Macroeconomic Policy Coordination among the Industrial ... · that all countries can benefit, in terms of their own policy goals, from a coordinated package of macroeconomic policies,

GILLES OUDIZInstitut National de la Statistique et des Etudes Economiquesand National Bureau of Economic Research

JEFFREY SACHSHarvard University and National Bureau of Economic Research

MacroeconomicPolicy Coordinationamong theIndustrial Economies

THE TURBULENT EVENTS in the world economy since 1973 have severaltimes prompted the call for the major countries in the Organization forEconomic Cooperation and Development (OECD) to coordinate theirmacroeconomic policies.' In the immediate aftermath of the 1973 oil

We would like to thank Peter Hooper of the Board of Governors of the Federal ReserveSystem, Stephen Marris and John Williamson of the Institute for Intemationai Economics,and members of the Brookings Panel for helpful discussions. Data Resources, Inc.,generously made available computer facilities for this study. The paper was written whileGilles Oudiz was a visiting scholar at the Massachusetts Institute of Technology, and hegratefully acknowledges the financial support of the North Atlantic Treaty Organizationand the Fulbright fellowship program during this visit.

1. For useful discussions of the policy coordination debate in the context of theeconomic summit meetings, see George de Menii and Anthony M. Solomon, EconomicSummitry (New York: Council on Foreign Relations, 1983), and Robert D. Putnam andNicholas Bayne, Hanging Together: The Seven-Power Summits (Harvard UniversityPress, 1984). Michael Stewart, in The Age of Interdependence: Economic Policy in aShrinking World (MIT Press, 1984), offers an interesting brief for greater policy coordi-nation and discusses the historical experience in several chapters. For a view of the debateover policy coordination in 1983, see Sylvia Ostry, "The World Economy in 1983:Marking Time," America and the World 1983, special issue. Foreign Affairs, vol. 62, no.3(1984), pp. 533-60.

1

2 Brookings Papers on Economic Activity, 1:1984

price shock, for example, the finance ministers of the main industrialcountries made a commitment, only partly fulfilled, to avoid deflationarypolicies designed to pass current account deficits on to partner countries.Following the deep recession of 1974-75, the Carter administration urgedin 1977-78 a "locomotive approach" for world recovery, in which themajor economies were to act jointly to stimulate a world expansion. Thispolicy was adopted by the heads of state at the 1978 Bonn summitconference. After the world recession of 1980-82, several policymakersand economists called for a joint world reflation, but in this case the U.S.administration stood firmly opposed to such a coordinated policy.^ Andrecently, several economists have advocated that the European econ-omies embrace more expansionary fiscal policies in return for reducedlong-run U.S. deficits.' The implication appears to be that while boththe United States and Europe would benefit from such a swap in policy,neither side can or will undertake the prescribed policies independently.

Advocacy of international coordination has been far more plentifulthan actual implementation. The 1978 Bonn summit is the principalexample of a macroeconomic policy package adopted by the majoreconomies. While there are few cases of successful policy coordination,advocates of coordination argue that there are many illustrations of theneed for coordination. Individual economies have on several occasionstried to expand in the midst of a world contraction. The United Kingdomand Sweden tried to bridge the world recession of 1974, and while theysucceeded in the short run in maintaining gross national product, thelonger-run consequences were large balance of payments deficits, cur-rency depreciation, and eventually a sharp policy reversal (in 1976Britain actually required a stabilization loan from the International

2, A clear statement of the administration' s position may be found in Martin Feldstein,"The World Economy Today," The Economist, June 11-17,1983. He was responding toother writers in The Economist who had urged a coordinated global expansion; thesewriters and the dates their articles appeared were Helmut Schmidt (February 26-March4,1983), Val6ryGiscardd'Estaing(May21-27,1983),andC, Fred Bergsten and LawrenceR, Klein (April 23-30, 1983), One of the most widely publicized calls for a coordinatedreflation came in 1982 from a group of 26 economists from several countries in Institutefor International Economics, "Promoting World Recovery: A Statement on GlobalEconomic Strategy" (Washington, D,C,: HE, 1982),

3, See Richard Layard and others, "Europe: The Case for Unsustainable Growth,"Discussion Paper (Brussels: Centre for European Policy Studies, Macroeconomic PohcyGroup, May 1984). Others in the Macroeconomic Policy Group participating in the studywere Giorgio Basevi, Olivier Blanchard, Willem Buiter, and Rudiger Dornbusch,

Gilles Oudiz and Jeffrey Sachs 3

Monetary Fund). As one Swede remarked, "We tried to build a bridgein 1974, but ended up with a pier instead." Similar episodes include theU.S. expansion during 1976-78 and the Mitterrand policy in France in1981. In all of these cases, external constraints played a significant rolein limiting the benefits of expansion.

These cases suggest that unilateral expansionary policies may bedifficult to sustain and costly in terms of inflation and foreign borrowing.Advocates of coordination point out that if every country fears unilateralexpansion, then all can get stuck in a low-level equilibrium even if allwould like to expand. But it is too facile to jump to the conclusion thatabsence of coordination explains much or most of the worldwidecontraction in recent years. When West Germany stuck with contrac-tionary policies in 1981 at the time of the French expansion, it was notmerely a German fear of external imbalance that was to blame but alsoGerman fears of rekindling inflation through any demand stimulus at Eill,whether or not matched from abroad. Moreover, there are cases wherecountries have successfully expanded without a currency collapse, themost recent being the U.S. expansion since the fourth quarter of 1982.Perhaps it is the policy mix, as well as the overall policy stance, thatdetermines whether a unilateral expansion is feasible.

In our view, the case for coordination must rest on the demonstrationthat all countries can benefit, in terms of their own policy goals, from acoordinated package of macroeconomic policies, and not on the merefact that a unilateral expansion is painful. More precisely, the case forcoordination must rest on the demonstration of a Pareto improvementin the economic outcome. If German-French cooperation in 1981 hadraised output and inflation in both countries, it may well be true thatFrance would have been better off relative to French goals, but couldwe guarantee the same for inflation-minded Germany?

Most formal exercises arguing for a global policy package miss thispoint. A demonstration that "global multipliers" are higher than "indi-vidual country" multipliers is not a proof of the Pareto improvementfrom a joint reflation.* Similarly, a demonstration that a policy package

4. An example of a study comparing single-country and multicountry multipliers isFlemming Larsen, John Llewellyn, and Stephen Potter, "International Economic Link-ages," OECD Economic Studies, no. 1 (Autumn 1983), pp. 43-91. The multipliers arevaluable for macroeconomic forecasting and are suggestive regarding the gains fromcoordination but are not in themselves a proof of the Pareto improvement from policycoordination.


has "nice outcomes" for several countries is also not sufficient. A widelypublicized Project Link analysis of global reflation showed that WestGermany, Japan, the United Kingdom, and the United States togethercould engineer a noninflationary recovery.^ But it did not show whateach country could do on its own nor how much gain was to be had fromcoordination per se (in fact, in the Link model, some countries on theirown can engineer a recovery with failing prices because some of thecountry models suppose that cyclical productivity gains in recovery arepassed through to lower prices).

Our goal in this paper is to recast the arguments for coordination interms that consider each country's macroeconomic goals so that we mayevaluate whether the major countries can each raise economic welfarethrough a joint policy action. In doing this we spell out the reasons tobelieve that uncoordinated policymaking across countries will indeed beinefficient (in the sense that Pareto improvements are possible); ourreasoning about such policymaking follows the theoretical work ofHamada, Canzoneri and Gray, Johansen, Miller and Salmon, and Sachs.*We then attempt to measure how large the gains to coordination arelikely to be. For this purpose, we take two large-scale econometricmodels, the Japanese Economic Planning Agency (EPA) model and theFederal Reserve Board's Multicountry model (MCM) as "true" models

5. The analysis was described by Bergsten and Klein in The Economist, April 23-30,1983.

6. The pioneering studies in this area are by Koichi Hamada and include "AlternativeExchange Rate Systems and the Interdependence of Monetary Policies," in Robert Z.Aliber, ed., National Monetary Policies and the International Financial System (Univer-sity of Chicago Press, 1974), pp. 13-33, and "A Strategic Analysis of Monetary Interde-pendence," Journal of Political Economy, vol. 84 (August 1976), pp. (>ll-'¥i. Recentstudies include Matthew E. Canzoneri and Jo Anna Gray, "Two Essays on MonetaryPolicy in an Interdependent World," International Finance Discussion Paper 219 (Boardof Governors of the Federal Reserve System, February 1983); Leif Johansen, "A Note onthe Possibility of an International Equilibrium with Low Levels of Activity," Journal ofInternational Economics, vol. 13 (November 1982), pp. 257-65; M. Miller and M. Salmon,"Dynamic Games and the Time Inconsistency of Optimal Policies in Open Economies,"paper presented at the National Bureau of Economic Research Conference on theInternational Coordination of Economic Policy, August 1983; and Jeffrey Sachs, "Inter-national Policy Coordination in a Dynamic Macroeconomic Model," Working Paper 1166(National Bureau of Economic Research, July 1983). For a recent survey of theoreticalissues, see Richard N. Cooper, "Economic Interdependence and Coordination of Eco-nomic Policies," in R. Jones and Peter B. Kenen, eds. Handbook of InternationalEconomics (Amsterdam: North-Holland, forthcoming).


of the world and focus on policy cooordination among the United States,West Germany, and Japan.

Our strategy for measuring the gains from coordination is to comparetwo equilibriums: one in which each country's macroeconomic author-ities pursue optimal policies taking as given the actions abroad, and onein which the authorities bargain over a coordinated package of policies.The first type of equilibrium is referred to as a "Nash" or "noncooper-ative" equilibrium, and the second as a "cooperative" or "bargaining"equilibrium. We then ask how much each country's welfare (measuredin units of GNP, as described later) is raised in moving from thenoncooperative to cooperative equilibrium.

The gains from coordination in this sense are certainly present, butthey appear to be modest, at least when the United States, Germany,and Japan are the only countries taking policy actions in response to thecoordination. Perhaps the United States could gain the utility equivalentof one-half percentage point of GNP in each of the next few years froma more coordinated expansion; the West German gain is about the same,and the Japanese gain is somewhat higher. It does not appear thatcooperation among the leading three economies could be the decisivefactor in world recovery. We note later several qualifications to thisconclusion. Most important, these estimates ignore any policy responsesoutside of the United States, Germany, and Japan that might arise fromthe coordinated decisions of these three large countries. For example, ifGerman macroeconomic policy is matched throughout the EuropeanCommunity (EC), then the gains to coordination should be at least twiceas large.

It should be stressed that our measures refer to only one type of gainfrom coordination. We abstract from many other possible gains thatadvocates of coordination often mention. We assume, for example, thatpolicymakers know the "true" model of the world economy and haveperfect knowledge of the actions taken in other countries. Thus, weabstract from the informational gains that might emerge from closercoordination of policies. Also, we abstract from the possible strength-ening of political ties that might follow a closer harmonization ofmacroeconomic policies.

Though the major economies are richly linked in commodity andfinancial markets, the direct effects of commodity trade on macroeco-nomic interdependence remain surprisingly small; at the core, it is these

Brookings Papers on Economic Activity, 1:1984

Table 1. Exports and Imports as Share of Country's GNP,Percent

Country

UnitedStates

ExportsImports

EuropeanCommunity

ExportsImports

JapanExportsImports

WestGermany

ExportsImports

FranceExportsImports

UnitedKingdom

ExportsImports

UnitedStates

1.72.2

3.42.3

1.81.8

0.91.7

2.82.5

WestGermany

0.30.4

2.93.3

0.50.2

2.43.6

2.02.6

Trading

Japan

0.71.3

0.20.8

0.30.8

0.20.6

0.21.0

partner

Euro-peanCom-

munity

1.61.4

12.912.9

1.60.7

12.811.2

8.010.2

8.69.3

Otherindus-

trializedcountries

1.61.9

3.13.1

1.11.4

4.63.2

1.72.1

2.93.7

Rest ofworld

3.13.5

7.07.4

6.87.9

7.26.3

6.37.0

6.14.6

Total'

7.08.1

24.926.4

13.012.3

26.623.4

17.121.4

20.621.1

Source: Data on exports and imports are from International Monetary Fund, Direction of Trade Stalisiics.Yearbook 1983 (IMF, 1983); data on GNP and exchange rates are from Organization for Economic Cooperation andDevelopment, OECD Economic Outlook, no. 34 (Paris: OECD. 1983).

a. Components may not add to totals because of rounding.

relatively small trade links that condition our conclusions regarding thereturns to coordination. Table 1 shows a merchandise trade matrix formajor industrialized countries and the rest of the world. Incredibly, totalU.S. merchandise exports to the EC amounted in 1982 to only I.6percentof U.S. GNP and 2.2 percent of EC GNP. Similarly, U.S. imports fromthe EC amounted to 1.4 percent of U.S. GNP and 1.7 percent of ECGNP. The simple fact is that although the European economies arehighly open, fully one half of European trade remains within Europe,and of the rest, only about 15 percent is with the United States and 4


percent with Japan. With these trade links, the direct demand effects ofU.S. stimulus on Germany or of Germany on the United States arenaturally quite small. A 1 percent increase in U.S. import demand,leading to a 1 percent larger import volume from Germany, would havea direct effect of raising German GNP by 0.02 percent. In this case,indirect effects on German export sales of higher U.S. imports from therest of Europe and elsewhere might triple or quadruple the demandeffect, but it would still remain rather small. The effects of Germanpurchases on the United States are likely to be far smaller. A 1 percentrise in German imports from the United States amounts to 0.003 percentof U.S. GNP.

Of course U.S. influences on the rest of the world are much morepronounced than such simple multiplier calculations suggest. The U.S.dollar remains the linchpin of the world monetary system. As shown intable 2, the currency of denomination of international reserves. Euro-dollar loans, new issues of Eurobonds, and OPEC portfolio wealth re-mains to a far higher extent in U.S. dollars than the U.S. share of worldGNP would suggest. The special role of the dollar leads to importantasymmetries between the effects of U.S. policies on Europe and Japan,and the effects of European and Japanese policies on the United States.Shifts in the value of the dollar can have significant income redistribu-tional effects throughout the world that may also have important aggre-gate demand consequences; changes in the value of the Europeancurrencies or the Japanese yen do not have such effects.^ Also, by virtueof the dollar's role in world currency, it appears that the United Statescan run high budget and current account deficits without a majordepreciation of the dollar, while in Europe and Japan, a similar level ofbudget and external deficits would probably cause a significant deprecia-tion of the currency. Unfortunately, only some of these asymmetries arewell captured by the macroeconomic models that we employ here.

The rest of the paper is divided into four sections. In the first wepresent a two-country macroeconomic model to trace the major channelsfor macroeconomic policy interdependence. The goal is to show howvarious structural characteristics determine the effects of one country's

7, Of most importance in recent years, the sharp appreciation of the U,S, dollar raisedthe real value of the less-developed countries' debts to international commercial banksand thereby contributed to the drop in LDC imports from the OECD area in the past twoyears.


