetermined in the short run.

— This is graphically represented by the FX market diagram.

∗ The spot exchange rate is determined at a point where domestic and foreign return curves intersect,given fixed values of home and foreign nominal interest rates and the expected future exchange rate.

· Any change which raises (lowers) the foreign return relative to the domestic return makes eurodeposits more (less) attractive to investors, so that traders will buy (sell) euro deposits, causing thespot exchange rate to increase (decrease).

— It is natural to ask the following questions:

1. In the short run, where do (home and foreign) nominal interest rates come from?

∗ It will be answered in the next section.

2. Where does the expected future exchange rate come from?

∗ The future exchange rate can be forecasted using the long-run monetary approach to exchange ratespresented in the previous chapter.

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3. INTEREST RATES IN THE SHORT RUN: MONEY MARKET EQUILIBRIUM

3 Interest Rates in the Short Run: Money Market Equilibrium

3.1 Money Market Equilibrium in the Short Run: How Nominal Interest Rates are Determined

• We now make short-run assumptions that are quite different from the long-run assumptions of the last chapter:

1. In the short run, the price level is sticky; it is a known predetermined variable, fixed at P = P .

— The assumption of sticky prices, also called nominal rigidity, is common to the study of macroeconomicsin the short run.

∗ Economists have many explanations for price stickiness. For example, nominal product prices maybe sticky because of menu costs; that is, firms may find it costly to frequently change their outputprices.

∗ Thus, while it is reasonable to assume that all prices are flexible in the long run, they may not bein the short run.

2. In the short run, the nominal interest rate i is fully flexible and adjusts to bring the moneymarket to equilibrium.

— We made long-run assumptions that the price level is flexible, and adjusts to put the money market inequilibrium. As a result, the nominal interest rate is pinned down by the Fisher effect (or real interestparity) in the long run: that is, the nominal interest rate is equal to the world real interest rate plusdomestic inflation.

∗ However, this result does not apply in the short run because it is derived PPP —which, as we know,only applies in the long run. Indeed, we also saw that in the short run real interest rates fluctuatein ways that deivate from real interest parity.

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• Then, based on the same general monetary model of the previous chapter, the short-run money marketequilibrium in each country that is another building block of the asset approach is as follows:

MUS

PUS

(MEUR

PEUR

)︸︷︷︸

U.S. (European) supply of real money balances

= L (i$)× YUS (L (i€)× YEUR)︸︷︷︸U.S. (European) demand of real money balances

where in each country the price level is treated as fixed and known, and the money supply (controlled by thecentral bank) and real income are also assumed to be known, so that the nominal interest rate is determinedwhen the money market is in equilibrium:

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3.2 Money Market Equilibrium in the Short Run: Graphical Solution

• The supply and demand for real money balances de-termine the nominal interest rate in the short run.

1. The real money supply curve (MS) is ver-tical: The quantity of nominal money M isset by the central bank and the price level Pis assumed to be fixed in the short run. Thus,real money supply M

Pdoes not depend on the

interest rate.

2. The real money demand curve (MD) isdownward-sloping: An increase in the inter-est rate raises the opportunity cost of holdingmoney, thus lowering the quantity demanded.Thus, given a level of real income Y , realmoney demand L (i)Y decreases with the in-terest ratei.

At Point 1, the short-run money market is inequilibrium when the nominal interest rate i1

$is such that the real money demand equals thereal money supply.

• Points 2 and 3 are off the equilibrium.

1. i2$is “too high”at Point 2 so that there is

the excess money supply.

— The public will want to reduce cash hold-ings by exchanging money for assets suchas saving accounts. That is, they will save

more and seek to lend their money to bor-rowers. But borrowers will not want to bor-row more unless the cost of borrowing i$falls. So, the interest rate will be drivendown as eager lenders compete to attractscarce borrowers.

2. i3$is “too low” at Point 3 so that there is

the excess money demand.

— The public will want to increase cash hold-ings by exchanging interest-bearing assetsfor money. That is, they will save less andreduce the amount available to borrowers.But borrowers want to borrow the sameamount. So, the interest rate will be drivenup as eager borrowers compete to attractscarce lenders.

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3.3 Changes in Money Supply and Demand and the Nominal Interest Rate

• Money market equilibrium depends on money supply and money demand. If either changes, the equilibriumwill change.

— To help us better understand how exchange rates are determined, we need to understand how thesechanges occur.

