The foundations of the Mundeli-Fleming model of international macroeconomics were laid a quarter century ago in the classic writings of Robert A. Mundell (1960, 1961a, 1961b, 1963, 1964; collected in 1968) and J. Marcus Fleming (1962). The great contribution of this model has been its systematic analysis of the role played by international capital mobility in determining the effectiveness of macroeconomic policies under alternative exchange rate regimes. The analysis extended the simple version of the Keynesian income-expenditure model developed by Machlup (1943) and Metzler (1942), as well as the policy-oriented model developed by Meade (1951), to include economies open to international trade in both goods and financial assets. Over the years the model has been extended in further directions and is still the “work horse” of traditional open-economy macroeconomics. Noteworthy among such applications are stock (portfolio) specifications of capital mobility by McKinnon (1969), Branson (1970), Floyd (1969), and Frenkel and Rodriguez (1975); analyses of the debt-revaluation effects induced by exchange rate changes by Boyer (1977) and Rodriguez (1979); a long-run analysis by Rodriguez (1979); and analyses of expectations and exchange rate dynamics by Kouri (1976) and Dornbusch (1976). A recent critical evaluation of the model has been provided by Purvis (1985).1
The present paper provides an exposition of the model that integrates its various facets into a unified analytical framework. Our specification of the model incorporates the principal extensions that have been made since the 1960s. Special attention is given to the distinction between short-run and long-run consequences of policies, the implications of debt and tax financing of the government budget, and the role the exchange rate regime plays in this regard. The resultant integration clarifies the key economic mechanisms operating in the Mundell-Fleming model and helps to identify its limitations. Because our formulation casts the model in a way that facilitates model comparisons, the exposition provides a bridge between the traditional and more current analytical approaches in international macroeconomics. The specification of the model is sufficiently general to permit analysis of a wide variety of macroeconomic policies. To conserve space, however, we illustrate the model’s applications by focusing on the instrument of fiscal policy.
The organization of the paper is as follows. Section I outlines the analytical framework. Section II considers the operation of the economic system under a fixed exchange rate regime—first for the small-country case, and then for the two-country model of the interdependent world economy. Section III contains a parallel analysis appropriate for the flexible exchange rate regime. Section IV is an integrated summary and overview of the Mundell-Fleming model. To facilitate the exposition, the main analysis is carried out diagrammatically. Appendices I and II to the text provide algebraic derivations and a formal treatment of exchange rate expectations (in the final section of Appendix II).
Fixed Exchange Rates
This appendix contains algebraic derivations pertinent to the fixed exchange rate regime: for long-run equilibrium in the small-country case, and for short-run and long-run equilibrium in the two-country world.
Long-Run Equilibrium: The Small-Country Case
The long-run equilibrium conditions are specified by equations (12)–(15) of the text. Substituting the government budget constraint (15) into equations (12)–14 yields
equations (40) and (42) yield the combinations of output and private sector debt underlying the CA = 0 schedule, and equations (41) and (42) yield the combinations of these variables underlying the YY schedule, in Figure 2 of the text. To obtain the slope of the CA = 0 schedule, we differentiate equations (40) and (42) and obtain
where s = 1 – Ey and a = βmEy. Solving equation (43) for dY/dM and dividing the resultant solutions by each other yields the expression for dB”läY along the CA =0 schedule. This expression is reported in equation (16) of the text. Similarly, differentiating equations (41) and (43) yields
Following a similar procedure, we obtain the expression for dBp/dY along the YY schedule. This expression is reported in equation (17) of the text.
To obtain the horizontal displacements of the CA = 0 schedule following a balanced-budget rise in government spending (Figure 3), we differentiate equations (40) and (42) while holding B8 and Bp constant. Accordingly, equation (40) implies that (1 – s)(dY – dG + dM) = dY – dG, and equation (42) implies that dM = My(dY – dG)t(1 – My). Substituting the latter expression into the former reveals that dY/dG = 1. Thus, a unit balanced-budget rise in government spending induces a unit rightward shift of the CA =0 schedule.