TaMe 2. The Rote irf the V.S. DaUar in Internatknal Fiaaace

Measure

Official reserves"Eurodollar loans'"Eurobond issuesOPEC reserves (1975-79)

AddendumU.S. share of world GNP

Percent

1975

19A73.747.2n.a.

24.3

in U.S.

1978

76.967.648.260.0

25.0

dollars

1981

70.670.680.2n.a.

n.a.

Source: For official reserves. Eurodollar loans, and Eurobond issues, Peter B. Kenen, "The Role of the Dollaras an International Currency," Occasional Papers, 13 (New York: Group of 30, 1983), pp. 17, 25, 28; the estimateof OPEC reserves in dollars is from Organization for Economic Cooperation and Development, "Exchange Rates inInterlink" (Paris: OECD, September 1983), p. 27; the U.S. share of world GNP is from the World Bank Atlas, 1977and 1980 editions.

n.a. Not available.a. For all countries.b. Foreign currency claims on nonresidents reported by European banks.

policies on another; these characteristics include the degree of interna-tional asset substitutability and the extent of wage indexation in eacheconomy.

With these cross-country channels explained, we describe in thesecond section the logic of macroeconomic coordination. Two types ofequilibriums are distinguished: an uncoordinated policy equilibrium, inwhich each country selects macroeconomic policies while taking theactions abroad as given; and a cooperative equilibrium, in which policiesare a bargained outcome among the participating countries. We showthat a cooperative equilibrium will in general allow all countries to reacha higher level of economic welfare.

In the third section of the paper, we use two large-scale econometricmodels to quantify the gains to a coordinated (or bargained) policypackage relative to the uncoordinated policy settings. Three cases areexamined here: the scope for coordination at the current macroeconomicjuncture; the implications of a shift in U.S. policy toward fiscal restraintand monetary ease; and the role for coordination in the event of anothermajor rise in oil prices.

In the final section of the paper we discuss some of the weaknesses ofthe analysis and some of the possible shortcomings of the macroeconomicmodels that we employ. We detail various ways in which we may haveunderstated or overstated the benefits of policy coordination and pointout some of the greatest uncertainties lurking in the parameters of theunderlying models.


Macroeconomic Policy under Floating Exchange Rates

International linkages in commodity markets and financial marketssubstantially complicate the standard closed-economy analysis of mac-roeconomic policies. The effect of domestic policies on the domesticeconomy ("own-country" multipliers) depends crucially on the degreeof capital mobility between the home country and the rest of the worldand on the substitutability of home and foreign goods in aggregatedemand. The price effects of various policies may be heavily affected byexchange rate movements in the wake of policy changes. A fiscalexpansion, for example, may raise output while actually reducinginflation via an appreciation of the domestic exchange rate. To illustratesome of the possible effects of openness on policy effectiveness, webegin with a simple static model of two economies. Elsewhere we havestudied dynamic perfect-foresight models of economies with the sameessential structure described here, and the qualitative conclusions of thestatic model are the same as those of its more appropriate dynamiccounterpart.* In presenting the model we list only the behavioral equa-tions for the home economy, with the understanding that comparableequations hold abroad (an asterisk denotes foreign variables).

The domestic economy produces an output Q at price P. Home outputcompetes with foreign output Q* at price P*. The exchange rate E willmeasure units of the home currency per unit of foreign currency, so thatincreases in E imply a depreciation of the home currency. The realexchange rate for the home economy is A = EP*IP, and demand for thehome good relative to the foreign good will be a rising function of A.

Aggregate demand at home is the sum of private absorption, A (equalto consumption plus investment demand), government spending, G, andnet exports, Z - A/:

(1) Q = A + G + X-M.

Absorption is a function of output net of taxes, Q - T, the interest rateat home, /, and the private sector's wealth, W. In particular, A =

8, See Jeffrey Sachs and Charles Wyplosz, "Real Exchange Rate Effects of FiscalPolicy," Working Paper 1255 (National Bureau of Economic Research, January 1984),and Sachs and Wyplosz, "La Politique Budg6taire et le Taux de Change R6el,'' in AnnatesdeL'INSEE, vol. 53 (January-March 1984), pp, 63-91,


(1 - s}(Q - T) - vi + bW, where s is the marginal propensity to saveout of current disposable income and 6 is the marginal propensity toconsume out of financial wealth. Real private wealth, W, is the sum ofthe real value of home bonds, B, and foreign bonds, B*, held by thedomestic private sector. Let b = B/P and b* = B*/P*. Then W = BIP+ EB*IP = b + Ab*.

Private absorption is divided between home goods, C^, and imports,so that A = C + Ai^, where F is private-sector imports. In particular,F = (nA)A"P, where p, is the marginal propensity to import out of totalabsorption and p is the real exchange rate elasticity of import demand.The government is assumed to import with a constant marginal propen-sity |x^. Thus, AI^ = iJi' G. The total value of imports is therefore A(/''+ /^), which equals (fJu4)A'~p -I- [i^G. Similarly, exports, X, equal(|X*A*)AP* + M,G*AG*.

Next, we turn to aggregate supply and price level determination. Theconsumer price level, P^, is a geometrically weighted average of homeand foreign goods prices, with P,, = P" (F*E)<'"'. Denoting the loga-rithms of upper-case price variables by lower-case variables, we have:

(2) p , = Kp + {1 - K){e 4- p*).

Note as well that Pc may be written as Pc = p + {I - K)\, where \ =log(A). Thus, a real-exchange-rate depreciation raises consumer pricesat a given level of domestic prices. The (log) wage is a function of theconsumer price level and the output level:

(3) w = ap, + yQ.

Domestic prices are taken to be a fixed markup over domestic wages, sothat

(4) p = w.

The model is completed by specifying the asset market equilibriumconditions. First, demand for (log) real money balances tn - p is a.function of output and nominal interest rates in a standard equation forthe transactions demand for money:

(5) m-p = ^Q- pj.

The bond market equilibrium conditions are particularly importantfor the workings of fiscal policy. Home and foreign wealth holders divide


their portfolios between home and foreign bonds based on relative ratesof return of the two assets. For simplicity we assume that wealth holdersat home and abroad have identical portfolio preferences and thus dividetheir wealth between home and foreign bonds in proportions ^ and(1 - ^) with an adjustment according to relative rates of return. Withstatic expectations the rates of return differ by / - /*, and world demandfor the home asset is written as

(6) b^ = ^(W + AW*) + (j{i - /*).

Here, b^ is the real total government debt outstanding, which is dividedbetween home, b, and foreign holdings, ¥, and cr is the degree of assetsubstitutability. A crucial asymmetry between the United States and allother countries in the world involves the parameter %. The U.S. dollaris the preeminent international asset, and we have cited evidence toshow that this preeminent role has remained despite the declining U.S.share of the world real economy. The presumption therefore is that %^^» ôECD^ where ÔECD J tf,g marginal propensity to hold wealth in thecurrencies of the other OECD economies. We shall see shortly that thesize of d has strong impHcations for the impact of fiscal policy.

In a dynamic model, the supply of bonds fe^ would equal the cumulationof government deficits through time, net of changes in central bankholdings of the public debt. In this static model, we simply assume thatinitial outstanding debt is zero, so that b^ equals G - T, the contempo-raneous government deficit. Similarly, household wealth would equalthe cumulation of private savings, adjusted for capital gains and losses.Here, we set W equal to contemporaneous private saving Q ~ T - A(see the Sachs and Wyplosz papers cited in note 8 for the corre-sponding equations in a dynamic setting). Note that under ourassumptions, W + AW* equals ( g - J - A ) + A(Q*-r*-A*), whichinturn equals b^ + Ab*^.

The full model is shown in table 3 (with only home-country equations).The trade equations and the bond market equilibrium condition havebeen linearized around an initial equilibrium of X = 0 (that is, A = 1)and b*^ = 0. The import demand equation / = ((JLA)A-P + \iPGIA be-comes/ = -(pfjiAo + \xPGo)\ + |JLA + \iPG. The export demand equa-tion X = (|x*A*)Af>* + |JLG*AG* becomes X = (p*M,*Ag= + |x«*Go*)X +M.*A* + ii.°*G*. Last, the trade balance X - Al becomes TB =


TaUe 3. The Two-Coimtry Model

DemandAggregate demandNet exportsAbsorptionReal private wealthExport demandImport demand

PricesReal exchange ratePdce level (home good)Wage levelConsumer price level

Asset marketsMoney demandDomestic bond supplyBond market equilibrium

Equations'

QNX

AWXI

X

Pw

Pc

m - p

i - i*

= A += X -

1

G + NXAJ

= {\-s)(Q-T) - vi + bV/

= g -= (P*M-'= -(pfj

= p* += w

T - AÂ* 4- i i G * /^*\ \ 4- i,*A* 4- ..G*/^*/ 1 Q \ |X tjQ ^ A, T" |X j*l T fJL \J

LAO + |J.°Go) X + (jiA + \x.^G

e - p

= aPc + iQ= Kp +

= G -= [(!--

Definitions

A Absorption of the private sectorb^ Stock of domestic bondse log (Nominal exchange rate)

G Fiscal expenditure in homeunits

/ Import demand(• Interest rate

m log (Money demand)NX Net exports in home goods

goods

units

PPc

QT

WwXAX

(,l-K)(p* + e)

- U 'rdW - •db*m\l(j)a

log (Home price)log (Consumer price)OutputTaxesReal wealthlog (Nominal wage)Export demandReal exchange ratelog (Real exchange rate)

a. Equations apply to the home country. Asterisks denote foreign-country variables. Symmetric equations applyto the foreign country.

M,GG). The term [p*fjL*Af + )x«*G? - (1 - p)|xAo] is the partial effect ofX. on TB and is hereafter denoted e. For |x*Ao = iiAo and Go = 0, theterm is positive if and only if p + p* > 1, which is the traditional Marshall-Lemer condition for the effectiveness of a devaluation. Most empiricalstudies suggest that dTB/dX is negative over a short horizon (six months)following a devaluation but is positive afterward as trade volumes adjustto relative price changes. We ignore this so-called J-curve effect andhereafter assume e > 0.

9. In the EPA model and the MCM, which we use later in the paper, the J-curve effectis typically eliminated in one to three quarters, and in spite of a current account worseningon impact, an exchange rate depreciation is typically expansionary on impact.


Table 4. Policy Multipliers in the Two-Country Model*

Fixed

prices''

a = 0a = 30

Foreign

indexation'

CT = 0

Domestic

indexation'^

a = 0O" = 00

dQ

dm

+

0

0

dX

dm

+

0

0

Monetary policy

dp,

dm

+

11

dQ*

dm

-

0

0

dm

-

0

0

dNX

dm

+

0

0

dG

+

dk

dG

-

Fiscal policy

dp, dQ*

Id ~dG

+

H 1 +

1 +1

+1

dp*,

dG

+

-

dNX

dG

-

Source: Derived from equations in the text; detailed calculations available from the authors.a. See definitions of variables in table 3 and equation 3: a denotes asset substitutability.b. a = a* = •y = 7* = 0.c. a = 7 = 0; a* = I, 7* > 0.d. a* = 7* = 0; a = 1, 7 > 0.

The short-run effects of a bond-financed fiscal expansion (dG > 0,d r = 0) and a monetary expansion (dm > 0) are shown in table 4. Foreach set of policies, three cases are compared. First, we have thestandard Mundell-Fleming assumptions of fixed prices (that is, nocontemporaneous indexing) with perfect or zero asset substitutability.Second, we assume full foreign indexation (a* = 1, -y* > 0) but stillmaintain fixed prices domestically. Third, we consider the inverse caseof full domestic indexation and fixed foreign prices.

Monetary expansion is the easiest policy to consider. For a < 1,output and consumer prices necessarily rise. The nominal and realexchange rate depreciate. The well-known lesson with regard to index-ation is that a rise in indexation (higher a) reduces the output gain andincreases the price consequences of the monetary expansion. In theextreme case where a = 1, the monetary expansion raises prices andthe nominal exchange rate in equiproportion (keeping the real exchangerate constant) and has no effect on the output level at home or abroad.In effect, constant real wages prevent a depreciation of the home realexchange rate.

For the foreign country, the degree of wage indexation a* is crucialto the effects of a rise in m. In the Mundell-Fleming model, with a* = 0,a home monetary expansion reduces foreign income and foreign prices.


This is the traditional beggar-thy-neighbor interpretation of flexibleexchange rates. The home expansion causes the domestic exchange rateto depreciate, shifting demand from foreign to domestic goods. Foreigndemand drops and output falls. At the same time, the home depreciationreduces the other country' s import prices, and thus the foreign consumerprice index. In summary, dg*/dm < 0 and dp*/dm < 0. In this view,tight monetary policies in the United States should be expected to raiseEuropean output and prices via the appreciation of the dollar.

Once we allow the foreign CPI to feed back into w* and p*, thesimplicity of the first story is lost; now, a home monetary expansionhelps to slow foreign wage and price inflation via the change in currencyvalues, and the real depreciation of the home currency is diminished.With prices fixed, a change in e changes p* + e - p in equal amount.With foreign wage indexing, however, a rise in e now causes p* to fall,so that the foreign country's competitive loss (which is measured by theriseinp* + e - p) is diminished. Meanwhile, the foreign country enjoysthe expansionary demand effects of lower world interest rates broughtabout by the home monetary expansion. Formal analysis leads to thefollowing conclusions in the static model. When a* is low, dg*/dm < 0;when a* is near 1.0, dQ*/dm > 0. In fact there exists a threshold degreeof indexing, a*, such that dQ*/dm > 0 if and only if a* > a*. Moreover,if 7* is small, then for all a*, dp*/dm < 0. Thus, with very high wageindexation in Europe, a restrictive U.S. monetary policy might actuallyraise prices and lower output abroad and thus be a stagflationary shock.

Fiscal policy effects are more subtle than monetary policy effects,since the degree of asset substitutability now plays an important role.When a = °o, then the own-country effects of a fiscal expansion are toraise output and appreciate the currency. Prices may rise or fall, sinceon the one hand higher output tends to raise prices in the amount -ydQ,while on the other hand currency appreciation reduces import pricesand the CPI. With indexation, the reduction in import prices feedsthrough to domestic wages and prices.