1. An increase in money supply, all else equal.

— In Panel (a), with a fixed price level P 1US, anincrease in nominal money supply from M1

USto M2

US causes real money supply to increase

from MS1 =M1US

P1

US

to MS2 =M2US

P1

US

. As a result,

the nominal interest rate falls from i1$to i2

$to restore equilibrium at Point 2.

∗ Our graphical analysis shows that, for agiven money demand curve, setting a moneysupply level uniquely determines the interestrate and vice versa. Hence, for many pur-poses, the money supply or the interest ratemay be used as a policy instrument.

In practice, however, most central bankstend to use the interest rate as their pol-icy instrument because the money demandcurve may not be stable, and the fluctua-tions caused by this instability would leadto unstable interest rates if the money sup-ply were set at a given level as the policyinstrument.

2. An increase in money demand, all else equal.

— In Panel (b), an increase in real income fromY 1US to Y

2US causes real money demand to in-

crease from MD1 = L (i$)Y1US to MD2 =

L (i$)Y2US for every level of the interest rate.

As a result, the nominal interest rate risesfrom i1

$to i2

$to restore equilibrium at Point 2.

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3.4 The Monetary Model: The Short Run versus the Long Run

• The short-run implications of the monetary model we have just discussed differs from the long-runimplications of the monetary approach we presented in the previous chapter.

— So it is important that we look at these differences and understand how and why they arise.

• Consider the following example: Suppose the Home central bank that previously kept the money supply Mconstant (i.e., its growth rate equal to zero) suddenly switches to an expansionary policy by now letting Mgrow at a rate of 5% per year.

1. If this expansion is expected to be a permanent policy in the long run, the predictions of the long-runmonetary approach and Fisher effect are clear:

— All else equal, a five-percentage-point increase in the home money growth rate causes a five-percentage-point increase in the Home inflation rate because the price level is fully flexible in the long run.In addition, the Fisher effect predicts that that increase in the Home inflation rate causes a five-percentage-point rise in the nominal interest rate (note that the real money supply falls in the longrun, and is constant at a lower level than before) — i ↑ in the long run.

2. If this expansion is expected to be temporary, the short-run monetary approach we just studies tells a verydiffferent story:

— All else equal, if the Home money supply expands, the immediate effect is an excess supply of realmoney balances because the price level is fixed in the short run. As a result, the nominal interest ratefalls in the short run — i ↓ in the short run.

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• This example gives lessons:

1. These different outcomes illustrate the importance of the assumptions we make about “price flexibility.”

2. They also underscore the importance of the nominal anchor in monetary policy formulation and the limitsthat central banks have to confront.

— In the short run, if the central bank temporarily changes its money supply without causing prices tobecome unstuck (i.e., triggering inflation), then looser money means lower interest rates, which mightbe temporarily desirable for some purposes (e.g., job creation).

— But, if the same loose monetary policy turns out to be permanent and persist, then prices will notremain fixed in the long run, and eventually looser money will mean higher inflation rates and higherinterest rates in the long run, which might be rather undesirable.

3. They also explain some apparently puzzling linkages among money, interest rates, and exchange rates:

— In both of the short- and long-run cases, an expanded money supply leads to a weaker currency (i.e.depreciation). However, in the short run, lower interest rates and a weaker currency go together (seethe UIP equation), whereas in the long run, high interest rates and a weaker currency go together (seethe PPP equation).

∗ The intuition is that in the short run, when we study the impact of a lower interest rate and we say"all else equal", we have assumed that expectations have not changed concerning future exchangerates. In other words, we envisage (implicitly) a temporary policy that does not tamper with thenominal anchor. However, it is not the case in the long run.

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• Once again, the change in the money supply in our example (i.e., a five-percentage-point increase in the moneygrowth rate) could be temporary or permanent.

— In applications, it is important to distinguish between temporary and permanent shocks to moneysupply (policy changes).

1. Temporary shocks dissipate before prices adjust, so they affect the economy only in the shortrun and expectations about the future will remain unaffected.

∗ This is because a temporary policy change will not tamper with the nominal anchor. Thus, we canstudy the impact of a change in the interest rate caused by a temporary change in the money supply,assuming all else equal, for example, assuming expectations about the future exchange ratedo not change (i.e., P and E will be unchanged in long run).

∗ There is no long-run policy analysis for temporary shocks.

2. Permanent shocks affect the economy in the long run, so that price adjustment will occur.As a result, expectations about the future is immediately affected in such a way.

