Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

lomy and nominal yaw

- -lulating domestic ou !nt target, p > 0) without 'tiive rise to large deficit )me cost function, LG:

(11.55

domestic economy, given e foreign policy maker I-1-

(11.5r

reduced form expressir assumed that the domestic

• c. i.e. y features in bot'•

ending level independently, country into account. In chooses its spending level sample, the policy maker

(11.57)

(11.58)

which relates its optimal ill employment target and

RR*. (11.59)

qu " briu m in which each try's spending plan. Since mal spending plans, the the intersection of RR

Chapter 11: The Open Economy

Figure 11.14. International coordination of fiscal policy under nominal wage rigidity in both countries

and RR*, i.e. by solving (11.58)-(11.59) for g and g*. For the special case of 4- = r, we obtain:

where the subscript "N" indicates that these solutions are non-cooperative. In terms of Figures 11.14 and 11.15, the two reaction functions can be drawn as RR and RR*, respectively. In both diagrams we impose that 4- = which means that the two countries have the same wage-setting regime. In Figure 11.14 both countries have

nominal wage rigidity (4- = 4- * = 1), and in Figure 11.15 both countries experience real wage rigidity (. = 4- * < 0). In both cases the stable 7 non-cooperative solution

is at point N, where the two reaction functions intersect.

What would a coordinated policy look like? In the coordinated solution, the policy maker in one country takes into account the (positive or negative) effect that its own spending has on the other country. One way to analyse the coordinated policy is to assume that both policy makers relinquish control over spending to some international agency which is instructed to minimize the total welfare loss,

by choosing spending levels in the two countries. Formally, the problem solved

It is easy to show that the non-cooperative Nash equilibrium is stable. In terms of Figure 11.14,

suppose that g = go initially. It is then optimal for the foreign policy maker to choose g* = 4. But for this value of g*, it is optimal for the domestic policy maker to set g = Repeating the argument shows

that the only stable Nash equilibrium is at point N.

293

The Foundation of Modern Macroeconomics

W(1 +0)

Figure 11.15. International coordination of fiscal policy under real wage rigidity in both countries

under a coordinated fiscal policy is:

which yields the first-order conditions:

By comparing these first-order conditions under cooperative behaviour to the ones relevant under non-cooperative behaviour (given in equations (11.58)-(11.59)), it is clear that in the cooperative solution the policy maker explicitly takes into account the international spill-over effects that exist (represented by the terms premultiplied by and r in (11.62) and (11.63), respectively). By solving (11.62)-(11.63) for g and g* (again for the special case = .*), the spending levels under coordination are obtained:

where the subscript "C" is used to designate cooperation.

The relative size of government spending in the cooperative and non-cooperative scenario's can be judged by comparing (11.60) and (11.64). If there is nominal

wage rigidity in both cc the higher spending it where point C designatL: is obvious. With nomina locomotive policy. In the not take into account tha therefore both undere' choose spending levels t hand, this external eft- , use of the locomotive IL. The opposite holds if t

is illustrated in Figure 11. and uncoordinated actioi too high. The coordin.. of government spenu... 6 Up to this point we hi or real wage rigidity in where there is real wag( wage rigidity in the for. a: .d 0 < r < 1. Followl.., it is possible to derive the

so that:

(1 + gc — gN = r + 0 +

[1 gc- = [ 1 + 0 +

From (11.65) we can con under the symmL

and (11.60). Furthermore * it gN < gc and Ar. > 4.:erest rate is too hibri In Europe due to the eci s_..ce fiscal policy is a I spends too much in the

RR*

9sCal , tries

(11.62)

, • , ye behaviour to the ones ons (11.58)-(11.59)), it is Ynlicitly takes into account v the terms premultiplied lying (11.62)-(11.63) for g 'eels under coordination

(11.64)

rative and non-cooperative 1.64). If there is nominal

Chapter 11: The Open Economy

wage rigidity in both countries “. = = 1), the cooperative solution involves the higher spending levels in the two countries. This is illustrated in Figure 11.14, where point C designates the cooperative solution. The intuition behind this result is obvious. With nominal wage rigidity in both countries, fiscal policy constitutes a

• , comotive policy. In the absence of coordination, however, individual countries do not take into account that their own fiscal spending also aids the other country. They therefore both underestimate the benefit of their own spending and consequently choose spending levels that are too low. In the cooperative solution, on the other hand, this external effect is internalized, and spending levels are raised to make full use of the locomotive feature of fiscal policy.