The effect on foreign output and prices is ambiguous, dependingheavily on the extent of foreign wage indexation. When a* = 0, as in thetraditional Mundell-Fleming model, then dQ*/dG > 0, and dp*/dG > 0:the domestic expansion raises foreign output and prices. The reason isstraightforward. The home currency appreciation causes aggregatedemand to shift toward the foreign good. The expansion "spills over"


to foreign output. Foreign prices rise for two reasons: the direct effectof g* and the impact of the domestic appreciation on the foreign country' simport prices. When a* is large, it might well be that dj2*/dG < 0.Without indexing, the domestic nominal appreciation causes a realappreciation, and a shift in demand abroad. With indexing, the nominalappreciation causes foreign wages to rise when import prices increase.As e falls, p* rises, so thatp* + e - p changes little. Thus, the rise in Gdoes not cause as much (or any) real exchange rate appreciation, anddemand does not shift to the foreign country. Meanwhile, higher G raisesworld interest rates, depressing foreign demand. On balance, if thecontractionary interest rate effect is dominant, dQ*/dG < 0. Since p*will tend to rise because of the home nominal exchange rate appreciation,we may see d|g*/dG < 0 and dp*/dG > 0. In this case, a U.S. fiscalexpansion would be a stagflationary shock to the European economies.

Once we allow for imperfect asset substitutability, most of theseeffects can be reversed. A fiscal expansion causes the risk premium onhome assets to rise because the increase in b^ relative to ft*^ leads to anex ante excess supply of domestic bonds. The partial effect of a rise inb^ is twofold. As portfolio holders attempt to shift from domestic toforeign assets at the initial levels of the exchange rate and interest rates,domestic bond prices are driven down and foreign bond prices are drivenup, so that i - i* rises. Also, the shift toward foreign bonds causes theexchange rate to depreciate, which helps restore portfolio equilibriumfor two reasons. First, the domestic depreciation reduces the share ofportfolio wealth devoted to home assets (which were initially in excesssupply); second, the depreciation raises the expectation of a futureappreciation of the home currency, increasing the demand for the homeasset.

These partial effects of the portfolio shift can be added to the effectsof fiscal policy under perfect asset substitutability to find the overalleffect of a fiscal expansion when cr < oo. On the one hand, the fiscalexpansion raises demand for home goods and thereby tends to cause anappreciation; on the other hand, the rise in b^ causes / to rise, reducesthe demand effect, and tends to cause a depreciation. In fact, the sum ofthe effects is ambiguous. The greater is a, the more likely is an outputexpansion and currency appreciation; the smaller is a, the more likely isa contraction (due to rising interest rates) and a currency depreciation(due to the excess supply in portfolio wealth of b^, and the consequent


shift in foreign bonds). The depreciation and contraction do not neces-sarily go hand in hand. For reasonable parameter values, the fiscalexpansion can raise output while simultaneously inducing a depreciation.

The slope of the LM curve ((p/p) is another determinant of the exchangerate effect of fiscal expansion. When cp/p is large (that is, the LM curveis steep), the fiscal expansion necessitates a large rise in i in order toequate money supply and demand at the initial exchange rate. The largeincrease in i needed to clear the money market contributes to an excessdemand for home bonds, which tends to cause a capital inflow andexchange rate appreciation.

The implications of low o- for cross-country multipliers are similarlyambiguous. When a* is very low (so that nominal wages are rigid), theabsence of high capital mobility can make dQ*/dG turn negative. Withlow CT, the home currency depreciates, and demand no longer spills overto the other country. Although foreign interest rates fall, because of theportfolio shift towards fe*^, the expansionary effects of the decline in /*are smaller than the demand effects of the home country depreciation.When a* is high (so that real wages are rigid), then the home country'snominal depreciation does not have much effect on the real exchangerate. As e rises, p* falls, so that p* + e - p remains substantiallyunchanged. Then, the foreign country does not lose much in externalcompetitiveness, but it gains by the reduction in interest rates. In thiscase, dQ*/dG is more likely to be positive.

It is important to note that the higher is the world' s marginal propensityto hold domestic bonds out of wealth {&), the more likely is a currencyappreciation following a fiscal expansion. At initial interest rates andexchange rate, a rise in b causes supply of home bonds to rise by b anddemand to rise by ^b. Thus, the excess supply of home bondsis (1 - ^)b, and the interest rate differential, / - /*, must rise by(1/CT)(1 -^)b. Evidently, the larger is ^, the smaller is the necessaryincrease in the interest rate differential, and the more likely is a currencyappreciation following a fiscal expansion. The fact that d is large for theUnited States and small for all other major currencies is an importantfactor in explaining why a U.S. fiscal expansion tends to strengthen thedollar while a similar expansion in France, West Germany, Japan, or theUnited Kingdom is perceived to weaken the currency. We return to thispoint in the empirical evidence below.


SOME LONG-RUN EFFECTS OF MACROECONOMIC POLICIES

Long-run effects of monetary and fiscal policy may differ substantiallyfrom the short-run effects. First, in the long run, prices adjust to restorefull employment, so that all long-run demand effects of m, G, and T showin prices rather than output. But less obvious, permanent changes in Gand T lead to long-run changes in the economy's net internationalinvestment position, and therefore in the long-run real exchange rate.Interestingly, these long-run effects can move in the direction oppositeto that of the short-run effects.

To discuss this issue, we must be clear on the meaning of "long-run" policies. First, we redefine b^, G, and J to be in units per potentialGNP, which is assumed to grow at the exogenous rate n. The evolutionof public debt now is governed by bj+i = {I + r - n)bj + (G - T).Assuming that real interest rates, r, exceed an economy's trend growthrate, n, then a permanent rise in G for given T is not feasible. If G israised permanently above Tg (with ftj = 0), then b^ would grow withoutbound. Eventually government debt servicing alone would exceednational product. The government's long-run budget constraint requiresthat b^ remain bounded. One feasible policy, which we study here, is achoice of G, and T, such that the deficit relative to potential GNP remainsconstant at some level.

A fixed deficit, G + rb^ - T, leads to a steady-state debt/GNP ratioof (l/n)(G + rb^ - T). For an economy growing at 3 percent per year,for example, a permanent rise in the deficit of 1 percent of GNP (forgiven r) leads to a steady-state increase of b^ of (0.01/0.03) = VS (forexample, a rise in the debt/GNP ratio from 0.0 to 0.33). Of course, manycombinations of G and T can stabilize the deficit at a particular level.The policy that we study is one in which G is permanently raised at timezero by dG, and taxes are thereafter adjusted in line with rising debtservicing so that the overall deficit relative to GNP remains permanentlyhigher by the amount dG. Moreover, to keep the story simple, we assumethat the real interest rate is fixed (for example, determined from abroad).(A rise in r after the fiscal expansion would merely amplify the resultsthat we find below.) Then the change in taxes, dT, follows the path ofchanging debt,


(7) dr, = rdbj.

When G rises, taxes are initially unchanged. As debt accumulates, taxesare raised to service the increased debt payments. Long-run debtobligations rise in the amount (l/«)dG, so that in the long run taxes risein the amount rin. Assuming, as we do, that r > n, then dT/dG =rin > 1. Eventually, taxes rise by more than dG, even though thegovernment deficit is maintained forever. It is easy to show that private-sector financial wealth falls, in the steady state, as follows.'"

(8) dM = - [{srinm - r 4- n)]dG < 0.

The rest of the world ends up holding the entire increase in nationalgovernment debt, and then some, since private-sector holdings of debtactually drop. In the long run, the home economy must run tradesurpluses to service this increase in debt held abroad.

Because of the rise in taxes and the fall in wealth, private spending Afalls by more than the rise in G:"

(9) dA = [(Wn)/(8 - r + «)][(8 - r + n) + s{r - n)](-dG) < -dG.

The rise in G raises aggregate demand for the home good in the amount(1 - |x°)dG. On the other hand, domestic private spending on homegoods falls by (1 - yi)dA. The real exchange rate must depreciate inthe long run to raise demand for home goods as long as [(1 - |x)dA +(1 - ix'^dG] is negative. More precisely.

(10) d\= - (l/e)[(l - |x)dA + (1 - j

For |x = (JL°, there is a long-run real depreciation, while for fjL » \x,^, Awill appreciate.'2

10. A = (I - s) (,Q - T) - vr + &W, mdW = (I + r - n) W + Q - T - A. With Qand r fixed, we can solve for dW as a function of dT: dW = - [i/(8 - r + n)] AT. Sinced r = (r/n)dG, we arrive at equation 8 in the text.

11. SinceA = (1 - s)(Q - T) - vr + hW,dA = - ( ! - .s)d7'+ 8 dW. Now substitutedT = (rln)dG and equation 8 to arrive at equation 9.

12. The fiscal expansion has two effects: reducing aggregate domestic absorption andshifting the structure of absorption between home and foreign goods. The fall in A tendsto cause a long-run depreciation. A shift in the structure of absorption toward the homegood tends to cause an appreciation. When (ji = itP, only the absorption effect is operative,because the marginal propensities to import of the private and public sectors are equal.Therefore, when p, = \xP, there must be a long-run depreciation. For \i.> \xp there may bean appreciation, because the fiscal expansion serves to shift demand toward home goods.See Sachs and Wyplosz, "Real Exchange Rate Effects."


In this context, then, consider the effects of sustaining the U.S. budgetdeficits for a prolonged period into the future, holding the deficit/GNPratio constant, and taking the optimistic case that real interest ratesremain constant. As interest payments on the debt mount, taxes willhave to be raised merely to service the debt. As taxes rise, domesticabsorption will fall, and eventually the fall in A must exceed the rise inG. As long as jji == |x°, the net effect of falling A and rising G will be anexcess supply of U.S. goods. A real exchange rate depreciation will thenbe necessary to maintain demand equal to output. Thus, while the fiscalexpansion appreciates the dollar in the short run, it depreciates the dollarin the long run.

EVIDENCE ON POLICY MULTIPLIERS IN THE UNITED STATES,WEST GERMANY, AND JAPAN

We have seen that the magnitude of effects of monetary and fiscalpolicies on home and foreign variables depends on several parameterssuch as those measuring the degree of asset substitutability, the wageresponsiveness to price changes, and the interest elasticity of moneydemand. It is beyond our capacity in this paper to provide independentevidence on each of these variables. Instead we rely heavily on theevidence contained in several large-scale multicountry models. Themajor conclusions from this evidence are as follows: (1) monetaryexpansion causes a much larger depreciation of the currency than doesfiscal expansion per unit of GNP increase; (2) the United States is theonly large country that shows a systematic tendency toward currencyappreciation following a bond-financed fiscal expansion; (3) fiscal expan-sion has a smaller effect on prices than does monetary expansion perunit of GNP increase as a result of their differential impact on theexchange rate; and (4) fiscal expansion has a larger effect on currentaccount deficits than does monetary expansion per unit of GNP increase,also as a result of the differential effects on the exchange rate.

The normalized own- and cross-country multipliers for monetary andfiscal policy are shown in table 5 (for the MCM) and table 6 (for the EPAmodel). The policies are scaled to produce one unit of GNP increase inthe expanding country. The multipliers are measured as averages for atwo-year period: GNP is measured as a percentage deviation from thebaseline; inflation is the percentage-point increase relative to baseline;

i^ 5

S 1.2

I

O

I

1)

03

:S

1.28 ^

p qo o

oo go o

o oo o

g gp

d d

g D6 d

p ¥o d

I I

00 r4

d d

00 00I I

2= ggd d d d

8g =:S-H — d d

00 00

88 g8do d d

—' — 0 0 0 0

3S3

cO 5! ^ o o!

E 2 S E

4> 3 —5M n nt

2 '> '>

sS2

>^li

5 §.s

I

^ § • 2

o oI

S5 88o d « —

d d1

od d

OS 00 O f*%

d d d d

—' - . O O

S 85 o8o oI I

d dSo S 8o S do

88 = o o

I I

d —' d

I I


and the current-account/GNP ratio (current account ratio) is measuredas an absolute difference from the baseline. The monetary policy is apercentage-point reduction in the central bank discount rate, and thefiscal policy is an increase of 1 percent of GNP in fiscal expenditures ongoods and services. For the fiscal expansion, the monetary stance ischaracterized by an unchanged money base. In table 5, for example, wesee that a 3.64 percentage point cut in the U.S. discount rate, sustainedfor two years, is estimated to raise U.S. GNP by 1 percent, raise U.S.inflation by 0.18 percentage points, and lower the U.S. current accountshare of GNP by 0.02 percent, all averaged over two years.

Examining first the own-country effects of monetary policy, we seethat monetary policy is more inflationary than fiscal policy, and withonly one exception (Japan, in the MCM), fiscal policy has a considerablylarger effect on external deficits than does monetary policy. The modelsalso all show that a monetary expansion causes a current account deficit.This finding will prove important in our discussion of policy coordination.

These differing effects of M (monetary policy) and G (fiscal policy)work in large part through the exchange rate. The normalized exchangerate multipliers for the MCM and the EPA and OECD Interlink modelsare shown in table 7. In every case, a monetary expansion causes a largerdepreciation than does a fiscal expansion. The United States stands outas the only country with a tendency toward appreciation following afiscal expansion. According to descriptions of the models, this asym-metry has two causes, and they are in line with our earlier discussion.First, all of the models incorporate an asymmetry in portfolio composi-tion that gives a high marginal propensity to hold U.S. dollars out offinancial wealth. Second, the econometric estimates of the monetarysystem all find a more steeply sloped LM curve (that is, a lower interestelasticity of money demand) in the United States than elsewhere. Wesaw earlier that an inelastic demand for money favors a currencyappreciation following a fiscal expansion.

The differential impact of M and G on inflation (IT) and the currentaccount ratio (CA) suggests how different mixes of policy can achievevarious targets among output (Q), inflation, and external balance.Suppose that (2 = M + G, ir = m,M + gjG, and CA = m2M + gjG,with Wi > ^1 > 0, and g2 < m2< 0. If the goal is to change inflation byAIT < 0 without reducing output, it can be brought about by a fiscalexpansion and monetary contraction, such that


Table 7. Normalized Policy Multipliers for the Exchange Rate in the EconomicPlanning Agency, Multicountry, and Interlink Models*

Countryacting, and

policy

United StatesMonetaryFiscal

JapanMonetaryFiscal

West GermanyMonetaryFiscal

EconomicAgency

Size ofpolicy

4.080.48

2.500.64

1.110.51

Planningmodel

Exchangerate effect

-1.84-0.02

-6.82-1.63

-2.82-1.42

Multicountry model

Size ofpolicy

3.640.83

2.670.71

4.441.03

Exchangerate effect

-1.910.49

-1.07-0.45

-4.00-1.17

Interlink model

Size ofpolicy

8.000.64

6.670.59

4.000.80

Exchangerate effect

-4.800.29

-5.00-0.15

-3.30-0.02

Source: A. Amano, "Exchange Rate Simulations: A Comparative Study," European Economic Review (forthcom-ing).

a. See table 5, note a. For Japan and Germany, the exchange rate is dollars per unit of national currency; for theUnited States, it is the trade-weighted effective exchange rate. A negative sign indicates a depreciation.

(11)AG = -AM>0.

If the goal is to improve the trade balance without a loss of output, thenthere should be a monetary expansion with fiscal contraction:

(12) AM = ACA/(m2 - , 2) > 0AG = - A M < 0 .

This simple illustration suggests that the Reagan administration's mix ofexpansionary fiscal policy and contractionary monetary policy, from theU.S. viewpoint alone, may make sense if the principal targets are outputgrowth and reduced inflation, rather than output growth with currentaccount balance.