Analogously, to obtain the horizontal shift of the YY schedule we differentiate equations (41) and (42) while holding B8 and BP constant. Equation (41) implies that (1 – s – a)(dY – dG + dM) + (1 – a8)dG = dY, where
Thus, in contrast with the unit rightward displacement of the CA = 0 schedule, the unit balanced-budget rise in government spending shifts the YY schedule to the right by less than one unit.
The long-run effects of fiscal policies are obtained by differentiating the system of equations (12)–(14) of the text and solving for the endogenous variables. Accordingly,
Using this system, one finds that the long-run effects of a debt-financed rise in government spending (that is, dT = 0) are
Short-Run Equilibrium: The Two-Country World
In this section we analyze the short-run equilibrium of the system of equations (5)–7 in the text. This system determines the short-run equilibrium values of Yt,
where Hr denotes the partial (negative) effect of a change in the rate of interest on the world demand for domestic output; that is,
Analogously, differentiating equations (13) and (14) of the text yields
A comparison of the slopes in equations (53) and (55) shows that there are various possible configurations of the relative slopes of the YY and Y*Y* schedules. Two configurations, however, are ruled out. First, if both schedules are positively sloped, then the slope of Y*Y* cannot exceed the slope of YY. This can be verified by noting that in the numerator of equation (53) the negative quantity
A rise in domestic government spending alters the position of both schedules. To determine the horizontal shift of the YY schedule, we use equations (5) and (7) of the text, holding Y* constant and solving for dY/dG after eliminating the expression for dr/dG. A similar procedure is applied to determine the horizontal shift of the Y*Y* schedule from text equations (6) and (7). Accordingly, the horizontal shifts of the schedules induced by a debt-financed rise in government spending are
The corresponding shifts for the tax-financed rise in government spending are
Comparisons of equation (56) with equation (57) and of equation (58) with equation (59) reveal the difference between the shifts of the YY and the Y*Y* schedules.
To compute the short-run multipliers of fiscal policies, we differentiate the system of equations (5)–7 in the text. Thus,
With a debt-financed rise in government spending, dTt =0; thus, the short-run effects are
Differentiating the domestic money demand function (equation (8) of the text) and using equations (61) and (63) yields the short-run change in the domestic money holdings—that is, the balance of payments:
With a balanced-budget rise in government spending, dG = dTt = dT. Accordingly, the solutions of the system of equations in (60) are
Differentiating the domestic money demand function and using equations (65) and (67) yields
Long-Run Equilibrium: The Two-Country World
The long-run equilibrium of the system is specified by equations (69)–75 below, where the first five equations are the long-run counterparts to the short-run conditions (5)–(9) of the text, and the last two equations are the zero-savings requirements for each country, implying (once the government budget constraint is incorporated) the current account balances; by using a common rate of interest, this long-run system embodies the assumption of perfect capital mobility:
By Walras’s law, one of the seven equations can be omitted, and the remaining six equations can be used to solve for the long-run equilibrium values of Y, Y*, Bp, M, M*, and r as functions of the policy variables.
APPENDIX II: Flexible Exchange Rates
This appendix provides algebraic derivations pertinent to the flexible exchange rate regime: for short-run and long-run equilibrium in the two-country world, and for exchange rate expectations.
