The Mundell-Fleming Model A Quarter Century Later A Unified Exposition

doi:10.5089/9781451930719.024.A001

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The Mundell-Fleming Model A Quarter Century Later A Unified Exposition

Publication Date:: 01 Jan 1987

eISBN:: 9781451930719

Language:: English

Keywords:: SP; exchange rate; rise in government spending; exchange rate expectation; equilibrium condition; interest rate effect; unit rise; Exchange rate flexibility; Exchange rate arrangements; Conventional peg; Exchange rates

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The Mundell-Fleming model of international macroeconomic originated in the early 1960s and has been extended during the ensuing quarter century. This paper develops an exposition that integrates the various facets of the model and incorporates its extensions into a unified analytical framework. Attention is given to (1) the distinction between short-run and long-run effects of policies, (2) the implications of debt and tax financing of government expenditures, and (3) the role of the exchange rate regime in this regard. By identifying the key mechanisms operating in the model, the exposition clarifies the model’s limitations and facilitates comparison with other, more current approaches.

Abstract

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).

I. The Analytical Framework

Consider a two-country model of the world economy. The two countries are referred to as the home (domestic) country and the foreign country. Each country produces a distinct commodity: the domestic economy produces good x, and the foreign economy produces good x, The domestic level of output is denoted by Y, and the foreign level of output by Y^*. In specifying the behavioral functions, it is convenient to focus on the domestic economy. Accordingly, the budget constraint is

Z_{t} + M_{t} - B_{t}^{p} = p_{t} (Y_{t} - T_{t}) + M_{t - 1} - R_{t - 1} B_{t - 1,}^{p} (1)

where B^p_t denotes the domestic currency value of the private sector’s one-period debt issued in period t, and R_t denotes unity plus the rate of interest. The right-hand side of equation (1) states that, in each period t, the resources available to individuals are disposable income, P_t (Y_t— T_t)—where the deflator for gross domestic product (GDP) is P_t, domestic output is Y_t, and taxes are T_t—and the net value of assets carried over from period t–1, defined as money, M_t–1, net of debt commitment, R_t–1 B^p_t-1(which includes principal plus interest payments). For subsequent use, we denote these assets by A_t–1, where

A_{t - 1} = M_{t - 1} - R_{t - 1} B_{t - 1}^{p} . (2)

The left-hand side of equation (1) indicates the uses of these resources, including nominal spending, Z_t’ money holding, M_t’ and bond holding, –B^p_t.

In conformity with the original Mundell-Fleming formulation, the GDP deflator P_t is assumed to be fixed and is normalized to unity. Nominal spending thus equals real spending, E_t. Because changes in prices are absent, we identify the real rate of interest, r_t = R_{t – 1}, with the corresponding nominal rate of interest (we return to this issue in Section III and in the final section of Appendix II).

If the various demand functions are assumed to depend on available resources and on the rate of interest, we may express the spending and the money demand functions, respectively, as

E_{t} = E (Y_{t} - T_{t} + A_{t - 1,} r_{t}) (3)

M_{t} = M (Y_{t} - T_{t} + A_{t - 1,} r_{t}) . (4)

For simplicity we assume that the marginal propensities to spend and to hoard from disposable income are the same as the corresponding propensities to spend and to hoard from assets. These assumptions, which simplify the exposition, do not affect the basic thrust of the analysis. A similar specification underlies the demand for bonds, which is omitted because of the budget constraint. We also assume that desired spending and money holdings depend positively on available resources and negatively on the rate of interest.²

The domestic private sector is assumed to allocate its spending between domestic goods, C_xt, and foreign goods, C_mt. The real value of domestic spending, E_t is C_xt + p_xt C_mt, here p_mt denotes the relative price of good m in terms of good x. This relative price is assumed to be equalized across countries through international trade. The relative share of domestic spending on good m (the foreign good) is denoted by β_m p_mtC_mt/E_t.

The level of real government spending in period t, measured in terms of own GDP, is denoted by G_t. As does the private sector, the government allocates its spending between the two goods. Domestic government spending on importables (good m) is β^g_m G_t/P_mt.

A similar set of demand functions and government spending patterns characterizes the foreign economy, whose variables are denoted by an asterisk and whose fixed GDP deflator, P^*, is normalized to unity. As for the domestic economy, the relative share of foreign private spending on good x (the good produced by the home country) is denoted by $β_{x}^{*} = C_{x t}^{*} / p_{m t} E_{t}^{*};$ correspondingly, the foreign government spending share on good x is B^g_x*

The relative price of good m in terms of good x, p_mt, which is assumed to be equal across countries, can be written as $p_{m t} = e_{t} P_{t}^{*} / P_{t},$ where e_t is the nominal exchange rate expressed as the price of the foreign currency in terms of the domestic currency. The specification of equilibrium in the world economy depends on the exchange rate regime. We start with the analysis of equilibrium under a fixed exchange rate regime.

II. Capital Mobility Under Fixed Exchange Rates

For equilibrium in the world economy, the markets for goods, money, and bonds must clear. Under a fixed exchange rate, domestic and foreign money (as assets) are perfect substitutes. Therefore, money-market equilibrium can be specified by a single equilibrium relation stating that the world demand for money equals the world supply. Similarly, the assumptions that bonds are internationally tradable assets and that domestic and foreign bonds are perfect substitutes imply that in equilibrium the rate of return on domestic bonds, r_t, equals the corresponding rate on foreign bonds, r_ft, and that bond-market equilibrium can also be specified by a single equation pertaining to the unified world bond market. These considerations further imply that the world economy can be characterized by four markets: those for domestic output, foreign output, world money, and world bonds. By Walras’s law, the bond market can be omitted from the equilibrium specification of the two-country model of the world economy. Accordingly, the equilibrium conditions are

(1 - β_{m}) E (Y_{t} - T_{t} + A_{t - 1,} r_{t}) + (1 - β_{m}^{8}) G + β_{x}^{*} \bar{e} E^{*} (Y_{t}^{*} + A_{t - 1,}^{*} r_{t}) = Y_{t} (5)

β_{m} E (Y_{t} - T_{t} + A_{t - 1,} r_{t}) + β_{m}^{8} G + (1 - β_{x}^{*}) \bar{e} E^{*} (Y_{t}^{*} + A_{t - 1,}^{*} r_{t}) = \bar{e} Y_{t^{*}} (6)

M (Y_{t} - T_{t} + A_{t - 1,} r_{t}) + \bar{e} M^{*} (Y_{t}^{*} + A_{t - 1,}^{*} {\bar{r}}_{t}) = M, (7)

where ē denotes the fixed exchange rate expressed as the price of foreign currency in terms of domestic currency. To focus on the effects of domestic government policy, we assume in what follows that foreign government spending and taxes are zero. The (predetermined) value of foreign assets is measured in foreign currency units, so that $A_{t - 1}^{*} = M_{t - 1}^{*} R_{t - 1} B_{t - 1}^{p} / \bar{e} .$ Given the assumed fixity of the GDP deflators, ē also measures the relative price of importables in terms of exportables. The world supply of money, measured in terms of domestic goods (whose domestic currency price is unity) is denoted by M. In equation (7) we assume that the government does not finance its spending through money creation. This assumption permits a focus on the pure effects of fiscal policies.

The specification of the equilibrium system (5)–(7) embodies the arbitrage condition by which r_t = r_ft so that the yields on domestic and foreign bonds are equal. This equality justifies the use of the same rate of interest in the behavioral functions of the domestic and the foreign economies. The system of equations (5)–7 determines the short-run equilibrium values of domestic output, Y_t, foreign output, Y^*_t and the world rate of interest, r_t, for given (predetermined) values of domestic and foreign net assets, A_t–1 and and for given levels of government spending, G_t, and taxes, T_t.

The international distribution of the given world money supply associated with the short-run equilibrium is determined endogenously according to demand. Thus,

M_{t} = M (Y_{t} - T_{t} + A_{t - 1,} r_{t}) (8)

M_{t^{*}} = M^{*} (Y_{t^{*}} + A_{t^{*} - 1,} r_{t}) . (9)

This equilibrium distribution of the world money supply obtains through international assets swaps.

This formulation of the short-run equilibrium system reveals the significant role played by international capital mobility. In the absence of such mobility, the short-run equilibrium would have determined the levels of domestic and foreign output from the goods-market equilibrium conditions. Associated with these levels of outputs, there would be equilibrium monetary flows. These flows cease in the long run, in which a stationary equilibrium distribution of the world money supply obtains. In contrast, the equlibrium system (5)–(7) shows that, with perfect capital mobility, equilibrium in the world money market obtains through instantaneous asset swaps involving exchanges of money for bonds. These instantaneous stock adjustments are reflected in equation (7).

Fiscal Policies in a Small Country

To illustrate the effects of fiscal policies under a regime of fixed exchange rates with perfect capital mobility, it is convenient to begin with an analysis of a small country that faces a given world rate of interest, r_f, and a given world demand for its goods, $D^{*} = β_{x}^{*} E^{*}$ Under these circumstances, the equilibrium condition for the small economy reduces to

(1 - β_{m}) E (Y_{t} - T_{t} + A_{t - 1,} {\bar{r}}_{f}) + (1 - β_{m}^{g}) G + \bar{e} {\bar{D}}^{*} = Y_{t} . (5 a)

This equilibrium condition determines the short-run value of output for the given (predetermined) value of assets and for given levels of government spending and taxes. The money supply, M_t, associated with this equilibrium is obtained from the money-market equilibrium condition:

M (Y_{t} - T_{t} + A_{t - 1,} {\bar{r}}_{f}) = M_{t} . (8 a)

This quantity of money is endogenously determined through instantaneous asset swaps at the prevailing world interest rate.

To analyze the effects of fiscal policies, we differentiate equation (5a). Thus,

\frac{d Y_{t}}{d G} = \frac{1 - a^{g}}{s + a'} f o r d T_{t} = 0 (10)

\frac{d Y_{t}}{d G} = 1 - \frac{a^{g}}{s + a'} f o r d T_{t} = d G, (11)

where s and a denote, respectively, the domestic marginal propensities to save and to import from income (or assets), $a^{g} = β_{m}^{g}$ is the government marginal propensity to import, and 1/(S + a) is the small-country foreign trade multiplier. Equations (10) and (11) correspond, respectively, to a bond-financed and to a tax-financed rise in government spending. If all government spending falls on domestic goods (so that a⁸ = 0), then the fiscal expansion that is financed by government borrowing raises output by the full extent of the foreign trade multiplier, whereas a balanced-budget fiscal expansion yields the closed-economy balanced-budget multiplier of unity. In contrast, if all government spending falls on imported goods (so that a⁸ = 1), then the bond-financed multiplier is zero, whereas the balanced-budget multiplier is negative and equal to (s + a – l)/(s +a).

The changes in output induce changes in the demand for money. The induced changes in money holding can be found by differentiating equation (8a) and using equations (10) and (11). Accordingly, the debt-financed unit rise in government spending raises money holdings by (1 – a⁸)M_y /(s + a) units, where M_y denotes the effect of a rise in income on money demand (the inverse of the marginal income velocity). Similarly, the balanced-budget rise in government spending lowers money holdings by a⁸M_y/(s +a).

This analysis is summarized by Figure 1, in which the IS schedule portrays the goods-market equilibrium condition (5a). The curve is negatively sloped because both a rise in the rate of interest and a rise in output create an excess supply of goods. The initial equilibrium obtains at point A, at which the rate of interest equals the exogenously given world rate, r_f, and the level of output is Y₀. As indicated, the schedule IS is drawn forgiven levels of government spending and taxes, G₀ and T₀. The LM schedule passing through point A portrays the money-market equilibrium condition (8a). The curve is positively sloped because a rise in income raises the demand for money, whereas a rise in the rate of interest lowers money demand. As indicated, the LM schedule is drawn for a given level of (the endogenously determined) money stock, M₀.

Figure 1.