Several systematic conclusions emerge from the cross-country mul-tipliers. In both the MCM and the EPA model, the short-run wageresponsiveness is too low to reverse the Mundell-Fleming conclusionthat fiscal policy is positively transmitted. Similarly, the cross-countryeffect of monetary policy is negative (as in the Mundell-Fleming model)or, if positive, generally quite small. In all cases, a foreign fiscal expansionimproves the home current account and raises (or leaves unchanged)domestic prices. The implied price rise per unit of GNP increase is


smaller than occurs with a domestic expansion because the exchangerate consequences are generally better if the other country engineers theexpansion.

The other point about the multipliers is that while the United Stateshas some effect on West Germany and Japan, the reverse effects aresomewhat smaller in view of the relative sizes of the economies.Naturally, this will make it harder to interest the United States in acoordinated policy program, as the following section shows.

The Coordination of Macroeconomic Policies

In the absence of competitive markets, there is no reason to expectthat individuals will fully exploit their gains from trade. This conclusionis most striking and obvious in the case of pure externalities, where thefailure of a market to exist leads to overproduction of social harms (suchas pollution) or underproduction of social goods. It is not surprising,therefore, that in the realm of macroeconomic policymaking, where nomarkets for policies exist, there may be unexploited opportunities forcountries to "trade" macroeconomic policies that could leave all coun-tries closer to their macroeconomic targets. The goal of this section is todiscover what it is that countries can offer each other in' 'package deals"that swap macroeconomic policies.

Before turning to that question, we should note an unavoidablelimitation to our analysis. Once it is recognized that countries havepolicy actions that can be offered to others in exchange for policy movesfrom abroad, there is really no reason for assuming that macroeconomicpolicies must be swapped only for macroeconomic policies, as opposed,for example, to trade or security concessions. The possibility of negoti-ating a package of international moves and agreements across a varietyof fields is beyond our scope. Our focus here is on the gains fromcooperation purely within the macroeconomic realm.

We use the classic Tinbergen targets-and-instruments framework, asadapted to a multicountry environment by Niehans, Cooper, and espe-cially Hamada." Recent work in this area includes Johansen, Canzoneri

13. Jurg Niehans, "Monetary and Fiscal Policies in Open Economies under FixedExchange Rates: An Optimizing Approach," Journal of Political Economy, vol. 76, part2 (July/August 1968), pp. 893-920; Richard N. Cooper, "Macroeconomic Policy Adjust-


and Gray, Miller and Salmon, and Sachs (see note 6). Consider ann-country world economy, where each of the n countries has m policytargets. For country /, call the vector of targets T, which equals the/n-tuple (r,, r i , . . ., T'J. The country has / controls (policy instruments),with the vector of controls C' = (C',, Q, . . .,Ci). The macro-authoritieschoose C' in order to maximize a welfare function [/'(P)-

In an interdependent world, each country's T' will be a function ofthe control settings in all of the countries, and of a set of exogenous varia-bles L:

(13) r = Fia,a,...,C'',L).

In a dynamic setting, T' will also be a function of the "inheritedconditions" of the world economy in any period, defined by a statevector 5:

(14) T = F%O,a,. . .,€",5,1).

In this case, policymakers will also have to take into account the effectsof their actions today on future values of S. (In dynamic rationalexpectations models, T' will also be a function of anticipated levels of Cand L in the future.)

To formalize the idea of unexploited gains from trade, we describeuncoordinated policymaking as a situation in which each country choosesits policy instruments while taking as given the actions selected in theother n — I countries. Thus, in this case, no attempt is made to trade offan action at home for an action abroad, because all of the actions abroadare assumed to be given. This so-called Nash equilibrium is formalizedas follows. A Nash equilibrium is an «-tuple (C"^, C^^, . . ., C"^ suchthat for all countries /, C"^ maximizes U%T') with respect to C, giventhat

This formulation of each country's problem assumes away one verybasic reason for international cooperation: the exchange of information.

ment in Interdependent Economies," Quarterly Journal of Economics, vol. 83 (February1969), pp. 1-24; and Hamada, "Alternative Exchange Rate Systems" and "A StrategicAnalysis."


In a Nash equilibrium, every country knows exactly what every othercountry is doing, and all policymakers agree on the "true" model. Evenopponents of active international policy coordination generally recog-nize the need for the international exchange of information on policychoices.

The important fact about a Nash equilibrium is that it is rarely efficient(or Pareto optimal), in the sense that at least some countries can be madebetter off without any countries being made worse off by an alternativechoice of policy instruments. This fact can be most simply illustrated inthe two-economy case where each economy has a single policy instru-ment. When the foreign country (country 2) chooses its optimal policyC , it sets dUVdC^ = 0. However, for the home country, dUVdC^ willgenerally not equal zero. Then, a change in C can (to a first-orderapproximation) leave foreign welfare unchanged while raising utility athome. Consider a change in policy mix dC^ = ndidU'/dO), where w is asmall positive number. We calculate the resulting changes in t/' and U^,to a first order, as dt/' = idUydC^)dC^ and dU^ = {dUVdC^)dC^. Thuswith dC2 = (oO[/'/dC2), we see that dt/' = wOf/VaCZ) while dU^ = 0(since dUVdC^ equals 0). Since we can make the same calculation forthe home country's policy, it is easy to see that a change in dC =(xiidUVdO) and dC^ = iaidWIdC^) will leave both countries better offthan in the Nash, noncooperative equilibrium.

It should be noted that when C is perturbed, thereby raising t/' andleaving W unchanged to a first order, foreign utility U^ is in fact reducedto a second order. This is because, to a second-order approximation,df/2 = (a[/2/aC2)dC2 + '/2[a2(f/2)/(aC2)2](dC2)2, and at the original Nashequilibrium [d\W)l(dC'^Y] < 0. This explains why country 2 cannotsimply do country 1 a "favor" by perturbing C . Country 1 gains a lot,but country 2 still does lose a little. Only a joint policy of dC and dC^gives both countries a first-order welfare improvement.

A simple diagram can help to clarify the argument for coordination.In figure 1, we draw the indifference curves for countries 1 and 2 in (C,C~) space. The figure is drawn under the assumption that dU^/dO anddUysC^ are both positive. At the Nash equilibrium, N, C is chosen tomaximize t/' given C^ , so that the indifference curve for 1 is horizontalat N (that is, dU^dO = 0); similarly the indifference curve for 2 isvertical at N. Now, when C is changed in the direction (MidUVdO), thedomestic control is moved by the vector dC. For small changes, dU' ~

Gilles Oudiz and Jeffrey Sachs

Figure 1. The Geometry of Policy Coordination

27

Rising

dC,

Rising U'

0 and df/2 > 0 (actually, [/' falls by a second-order term, while C/ risesby a first-order term). The vertical vector in the figure represents dC^. Asmall rise in C^ leads to dC/' > 0 and dU^ = 0. A cooperative equilibriumwould be given by a sum of vectors dC and dC^, shown as the upward-sloping vector at point A . It clearly moves into a region of joint welfareimprovement. The region between the two indifference curves f/ andUji describes the entire set of policy moves that are Pareto improvingvis-a-vis A . Note that at point E, the indifference curves of 1 and 2 aretangent. As we shall note momentarily, no movement of O and C^ fromE can be Pareto improving, so E is an efficient policy equilibrium.

Thus, the gains from cooperation are achieved because uncoordinated


policies leave cross-country policy effects like dU^dCf nonzero, whileown-country policy effects are set to zero. Let us look at dU^ldC} moreclosely to see the particular circumstances in which dU^/dCf might(inadvertently) be equal to zero. In fact dU^dC} = (aC/VaTOOrVaC?).That is, the effect of C? on [/' is given by the effects of C? on the targetsin country 1, multiplied by the marginal welfare effects of T' on t/'.There are three major ways in which this total effect may be zero. Mostdirectly, BT^/dC} might equal zero because there is no effect of country2's policies on the foreign target variables. The economies are simplydecoupled, at least for that policy instrument.

Second, the effects of Cj on T" might be the same as the effects of alinear combination of country l's own controls on its own targets, sothat dr/dC} = S{=, Xiidr/dCj). In this case, country 1 can undo anyeffects of C? on its targets. Since in its own optimization program it sets{dU^ldV){dTldC]) = 0 for / = 1, . . . , / , we see immediately that(dUydrXdr/dCf) = S{=, M^t/VaDCarVaC/) = O. This is a crucialpoint: the inefficiency of uncoordinated policymaking arises not fromthe mere fact of interdependence, but because one country's policiesaffect another's targets in a way that is (linearly) distinct from thatcountry's abilities to affect its own targets.

The third, and least interesting way, that dU^dCj may equal zero isthat country 1 has, on its own, enough policy instruments to reach all ofits targets. Define the "bliss" point for country 1 as the m-tuple J ' =(ti, n , . . ., rj such that U(T) > U(r) for all other possible values ofthe targets. At the bliss point, dU^ldV = 0 as a property of an optimum.Thus at fi, W^ldQ = (af/Var')(aTVaC?) = O. if the home country hasreached its bliss point, it does not care about small perturbations in C ,since these will have (at most) second-order consequences for nationalwelfare.

Perturbation arguments at the Nash equilibrium establish a directionof movement of the policy variables that leaves both countries betteroff. Such arguments do not, however, establish the distance that policiesshould be moved. At what point is a further coordinated movement ofpolicies futile? We define a vector of policies (C , C ) as efficient if thereis no Pareto-improving selection of policies, and we define C^ as the setof efficient policy vectors.'''

14. Formally, (C, C ) is efficient if and only if there does not exist a feasible vector(C,, C,) such that UWiCu Cd] & U'[V{O, O-)] and mnc,, C^)] a 6"[P(C', a)], withstrict inequality in at least one case.


Mathematically, it is easy to characterize efficient policy choices,since every efficient policy vector maximizes the weighted sum of utilitiesw'f/'(r') -I- (I - wOf/KT^), for some weight Osw ' < 1. By maximizingthis weighted sum with respect to C and C^ for all possible weights w'and (1 - w'), we can identify all efficient policy packages. Consider a setof policies that maximizes w'C/' + (1 - w^)W for some wK At amaximum, we know that w^dU^/dC} + (1 -w^)dUf/dC} = 0. It is noweasy to verify that at such an equilibrium, any policy perturbation thatraises t/^ must lower t/'. That is, all gains from trade have been exploited.For small changes in Cj we have

dC/' = {dU]/dC})dCj= -[(1 -w')/w'](dUydC})dCj= - [ (1 - w^)/

Thus, for any change in C , dC/' and dlP necessarily move in oppositedirections.

SOME ILLUSTRATIONS OF THE GAINS FROM TRADE

A major task of international economics should be to discover thesources of gains from trade in macroeconomic policies. In the study ofreal trade theory, for example, economists have long recognized thepossibility of mutual advantage in multilateral tariff reductions, but muchless thought and energy has so far gone into the question of advantageouscoordination in the monetary and fiscal sphere. In the remainder of thissection we offer illustrations of those gains. Then we turn to large-scalemacroeconometric models to find, via numerical simulation, the empir-ical importance of some of these channels. It should be noted at theoutset that while an analytical characterization of efficient policies C^ isdifficult or impossible for a large-scale model, a full numerical treatmentis relatively straightforward.

Let us turn first to a case where interdependence exists but wherethere are no gains to cooperation. Suppose inflation is given hyn = TQand the GNP gap is a function of domestic monetary (M) and fiscal (G)policies and foreign policies M* and G*: Q = a^M -¥ a^G + a^M* -\-a4,G*. We know from our theoretical work that a^ and a^ may be positiveor negative. For our purpose here we assume only that ai -I- 03 >0 and a2 + a^> 0, that is, that direct effects dominate indirect effects ifthe latter are negative. Comparable equations hold for foreign output


and inflation. Domestic utility is a function of the target vector T =T{Q, TT), with U = U(T). Clearly, domestic authorities will chooseM such that idUldT)(dT/dM) = 0. Here, iiTlbU = (a,, aix). A change inM* will affect utility as {dU/dT)idT/dM*), but since BTldM* = (aj, UJT) =aM)idT/dM), we see that {WldT){dTldM*) = {aM)idUldT)(dT/dM) =0. There will be no scope for cooperation. Even if the home countrycould choose M* and G* it would find it superfluous to do so, since M*and G* affect home country targets in exactly the same way as A/and G,up to a constant of proportionality.

Suppose now that the country's authorities target the current accountbalance (or changes in external indebtedness) as well as IT and Q. Now,U = U{Q, IT, CA). With symmetric countries, the current balance willdepend only on the differences M - M* and G - G*, since CA* =-CA. Then, CA = p,(M - M*) + ^G - G*). A fiscal expansion willalmost surely worsen the external balance, so that |32 < 0. A monetaryexpansion, we have noted, tends to improve CA via currency deprecia-tion, but also to worsen CA via the direct effect demand expansion. Inline with the empirical evidence in tables 5 and 6, we assume p, < 0.Consider the effects of the controls on the country targets:

Q = aiM + ajG +

(15) TT = a,TM + OZTG + ajTM* +

CA = p,(M - M*) + p2(G - G*).

Now, dTldM = (a,,a|T,Pi) and dT/dM* = (0^,02,7,-^^). The vectorsdT/dM and dT/dM* are no longer linearly dependent, thus dU/dM* willbe nonzero. To be more precise: dU/dM = i/iOi + «2fl|T + "3Pi = 0,where M, = dUfdTi. We assume that «, > 0 (more output preferred toless), U2<0 (less inflation preferred to more), and M3 > 0 (higher tradebalance preferred). Now dU/dM* = u,a^ + UJO^J - u^^^, which uponsubstituting 3f//dM = 0 yields aC//aM* = -[(a, + a3)/a,]M3p,, which isgreater than zero. Thus higher M* raises home welfare. But since at theinitial equilibrium dU*/dM* = 0, a slight rise in M* will raise U withoutchanging (to a first order) U*. By symmetric reasoning, M can be raisedat home without a loss of welfare while providing a (first-order) gain inwelfare abroad. A joint expansion of M and M* will therefore raise bothU and U*, and a similar argument guarantees that ajoint fiscal expansionis also welfare improving. In sum, when policymakers prefer a largertrade surplus, and macroeconomic expansion worsens the trade balance.


there will be a tendency toward overcontraction in the world economy.Geometrically, the Nash equilibrium will lie to the lower left of theefficient, symmetric equilibrium, as shown in figure 1.

Now let us refine the model further, to allow for differential exchangerate effects of monetary and fiscal policy. With symmetric economies,the real exchange rate will be given as a function of the differencebetween M and M* and the difference between G and G*:

(16) X = a, (M - M*) - a2(G - G*) a, > 0, aj § 0.

