monetary and fiscal policy in open interdependent economies with

7/28/2019 Monetary and Fiscal Policy in Open Interdependent Economies With

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Carnegie Mellon University

Research Showcase

Tepper School of Business

1-1-1976

Monetary and Fiscal Policy in Open,Interdependent Economies with Fixed Exchange

RatesKarl BrunnerUniversity of Rochester

Allan H. MeltzerCarnegie Mellon University, [email protected]

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Recommended CitationBrunner, Karl and Meltzer, Allan H., "Monetary and Fiscal Policy in Open, Interdependent Economies with Fixed Exchange Rates"(1976). Tepper School of Business. Paper 690.hp://repository.cmu.edu/tepper/690
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GR A D U A T E S CH O O LOF INDUSTRIAL A DMINISTRATIONW I L L I A M L A R I M E R M E L L O N , F O U N D E R

REPRINT NO. 714

Monetary and Fiscal Policy inOpen, Interdependent EconomiesW ith Fixed Exchange Ratesiw

Karl Brunner and Allan H. Meltzer

1976

Carnegie-JVIel Ion Un iversityPITTSBURGH, PENNSYLVANIA 15213


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Graduate School of Industrial AdministrationWilliam Larimer Mellon, FounderCarnegie-Mel lon Univers i tyPittsburgh, Pennsylvania 15213

SOME CURRENT REPRINTS578. Interest Rates and Price Expectations During the Civil War, by Richard Roll.580. Accelerated Algorithms for Labeling and Relabeling of Trees, with Applications to Dis-tribution Problem s, by G. L. Thompson and V. Srinlvasan.581. The Appeal of Buying Black, by Dennis Gensch.582. On the Wickselllan Point-Input, Point-Output Model of Capital Accumulation: A Modern

View, by David Cas s.584. What the Com mission Didn 't Recommend, by Allan H. Meltzer.585. Measurement of a Composite Criterion of Managerial Success, by Allan Shocker, V.Srinivasan a nd Allan Weinstein.587 The Covariance Matrix of the Limited Information Estimator and the Identification Test:' Comment, by Franklin M. Fisher and Joseph B .Kad ane .588. Measuring and Testing Advertising Effectiveness with Split-Cable TV Panel Data, by589 Care to the Poor, by Judith Lave and Samuel Leinhardt59o! A Concave Property of the Hypergeometric Function with Respect to a Parameter, byJoseph B. Kadane. ,581. On the Set Covering Problems, by Egon Ba las and Manfred Padberg.592! A Structural Comparison of Gomory's Fractional Cutting Planes and Hermltian BasicSolution, by V. J. Bowman.593. Errors in Judgmental Sale s Forecasts, by Richard Staelin and Ro nald Turner.594. Wag e Inflation and the Structure of Regional Unemployment, A Comment, by Robert E.Lucas.595 Mr Hicks and the "Monetarists", by Karl Brunner and Allan H. Meltzer.596." A n Operator Theory of Parametric Programm ing for the Transportation Problem, by G. LThompson and V. Srinivasan. _ , t , B .97. Fiscal an d Monetary Policies In Moderate Inflation, by K. Brunner, M. Fratiannl, J. Jordan,598. Ma^ernatlcai Control Th e ^ So lu ti o n of an Interactive Accounting Flow Model, by YuJI" lilri and Gerald L Thomp son.599. Sensitivity An alysis in Linear Integer Programming, by V. Joseph Bowman, Jr.600. The Market for Housing and Hou sing Services, by Francisco Arcelu s and Allan H. Meltzer.601. There C annot be any Algorithm for Integer Programming with Quadratic Constraints, by602. A Propo^t for Incentive Reimbursement for Hospitals by Judith R. Lave, Lester B. Lave" and Lester P. Silverman.603. Product Safety: An Econom ic View by Lester B. Lave. l ^ , , - .604 Computation in Discrete Stochastic Programs with Recourse, by Stanley J. Garstka andDavid P. Rutenberg; and Risk Aversion in Stochastic Programming with Recourse, by605. A &N


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Chapter 12.1

MONETARY AND FISCAL POLICY IN OPEN, INTERDEPENDENTECONOMIES WITH FIXED EXCHANGE RATES

Ka r l BRUNNE R a n d A l l a n H . M E L T Z E R*

1. IntroductionAnalysis of open economies has been restr icted in several important wa ys. Oneis the assumption, common also in much of the macro-economic analysis of aclosed economy, that total output is f ixed and invariant . A second restr ict ionarises from treatment of the representative country as a small unit in a largemarket. All pr ices are set in competi t ive world markets, and exchange ratesadjust to equate domestic and foreign prices. Three, asset portfolios arerestricted to money and real capital, the latter is generally fixed or grows at asteady rate. Bonds and real capital are perfect substi tutes, as in the Metzlermodel (1951) or Mundell 's several extensions of that model (1968).Lending and borrowing is the most common means by which countr ies withf ixed exchange rates ad just short- term imbalances in trade or payments. Short-or long-term capital movements have long been recognized as a means ofadjusting or disturbing the equilibrium of open economies with fixed or floatingexchange rates. Recent work by Dornbusch (1973), McKinnon (1969) andMy hrman (1976) at tem pts to analyze stock-f low interaction in open e conom ies.However, there is no analysis l inking short- term movements of output andprices to the long-run analysis that is the standard fare of internationaleconomics .In this paper , we analyze economies with markets for assets and output.Countr ies and their ci tizens borrow and lend at home and abroad . G overnm entshave budget deficits or surpluses and issue or retire bonds or money. All ofthese decisions affec t interest rates, output, and the pr ices of assets and outputin the home country and abroad. They affect , also, the balance-of-paymentsposition in a system with fixed exchange rates.

*We have had helpful discussions with Rudiger Dornbusch, Michael Hamburger, PieterKorteweg and Michael Mussa. We are indebted to the National Science Foundation for continuedsupport of our work.


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32 8 Karl Brunner and Allan H. MeitzerWe begin with a closed econ omy. Changes in fiscal and m onetary policy alterthe short- and long-run position of the economy and the prices of assets andoutput. We show the adjustments as a sequence of equilibria, from short- tolong-run equilibrium. Then we open the economy to trade and capital move-

ments and, using the closed economy short- and longer-run equilibria asbuilding blocks, we show the interaction of the home country and the rest ofthe world. Throughout capital stocks generally remain fixed. Changes inanticipations of future prices and in technology are neglected throughout.

2. A Model of a Closed EconomyThe closed economy from which we start has three main sectors described bymarkets for assets and output and a government budget equation. In thebackground is a labor market, important for long-run but not short-runadjustment. Four processes of adjustment occur: (1) a short-run flow adjust-ment to given stocks represented by the response of the output market tochanges in the position of the asset markets ; (2) an intermediate-run adjustm entof the asset markets determined by the interaction of the asset markets, theoutput market and the government's budget position; (3) a longer-run adjust-ment of employment and the labor and output markets; and (4) long-runadjustment of capital stock and wealth. This section presents the model.Equilibrium on the output market occurs when the output of the privatesector, y, equals the real expenditure of the private sector, d, and of thegovernment, g,

y = d(i - tr, p, P, W n, W h9 e) + g, d d* < > (la)d3,...,d6>0.Private decisions to purchase depend on the market rate of interest, net of anyinflation premium, i - 7r, the price level of current output, p, the price ofoutstanding ass ets (or the mark et value of a unit of real capital), P, the m arketvalue of wealth both human, W h, and non-human, W n, and the anticipatedreturn to real capital, e. W h an d e depend on tax rates, T, and income oranticipated income if the two are distinguished. W h also depends on moneywages, w, and the absorption of labor by the government, Ig,

W h = W(y, w, p, Ig, r ) , W l9 W 2, W 3, W 4 > 0, W 5 < 0, (lb)e=e(y9K,r), 1 >0, e2, e3


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Monetary and fiscal policies 32 9

Non-human wealth consists of base money, B, government securities , 5, andreal capital, K,W D = PK + v(i9T)S + (l +


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33 0 Karl Brunner and Allan H. Meitzer

m(/, P, W n9 W h9e.. ,)B = L(/, e, p, P , W n9 W h)9 (3)mi, m 4, m 5 > 0 , m 2, m 3 < 0 ,L l9L2< 0, L 3 , . . . , L 6 > 0.

The government's budget equation describes the budget position and thefinancing of deficits or surpluses. Expenditure consists of purchases of goods,pg , purchases of labor services, wlg9 and interest payments, I(i)S. Thegovernment hires labor at the market wage rate without regard to productivityin governmental activities. Interest payments depend on the maturity structureof the debt and increase with market rates; 1 > 0. Tax collections rise and fallproportionally as prices and output change. Tax rates are fixed.2 Base moneyand securities,pg + wig + I(i)S t(p, y, wlg;r) = B + , (4)

are issued to finance deficits and withdrawn in the event of a surplus.Equation (5) is a summary description of the labor market in the form of ageneralized Phillips curve. The acceleration or deceleration of money wagesdepends on changes in the rate of inflation and on the deviations of currentoutput from the output that prevails in long-run equilibrium.3 With

d (dw/w) = h(y y0) + d7r, hx> 0, (5)efficient use of resources, all profitable opportunities realized, unchangingpolicies and a given stock of capital, y = y0. Increa ses in capital and labor forceraise y0; increased absorption of labor by the government lowers y0.4

2Proportional tax rates could be replaced by progressive tax rates and the assumptions thathouseholds expect either (1) tax reduction or (2) a rising share of output to be absorbed bygovernment as prices and output r ise and conversely when prices and output fa l l .3If technology were permitted to change, money wages would not be required to fa l l a t t imes ofexce ss supply . Deceleration of w ages of ten would b e suffic ient to restore equil ibrium. Equation (5)would be rewritten as a re lation between the acceleration or deceleration of money wages perefficiency unit and the acceleration or deceleration of prices.4Long-run output, y0, also depends on K, bu t K is fixed. Extension of the analysis to a world ofchanging capita l can be made by lett ing the sum of net investment, K, plus depreciation, 8K , beproportional to total private expenditure, d. The derivatives of the d-function are then weightedaverages of the response of consumer expenditure and investment expenditure, and the distr ibu-tion of output between investment and consumption depends oon relative prices. The currentcapital stock is the sum of prior net investment. Specifically, (K + 8K )/d = k(i tt, p, P, e) an dK = f K.