Short-Run Effects of Fiscal Policy Under Fixed Exchange Rates: The Small-Country Case

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A001

A unit rise in government spending creates an excess demand for domestic product (at the prevailing level of output). If the rise is bond financed, then the excess demand is 1 – a⁸ units; if it is tax financed, then the excess demand is s + a – a⁸ units (which, depending on the relative magnitudes of the parameters, may be negative). The excess demand is reflected by a horizontal shift of the IS schedule from IS (G₀) to /5(G_t). The IS shedule shifts to the right, reflecting the positive excess demand at the prevailing level of output. The new equilibrium obtains at point B, at which the level of output rises to Y₁. This higher level of output raises the demand for money, which is met instantaneously through an international swap of bonds for money that is effected through the world capital markets. The endogenous rise in the quantity of money from M₀ to M₁ is reflected in the corresponding rightward displacement of the LM schedule from LM(M₀) to LM(M₁).

The foregoing analysis determines the short-run consequences of an expansionary fiscal policy. The instantaneous asset swap induced by the requirement of asset-market equilibrium alters the size of the economy’s external debt. Specifically, if the economy was initially in a long-run equilibrium (so that $B_{t}^{p} = B_{t - 1}^{p}$ = B^p, M_t = M_t–1, A_t = A_t–1 = A, and Y_t= Y_t–1 = Y), then the fiscal expansion, which raises short-run money holdings as well as the size of the external debt, raises the debt-service requirement and (in view of the positive rate of interest) lowers the value of net assets $M_{t} - (1 + {\bar{r}}_{f}) B_{t}^{p}$ carried over to the subsequent period. This change sets in motion a dynamic process that is completed only when the economy reaches its new long-run equilibrium.

The long-run equilibrium conditions can be summarized by the following system:

E [Y - T + M - (1 + {\bar{r}}_{f}) B^{p}, {\bar{r}}_{f}] = Y - {\bar{r}}_{f} B^{p} - T (12)

(1 - β_{m}) E [Y - T + M - (1 + {\bar{r}}_{f}) B^{p}, {\bar{r}}_{f}] + (1 - β_{m}^{g}) G + \bar{e} {\bar{D}}^{*} = Y (13)

M [Y - T + M - (1 + {\bar{r}}_{f}) B^{p}, {\bar{r}}_{f}] = M, (14)

where the omission of the time subscripts indicates that in the long run the variables do not change over time. Equation (12) is obtained from the budget constraint (1) by using the spending function from equation (3) and by imposing the requirement that in the long run M_t = M_t–1 and $B_{t}^{p} = B_{t - 1}^{p} .$ This equation states that in the long run private sector spending equals disposable income, so that private sector savings are zero. Equation (13) is obtained from equations (5a) and (8a) and the long-run stationarity requirement. This equation is the long-run market-clearing condition for domestic output. Finally, equation (14), which is the long-run counterpart to equation (8a), is the condition for long-run money-market equilibrium.

Up to this point we have not explicitly incorporated the government budget constraint. In the absence of money creation, the long-run government budget constraint states that government outlays on purchases, G, and debt service, ${\bar{r}}_{f} B^{g}$ (where B⁸ denotes government debt), must equal taxes, T. Accordingly,

G + {\bar{r}}_{f} B^{g} = T . (15)

Substituting this constraint into equation (12) yields

E [Y - G + M - B^{p} - {\bar{r}}_{f} (B^{p} + B^{g}), {\bar{r}}_{f}] + G = Y - {\bar{r}}_{f} (B^{p} + B^{g}) . (12 a)

equation (12a) states that in the long run the sum of private sector and government spending equals gross national product (GNP). This equality implies that in the long run the current account of the balance of payments is balanced.

Using equation (12), (14), and (15), we obtain the combinations of output and debt that satisfy the long-run requirement of current account balance as well as money-market equilibrium. These combinations are portrayed along the CA = 0 schedule in Figure 2. Similarly, using equations (13)—(15), we obtain the combinations of output and debt that incorporate the requirements of goods-market and money-market equilibrium. These combinations are portrayed along the YY schedule in Figure 2. The slopes of these schedules are

Figure 2.

Long-Run Effects of a Unit Debt-Financed Rise in Government Spending Under Fixed Exchange Rates: The Small-Country Case

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A001

\frac{d B^{p}}{d Y} = - \frac{(s - M_{y})}{(1 - s) - {\bar{r}}_{f} (s - M_{y})}, a l o n g t h e C A = 0 s c h e d u l e (16)

\frac{{d B}^{p}}{d Y} = - \frac{(s - M_{y}) + a}{(1 - {\bar{r}}_{f}) (1 - s - a)}, a l o n g t h e Y Y = 0 s c h e d u l e . (17)

In equations (16) and (17) the term M_y is the marginal propensity to hoard (the inverse of the marginal income velocity), and s – M_y represents the marginal propensity to save in the form of bonds. The numerators in equations (16) and (17) are positive; the denominator of equation (17) is positive because 1 – s – a > 0, and the denominator of equation (16) is positive on the assumption that (1 – s) $(1 - s) > {\bar{r}}_{f} (s - M_{y})$ This assumption in equation (16) is a stability condition ensuring that the perpetual rise in consumption (1 – s) made possible by a unit rise in debt will exceed the perpetual return on the saving in bonds ${\bar{r}}_{f} (s - M_{y})$ made possible by the initial unit rise in debt. If this inequality does not hold, then consumption and debt will rise over time and will not converge to a long-run stationary equilibrium. The foregoing discussion implies that the slopes of both the CA = 0 and the YY schedules are negative. Further, because the numerator of equation (17) exceeds that in equation (16) and the denominator of equation (17) is smaller than that in equation (16), the YY schedule in Figure 2 is steeper than the CA = 0 schedule. The initial long-run equilibrium is indicated by point A in Figure 2, at which the levels of output and private sector debt are Y₀ and $B_{o}^{p}$

Consider the long-run effects of a debt-financed rise in government spending. As is evident from the system of equations (12)—(14), as long as taxes remain unchanged, the CA = 0 schedule (which is derived from equations (12) and (14)) remains intact. In contrast, the rise in government spending influences the YY schedule, which is derived from equations (13) and (14). Specifically, to maintain goods-market equilibrium for any given value of private sector debt, B^p, a unit rise in government spending must be offset by a rise of (1 – a⁸)/(s + a) units in output. Thus, as long as some portion of government spending falls on domestic goods, so that a⁸ < 1, the YY schedule in Figure 2 shifts to the right, to the position indicated by YY’. The new equilibrium is indicated by point B, at which the level of output rises from Y₀ to Y₁ and private sector debt falls to B^p₁ The new equilibrium is associated with a rise in money holdings, which represents the cumulative surpluses in the balance of payments during the transition period.

A comparison between the short-run multiplier shown in equation (10) and the corresponding long-run multiplier (shown in equation (46) of Appendix I) reveals that the latter exceeds the former. In terms of Figure 2, in the short run the output effect of the debt-financed rise in government spending is indicated by point C, whereas the corresponding long-run equilibrium is indicated by point B.

Consider next the effects of a tax-financed rise in government spending. Such a balanced-budget rise in spending alters the positions of both the CA = 0 and the YY schedules. By using equations (12) and (14) with the balanced-budget assumption that dG = dT, it can be shown that a unit rise in government spending induces a unit rightward shift of the CA = 0 schedule. By keeping the value of Y – T intact and holding B^p constant, such a shift maintains the equality between private sector spending and disposable income and also satisfies the money-market equilibrium condition. Similarly, by using equations 13 and 14with the balanced-budget assumption, it is shown (see Appendix I) that, as long as the government import propensity, a⁸, is positive, the YY schedule shifts to the right by less than one unit. The resultant new long-run equilibrium is indicated by point B in Figure 3. For the case drawn, the long-run level of output falls from Y₀ to Y₁ and private sector debt rises from $B_{0}^{p}$ to $B_{0}^{p}$ . Because government debt remains unchanged, the rise in private sector debt corresponds to an equal rise in the economy’s external debt position. In general, however, and depending on the parameters, domestic output may either rise or fall in the long run.

Figure 3.

Long-Run Effects of a Unit Balanced-Budget Rise in Government Spending Under Fixed Exchange Rates: The Small-Country Case

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A001

The size of the long-run multiplier of the balanced-budget rise in government spending depends on the government’s propensity to import. At the limit, if all government spending falls on domestic output, so that a⁸ = 0, the long-run balanced-budget multiplier is unity. In this case the YY schedule in Figure 3 shifts to the right by one unit, the long-run level of output rises by one unit, and private sector debt (and the economy’s external debt) remains unchanged. At the other limit, if all government spending falls on foreign goods, so that a⁸ = 1, the long-run balanced-budget multiplier is negative. In that case the rise in the economy’s external debt is maximized.

The comparison between the short-run balanced-budget multiplier shown in equation (11) with the corresponding long-run multiplier (shown in equation (49) of Appendix I) highlights the contrasts between the two. If the government’s propensity to spend on domestic goods (1 – a⁸) equals the corresponding propensity of the private sector (1 – s – a), then the short-run multiplier is zero, and the long-run multiplier is negative. If the government’s propensity (1 – a⁸) exceeds the private sector’s propensity (1 – s – a), however, both the short-run and the long-run balanced budgets are negative, but the absolute value of the long-run multiplier exceeds the corresponding short-run multiplier. Finally, if government spending falls entirely on domestically produced goods (so that a⁸ = 0), then the short-run and the long-run multipliers are equal to each other, and both are unity.

Fiscal Policies in a Two-Country World

In this section we return to the two-country model outlined in equations (5)–7 and analyze the short-run effects of a debt- and a tax-financed rise in government spending on the equilibrium levels of domestic and foreign output as well as on the equilibrium world rate of interest. The endogeneity of foreign output and the equilibrium world interest rate distinguishes this analysis from the one conducted for the small country case. To conserve space, we do not analyze the long-run effects here; the formal system applicable to long-run equilibrium in the two-country world is presented in the third section of Appendix I.

The analysis is carried out diagrammatically with the aid of Figures 4 and 5. In these figures the YY schedule portrays combinations of domestic and foreign levels of output that yield equality between the levels of production of domestic output and the world demand for it. Similarly, the y^*y^* schedule portrays combinations of output that yield equality between the level of production of foreign output and the world demand for it. The two schedules incorporate the requirement of equilibrium in the world money market. It is shown in Appendix I that the slopes of these schedules are

\frac{d Y_{t}^{*}}{d Y_{t}} = \frac{1}{\bar{e}} \frac{(s + a) (M_{r} + e M_{r}^{*}) + M_{y} H_{r}}{a^{*} (M_{r} + \bar{e} M_{r}^{*}) - M_{y}^{*} \cdot H_{r}}, a l o n g t h e Y Y s c h e d u l e (18)

and

\frac{d Y_{t}^{*}}{d Y_{t}} = \frac{1}{\bar{e}} \frac{a (M_{r} + e M_{r}^{*}) - M_{y} F_{r}}{(s^{*} + a^{*}) (M_{r} + \bar{e} M_{r}^{*}) + M_{y}^{*} \cdot F_{r}}, a l o n g t h e Y^{*} Y^{*} s c h e d u l e, (19)

Figure 4.

A Unit Debt-Financed Rise in Government Spending Under Fixed Exchange Rates: The Two-Country Case

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A001

N o t e : a^{*} (M_{r} + \bar{e} M_{r}^{*}) - M_{y}^{*} . H_{r} < 0; a (M_{r} + \bar{e} M_{r}^{*}) - M_{y} F_{r} < 0.

where H_r and F_r denote the partial (negative) effect of the rate of interest on the world demand for domestic and foreign outputs, respectively, and where E_r, M_r, E_r^*, and M^*^r denote the partial (negative) effects of the rate of interest on domestic and foreign spending and money demand. As may be seen from Figures 4 and 5, the slopes of the two schedules may be positive or negative. To gain intuition, we note that, in the special case for which spending does not depend on the rate of interest (so that H_r = F_r = 0), both schedules must be positively sloped. But if the rate of interest exerts a strong negative effect on world spending, then the excess supply induced by a rise in one country’s output may have to be eliminated by a fall in the other country’s output. Even though this fall in foreign output directly lowers the foreign demand for the first country’s exports, it also induces a decline in the world rate of interest that indirectly stimulates spending and may more than offset the direct reduction in demand. In that case market clearance for each country’s output implies that domestic and foreign outputs are negatively related.

Figure 5.

A Unit Debt-Financed Rise in Government Spending Under Fixed Exchange Rates: The Two-Country Case

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A001

N o t e : a^{*} (M_{r} + \bar{e} M_{r}^{*}) - M_{y}^{*} . H_{r} < 0; a (M_{r} + \bar{e} M_{r}^{*}) - M_{y} F_{r} > 0.