Because a monetary expansion depreciates the real exchange rate, aj issurely positive. With a high substitutability, CT, of home and foreignassets, a2 will be negative, while with CT small, a2 will be positive. Thecurrent balance and output are written as before. Finally, inflation iswritten as a rising function of \ :

(17) TT = T^ + ex.

In choosing domestic monetary policy in the Nash regime, the homeauthority will set (dU/dT){dT/dM) equal to zero, or «,fl, -I- Uji-rai + 9a,)+ M3P1 = 0, with Ui the partial derivatives of UiQ, TT, CA). At the Nashequilibrium, {dUldT){dTldM*) = uâ^ + Uiita^ - Oa,) - M3P,. Using(dU/dT)(dT/dM) = O,weh&\e(dU/dT)(dT/dM*) = -(«3p, + «26a,)[(a| +a^la) ]. Under the assumptions that (1) a higher trade balance is preferred,M3 > 0; (2) a monetary expansion worsens or has little effect on thecurrent account balance, p, s 0; and (3) less inflation is preferred, M2 <0; then {dU/dT)(dTldM*) is positive. That is, the countries would gain byajoint monetary reflation.

Consider {dU/dT)idT/dG*). By direct substitution this term equals M,a4-I- U2{ra4-Ba2) - "3^3. At the Nash equilibrium, 0 = {dU/dT)(dT/dG) =

+ M2(T«2 + 6«2) + Ui^2^ SO that

Since aj S 0, it appears that {dU/dT){dT/dG*) is of ambiguous sign.However, as a property of the Nash equilibrium, we can show that U3^2+ M26«2 < 0, so that the sign is positive (assuming, as before, that«, >0, «2 < 0> and M3 < 0). Since {dU/dT){dT/dG*) is positive, we again find atendency toward overcontraction, this time in fiscal policy. Ajoint fiscalreflation at the Nash equilibrium raises welfare in both countries.


To show that «3 2 + U2Ba2 < 0, start with 0 = {dU/dT){dT/dM) =+ M2(Tai-l-0ai) + M3pi. By rearrangement, «, + ru2 =

«26ai)- Assuming p, < 0, a, > 0, Uy > 0, and M2 < 0,we see that«, + T«2 > 0. Now consider 0 = {dUldT){dTldG) = «, a, +«2 (Ta2 + 8a2) + «3P2- We see that «, + T«2 = -(l/a2)(«3Since 2 > 0 and U\ + TM2 > 0, we find immediately that u^^^ +must be negative, as we wanted to show.

Under our specific assumptions, both M and G will tend to be toocontractionary at the Nash equilibrium, so that utility will rise whenboth dG = dG* > 0 and dM = dAf* > 0. Under alternative assumptionson the signs of ai, M2. "3; on the policy multipliers; or on the targets inthe objective function, the bias towards overcontraction can be re-versed. Indeed, in cases where fiscal expansion causes a currencyappreciation, and thus allows an economy to export its inflation abroad,it is not difficult to construct examples where monetary policy isovercontractionary while fiscal policy is overexpansionary, with theoverall mix being overcontractionary. To summarize, an uncoordinatedselection of macroeconomic strategies is likely to lead to an inefficientmix of monetary and fiscal policies and to an inefficient overall stanceon the level of output selected.

In the empirical work that follows, we will use a quadratic utilityfunction, since it results in linear policy rules. For example, we willspecify I/as -V2[\i.iQ-Qf + ^(-n-Ttf + ^CA-CAf], where Q, %,and CA are the targets (or bliss points) for g, n, and CA. In this case,the marginal utility of Q, IT, and CA depend on their respective distancesfrom Q, *, fB, with«, = -\iiQ- 0 , M2 = - <})(TT - TT), M3 = - MCA - CA).Thus, inflation will be important on the margin when inflation is veryhigh; the current account deficit is important on the margin when CA isvery low relative to CA; and so on.

It is not hard to generalize our results to cases of asymmetriceconomies. If fiscal expansion in the United States tends to appreciatethe dollar while a foreign fiscal expansion depreciates the foreigncurrency, then it is possible that a U.S. fiscal contraction will lowerforeign utility while a foreign fiscal expansion will raise U.S. utility.Thus a move from the Nash equilibrium to the cooperative equilibriummay involve a move of G and G* in opposite directions. We will returnto the U.S. policy mix shortly.


SOME DYNAMIC CONSIDERATIONS IN POLICY COORDINATION

So far, we have analyzed the possibility of welfare-improving swapsof macroeconomic policy in a static planning environment. Now weconsider some of the implications of moving to a more appropriate,multiperiod setting. At one level little is changed; it is still easy todemonstrate conditions under which policy actions in the two countriesare Pareto improving. But at another level, much is changed. To theextent that the private sector acts in anticipation of govemment policies,the nature of govemment policy optimization may be radically altered.

The formal apparatus for the intertemporal optimization problem isfairly intricate, so only the general approach is sketched here." Weconsider that each economy has an intertemporal objective function ofthe form VQ ='2Tôb'U(Q,,TT,,CA,). In the dynamic setting, withforward-looking agents, it is typical that in reduced form Q, IT, and CAare functions of current and future values of M, M*, G, and G*. For themoment let us avoid that complexity and write in the usual way thatQo = a,Afo + a2Go + a^MS + a^G^ and CA^ = 3,(Mo-M^) +P2(Go - G*)• Also, write ir, in the simple form TT, = IT,- i -f- iQ,.

In this case, IT is a state variable of the system, and with TT there is aco-state variable x < 0 that measures dVJdTT,; that is, x is the marginalloss in intertemporal utility caused by inheriting a higher rate of inflation.It is well known that the dynamic optimization problem may be rewrittenas a static optimization problem by using the co-state variable:

(18) max H = u{Qo, TTQ, CAQ) +

such that

IT, = iTo + TQU CA^ = 3,(Mo-Afo*) +

Now the argument proceeds as before.

15, See Miller and Salmon, "Dynamic Games," and Sachs, "Intemationai PolicyCoordination," for some details.


At the noncooperative equilibrium, it must be that dH/dMo =0 = Mifli + M2fliT + M3P| + XlTfll- Also, dH/dM* = «|fl| + «2fl3T "

«33i + XiT«3- By combining these two expressions we find dH/dM* =-Mj3i[(ai + a3)/a,]. Once again, assuming that a monetary expansionworsens the trade balance (Pi < 0) and that a larger trade balance surplusis preferred to a smaller trade balance surplus (M3 > 0), then dH/dMo >0, and a foreign monetary expansion would tend to raise home welfare.With symmetric countries, a common rise in MQ and M$ would raiseboth V and V*. In summary, the fact that the optimization problem isnow dynamic does little, in this case, to change the method of analysisor the specific conclusions regarding monetary policy.

The problem becomes considerably more complicated when currenttarget variables are functions, via rational expectations, of future policyvariables. Not only is the computational complexity increased, but thelogic of optimizing Vo = ^"=0 ^'U{Q,, TT,, CA,) is called into question, asKydland and Prescott first explained.'* In maximizing VQ, the policy-maker must choose at ^ = 0 an entire path of Af and G, that is, Afo, M,,. . ., Go, G,, . . .. The problem arises that at t = !, when the policyauthority reconsiders the problem of maximizing V,, it will typically beoptimal to choose a new path M,, Mj, M3,. . ., Gj, G2,. . ., where M, ¥=M, and G, 7 G,. Policymakers will always want to deviate from theirinitial "optimal" plans. They will announce one thing and then have anincentive to do another after one planning period. Time inconsistencyarises whenever the private sector takes action dependent on anticipa-tions of future policies (for example, in formulating asset demands).Time inconsistency is "solved" in one of two ways. The policymakermay value his reputation for consistency so much that he decides to stickwith the original plan, even though it is suboptimal from the currentvantage point; or the policymaker may announce a suboptimal but time-consistent set of policies, in which there is no incentive to alter theoriginal plans over time. We pursue this issue in Oudiz and Sachs butnot further here.'^

16. See Finn E. Kydland and Edward C. Prescott, "Rules Rather than Discretion: TheInconsistency of Optimal Plans," Journal of Political Economy, vol. 85 (June 1977), pp.473-91.

17. See Gilles Oudiz and Jeffrey Sachs, "Dynamic Games of Macroeconomic Policyin a Multicountry Model," to be presented at the Centre for Economic Policy ResearchConference on Policy Coordination, June 1984.


ACHIEVING A COOPERATIVE EQUILIBRIUM

We have shown so far that there generally exist policy options at anoncooperative (N) equilibrium in which all countries can be made betteroff. Getting from N to a Pareto-improving point is not, however, assimple as it might appear. Precisely because the Pareto-improving pointsare not Nash equilibriums, it means that at least one country will havean incentive to deviate from such a point if it assumes that the othercountry's policy is fixed. Figure 2 is instructive. The Nash equilibriumis N, Pareto dominated in welfare terms by C. However, if the foreigncountry expands its money supply from M*'^ to M*^, the best responsefor the home country is Af, given by the tangency of the home country'sindifference curve with the horizontal line M** ; yet, if the foreign countrychooses M*^ while the home country "responds" with Af'', the foreigncountry is actually worse off than at A .'* Assuming a unique Nashequilibrium, A is the only point at which both countries are content tostay put, taking as given what the other country is doing.

There are two related issues in the move from N to a point like C.First, which point C should be (or will be) chosen among all of the Pareto-improving points? Second, how can the equilibrium C be enforced giventhe incentives of each country to move unilaterally from C? We havelittle to add to various well-known comments on these questions. On theset of desirable points, most models of bargaining restrict the outcometo lie in the efficient set, from which further improvements in onecountry's welfare are possible only at the expense of losses elsewhere.To enforce such an equilibrium, there might be (1) a policing authoritythat imposes sanctions on violators, (2) a set of rules (such as a fixedexchange rate linking M and A/*) that are enforced but within which thevarious countries are free to act without external sanction, or (3) anequilibrium upheld by reputation, in which the failure to stick by one'sword reduces the scope for making agreements with other countries inthe future. We will return to questions of institutional arrangements forcooperation in the concluding section.

18. Actually, F could have been to the right of the foreign indifference curve throughN, in which case both countries would be better off than at N. However, even in this case,the foreign country would have an incentive to move away from M*^, assuming that thehome country stays at Af.


Figure 2. EoforcNiieBt Pn^kms with tiie Cooperative Equilibriiiin

M*

In our numerical illustrations, we choose the cooperative point to bethe "Nash bargaining solution" to the policy game played by themacroeconomic authorities in the various countries. (Note well that theNash bargaining solution is not the same as the Nash equilibrium, whichis the point iV in figure 1.) In a series of influential articles, Nash describedprocedures for picking a point C in a bargaining environment, assumingthat the outcome at Cis fully enforceable. In afirst approach he describeda series of axioms to guide the choice. In later studies, Nash and othersproposed various noncooperative games whose rules lead to preciselythe same point as determined by the axioms."

In the Nash bargaining solution there is a "threat point" that isassumed to occur if cooperation breaks down. It is natural to take thispoint to be the noncooperative equilibrium point N in figures 1 and 2. AtN, each country / has utility U"^. The point C is then determined as thefeasible point that maximizes the gain in utility over the threat point A ,where the gain is measured by the following product:

19. For a detailed discussion of the Nash bargaining solution and related concepts, seeAlvin E. Roth, Axiomatic Modei of Bargaining, Lecture Notes in Economics andMathematical Systems, no. 170(Springer-Verlag, 1979).


Gain =

The point C will have to be efficient (otherwise it is obvious that the gaincould be raised by moving to a Pareto-superior point). We will solve forC numerically in the examples that follow.

Simulating Coordination of Economic Policies with a Large-ScaleEconometric Model

The gains from cooperation seem obvious when one refers to a simpletwo-country symmetric model. It is, however, much more difficult toassess these gains empirically. Real-world policymaking involves neithersymmetric countries nor only two countries. On the contrary it is thediversity of the countries involved and the wide range of their objectivesthat make cooperation a delicate issue and cooperation so hard toachieve.

In this section we shall try to give an empirical evaluation of theoutcomes of cooperative or noncooperative policymaking among theUnited States, West Germany, and Japan. To simplify the problem andmake it tractable we will retreat from a full dynamic framework andconsider instead the static model in which the economies are representedby a set of multipliers that link the various "targets" of each country tothe policy instruments of all of the countries. These multipliers are takenfirst from the MCM and then from the EPA model.

Our strategy is as follows. Let Jbe the vector of targets, T = (J ' , P ,. . ., J"), with T = (P/ 71,. . .,VJ. We start with a baseline or "centralvariant" projection of T, denoted T*; in fact T* will be taken essentiallyfrom a simulation of the MCM for the period 1984-86. Let C be thevector of policy controls, C = {C\C^, . . ., C"). The matrix F containsthe policy multipliers linking C to T, so that I = CF + T* if we make theimportant assumption of linearity. Thus when C = 0, then T = Tâccording to this normalization.

Next we assume that the baseline is a Nash equilibrium for the ncountries. That is, we assume that if C',C2,. . . ,C ' - ' , C'+',. . .,C''areall zero at J*, the optimal policy for the ith country is also C' = 0. Thisassumption allows us to identify key parameters of each country's utilityfunction in the case of three targets per country and two instruments.To be specific we assume that U' = U'iQ', IT', CA") and that the controls


are M' and G'. At a Nash equilibrium, dU'lBM' = 0, so that 0 =4- U2{dv'/dM') + UjidCA'/dM''). Similarly, 0 = uiidQ'/BG') ++ UiidCA'IdG'). The policy multipliers (such as dQIdM') are

taken from the econometric models and are therefore "known." Theutility function can be normalized by setting «i = 1 so that we are leftwith two equations to find two unknowns, Uj and u^. Assuming that thebaseline projection is a Nash equilibrium, we solve the equations to getestimates of the marginal utilities of inflation (u^) and the trade balance{Ui). Once these marginal utilities are known we can calculate directlythe marginal returns to policy coordination.

The baseline estimates come from a simulation of the MCM made inlate 1983 on the assumption of no dramatic change in policy instrumentsin the 1984-86 period. The baseline yields a fairly flat path for outputinflation and the current account. We converted the MCM trajectory ofreal GNP into a 1984-86 trajectory of GNP gaps based on our ownestimates of Okun's law. Table 8 shows the results of these calculations.We estimate the annual long-run trend growth to be 3.2 percent in theUnited States, 4.4 percent in Japan, and 3.2 percent in West Germany.According to the MCM baseline, the U.S. GNP continues to grow morerapidly than trend from 1984 to 1986, with the GNP gap averaging 5.5percent over the period. Japanese growth is projected to be slightlybelow 4.4 percent, with the GNP gap averaging 6.0 percent over thethree-year horizon. German growth is almost exactly 3.2 percent. Asshown in the table, U. S. inflation averages 4.4 percent along the baseline;Japanese inflation, 2.6 percent; and German inflation, 3.0 percent. Theexternal balance as a percent of GNP is a deficit of 2.2 percent for theUnited States and a surplus of 1.5 percent for Japan and 1.1 percent forWest Germany. Overall, this baseline accords rather closely with otherforecasts that assume unchanging policies in the major countries.^''

Next, we turn to the marginal utilities of output, inflation, and thecurrent account ratio (current-account/GNP). The marginal utility of aGNP increase (relative to basehne), sustained for three years, is nor-

20. For example, we may compare the baseline with OECD forecasts in OECDEconomic Outlook (fans: OECD, December 1983), p. 14. The OECD projects annual U.S.GNP growth to be 5 percent for 1984, with growth back to trend at 3 percent in the firsthalf of 1985. Japanese growth is forecast to be 4 percent for 1984 and 3 percent in the firsthalf of 1985 (and thus below long-run trend, as in our baseline). German growth is projectedat 2.0 percent for 1984, rising to 2.25 percent in the first half of 1985. The price and currentaccount forecasts are also very close.


