Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

m

time

I -)es not feature the price ion, following an unanticdiscrete adjustment of the ately before and immedi- n) so that the domestic rate Unanticipated monetary

tly flexible.

m possible when the price n also cause overshooting se is announced at time tA ave perfect foresight, the ne tA from e0 to e', followed

Chapter 11: The Open Economy

Figure 11.19. Exchange rate dynamics with perfectly flexible prices

by gradual further depreciation between tA and ti, represented by the movement from point a' to a" along the e(mo) line. Exactly at time ti the money supply is increased (as was announced), the e = 0 line shifts to the right to e(m i ), and the exchange rate settles at its new equilibrium level el. Agents anticipate a depreciation of the currency in the long run since the money supply increases. There can be no anticipated jumps in the exchange rate, since these would imply infinitely large expected capital gains/losses, so that one side of the market would disappear. Consequently, interest parity dictates adjustment, and the exchange rate starts to depreciate immediately. 8 There is still no overshooting in this case.

Matters are different if the monetary impulse is implemented immediately (tA = ti) but is of a temporary nature. Specifically, it is announced (and believed by the agents) that the money supply will be decreased to its old level at some time tE in the future. In that case, the adjustment path is given by an immediate depreciation at tA = ti from eo to e", followed by gradual appreciation between tA and tE (described by the movement from point b' to b"). At the time the money supply is decreased again, the exchange rate has fallen back to its initial level, the e = 0 line shifts from e(mi ) = 0 to e(mo) = 0, and equilibrium is restored. A temporary monetary expansion causes the exchange rate to overshoot its long-run (unchanged)

8 The smaller the difference between implementation and announcement dates (ti — tA), the larger is

and nothing happens to the exchange rate.

The Foundation of Modern Macroeconomics

level. Agents expect no long-run depreciation but the domestic interest rate is temporarily below the world rate of interest, so that interest parity predicts that e < 0 along the transition path.

Imperfect capital mobility and overshooting

Frenkel and Rodriguez (1982) have shown that Dornbusch's conclusion regarding the crucial role of slow price adjustment for the overshooting result is somewhat misleading. They do so by modifying the Dornbusch model to incorporate imperfect capital mobility. The Frenkel-Rodriguez model is given in Table 11.6. Equation (T6.1) shows that aggregate demand, yd , is equal to fixed output, p, plus a term depending on the real exchange rate. Underlying (T6.1) is the assumption that output and domestic absorption are fixed, and that the long-run trade balance is zero. Equation (T6.2) is the inverse LM curve, expressing the domestic interest rate that clears the money market as a function of fixed output and the real money supply. In view of (T5.2), the semi-elasticities are defined as: ERy EMy/EMR and ERM 1/EmR. Equation (T6.3) shows that the domestic price level changes as a result of goods market disequilibrium, and (T6.4) shows that the trade balance, X, depends positively on the real exchange rate. In (T6.5), net capital inflows, KI, depend on the yield gap between domestic and foreign assets (see (11.70)). Depending on the value of (T6.5) can be used to describe different assumptions regarding capital mobility. If capital is immobile, 4 = 0, if it is perfectly mobile, oo, and the intermediate case of imperfect capital mobility is obtained if 0 < oo. Under perfect capital mobility, yield gaps are closed instantaneously, uncovered interest parity holds (r = r* + ë), and the balance of payments restriction (T6.6) is redundant (since it holds as an identity in that case).

By using (T6.1) and (T6.3), the price adjustment equation is obtained:

= 95ED(2 + e —

Similarly, by substituting (T6.2), (T6.4), and (T6.5) into (T6.6), the dynamic

Table 11.6. The Frenkel—Rodriguez Model

equation for the

= (ExQM

which shows th,.. the exchange rate. the", = 0 and = I

e = P —

e = [1 —

" 11

The p = 0 line ( ambiguous. If ca if capital mobiliI ;