The opposite holds if there is real wage rigidity in both countries = < 0), as is illustrated in Figure 11.15. Fiscal policy constitutes a beggar-thy-neighbour policy and uncoordinated actions by national governments lead to spending levels that are too high. The coordinated policy solution internalizes this "pollution-like" aspect of government spending and consequently leads to lower spending levels.

Up to this point we have only analysed the symmetric cases of either nominal or real wage rigidity in both countries. As a final case, consider the mixed case where there is real wage rigidity in the domestic country (Europe) and nominal wage rigidity in the foreign country (the US). This configuration implies that < 0 and 0 < < 1. Following the same reasoning as before, but noting that now

it is possible to derive the uncoordinated and coordinated solutions for government spending:

From (11.65) we can conclude that gN is larger, and gN is smaller, in the asymmetric than under the symmetric case (for which = > 0)—compare (11.65)-(11.66) and (11.60). Furthermore, in view of (11.65)-(11.66) and (11.67)-(11.68) we observe that gN < gc and gN > This means that, in the absence of cooperation, the world interest rate is too high, the dollar is too strong, and there is high unemployment in Europe due to the economic policy pursued by the US. This result is intuitive since fiscal policy is a beggar-thy-neighbour policy for the US, which consequently spends too much in the absence of coordination. Under cooperation this external

295

The Foundation of Modern Macroeconomics

effect is internalized. Similarly, European fiscal policy is a locomotive policy, which consequently spends too little.

11.3Forward-looking Behaviour in International Financial Markets

Up to this point we have been somewhat inconsistent in our discussion of the economy operating under flexible exchange rates. The nature of this inconsistency can be gleaned by looking at the uncovered interest parity condition. Consider a domestic investor who has to invest either at home, where the interest rate on bonds is r, or in the US, where the interest rate on bonds is r* . If the investor chooses to purchase a domestic bond, he will get f 100x (1 + r) at the end of the period, so that the gross yield on his investment is equal to 1 + r. If, on the other hand, the investor purchases the US bond, he must first change currency (from guilders to dollars), and purchase US bonds to the amount of (f100x(11E0) = $100, where E0 is the nominal exchange rate at the beginning of the period (the dimension of E is, of course, f per $). At the end of the period he receives ($100E 0 ) x (1 + r*), which he converts back into guilders by taking his dollars to the foreign exchange market, thus obtaining (1 + x (1 + r*) x (E1lE0). Of course, the investor must decide at the beginning of the period on his investment, and he does not know the actual exchange rate that will hold at the end of the period. The estimated gross yield on his foreign investment therefore equals (1 +

where Eel is the exchange rate the investor expects at the beginning of the period to hold at the end of the period. If the investor is risk-neutral, he chooses the domestic (foreign) bond if 1 + r > ( < )(1 + r*) x (E1lE0), and is indifferent between the two investment possibilities if the expected yields are equal.

The point of all this is that the expected yield differential between domestic and foreign investments depends not only on the interest rates in the two countries (r and r*) but also on what is expected to happen to the exchange rate in the period of the investment:

where the cross-term r* AEe 1E0 can be ignored because it is of second-order magnitude. Equation (11.69) can be written in continuous time as:

where e E:- - log E, so that e -.- dee I dt =--- Ee IE. Expressions (11.69) and (11.70) are intuitive. If the domestic currency is expected to appreciate during the period (e < 0),

then the domestic cu ings on the bond are e expected. In the case o L:.:ferential is elimin_. interest parity conditic

r = r* + ëe .

11.3.1 The Dornbu!

Up to this point we which would be correct this may be reasonable what inconsistent as, of freely flexible excha

nerally will) fluctut:I. in the exchange rate. T duce the assumption oi ex dectations; see Chap perfect capital mobility E., nations (T5.1) an('_ a small open economy es.::ation (T5.4) is the 1 level y, prices gradual.,. price level is finite, du rms that 0 < < Luresight. Agents' expo with the actual path The model exhibits and e = 0 implies that Iu: run, the dorm.: i-urthermore, there is al with y = p and r = r*

Table 11.5. The Do' DI

f=r-Fee ,

= [y - ,

e=e.