Table 8. Characteristics of thePercent

Country

United StatesJapanWest Germany

GNP gap,1983'°

-7.3-4.4

-10.4

Multicountry Model Baseline,

Output

Growth ofpotential

GNP

3.24.43.2

GNP gap,1984-86^

-5.5-6.0

-10.7

1984-86 Averages'

Inflation

4.42.63.0

Currentaccount

ratio

-2.21.51.1

a. Baseline is assumed to be a Nash equilibrium.b. E)erived from Okun's law estimates.c. Using Multicountry model baseline assumptions.

malized to equal 1.0. The other marginal weights are calculated usingthe two equations dU/dM = 0 and dU/dG = 0 at the baseline, accordingto the procedure described in the appendix. The welfare costs, in GNPequivalents, of a 1 percentage point increase in inflation held for threeyears is measured by U2. A value of M2 = ~ 2.0, for example, means thaton the margin, policymakers are indifferent between a sustained 1percentage point rise in infiation and a sustained GNP loss of 2 percentrelative to baseline. Similarly, u^ measures the marginal utility of anincrease in the current account ratio of 1 percentage point, sustainedover three years. A value of M3 = 2 equates a 1 percentage point increasein the current account ratio with a 2 percent rise in GNP for three years.

Since the EPA policy multipliers differ from those of the MCM, theysuggest different values of M2 and u^, along the baseline path. Thecalculated values of M2 and M3 for the two models are shown in table 9. Ingeneral, we find very high marginal weights for inflation and the currentaccount balance (relative to «, = 1 for GNP). It is not hard to understandthis finding. In both the MCM and the EPA model it is possible to use acombination of M (monetary policy) and G (fiscal policy) to arrive at aGNP expansion with only a slight loss in inflation (ir) and the currentaccount. However, if we accept the baseline as a Nash equilibrium,countries are refusing to take this option even though the trade-offs areso favorable. Implicitly this suggests a very high weight on TT and CA(the current account ratio) in the objective function. Another interpre-tation is that the policymakers in the various countries perceive thetrade-offs of Q (output) with IT and CA to be much less favorable than issuggested by the models. Then, even if they care little about inflation.


TaMe 9. Partial Derivatives <rf National Utility Functioiis at Nash Equiiibrium'

Percent per year

Country


Economic Planningmodel

Output,

111

Inflation,

-5.9-2.9-4.9

Agency

Currentaccount

ratio,u,

2.94.61.0

Multicountry

Output, Inflation«, Uz

1 -4.51 -3.61 -3.0

model

Currentaccount

ratio,u,

0.05.91.9

a. The marginal utility of a GNP increase (relative to baseline) sustained for three years, ut,is normalized to equalone; «2 and «; give the inflation and current account deviations that give the same marginal utility. The Nashequiiibrium is taken as the baseline in the Multicountry model shown in table 8.

for example, the perceived rise in inflation for a given increase in GNPmight be so high as to rule out an expansionary policy.

Once we have these marginal weights, we can examine the scope forpolicy coordination. Consider, for example, the effect on utility ofcountry i of a rise in Min country J, d U'ldM. We know that this expressionequals idQIdM') + UzidTr'/dMJ) + Uj{dCA'/dMJ), which can now becalculated directly. Table 10 reports the values of dU%M and dU'ldGifor all countries /, j . By construction, the own-effects are zero at theNash equilibrium; all other effects are positive, except for the effect ofa Japanese monetary expansion on Germany in the EPA model. Con-sider, for example, the effect of a U.S. fiscal expansion (1 percent ofGNP) on Japan. In the EPA model, dU-^/dG^^ = 0.78. In other words, aU.S. fiscal expansion is equivalent for Japanese utility to a sustainedincrease of Japanese GNP of 0.78 percent for three years. According tothe MCM the gain is 0.43. Other cross-country effects are considerablysmaller. And notably, neither Japanese nor German policies have asignificant effect on U.S. utility.

We have established the marginal welfare effects on each country ofpolicy changes in another. But this incremental analysis does not tell ushow far the countries should move in the Pareto-improving direction inorder to reach an efficient worldwide policy mix. To find the necessaryoverall movement, we must define global rather than local properties ofthe utility function. We choose to do this in a simple but admittedlyrestrictive way by assuming that t/'(g', IT', CA') is quadratic in Q', TT'.

Gi7/e5 Oudiz and Jeffrey Sachs

Table 10. Cross-Country Gains from Fiscai and Monetary Expansionat Nash Equilibrium*

Percent per year

41

Countryacting,

and policy

United StatesFiscalMonetary

JapanFiscalMonetary

West GermanyFiscalMonetary

Economic Planning Agencymodei

UnitedStates

0.000.00

0.020.05

0.010.00

Japan

0.780.13

0.000.00

0.530.10

WestGermany

0.180.03

0.01-0.03

0.000.00

Multicountry model

UnitedStates

0.000.00

0.070.02

0.070.05

Japan

0.430.15

0.000.00

0.170.12

WestGermany

0.350.05

0.000.02

0.000.00

iiic uiiiL ui iistû] pulley IS A itusuuncu iiiLrcct!»c ui (ûvcimiiciii »pciiuiiit$ cûtumonetary policy is a sustained decrease of the discount rate by 100 basis points.

CA', with a bliss point at a zero GNP gap, zero inflation, and a CA targetof CA'. (For the United States, the external balance goal is taken to bezero; for Germany and Japan, the goal is taken to be 2 percent of GNP.)Let {QY, (TT')*, and {CA^Y be the values of Q, IT', and CA' along thebaseline. The following utility function satisfies the bliss point and hasthe marginal utilities (1, « , M(|) that we calculated earlier:

(19)

where CA'^ = CA'" - CA', and CA' = CA' - CA'. It is easy to verifythat C/'(0, 0, CA') = 0 and that W'ldQ = 1, aC/Vdir' = u{, and dU'/dCA'= ui when the derivatives are calculated at the baseline. We rewrite thisfunction as:

(20)

where (JI;, <i),, and i|», are as shown in equation 19. The numerical valuesof (ji;, (j),, and i(i, are shown in table 11.

By construction, the baseline path is the noncooperative (N) equilib-


Table 11. Utility FunctioB Parameters '

Economic PlanningAgency model Multicountry model

Current Currentaccount account

Output, Inflation, ratio. Output, Inflation, ratio.Country n, <t>, ii, |JL, 4)/ i|/;


0.070.060.03

0.490.400.60

0.473.380.40

0.070.060.03

0.370.520.37

0.004.350.68

a. The parameters are normalized so thai the marginal utility, at the baseline, of an increase in GNP maintainedfor three years is equal to one. See equations 19 and 20 for definitions of parameters.

rium. We find the cooperative equilibrium (C) as the solution to the Nashbargaining problem:

M',M\. . .,W«G\G\. . .,G"

This maximization is restricted to the set of feasible policies for M andG. We impose no restrictions on G but for M we require that discountrates remain positive. In practice we allow a maximum cut of 5.8percentage points in the German discount rate and 5.5 percentage pointsin the Japanese rate (the U.S. constraint did not prove to be binding inany of the simulations). The solution is calculated numerically by anoptimal gradient search routine.

At this point it should be noted that the parameters of the utilityfunctions are dependent both on the baseline and on the policy trade-offs the countries face. Let us make this point clear by using a simpleexample. Consider a single country with two objectives: the output gap,Q, and inflation, TT; and one instrument: fiscal policy, G. The policymultipliers are 1 for the output and T for inflation. Thus we have thefollowing equations:

e = G + e*IT = T G + IT*,

with the same notation as above. For the baseline to be a Nashequilibrium, the marginal welfare gain for a change in fiscal policy mustbe zero:

dV dUdO dUd-ndG dQ dG Sir 3G


(Note that all of the partial derivatives are evaluated at the baseline.)The partial derivatives are normalized by assuming that

dU

Thus

M2 = - 1 / T .

Given the assumptions, M2 is nothing other than a measure of the output-inflation trade-off. In other words, the partial derivatives of the utilityfunction at the Nash equilibrium are dependent only on the modelmultipliers.^'

We now assume that U is quadratic and compute the parameters n-and<)):

f/= -

Since M, = 1 and U2 = — 1/T, we have the following equations:

SO that

=^ -\/Q»

Note that when TT* is positive, Q" must be negative; otherwise thebaseline cannot be a Nash equilibrium. For example, with IT > 0 and Q^> 0, it is always possible to gain on both targets by a fiscal contraction.

Since the revealed preferences of governments, as measured by fi,,4),, and î, are reflected in the paths of output, inflation, and the currentaccount, we can examine the implicit changes in ix,, <}),, and»}), over time.For example, let us assume that for the 1976-78 period the output gap,inflation, and current account reflect a Nash equilibrium.

Recomputing the parameters of the U.S. government implicit utilityfunction using the multipliers of the MCM for 1976-78, we find quite

21. When three periods instead of one are considered, this is no longer exactly true.The partial derivatives will be affected by a change in the baseline, as is clear from theformulas given in the appendix for u\, wj, «;,.

44 Broolcings Papers on Economic Activity, 1:1984

different parameter values from those in table 11. The values of fi-i, ( i,and ifi are now 0.10, 0.14, and 2.68, respectively. These new valuesshow a much smaller emphasis on inflation relative to the output gap asmeasured by the ratio \i.\lû which increases from 0.2 to 0.7. Similarly,the implied importance of the current account, as measured by il)|/|ji|,was also very much higher in the earlier period.

Each utility function will of course lead to different conclusionsconcerning the desirability of policy coordination for the United States.In this sense, the advent of the Reagan administration and the muchsmaller weight it placed on the current account deficit probably reducedthe attractiveness of policy coordination for the United States.

COOPERATION IN THE CURRENT MACROECONOMIC

ENVIRONMENT

We now proceed to three sets of simulations in order to address thefollowing questions: (1) What improvement of the present situation couldbe achieved through cooperation among the United States, West Ger-many, and Japan given unchanged objective functions? (2) What wouldbe the implications for these three economies if the United Statesunilaterally shifted its policy mix to fiscal contraction and monetaryexpansion? (3) How beneficial would cooperation be if the three countrieshad to face a third oil shock about half as large as that of 1979?

Suppose that we regard the baseline trajectory as a Nash equilibrium.Can all countries materially benefit from a coordinated package? Quali-tatively, the answer is almost surely yes, and since we have seen thatdU'/dGJ > 0 and dU'/dMJ > 0 for almost all i, j , the nature of coordinationwill be ajoint reflation. Quantitatively, however, it appears that the gainsare slight, at least when policy actions are restricted to the three countriesunder study. Those who advocate a coordinated expansion as thesolution to global unemployment must be presuming (a) a much largergroup of countries taking policy actions in response to coordination, {b)a much higher degree of macroeconomic interdependence than appearsin the EPA model and the MCM, or (c) objective functions that differsignificantly from those of current policymakers. To put the last pointanother way, it appears to be the anti-inflation bias (or anti-Keynesianviews) of policymakers rather than the absence of effective coordinationthat blocks a genercd reflation.


Table 12. Policy Optimization in the Muiticountry Model, 1984-86

45

Policy andoutcome

Welfare gain"Fiscal policy''Monetary policy'

Output198419851986

Inflation198419851986

Currentaccount ratio

198419851986

United

Baseline(Nosh)

-5.68-4.97-5.67

4.244.814.10

-2.25-2.20-2.25

States

Coopera-tion

0.170.522.14

West Germany

Baseline(Nash)

Coopera-tion

0.33-0.21

5.80

Japan

BaselineiNashj

Deviations from target values''

-4.72-3.80-4.86

4.355.084.18

-2.42-2.44-2.45

-10.50-10.70- 10.91

3.162.922.89

-0.95-0.93-0.99

-9.95-9.65-9.61

3.333.412.94

-0.90-0.81-0.80

-5.23-6.00-6.80

2.202.862.89

-0.31-0.56-0.64

Coopera-tion

0.99-1.15

5.50

-5.41-4.45-4.42

2.262.952.86

-0.21-0.51-0.70

a. The unit of welfare gain is equivalent to a percentage change in GNP, averaged over the three years.b. The unit of fiscal policy is a sustained increase of government spending equal to I percent of GNP.c. The unit of monetary policy is a sustained decrease of the discount rate by 100 basis points.d. Target values are as follows; output, full employment; inflation, zero; and current account ratio, zero for the

United States and 2 percent for West Germany and Japan. Deviations are in percent for output and percentage pointsfor annual inflation rates and the current account ratio.

The gains from coordination are larger in the MCM (table 12) than inthe EPA model (table 13). Consider table 12. The first column for eachcountry shows the baseline for output (GNP gap), inflation, and thecurrent account ratio (relative to target) for the years 1984 , 1985, and1986. By construction, the Nash equilibrium is the same as the baseline.The "cooperation" column shows the result of employing the Nashbargaining solution for each of the three countries. In the first row of thetable we measure the welfare gain relative to baseline that comes fromcooperation. The magnitude 0,17 for the United States signifies, forexample, that coordination is worth an equivalent of 0.17 percent higherGNP over the three-year period. The gain of 0.17 reflects a somewhatlarger actual gain in GNP (the GNP gap falls by 0.96 in 1984, 1.17 in1985, and 0.81 in 1986), minus the welfare costs of a small rise in inflationand a slight worsening of the trade deficit. In West Germany, the welfaregain is 0.33 percent of GNP for three years. Japan is the big winner. The


Table 13. Policy Op^nization in the Economic Pianniag Agency Model, 1984-86*

Policy andoutcome

Welfare gainFiscal policyMonetary policy

Output198419851986



198419851986

a. See notes to table

United States

Baseline(Nash)

-5 .68-4 .97-5.67

4.244.814.10

-2 .25-2.20-2 .25

12.