Although the two schedules may be positively or negatively sloped, it may be verified (and is shown in Appendix I) that the YY schedule must be steeper than the y^*y^* schedule. This restriction leaves four possible configurations of the schedules. The common characteristic of these configurations is that, from an initial equilibrium, if there is a rightward shift of the YY schedule that exceeds the rightward shift of the Y^*Y^* schedule, then the new equilibrium must be associated with a higher level of domestic output.

Two cases capturing the general pattern of world output allocations are shown in Figures 4 and 5. The other possible configurations, which are omitted, do not yield different qualitative results concerning the effects of fiscal policies. In both figures the initial equilibrium is indicated by point A, at which the domestic level of output is y₀ and the foreign level is $Y_{0}^{*}$ .

A debt-financed rise in government spending raises the demand for domestic output and induces a rightward shift of the YY schedule from YY to YY’. In contrast, the direction of the change in the position of the Y^*Y^* schedule depends on the relative magnitudes of the two conflicting effects that influence world demand for foreign output. On the one hand, the rise in domestic government spending raises the demand for foreign goods; on the other hand, the induced rise in the world rate of interest lowers that demand. If the Y^*Y^* schedule is positively sloped, as in Figure 4, then the rise in domestic government spending induces a leftward (upward) shift of the Y^*Y^* schedule. The opposite holds if the Y^*Y^* schedule is negatively sloped, as in Figure 5. The formal expressions indicating the magnitudes of the displacements of the schedules are provided in Appendix I.

The new equilibrium obtains at point B, at which domestic output rises from Y₀ to Y₁. In the case shown in Figure 4 (for which the interest rate effect on the world demand for foreign output is relatively weak), foreign output rises. But in the case shown in Figure 5 (for which the interest rate effect on the world demand for foreign output is relatively strong), foreign output may rise or fall depending on the magnitude of the parameters—in particular, the composition of government spending. For example, if government spending falls entirely on domestic output (so that a⁸ = 0), the Y^*Y^* schedule does not shift, and the new equilibrium obtains at a point such as point C in Figure 5, at which foreign output falls. At the other extreme, if government spending falls entirely on foreign goods (so that a^g— 1), then the YY schedule does not shift, and the new equilibrium obtains at a point such as D, at which foreign output rises.

It is shown in Appendix 1 that, independent of the direction of output changes, the debt-financed rise in government spending must raise the world rate of interest. The expressions reported in Appendix I also reveal that, if the (negative) interest rate effect on the world demand for domestic output is relatively strong, then domestic output might fall. The balance of payments effects of the debt-financed rise in government spending are not clear-cut, reflecting “transfer-problem criteria” (familiar from the theory of international transfers). But if the behavioral parameters of the domestic and foreign private sectors are equal, then the balance of payments must improve, and domestic money holdings increase.

A tax-financed rise in government spending also alters the positions of the various schedules, as shown in Appendix I (where we also provide the formal expressions for the various multipliers). In general, in addition to the considerations highlighted in the case of debt finance, the effect of tax-financed fiscal spending also reflects the effects of the reduction in domestic disposable income on aggregate demand. This effect may more than offset the influence of government spending on domestic output. The effect on foreign output is also modified. If the interest rate effect on world demand for foreign output is relatively weak (the case underlying Figure 4), then the shift from debt finance to tax finance mitigates the expansion in foreign output. If, however, the interest rate effect on the demand for foreign output is relatively strong (the case underlying Figure 5), then the shift from debt finance to tax finance exerts expansionary effects on foreign output.

The direction of the change in the rate of interest induced by the tax-financed rise in government spending depends on a transfer-problem criterion indicating whether the redistribution of world disposable income consequent on the fiscal policy raises or lowers the world demand for money (see Appendix I). Accordingly, the interest rate rises if the domestic country ratio, s/M_y, exceeds the corresponding foreign country ratio, S^* /M^*_y., and vice versa. Independent of the change in the rate of interest, however, the tax-financed rise in government spending must worsen the domestic country balance of payments and reduce domestic money holdings.

III. Capital Mobility Under Flexible Exchange Rates

In this section we assume that the world economy operates under a flexible exchange rate regime. Under this assumption, national currencies become nontradable assets whose relative price (the exchange rate, e) is assumed to be determined freely in the world market for foreign exchange. We continue to assume that in each country the GDP deflators, P and P^*, are fixed and equal to unity. In such circumstances the nominal exchange rates represent the terms of trade, and the nominal rates of interest in each country equal the corresponding (GDP-based) real interest rates. Further, in keeping with traditional postulates in the early literature on modeling macroeconomic policies in the world economy, we start the analysis by assuming that exchange rate expectations are static. In such circumstances the international mobility of capital brings about equality among national (GDP-based) real interest rates. The issue of exchange rate expectations is addressed in the final section of Appendix II.

Equilibrium in the world economy requires that world demand for each country’s output equals the corresponding supply and that in each country the demand for cash balances equals the supply. Accordingly, the system characterizing equilibrium in the two-country world economy is

(1 - β_{m}) E (Y_{t} - T_{t} + A_{t - 1}, r_{t}) + (1 - β_{m}^{g}) G + e_{t} β_{x}^{*} E^{*} (Y_{t}^{*} + A_{t - 1}^{*}, r_{t}) = Y_{t} (20)

β_{m} E (Y_{t} - T_{t} + A_{t - 1}, r_{t}) + β_{m}^{g} G + e_{t} (1 - β_{x}^{*}) E^{*} (Y_{t}^{*} + A_{t - 1}^{*}, r_{t}) = e_{t} Y_{t}^{*} (21)

M (Y_{t} - T_{t} + A_{t - 1}, r_{t}) = M (22)

M^{*} (Y_{t}^{*} + A_{t - 1}^{*}, r_{t}) = M^{*} . (23)

Equations (20) and (21)are the goods-market equilibrium conditions (analogous to equations (5) and (6)), and equations (22) and (23)are the domestic and foreign money-market equilibrium conditions, where M and M ^* denote the supplies of domestic and foreign money. In contrast with the fixed exchange rate system, in which each country’s money supply was determined endogenously, here a country’s money supply is determined exogenously by the monetary authorities. We also note that by Walras’s law the world market equilibrium condition for bonds has been left out.

Finally, it is noteworthy that the value of securities may be expressed in terms of domestic or foreign currency units. Accordingly, the domestic currency value of private sector debt, B^p_t, can be expressed in units of foreign currency to yield $B_{f t}^{p} = B_{t}^{p} / e_{t}$ . Arbitrage ensures that the expected rates of return on securities of different currency denomination are equalized. Thus, if r_t and r_ft are, respectively, the rates of interest on bonds denominated in domestic and foreign currency, then 1 + r_t = (ē_t+1/e_t)(1 + r_ft), where denotes the expected future exchange rate. By equating r_t to r_ft, the system of equations (20)–23 embodies the assumption of static exchange rate expectations and perfect capital mobility (see Appendix II).

Fiscal Policies in a Small Country

Analogous with the procedure in our analysis of fiscal policies under fixed exchange rates, we start the analysis of flexible exchange rates with an examination of the effects of fiscal policies in a small country facing a given world rate of interest, r_f, and a given foreign demand for its goods, D^*. The equilibrium conditions for the small country state that world demand for its output equals domestic GDP and that the domestic demand for money equals the supply. Whereas under a fixed exchange rate regime the monetary authorities, committed to peg the exchange rate, do not control the domestic money supply, under a flexible exchange rate regime the supply of money is a policy instrument actively controlled by the monetary authorities.

The goods-market and money-market equilibrium conditions are

(1 - β_{m}) E (Y_{t} - T_{t} + A_{t - 1}, {\bar{r}}_{f}) + (1 - β_{m}^{g}) G + e_{t} {\bar{D}}^{*} = Y_{t} (20 a)

M (Y_{t} - T_{t} + A_{t - 1}, {\bar{r}}_{f}) = M, (22 a)

where

A_{t - 1} = M_{t - 1} - (1 + {\bar{r}}_{f}) e_{t} B_{f, t - 1}^{p} .

As indicated, valuation of the debt commitment denominated in foreign currency, $(1 + {\bar{r}}_{f}) B_{f, t - 1}^{p}$ uses the current exchange rate, e_t. These equilibrium conditions determine the short-run values of output and the exchange rate, and for comparison we recall that under the fixed exchange rate regime the money supply rather than the exchange rate was endogenously determined.

The equilibrium of the system is exhibited in Figure 6. The downward-sloping IS schedule shows the goods-market equilibrium condition (20a). It is drawn for given values of government spending, taxes, and the exchange rate (representing the terms of trade). The upward-sloping LM schedule portrays the money-market equilibrium condition (22a). It is drawn for given values of the money supply, the exchange rate, and taxes. The initial equilibrium obtains at point A, at which the rate of interest equals the world rate, r_f, and the level of output is Y₀. The endogenously determined exchange rate associated with this equilibrium is e₀. Note that in this system, if the initial debt B^p_f, t-1 is zero, the LM schedule does not depend on the exchange rate, and the level of output is determined exclusively by the money-market equilibrium condition; given the equilibrium level of output, the equilibrium exchange rate, however, is determined by the goods-market equilibrium condition. This case underlies Figure 6. Again a comparison with the fixed exchange rate system is relevant. There, the equilibrium money stock is determined by the money-market equilibrium condition, whereas the equilibrium level of output is determined by the goods-market equilibrium condition.

Figure 6.

Short-Run Effects of a Unit Debt-Financed Rise in Government Spending Under Flexible Exchange Rates: The Small-Country Case

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A001

N o t e : B_{f, - 1}^{p} = 0.

Consider the effects of a debt-financed unit rise in government spending, from G₀ to G₁, and suppose that the initial debt commitment is zero. At the prevailing levels of output and the exchange rate, this rise in spending creates an excess demand for domestic output and induces a rightward shift of the IS schedule by (1—a⁸)/(s + a) units. This shift is shown in Figure 6 by the displacement of the IS schedule from the initial position, indicated by IS(G₀, T₀, e₀), to the position indicated by IS (G₁, T₀, e₀). Because with zero initial debt the LM schedule is unaffected by the rise in government spending, it is clear that, given the world interest rate, the level of output that clears the money market must remain at Y₀, corresponding to the initial equilibrium indicated by point A. For the initial equilibrium to be restored in the goods market, the exchange rate must fall (that is, the domestic currency must appreciate). The induced improvement in the terms of trade lowers the world demand for domestic output and induces a leftward shift of the IS schedule. The goods market clears when the exchange rate falls to e₁, so that the IS schedule indicated by IS(G₁ T₀, e₁) also goes through point A. We conclude that, under flexible exchange rates with zero initial debt, a debt-financed fiscal policy loses its potency to alter the level of economic activity; its full effects are absorbed by changes in the exchange rate (the terms of trade).

Consider next the effects of a tax-financed unit rise in government spending, from G₀ to G₁, as shown in Figure 7. In that case, at the prevailing levels of output and the exchange rate, the excess demand for domestic output induces a rightward displacement of the IS schedule by 1 – a⁸/(s + a) units to the position indicated by IS (G₁, T₁ e₀). In addition, the unit rise in taxes lowers disposable income by one unit and reduces the demand for money. For money-market equilibrium to be maintained at the given world rate of interest, the level of output must rise by one unit so as to restore the initial level of disposable income. Thus, the LM schedule shifts to the right from its initial position, indicated by LM(M₀, T₀), to the position indicated by LM(M₀, T₁). With a zero level of initial debt (the case assumed in the figure), the LM schedule does not depend on the value of the exchange rate, and the new equilibrium obtains at point B, where the level of output rises by one unit from Y₀ to Y₁. Because at the initial exchange rate the horizontal displacement of the IS schedule is less than unity (as long as government spending falls in part on imported goods), it follows that at the level of output that clears the money market there is an excess supply of goods. This excess supply is eliminated through a rise in the exchange rate (that is, a depreciation of the domestic currency) from e₀ to e₁. This deterioration in the terms of trade raises the world demand for domestic output and induces a rightward shift of the IS schedule to the position indicated by IS(G₁, T₁ e₁). We conclude that, under flexible exchange rates with zero initial debt, the tax-financed rise in government spending regains its full potency in effecting the level of economic activity.

Figure 7.

