Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

e is downward sloping and ) that the money supply and rere is nominal wage rigidity ,ndent of the real exchange shifts the IS curve up from y (A > 0), the real exchange ado the expansionary effect estic price level falls as does lal wage rigidity (A = 0), on 'e unchanged, and the real Five effect of the additional at happens to real wages (as must be free to fall (along Dsitive output effects. This ;e rigidity.

untry World

g type model with a rudi- 'ndations provided for the The model of section 1.4 exchange rates and perfect was paid to the details of ically consistent) model of

ions) that are identical ussed in section 1.4. One nust do away with the ad n (11.25)-(11.27) that the

r world) just the foreign metry assumption, take a

(11.43)

Chapter 11: The Open Economy

where stars denote foreign variables, e.g. C; is the demand for domestically produced consumption goods by foreign residents.6 By loglinearizing (11.43) we

obtain:

EX = aQ + WCECYY* — wiem dr* + (1 - we - (0I) . (11.44)

By substituting this export demand function in the domestic economy's IS curve (equation (T2.1) in Table 11.2) we obtain the IS curve for the domestic economy in a two-country setting:

where we have used the fact that dr = dr* due to perfect capital mobility. By comparing (T2.1) and (11.45), it is clear that the IS curve is augmented in a number of ways. First, the interest rate exerts a stronger effect on domestic production than before. The reason is that changes in the interest rate decrease investment in both countries, and since some investment goods are imported, spillover effects exist. Second, foreign government spending spills over into the domestic economy, both directly (via the term involving G*) and indirectly (via the term with i'*).

Of course, the foreign country also has an IS curve (labelled IS*) which is similar in form to (11.45). By making the appropriate substitutions, the IS* curve can be written as:

where we have once again used dr = dr* . The real exchange rate affects foreign spending negatively because it is measured from the point of view of the domestic country (i.e. Q EP* /P). By using (11.45)-(11.46) to solve for Y and Y*, the

6 Note that the real exchange rate from the perspective of the foreign country is

explains the positive sign of the exponent on the real exchange rate in (11.43). Comparing (11.43) and (11.29) shows that the two coincide if a = $ and EX() (1 — a)C20[A(r*, Y*) G*). This shows that EXo is no longer exogenous in a two-country model.

283

Table 11.4. A two- co..

Y = — EyRr* + Emq + Et, y* = —EyR r* — Ey0 E

m P = EMYY EuRr s

M * = EMYY* —Ewe' -

Y = — conic Nw [w — Pi

Y* —(0NENw [w* — Pl.

w = wo + APc ,

w* = wo ± A* PC , Pc = + p + (1 —

14- = (00 + p* — (1 —

Notes: All variables exce-t th country. Endogenous variac`---

price levels (p, p*), nominal spending (g, g*), the money recovered from (11.47)—(11. 4

and

CONENW [m + 0111

The curves LM(ASN ) and and coincide in the market equilibrium sche

, stituting LM(ASN ) exchange rate and the ex

:MEN is upward sloi . _

stimulates domestic outpo

Money market equili: uope of GME7,,, is reverseki country's perspective).

+040 - O* yJ

(11.4'

cox (1 — y)]

(11.48)

ign government spending however, not a priori clear i llover effect (via G*). By

.48), it can be seen that the e economies are not "too an one-half (wx < 1). This yes that the two economies in colloquial terms, if the

cold if wx is high). version of the model

17)- (11.48) are rewritten in

11.4.

some prototypical cases he model.

5, the relevant model is , ulting model can then M(ASN ) curve is obtained

'.7) combined and with the LM curve (LM*(AS'k) -)ns for price and output

VIVEA4-wW;

(11.49)

Chapter 11: The Open Economy

Table 11.4. A two- country extended Mundell— Fleming model

Notes: All variables except the interest rate are in logarithms and starred variables refer to the foreign country. Endogenous variables are the outputs (y, y*), the real exchange rate (q), the rate of interest (r*), price levels (p, p*), nominal wages (w, w*), and consumer price indexes (pc , 14). Exogenous are government spending (g, g*), the money stocks (m, m*), and the wage targets (wo, wo). Elasticities of (T3.1)—(T3.2) can be recovered from (11.47)—(11.48), and wo log Qo.

and

The curves LM(ASN ) and LM*(AS7v ) are drawn in the left-hand panel of Figure 11.9, and coincide in the initial equilibrium due to the symmetry assumption. The goods market equilibrium schedule under nominal wage rigidity, GME N , is obtained by substituting LM(ASN) into the IS curve and solving for r* in terms of the real exchange rate and the exogenous variables (and similarly for GMEN):

GMEN is upward sloping in (r*, q) space because a real depreciation (a rise in q) stimulates domestic output and, consequently, the demand for real money balances. Money market equilibrium can only be restored if the interest rate is higher (the slope of GMEN is reversed since —q measures the real exchange rate from the foreign country's perspective).