0

a locomotive policy, which

emotional

ens in our discussion of the nature of this inconsistency Parity condition. Consider a where the interest rate on is is r*. If the investor chooses

1 at the end of the period, so r. If, on the other hand, the

e currency (from guilders to r1 0 0 x (1/E0) = $100, where he period (the dimension of --ceives ($100E0) x (1 + r*), :Ts to the foreign exchange

1 + x (E1 /E0). Of course, d on his investment, and he it the end of the period. The equals (1 + r*) x (EVE0),

5eginning of the period to ral, he chooses the domestic I fferent between the two

tial between domestic and :es in the two countries (r exchange rate in the period

1AEe

E0

se it is of second-order DUS time as:

(11.70)

11.69) and (11.70) are intu- !uring the period (e < 0),

Chapter 11: The Open Economy

_len the domestic currency yield on the US bond is reduced because the dollar earn- ^gs on the bond are expected to represent fewer guilders than if no appreciation is pected. In the case of perfect capital mobility, arbitrage will ensure that the yield differential is eliminated, in which case (11.70) reduces to the famous uncovered

serest parity condition:

11.3.1 The Dornbusch model

Up to this point we have always assumed that r = r* under perfect capital mobility, - hich would be correct if investors never expect the exchange rate to change. Whilst this may be reasonable under a (tenable) fixed exchange rate regime, it is a somewhat inconsistent assumption to make about investors' expectations in a regime of freely flexible exchange rates. Investors know that the exchange rate can (and generally will) fluctuate, and consequently will form expectations about the change in the exchange rate. The seminal contribution by Dornbusch (1976) was to introduce the assumption of perfect foresight (the deterministic counterpart to rational expectations; see Chapters 1 and 3) into a model of a small open economy facing perfect capital mobility and sticky prices. The model is summarized in Table 11.5. Equations (T5.1) and (T5.2) are, respectively, the IS curve and the LM curve for a small open economy. Uncovered interest parity is given in equation (T5.3) and equation (T5.4) is the Phillips curve. If output is higher than its full employment level y, prices gradually adjust to eliminate Okun's gap. The adjustment speed of the price level is finite, due to the assumption of sticky prices. This means in formal terms that 0 < < oo. Finally, equation (T5.5) represents the assumption of perfect foresight. Agents' expectations regarding the path of the exchange rate coincide with the actual path of the exchange rate.

The model exhibits long-run monetary neutrality, as --- 0 implies that y = and e = 0 implies that so that (T5.2) shows that m — p is constant. In the long run, the domestic price level and the nominal money supply move together. Furthermore, there is also a unique equilibrium real exchange rate, defined by (T5.1) with y = y and r = r* substituted. This equilibrium exchange rate is not affected

The Foundation of Modern Macroeconomics

by monetary policy, but can be affected by fiscal policy. But we are really interested in the short-run dynamics implied by the model. To study this, we first reduce the model to two differential equations in e and p. For given values of the nominal exchange rate and the domestic price level, the domestic interest rate and output can be written as:

EMR EMYEYR

By substituting (11.72)-(11.73) and (T5.5) into (T5.3) and (T5.4), we obtain the dynamic representation of the model:

EmEmp EMEYGg m *

The only sign that is ambiguous in the Jacobian matrix on the right-hand side of (11.74) is the one for ae/ap. This is because an increase in the domestic price level has an ambiguous effect on the domestic interest rate. On the one hand, real money balances decrease, which leads to upward pressure on the interest rate, but on the other hand the domestic price increase also leads to a real appreciation of the exchange rate which decreases output and hence the (transactions) demand for money. This money demand effect causes downward pressure on the interest rate. We assume for simplicity that the money supply effect dominates the money demand effect, so that EmyEm < 1 and ae/ap > 0.

The model can be analysed with the aid of Figure 11.16. The e = 0 line is obtained by taking the first equation in (11.74) and solving it for e as a function of p and the exogenous variables:

EMYEYQ

Along the e = 0 line the domestic interest rate equals the foreign interest rate (r = r*). It is downward sloping in view of our assumption (made above) that EmyEm < 1. For points above the e = 0 line the nominal (and the real) exchange rate is too high, output is too high, and the domestic rate of interest is higher than the world rate (r > r*). Uncovered interest parity predicts that an exchange rate depreciation is expected and occurs (ee = e > 0). The opposite holds for points below the e = 0 line. These dynamic forces on the nominal exchange rate are indicated by vertical

e

eo

Figure 11:

arrows in Figure 11.16 (11.74) implies:

which shows that the . the economy in the set dampened, accord i n The p = 0 line is obi

it for e as a function ,

e + p* = ( E YR ± E

Along the p = 0 line ti an increase in the dorn store full employi:. _ right of the p = 0 domestic price level i•

The dynamic for, arrows in Figure 11.16 e real side of the 11.1/4,

= CEYR ap ) Emit+

A ne long-run steady-st so that both r = r*

cy. But we are really inter-- 0". v this, we first reduce ir„ ven values of the nom i^ ,

..-ctic interest rate and ot.