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3. Solution ProcedureThe system of equations yields solutions for prices and output once the valuesof the policy variables-g, lg , r, and either 6 or S-and the capital stock andlabor forc e are given or fixed. Our procedu re distinguishes short-, intermediate-and longer-run solutions by first imposing and later relaxing restrictions onadjustment. In this section, we discuss the sequential procedure and thesolution to the closed econom y m odel at various runs. In the following section,we analyze monetary and fiscal changes and determine the signs of theprincipal responses on the markets for assets and output.There are four types of variables. One is policy variables; the current valuesof these variables are set by the decision of government. These include g, lg, r,and either 6 or or some combination of 6 and 5, for exam ple, the portion ofthe deficit or surplus financed by issuing or withdrawing base money andsecurities. Such other policy variables as reserve requirement ratios, therediscount rate, borrowing quotas and the like can be included in the assetmarket equations. In the open economy model with fixed exchange rates, theexchange rate is an additional policy variable. Two, in a closed economycurrent values of B an d S represent the history of deficit finance and openmarket operations. In an open economy, B includes the cumulated balance-of-payments deficit or surplus. We treat B an d S as determined relative to thecurrent market process. Three, w, K, y0 an d TT are neither controlled bypolicy-makers nor affected by short-run changes on the markets for assets andoutput. Money wages adjust gradually to market conditions, as shown byequation (5), and our longer-run equilibrium recognizes the effects of changesin w on prices and output. Additional equations would be required to analyzethe adjustme nt of K an d TT and the effect of their adjustment on the marketsfor assets and output. Four, all remaining variables are determined by thesystem of equations. Our stylized procedure treats the solution as a series ofruns to recognize differences in the adjustment process on the markets forassets, output and labor.The notation attempts to make explicit the variables held constant in aparticular adjustment. The short-run response of the asset markets to changesin policy variables is an adjustment of the prices, P an d i, at which nominalstocks are willingly held. The solutions are obtained fro m equations (2) and (3)holding constant the position of flow equilibrium but recognizing the depen-dence of W h an d e on y. The solutions for P an d i can be written as

P = P(y,p,B,S;K, w9ir) , (6a)


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an di =i(y,p,B,S;K, w , t t ) . (6b)Partial elasticit ies are obtained from these solution equ ations by differentiating

and expressing the results as elasticities. The partial elasticities describe theresponse of P and i to current values of B , 5, p and y holding constant theposition of the output market and the government budget equation. We use thesymbol AM , for example, e(P, B\AM)9 to denote th e elasticit ies obtained fromthe asset market equations.The solutions for P an d i that satisfy the two-asset market equations alsodetermine the nominal s tocks of money and credit . The equilibrium stocks ofmoney and bank credit , M and &, depend on P and / and on the variable inequations (6a) and (6b).To find the short-run equilibrium position of the output market, we substitutethe solutions for P and /, denoted P and i, obtained from the asset marketequations in equation (la) . The d + g curve of figure 1 is an equ ilibrium

d + g1vd + 9o

bbe

yF I G U R E 1


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relation, equation (7), drawn in the p, y plane. K , w and 7r are held constant,and as before, the dependence of W h an d e on y and p is recognized,y= d [ i (B, S, y, p | AM ), P (B 9 S, y, p | AM ), p, y, J3, S ; K, w, IT] + g.

(7)The d + g line is the locus of all p, y combinations satisfying simultaneouslythe markets for output and assets for given values of all stock variables andanticipations. Equation (7) implicitly defines p as a function of y for anyvalues of the remaining variables. We can derive a measure of the slope of thed + g line by differentiating (7) with respect to y and expressing the result as anelasticity. We use the notation s(p, y\d + g) to denote this slope, and we usee(p,B\d 4- g), e(p, g\d + g), or e(p, S\d + g) to denote the change in p, holdingoutput c onstant, induced by m onetary and fiscal policies. These elasticities areshown as vertica l sh ifts of d + g in figure 1. Th e vertical shift p 2 - p 0 , withy = y0, shows the response to an expansive policy action obtained fromequation (7).The sho rt-run equilibrium position of the output market is at piy l9 not at p 2y0.Short-run changes in output are described by the s -curve of figure 1, equation(le) with K an d w held constant. The short-run equilibrium reached after achange in fiscal or monetary policy is obtained by solving equations (7) and(le), given the values of B, S, K, >v and IT and the position of the budgetequation. We use the n otation O, A M to show that the short-run positionincludes the response of the output market (O) and the asset market (AM).Short-run equilibrium is a flow equilibrium. Asset prices and interest rateschange, and the stocks of money and credit change, but the stock equilibriumposition a t the intersec tion of the budget e quation and y = y0 remains un-changed. The stocks of financial assets have not adjusted to an equilibriumposition consistent with the prevailing budget position, and p and y are notfully adjusted to the values of asset stocks that must obtain in a stock-flowequilibrium.A balanced budget is a necessary and sufficient condition for stock equilib-rium in a closed economy with fixed capital stock. From equation (4), we seethat when 6 = = 0, the budget is balanced, asse t stocks are con stant, and totalnominal governmen t expen diture, G, equals tax collections t. Af ter substitutingfo r i in equation (4), we can write the stock equilibrium asG[f( p , y, B9 S\AM)9 S; g, w, Ig] = t(p9 y; r) . (8)

Equation (8) is shown in figure 1 as the bb e line. The line shows positions ofbudget balance. T o the right of the line, the budget has a surplus; to the le ft, thebudget has a deficit. In both cases, the stocks of financial assets change. The


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slope of the line, expressed as a partial elasticity, is denoted s(p, y\bbe). Theposition of the line depends on the values of current policy. Changes in policychange the position of the bb e line. The response to the base is denotede(p, B\bbe) and similarly for other variables.An interme diate-run equilibrium is a position of stock-flow equilibrium at theintersection of the bb e line and the flow equilibrium. The budget is balanced,an d P, i, p an d y have adjusted to the values of B , S, g and r consistent withbudget balance. Th ere is no change in K, w or it, so the position of the s -curveremains unchanged . In figure 1, the intersection of a d + g curve, s, and bb e atp2y2 is a position of intermediate-run equilibrium.Gradual adjustment of money wages, as shown by equation (5), moves theeconom y fr om an intermed iate-run to a longer-run equilibrium. Capital stock isheld constant in the longer-run equilibrium, but output and prices change inrespon se to a change in w. Changes in w alter the govern men t's budget and theposition of the bb e line and, by changing W h, change expenditure. Outputprices rise and f all with w, and the equilibrium position m oves in the d irectionof full equilibrium at y = y0. To identify the longer-run equilibrium respon se ofp an d y to g, we use e(y, g\0, AM, s) and e(p, g\0, AM, s) and similarly for B,S, or other policy variables.A return to full steady-sta te equilibrium following policy changes, pa rticularlyfiscal changes, requires adjus tme nt of K an d y0. We do not analyze chang es inthe composition of output between consumption and investment here, and wedo not take into account the effects on output and prices of the adjustment ofthe capital stock.

4. Responses to Fiscal and Monetary PolicyThe general procedure we have just described provides the framework withinwhich we analyze the response of the closed economy to fiscal and monetarychange. The fram ework becom es applicable to an open economy after adjust-ment to permit interaction of home country markets with markets in othercountries and to recognize the influence of the balance of payments. In thissection, we develop the closed economy framework more fully and show thedeterminants of the size and direction of responses on the markets for assetsand output.We begin with the output market. The d + g curve, e quation (7), relatesaggregate real expenditures to market prices, to existing stocks and to policyvariables. The slope of the curve in the p, y plane can be expressed as anelasticity,


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Monetary and fiscal policies 33 5l-(l~y) (d ,y)(1 -y)(d,p) < 0 .