Short-Run Effects of a Unit Tax-Financed Rise in Government Spending Under Flexible Exchange Rates: The Small-Country Case

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A001

N o t e : B_{f, - 1}^{p} = 0.

Up to this point we have assumed that the initial debt position was zero. As a result, the only channel through which the exchange rate has influenced the system has been through altering the domestic currency value of the exogenously given foreign demand, ${\bar{D}}^{*}$ . In general, however, with a nonzero level of initial debt, $B_{f, t - 1}^{p}$ (denominated in units of foreign currency), the change in the exchange rate also alters the domestic currency value of the initial debt and, thereby, of the initial assets, A_t–1 The revaluation of the debt commitment constitutes an additional channel through which the exchange rate influences the economic system. As a result, the demand for money and, thereby, the LM schedule also depend on the exchange rate.

To appreciate the role played by debt-revaluation effects, we examine in Figure 8 the implications of a nonzero level of initial debt. The various IS and LM schedules shown in the figure correspond to alternative assumptions concerning the level of initial debt $B_{f, t - 1}^{p} = 0$ and the rest of the arguments governing the position of the schedules are suppressed for simplicity. The initial equilibrium is shown by point A and the solid schedules along which $B_{f, t - 1}^{p} > 0$ corresponds to the cases analyzed in Figures 6 and 7. With a positive value of initial debt, a rise in the exchange rate lowers the value of assets and lowers the demand for money. Restoration of money-market equilibrium requires a compensating rise in output. As a result, the LM schedule in that case is positively sloped. By similar reasoning, a negative value of initial debt corresponds to a negatively sloped LM schedule. The level of initial debt also influences the slope of the IS schedule. As shown in the figure, under similar considerations, the IS schedule is steeper than the benchmark schedule (around point A) if $B_{f, t - 1}^{p} > 0$ , and vice versa.

We can now use Figure 8 to illustrate the possible implications of the initial debt position. For example, a debt-financed fiscal expansion induces a rightward shift of the IS schedule and leaves the LM schedule intact. The short-run equilibrium of the system is changed from point A to point B if the level of initial debt is zero, to point C if the level of initial debt is positive, and to point D if this level is negative. Thus, the debt-revaluation effects critically determine whether a debt-financed rise in Government spending is contractionary or expansionary.

From the system of equations (20a) and (22a), the changes in the level of output are

Figure 8.

Short-Run Effects of a Unit Debt-Financed Rise in Government Spending Under Flexible Exchange Rates: The Debt-Revaluation Effect

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A001

\frac{d Y_{t}}{d G} = \frac{(1 - a^{g}) (1 + {\bar{r}}_{f}) B_{f, t - 1}^{p}}{(1 + {\bar{r}}_{f}) B_{f, t - 1}^{p} - {\bar{D}}^{*}}, f o r d T_{t} = 0 (24)

\frac{d Y_{t}}{d G} = 1 - \frac{a^{g} (1 + {\bar{r}}_{f}) B_{f, t - 1}^{p}}{(1 + {\bar{r}}_{f}) B_{f, t - 1}^{p} - {\bar{D}}^{*}}, f o r d T_{t} = d G . (25)

Similarly, the induced changes in the exchange rates are

\frac{d e_{t}}{d G} = \frac{1 - a^{g}}{(1 + {\bar{r}}_{f}) B_{f, t - 1}^{p} - {\bar{D}}^{*}}, f o r d T_{t} = 0 (26)

\frac{d e_{t}}{d G} = \frac{- a^{g}}{(1 + {\bar{r}}_{f}) B_{f, t - 1}^{p} - {\bar{D}}^{*}}, f o r d T_{t} = d G . (27)

These results highlight the role played by the debt-revaluation effect of exchange rate changes. Specifically, as is evident from equations (24) and (25), a rise in government spending may be contractionary if the initial debt commitment is positive. If, however, the private sector is initially a net creditor, then government spending, however it is financed, must be expansionary. In the benchmark case shown in Figures 6 and 7, the initial debt position is zero, a tax finance is expansionary (yielding the conventional balanced-budget multiplier of unity), and debt finance is not. The key mechanism responsible for this result is the high degree of capital mobility underlying the fixity of the interest rate faced by the small country. With a given interest rate and a given money supply, there is in the short run a unique value of disposable income that clears the money market as long as the initial debt commitment is zero. Hence, in this case, a rise in taxes is expansionary and a rise in government spending is neutral.

A comparison between the exchange rate effects of government spending also reveals the critical importance of the means of finance and of the debt-revaluation effect. In general, for the given money supply, the direction of the change in the exchange rate induced by a rise in government spending depends on whether the government finances its spending through taxes or through debt issue. If the initial debt commitment falls short of the (exogenously given) foreign demand for domestic output, then a debt-financed rise in government spending appreciates the currency, whereas a tax-financed rise in government spending depreciates the currency. The opposite holds if the initial debt commitment exceeds exports.

The foregoing analysis has determined the short-run effects of government spending. We now proceed to analyze the long-run effects of these policies. The long-run equilibrium conditions are shown in equations (28)–(30) below. These equations are the counterpart to the long-run fixed exchange rate system of equations (12)–14. Accordingly,

E [Y - T + M - (1 + {\bar{r}}_{f}) e B_{f}^{p}, {\bar{r}}_{f}] = Y - {\bar{r}}_{f} e B_{f}^{p} - T (28)

(1 - β_{m}) E [Y - T + M - (1 + {\bar{r}}_{f}) e B_{f}^{p}, {\bar{r}}_{f}] + (1 - β_{m}^{g}) G + e {\bar{D}}^{*} = Y (29)

M [Y - T + M - (1 + {\bar{r}}_{f}) e B_{f}^{p}, {\bar{r}}_{f}] = M . (30)

In preparation for the analysis, consider first the benchmark case, in which the initial equilibrium was associated with zero private sector debt. For this case the long run is analyzed in Figure 9. The CA =0 schedule portrays combinations of private sector debt and output that yield equality between spending and income, thereby satisfying equation (28). In view of the government budget constraint shown in equation (15), this equality between private sector income and spending also implies current account balance. The MM schedule portrays combinations of debt and output that yield money-market equilibrium, thereby satisfying equation (30). Around zero private sector debt, both of these schedules are independent of the exchange rate. The slope of the CA =0 schedule is $- s / e [1 - s (1 + {\bar{r}}_{f})]$ . Analogous to the previous discussion of the long-run equilibrium under fixed exchange rates, for stability this slope is assumed to be negative. The slope of the MM schedule is $1 / (1 + {\bar{r}}_{f}) e$ It indicates that a unit rise in long-run private sector debt raises debt commitment (principal plus debt service) by $(1 + {\bar{r}}_{f}) e$ and lowers the demand for money. For the reduction in disposable resources to be offset and for the demand for money to be restored to its initial level, output must be raised by $(1 + {\bar{r}}_{f}) e$ units.

Figure 9.

Long-Run Effects of a Unit Rise in Government Spending Under Flexible Exchange Rates: The Small-Country Case

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A001

The initial long-run equilibrium is shown by point A, at which the level of private sector debt is assumed to be zero, and the level of output is Y₀. As is evident from equations (28) and (30), changes in the levels of government spending and government debt do not alter the CA = 0 and MM schedules. It follows that, with zero private sector debt, a debt-financed rise in government spending does not alter the long-run equilibrium value of private sector debt indicated by point A in Figure 9. In this long-run equilibrium, the level of output remains unchanged, and the currency appreciates to the level shown in the short-run analysts of Figure 6.

A rise in taxes alters both the CA = 0 and the MM schedules. As is evident from equations (28) and (30), a rise in output that keeps disposable income unchanged (at the given zero level of private sector debt) maintains the initial current account balance as well as money-market equilibrium intact. Thus, a tax-financed unit rise in government spending induces a rightward unit displacement of both the CA = 0 and the MM schedules and yields a new long-run equilibrium at point B. At this point private sector debt remains at its initial zero level. In addition, the level of output rises to y₁, and the currency depreciates to e₁ as shown in the short-run analysis of Figure 7.

The above discussion shows that, under flexible exchange rates with zero initial private sector debt, the long-run and the short-run effects of fiscal policies coincide. This characteristic is in contrast to the one obtained for fixed exchange rates, in which the long-run effects of fiscal policies differ from the corresponding short-run effects. In interpreting these results we note that, because of the nontradability of national monies under a flexible exchange rate regime, the mechanism of adjustment to fiscal policies does not permit instantaneous changes in the composition of assets through swaps of interest-bearing assets for national money in the world capital markets. As a result, the only mechanism through which private sector debt can change is through savings. Because with zero initial private sector debt both debt-financed and tax-financed government spending do not alter disposable income (as seen from equations (24) and (25)), it follows that these policies do not affect private sector saving. Hence, if the initial position was that of a long-run equilibrium with zero savings and zero debt, the instantaneous short-run equilibrium following the rise in government spending is also characterized by zero savings. This implies that the economy converges immediately to its new long-run equilibrium.

The foregoing analysis of the long-run consequences of government spending has abstracted from the debt-revaluation effect that arises from exchange rate changes. In general, if in the initial equilibrium the level of private sector debt differs from zero, then the debt-revaluation effect breaks the coincidence between the short- and the long-run fiscal policy multipliers. Using the system of equations (28)–30, the long-run effects of a debt-financed rise in government spending are

\frac{d Y}{d G} = 0, f o r d T = 0 (31)

\frac{d B_{f}^{p}}{d G} = \frac{(1 - a^{g}) B_{f}^{p}}{e {\bar{D}}^{*}}, f o r d T = 0 (32)

\frac{d e}{d G} = \frac{(1 - a^{g})}{{\bar{D}}^{*}}, f o r d T = 0. (33)

Similarly, the long-run effects of a balanced-budget rise in government spending are

\frac{d Y}{d G} = 1, f o r d T = d G (34)

\frac{d B_{f}^{p}}{d G} = \frac{a^{g} B_{f}^{p}}{e {\bar{D}}^{*}}, f o r d T = d G (35)

\frac{d e}{d G} = \frac{a^{g}}{{\bar{D}}^{*}}, f o r d T = d G . (36)

These results show that, independent of the debt-revaluation effects, a rise in government spending does not alter the long-run level of output if it is debt financed, whereas the same rise in government spending raises the long-run level of output by a unit multiplier if it is tax financed. Thus, in both cases the long-run level of disposable income, Y – T, is independent of government spending. The results also show that if government spending is debt financed, then, in the long run, if initial private sector debt was positive, the debt rises while the currency appreciates. The opposite holds for the case in which government spending is tax financed.

In comparing the extent of the long-run changes in private sector debt -with the corresponding changes in the exchange rate, we note that the value of debt, $e B_{f}^{p}$ (measured in units of domestic output), remains unchanged. This invariance facilitates the interpretation of the long-run multipliers. Accordingly, consider the long-run equilibrium system of equations (28)–30 and suppose that government spending is debt financed. In that case, as is evident from the money-market equilibrium condition (30), the equilibrium level of output does not change as long as the money supply, taxes, and the value of the debt commitment are given. Because, however, the rise in government spending creates an excess demand for domestic output, it can be seen from equation (29) that the currency must appreciate (that is, e must fall) so as to lower the value of foreign demand, eD^*, and thereby maintain equilibrium output unchanged. Obviously, since e falls, (the absolute value of) private sector debt, B^p_f must rise by the same proportion so as to maintain the product eB^p_f unchanged. Finally, these changes ensure that the zero-saving condition (28) is also satisfied. A similar interpretation can be given to the effects of a tax-financed rise in government spending, except that in this case the level of output rises in line with the rise in taxes so as to keep disposable income unchanged.

A comparison between these long-run effects and the corresponding short-run effects shown in equations (24) and (25) reveals that the relative magnitudes of these multipliers depend on the initial debt position. For example, if the initial debt commitment is positive but smaller than export earnings, then the short-run multiplier of tax finance is positive and larger than unity. In this case the long-run multipliers are more moderate than the corresponding short-run multipliers. If, however, the initial debt commitment exceeds export earnings, then the short-run debt-finance multiplier is positive (in contrast with the long-run multiplier), and the short-run tax-finance multiplier is smaller than unity (and could even be negative, in contrast to the unitary long-run balanced-budget multiplier).