3) and (T5.4), we obtain th.-

(11.74►

, *rix on the right-hand side crease in the domestic price t rate. On the one hand, real re on the interest rate, but ads to a real appreciation of the (transactions) demand card pressure on the interest cfect dominates the money

16. The e = 0 line is obtained r e as a function of p and the

•frR)r* (11.75)

reign interest rate (r = r*).

above) that EMYE YQ < 1.

\ exchange rate is too high, higher than the world rate :hange rate depreciation is 7 points below the é = 0 to are indicated by vertical

Chapter 11: The Open Economy

Figure 11.16. Phase diagram for the Dornbusch model

arrows in Figure 11.16. More formally we can derive the same result by noting that I 1.74) implies:

which shows that the interest parity condition introduces an unstable element into the economy in the sense that exchange rate movements are magnified, rather than

dampened, according to (11.76).

The p = 0 line is obtained by taking the second equation in (11.74) and solving it for e as a function of p and the exogenous variables:

Along the p = 0 line there is full employment (y = y). It is upward sloping because an increase in the domestic price level reduces output via the real balance effect. To restore full employment, the nominal exchange rate must depreciate. For points to

the right of the p = 0 line, output is below its full employment level (y < y/) and the domestic price level is falling. The opposite holds for points to the left of the p = 0

line. The dynamic forces operating on the price level are indicated by horizontal arrows in Figure 11.16. In formal terms, the second equation of (11.74) shows that the real side of the model exerts a stabilizing influence on the economy:

The long-run steady-state equilibrium is at point ao in Figure 11.16, where p = e = 0 so that both r = r* and y = k hold.

299

The Foundation of Modern Macroeconomics

What about the stability of this steady-state equilibrium? Will a shock away from ao eventually and automatically be corrected in this model? The answer is an emphatic "no" unless we invoke the perfect foresight hypothesis. The dashed trajectories drawn in Figure 11.16 eventually all turn away from the steady-state equilibrium. There is, however, exactly one trajectory which does lead the economy back to equilibrium. This is the saddle path, SP. If and only if the economy is on this saddle path, will the equilibrium be reached. Since agents have perfect foresight they know that the economy will fall apart unless it is on the saddle path (p and/or e will go to nonsense values). Consequently, they expect that the economy must be on the saddle path, and by their behaviour this expectation is also correct. If anything unexpected happens, the nominal exchange rate immediately adjusts to place the economy on the new saddle path. Since the price level is sticky, it cannot jump instantaneously and consequently the nominal exchange rate takes care of the entire adjustment in the impact period. (See Chapter 4 above for other examples of saddle-point stable models.)

As an example of adjustment, consider the case of an unanticipated expansionary fiscal policy. In terms of Figure 11.17, the increase in g shifts the p = 0 line to the right and the e = 0 line to the left, leaving the long-run price level unchanged. At impact the exchange rate adjusts downward from point ao to al . There is no transitional dynamics, and the Dornbusch model predicts exactly the same adjustment pattern as the traditional Mundell—Fleming approach does in this case. Since there is no need for a long-run price adjustment the assumption of price stickiness plays no role in the adjustment process, and because the fiscal impulse is unanticipated, the interest parity condition does not introduce transitional dynamics into the

e

eo

(e= 0)1

Figure 11.17. Fiscal policy in the Dornbusch model

exchange rate in this

a future permanent incr

ciation of the curren, e exchange rate, in ti

the policy. Once goven _ain and the exchan, is at al, with a permane adjustment path is a. t

_:lnouncement and in, k.

after implementation. An unanticipated ant;

overshooting result in ti

.pply shifts both the ë n equilibrium real e:,„ long run). In the short n a discrete adjustment • -

..iwrease in the demand arts to rise. A gradual —g real exchange rate, 1

nominal exchange rate a le intuition behind 1.

we nominal exchange r a net capital outflow

order for domestic IL: adjustment by an exchai

m a north-westerly

Price stickiness and over

:e finite speed of adj.. a crucial role in t: . at —> co, so that (T5 :s means that we can s

...el as a function of tilt at domestic interest r.