The Foundation of Modern Macroeconomics

r*

LM (ASN) LM*(ASN*)

Figure 11.9. Fiscal policy with nominal wage rigidity in both countries

in the domestic country (represented by a rise in g) shifts up both GMEN and GMEN but, provided the own effect of government spending dominates (so that ri < 1), the former shifts by more than the latter (i.e. ar*/ag is largest for GMEN ). The new equilibrium is at el , the domestic economy experiences a real appreciation, and output in rises. Hence, the fiscal stimulus in the domestic economy also stimulates the foreign economy. This is why this phenomenon is called a the one country is able to pull itself and the other country out of a recession by means of fiscal policy. Why does it work? The increased government spending in the domestic economy leads to upward pressure on domestic interest rates. The resulting capital inflows cause the domestic currency to appreciate, so that the demand for foreign goods is increased. This stimulates output in the foreign country. The resulting increase in the interest rate causes the price levels of both countries to rise by the same amount. Since nominal wages are fixed, the real producer wage falls in both countries, which explains the increase in output and employment.

For future reference we derive the expressions for the output multipliers. First, we use (GMEN) and (GMEN) to derive the effect of domestic and foreign fiscal policy on the world interest rate:

Next, we use (LM(ASN )), (LWAS7,T )), and (11.50) to derive the output effects:

LM (ASN)i

Figure 11.10 in both cot..

The key thing to note is output effects in both co in thL but harm the foreign col

increase in the domes:.. rium locus from GMEN-(ti LM(ASN) l . There is cloy outflows lead to a depre,. domestically produced g towards goods produced price level falls and con! fall in output and emplc etary policy is referred stimulated at the expense

11.2.2 Real wage

If both countries experi,. Table 11.4 by setting :. = analysis. Under real war,, are equal to:

Y = -- NNENtv [wo + Y* -- (DNENw [ +

I go

ge rigidity in

y a rise in g) shifts up both ment spending dominates latter (i.e. ar*/ag is largest C economy experiences a fence, the fiscal stimulus in

This is why this pheable to pull itself and the icy. Why does it work? The v leads to upward pressure :ause the domestic currency - -eased. This stimulates out- -.erest rate causes the price ce nominal wages are fixed, 'lins the increase in output

tput multipliers. First, we and foreign fiscal policy

(11.50)

e the output effects:

■VENfid

Figure 11.10. Monetary policy with nominal wage rigidity in both countries

The key thing to note is that own and foreign fiscal policy affect have the same

output effects in both countries.

in the domestic country, on the other hand, does not benefit but harm the foreign country. This is illustrated with the aid of Figure 11.10. The increase in the domestic money stock shifts the domestic goods market equilibrium locus from GMEN(mo) to GME N (ml ) and the LM(AS) curve from LM(AS N )0 to LM(ASN)i . There is downward pressure on domestic interest rates, and the capital outflows lead to a depreciation of the currency. This shifts domestic demand towards domestically produced goods and away from foreign goods. Also, foreigners shift towards goods produced in the domestic economy. In view of (11.49), the foreign price level falls and consequently the real producer wage rises. This explains the fall in output and employment in the foreign country. For obvious reasons monetary policy is referred to as a the domestic economy is stimulated at the expense of the foreign economy.

11.2.2 Real wage rigidity in both countries

If both countries experience real wage rigidity, the relevant model is obtained from Table 11.4 by setting X = X* = 1. Again the resulting model is amenable to graphical analysis. Under real wage rigidity, the aggregate supply curves in the two countries are equal to:

The Foundation of Modern Macroeconomics

The goods market equilibrium schedules for the two countries are obtained by equating the respective AS and IS curves and solving for r* in terms of the real exchange rate and the exogenous variables. The subscript "R" is used to indicate that real wages are rigid in the two countries.