Short-Run Equilibrium: The Two-Country World
To analyze the short-run equilibrium of the two-country model under flexible exchange rates, we begin by using the domestic money-market equilibrium condition (22) of the text to obtain the domestic market-clearing rate of interest:
where a rise in disposable resources raises the equilibrium rate of interest, and a rise in the money supply lowers the rate of interest. Similarly, using the foreign money-market-clearing condition (23) of the text (but not imposing yet an equality between the foreign rate of interest,
Substituting equation (76) into the domestic expenditure function (3) of the text and substituting equation (77) into the corresponding foreign expenditure function yields
Equations (78) and (79) are the reduced-form expenditure functions that incorporate the conditions of money-market equilibrium. A rise in disposable resources exerts two conflicting influences on the reduced-form expenditure functions. On the one hand, it stimulates spending directly; on the other hand, by raising the equilibrium rate of interest it discourages spending. Formally,
Substituting the reduced-form expenditure functions (78) and (79) into the goods-market-clearing conditions yields
where we recall that
To obtain the slope of the ee schedule, we divide equation (84) by equation (83) to yield
Around a trade-balance equilibrium with zero initial debt (that is,
To determine the effects of changes in government spending, we compute the horizontal shift of the ee schedule by setting
Thus, around trade-balance equilibrium and zero initial debt, the schedule shifts to the right by
Thus, around trade-balance equilibrium and zero initial debt, schedule ee shifts to the left by
By combining the results in equations (86) and (87), we obtain the effect of a balanced-budget unit rise in government spending. Accordingly,
for the ee schedule, with dG = dTt. (88)
Thus, around trade-balance equilibrium with zero initial debt, a balanced-budget unit rise in government spending shifts the ee schedule to the right by one unit.
In the second step of the diagrammatic analysis, we assume that H = 0 and derive the rr* schedule in Figure 10 of the text, which portrays the combinations of Y and Y* along which the money-market-clearing rates of interest (under the assumption of static exchange rate expectations) are equal across countries, so that
The slope of this schedule is
The effects of fiscal policies can be formally obtained by differentiating the system of equations (80), (81), and (89). Thus,
By solving equation (91), we find that the short-run effects of a debt-financed rise in government spending are
Thus, with initial balanced trade and with zero initial debt, ∆ < 0.
Differentiating the money-market equilibrium condition (equation (8) of the text) and using equation (92), we obtain the equilibrium change in the rate of interest:
Similarly, the short-run effects of a tax-financed rise in government spending are
Using the money-market equilibrium condition together with equation (96) yields
Long-Run Equilibrium: The Two-Country World
The long-run equilibrium of the system is characterized by equations (100)–104 below, where the first three equations are the long-run counterparts to equations (80), (81), and (89), and the last two equations are the requirements of zero savings in both countries, implying (once the government budget constraint is incorporated) the current account balances; embodied in the system are the requirements of money-market equilibrium and perfect capital mobility:
This system, which determines the long-run equilibrium values of Y, Y*, e, Bp, and r, can be used to analyze the effects of government spending and taxes on these endogenous variables.
Exchange Rate Expectations
Up to this point we have assumed that expectations about the evolution of the exchange rate are static. This assumption implied that the rates of interest on securities denominated in different currencies are equalized. But because the actual exchange rate does change over time, it is useful to extend the analysis to allow for exchange rate expectations that are not static. Specifically, in this section of Appendix II we assume that expectations are rational in the sense of being self-fulfilling. We continue to assume that the GDP deflators are fixed. To illustrate the main implication of exchange rate expectations, we consider a stripped-down version of the small-country flexible exchange rate model; for expository convenience, we present the analysis using a continuous-time version of the model.
The budget constraint can be written as
where a dot over a variable indicates a time derivative. The spending and money demand functions (the counterparts to equations (3) and (4) of the text) are
where the demand for money is expressed as a negative function of the expected depreciation of the currency, ėt/et. In what follows, we simplify the exposition by assuming that the world interest rate, rf, is very low (zero) and that the effect of assets,
Equation (108) implies that the level of output that clears the goods market depends positively on the level of the exchange rate and on government spending and negatively on taxes. This dependence can be expressed as
and where MA and Mr denote, respectively, the derivatives of the demand for money with respect to assets
Equation (111) constitutes the first differential equation of the model to govern the evolution of the exchange rate over time. The second variable whose evolution over time characterizes the dynamics of the system is the stock of private sector debt. Substituting the goods-market equilibrium condition (110) into the budget constraint (105), and using the fact that in the absence of monetary policy Mt = 0, we can solve for the dynamics of private sector debt:
Equation (112) expresses the rate of change of private sector debt as the difference between private sector spending and disposable income. The previous discussion implies that
In interpreting these expressions, we note that the function h represents the negative savings of the private sector. Accordingly, a unit rise in e, or G raises savings by the saving propensity times the corresponding multiplier. Analogously, a unit rise in taxes that reduces disposable income lowers savings by the saving propensity times the corresponding multiplier for disposable income.