Figures 11.20 and

Figure 11.20 illu monetary impul)L causes the domest At the same time,

capital mobility is payments equilil + KI = 0 at time rise along the sack with high mobil and the associateu its long-run level

trade account at

I

e

Figt cap

11

I

:nestic interest rate is temst parity predicts that e < 0

h's conclusion regarding hooting result is somewhat to incorporate imperfect Table 11.6. Equation (T6.1) it, j7, plus a term dependumption that output and de balance is zero. Equation - lterest rate that clears the it money supply. In view of

and ERM 1/EmR• Equa-

as a result of goods market X, depends positively on I, depend on the yield gap

)ending on the value of ,A- ding capital mobility. If

Do, and the intermedioo. Under perfect uncovered interest parity 1 (T6.6) is redundant (since

►1-1 is obtained:

ak/ap = —Ow < 0. into (T6.6), the dynamic

(T6.1)

(T6.2)

(T6.3)

(T6.4)

(T6.5)

(16.6)

Chapter 11: The Open Economy

equation for the exchange rate is obtained:

e = (ExQM [p* + e — p] + ERyP - ERm [m — p] - r*, (11.82)

which shows that, just as in the Dornbusch model, the instability originates from the exchange rate, i.e. ae/ae = ExQ / > 0. Following the same procedures as above, the p = 0 and e = 0 lines can be derived:

e = p — p* , (11.83)

The p = 0 line (11.83) is upward sloping, but the slope of the e = 0 line (11.84) is ambiguous. If capital mobility is low low), it is likely to be upward sloping, but if capital mobility is high it will be downward sloping. The two cases are drawn in Figures 11.20 and 11.21, respectively.

Figure 11.20 illustrates that there is no overshooting of the exchange rate after a monetary impulse under low capital mobility. At impact, the higher money supply causes the domestic interest rate to fall. This causes net capital outflows (KI < 0). At the same time, the exchange rate depreciates and the trade account improves. If capital mobility is low, the former effect is dominated by the latter, and balance of payments equilibrium requires a slight appreciation of the currency (to ensure that X + KI = 0 at time t = 0). After that, the domestic price level and the exchange rate rise along the saddle path towards their new equilibrium levels. The opposite case with high mobility of capital is illustrated in Figure 11.21. Here, both the e = 0 line and the associated saddle path are downward sloping. The exchange rate overshoots its long-run level at impact, as the capital inflow effect dominates the effect on the trade account at impact.

e

Po

Figure 11.20. Exchange rate dynamics with low capital mobility

305

The Foundation of Modern Macroeconomics

e

Po

Figure 11.21. Exchange rate dynamics with high capital mobility

So what is the lesson that is learnt from this model? The role of asset market adjustment speed is vital in the discussion about overshooting. As long as the speed

of price adjustment is finite, the sign of the parameter (EXQ — GERM) determines whether or not there is overshooting. In other words, the assumption of sticky

prices is necessary but not sufficient for the exchange rate overshooting result. By only considering the extreme case of perfect capital mobility, one is unable to disentangle the effects of adjustment speeds in goodsand assets markets, and one is tempted to infer (incorrectly) that price stickiness alone automatically implies exchange rate overshooting.

Monetary accommodation and overshooting

Up to this point we have assumed that the policy maker pursues discrete monetary policy, consisting of once-off changes in the money supply. Suppose now, however, that the policy maker wishes to accommodate any price shocks that may occur. Specifically, we continue to use the Dornbusch model of Table 11.5, but we postulate that the money supply reacts to the price level according to:

m = m + 8p, (11.85)

where 8 is the accommodation coefficient. If 8 = 0, we have the "pure float" case analysed by Dornbusch, but if 0 < 8 < 1, we have a "dirty float". There is some

degree of exchange rate management in the form of adjustments in the money supply.

Since the money sui replaced by:

Y — EmoyQ[p* + e -

r = EMY EYQ [pa e -

so that the = 0 and e

e= [(1 — (5)EyR + (%4

È 0 line (11.89) is am

A

(clipe) y y EmRE

E

1—

(:) r=r*

If there is little accommo rise in in) leads to ove:

8 = 0 and 1 — EmyEN >

however, the overshoe rate is the result. This

in th shifts both the p real exchange rate ur._ have not been drawn 1

long-run equilibrium 1 gradual adjustment given in the lower par along with the price I a falling interest rate. effect on the price le\ r = r*, so that the re,t, dp(oo) = 71(1 — 8) >

m increases by

=0

SPi

=0), Po

p

`iigh

Y = EMREYQ [p* + e — p] + EMRCYGg + EYR [fn — (1 — 8)131

EMR EMYEYR

r= EMREYQ[p* + e — pi+ EMY EYGg —m +(1- 8)p

EMR EMYEYR

so that the p = 0 and é = 0 lines are changed to:

[(1 8)EyR + EMREYQ] + (EMR + emvEyRV

e=

EMREYQ

EMR 6 YQP* EMREYGg EYRtil

EMREYQ

e _ [1 — 8 — EmEy(dp — EmE mp* — EmEyGg + fh + EMR EM E YR

EM E YQ

(11.86)

(11.87)

The Foundation of Modern Macroeconomics

e

e'

e0

Pi

m

m

el

e0

y

y

time

Figure 11.22. Monetary accommodation and undershooting

11.4 Punchlines

In this chapter we conclude our discussion of the IS-LM model that was commenced in Chapter 1, by discussing the contributions made by Mundell and Fleming (MF) and subsequent work in the area. In the MF framework it is explicitly recognized that most countries are open economies, i.e. they trade goods and financial assets with each other. There are two crucial aspects characterizing the open economy, namely its "financial openness" and the exchange rate system it maintains.

By financial openness we mean the ease with which domestic residents substitute domestic and foreign assets in their portfolios as yields between assets differ. If substitution is very easy then yields will equalize. This situation is often referred to as one of perfect capital mobility. At the other extreme, if domestic residents are not willing to hold foreign assets at all (or if there are strictures against it) then the

economy is "final

The intermediat There are two exchange rates, - currency fixed by

the policy maker endogenous unc. etary authority da

equilibrium exchai supply in the fort ., The results of m

mobility and on exchange rates nea

output. With perfei policy is ineffectiN

output. All these re In order to end _

the MF framewu

competitive firms I ods are distinct

model some Keyne is fixed and ti anally, because doi sumer price index, both the domestic Armed with this al policy under I

pays a crucial role fective (effective). ' mestic price, an

exchange rate. In c output and the G .

nominal exchange an exogenously

In order to endq

of two identical coo

The two-country

Depending on the icy initiatives may

:..odel we show tht In the last part of :ice model of a

m

time

on and

odel that was commenced Mundell and Fleming (MF) -' it is explicitly recognized le goods and financial assets *Prizing the open economy, system it maintains. lomestic residents substitute Ids between assets differ. If

uation is often referred to Ike, if domestic residents are ctures against it) then the

Chapter 11: The Open Economy

economy is "financially closed" and there is said to be no capital mobility at all. 'le intermediate case, with imperfectly mobile capital, can also be distinguished. There are two prototypical exchange rate systems. Under a system of fixed exchange rates, the monetary authority keeps the exchange rate for the domestic currency fixed by means of interventions on the foreign exchange market. Unless the policy maker engages in sterilization operations, the money supply will be endogenous under this regime. With a system of flexible exchange rates, the monetary authority does not intervene in the foreign exchange market. As a result the equilibrium exchange rate is endogenously determined by the forces of demand and

supply in the foreign exchange market.

The results of monetary and fiscal policy depend both on the degree of capital mobility and on the exchange rate system. With immobile capital and under fixed exchange rates neither monetary nor fiscal policy can permanently affect aggregate output. With perfectly mobile capital and fixed (flexible) exchange rates, monetary policy is ineffective (effective) and fiscal policy is effective (ineffective) at influencing output. All these results are based on the assumption of a fixed price level.

In order to endogenize the price level we add a simple model of aggregate supply to the MF framework. The key features of this model are as follows. First, perfectly competitive firms set prices of the domestic good. Second, domestic and foreign goods are distinct and are imperfect substitutes for each other. Third, to give the model some Keynesian features it is assumed that the (real or nominal) consumer wage is fixed and that the demand for labour determines employment and output. Finally, because domestic consumers use both domestic and foreign goods, the consumer price index, upon which the wage claims are potentially based, depends on both the domestic and the foreign price (and thus on the nominal exchange rate).