∗ If the policy change turns out to be permanent, the assumption that the expected future price orexchange rate remains unaffected in the short-run policy analysis fails.

∗ We must examine both short-run and long-run impacts of permanent shocks.

— In what follows, this distinction is very important for the short-run and long-run policy analysis.

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4. THE ASSET APPROACH: APPLICATIONS AND EVIDENCE

4 The Asset Approach: Applications and Evidence

• To simplify the graphical presentation of the asset approach, we focus on conditions in the Home countryand thus don’t provide the diagrams for the Foreign country; a similar approach can be used for the Foreigncountry. We again assume that Home is the U.S. and Foreign is Europe.

4.1 The Asset Approach to Exchange Rates: Graphical Solution

• This figure two asset markets, the home moneyand FX markets, summarizing the asset approachin the short run.

1. Panel (a) shows the home (U.S.) moneymarket in which the home nominal interestrate i1

$is determined by the levels of real money

supply MS and demand MD with equilibriumat Point 1.

— Similarly, the foreign (European) moneymarket is in equilibrium where the foreignnominal interest rate i1€ is determined.

2. Panel (b) show the dollar-euro FX marketwhere the spot exchange rate E1

$/€ is deter-mined by domestic return DR and expectedforeign return FR with equilibrium at Point 1′.

— We assume that the FX market is subject tothe arbitrage forces and that UIP will hold.But this is true only if there are no capitalcontrols: as long as capital can move freelybetween Home and Foreign capital markets,

domestic and foreign returns will be equal-ized. Thus, if capital controls are imposed,there is no arbitrage and no reason why DRhas to equal FR.

• With this graphical apparatus in place, it isrelatively straightforward to solve for the ex-change rate given all the known exogenousvariables we have specified previously.

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4.2 Short-Run Policy Analysis: A Temporary Shock to Each of Home and Foreign Money Supply

• We now use the model to see what happens when there is a temporary, short-run increase in the money supplyby the central bank. Since such a change is temporary, expectations about the future (i.e., the expectedfuture exchange rate Ee

$/€) remain unaffected.

1. Temporary expansion of home money supply

• In the home money market, an increase in thehome money supply from M1

US to M2US causes

the home interest rate to fall from to i1$to

i2$. As a result, the domestic return drops from

DR1 to DR2 in the FX market, causing theexchange rate to rise from E1

$/€ to E2$/€

(i.e., the dollar depreciates).

2. Temporary expansion of foreign money supply

• There is no change in the home money market.

• In the foreign money market, an increase inthe foreign money supply leads to a fall in theforeign interest rate, lowering the foreign re-turn from FR1 to FR2 in the FX market. Asa result, the exchange rate falls (i.e., thedollar appreciates).

• Intuitively, a home monetary expansion lowers the home nominal interest rate, which is also the domestic returnin the FX market. This makes foreign deposits more attractive and makes traders wish to sell home depositsand buy foreign deposits, This, in turn, makes the home exchange rate increase (i.e., the home currencydepreicates). However, this depreciation makes foreign deposits less attractive (all else equal). Eventually,the equality of foreign and domestic returns is restored, UIP holds again, and the FX market reaches a newshort-run equilibrium. (A similar intuition applies to a foreign monetary expansion).

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• The Rise and Fall of the Dollar, 1999—2004.

— Let’s look at the data on U.S.—Eurozone interest rates and exchange rates from 1999 to 2004.

1. From the euro’s birth in 1999 until 2001, as interest rates in the United States were raised well abovethose in Europe (seen as a temporary Home monetary contraction relative to Foreign), the dollarsteadily appreciated against the euro.

∗ The Fed was more worried about the U.S. economy "overheating" with higher inflation.

2. In early 2001, however, the Federal Reserve began a long series of interest rate reductions (seen as atemporary Home monetary expansion relative to Foreign). By 2004, the Fed Funds rate was well belowthe European Central Bank (ECB) refinancing rate. So during this period, the dollar had depreciatedagainst the euro.

∗ The U.S. economy had slowed after the boom and the Fed hoped that lower interest rates wouldavert a recession; the terrorist attacks of September 11, 2001, led to fears of a more serious economicsetback and ecouraged further monetary easing.

— This is exactly what our model predicts: The asset approach to exchange rates predicts a dollarappreciation (1999—2001) when U.S. interest rates were relatively high, followed by a dollardepreciation (2001—2004) when U.S. interest rates were relatively low.

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1 introduction in the data, however, substantial...

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