The equilibrium of the system is exhibited in Figure 12. The positively sloped et=0 schedule shows combinations of the exchange rate and private sector debt that maintain an unchanged exchange rate. The schedule represents equation (111) for et — 0. Its slope is positive around a zero level of private sector debt, and its position depends on the policy variables G, Tt, and M. Similarly, the
The effects of a unit debt-financed rise in government spending from G0 to G1 are shown in Figure 13. From an initial long-run equilibrium at point A, the rise in G shifts the
The effects of a unit tax-financed rise in government spending are shown in Figure 14. With dG – dT, the
Boyer, Russell S., “Devaluation and Portfolio Balance,” American Economic Review (Nashville, Tennessee), Vol. 67 (March 1977), pp. 54–63.
Branson, William H., “Monetary Policy and the New View of International Capital Movements,” Brookings Papers on Economic Activity: 2(1970), The Brookings Institution (Washington), pp. 235–62.
Dornbusch, Rudiger, “Expectations and Exchange Rate Dynamics,” Journal of Political Economy (Chicago), Vol. 84 (December 1976), pp. 1161–76.
Fleming, J. Marcus, “Domestic Financial Policies Under Fixed and Under Floating Exchange Rates,” Staff Papers, International Monetary Fund (Washington), Vol. 9 (November 1962), pp. 369–79.
Floyd, John E., “International Capital Movements and Monetary Equilibrium,” American Economic Review (Nashville, Tennessee), Vol. 59 (September 1969), pp. 472–92.
Frenkel, Jacob A., and Michael L. Mussa, “Asset Markets, Exchange Rates and the Balance of Payments,” in Handbook of International Economics, Vol. 2, ed. by Ronald W. Jones and Peter B. Kenen (Amsterdam: North-Holland, 1985), pp. 680–747.
Frenkel, Jacob A., and Assaf Razin, Fiscal Policies and the World Economy: An Intertemporal Approach (Cambridge, Massachusetts: MIT Press, 1987).
Frenkel, Jacob A., and Carlos A. Rodriguez, “Portfolio Equilibrium and the Balance of Payments: A Monetary Approach,” American Economic Review (Nashville, Tennessee), Vol. 65 (September 1975), pp. 674–88.
Kenen, Peter B., “Macroeconomic Theory and Policy: How the Closed Economy Was Opened,” in Handbook of International Economics, Vol. 2, ed. by Ronald W. Jones and Peter B. Kenen (Amsterdam: North-Hoiland, 1985), pp. 625–77.
Kouri, Pentti J.K., “The Exchange Rate and the Balance of Payments in the Short Run and in the Long Run: A Monetary Approach,” Scandinavian Journal of Economics (Stockholm), Vol. 78 (May 1976), pp. 280–304.
McKinnon, Ronald T., “Portfolio Balance and International Payments Adjustment,” in Monetary Problems of the International Economy, ed. by Alexander K. Swoboda and Robert A. Mundell (Chicago: University of Chicago Press, 1969), pp. 199–234.
Marston, Richard C., “Stabilization Policies in Open Economies,” in Handbook of International Economics, Vol. 2, ed. by Ronald W. Jones and Peter B. Kenen (Amsterdam: North-Holland, 1985), pp. 859–916.
Meade, James E., The Theory of International Economic Policy, Vol. 1 (Supplement), The Balance of Payments (London, New York: Oxford University Press, 1951, reprinted 1965).