The parameter y is the proportion of output absorbed by the government, g/y.The numerator and denominator contain total elasticities (shown by a bar'overs) of the output market, including the respons e of P and i on the asset market.Signs of components appear beneath the components,e(d, p) = e(d, p) + e(d, i)s(i, p |AM)

e(d, y) = e(d, i)e(i, y\AM) + e(d , P )E(P , Y|AM)- + + -

+ + + +The elasticities of i an d P are the response s of interest rates and asset prices toany variable taken as predetermined when solving for P an d i on the assetmarkets. We use e(d, i) and e(d, P) to note that these elasticities include thechange in wealth induced by changing i and P.The total price elasticity of expenditure, e(d,p), is negative despite thepositive term at the end. Homogeneity of degree zero of the -function inprices and nominal wealth assures that e(d,p) is much larger than e(d, W h).The positive sign of the numerator requires that the last two terms in e(d, y)dominate the elasticity. We constrain e(d, v) to positive values.The short-run response of the flow equilibrium to changes in B, S and gdepends on the slope of the d +g curve, e(p, y\d +g), the slope of the pricesett ing function, e(p,y\s)>0, and on the shift in d + g resulting from thepolicy change. Exp ansive policies shif t thc d+g curve of figure 1 upward, andcontractive policies shift the curve downward. The vertical shift of d + ginduced by a change in the base, government expenditure or debt is shown inequations (9); signs of components are shown below the components,

+ (d,P)s(P,p I AM) + e (d, W h)e (W h,p)< 0,+ - + +an d

e(p,g\d + g) = s(d,p ) l - y > 0 , (9a)(9b)


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withs (d, B) = (d , i)e (i, BI AM ) + s(d, P)e (P, B |AM )

+ s(d9Wn)^^> 0;+ W n(9c)

with i>Se(d, S) = s(d, i)e(i, S\AM) + e(d, P )(P , S\AM) + e(d , W) >0._ + + + + rrThe size of the respons es of d + g to B, S, and g depends on s(d, p). A largeprice elasticity of expenditure lowers the response to fiscal and monetarychanges. The respons e to government expen diture increases as the relative sizeof governm ent, y, increases. The res ponse to a change in the base is larger thanthe resp onse to a change in S, and both ar e positive. The stability of the system

requires that e (d , S) b e positive, so e (d , i)e (i, S |AM ) must be smaller than otherterms of s(d, S).5The elasticities in equation (9) describe the change in expenditure induced bychanging B, S or g, holding output co nstant. They are the vertical shifts of thed + g line in figure 1. The short-run flow equilibrium depends on theseresponses and on the slopes of the expenditure and price-setting functions.Equation (10) shows the short-run r espon ses of prices and output to a change in gallowing as before the interaction with the asset market. The denominatorcontains the slopes of the expend iture and price-setting functions, expressed aselasticities. Similar respon ses f or B an d S can be obtained by substituting e (p ,B\d + g ) o r e(p, S\d + g) in the numerator of equations (10),

5Our hypothesis also contains the restriction e(P,B)> 0. This requires the money marketresponse to dominate the response of P and the credit market response to dominate the response ofi. See footn ote 1 and the accompanying text.

-e(p,z\d + g)e(p,y\s)>0e(p,y\d + g)-e(p9y\s) > 0 , (10a)


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an de(y9g\0, AM) = , y 0 . (10b)g ( p ,y k / + g ) - g ( p , y\s)

Monetary and fiscal policies also change the budget position. The budgetposition depends on price and output and, therefore on g, B and 5. With giventax rates and government purchases of goods and labor services, the outstand-ing stocks of financial assets, B and S, increase or decrease until output andprices reach a level at which the budget is balanced.Equation (8) above defines budget balance in terms of p, y, B and S. Theslope of the bud get equ ation in figure 1 depe nds o n fiscal policies, particu larlythe decision to use g (rather than pg ) as a policy variable and on theprogressivity of taxes. We use e(p, y| b b e ; g ) to denote the slope of the lineobtained on the assumption that g (rather than pg ) is held constant,/ i n >> g (*, y ) - g (I i )g 0> y \AM) is It , m

Proportional tax rates are assumed throughout.The position of the bb e line also depends on fiscal and m onetary policy. Theelasticities in equation (12) show the shift in the position of the line for changesin g, /g, B or 5. The response to a change in w (not shown) is identical to theresponse to /g.6 Increases in g, /g, w and 5 raise the bb e line and increase thedeficit or reduce the budget surplus; increases in the base reduce the deficit orincrease the surplus,g ( p , g | b ^ ; g ) = g ^ ; > 0 , (12a)

( 1 2 b )

g (P, B \bbe ; g) - ' I V M B ^ l S I t < 0f (12c)6lf tl ie government pays competitive wage rates, the government's wage bill rises with moneywages during periods of economic expansion, and falls if money wages fall during recession. With aconstant level (Ig) of employment in the government sector, the government's wage bill has apro-cyclical effect on the budget even if the private sector maintains constant money wages perefficiency unit. If money wages are slow to decline in recession, wage changes have an inflationarybias even if unit labor costs in the private sector remain constant.


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s (p, S\bbe ; g ) = ~ n + * ( ! , / ) * ( i ,S | A M ) U S / fA hhc> a > 0 , (12d)with

Abbe ;g = (pglt) + e(I, i>(i, p |AM) IS/t-e(t,p)< 0,The elasticities in equation (12) determine the direction in which priceschange to reach stock equilibrium. Open market purchases reduce, and openmarket sales raise, the price level at the new stock equilibrium. E xpansive fiscalpolicies induce a larger increase in the price level at which the economyreaches stock equilibrium if budget deficits are financed primarily by issuingdebt or if budget su rpluses are used to retire base money . Since the position ofth e bb e line divides the plane into deficits and surpluses, the financing ofdeficits and surpluses influences the size of subsequent deficits or surplusesand, given both stock and flow adjustments induced by changes in B and 5,affects the speed of adjustment to a new stock-flow equilibrium.7Return to figure 1. An e xpansive fiscal policy has shifted the bb e line to bb e t.Comparison of equations (10a) and (12a) shows that the bb e line shifts muchmore than the d + g curve. The new bb e line is to the right of the shor t-run flowequilibrium at pu yx. There is a budget deficit. B an d S increase; the d + gcurve moves to the right; output and prices rise. The new short-run flowequilibrium lies to the right of the old, the distance depending on th e m ethod offinancing the deficit. In figure 1, deficit finance leaves the bb e line at bb eu so thed + g curve converges to the intersection of s an d bb euIf wages, capital and anticipations rem ain fixed, an intermediate-run equilib-rium is reached where the d + g, s and bb e lines intersect. The budget isbalanced at the values p2 an d y2 that clear the output market. The outputmarket equilibrium is defined relative to the asset prices and interest ratesdetermined by the asset marke t equilibrium. T he two conditions - budget

7With proportional tax rates, constant population and a fixed capital stock, the long-run positiondepend s on the ratio of S to B. The long-run flow equilibrium, y 0 , can be so lved for B IP an d i in termsof SI B and the fiscal variables. The budget constraint is then

The bud get equation determines the ratio of S to B and, for given fiscal policy, is independent ofthe levels of S an d B.

With a l inear, homogenous tax revenue function,


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Monetary and fiscal policies 33 9balance and f low equil ibrium - assure that a sset stocks are c onstant andwillingly held at prevailing prices.To prove that the economy reaches intermediate-run equil ibr ium, we substi-tute in the budget equation until the equation contains only variables taken aspredetermined in reaching flow equilibrium. The price level, /?, is replaced bythe price-sett ing function, equation ( le) . T hen all values of i and y are replacedby their flow equilibrium solutions. The solutions depend on B, 5, g, wig,, r and,of course, on K and w, so the revised budget equation can be writ ten as

B+=F(B,S;g,wlg9 r) . (13)In a closed economy, the stocks of B and S tell the history of past budgetsand open market operations. Let D be the cumulated deficit and ^ the (average)share of the deficit or surplus financed by issuing or withdrawing base money.B0 and S0 are the nominal stocks of B and S that were produced independentlyof deficit finance, for example the result of open market operations with abalanced budget,B = B 0 + ilD an d 5 = 5 0 + (l - n)D, O^FX^l. (14)After replacement of B and S by the values in (14), equation (13) relates thecurrent defici t , D, to the cumulated defici t , D, to JL and to the fiscal policyvariables. The budget converges to an intermediate-run equilibrium if thebudget deficit or surplus reaches zero at the flow equilibrium values of p and y.Convergence is assured if dFIdD is negative for any admissible value of ^

n > d F3D ^dB+^^^Js' (15)where

j = f(e(y>B\0,AM)\e(p,y\s)\l-e(t,p)-!-}-e(t,y)-!-]l PS) pgJ+ e(I, i)i(i,B\0, AM) \ < 0 ,Pg )and

= f (E(Y, SIO, AM)[s(p, y | , ) f 1 - pyJL\ _ e ( i YL ]L 1 Pg) Pg J+ r e(J, i)e(i, S | 0 , i 4 M ) + l ] 2 | ) .

The elast ici t ies denoted 0,AM are short-run flow equilibrium responses


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34 0 Karl Brunn er and Allan H. Meitzer

similar to the elasticities in equation (10). The negative sign of dF/dB fol lowsfrom: (1) the positive value8 of e(y, B\0, AM), (2) proportional ta xes, an d (3)the relatively small negative values of the interest payments effect in the lastterm. A negative value of dFldS, how ever, is less certain. With e(y, S | 0 , AM)positive, the first term is negative but much smaller than the correspondingterm in dF/dB. The interest p aym ents ef fect is positive and (num erically) largerthan the corresponding term in dFldB. However, the weight on the firstcomponent, tlpg, is much larger than ISIpg, so dF/dS is rather small, anddFldD is negative for all values of The system converges to intermediate-run equilibrium.Equations (13) and (15) permit the response of the financial stocks to fiscalpolicy variables to be expressed as derivatives or elasticities of the F-fu nct ion .The elasticity of D with respect to g is

e(F, D) >0 'where

s ( F , g ) = ^ [ l + s(y , g |0 ,+ e(I,i)e(i,g\0,AM)^],

and the denom inator is the elasticity corresponding to dFldD in equation (15).Similarly, we obtain the response of the cumulated deficit and the stocks offinancial assets to wig and to r.Our analysis implies that fiscal policy has a powerful influence on theequilibrium position the economy reaches in the intermediate run. Thisinfluence differs fro m the influence of fiscal variables in Keyn esian analysis orin the familiar IS-LM model. There, changes in government expenditure andtax rates affect mainly flow variables via "the multiplier" mechanism. Ouranalysis implies that the dominant effect of fiscal policy is on the stockequilibrium position and is transmitted mainly by changes in the stocks of debtand base money. In a closed economy, the behavior of financial stocks isgoverned by fiscal policy and, to a lesser extent, by open ma rket operations that

8The sign of e(y,B\0,AM) can be checked by substituting e(p,B\d + g) for e(p,g\d + g) ineq 9T lh n eh t10 p bositive value of dFldD would not require any important change in our analysis.Sl i ^t ly pro ^es sive tax rates or a minimum value of ^ would replace proportional tax rates or anunrestricted value of ja .