In sharp contrast to our conclusion in the previous section, fiscal policy constitutes a beggar-thy-neighbour policy under real wage rigidity. This can be illustrated with the aid of Figure 11.11. The increase in government spending in the domestic country (g) raises the interest rate and causes a real appreciation of the domestic economy (provided ri < 1, which we assume). Since consumer wages are fixed, the producer wage falls in the domestic economy and output and employment are stimulated. The opposite holds in the foreign country, where the producer wage rises. By raising g, the domestic policy maker causes the foreign producer wage to rise, as foreign workers demand higher nominal wages in order to keep their consumption wage constant after the real depreciation of the foreign currency. For future reference we derive the expressions for the various output multipliers. First we use (GMER) and (GMER) to derive the effect of domestic and foreign fiscal policy on the real exchange rate:

Next, we use (ASR ), (ASR), and (11.52) to derive the output effects:

Equation (11.53) provides a clear statement of the beggar-thy-neighbour property of fiscal policy when both countries experience real wage rigidity.

Not surprisingly, monetary policy has no real effects under real wage rigidity. As none of the equilibrium conditions is affected, the interest rate, output levels, and the real exchange rate are also unaffected and the increase in m causes an (equal) increase in the domestic price level and the nominal wage rate (dp = dw). Since the real exchange rate is unaffected, the nominal exchange rate depreciates by the full amount of the change in the domestic price (de = dp).

11.2.3Real wage rigidity in Europe and nominal wage rigidity in the United States

In an influential paper, Branson and Rotemberg (1980) argue on the basis of empirical evidence, that nominal wage rigidity characterizes the US economy whilst real

r*

0

Yi *

Yo=- Yo *

Yi

Y,Y *

Figure 11.1' both counit

wage rigidity well describe country and the US

time being), the model de setting A. = 1 and A* = 0. 1 once again proceed by ity, it is fully described I The US economy, on the described by LM* (AS;- ) L. The different

is at eo.

A European fiscal eA, . and GME'k, with the fa

untries are obtained by equat- n terms of the real exchange is used to indicate that real

(GMER)

7/g1

- (GMER)

lion, fiscal policy constitutes This can be illustrated with 'nding in the domestic coun- n of the domestic economy ges are fixed, the producer !mployment are stimulated. ,lucer wage rises. By raising icer wage to rise, as foreign 71 their consumption wage rrency. For future reference ipliers. First we use (GMER) '1 fiscal policy on the real

(11.52)

-silt effects:

.r-thy-neighbour property Se rigidity.

under real wage rigidity. As rest rate, output levels, and

se in m causes an (equal) rate (dp = dw). Since the rate depreciates by the full

I wage rigidity

--71e on the basis of empirUS economy whilst real

Chapter 11: The Open Economy

Figure 11.11. Fiscal policy with real wage rigidity in both countries

wage rigidity well describes the European countries. Letting Europe denote the home country and the US the foreign country (and ignoring the rest of the world for the time being), the model describing this configuration is obtained from Table 11.4 by setting A = 1 and A* = 0. The analysis of the effects of fiscal and monetary policy can once again proceed by graphical means. Since Europe experiences real wage rigidity, it is fully described by GMER and ASR (given in (GMER) and (ASR), respectively). The US economy, on the other hand, experiences nominal wage rigidity, and is described by LM*(AS7v) and GME7v (given in (LM*(ASO) and (GME7„), respectively). The different schedules have been drawn in Figure 11.12. The initial equilibrium

is at eo.

A European fiscal expansion (a rise in g) leads to an upward shift of both GMER and GME1,'„ with the former experiencing the larger shift (as ri < 1). The real

289

The Foundation of Modern Macroeconomics

United States

GM ER (gi, go*)

LM*(AS)

GMER (go,g1 *)

GM ER (go, go*)

GME,; (go, g1 *)

GMV; (g1, go*)

GME,; (go, go*)

y =7 *

Europe

y

Figure 11.12. Fiscal policy with real wage rigidity in Europe and nominal wage rigidity in the United States

exchange rate of Europe appreciates and the new equilibrium is at el. Both y and y* increase, though the latter increases by more than the former (see the third quadrant). The European fiscal impulse constitutes a locomotive policy since it ends up simultaneously stimulating US output and employment.