Coopera-tion

0.03-0.11

4.30

West Germany

Baseline(Nash)

Coopera-tion

0.03-0 .16

0.86

Japan

Baseline(Nash)

Deviations from target values

-5 .15-4 .06-5.11

4.324.834.19

-2 .30-2 .33-2.32

- 10.50- 10.70-10.91

3.162.922.89

-0 .95-0.93-0 .99

-10.79- 10.84-10.44

3.102.802.94

-0 .96-1 .14-1.27

-5.23-6 .00-6.80

2.202.862.89

-0.31-0.56-0.64

Coopera-tion

0.37-0 .08

1.88

-4.97-5 .07-5.11

2.303.153.21

-0.25-0.51-0 .69

move to a cooperative equilibrium raises Japanese welfare the equivalentof a 0.99 percent rise in GNP over the three-year period.

The cooperative equilibrium is achieved by more expansionary mon-etary and fiscal policies in the United States, and a mixed policy of fiscalcontraction with monetary expansion in West Germany and Japan. Itmay seem paradoxical that U.S budget deficits actually increase alongthe path to cooperation but it must be remembered that the objectivefunction weights were selected so that U.S. policymakers are indifferent,on the margin, between fiscal expansion and fiscal contraction. In anyevent, the fiscal actions are small relative to the interest rate actions.The biggest gain in coordination comes in making possible a synchronized"worldwide" reduction in central bank discount rates (which fall 2.1percent in the United States, 5.8 percent in West Germany, and 5.5percent in Japan).

In table 13, the same exercise is undertaken with the EPA model. Themovement from Nash to cooperative equilibrium involves contraction-ary fiscal policies and expansionary monetary policies in all countries.


Once again, Japan is the big winner (0.37 percent increase in GNP inutility units), while for West Germany and the United States welfare isalmost unchanged relative to the Nash equilibrium. In this case, asbefore, coordination mainly permits a drop in central bank discountrates of almost I percentage point in Germany, 2 percentage points inJapan, and 4 percentage points in the United States.

Thus the policy effects of coordination are neither trivial nor huge,while the welfare effects of those policy changes seem rather smalloutside of Japan, In a sense, as we have noted, much of this could havebeen gleaned directly from table 6, where we saw that the German andJapanese policy links to the United States are almost nonexistent in theEPA model. We stress one important qualification to this conclusion.The simulations assume that no countries other than the three engagedin the bargaining undertake any policy actions in response to the actionsof the United States, Germany, and Japan. However, even if France andthe United Kingdom are not direct parties to the bargaining, they mayfind it desirable to respond with expansionary policies of their own.Unfortunately, we simply did not have available the relevant policymultipliers for the other countries to allow us to incorporate suchspillover effects; the MCM, for example, has no French block, so itwould be impossible to assess directly the French policy response inthat model. (Below, we extend our analysis by assuming that Europecan be modeled as a mc^nification of West Germany.)

EFFECTS OF A SHIFT IN U . S . POLICY

Our analytical procedure has been to assume that the baseline pathrepresents a Nash equilibrium. For the United States this assumptionmeans that when policymakers balance the pros and cons of fiscjilcontraction from a macroeconomic point of view, the contractionaryeffects on output just cancel the gains of lower inflation and a smallertrade deficit. Of course, there are several other interpretations of ihepresent policy stance, the main alternative holding that the costs oftoday's U.S. fiscal policy are well recognized, and are deemed too high,but a deadlock over how to close the deficit has prevented a change inpolicy. Would a change in U.S, policy that aimed at reducing the tradedeficit dramatically affect the welfare of Germany and Japan, and wouldit modify our previous appraisal of the effects of coordination?


Table 14. Alternate BueUne, Mdtfcoimtry Model, 1984-86 Averages'

Country


Policy

Fiscal*'

-2.0-0.4-0.3

shifts

Monetary^

4.61.85.4

Characteristics of baseline

GNP gap

-5.9-6.0

-10.9

Inflation

4.22.63.0

Currentaccount

ratio

-1.81.51.0

a. The utility weight of the current account ratio is raised to 0.24 from the value of zero used in table 11. As aresult, U.S. policy is shifted, as shown, in order to produce the new baseline shown, Germany and Japan alsoreoptimize their policies and performance.

b. The unit ofliscal policy is a sustained increase of government spending equal to 1 percent of GNP.c. The unit of monetary policy is a sustained decrease of the discount rate by 100 basis points.

Table 14 presents the main features of an alternate baseline using theMCM in which the utility weight on the U.S. current account, i)>i, israised from 0.0 to 0.24. As a result, the United States modifies themacroeconomic policy mix by reducing government spending by 2percent of GNP and by lowering the discount rate by 460 basis points,and Germany and Japan reoptimize given their previous utility functions(table 15). The new baseline is assumed, as before, to be a Nashequilibrium.^^

The policy shifts for Germany and Japan implied by these assumptionsare qualitatively similar to the U.S. policy shift. Both countries, thoughto a smaller extent, reduce government spending. The change is morenoticeable for monetary policy. Japan lowers its discount rate by 180basis points while the German discount rate is reduced by 540 points,that is, by a larger amount than in the United States.

One important conclusion from this first step is that if the UnitedStates were to implement the above policy shift, interest rates would fallmarkedly without any coordination among the leading economies; thescope for further expansionary monetary policy thus would be greatlyreduced. Surprisingly, this new baseline is, on average, very similar tothe original one (table 8) for Japan and Germany. The new U.S. policyleads ex ante to a decrease of output of more than 1 percent for Germanyand of 0.4 percent for Japan. However, both countries react by imple-menting expansionary monetary policies that prevent an excessiveappreciation of their currencies and a fall in output. For the United

22. Thus the new baseline is designed to include the German and Japanese responsesto the U.S. change in revealed preference.


Table 15. UtDity Function Parameters in Alternate Baseline, Muiticountry Model

Country

United States

Japan

West Germany

Output,

0.06

0.06

0.03

Parameters'

Inflation,

<!>,•

0.34

0.52

0.36

Currentaccount

ratio,

«v,0.24

4.35

0.67

a. See equations 19 and 20 for definitions of parameters. The parameters for Germany and Japan are slightlydifferent from those in table 11 because the normalizing condition, dV'/dQ = 1, is imposed on a different baseline.

States the policy shift induces a reduction in GNP, lower inflation, anda reduction of the current account deficit of close to 0.5 percent of GNP.

We now turn to table 16, which compares the Nash and cooperativeequilibria. Contrary to the common presumption, the U.S. policy shiftleaves West Germany worse off, with a welfare reduction equivalent to0.4 percentage point of output on the new baseline. Japan, however,benefits from the depreciation of the dollar. In the cooperative equilib-rium, output in the three countries rises by an average of more than 1percent relative to the new baseline, but the welfare gain is markedlysmaller than in our first simulation. Moreover, cooperation fails torestore German welfare to its level under the original baseline, beforethe U.S. policy mix was changed.

As already noted, the scope for cooperation is here greatly reducedby the simple fact that interest rates are now already low at the Nashequilibrium. The change in monetary policies induced by cooperationamong the three countries is correspondingly far smaller. Comparingtables 12 and 16 shows that Germany lowers its discount rate by a mere0.4 percent. More strikingly, Japan increases its interest rate by morethan 1 percentage point.

The results of these simulations call into question the conventionalwisdom that U.S. policies are precluding a European recovery. Thatview makes sense if the U.S. fiscal expansion has a contractionary effecton Europe via high interest rates that overwhelm a direct export effect.We showed above that a U.S. fiscal expansion may be negativelytransmitted if the expansion causes a dollar appreciation and a largecorresponding price rise in Europe via wage indexation. The econometricestimates of the MCM and the EPA model do not suggest that this


Table 16. Piriky Optiadzatioa in tiM Multkiwatry Model, 1^4-86: Alternate Basetae*

Policy andoutcome

Welfare gains"'Fiscal policyMonetary policy

Output198419851986



198419851986

United States

Baseline(Nash)

-8.07-5.21-4 .29

4.474.443.69

-1 .70-1.71-2 .15

Coopera-tion

0.090.571.46

West Germany

Baseline(Nash)

-0 .43

Deviations from

-6 .82-4 .02-3 .72

4.544.683.98

-1 .79-1.87-2.21

-10.72-11.00- 10.99

3.382.732.96

-1.13-0.95-0 .94

Coopera-tion

-0 .230.280.40

Japan

Baseline(Nash)

0.31

target values^

-10.19-9.87-9.79

3.422.923.07

-1 .18-1.01-1.04

-5.75-5.81-6.34

2.032.673.07

-0.39-0.58-0.54

Coopera-tion

0.641.40

-1.28

-4.20-4 .10-4.83

2.032.943.26

-0.42-0.64-0 .65

a. The alternate baseline is evaluated under the assumption of a more restrictive U.S. fiscal policy and a moreexpansionary U.S. monetary policy than in the original baseline.

b. The welfare gain is measured from the original baseline except for the United States.c. See notes to table 12.

negative transmission exists. The U.S. fiscal expansion is measured asraising output and improving the foreign external balance in Germanyand Japan, enough to compensate, according to revealed preferences,for any inflation loss from the strong dollar.

COOPERATION FOLLOWING AN OIL PRICE SHOCK

The deep recession of 1980-82 in the OECD economies came in thewake of the second oil price shock. All of the major economies exceptJapan adopted sharply contractionary monetary policies in an effort tobattle the inflationary consequences of the price shock. One argumentholds that the resulting global deflation was excessive from each coun-try's point of view because there was no coordinated policy. In thatview, each country tightened its monetary policy in order to strengthenits exchange rate and thereby export some of the inflationary shock toother countries. Given the tight policies pursued elsewhere, each country

Gilles Oudiz and Jeffrey Sachs 5.

had an incentive to tighten up even further until, finally, unemploymentrates rose so much that inflation fighting on the margin lost its appealSmce one country's gain in exchange rate is another's loss, it is clearthat the attempt of each country to appreciate vis-a-vis the others isglobally futile. If this argument were correct, then cooperation wouldmake possible a general decline in interest rates and a smaller loss ofoutput.

To examine this question, we use the MCM to ask how noncoopera-tive and cooperative policies would be altered if West Germany Japanand the United States were hit by a 50 percent increase in oil prices overthe 1984-86 period. This shock is about one-half the size of the 1979-80mcrease. According to the MCM, suchashockhasadirect, stagflationaryimpact; with unchanged policies it causes a decline in output a rise inmflation, and a worsened external balance. The direct effects of theshock are evident in table 17 by comparing the (before-shock) baselinefor each country with the column labeled baseline plus oil shock.

According to the simulation, an oil shock would induce monetaryexpansion in the United States and Germany, accompanied by a mod-erate U.S. fiscal expansion. In Japan, monetary policy turns sharplycontractionary and fiscal policy is slightly restrictive. The move tocoordination involves a sharp interest rate reduction in the three coun-tries. According to the results of table 17, the swing in U.S. policy isfrom a very limited fall in interest rates of less than I percentage point inthe noncooperative regime to a fall in rates of almost 2.5 percentagepomts under cooperation. The German swing is from a fall of 1 5percentage points to a noticeable fall of 5.8 percentage points. In Japana sharp monetary contraction under Nash equilibrium is abandoned andinterest rates remain stable. It must be noted that we have added the oilshock to the 1984-86 baseline, so the gains from cooperation involveboth the gams in reaction to higher oil prices and the gains that can beachieved from the initial baseline itself. To get some sense of the role ofthe oil shock alone in inducing gains from cooperation, we can comparethe Nash and cooperative equilibria in tables 17 and 12. The oil shockdoes not appear to induce any special gains from coordination amongthe United States, Japan, and West Germany. On the contrary theincrease in welfare when moving from the Nash to the cooperativeeqmhbnum is smaller in the oil-shock case for the United States andJapan and essentially the same for Germany.

I

-a

as1 I

(N O ^00 <N 00

•s .a

Is

S '

Ri

I 1 I

^ ^

S5; i £d •-'

I 1

r>) CA i<-^ r*^ r-i

r-J rJ rn ON "<:r —'— (N (N rO r^ r*

• Q O O — ^ (N ON

^ 00 O

\ I I

l - - - § - -|i§i

5 ^

111

i l l


Extensions and Qualifications

We offer our estimates of the gains from cooperation as illustrativerather than definitive. The issue of policy coordination is too importantto depend on a small set of estimates based on particular objectivefunctions and specific macroeconometric models. Unfortunately, thereis no way to test our results against the findings of others, since, as faras we know, ours is the first attempt to quantify the gains from cooper-ation in large-scale macroeconometric models. We therefore think itworthwhile to mention the sensitivity of our analysis to the followingfeatures: the group of countries under study; the particular models understudy and the use we made of them; the absence of uncertainty in thetreatment of cooperation; and the time horizon for policy planning. Weconclude with a brief mention of some institutional aspects of policycooperation.

THE GROUP OF COUNTRIES

Our empirical study focused on a bargaining game among WestGermany, Japan, and the United States. This choice was partly tacticaland partly strategic. Tactically, the cross-country multipliers are readilyavailable for these, the three largest market economies; exploringcooperation for a wider group of countries would have required that newpolicy simulations be undertaken with the MCM and the EPA model.(Conceptually, and computationally, there is no difficulty in extendingthe analysis to a much larger set of countries.) Strategically, our choiceof countries is probably realistic. In general, the smaller economies canprobably have a free ride on the policy decisions of the three largesteconomies. It would be difficult to engage in successful negotiation witha much larger group of countries and still more difficult to monitor anagreement; at most, we might imagine the seven summit countries(Canada, France, Italy, Japan, the United Kingdom, the United States,and West Germany) as formal participants in an enlarged negotiatingprocess.

What is unrealistic, however, is our assumption that no other countrieschange their policies in response to the bargain struck among the bigthree. We simply lacked the relevant policy multipliers to incorporatemany other countries. It is certainly plausible, however, that German


agreement on a policy package with the United States and Japan mightbring about de facto agreement with the rest of the EC on the essentialelements. The policy constraints of the European Monetary Systemwould likely push other countries in the EC toward matching the Germanactions. In that case, the United States would have a much weightierbargaining counterpart, and the U.S. gains from policy coordinationmight be ipso facto substantially enlarged.

To test this view in a simple way, we have magnified the Germanpolicy effects on the United States and Japan by 3, and interpreted theGerman outcome as an "EC" outcome. The factor of proportionalitywas selected by examining the effects on the United States of an ECfiscal expansion, dxid a German fiscal expansion, in a 1980 version of theOECD Interlink model. ^ The effects of the EC expansion on output andthe current account were approximately 3 times the effects of Germanyalone.

The results of this extension using the MCM are shown in table 18.Comparing tables 12 and 18, we see that the U.S. and Japanese gainsfrom policy coordination are increased by a factor of 3 and the "Euro-pean" gain by a factor of about 1.7. Once again, the gain is brought aboutchiefly by a worldwide reduction in interest rates with U.S. rates droppingby more than 400 basis points. All countries have much higher outputrelative to the Nash equilibrium; Japan gains about 1.8 percent in GNP,on average, for the three years, with virtually unchanged inflation and alarger current account surplus.