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Monetary and fiscal policies 34 1proceed independently of fiscal policy. The stock disequilibrium generated bychanges in g, wig or r has a much greater effect on the price level than theinitial flow adjustment resulting from the increase in expenditure.An increase in the size of the government or a reduction in tax rates raisesthe price level in intermediate-run equilibrium. Money wages are unch anged, soreal wages are lower. Open market sales also raise the price level and reducereal wages in intermediate-run equilibrium. Open market purchases andreductions in the relative size of government lower the price level inintermediate-run equilibrium. With money wages fixed, real wages rise.The adjustment of money wages occurs slowly in our analysis. With thepassage of time, however, the gradual acceleration or deceleration of moneywages cumulates as a rate of change, dw/w, and the cumulated rate of changeshifts the supply curve of output, raising or lowering prices and changing theequilibrium position of the output market.Let e(p,w\s)h(t) denote the shift in the price-setting function induced by achange in the money wage rate. An increase in money wages raises prices andreduces output, and a reduction in money wages lowers prices and raisesoutput. The flow equilibrium moves from the intermediate-run equilibrium inthe direction of y0. Equation (16) shows the longer-run response of prices andoutput to a change in g, e(p,g\0, AM, s) and e(y, g\0, AM, s). Similar expres-sions for B and 5 can be written by replacing g with B or 5 and makingappropriate adjustments on the right-hand side of the elasticities,

\N AAJ v ) - ~ e(P>g\d + g)e(p, y\s) + e(p,y\d + g)e(p, w\s)h(t)e(P,y\d+g)-e(p,y\s)> (16a)an dWv a\n am -e(p,g\d + K) + 8(p,w\s)h(t)e(P,y\d + g)-e(p,y\s) ' (16b>

The adjustment of money wages also affects the stock equilibrium position, ^ s o n 1 S t h a t t h e government's budget equation includes wage paymentswig. Changes in money wages change the size of the deficit, per unit of dw/wby e(p, w\bbe) = e(p,lg\bbe), shown above as equation (12b). The stockequilibrium position changes in the same direction as the flow equilibrium butby a smaller amount. The adjustment of money wages reinforces the effect ofmone tary and fiscal policies on prices. If prices w ere higher in the intermediate-run equilibrium than at the initial position, prices rise more; if prices fall toreach th e intermediate-run equilibrium, prices fall more to reach the longer-runequilibrium. 6


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The adjustment of money wages returns the system to the neighborhood offull employment but does not assure the return to full employment at y0. Thechoice of fiscal policies, g, Ig, and r, affects the position of full-employmentoutput, y0, by changing the composition of outp ut and by absorbing or releasinglabor from the government sector. Moreover, the method of financing deficitsor surpluses, and open market operations, change the composition of financialassets and the relative prices of ass ets and output. For full, long-run, stock-flowequilibrium, we must hav e p = P. The full response to monetary and fiscal policyinvolves adju stm ent of the capital stock if these cond itions for full equilibriumare not m et. In general, the capital stock mu st adju st to restor e full equilibriumfollowing monetary and fiscal changes.The sequential adjustment from short-run to longer-run equilibrium is ahighly stylized representation of the adjustment process in a closed economy.Actual adjustment is, of course, more of a continuous process and less asequence of steps than our proced ure suggests. The interaction of stocks, flowsand the government budget in a closed economy is more clearly revealed,however by the sequential process. Of importance for present purposes is thatthe framework permits extension to an open economy in which output changesand in which foreigners respond to relative prices by purchasing and sellingassets and output on the home country markets.5. Extension to an Open EconomyThe responses obtained for the closed economy form the base for our analysisof interdependent, open economies. Changes modify the descriptions of themarkets for credit and output and the definition of non-human wealth.Foreigners buy and sell on the home country markets for output and in thecredit mar ket; citizens of the hom e country bu y and sell goods and securities inforeign markets for output and assets. The balance of payments constrains theworld economy and acts as an additional link between the home country andthe rest of the world.In this section we make adjustments to open the model to trade in goods,services and securities. The description of the "rest of the world" is the sameas our description of the home cou ntry. Asterisks are used to denote rest of theworld variables. Technology and capital stocks are fixed, and population isconstan t. There is no migration of labor for ce or population. All countries haveproportional tax rates.Real expenditure n ow has an additional com ponent, the real value of expor ts,denoted X. Exp orts depen d on economic activity abroad, on relative prices andon the exchange rate, p. Domestic expenditure, d, depends on the prices at


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Monetary and fiscal policies 343

home and abroad and on the exchange rate. Government expenditure is , asbef ore , set in real terms. The equilibrium condition for the outpu t market is nowy = d + + X, ( 1 7 a )d = d(i-ir,p,P,W n,W h,e,pp*), dx,d 2< 0, d3,...,d7> 0, (17b)X = X(i* - 7T*, p *, P*, W*9 Wt, e*,plp),

XuX7 0 .The price-setting function is adjusted to permit substitution of imports fordomestic production. The price-setting function becomes

p = p(y,K, w,pp*)> Pi,P3,P4>0, p2< 0. (17c)Dom estic non-human wealth now includes foreign assets owned by do mesticresidents and excludes l iabili t ies to foreigners ,

W n = PK + v(i)(S - Sd + v*(i*)S1p + (1 + [v(i)St - v*(i*) PS?], (18b)Bn = B - v(i)St + v*(i*)pS? = Bo + /xD + B2. (18c)

B2 is the s tock of base money resulting from surpluses or deficit on currentaccount, the accumulated current account balance, and B0 now includes anyinitial reserve of com modities used a s money. S ecurities are valued in equation(18c) at weighted average values, v and v*, and at market value in equation(18b).10 The last term of equation (18b) measures the contribution of the netforeign position to the net worth of the financial system and is set at zero.The open economy imposes an additional constraint on asset s tocks. The

10The difference in valuation between (18b) and (18c) arises because wealth is valued at currentmarket prices but international reserves and base money are valued at the time they are received.Initially, wealth and international reserves change by the same amount, the market value of thechange in the public's net foreign position. Later, wealth and the market value of securities changewith interest rates, and the capital gain or loss is included in wealth. The value of internationalreserves and the base are not affected by capita l gains and losses. The average values v an d v*reflect the convenient assumption that over time changes in the public's net foreign position andchanges in international reserves occur at the average market value of securities.


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34 4 Karl Brunner and Allan H. Meitzercurrent a ccount balance each period is the sum of the trade balance and interestpayments,

pX-p*X*p* + i*v*(i*)S1p ~ iv(i)Sf = 2. (19)Devaluation raises the exchange rate, p. With fixed exchange rates, p isconstant and the equation proximately determines the balance on currentaccount and the related change in the base, 62. The net base, BN, is taken aspredetermined relative to the current market process. Net foreign liabilitiesB-B are determined by relative prices.The credit market distributes the stock of domestic securities betweenbanks, S b , the dom estic non-bank public, S p , and foreigners, S f . The total stock,S, depends on the cumulated budget deficit, >, as in the closed economy. Thedistribution of S now depends on the decisions of domestic and foreignresidents,

S = S0 + (l - FI)D = S p + S b + S f .In open economies, asset markets are interdependent. The public's supply of

earning assets to banks, a, now excludes absorption of domestic debt byforeigners, S fl , and includes absorption of foreign debt by the dome stic m arket,Sf. Changes in relative interest rates induce lenders or borrowers to shift fromone country to another. A djustm ent of interest rates and the value of net foreignliabilities affects the model in three ways. One, with fixed exchange rates,changes in the net foreign position change the base, B, and changes in the baseinduce changes in the stocks of money and credit. We formalize the effects ofrelative prices on the net foreign liability position in an equation for the netforeign position,(B-B n) = b(i-7r,P,p,e,i*-7r*,P*,p*,e*9p), bu b4, b6, b7, b9> 0,

b2, b3, b5, b8< 0.Two, foreign purchases and sales of securities (S f) on the home credit markethave the same effe ct on the supply of earning assets (or) as purchases or sales bythe domestic public. Increases in domestic rates increase S f and lower thevolume of outstanding securities offered to banks; domestic liabilities toforeigners rise. Increases in rates abroad induce sales by foreigners. S f declinesand the net foreign position is reduced,

S f =


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changes in the net fore ign liability position change th e value of dom estic w ealthand, therefore, change spending and money holding.As before , a()B =a is the equilibrium condition for the credit m arket. In anopen econo my, the credit market distributes the stocks of foreign and dom esticsecurities. Loans by banks can be cancelled on both sides of the equilibriumcondition. Domestic securities and the net foreign position remain. Thesecurities are distributed between banks and non-banks by the adjustment ofinterest rates and prices,vSb + v*St = v(S S P SF) + I ; * ( S - S ) .