Fiscal Policies in a Two-Country World

In this section we extend the analysis of the small-country case to the two-country model outlined in equations (20)–23. To develop a diagrammatic apparatus useful for the analysis of fiscal policies, we proceed in three steps. First, we trace the combinations of domestic and foreign output levels that clear each country’s goods market, incorporating market-clearing conditions in the two national money markets (which under flexible exchange rates are the two nontradable assets). Second, we trace the combinations of domestic and foreign output levels that bring about money-market equilibrium in each country and, at the same time, yield equality between the domestic and the foreign rates of interest, thereby conforming with the assumption of perfect capital mobility. Finally, in the third step, we find the unique combination of domestic and foreign levels of output that satisfy simultaneously the considerations underlying the first two steps.

Using the domestic money-market equilibrium condition (22), we can express the domestic money-market-clearing rate of interest, r_t, as a positive function of disposable resources, Y, – T_t + A_t–1 and as a negative function of the domestic money stock, M; that is, r_t = r(Y_t– T_t + A_t–1, M). Applying a similar procedure to the foreign country, we can express the foreign money-market-clearing rate of interest, r_t, as a function of foreign disposable resources and money stock; that is, $r_{t}^{*} = r^{*} (Y_{t}^{*} + A_{t - 1}^{*}, M^{*})$ , where $A_{t - 1}^{*} = M_{t - 1}^{*} + R_{t - 1} B_{t - 1}^{p} / e_{t}$ . By substituting these money-market-clearing rates of interest into the goods-market equilibrium conditions (20) and (21), we obtain the reduced-form equilibrium conditions:

(1 - β_{m}) \tilde{E} (Y_{t} - T_{t} + A_{t - 1}, M) + (1 - β_{m}^{g}) G + e_{t} β_{x}^{*} {\tilde{E}}^{*} (Y_{t}^{*} + A_{t - 1}^{*}, M^{*}) = Y_{t} (37)

β_{m} {\tilde{E}}^{*} (Y_{t} - T_{t} + A_{t - 1}, M) + β_{m}^{g} G + e_{t} (1 - β_{x}^{*}) {\tilde{E}}^{*} (Y_{t}^{*} + A_{t - 1}^{*}, M^{*}) = e_{t} Y_{t}^{*}, (38)

where a tilde (-) indicates a reduced-form function incorporating the money-market equilibrium conditions. For each and every value of the exchange rate, e_t, equations (37) and (38) yield the equilibrium combination of domestic and foreign output that clears the world markets for both goods. The schedule ee in Figure 10 traces these equilibrium output levels for alternative values of the exchange rate. The detailed derivation of this schedule is provided in Appendix II, where it is shown that—around balanced-trade equilibria with a zero initial private sector debt (so that exchange rate changes do not exert revaluation effects)—this schedule is negatively sloped. In general, the ee schedule is negatively sloped if a rise in the exchange rate (a deterioration in the terms of trade) raises the world demand for domestic output and lowers the world demand for foreign output, allowing for the proper adjustments in each country’s rate of interest so as to clear the national money market.

Figure 10.

A Debt-Financed Unit Rise in Government Spending Under Flexible Exchange Rates: The Two-Country Case

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A001

N o t e : I M_{0} = I M_{0}^{*}; B_{f, - 1}^{p} = 0

So far we have not introduced the constraint imposed by the perfect international mobility of capital. To incorporate this constraint, the two national money-market-clearing rates of interest, r_t and $r_{t}^{*}$ must equal each other. This equally implies that

r (Y_{t} - T_{t} + A_{t - 1}, M) = r^{*} (Y_{t}^{*} + A_{t - 1}^{*}, M^{*}) . (39)

The combinations of domestic and foreign output levels conforming with the perfect capital mobility requirement are portrayed by the rr^* schedule in Figure 10. With a zero level of initial debt (so that the debt-revaluation effects induced by exchange rate changes are absent), this schedule is positively sloped because a rise in domestic output raises the demand for domestic money and raises the domestic rate of interest. International equalization of interest rates is restored through a rise in foreign output that raises the foreign demand for money and the foreign interest rate.

The short-run equilibrium is indicated by point A in Figure 10. At this point both goods markets clear, both national money markets clear, and the rates of interest are equalized internationally. The levels of output corresponding to this equilibrium are Y₀ and $Y_{0}^{*}$

A debt-financed unit rise in government spending alters the position of the goods-market equilibrium schedule ee but does not affect the capital market equilibrium schedule rr^*. It is shown in Appendix II that, for an initial trade balance equilibrium with zero debt, the ee schedule shifts to the right by $1 / \bar{s}$ units. The new equilibrium is indicated by point B in Figure 10. Thus (in the absence of revaluation effects), in the new short-run equilibrium both the domestic and the foreign levels of output rise, respectively, from Y₀ and $Y_{0}^{*}$ to Y₁ and Y^*₁

For the given supply of money and for the higher level of output (which raises the demand for money), money-market equilibrium obtains at a higher rate of interest (which restores money demand to its initial level). Finally, it is shown in Appendix II that the exchange rate effects of the debt-financed rise in government spending are not clear-cut but reflect transfer-problem criteria. These criteria embody the relative pressures on the rates of interest in the domestic and foreign money markets that are induced by the changes in world demand for domestic and foreign output. If these pressures tend to raise the domestic rate of interest above the foreign rate, then the domestic currency must appreciate so as to lower the demand for domestic output and reduce the upward pressure on the domestic interest rate. The opposite follows in the converse circumstances. But, if the behavioral parameters of the two private sectors are equal to each other, then the domestic currency must appreciate.

A tax-financed unit rise in government spending alters the position of both the ee and the rr^* schedules. As is evident from equations (37)–39, both schedules shift to the right by one unit. This case is illustrated in Figure 11, in which the initial equilibrium is indicated by point A and the new short-run equilibrium by point B. At the new equilibrium the domestic level of output rises by one unit, so that disposable income remains unchanged. With unchanged levels of disposable income, the demand for money is not altered, and the initial equilibrium rate of interest remains intact. As a result the initial equilibrium in the foreign economy is not disturbed, and the foreign level of output remains unchanged. Finally, to eliminate the excess supply in the domestic goods market that arises from the increase in domestic output and the unchanged level of disposable income, the currency must depreciate so as to raise the domestic currency value of the given foreign demand. It follows that, in the absence of revaluation effects, the flexible exchange rate regime permits a full insulation of the foreign economy from the consequences of the domestic tax-financed fiscal policies. The more general results, which allow for revaluation effects, are provided in Appendix II. Analogous to the procedure adopted in the fixed exchange rate case, we do not analyze explicitly here the long-run equilibrium of the two-country world under the flexible exchange rate regime. The formal equilibrium system applicable for such an analysis is presented in the second section of Appendix II.

Figure 11.

A Tax-Financed Unit Rise in Government Spending Under Flexible Exchange Rates: The Two-Country Case

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A001

N o t e : I M_{0} = I M_{0}^{*}; B_{f, - 1}^{p} = 0

IV. Summary and Overview

In this paper we have analyzed the effects of government spending under fixed and flexible exchange rate regimes in a unified exposition of the Mundell-Fleming model. We assumed throughout that the world Capital markets are highly integrated, so that capital is perfectly mobile internationally. To conserve space, we focused on the pure effects of fiscal policies and assumed that there is no active monetary policy. In particular, we abstracted from money-financed government spending and, accordingly, analyzed the predictions of the Mundell-Fleming model with respect to the short-run and long-run consequences of debt-financed and tax-financed changes in government spending. In this context we focused on the effects of fiscal policies on the levels of output, debt, and the rate of interest under the two alternative exchange rate regimes. In addition, for the fixed exchange rate regime we examined the induced changes in the money supply; for the flexible exchange rate regime we determined the induced change in the exchange rate.

The short-run and long-run effects of a unit debt-financed and tax-financed rise in government spending for a small country facing a fixed world interest rate are summarized in Table 1. This table shows the various multipliers applicable to the fixed as well as to the flexible exchange rate regimes. The output multipliers under the fixed exchange rate regime are the typical, textbook version of the foreign trade multipliers. These results were entirely expected, since the rate of interest is exogenously given to the small country. The fixity of the rate of interest implies that the typical crowding-out mechanism induced by changes in the rate of interest is not present.

Table 1.

Short- and Long-Run Multipliers of a Unit Rise in Government Spending Under Fixed and Flexible Exchange Rates: The Small-Country Case

Note: See the text for definitions of the affected variables.

{\bar{D}}^{*}

denotes export earnings measured in units of foreign currency;

R_{f} = 1 + {\bar{r}}_{f};

and

Δ = a - {\bar{r}}_{f} (s - M_{y}),

where ∆ > 0 under the assumption that a rise in income worsens the current account of the balance of payments. For stability, the term

1 - s - {\bar{r}}_{f} = (s - M_{y}) > 0.

Table 1.

Short- and Long-Run Multipliers of a Unit Rise in Government Spending Under Fixed and Flexible Exchange Rates: The Small-Country Case

Affected Variable	Multiplier
	Debt-financed rise		Tax-financed rise
	Short-run	Long-run	Short-run	Long-run
		Fixed Exchange Rates
Y	$\frac{1 - a^{g}}{s + a}$	$\frac{1 - a^{g}}{Δ} [1 - s - {\bar{r}}_{f} (s M_{y})]$	$1 - \frac{a^{g}}{s + a}$	$1 - \frac{a^{g}}{s + a} [1 - s - {\bar{r}}_{f} (s - M_{y})])$
$B_{f, t - 1}^{ρ}$	0	$- \frac{1 - a^{g}}{Δ} (s - M_{y})$	0	$\frac{a^{g}}{Δ} (s - M_{y})$
M	$\frac{(1 - a^{g}) M_{y}}{s + a}$	$\frac{(1 - a^{g})}{Δ} M_{y}$	$- \frac{a^{g}}{s + a} M_{y}$	$\frac{a^{g}}{Δ} M_{y}$
		Fixed Exchange Rates
Y	$\frac{(1 - a^{g}) R_{f} B_{f, t - 1}^{ρ}}{R_{f} B_{f, t - 1}^{ρ} - {\bar{D}}^{*}}$	0	$1 - \frac{a^{g} R_{f} B_{f, t - 1}^{ρ}}{R_{f} B_{f, t - 1}^{ρ} - {\bar{D}}^{*}}$	1
$B_{f, t - 1}^{ρ}$	0	$\frac{(1 - a^{g}) B_{f}^{ρ}}{e {\bar{D}}^{*}}$	0	$- \frac{a^{g} G_{f}^{ρ}}{e {\bar{D}}^{*}}$
e	$\frac{(1 - a^{g})}{R_{f} B_{f, t - 1}^{ρ} - {\bar{D}}^{*}}$	$- \frac{(1 - a^{g})}{{\bar{D}}^{*}}$	$1 - \frac{a^{g}}{R_{f} B_{f, t - 1}^{ρ} - {\bar{D}}^{*}}$	$\frac{a^{g}}{{\bar{D}}^{*}}$

Note: See the text for definitions of the affected variables.

{\bar{D}}^{*}

denotes export earnings measured in units of foreign currency;

R_{f} = 1 + {\bar{r}}_{f};

and

Δ = a - {\bar{r}}_{f} (s - M_{y}),

where ∆ > 0 under the assumption that a rise in income worsens the current account of the balance of payments. For stability, the term

1 - s - {\bar{r}}_{f} = (s - M_{y}) > 0.

Table 1.