r = (EYQEMY 1)y-

Ej

h, together with ,...4; rate of depreciation

e = (E R2Em -- 1)5' —

Will a shock away his model? The answer it hypothesis. The dash, say from the steady-state

does lead the econand only if the economy Since agents have perfect it is on the saddle path hey expect that the econar this expectation is also xchange rate immediately re the price level is sticky, i nal exchange rate takes Chapter 4 above for other

0

unanticipated expansionary

', ifts the p = 0 line to the price level unchanged. At a4, to al . There is no trantly the same adjustment in this case. Since there is nrice stickiness plays no 1pulse is unanticipated, tional dynamics into the

p

odel

Chapter 11: The Open Economy

exchange rate in this case. Students are advised to verify that the announcement of a future permanent increase in government spending leads to an immediate appreciation of the currency, followed by falling prices and a further appreciation of the exchange rate, in the period between announcement and implementation of the policy. Once government spending has gone up, the price level starts to rise again and the exchange rate appreciates further. In the long run, the equilibrium is at al, with a permanently lower exchange rate and the same price level, and the adjustment path is ao to a' at impact, gradual movement from a' to a" between announcement and implementation, followed by gradual movement from a" to al after implementation.

An unanticipated and permanent expansionary monetary policy produces the famous overshooting result in this case. In terms of Figure 11.18, an increase in the money supply shifts both the e = 0 line and the p = 0 line to the right, leaving the longrun equilibrium real exchange rate unchanged (recall that money is neutral in the long run). In the short run, however, prices are sticky and the exchange rate makes a discrete adjustment from e0 to e'. The depreciation of the currency leads to an increase in the demand for aggregate output (y > y) and the domestic price level starts to rise. A gradual adjustment along the saddle path SP 1 , with an appreciating real exchange rate, leads the economy back to the long-run equilibrium. The nominal exchange rate actually overshoots its long-run target in the impact period. The intuition behind this result is that agents expect a long-run depreciation of the nominal exchange rate, and hence domestic assets are less attractive. There is a net capital outflow and the spot rate depreciates. The exchange rate overshoots in order for domestic residents to be compensated (for the fact that r < r*) during adjustment by an exchange rate appreciation. Hence, point a l must be approached from a north-westerly direction.

Price stickiness and overshooting

The finite speed of adjustment in the goods market (a distinctly Keynesian feature) plays a crucial role in the exchange rate overshooting result. Suppose, for example, that (/), -÷ oo, so that (T5.4) predicts that y = p always, as prices adjust infinitely fast. This means that we can solve (T5.1)-(T5.2) for the domestic rate of interest and price level as a function of the nominal exchange rate e and the exogenous variables. For the domestic interest rate we obtain:

r - (EmEmy - 1)y, + EyQ(p* + e) + EyGg - Emni (11.79)

EMR EYQEMR

which, together with (T5.5), can be substituted into (T5.3) to get the expression for the rate of depreciation of the exchange rate under perfectly flexible prices:

(EYQ EM — 1)y + E yQ (p* + + EYGg EYQM

e=

EMR EYQEMR

The Foundation of Modern Macroeconomics

Po

el

eo e

r

r*

y

y

tA = tl time

Figure 11.18. Monetary policy in the

Dornbusch model

This is an unstable differential equation in e only (it does not feature the price level, p). In terms of Figure 11.19, the only stable solution, following an unantic-

ipated increase in the money supply, is an immediate discrete adjustment of the exchange rate from e0 to el. Consequently, both immediately before and immediately after the shock, the exchange rate is constant (é = 0) so that the domestic rate of interest stays equal to the world rate at all times (r = r*). Unanticipated monetary policy does not lead to overshooting if prices are perfectly flexible.

This does not mean, of course, that overshooting is impossible when the price level is fully flexible. In some cases, anticipation effects can also cause overshooting of the exchange rate. Assume that the monetary impulse is announced at time tA to be implemented at some later time ti (>tA). If agents have perfect foresight, the adjustment path will be an immediate depreciation at time tA from e0 to e', followed

302

e

0

Figure 1 prices

by gradual further :n point a' to a'

increased (as was a exchange rate se-.

a of the currei.,

be no anticipated expected ca - Consequently, in -,

dt , reciate imme, Matters are di..

= ti ) but is of a y the agents) th_.

4 in the future. In ci - ion at tA = fr

...,scribed by the

decreased again, th st-_•:ts from ë(rn i )

nary expansion ca

I

$ I lie smaller the jump in the exchan

p is instantaneous I aid nothing happens •