Domestic and foreign securities are substitutes in the portfolios of wealthowners, but m oney and real capital are, by hypothesis, owned only by dom esticresidents. Achieving equilibrium values of domestic and foreign asset pricesrequires internal adjustment, as in closed economies, and adjustment ofinterest rates on domestic and foreign markets. The equilibrium conditions forthe bank credit and money markets show the interdependence of domestic andforeign asset markets,11a( i, P , . . ,)B = 0,cr u c r 2 < 0 ,o - 3 , . . . , (TS > 0,m(/, P , . . .)B = L( / , P ,p , W n, W h9 e) , m . > 0 , m 2 0.

Other equations of the closed economy model remain as before. Opening theeconomy to trade and capital movements affects the government budgetposition and the value of human wealth by changing the prices of assets andoutput and speeds of resp onse. In the following sections, we develop the inter-action of the asset and output markets, the government budget equation andthe balance on current account for open economies with fixed exchange rates.6. Flow Equilibrium in Open Economies with Fixed Exchange RatesSolutions for the asset and output market equations of the open economymodify the responses of the closed economy. At each step of our stylizedprocedure, moving from short-run through intermediate- to longer-run solu-

u If we disregard the effects of devaluation on wealth, changes in exchange rates affect themoney market only through the adjustment of asset prices and interest rates, and p does not enterequation (20b).


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tions, the open economy responses differ. The differen ces depend on the choiceof monetary arrangements. In this paper, we consider only economies withfixed exchange rates. This section develops the response of the output marketto changes in policy variables. We allow for the interdependence of worldmarkets for assets and output and the effects of interdependence on p, y, p *and y*. In the following section, we discuss the adjustment of asset stocks inthe two countries and the simultaneous solutions on the asset and outputmarkets in a world with fixed capital stock.We begin with the asset ma rkets. There are now fo ur interacting asset m arketequations that simultaneously determine i, /*, P, P* for given stocks of assetsand given economic activity and output prices at home and abroad. As in theclosed econom y, first, we hold output and output prices constant and de terminethe set of asset prices and interest rates at which the stocks are willingly held.The stocks of money and bank credit are determined in this process for thegiven price levels and outputs at home and abroad. The net foreign liabilityposition B - Bn depends on the relative prices and is determined at the assetmarket equilibrium. The notation A, A* identifies the short-run asset marketequilibrium as a world equilibrium.Next we analyze the response of the output market allowing for the changein the equilibrium position of the asset markets. The initial response ofexpenditure and output to any policy change does not include the effect ofinteraction between domestic and foreign output markets. We uses(y,B n\OA, A*) to denote the response to the base and similarly for otherelasticities. Then, we permit interaction between the output markets anddetermine the short-run equilibrium position of the open economy, denotedOAO*A *. Output res ponds to price changes as in the short-run equilibrium ofthe closed economy, and exports and imports respond to relative prices. At theshort-run equilibrium position, stocks of financial assets are not fully adjustedto policy (or other) changes and K, w, tt, K*, w * and 7r* are held co nstant.The longer-run adjustment of output and prices involves gradual changes inmoney w ages. In an open econom y, wage adjustments affect prices and outputat home and abroad. The response, obtained from the price-setting functions,include these interactions. In our notation, these responses are e(p, y | s , s* ) .The solution of the asset market equations for a closed economy shows thatthe relative change in i is

- e(i, B\AM )^+ e{i, S | A M ) ^ + e(i, y | s ( i , p \ A MI rS o y pA similar equation determines the short-run response of P. The elasticities inthe equations for i and P are ratios expressing the responses of the excesssupply functions of the credit and money markets to changes in the proximate


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determinants (including any induced response of wealth). With interactingcredit and money markets, changes in net liabilities to foreigners modify theresponse of interest rates and asset prices. The solutions for / and P now havethe general form of equation (21),i = i(Bn9S,i*,P*,y,y*,p 9p*). (21)If /* and P * are now rep laced by the solutions of the equations for the foreignasset market, analogous to equations (20a) and (20b) we can obtain the totalresponse of i an d P (and of /* and P*) to changes in the proximatedeterm inants. Som e elasticities obtained fro m equation (21), after replacing /*and P* by their solutions, are shown in table 1.The response of i or P to Bn in an open economy is a weighted average of theclosed economy responses with weights expressing the interaction of the assetmarkets. Similar responses to S9 p, and y are shown by e( i9 y\A,A*) an de(P , y |A, A*). P an d i also depend on B*9 S*, y* and p* in an open economy;e( i9B*\A9A*) shows a typical elasticity.

The size of the elasticities in table 1 depend s on the relative size of the ho mecountry. F or a relatively small or a relatively large country, the respo nse to B9S9 y an d p are approximately the same in an open economy as in thecorresponding closed economy. The reason is that aU9 a22 and the denominatorapproach unity for both large and small countries, and a i2 an d a2i approachzero. The reasons differ. In large countries, the effec t of foreign asset prices ondomestic prices is relatively small; all elasticities of i and P with respect to /*TABLE 1

e (i , BI A, A *) - g (i> B \AM)a22 + e (P,B \AM)a i2 cQaua22- a l2a2ie (P, BI A, A *) - + g ( / , B\AM)a2l . Q011 22" 120211 > an = 1 - e(i, i*\AM)e(i*, i\AM*)~ e(i, P*\AM )e(P*, i\AM*)>0a l2 = e a i*\AM)e (/*, P\AM*) + P*\AM)e ( P * , P\AM*) < 0

a21 = e(P, i*lAM)e(i*, i\AM*) + e(P, P*\AM )e(P*, i\AM*) >01 > a22 = 1 - P*\AM)e ( P * , P\AM*)~ e ( P , i*\AM)e(i*, P\AM*)>0p ( i y | A A* ) = g ft y 1 AM)a22 + g (P, y \ A M ) a X2 ^ Q^ aua22-a i2a2ls (P, y IA, A *) = g (P> y \ A M ) a n + & y lA M ) a 2 1aua22- a 12a21

r r * U [e(i9i*)e(i*,B*\AM*) + e(i,P*)e(P* 9B*\AM*)]a22; + [ g (P , i * ) g ( i * , B*\AM*) + e (P, P *)c (P *, B * [AM * ) ]q 12011022-012021


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and P * appr oach zero . In a small country, the respon ses of /* and P* to i and Pare small. Since home country and foreign responses always appear as aproduct, the product approaches zero whenever there is substantial differencein relative size.Interdependence of the asset markets is most important if countries orcurrency areas are of app roximately equ al size. In small countries, the effect ofinterdependence can be approximated by the response to foreign variables. Asshown by e (/, B*\A, A *), the influence of foreign variables does not vanish. Ina large country, all influences fro m abroad are of small order of m agnitude andcan be neglected. The responses on the asset markets of a large open economycan be approximated by the elasticities obtained from the model of a closedeconomy.Opening the economy to trade and capital movements modifies our analysisof the output market in four ways. First, output and prices become subject toinfluences from both domestic and foreign asset markets. The elasticitiesdenoted A, A* replace the AM elasticities. Second, the dependen ce of d o n p *and the inclusion of exports in expenditure provide channels for interactionbetween foreign and domestic expenditure. These interactions modify theslope of the expenditure function and the response of real expenditure tochanges in B, 5, and g. Third, the price setting function now includes p* .Interaction between p an d p * affects output and the slope of the price settingfunction. Fourth, both output and asset market equations show that changes iny* affect the home country. Interaction between y and y* alters the equilib-rium positions of the two output markets and the two asset markets throughW h, e, Wt an d e* . The partial derivatives of d an d X with respect to y and y *are combinations of the derivatives w ith respect to W h an d e or Wf an d e* .From equations (17a) and (17b) we obtain the slope of the expenditurefunction in the p, y p la ne -t he counterpart of e(p, y\d + g) for the closedeconomy - and the shifts induced by changes in g, B and 5. The responsesrecognize interaction on the asset mark ets and the response of the price level toasset prices holding output constan t and neglecting interaction between y, p, y *and p*. The slope is denoted e(p, y\d + X + g) and the shifts in position areno w e(p, g \d + X + g), s (p, B \d + X + g), etc. These elasticities are defined forgiven values of g, Bn, 5, B *, 5*, and y*. Table 2 shows typical responses todomestic and foreign variables.Opening the economy to exchanges of goods and securities lowers the slopeof the expenditure function in small and large economies, but the change inslope is relatively small. The total price elasticity of domestic expenditure,e(d,p) contains e(p*,p) and e(p,p*). One of the two vanishes in large andsmall countries. We have shown that the AA * com ponents differ little fro m theAM components so that e(d, y) and e(d,p) in table 2 are similar to the


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T A B L E 2/ I, , v , , l - r a - P - 7 ) g ( d , y ) + g e ( X ,y ) ] 0e(p,y\d+X + g)- ( 1 _ p _ 7 ) E - ( d , p ) + p e ( X , p ) < 0

e(p,g\d+X +g) = - ^ > 0

eip,Bt\d +X + g ) ^ ^ > 0with j3 = X/ y , y =gly, and O M = the denominator of y + X 4- g ) .Typical components and signs are