Short- and Long-Run Multipliers of a Unit Rise in Government Spending Under Fixed and Flexible Exchange Rates: The Small-Country Case

Affected Variable	Multiplier
	Debt-financed rise		Tax-financed rise
	Short-run	Long-run	Short-run	Long-run
		Fixed Exchange Rates
Y	$\frac{1 - a^{g}}{s + a}$	$\frac{1 - a^{g}}{Δ} [1 - s - {\bar{r}}_{f} (s M_{y})]$	$1 - \frac{a^{g}}{s + a}$	$1 - \frac{a^{g}}{s + a} [1 - s - {\bar{r}}_{f} (s - M_{y})])$
$B_{f, t - 1}^{ρ}$	0	$- \frac{1 - a^{g}}{Δ} (s - M_{y})$	0	$\frac{a^{g}}{Δ} (s - M_{y})$
M	$\frac{(1 - a^{g}) M_{y}}{s + a}$	$\frac{(1 - a^{g})}{Δ} M_{y}$	$- \frac{a^{g}}{s + a} M_{y}$	$\frac{a^{g}}{Δ} M_{y}$
		Fixed Exchange Rates
Y	$\frac{(1 - a^{g}) R_{f} B_{f, t - 1}^{ρ}}{R_{f} B_{f, t - 1}^{ρ} - {\bar{D}}^{*}}$	0	$1 - \frac{a^{g} R_{f} B_{f, t - 1}^{ρ}}{R_{f} B_{f, t - 1}^{ρ} - {\bar{D}}^{*}}$	1
$B_{f, t - 1}^{ρ}$	0	$\frac{(1 - a^{g}) B_{f}^{ρ}}{e {\bar{D}}^{*}}$	0	$- \frac{a^{g} G_{f}^{ρ}}{e {\bar{D}}^{*}}$
e	$\frac{(1 - a^{g})}{R_{f} B_{f, t - 1}^{ρ} - {\bar{D}}^{*}}$	$- \frac{(1 - a^{g})}{{\bar{D}}^{*}}$	$1 - \frac{a^{g}}{R_{f} B_{f, t - 1}^{ρ} - {\bar{D}}^{*}}$	$\frac{a^{g}}{{\bar{D}}^{*}}$

Note: See the text for definitions of the affected variables.

{\bar{D}}^{*}

denotes export earnings measured in units of foreign currency;

R_{f} = 1 + {\bar{r}}_{f};

and

Δ = a - {\bar{r}}_{f} (s - M_{y}),

where ∆ > 0 under the assumption that a rise in income worsens the current account of the balance of payments. For stability, the term

1 - s - {\bar{r}}_{f} = (s - M_{y}) > 0.

Under flexible exchange rates the short-run output multipliers of fiscal policies depend crucially on the debt-revaluation effect induced by exchange rate changes. Indeed, in the absence of such an effect (as would be the case if the initial debt position were zero), fiscal policies lose their capacity to alter disposable income. Accordingly, with debt finance the output multiplier is zero, and with tax finance the corresponding multiplier is unity. In general, however, the signs and magnitudes of the short-run output multipliers depend on the size of the initial debt. In contrast, these considerations do not influence the long-run output multipliers. As can be seen in the table, with perfect capital mobility and flexible exchange rates, the long-run value of disposable income cannot be affected by fiscal policies.

One of the important points underscored by the results reported in Table 1 is the critical dependence of the direction of change in the key variables on the means of fiscal finance. Specifically, a shift from a debt-financed unit rise in government spending to a tax-financed unit rise reverses the signs of the multipliers of $B_{f}^{p}$ , M, and e.

For example, a tax-financed rise in government spending under a fixed exchange rate regime induces a balance of payments deficit and reduces both short- and long-run money holdings. In contrast, a similar rise in government spending that is debt financed induces a surplus in the balance of payments and raises money holdings in the short run as well as in the long run. Similarly, under a flexible exchange rate regime the tax-financed rise in government spending depreciates the long-run value of the currency, whereas the debt-financed rise in government spending appreciates the long-run value of the currency. As indicated earlier, a similar reversal in the direction of the change in the exchange rate also pertains in the short run, but whether the currency depreciates or appreciates in the short run depends on the size of the debt, which in turn governs the debt-revaluation effect.

To study the characteristics of the international transmission mechanism, we extended the exposition of the Mundell-Fleming model to a two-country model of the world economy. The new channel of transmission is the world interest rate, which is determined in the unified world capital market. Table 2 summarizes the short-run effects of fiscal policies under the two alternative exchange rate regimes. To avoid a tedious taxonomy, the summary results for the flexible exchange rates reported in the table are confined to the case in which the twin revaluation effects—debt revaluation and trade balance revaluation—induced by exchange rate changes are absent; it is accordingly assumed that the initial debt is zero and that the initial equilibrium obtains with balanced trade.

Table 2.

Direction of Short-Run Effects of a Rise in Government Spending Under Fixed and Flexible Exchange Rates: The Two-Country World

Note: See the text for definitions of the affected variables. The signs indicated for the case of flexible exchange rates are applicable to the case of an initial equilibrium with balanced trade and zero initial debt. For the fixed exchange rate regime, H_r and F_r denote, respectively, the negative effect of the rate of interest on the world demand for domestic and foreign goods;

A = s / M_{y} - s^{*} / M_{y} .;

B = \bar{e} (M_{y} / M_{r}) [a^{*} + s^{*} (1 - a^{g})] - (M_{y}^{*} . / M_{r}^{*}) (a + s a^{g});

and

C = M_{y} M_{y}^{*} \cdot M_{r} M_{r}^{*}

[F_{r} (1 - a^{g}) - H_{r} a^{g}]

For the flexible exchange rate regime,

B = e_{t} (M_{y} / M_{r})

[a^{*} + {\bar{s}}^{*} (1 - a^{g})] - (M_{y}^{*} \cdot / M_{r}^{*}) (\bar{a} + \bar{s} a^{g}) .

Table 2.

Direction of Short-Run Effects of a Rise in Government Spending Under Fixed and Flexible Exchange Rates: The Two-Country World

	Expected Sign of Short-Run Effect
Affected Variable	Debt-financed rise	Tax-financed rise
	Fixed Exchange Rates
Y	+ (for small H_r)	+ (for a^g≤a)
Y^*	+ (for small F_r)	+
r	+	+ (for A > 0)M –(for A < 0)
M	+ (for B + C < 0) (for B + C > 0)	–
	Fixed Exchange Rates
Y	+	+
Y^*	+	0
r	+	0
e	+(for B > 0)	+
	+(for B < 0)

A = s / M_{y} - s^{*} / M_{y} .;

B = \bar{e} (M_{y} / M_{r}) [a^{*} + s^{*} (1 - a^{g})] - (M_{y}^{*} . / M_{r}^{*}) (a + s a^{g});

and

C = M_{y} M_{y}^{*} \cdot M_{r} M_{r}^{*}

[F_{r} (1 - a^{g}) - H_{r} a^{g}]

For the flexible exchange rate regime,

B = e_{t} (M_{y} / M_{r})

[a^{*} + {\bar{s}}^{*} (1 - a^{g})] - (M_{y}^{*} \cdot / M_{r}^{*}) (\bar{a} + \bar{s} a^{g}) .

Table 2.

Direction of Short-Run Effects of a Rise in Government Spending Under Fixed and Flexible Exchange Rates: The Two-Country World

	Expected Sign of Short-Run Effect
Affected Variable	Debt-financed rise	Tax-financed rise
	Fixed Exchange Rates
Y	+ (for small H_r)	+ (for a^g≤a)
Y^*	+ (for small F_r)	+
r	+	+ (for A > 0)M –(for A < 0)
M	+ (for B + C < 0) (for B + C > 0)	–
	Fixed Exchange Rates
Y	+	+
Y^*	+	0
r	+	0
e	+(for B > 0)	+
	+(for B < 0)

A = s / M_{y} - s^{*} / M_{y} .;

B = \bar{e} (M_{y} / M_{r}) [a^{*} + s^{*} (1 - a^{g})] - (M_{y}^{*} . / M_{r}^{*}) (a + s a^{g});

and

C = M_{y} M_{y}^{*} \cdot M_{r} M_{r}^{*}

[F_{r} (1 - a^{g}) - H_{r} a^{g}]

For the flexible exchange rate regime,

B = e_{t} (M_{y} / M_{r})

[a^{*} + {\bar{s}}^{*} (1 - a^{g})] - (M_{y}^{*} \cdot / M_{r}^{*}) (\bar{a} + \bar{s} a^{g}) .

As shown, independent of the exchange rate regime, a debt-financed rise in government spending raises the world interest rate. Under the flexible exchange rate regime, the debt-financed rise in government spending stimulates demand for both domestic and foreign goods and causes an expansion in the output of both. Thus, in this case the international transmission of the rise in government spending, measured by the comovements of domestic and foreign output, is positive. In contrast, under a fixed exchange rate regime the rise in the world interest rate may offset the direct effect of government spending on aggregate demand and may cause lowered output. But if the (negative) interest rate effect on aggregate demand is relatively weak, then both domestic and foreign output rise, thereby resulting in a positive international transmission. Finally, we note that there is no presumption about the direction of change in money holdings (under fixed exchange rates) and in the exchange rate (under flexible exchange rates) in response to the debt-financed fiscal expansion. As indicated, depending on the relative magnitudes of the domestic and foreign propensities to save and to import, and on the domestic and foreign sensitivities of money demand with respect to changes in the rate of interest and income, the balance of payments may be in deficit or in surplus, and the currency may depreciate or appreciate.

The results in Table 2 also highlight the significant implications of alternative means of budgetary finance. Indeed, in contrast to debt finance, a tax-financed rise in government spending under a flexible exchange rate regime leaves the world interest rate unchanged, raises domestic output, and depreciates the currency. The reduction in the domestic private sector demand for foreign output, induced by the depreciation of the currency, precisely offsets the increased demand induced by the rise in government spending. As a result, foreign output remains intact, and the flexible exchange rate regime fully insulates the foreign economy from the domestic tax-financed fiscal policy. In this case the analysis of the two-country world economy reduces to the one carried out for the small-country case. Therefore, the long-run multipliers for the two countries operating under flexible exchange rates coincide with the short-run multipliers, the domestic short-run and long-run output multipliers are unity, and the corresponding foreign output multipliers are zero.

In contrast to the flexible exchange rate regime, in which the currency depreciates to the extent needed to maintain world demand for (and thereby the equilibrium level of) foreign output unchanged, the fixed exchange rate regime does not contain this insulating mechanism. As a result, the tax-financed rise in domestic government spending raises the world demand for (and thereby the equilibrium level of) foreign output. Depending on the relative magnitude of the domestic government’s propensity to import, however, the domestic level of output may rise or fall. But if the government’s propensity to import does not exceed the corresponding propensity of the private sector, then domestic output rises, and the international transmission, measured by the comovements of domestic and foreign output, is positive. Finally, because at the prevailing rate of interest domestic disposable income falls and foreign disposable income rises, these changes in disposable incomes alter the world demand for money and necessitate equilibrating changes in the world interest rate. As shown in Table 2, the change in the world demand for money (at the prevailing rate of interest) reflects a transfer-problem criterion. If the ratio of the domestic propensities to save and to hoard, s/M_y, exceeds the corresponding foreign ratio, $s^{*} / M_{y}^{*} \cdot$ , then the international redistribution of disposable income raises the world demand for money and necessitates a rise in the world interest rate. The opposite holds if s/M_y falls short of $s^{*} / M_{y}^{*} \cdot$ Independent, however, of the direction of the change in the world interest rate, the tax-financed rise in government spending must worsen the domestic balance of payments and lower the short-run equilibrium of domestic money holdings.

Throughout the exposition of the model it was assumed that expectations were static. Because the actual exchange rates do change under flexible exchange rates, the assumption that exchange rate expectations are static results in expectational errors during the period of transition toward the long-run equilibrium. The incorporation of a consistent expectations scheme into the Mundell-Fleming model introduces an additional mechanism governing short-run behavior. Aspects of this mechanism are examined in the final section of Appendix II.

We conclude this summary with an overview of the Mundell-Fleming model. A key characteristic of the formulation of the income-expenditure framework underlying the Mundell-Fleming model is the lack of solid microeconomic foundations for the behavior of the private and public sectors, and the absence of an explicit rationale for the holdings of zero interest-bearing money in the presence of safe interest-bearing bonds. The latter issue is of relevance in view of the central role played by monetary flows in the international adjustment mechanism. Furthermore, no attention was given to the intertemporal budget constraints, and the behavior of both the private and the public sectors was not forward-looking in a consistent manner. As a result, there is no mechanism ensuring that the patterns of spending, debt accumulation, and money hoarding—which are the key elements governing the equilibrium dynamics of the economic system—are consistent with the relevant economic constraints. The implication of this shortcoming is that, in determining the level and composition of spending, saving, and asset holdings, the private sector does not incorporate explicitly the intertemporal consequences of government policies.

To illustrate the significance of this issue, consider a debt-financed rise in current government spending. A proper formulation of the government’s intertemporal budget constraint must recognize that, to service the debt and maintain its solvency, the government must accompany a current fiscal expansion either by cutting future spending or by raising future (ordinary or inflationary) taxes. Furthermore, a proper specification of the private sector’s behavior must allow for the fact that forward-looking individuals may recognize the future consequences of current government policies and incorporate these expected consequences into their current as well as planned future spending, saving, and asset holdings.