Armed with this extended MF model we investigate the effects of monetary and fiscal policy under perfect capital mobility. Not surprisingly, the wage setting regime plays a crucial role. Under real (nominal) wage rigidity, monetary policy is ineffective (effective). With real wage rigidity fiscal policy boosts output, reduces the domestic price, and leads to an appreciation of both the nominal and the real exchange rate. In contrast, with nominal wage rigidity fiscal policy does not affect output and the domestic price and merely leads to an appreciation of the real and nominal exchange rate. All these results hold for a small open economy which faces an exogenously given world interest rate.

In order to endogenize the world interest rate we assume that the world consists of two identical countries which can each be described by the extended MF model. The two-country MF model shows how shocks are transmitted internationally. Depending on the configuration of wage-setting regimes in the two countries' policy initiatives may spill over across countries. As an application of the two-country model we show the effects of policy coordination.

In the last part of this chapter we introduce forward-looking elements in a stickyprice model of a small open economy facing perfect capital mobility. A striking

309

The Foundation of Modern Macroeconomics

feature of this model is that an unanticipated and permanent monetary expansion may produce overshooting of the exchange rate. Intuitively, agents expect a long-run depreciation of the nominal exchange rate which, ceteris paribus, makes domestic assets less attractive than foreign assets. There is a net capital outflow and the spot exchange rate depreciates. During transition the domestic interest rate falls short of the world interest rate. As a result the exchange rate overshoots its long-run equilibrium value because part of the yield on domestic assets consists of a gradual appreciation of the exchange rate.

The overshooting result caused a big stir in the late 1970s because it provided an economically intuitive rationale for the large swings that are often observed in the exchange rate. Large changes in the exchange rate need not be due to the behaviour of irrational currency speculators after all! In the final part of the chapter we demonstrate that price stickiness is a necessary but not a sufficient condition for the overshooting result to hold. Both a high degree of capital mobility and price stickiness are needed to produce overshooting.

Further Reading

Obstfeld and Rogoff (1996) is a recent graduate text focusing on the open economy. The classic references on the open economy IS-LM model are Mundell (1968) and Fleming (1962). See Frenkel and Razin (1987) for a review article. Open economy models incorporating the rational expectations (or perfect foresight) hypothesis were developed by Dornbusch (1976, 1980, 1983), Kouri (1976), Niehans (1977), Buiter and Miller (1981, 1982), and Obstfeld and Rogoff (1984). See Gartner (1993) for a recent survey. Obstfeld and Rogoff (1995a) present a micro-founded model of the small open economy with sticky prices.

Students interested in multi-country models and the issue of policy coordination are referred to Cooper (1968), Mussa (1979), Aoki (1986), McKibbin (1988), Canzoneri and Henderson (1991), and McKibbin and Sachs (1991). Key references to the intertemporal approach to the current account are Sachs (1981), Buiter (1981), Obstfeld (1982), and Svensson and Razin (1983). A good survey of this literature is presented by Obstfeld and Rogoff (1995b). For empirical evidence, see Feldstein and Horioka (1980) and Feldstein (1994).

Calvo and Rodriguez (1977) study a perfect foresight model with currency substitution. For good surveys of the literature on balance of payments crises, see Agenor, Bhandari, and Flood (1992) and Blackburn and Sola (1993).

Money 1

The purpose of this L,

1.What are the phi

2.How can the role

3.What is the soc

4.How does money

as an inflation to

I

12.1 Functions

I

The question "What of any man or woma from such a question his/her wallet and • n it and possibly .. the question had ber wallet would probabl

to counterfeit) paper the stuff which sits in

Economists will s.. question and instead

unctions performed

..►I designating what

precisely what som.

I

An exhaustive and

*defies is found in Eir.

Wicksell (1935), and jaw

permanent monetary expan v. Intuitively, agents expect a which, ceteris paribus, makes !re is a net capital outflow and domestic interest rate falls rate overshoots its long-run tic assets consists of a gradual

to 1970s because it provided qs that are often observed rate need not be due to the the final part of the chapter not a sufficient condition for )f capital mobility and price

-on the open economy. The

`Lindell (1968) and Fleming

economy models incorporat-

• re developed by Dornbusch Iler (1981, 1982), and ObstObstfeld and Rogoff (1995a)

th sticky prices.

le of policy coordination are :)in (1988), Canzoneri and

.- ences to the intertemporal

.S1), Obstfeld (1982), and s presented by Obstfeld and orioka (1980) and Feldstein

..ith currency substitution. s. see Agenor, Bhandari, and

12

Money

The purpose of this chapter is to discuss the following issues:

1.What are the principal functions of money in advanced economies?