S ( 4 y) = (d,y) + e(d, i)s(i,y\A, A * ) + s ( d > ) e ( P , y A *) > 0e (X , y ) = e(X~i*)e(i*, y| A , A*) + e(X ,P*)e(P*, y\A, A * ) ~ 0e(d,p) = e(d,p) + s(d, i)e(/, p\A, A*) + e(d*P)e(P, p\A, A*) +

e(pip)[s (d, i)e(/, p *|A, A *) + e (U>)e (P, P 1 A, A *) + e (p ,+p *)]e(d, Ba) = e(d, i)e (/ , B|A, A*) + e( 0

n) = e{X~i*)e (/*, n |A , A *) + e(X,P*)e (P*, Bn)> 0e(d , B *) = e(d, i)e (i, B *|A, A *) + e(d , P ) s (P , B*|A, A *) > 0

corresponding elasticities in a small or large closed economy.The slope of the open econom y exp enditure fu nction in table 2 differs in twomain ways fr om the slope in a closed economy . One is the presen ce of E(X,P),the partial price elasticity of exports. The other is 3, the ratio of exports todome stic output. Differences in the respon se of open and closed economies arereduced by the relatively small size of fi in large economies and increased bythe relatively large value of /3 in small countries.The conclusion about the slope e(p, y|d + X + g) carries over to the re-sponses to policy variables. For large economies, the responses to policyvariables shown in table 2 differ little fro m the closed economy respon ses. Forsmall countries, the effects of B *, y *, p * and possibly 5 * cannot be neglected.The supply response of the open economy can be obtained directly fromequation (17c). We recognize the interdependence of p*, p, y*, and y byrewriting the equation as

p = p [y, K, w , p p * ( y * , K * , w * , p / p ) ] .The slope of the supply curve in the p- y plane, neglecting interaction between


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y and y* (as in the elasticities of the expenditure function), is 12l~e(p*,p)e(p,p*)

Opening the economy to trade increases the slope of the supply function.The chan ge is small, howev er, in small or large countries. In these cases, eithere (P> P *) or e (p*, p) vanishes. For a country approxim ately the same size as itstrading partne rs, the interaction between do mestic and foreign prices cannot beneglected.The sh ort-run respon se of output and prices in the home co untry to changes ing, Bn, S, Bt, S*, or y* is completely determined by the slopes and shifts. Theresponse abroad is the mirror image of the home country response. For eachcountry, w e have determ ined a position of short-run flow equilibrium that is anexact analogue of the short-run flow equilibrium of the closed econom y shownin figure 1 and equation (10). All variables held constant when determining theslopes of the expenditure and price-setting functions are treated similarly, andthe response in the rest of the world is again a mirror image of the homecountry response.Our analysis of the interaction of the flow markets with fixed money wagesand fixed capital stock requires one additional step. The responses justdescribed are obtained holding y* constant at home and y constant abroad.Changes in y and y * and their interaction affec t the position of flow equilibriumin two ways, by changing the equilibrium values of P, /, P* and /* determinedon the four-asset mar kets and by the interaction of the output m arket v ariables.To avoid additional, cumbersome notation, we rewrite the flow equilibriumcondition for the home c ountry and th e rest of the world in terms of the existingstocks and the variables y and y*,

y = d(B n,B*, S, S*, y, y* ) + X(B n,B*n, S, S*, y, y*) + g, (22a)an dy* = d*( ) + * * ( ) + g* . (22b)

The two equations express the full effect on expenditure of the interaction ofasset m arkets and outpu t mark ets in the two countries. The eff ects on d, X, d *,and X * of /, P, /* and P * are no w implicit in the elasticities with respect to th evariables in equations (22). Table 3 shows some principal responses obtained-12An additional effect occurs i f domestic money wages depend on foreign prices or on foreignwages. We neglect any direct effect of this kind. Below, we recognize an effect on wages fromexcess supply or demand as in the c losed economy.


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Monetary and fiscal policies 3 5 1

T A B L E 3

/ . X (1 - - y)it(d, Bn) + s(d, y*)g(y*, Bn)] + [E(X, Bn)+ (X, y *)(y *, Bn)]e(y,Ba\OAO A )- i _(1 _ _ )[i(d> )+i(d,*)e(y*t )]- i i(X, y) +s(X, y*)e(y*> y)]e(y,gjOAO*A*) = ^>0

> 0

e(y,g*\OAO*A*) = y*[(l ~ ~ y)(d, y*) + e(X, y*)]> 0Ae (y, B *\OAO *A *) = > 0A

from the two equations. The responses in the rest of the world are, again,mirror images of the home country responses.The first elasticity in table 3, e(y,B n | OA, A* ), is obtained f rom equation(22a) ignoring interaction with the output markets in the rest of the world,equation (22b). The co mpo nents of e(y , B n\OA, A *) are described more fully intable 2 where the numerator appears as the numerator of e(p, B n\d + X + g ) ,and the denominator is the numerator of e(p, y\d + X + g) .The full respons e of outpu t to a change in the base and other policy variablesincludes the interaction with output markets abroad, equation (22b). Allremaining elasticities in table 3 recognize the interaction and are denotedOAO*A*. The pattern is recognizable. The two terms in the numerator ofs (y, B n\ OAO * A *) contain the total response of domestic expenditure andexports to Bn on the output and asset market . Each has two components: Thefirst, s(d, Bn) and e(X, Bn) are the same terms appearing in the numerator ofe(y , Bn\O A , A *). The second component of each term allows for a response ofy* to Bn taking account of the full interaction of the markets for assets andoutput. The denominator contains e(d,y) and e(X, y) from table 2, modified bythe interaction of the asset and output markets expressed by e(d, y*) ande(X, y*). If the export response is the larger of the two, interaction lowers thedenominator . The numerator increases, so al lowing for interaction raises theresponse . The responses to S and S * are obtained by substi tuting S and 5* fo rB and B*.As bef ore, the values of the elast icit ies depend on th e relat ive size of the twomarke ts. For small countr ies e(y *, y) is small, and for large countr ies, e (d, y *)and e(X , y* ) are small . The total response over output and asset markets athome and abroad differs l i tt le f ro m the domestic respo nse. F or a large countrythe effects of g*, B* and S* are small also, so the closed economy resultsremain valid . For a small country, the closed economy results are approximate


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35 2 Karl Brunn er and Allan H. Meitzer

mea sures of the ef fect of Bn, g, and S, but output in the open econom y depend sheavily on B*, g* and S* .Determining the longer-run equilibrium price response requires one addi-tional step. Each resp onse of y is multiplied by the respons e of p to y obtainedfro m the price-setting fu nction allowing for the full interaction of dom estic andforeign markets. The adjustment of p induced by changes in Bn, B f , S or othervariables in table 3 is the produc t of the resp onse of real output to the particularvariable shown in table 3 multiplied by s(p, y\s, s*).

e(p,y\s,s*) = *


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influence from abroad. The determination of equilibrium stocks and flowsdiffers with the size of the country.The stocks of base money and debt in each open economy are a consequenceof current and past domestic and international monetary and fiscal policies. Inthis section, we discuss mainly the longer-run stock-flow equilibrium position,the determination of the stocks of assets consistent with the longer-run flowequilibrium of the previous section.Determination of equilibrium stocks of financial assets- B, B*, S an dS* - involves three equations introduced earlier, the government budget equa-tions for the two countries and the common current account balance. Table 3and equation (23) show that the longer-run equilibrium values of p, y an d idepend on financial asset stocks and policy variables. By substituting thesolutions for /, p, and y in the budget equations of each cou ntry, we can exp ressthe current budget deficit or surplus as a function of outstanding asset stocksand policy variables. The resulting equations, equations (24a) and (24b), are theanalogues in an open economy of equation (13) of the closed economy. F andF* determine the deficit or surplus in the budget of the home country and theconsolidated budget of the rest of the world.Equation (24c) is obtained in a similar way. All flow variables in the currentaccount balance, equation (19), are replaced by their solution in terms offinancial asset stocks and policy variables. The stocks of domestic assets arecombined as D and D*; the cumulated current account balance is B2,

The signs above the variables show the direction of change in f>, )* and 62for positive changes in the stocks and policy variables. As in the closedeconomy [equation (15)] the response of F to D may require some restrictionon the size of dF/dS. The same is true of dF/dD* because of the presence ofdF/dS*, but to a lesser degree because dF/dS* is small. A small minimumvalue of p. may be required for a negative derivative in open as in closedeconomies. Similar comments apply to the F* equation, and to a minimum p *,by the symmetry built into our solution. The signs of C require somerestrictions on the response of exports and imports to domestic and foreignprices. These are the usual restrictions on the size of direct responses relativeto feedback from abroad.

= F(D, D*, B2; g, g*, wig , u>/g*, r, * p, p),)* = F* (D, D*, B2; g, g* 9 wig, wig*, r, r* , p, />, p) ,2 = C(D, D*, B2; g, g, wig t w/g*, r9 r* , p, /I*, p).