The Mundell-Fleming model presented in this paper assumes that producer prices are given and that outputs are demand determined. In this framework nominal exchange rate changes amount to changes in the terms of trade. As a result, the key characteristics of the economic system are drastically different across alternative exchange rate regimes. More recent theoretical research has relaxed the fixed-price assumption and has allowed for complete price flexibility. With this flexibility, prices are always at their market-clearing equilibrium levels. Changes in the terms of trade induced by equilibrium changes in prices therefore trigger an adjustment mechanism that is analogous to the one triggered by nominal exchange rate changes in the Mundell-Fleming model.

The neglect of the intertemporal budget constraints and of the consequences of forward-looking behavior consistent with these constraints are among the main limitations of the model. Recognition of these limitations provides both the rationale for and the bridge to the growing body of newer theoretical developments aiming to rectify these shortcomings. This more current literature develops models that are derived from optimizing behavior that is consistent with the relevant temporal and intertemporal economic constraints. The resultant macroeconomic model that is grounded on solid microeconomic foundations is capable of dealing with new issues in a consistent manner. Among these issues are the effects of various time patterns of government spending and taxes. The newer literature thus distinguishes between temporary and permanent, as well as between current and future, policies. Similarly, such an approach is capable of analyzing the macroeconomic consequences of alternative specifications of the tax structure and, therefore, can distinguish between the effects of different types of taxes (such as income taxes, value-added taxes, and international capital flow taxes) used to finance the budget. An illustration of this literature is contained in Frenkel and Razin (1987). An important feature of the more current approach is that, being grounded on microeconomic foundations, it is capable of dealing explicitly with the welfare consequences of economic policies. This feature reflects the basic attribute of the macroeconomic model: the economic behavior underlying this model is derived from, and is consistent with, the principles of individual utility maximization. Therefore, in contrast to the traditional approach, the intertemporal optimizing approach provides a framework suitable for the normative evaluation of international macroeconomic policies.

APPENDIX I

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

E [Y - G + M - B^{p} - {\bar{r}}_{f} (B^{p} + B^{g}), {\bar{r}}_{f}] + G = Y - {\bar{r}}_{f} (B^{p} + B^{g}) (40)

(1 - β_{m}) E [Y - G + M - B^{p} - {\bar{r}}_{f} (B^{p} + B^{g}), {\bar{r}}_{f}] + (1 - β_{m}^{g}) G + \bar{e} {\bar{D}}^{*} = Y (41)

M [Y - G + M - B^{p} - {\bar{r}}_{f} (B^{p} + B^{g}), {\bar{r}}_{f}] = M . (42)

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

[\begin{matrix} - s & s (1 + {\bar{r}}_{f}) - 1 \\ M_{y} & - (1 + {\bar{r}}_{f}) M_{y} \end{matrix}] [\begin{matrix} d Y \\ d B^{p} \end{matrix}] = [\begin{matrix} - (1 - s) \\ 1 - M_{y} \end{matrix}] d M, (43)

where s = 1 – E_y and a = β_mE_y. 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

[\begin{matrix} - (s + a) & - (1 + {\bar{r}}_{f}) (1 - s - a) - 1 \\ M_{y} & - (1 + {\bar{r}}_{f}) M_{y} \end{matrix}] [\begin{matrix} d Y \\ d B^{p} \end{matrix}] = [\begin{matrix} - (1 - s - a) \\ 1 - M_{y} \end{matrix}] d M (44)

Following a similar procedure, we obtain the expression for dB^p/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 B^p constant. Accordingly, equation (40) implies that (1 – s)(dY – dG + dM) = dY – dG, and equation (42) implies that dM = M_y(dY – dG)t(1 – M_y). 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 B^P constant. Equation (41) implies that (1 – s – a)(dY – dG + dM) + (1 – a⁸)dG = dY, where $a^{g} = β_{m}^{g}$ and equation (42) implies that dM = M_y(dY – dG)/(1 – M_y). Substituting the latter into the former shows that the horizontal shift of the YY schedule is

1 - \frac{(1 - M_{y}) a^{g}}{s + a - M_{y}} .

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,

\begin{matrix} [\begin{matrix} - s & s (1 + {\bar{r}}_{f}) - 1 & 1 - a \\ - (s + a) & - (1 + {\bar{r}}_{f}) (1 - s - a) & 1 - s - a \\ M_{y} & - (1 + {\bar{r}}_{f}) M_{y} & - (1 - M_{y}) \end{matrix}] [\begin{matrix} d Y \\ d B^{p} \\ d M \end{matrix}] \\ = [\begin{matrix} 0 \\ - (1 - a^{g}) \\ 0 \end{matrix}] d G + [\begin{matrix} - s \\ 1 - s - a \\ M_{y} \end{matrix}] d T . & (45) \end{matrix}

Using this system, one finds that the long-run effects of a debt-financed rise in government spending (that is, dT = 0) are

\frac{d Y_{t}}{d G} = \frac{1 - a^{g}}{Δ} [1 - s - {\bar{r}}_{f} (s - M_{y})] \geq 0, f o r d T_{t} = 0 (46)

\frac{d B^{p}}{d G} = - \frac{1 - a^{g}}{Δ} (s - M_{y}) \leq 0, f o r d T_{t} = 0 (47)

\frac{d M}{d G} = - \frac{1 - a^{g}}{Δ} M_{y} \geq 0, f o r d T_{t} = 0, (48)

where $Δ = a - {\bar{r}}_{f} (s - M_{y) > 0,}$ under the assumption that a rise in income worsens the current account of the balance of payments. Correspondingly, the long-run effects of a balanced-budget rise in government spending (that is, dG = dT) are

\frac{d Y}{d G} = 1 - \frac{a^{g}}{Δ} [1 - s - {\bar{r}}_{f} (s - M_{y})] ≷ 0, f o r d G = d T_{t} (49)

\frac{d B^{p}}{d G} = \frac{a^{g}}{Δ} (s - M_{y}) \geq 0, f o r d G = d T_{t} (50)

\frac{d M}{d G} = - \frac{a^{g}}{Δ} M_{y} \leq 0, f o r d G = d T_{t} . (51)

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 Y_t, $Y_{t}^{*}$ and r_t. The YY and Y^*Y^* schedules in Figure 4 show combinations of Y_t and $Y_{t}^{*}$ that clear the markets for domestic and foreign output, respectively. Both of these schedules incorporate the world money-market equilibrium condition (7) of the text. To derive the slope of the YY schedule, we differentiate equations (5) and (7) of the text to yield

[\begin{matrix} - (s + a) & \bar{e} a^{*} \\ M_{y} & \bar{e} M_{y}^{*} \cdot \end{matrix}] [\begin{matrix} d Y_{t} \\ d Y_{t}^{*} \end{matrix}] = - [\begin{matrix} H_{r} \\ (M_{r} + \bar{e} M_{r}^{*}) \end{matrix}] d r_{t}, (52)

where H_r denotes the partial (negative) effect of a change in the rate of interest on the world demand for domestic output; that is, $H_{r} = (1 - β_{m}) E_{r} + \bar{e} β_{x}^{*} E_{r}^{*},$ where E_r, M_r, E^*_r and M^*_r denote the partial (negative) effects of the rate of interest on domestic and foreign spending and money demand. To eliminate r_t, from the goods-market equilibrium schedule, we solve equation (52) for dY₁/dr_t and $d Y_{t}^{*} / d r_{t}$ for and divide the solutions by each other. This yields

\frac{d Y_{t}^{*}}{d Y t} = \frac{1}{\bar{e}} \frac{(s + a) (M_{r} + \bar{e} M_{r}^{*}) + M_{y} H_{r}}{a * (M_{r} + e M_{r}^{*}) - M_{r}^{*} . H_{r}}, alone the YY schedule. (53)

Analogously, differentiating equations (13) and (14) of the text yields

[\begin{matrix} a \\ M_{y} \end{matrix} \begin{matrix} - \bar{e} (s * + a *) \\ \bar{e} M_{y}^{*} . \end{matrix}] [\begin{matrix} d y_{t} \\ d Y_{t}^{*} \end{matrix}] = - [\begin{matrix} F_{r} \\ M_{r} + \bar{e} M_{r}^{*} \end{matrix}] d r, (54)

where $F_{r} = β_{m} E_{r} + \bar{e} (1 - β_{r}^{*})$ denotes the partial (negative) effect of the rate of interest on the world demand for foreign output. Applying a similar procedure as before, we find that the slope of the Y^*Y^* schedule is

\frac{d Y_{t}^{*}}{d Y_{t}} = \frac{1}{\bar{e}} \frac{a (M_{r} + \bar{e} M_{r}^{*}) - M_{y} F_{r}}{(s * + a *) (M_{r} + \bar{e} M_{r}^{*}) + M_{y}^{*} . F_{r}}, along the Y*Y* schedule. (55)

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 $a (M_{r} + e M_{r}^{*})$ is augmented by additional negative quantities, whereas the same negative quantity in the numerator of equation (55) is augmented by an additional positive quantity. A similar comparison of the denominators of equations (53) and (55) shows that the negative quantity $a * (M_{r} + e M_{r}^{*})$ is augmented by additional negative quantities in equation (55) and by a positive quantity in equation (53). Second, if both schedules are negatively sloped, then by subtracting one slope from the other it can be verified that the Y^*Y_* schedule cannot be steeper than the YY schedule. These considerations imply that, for all situations in which there is a rightward shift of the YY schedule exceeding the rightward shift of the Y^*Y_* schedule, the new equilibrium must be associated with a higher level of domestic output.

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

\frac{d Y}{d G} = \frac{1 - a^{g}}{s + a + \frac{M_{y} H_{r}}{M_{r} + \bar{e} M_{r}^{*}}} \geq 0, for the YY schedule (56)

\frac{d Y}{d G} = \frac{- a^{g}}{a - \frac{M_{y} F_{r}}{M_{r} + \bar{e} M_{r}^{*}}} \geq 0, for the Y*Y* schedule (57)

The corresponding shifts for the tax-financed rise in government spending are

\frac{d Y}{d G} = 1 - \frac{a^{g}}{s + a + \frac{M_{y} H_{r}}{M_{r} + \bar{e} M_{r}^{*}}} \geq 0, for the schedule (58)

\frac{d Y}{d G} = 1 - \frac{a^{g}}{a - \frac{M_{y} F_{r}}{M_{r} + \bar{e} M_{r}^{*}}} \leq 0, for the Y*Y* schedule. (59)

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,

[\begin{matrix} - (s + a) & \bar{e} a * & H_{r} \\ a & - \bar{e} (s * + a *) & F_{r} \\ M_{y} & \bar{e} M_{y}^{*} . & M_{r} + \bar{e} M_{r}^{*} \end{matrix}] [\begin{matrix} d Y_{t} \\ d Y_{t}^{*} \\ d r_{t} \end{matrix}] = - [\begin{matrix} 1 - a^{g} \\ a^{g} \\ 0 \end{matrix}] d G + [\begin{matrix} 1 - s - a \\ a \\ M_{y} \end{matrix}] d T_{r} (60)

With a debt-financed rise in government spending, dT_t =0; thus, the short-run effects are

\frac{d Y_{t}}{d G} = \frac{1}{Δ} {[s* (1 - a^{g}) + a *] (M_{r} + \bar{e} M_{r}^{*}) + M_{y}^{*} . {[F}_{r} (1 - a^{g}) - a^{g} H_{r}]}, (61)

\frac{d Y_{t}^{*}}{d G} = \frac{1}{\bar{e} Δ} {(s a^{g} + a) (M_{r} + \bar{e} M_{r}^{*}) - M_{y} {[F}_{r} (1 - a^{g}) - a^{g} H_{r}]}, {for dT}_{t} = 0 (62)

\frac{d r_{t}}{d G} = - \frac{1}{Δ} {[s * (1 - a^{g}) + a *] M_{y} + (s a^{g} + a) M_{y}^{*} .} 0, {for dT}_{t} = 0, (63)

where

Δ = s [(s * + a *) (M_{r} + \bar{e} M_{r}^{*}) + M_{y}^{*} . F_{r}] + a [s * (M_{r} + \bar{e} M_{r}^{*}) + M_{y}^{*} . (F_{r} + H_{r})] + M_{y} [s * H_{r} + a * (F_{r} + H_{r})] < 0.