A US fiscal expansion (a rise in g*) shifts both GMER and GME'k. In terms of Figure 11.12, the new equilibrium is at e2. The rate of interest is higher, there is a real depreciation in Europe, but output falls because real producer wages in Europe rise. Output and employment in the US rise, so that the US fiscal expansion constitutes a beggar-thy-neighbour policy. It leads to lower output and higher unemployment in Europe.

A monetary expansion in Europe has no real effects (see above), but expansionary US monetary policy (a rise in m*) constitutes a locomotive policy for Europe. This has been illustrated in Figure 11.13. The increase in the US money stock shifts GME ,-- down and LM*(AS'„',) to the left. The European real exchange rate appreciates and the interest rate falls. Both y and y* rise, and the US impulse thus stimulates both economies. By inflating the foreign price level, the real producer wage abroad falls.

y<y*

Y=Y *

Figure 11.

Europe ano

.iis explains why fort.. *ion causes European

ut there.

International

symmetric two-cou.. rvious subsections can -ion. Since we do not v.., zitroduced in the develop

4summarized by rrk foreign output:

Y=Sr“g* ,

mere g and g* are inde :ty in both count: is real wage rigi

GM ER (gO, g1 *)

GM ER (go, g,*)

GM (go, g1 *)

GMEZ

GME,; (go, go*)

Pe

4 ty in Europe tes

i UM is at el . Both y and y* former (see the third quad- ' N,'e policy since it ends up t.

and GME7„. In terms of - ,'st is higher, there is a real kiucer wages in Europe rise. cal expansion constitutes and higher unemployment

above), but expansionary US

)olicy for Europe. This has -- loney stock shifts GME;cv range rate appreciates and pulse thus stimulates both , ducer wage abroad falls.

Chapter 11: The Open Economy

United States

GM ER

Figure 11.13. Monetary policy with real wage rigidity in

Europe and nominal wage rigidity in the United States

This explains why foreign output rises. Similarly, the real exchange rate appreciation causes European producer wages to fall, thus also enabling an increase in output there.

11.2.4 International policy coordination

The symmetric two-country model of the world economy that was developed in the previous subsections can be used to study the issue of international policy coordination. Since we do not wish to carry on with the rather extensive notational burden introduced in the development of this model, the insights of the two-country model are summarized by means of the following reduced form expressions for domestic and foreign output:

there is real wage rigidity in both countries (see section 2.2), and, finally, < 0 and 291

The Foundation of Modern Macroeconomics

0 < < 1 if there is real wage rigidity in the domestic economy and nominal wage rigidity in the foreign economy (see section 2.3).

Assume that the domestic government is interested in stimulating domestic output (to get as close as possible to some given full employment target, y > 0) without, however, creating a large government sector (which could give rise to large deficits). We assume that the domestic policy maker minimizes some cost function, LG:

subject to the reduced form expression summarizing the domestic economy, given by the first expression in (11.54). In a similar fashion, the foreign policy maker has the loss function:

that it minimizes subject to the constraint imposed by the reduced form expression for foreign output (the second equation in (11.54)). It is assumed that the domestic and foreign policy makers have the same output targets, i.e. y features in both (11.55) and (11.56).

Suppose that both governments choose their own spending level independently, i.e. without taking the possible repercussions for the other country into account. In this case, fiscal policy is uncoordinated and each country chooses its spending level conditional upon the other country's spending level. For example, the policy maker in the domestic economy solves:

Similarly, the foreign country has a reaction function (RR*) which relates its optimal (non-coordinated) level of government spending to its full employment target and the spending level of the domestic country:

The non-cooperative Nash equilibrium is defined as that equilibrium in which each country's spending plan is optimal given the other country's spending plan. Since the reaction functions designate such conditionally optimal spending plans, the non-cooperative Nash equilibrium is obtained by finding the intersection of RR

Figure 11.1 ,

under nor

and RR*, i.e. by solvir we obtain:

giv =gN— 1 +

I

i►liere the subscript ".\ of Figures 11.14 and 11

,pectively. In both countries have the sarr r :uinal wage rigidity ita wage rigidity (4- = is at point N, where th,

\\ :tat would a coor,. maker in one country :1 spending has on t is to assume that bozi '..-rnational agency IA by choosing spenu....

It is easy to show 7 Nose that g = go in: - value of g`, it is or -Al

thia the only stable Maui