(24a)(24b)(24c)


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35 4 Karl Brunner and Allan H. Meitzer8. The Scope for Independent Policies in Interdependent EconomiesInspection of the dynamic system, equations (24a) to (24c), shows that theadjustments of the two economies are determined by fiscal variables-g, g*, T, R*, wig, wig*-and by monetary policy expressed by the financialparameters i and jl* and by exchange rate arrange men ts. Some questionsabout the properties of the system arise. How m any independent policy choicescan be made without endangering the stability of the system? Can allcountries maintain independent fiscal policies and fixed exchange rates? Whatis the required policy in countries that seek to harmonize fiscal and monetarypolicies? This section attempts to answer these questions by examining thestability of the system and the conditions for stability. A diagram summarizesthe discussion.In principle, every policy change affects the net foreign positions, thebalances on current account and the budget positions of the rest of the world,but our analysis has shown that the size of any effects on the rest of the worldand from the rest of the world depends on the size of the country. Smallcountries have little influence on large countries but are greatly influenced bythe policies of large countries.The stability of the fixed exchange rate system depends on the properties ofthe differential equation describing the adjustment of financial assets in theinterdependent world economy. If the differential equation has only negativereal roots, the fixed exchange rate system is stable. The homogenous differen-tial equation formed from equations (24a) to (24c) has the general form 14

a 0 A 3 + a i A 2 + a 2 A + a 3 = 0 .The R outh-Hu rwitz conditions imply that a sufficient condition f or instability ofthe system is a 3 < 0. The sign of a 3 can be found from

A 3 = FD(F % 2CD* - F%*C B2) + F%FD*C BL - FB2CD*)+ CD(F%FB*-FD*F % 2).The sign of the first term of a3 depends on relative orders of magnitude, but isprobably positive. All other terms are negative, so a3< 0 and the fixedexchange rate is unstable under a wide variety of conditions. Moreover,conditions that a ssure a positive value of the first term, large F$* an d CB2 , alsoraise the absolute value of the other terms.

14The coefficient a0 > 0. All other coefficients are obtained from the matrix of partial derivativesused to form the characteristic equation Fd ~ FD* FB2-F % A -F%* -F % 2 = 0. Cd Cd* A Cs2


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Instability of the system means that once the world economy leaves anequilibrium position, there is no mechanism that restores equilibrium at thefixed rates. One reason is that governments engage in independent policyoperations. Financial assets are created and destroyed to finance budgetpolicies and the balance of payments. The world stock of money changes with/JLD, /x*>* an d B2. There is no mechanism assuring that the rates of change ofmoney and the stocks of financial assets remain consistent with prevailingexchange rates once the analysis incorporates independent budget processes.Suppose a country disturbs equilibrium by expansive fiscal policy, increasingG , keeping tax rates and financial policy (JL) unchanged . The budget deficit rises(> > 0) and the outstanding stock of financial assets, D , increases. Prices rise inthe expanding c ountry and in the rest of the world. There is a deficit on cur rentaccount (6 2 < 0) and a budget surplus in the rest of the world < 0), shownin equations (24b) and (24c) by the responses to g an d D. The budget surplusabroad r educes D* , reducing the stocks of foreign financial assets and slowingthe rate of increase of money and securities in the world. The reduction of B2works to equilibrate prices in the expanding country and the rest of the world.The familiar price-specie flow mechanism decelerates prices in the expandingcountry and accelerates prices in the rest of the world. In addition, the changesinduced by the movements of international reserves raise the budget deficit inthe expanding country and the budget surplus in the rest of the world. Theseresponses are shown by the effects of B2 on T> an d T>* in equations (24a) and(24b). The rate of increase in assets slows if fiscal policy and financial policyremain unchanged.The damping of the response to a change in g (or other expansive policyaction) depends not only on the price-spe cie flow mechanism but on the budgetpolicy mechanism. The rest of the world must absorb some of the assetscreated to finance the home country budget and must run a budget surplus toreduce their outstanding stocks of base money and securities.If foreigners choose to maintain fixed exchange rates, they cannot select anindependent fiscal policy. Every choice of g* and r* imposes restrictions onthe policy choices available to the home country.Maintenance of equilibrium with fixed exchange rates imposes restrictionson fiscal and financial policies. For a time, a country can offset some of theeffect on prices, output and asset stocks by changing current (marginal) /JL*relative to average /JL*. Opportunities of this kind are limited and decline withthe length of run. In the longer-run equilibrium at fixed exchange rates persistsif and only if wealth owners treat domestic and foreign assets as perfectsubstitutes at the prevailing exchang e rates and comm odities sell at equivalentprices.A diagram brings out some implications of our analysis. In figure 2, equations


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D

F I G U R E 2

(24a) to (24c) are shown as equilibrium relations. Each differential equation isset equal to zero and solved fo r D as a function of B2. The position of each linedepend s on D * and on the policy variables. The F F line defines a balance in thehome country budget , D = 0. The F * F * line defines a balanced budg et in the restof the wo rld, >* = 0. The CC line defines a current account b alance fo r bothcountries, B2 = 0.The intersection of the three lines is a position of world equilibrium. At allother positions at least one market is not in equilibrium. At values of B2 to theright of CC, FF and F*F*, B2 and t> are negative and f)* is positive. Thehome country has a deficit on current account and a surplus in the governmentbudget . B2 an d D decline, so Bn an d S decline. The rest of the world has asurplus on current account, equal to the home country deficit, and a deficit inthe budget. Domestic assets of foreign countries increase, and Bt an d S* rise.The point, or area, labelled I has these properties.The opposite set of circumstances is found at values of B2 to the left of CC,FF, and F*F*. The point labelled II has the properties B2>0, D >0 andD* < 0. The hom e country has a surplus on curren t accoun t and a deficit in the


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governm ent budge t; the rest of the world has a deficit on current ac count and abudget surplus. In the home country, stocks of base money and securities rise;in the rest of the world, assets stocks fall.From point / / , the home country moves toward the CC and FF l ines underthe impact of rising asset stocks. The movement is in the direction of stockequil ibrium fo r the home country but may be away from the F * F * curve. Thebudget surplus abroad, however, complicates the adjustment. The effect offalling Bt and S* is to raise the FF and F*F* lines and lower the CC line.F *F * and CC move toward point II and FF moves away.Whether the total effect is a convergence toward equilibrium stocks or amovement away from equilibrium depends on the choice of policies in the twocountries. There are sets of policies that move the system toward equilibrium.How ever, fixed policies - constant g, g*, r, r* - a r e inconsistent withworld equilibrium at fixed exchange rates as shown earlier.An example brings out the problem of holding exchange rates fixed whilechoosing independent monetary and fiscal policies in open, interdependenteconomies. Suppose, as before, that the home country increases g therebyputting the world economy inside the triangle formed by the CC, FF and F*F*lines of figure 2. At every point in the triangle, B2 < 0, D > 0 and D* < 0. Thehome country has a deficit in the curre nt acc ount balance and a budget deficit.The rest of the world has a surplus on current account and a budget surplus.With 2 < 0 and f> > 0, B2 falls and D rises in the home country, moving theworld economy toward the intersection of CC and FF. The surplus in theforeign budget, however, lowers CC (shifts CC to the left) and raises FF andF*F*. The FF and CC lines move away from equilibrium. Instability impliesthat these m ovem ents are large relative to the adjustm ent toward equilibrium inthe home country. Stocks of foreign exchange move toward a minimum,critical level, B2min in figure 2, before the payments imbalance is corrected.At the minimum level of B2, devaluation is a likely solution.Devaluation is not the only solution. Before reaching the minimum level ofB2 a reduction in g or an increase in r helps to restore equilibrium. An increasein g* or a reduction in r* also moves the system toward equilibrium. As weemphasized earlier, there are sets of policies that help to maintain fixedexchange rates, but the system is unstable with independent fiscal policies. Ifpolicy changes in a country of moderate or larger size disturb world equilibriumthe world economy does not return to the previous equilibrium. The diagramdemonstrates the point we have emphasized. In open, interdependenteconomies with fixed exchange rates, countries cannot maintain independentfiscal and monetary policies.


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9. ConclusionThe main policy conclusion reached in our analysis is that the fixed exchange-rate sy stem is likely to be unstable. D eparture s fr om stock-flow equilibrium d onot set off a process that restores equilibrium. There are too many sources ofmone y and debt creation in open econom ies to assure that the system returns toequilibrium at unchanged exchange rates. The many devaluations and revalua-tions under the Bretton-Woods system support this implication.Our conclusions are derived from a model that differs in several ways fromrecent analyses [Mundell (1968)]. Output is variable; prices of assets and outputchange; the conditions of world equilibrium do not hold at every instant but area consequence of the behavior of economic agents responding to policy andother changes. C ountries are n ot all "sm all". They differ in size, and the effectsof policy and other changes depend on size.Decisions of large countries have considerable influence on prices and outp utin small countries, but the reverse is not true. Large countries bent upon anindependent policy course find their influence on world prices and outputmagnified by the fixed exchange-rate system. C ountries approxim ately equal insize to their trading partners are in an intermediate position. Interdependenceincreases with the size of a country's trading partners.For small and large countries, the effects of domestic policy actions is verysimilar in open and closed economies. Opening the economy to trade in assetsand current o utput does little to enhance or weaken the effects of monetary andfiscal policies in these countries.In open and closed economies, fiscal policy has a powerful influence on thestock-flow equilibrium position. The influence comes from the effect of fiscalpolicy on the outstanding stocks of financial assets, money and bonds. Theeffect on asset stocks is considerably larger and m ore durable than the e ffect offiscal policy on flows, so much emphasized in the past. Fiscal policy is themajor determinant of asset stocks in a closed economy, and the level andcomposition of assets has a dominant effect on equilibrium prices and output.In an open economy, stocks of financial assets depend on fiscal policy and onthe balance of payments.The dependence of assets stocks on domestic and foreign fiscal policy and onthe balance of paym ents is the primary reaso n for instability of the system. T heBretton-Woods system did not restrict fiscal policy or establish rules limitingthe size of budget deficits or the power of central banks to finance budgetdeficits. Whenever rates of fiscal and monetary expansion in a particularcountry rem ained abo ve or below the rates in the rest of the world, devaluationor revaluation followe d. In the absenc e of restrictions on the use of fiscal policy


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and the financing of budget deficits, there is no reason to expect any futuresystem of fixed exchange rates to be durable or stable.ReferencesDornbusch, R., 1973, Capital mobility, portfolio balances and nontraded assets, multil ithedMcKinnon, R., 1969, Portfolio balance and international payments adjustment, in: R. Mundell andA. Swoboda, eds. , Monetary problems of the international economy (Aldine, Chicago).Metzler, L., 1951, Wealth, saving and the rate of interest, Journal of Political Economy.Mundell, R., 1968, International economics (Macmillan, London).Myhrman, J . , 1976, A macroeconomic model with asset equi l ibrium for an open economy,

Journal of Monetary Economics.