Another possible group of countries that might be analyzed is the ECitself. The trade and financial links within the EC are much greater, as aproportion of GNP, than the links among the United States, Europe,and Japan. As we saw in table 1, for example, French exports to theUnited States represented only 0.9 percent of French GNP, while itsexports to Germany are 2.4 percent of GNP. Thus, our findings of modestgains from cooperation among the big three should likely be multipliedseveralfold with respect to intra-European cooperation. We suspect thatthe greater scope for coordination among the European economies isthe key reason that European institutions for macroeconomic coordi-nation, such as the European Monetary System, have developed over

23. See Adrian Blundell-WignaU, Flemming Larsen, and Franciscus Meyer-zu-Schlochtem, "Fiscal Policy Simulations with the OECD International Linkage Model,"in OECD Economic Outlook: Occasional Studies (Paris: OECD, July 1980), pp. 3-32.


Table 18. Policy Optimization with a Coordinated Europe: Multicountry Model

Policy andoutcome

Welfare gain''Fiscal policy''Monetary policy''

Output198419851986



198419851986

United StatesBaseline(Nash)

-5.68-4.97-5.67

4.244.814.11

-2.25-2.21-2.25

Coopera-tion

0.540.874.06

Europe'Baseline(Nash)

Deviations frorr,

-3.92-3.31-4.16

4.455.283.90

-2.56-2.69-2.71

-10.50-10.70-10.91

3.162.922.89

-0.95-0.93-0.99

Coopera-tion

0.56-0.17

4.60

JapanBaseline(Nash)

! target values*'

-9.91-9.46-9.41

3.243.412.98

-0.88-0.78-0.81

-5.23-6.00-6.80

2.202.862.89

-0.31-0.56-0.64

Coopera-tion

2.96-1.01

5.50

-5.17-3.61-3.58

2.173.022.83

-0.14-0.36-0.49

a. Europe's impact on the United States and Japan is assumed to be three times Germany's impact on thesecountries.

b. See table 12, notes a-d.

time, while coordination among the summit seven remains less institu-tionalized. In a future paper, we plan to study the effects of Europeancooperation using the OECD Interlink model.

USE OF THE MCM AND THE EPA MODEL

There exist at least two serious limitations in our treatment of themacroeconometric models and two in the models themselves. Regardingour treatment, we assume that the models are nearly linear when wetreat policy outcomes as equaling the product of a fixed multiplier matrix,r , and the vector policy settings, C (remember that T = CT -\- T^, whereT^ is the baseline path for the target variables). In some cases thisassumption might not be bad; a fiscal expansion will probably have abouttwice the output effect if the expansion is doubled. However, certaineffects are inherently nonlinear. An exchange rate depreciation, forexample, is more likely to improve the current account balance if theeconomy is starting in surplus rather than deficit. Thus, the sign of dCAl


dM may depend on the policy setting of G. Similarly, the question ofwhether a devaluation is expansionary or contractionary may depend,via a wealth effect, on a country's ex ante net indebtedness in foreigncurrency to the rest of the world. France has pursued contractionarypolicies in 1983-84 partly because the appreciation of the U.S. dollarhas raised the franc value of French indebtedness to the rest of theworld. In a linearized model, however, the sign of dQ/dX is assumed tobe either positive or negative but unchanging as a function of thecountry's indebtedness.

A second difficulty in our treatment is the implicit assumption thatthe'' true'' model of the world is known with certainty and that exogenousshocks are absent during the planning period. It is well known sinceBrainard's 1967 work that model uncertainty can substantially affect theappropriate choice of policy instruments and in particular cause lesspolicy activism when multipliers are unknown.^" We have not yetinvestigated the implications of such uncertainty for the logic of policycooperation, but it is important to do so. We think Feldstein is correctwhen he says that such uncertainty is a major practical impediment togreater policy coordination.^'

Other limitations reside in the models themselves. Many of the crucialchannels of interdependence in recent years depend on the effects ofpolicies on less-developed countries (LDCs). Tight U.S. monetarypolicies, for example, have raised the real indebtedness of many LDCs,and this shift in income distribution has contributed to a dramatic declinein LDC imports from Europe in 1982-84. Given the rudimentary natureof the rest-of-the-world blocks in the EPA model and the MCM, thiseffect is surely not measured with appropriate magnitude (if at all). It isprobably safe to assume that the impact of U.S. monetary policies onother OECD countries is understated in the EPA model and the MCMbecause of their inability to model the links of the United States toEurope and Japan via the LDCs.

Another difficulty with the models is that expectations are treated ina wholly mechanical way, making policy simulations subject to the Lucascritique. For reasons suggested by Sims and by Sachs's comment onSims's paper, we regard the seriousness of this problem to be an empirical

24. William C. Brainard, "Uncertainty and the Effectiveness of Policy," AmericanEconomic Review, vol. 57 (May 1967, Papers and Proceedings, l%6), pp. 411-25.

25. See Feldstein,' 'The World Economy Today.''

Gilles Oudiz and Jeffrey Sachs en

matter and read the existing evidence as suggesting a very modestimportance of the Lucas critique for short-run policy simulations.^^

THE TIME HORIZON

Our simulations assume that monetary and fiscal policymakers seekto maximize a utility function with athree-year horizon. A longer horizonwould change the optimal macroeconomic policies of each country andwould likely change the gains from coordination. We have seen that afiscal expansion that causes a real appreciation in the short run is likelyto cause a depreciation in the long run. Thus, the attractiveness of a tightmonetary and loose fiscal policy mix for inflation control is probablydiminished when one takes into account the long-term implications ofthe mix. If the U.S. currency appreciation is buying a larger futuredepreciation, the ten-year view would likely look less attractive than thethree-year view.

What is less clear is how the gains from coordination would changewith longer planning horizons among the policy authorities. Qualita-tively, the gains from coordination will still be present, as illustrated inan eariier paper." The gains, however, may be reduced quantitativelysince the realization that short-run appreciations will be reversed in thelong run may lead noncooperative policymakers to choose policies thatare more like the cooperative settings.

One frequent argument holds that policymakers discount the futuretoo highly, since their sights are set on the next election. It is interestingto speculate whether increased cooperation would mitigate or exacerbatethis bias. Certainly some forms of policy coordination are helpful aswhen weak-currency countries peg to strong currencies (or even adoptthose currencies) in order to restrain the tendency toward overlyexpansionary policies that short planning horizons often engenderRogoff, on the other hand, has developed an ingenious model in whichpolicy coordination worsens the short-horizon bias.^s In his modelwages are set in advance of macroeconomic policies in each period but

mi n n ^ n ? ^ T ' ' H ^ ^ ^™' ' "^"""^ ^"^'^^'^ ^'"^ Econometric Models," BPEA,982, pp. 107-52, and the comment that follows.27. See Sachs, "International Policy Coordination "L ^ ' t r f ^f' "Productive and Counterproductive Cooperative Monetary


in anticipation of the macro policies that will be set. Once wages are set,governments have an incentive to expand the economy at a modestmarginal cost of higher prices. Since wage setters understand thistendency, they are induced to set high nominal wages in anticipation ofit, and the economy is beset with an inflationary bias. One constraint oninflation that remains, however, is each country's fear of a unilateralexpansion. Rogoff points out that policy coordination can remove thisconstraint and worsen the inflation bias by convincing each governmentthat the other governments are going to join in its expansion. The resultis that all countries intensify their bias toward excess inflation.

THE INSTITUTIONAL CONTEXT OF POLICY COORDINATION

Our analysis concerns the gains from cooperation without regard tothe institutional context in which policy cooperation might occur. Nodoubt the costs of negotiation must be weighed in a full assessment ofthe potential benefits from coordination. The Nash bargaining solutionassumes, for example, that a policing mechanism exists to enforce abargaining equilibrium. Does such a mechanism exist? Is reputationenough to sustain a bargaining outcome? What role, if any, shouldintemationai organizations like the IMF, the EC, and the OECD play infostering and overseeing cooperative arrangements? Are the summitsthe natural locus for such activity? These issues are a matter of activestudy among political scientists and economists. Our hope is that ourmore formal results can provide an input into this area of research.

One line of analysis is particularly important on the institutional frontand that is whether cooperative outcomes can be replicated by essentiallynoncooperative actions under a new set of rules of the game. Forexample, we have seen that one reason for cooperation is that underflexible exchange rates there is a tendency to choose monetary and fiscalpolicy with the goal of moving the exchange rate in one's favor. Whencountries are fighting inflation, each will try to contract the money supplyfor the disinflationary benefits of a currency appreciation. With sym-metric countries, no country achieves an appreciation, but all suffer areal output contraction.

We can think of at least two mechanisms for overcoming this problem.First, in summit style, the countries might agree to avoid a "competitiveappreciation," with the heads of state explicitly endorsing such acommon policy. Possibly, ajoint reduction in interest rates could be


engineered. Alternatively, new rules for target exchange rate zonesmight be instituted (as in the European Monetary System), within whichcountries pursue independent policies. A constrained noncooperativeequilibrium might then come very close to the optimal cooperativeequilibrium. This alternative approach brings economists deeply intothe institutional setting of macroeconomic policy, precisely where theyshould be in studying the possibility of a greater measure of internationalcooperation.

APPENDIX

Derivations

HERE are the detailed derivations to which the paper refers. The notationis the same. We consider an n-country world. Country / has m policytargets. Its vector of targets is T = (P,,. . ., T'^). It has/controls, whichare the elements of vector C' = (O,,. . ., Cf). The authorities maximizea welfare function [/'(P).

The targets are assumed to be linear functions of the controls:

T=cr + T",

where 7 = (J', P , . . ., P ) is the overall vector of targets, 7* = (T*',T^, . . ., T"") is the value of Ja t the baseline, C = (C, . . ., C«) is theoverall vector of controls, and F is the matrix of multipliers.

In our empirical examples the P have nine elements: the values of theoutput gap, inflation, and the current-account/GNP ratio as a deviationfrom target over the years 1984 to 1986; the O have two elements: themeasures of fiscal and monetary policies. More precisely:

2851 Qk^ '"'84! "J fei '^k'

O = (A/', G').

Derivation of the Utility Function

In the paper we describe a two-step procedure. First the marginalutilities of the targets are derived and then we assume that the utiUty


function is quadratic. Given three targets (output, inflation, and currentaccount) and two instruments (monetary and fiscal policy) the marginalutilities are exactly identified by imposing dUldM = 0 and dU/dG = 0with the normalizing constraint that M| = 1.

As soon as the number of targets is larger than the number of controlsby more than one, that is, m - / > 1, this procedure must be modified.This is the case for our empirical computation since each country hasnine targets (output, inflation, and current account for three years). Wehave thus proceeded in the reverse order. First we have specifiedquadratic utility functions:

where V^ denotes the transpose of T and i?, is a matrix of parameters ofthe utility function.

We assume that the baseline is a Nash equilibrium. Thus

dU'ldO = - VRHi = (0, 0, . . ., 0),

where F,, is the block of matrix F which contains the multipliers ofcountry i's targets with respect to country j's controls. If we assume thatRi is a diagonal matrix, we have m unknowns for / equations and onenormalizing restriction such as

dU'ldT\ = 1.

Here we further specify /?, by assuming that the utility functions arediscounted sums of an annual utility function:

1986

f = 1984

The corresponding /?, matrix is therefore

0

0


For all countries, 8 is assumed to be equal to 0.1. The three parameters|x,, c(),, and »|i, are solutions of the following system of three equations.

dU'/dM' = 0

dU'ldG' = 0

dU'/dQ- = 1,

1986

where at/'/ag'= 2 (dt/'/aQ;).(=1984

In table 9 we gave the partial derivatives of the national utility functionsat the baseline with respect to a sustained increase over three years ofeach target. With our specific utility function.

a 'ae' = u',

at/'/air' = u

dU'/dCA' = M'3

1986

(=1984

1986

= - S (1 +/=1984

1986

(=1984

Note that u\ is normalized to 1.0 for all i.The cross-country gains from fiscal and monetary expansion at the

baseline presented in table 10 are given by:

Because the baseline is a Nash equilibrium, by definition dU'ldC' = 0.

Derivation of the Nash and Cooperative Equilibriums

The Nash solution corresponds to the case where each countrymaximizes its welfare, taking as given the other countries' policies. Thusthe problem of country i is:

maxt/' = -ViTRiVâ •

subject to T = 2 CT,y + T*'j

C e "Q, where ' is the set of feasible policies.


For our empiricsil simulations we have imposed no bound on fiscalpolicy, but we have constrained the discount rate to remain positive.^^For all our empirical simulations the constraints on the controls provedto be nonbinding at the Nash equilibrium. The solution is thus straight-forward. The first-order conditions for country i are

dU>/dC' = - = 0.

The values of the controls, C^, which lead to the Nash equilibriumand of the corresponding target values T^ are given by

where

r =0

0The welfare gain for each country is

f/f - t/f = -1/2 Tf^Rjr + V2

A cooperative equilibrium corresponds to the case where all thecountries act jointly so as to maximize a collective utility function. Thiscollective utiUty function is assumed to be a weighted average of eachcountry's own utility function. Only a subset of the cooperative equilib-riums are Pareto improving. Among these, we define the optimal coop-erative equilibrium as the one that maximizes the collective gain of thecountries, as defined below.

A cooperative equilibrium is thus the solution of the followingproblem:

maxc

w") =

subject to r = c r +

29. The maximum cut in the discount rate is 7.5 percentage points for the UnitedStates, 5.8 percentage points for West Germany, and 5.5 percentage points for Japan.


where

63

, W2, . . . , Wn) =

w'i?.

0

0

+

and w', w , . . . , w" denote the weights granted to each country in thecooperative process. When the constraints are not binding, the solutionis simply

and the welfare gain is

The optimal cooperative equilibrium referred to in the paper is thesolution to the Nash bargaining problem:

max Gain = (f/'c - f/i

The set of weights that yield this optimal cooperative solution is calcu-lated numerically by an optimal gradient method.

In tables 12 to 17 we refer to the welfare gain from cooperation'' measured in units of GNP." This is a measure of compensating variationrelative to the baseline. Consider the baseline {2f984. 0985. 0 986. '''•f984,Tif985, 'iTf986. CAf984, CAfsgj, CAfsgft}; tMs has utility W. Now, raise Q byan amount A in every year 1984-86; the new target vector becomes

+ A, gf985 + A, ^986 + A, Trf984, irfsgj, nfsge, CAf984, CAf985,}, which has a new utility level we denote (/* (A).

Suppose that cooperation yields a utility level (7< > [/*. The "GNP-equivalent welfare gain" from cooperation is the level of A such that U^= [/* (A). It can be easily shown that A is the root with the smallestabsolute value of

2aA = 0,


where (JL is the parameter of the quadratic utility function correspondingto Q and

(1+8) - '

More precisely,

A = - -{1 - V[ l + (2a/p)(C/c_(7B)]}

It should be noted that A is approximately equal to U^ - [/* if thechange in utility is small.

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Macroeconomic Policy Coordination among the Industrial ... · that all countries can benefit, in terms of their own policy goals, from a coordinated package of macroeconomic policies,