2.How can the role of money be captured in simple models?

3.What is the socially optimal quantity of money?

4.How does money affect the government budget constraint (nominal money growth as an inflation tax)?

12.1 Functions of Money

The question "What is money?" will be answered with full confidence when asked of any man or woman in the street. Indeed, the typical response one may expect from such a question would probably consist of the person in question taking out his/her wallet and showing a colourful piece of paper with some numbers printed on it and possibly the portrait of some past or present monarch or president. If the question had been asked a few centuries ago, the object produced from the wallet would probably have been made of some precious metal rather than (hard to counterfeit) paper but the intended answer would have been the same: money is the stuff which sits in one's wallet and can be used to purchase goods and services. 1

Economists will show considerably less confidence if confronted with the same question and instead of formulating a straight answer will propose a number of functions performed by this elusive thing called "money". In other words, instead of designating what money "is" economists describe what money "does," or more precisely what something must do in order for it to be called money. In broad terms

1 An exhaustive and highly readable historical treatment of the emergence of money in different societies is found in Einzig (1949). See also Davies (1994), Jevons (1875), Menger (1892), Fisher (1913), Wicksell (1935), and Jones (1976).

The Foundation o Modern Macroeconomics

Figure 12.1. The barter economy

three major functions of money can be distinguished: (1) money as a medium of exchange, (2) money as a medium of account, and (3) money as a store of value (McCallum, 1989a, pp. 16-18).

The various aspects of money can be illustrated with the aid of Figure 12.1. Suppose there are four agents (labelled 1 through 4) in the economy who each produce a unique commodity but like to consume not just their own product but also all other products in the economy. In a barter economy all agents formulate their supply of the own good and demands for the other goods, meet at a central market place (which is located, say, at point A in Figure 12.1) in which the equilibrium relative prices are determined. Since there are four goods in our example, there are in total six relative prices which are determined. 2 Exchange takes place without the use of money, namely good 1 is directly exchanged ("bartered") for good 2, etc. Aside from obvious complications relating to indivisibilities of goods etc., a centralized market place would function perfectly well without money. Intuitively, without some kind of "friction" money is not likely to be a very useful thing to have.

In reality, of course, not all transactions take place in a centralized fullinformation setting and the process of trading becomes more complicated. Assume that the central market place in Figure 12.1 exists, but that the agent does not know beforehand which other trader he is going to meet there at any particular time. Suppose that at most two traders meet randomly at this market in each period. Then agents are confronted with a major problem due to the need for a double coincidence of wants. For example, agent 1 may find himself paired with agent 2 who may or may not want to trade with him. In fact, in the absence of money, an exchange of goods will only take place if agent 1 meets an agent who wants to have his good

2 These are the rates at which the goods are exchanged pair-wise. Denoting as the relative price of

good i in terms of good j, we have the following relative prices: P12, P13, P14, P23, P24, and p34. Obviously, we have that

and who himself has a _ it may take a lot of etiu, Even if agents are perfe

problem may still persi ble coincidence of wants their own good and th. wise direction), i.e. agei., agent 3 (3,4), and agent - each agent can at most :...

that agent 1, for example. and 3, etc. It is easy to se , for example, cannot tra,, any price. Similarly, agen double coincidence of 1•• situation of autarky persis Now assume there is a 1 across agents at zero cos able to trade with each o example, sells his good t, good 2 from agent 2. Sinc equilibrium can be anal: result of the existence of Of course, the circle mo

it is nevertheless useful t "test". Something serves that agents can attain a l - and in the "circle" mod, this proposed definition. 1 (but not totally elimina the latter the friction is cc There is nothing in the 1 be an intrinsically valuabl enhance people's utility a low-valued good (such as it is generally accepted in

a

3 This test is similar to (but nu ment is more strict in that it Indeed, he call this the "tradr

Agent 1 may meet an agt buy good 1. The transaction tam If agent 1 instead meets an a.. then no trade takes place. HeI