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612. The Sim plex Algorithm with the Pivot Rule of Maximizing Criterion Improvement, by R. G.Jeroslow.613. Duality in Fractional Programming, by Finn Kydland.614. Tests of an Adaptive Regression Model, by Thomas F. Cooley and Edward C. Prescott615. The Dollar as an International Money, by Allan H. Meitzer.616. Information Source s of Durable G oods, by Joseph W . Newman and Richard Staelin.617. S ome International Evidence on Output-Inflation Tradeoffs by Robert E Lucas.618. Determining Optimal Growth Paths in Lo gistics Operations, by V. Srinlvasan and GeraldL Thompson.619. Polaroids: A New Tool in Non-Convex and in Integer Programming, by Claude-AlainBrdet620. Evidence on the "Growth-Optimum" Model, by Richard Roll.621. Redundancies in the Hilbert-Bernays Derivability Conditions for Godel's Second Incom-pleteness Theorem by R. G. Jeroslow.622. An Analysis of the Association Between U. S. Mortality and Air Pollution by Lester B.Lave and Eugene P. Seskln.623. Optimal and Market Control in a Dynamic Economic System with Endogeneous Hetero-geneo us Labor by Timothy W. McGuire an d Suresh P. Sethi.624. An Analysis of Cooperation and Learning in a Duopoly Context by Richard M. Cyert andMorris H.DeGroot.625. Asymptotic Linear Programming by R . G. Jeroslow.626. A n Adaptive Regr ession Model, by Thoma s F. Cooley and Edward C. Prescott627. Bayesian Co mpariso ns of Simple Macroeconom ic Mod els by Martin S. Geisel.628. Ex ante and ex post Substitutability in Econom ic Growth, by Nan cy M. Gordon.629. T he Facial Decomposition Method by Claude-Alain Brdet.630. O n the General Solution to Systems o f. .. by V. J. Bowman and Claude-Alain B rdet631. Electoral Participation in the French Fifth Republic, by Howard Rosenthal and SubrataSen.632. Hiring, Training, and Retaining the Hard-Core Unemployed: A Selected Review, by PaulS. Goodman, Harold Paransky, and Paul Salipante.633. Variable and Self-Service Co sts in Reciprocal Allocation Mode ls by Robert S. Kaplan.634. Quadratic Cost-Volume Relationship and Timing of Demand Information by Yuji liiri andHiroyukl Itami.635. Linear Programs Dependent on a Single Parameter by R. G. Jeroslow.636. Ho using and Housing P olicies in Western Europe by John Bry ant637. An Optimum Budget Allocation Model for Dynamic, Interacting Market Segments byDennis H. Gen sch an d Peter Welam.638. Determinants of Physician Office Location by Robert S. Kaplan and Sam uel Le inhardt639. Market Structure and Mon opoly Profits: A Dynamic Theory by Edward C . Prescott641. Reply to Craig Swan by Francisco Ar celus an d Allan H. Meitzer.643. A n Empirical Study of the NA B-Jo bs Program by Otto A. Davis, Peter M. Doyle, Myron LJoseph, John S . Niles and Wayne D. Perry.644. T he Effects of Curtailment on an Ad missio ns Model for a Graduate Management Programby V. Srinlvasan and Alan G. Weinstein.645. Risk a nd the Value Line Contest by Robert S. Kaplan and Roman L. Well.646. Accoun ting Ch ange s and Stock Prices by Robert S. Kaplan and Richard Roll.647. Impact of Individual Differences, Reward Distribution, and Task Structure on Produc-tivity by Alan G. Weinstein and Robert L. Holzbach, Jr.648. Generating All the Facets of a Polyhedron by C laude-Alain Brdet.649. On Algorithms for Discrete Problems by R . G. Jeroslow.650. Interpretations of Departures from the Pareto Curve Firm-Size Distributions by Yuji IJiriand Herbert A. Simon.651. Structural Conditions of Interorganizational Power by Ha ns P ennings, C . R. Hinings, D. J.Hickson and R. E. Schneck.654. The Structure of Instructional Know ledge: An Operational Model by Steven Evans.655. Duality: A Symmetric Approach from the Econ omist's Vantage Point by David Cas s.656. Expectations and the Labor Supply by Charles L Hedrick.657. Transitive Majority Rule an d the Theorem of the Alternative b y V. J. Bowman and C. aColantoni.658. Trivial Integer Programs Unsolvable by Branch-and-Bo und by R. G. Jeroslow.

(continued on back cover)


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D m prescnt erto c^ntains i r l d M writton by th faculty of the Graduato Schoo lo I Industriai Administratlon. Publications began In the 1962-63 academlc yearand continua through lo tota. You may raquaat coplas and raoalva titanitram:Reprint Sacretary, GSIA, Carnegie-Mellon University, Pittsburgh, Panna. 16213.

660. Predicting Managerial Success o! Maater of Business Administration (MBA) Graduatesby Alan G. Weinstein and V. Srinivasan.661. Optima! Price and Promotion for Interdependent Market Segments by Dennis H. Genschand Ulf Peter Welam.662. Mi e n to Hedge Against Devaluation by David P. Rutenberg and Alan C. Shapiro.663. Further Comments o n Majority Rule Under Transitivity Constraints by V. Joseph Bowmanand C . S. Cofantoni.664. Credit Availability and Economic Decisions: Some Evidence from the Mortgage andHousing Markets by Allan H. Meitzer.665. Overhead Allocation with Imperfect Markets and Nonlinear Technology by Robert S.Kaplan a nd Ulf Peter Welam.666. Testing a Subse t of theOveridentifying Restrictions by Jose ph B. Kadane .667. A Constraint-Activating Outer Polar Method for Solving Pure or Mixed Integer 0-1 Pro-grams by Egon Balas.666. On Po laroid Intersections by Claude-Alain Brdet.660. The Structure of integer Programs Under the Hermitian Normal Form by V. JosephBowman.670. An Exam ination of Referents Use d in the Evaluation of Pay by Paul S . Goodman.671. On the Set Covering Problem. II. An Algorithm for Set Partitioning by Ego n Bala8.672. Decision Horizons in Discrete Time Undiscounted Markov Renewal Programming byT. E. Morton.673. Game-Theoretic Mod els of Bloc-Voting Under Proportional Representation: ReallySophisticated Voting in French Labor Elections by How ard Rosenthal.674. Rational Expectations and Bay esian Ana lysis by Richard M . Cyert and Morria H. DeGroot.675. T he Spatial Distribution of Urban Pha rmacies by Robert S. Kaplan and Sam uel Leinhardt.676. Branch and Bound Experimente in Zero-One Programming by Claude-Alain Brdet677. Dynamic Pricing of Resou rces in Computer Networks by Charles H. Krlebel and O samaI. Mikhail.676. Nonconvex Quadratic Programming Via Generalized Polars by Egon Balas.679. Information Systems and Organizational Structure by Cha rles H. Krlebel.660. O n Defining Se ts of Vertices of the Hypercube by Linear Inequalitiea by R. G. Jeroslow.681. Risk and Return: The C ase of Merging Firms by Gershon Mandelker.662. A Subadditive Approach to the Group Problem of integer Programming by Claude-AlainBrdet and E . L. Johnson.683. Computing the Natural Factors of a Closed Expanding Economy Model by Gerald L.Thompson.664. Faceta of the Knapaack Polytope by Egon Balas.665. Refolnder on Raid and Honeycutt by Baruch Lev and Gershon Mandelker.686. Multivariate Risk Aversion, Utility Independence by Scott F. Richard.687. Whither the Epidemic? Psychoactive Drug-Use Career Patterns of College Students byTerry C. Gieason, Joel W. Goldstein, and Jame s H. Korn.688. Effect of Perceived Inequity on Salar y Allocation Decisio ns by Paul S . Goodman.689. A Stochastic Mo del for Auditing by Robert S. Kaplan.690. Bayesian Analysis and Duopoly Theory by Richard M. Cyert and Morria H. DeGroot.691. Optimal Consumption, Investment and Life Insurance Decisions in a Continuous TimeModel by Scott F. Richard.692. Interdependence and Complementarity The C ase of A B rokerage Office by Johanne8Pennings.693. Planning Horizons for the Dynamic Lot Size Model: Protective Procedures and Compu-tational Results by Rolf A. Lundin and Thomas E Morton.

694. Statistical Sampling in Auditing by Robert S. Kaplan.695. Set Partitioning: A Survey by Egon Balas.*Management Information Systems: Progress and Perspectives (Carnegie P ress, 1971).Editors: C. H. Krlebel, R. L Van Horn, and J. T. Heamea. Price: $11.50.

monetary and fiscal policy in open interdependent economies with

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