Metzler, Lloyd A., “Underemployment Equilibrium in International Trade,” Econometrica (Evanston, Illinois), Vol. 10 (April 1942), pp. 97–112.
Mundell, Robert A., “The Monetary Dynamics of International Adjustment Under Fixed and Flexible Rates,” Quarterly Journal of Economics, Vol. 74 (May 1960), pp. 227–57.
Mundell, Robert A., (1961b), “Flexible Exchange Rates and Employment Policy,” Canadian Journal of Economics (Toronto), Vol. 27 (November 1961), pp. 509–17.
Mundell, Robert A., “Capital Mobility and Stabilization Policy Under Fixed and Flexible Exchange Rates,” Canadian Journal of Economic and Political Science (Toronto), Vol. 29 (November 1963), pp. 475–85.
Mundell, Robert A., “A Reply: Capital Mobility and Size,” Canadian Journal of Economics and Political Science (Toronto), Vol. 30 (August 1964), pp. 421–31.
Mussa, Michael L., “Macroeconomic Interdependence and the Exchange Rate Regime,” in International Economic Policy: Theory and Evidence, ed. by Rudiger Dornbusch and Jacob A. Frenkel (Baltimore: Johns Hopkins University Press, 1979), pp. 160–204.
Obstfeld, Maurice, and Alan C. Stockman, “Exchange Rate Dynamics,” in Handbook of International Economics, Vol. 2, ed. by Ronald W. Jones and Peter B. Kenen (Amsterdam: North-Holland, 1985), pp. 917–77.
Purvis, Douglas D., “Public Sector Deficits, International Capital Movements, and the Domestic Economy: The Medium-Term Is the Message,” Canadian Journal of Economics (Toronto), Vol. 18 (November 1985), pp. 723–42.
Rodriguez, Carlos A., “Short- and Long-Run Effects of Monetary and Fiscal Policies Under Flexible Exchange Rates and Perfect Capital Mobility,” American Economic Review (Nashville, Tennessee), Vol. 69 (March 1979), pp. 176–82.
Swoboda, Alexander K., and Rudiger Dornbusch, “Adjustment, Policy, and Monetary Equilibrium in a Two-Country Model,” in International Trade and Money, ed. by Michael B. Connolly and Alexander K. Swoboda (London: Allen & Unwin, 1973), pp. 225–61.
See Drucilla Ekwurzel and Bernard Saffran, “Online Information Retrieval for Economists—The Economic Literature Index,” Journal of Economic Literature (Nashville, Tennessee), Vol. 23 (December 1985), pp. 1728–63.
Mr. Frenkel, Economic Counsellor of the Fund and Director of the Research Department, is a graduate of the Hebrew University and the University of Chicago. Before joining the Fund in January 1987, he was David Rockefeller Professor of International Economics at the University of Chicago. Mr. Razin, Daniel and Grace Ross Professor of International Economics at Tel-Aviv University, is a graduate of the Hebrew University and the University of Chicago. He was a consultant in the Research Department when this paper was completed. The authors are indebted to Thomas Krueger for helpful comments.
Expositions of the mode! for alternative exchange rate regimes and for different degrees of international capital mobility were made by Swoboda and Dornbusch (1973) and Mussa (1979). The diagrammatic analysis used in this paper builds in part on these two sources. Recent surveys of various openeconomy macroeconomic issues, discussed in the context of this model, are contained in Frenkel and Mussa (1985) and Kenen (1985). In addition, Marston (1985) has surveyed applications of the model to the analysis of stabilization policies; Obstfeld and Stockman (1985) have provided a survey of exchange rate dynamics in this and other models. The most comprehensive treatment of the Mundell-Fleming model to date has been given by Dornbusch (1980).
The assumption that the demand for money depends on disposable income rather than on gross income serves to sharpen the contrast between tax-financed and debt-financed changes in government spending, which are analyzed in subsequent sections. A relaxation of this assumption would reduce somewhat the clarity of the contrast between these two means of finance but would not alter the qualitative nature of the analysis.