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:

\frac{d M_{t}}{d G} = \frac{1}{M_{r} M_{r}^{*} Δ} {\frac{\bar{e} M_{y}}{M_{r}} [a*+s* (a - a^{g}) - \frac{M_{y}^{*} .}{M_{r}^{*}} (a + s a^{8}) + M_{y} M_{y}^{*} . M_{r} M_{r}^{*} {[F}_{r} (1 - a^{g}) - H_{r} a^{g}]}, {for dT}_{t} = 0. (64)

With a balanced-budget rise in government spending, dG = dT_t = dT. Accordingly, the solutions of the system of equations in (60) are

\frac{d Y_{t}}{d G} = \frac{1}{Δ} {s[s*+a*) (M_{r} + \bar{e} M_{r}^{*}) + M_{y}^{*} . F_{r}] + (a - a^{g}) [s * (M_{r} + \bar{e} M_{r}^{*}) + M_{y}^{*} . (F_{r} + H_{r})] + M_{y} [s * H_{r} + a * (F_{r} + H_{r})]}, {for dG=dT}_{t} (65)

\frac{d Y_{t}^{*}}{d G} = \frac{a^{g}}{\bar{e} Δ} (M_{y} (F_{r} + H_{r}) + s (M_{r} + \bar{e} M_{r}^{*})] > 0, {for dG = dT}_{t} (66)

\frac{d r_{t}}{d G} = \frac{a^{g}}{Δ} [s * M_{y} - s M_{y}^{*} .], {for dG=dT}_{t} . (67)

Differentiating the domestic money demand function and using equations (65) and (67) yields

\frac{d M_{t}}{d G} = - \frac{a^{g}}{Δ} [(s M_{r} M_{y}^{*} . + s * \bar{e} M_{r}^{*} M y) + M_{y} M_{y}^{*} . (F_{r} + H_{r})] < 0, {for dG = dT}_{t} . (68)

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:

(1 - β_{m}) E [Y - T + M - (1 + r) B^{p}, r] + (1 - β_{m}^{g}) G + β_{x}^{*} \bar{e} E * [Y * + M * (1 + r) B^{p} / \bar{e}, r] = Y (69)

β_{m} E [Y - T + M - (1 + r) B^{p}, r] + β_{m}^{g} G + (1 - β_{x}^{*}) \bar{e} E * [Y * + M * + (1 + r) B^{p} / \bar{e}, r] = Y * (70)

M [Y - T + M - (1 + r) B^{p}, r] + \bar{e} M * [Y * + M * + (1 + r) B^{p} / \bar{e}, r] = \bar{M} (71)

M [Y - T + M - (1 + r) B^{p}, r] = M (72)

M * [Y * + M * + (1 + r) B^{p} / \bar{e}, r] = M * (73)

E [Y - T + M - (1 + r) B^{p}, r] = Y - r B^{p} - T (74)

E * [Y * + M * + (1 + r) B^{p} / \bar{e}, r] = Y * + r B^{p} / \bar{e} . (75)

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^*, B_p, 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:

r_{t} = (Y_{t} - T_{t} + A_{t - 1}, M), (76)

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, $r_{t}^{*}$ , and the domestic rate, r_t) yields

r_{t}^{*} = r^{*} + (Y_{t}^{*} + A_{t - 1}^{*}, M^{*}) . (77)

Substituting equation (76) into the domestic expenditure function (3) of the text and substituting equation (77) into the corresponding foreign expenditure function yields

E_{t} = \bar{E} (Y_{t} - T_{t} + A_{t - 1}, M) (78)

E_{t}^{*} = {\bar{E}}^{*} (Y_{t}^{*} + A_{t - 1}^{*}, M^{*}) . (79)

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, ${\bar{E}}_{y} = E_{y} - (E_{r} / M_{r}) M_{y} .$ In what follows, we assume that the direct effect dominates, so that ${\bar{E}}_{y} > 0.$ . For subsequent use, we note that the reduced-form saving propensity, $\bar{s} = 1 - {\bar{E}}_{y},$ exceeds M_y [1 +(E_r / M _r)]. This relationship follows from the assumption that bonds are normal goods (so that 1 – E_y – M_y > 0) together with the former expression linking ${\bar{E}}_{y}$ with E_y

Substituting the reduced-form expenditure functions (78) and (79) into the goods-market-clearing conditions yields

(1 - β_{m}) \bar{E} (Y_{t} - T_{t} + A_{t - 1}, M) + (1 - β_{m}^{g}) G + e_{t} β_{x}^{*} {\bar{E}}^{*} (Y_{t}^{*} + A_{t - 1}^{*}, M^{*}) = Y_{t} (80)

β_{m} \bar{E} (Y_{t} - T_{t} + A_{t - 1}, M) + β_{m}^{g} G + e_{t} {(1 - β_{x}^{*}) \bar{E}}^{*} (Y_{t}^{*} + A_{t - 1}^{*} M *) = e_{t} Y_{t}^{*}, (81)

where we recall that $A_{t - 1} = M_{t - 1} - (1 + r_{t - 1}) B_{t - 1}^{p}$ and $A_{t - 1}^{*} = M_{t - 1}^{*} + (1 + r_{t - 1})$ $B_{t - 1}^{p} / e_{t} .$ Thus, whereas A_t–1 is predetermined, the value of $A_{t - 1}^{*}$ depends on the prevailing exchange rate. Equations (80) and (81) are the reduced-form goods-market-clearing conditions. These conditions link the equilibrium values of domestic output, foreign output, and the exchange rate. In the first step of the analysis, we derive the ee schedule of Figure 10 of the text, which portrays alternative combinations of Y and Y* satisfying equations (80) and (81) for alternative values of the exchange rate (which is treated as a parameter). The slope of this schedule is obtained by differentiating equations (80) and (81) and solving for $d Y_{t}^{*} / d Y_{t} .$ Accordingly,

[\begin{matrix} - s (\bar{s} + \bar{a}) & e_{t} {\bar{a}}^{*} \\ \bar{\begin{matrix} a \end{matrix}} & - e_{t} ({\bar{s}}^{*}) \end{matrix}] [\begin{matrix} d Y_{t} \\ d Y_{t}^{*} \end{matrix}]

= [\begin{matrix} - I M_{t}^{*} + {\bar{a}}^{*} H \\ I M_{t} + (1 - {\bar{s}}^{*} - {\bar{a}}^{*}) H \end{matrix}] d e_{t} - [\begin{matrix} 1 - a^{g} \\ a^{g} \end{matrix}] d G + [\begin{matrix} 1 - \bar{s} - \bar{a} \\ \bar{\begin{matrix} a \end{matrix}} \end{matrix}] d T_{t}, (82)

where $H = (1 + r_{t - 1}) B_{t - 1}^{p} / e_{t}$ denotes the debt commitment of the home country; the reduced-form saving and import propensities are designated by a tilde (~) and $I M_{t}^{*} = β_{x}^{*} E^{*}$ and $I M_{t} = Y^{*} - (1 - β_{x}^{*}) E^{*}$ are, respectively, the foreign and domestic values of imports expressed in units of foreign goods. For given fiscal policies, we obtain

\frac{d Y_{t}}{d e_{t}} = \frac{{\bar{s}}^{*} I M_{t}^{*} + \bar{a} * (I M_{t}^{*} - I M_{t}) - \bar{a} * H}{Δ} (83)

\frac{d Y_{t}^{t}}{d e_{t}} = \frac{\bar{s} I M_{t} - \bar{a} (I M_{t}^{*} - I M_{t}) + [\bar{s} (1 - {\bar{s}}^{*} - {\bar{a}}^{*}) + \bar{a} (1 - {\bar{s}}^{*})] H}{e_{t} Δ}, (84)

where

Δ = {\bar{s s}}^{*} + {\bar{s a}}^{*} + {\bar{s}}^{*} \bar{a} > 0.

To obtain the slope of the ee schedule, we divide equation (84) by equation (83) to yield

\frac{d Y_{t}^{*}}{d Y_{t}} = - \frac{\bar{s} I M_{t} - \bar{a} (I M_{t}^{*} - I M_{t}) + [\bar{s} (1 - {\bar{s}}^{*} - {\bar{a}}^{*}) + \bar{a} (1 - {\bar{s}}^{*})] H}{e_{t} [{\bar{s}}^{*} I M_{t}^{*} + {\bar{a}}^{*} (I M_{t}^{*} - I M_{t}) - {\bar{a}}^{*} H]}, (85)

Around a trade-balance equilibrium with zero initial debt (that is, $I M_{t} = I M_{t}^{*}$ and H = 0), this slope is negative and is equal to $- \bar{s} / e_{t} {\bar{s}}^{*} .$ With the negatively sloped ee schedule, a downward movement along the schedule (that is, a rise in Y_t and a fall in $Y_{t}^{*}$ ) is associated with higher values of e_t.

To determine the effects of changes in government spending, we compute the horizontal shift of the ee schedule by setting $d y_{t}^{*} = d T_{t} = 0$ in the system of equation (82) and solving for dY_t/dG:

\frac{d Y_{t}}{d G} = \frac{I M_{t} + a^{g} (I M_{t}^{*} - I M_{t}) + [(1 - {\bar{s}}^{*})] (1 - a^{g}) - {\bar{a}}^{*}] H}{\bar{s} I M_{t} - \bar{a} (I M_{t}^{*} - I M_{t}) + [\bar{s} (1 - {\bar{s}}^{*} - {\bar{a}}^{*}) + \bar{a} (1 - {\bar{s}}^{*})] H}, (86)

Thus, around trade-balance equilibrium and zero initial debt, the schedule shifts to the right by $1 / \bar{s} .$

By setting $d Y_{t}^{*} = d G = 0$ and following a similar procedure, we find that the horizontal shift of the ee schedule induced by a unit rise in taxes is

\frac{d Y_{t}}{d T_{t}} = - \frac{\bar{a} (I M \frac{*}{t} - I M_{t}) + (1 - \bar{s}) I M_{t} + [1 - \bar{s}] (1 - {\bar{s}}^{*})] H}{- \bar{a} (I M_{t}^{*} - I M_{t}) + \bar{s} I M_{t} + [\bar{s} (1 - {\bar{s}}^{*} - {\bar{a}}^{*}) + \bar{a} (1 - {\bar{s}}^{*})] H}, (87)

Thus, around trade-balance equilibrium and zero initial debt, schedule ee shifts to the left by $(1 - \bar{s}) / \bar{s}$ units.

By combining the results in equations (86) and (87), we obtain the effect of a balanced-budget unit rise in government spending. Accordingly,

\frac{d Y_{t}}{d G} = \frac{\bar{s} I M_{t} + (a^{g} - \bar{a}) (I M_{t}^{*} - I M_{t} + [\bar{s} (1 - {\bar{s}}^{*} - {\bar{a}}^{*}) + (1 - {\bar{s}}^{*}) (\bar{a} + a^{g})] H}{\bar{s} I M_{t} - \bar{a} (I M_{t}^{*} - I M_{t}) + [\bar{s} (1 - {\bar{s}}^{*} - {\bar{a}}^{*}) + \bar{a} (1 - {\bar{s}}^{*})] H}, (88)

for the ee schedule, with dG = dT_t. (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

r (Y_{t} - T_{t} + A_{t - 1}, M) = r^{*} (Y^{*} + A_{t - 1}^{*}, M^{*}) . (89)

The slope of this schedule is $r_{y} / r_{y}^{*} .$ . which can also be expressed in terms of the characteristics of the demands for money:

\frac{d Y_{t}^{*}}{d Y_{t}} = \frac{M_{y}}{M_{y}^{*} .} . \frac{M \frac{*}{r} .}{M_{r}} > 0, a l o n g t h e r r^{*} s c h e d u l e . (90)

Obviously, around $r = r^{*}, M_{r}^{*} .$ equals $M_{r}^{*}$ As is evident, the level of government spending does not influence the rr^* schedule, whereas a unit rise in taxes shifts the schedule to the right by one unit.

The effects of fiscal policies can be formally obtained by differentiating the system of equations (80), (81), and (89). Thus,

[\begin{matrix} - (\bar{s} + \bar{a}) & e_{t} {\bar{a}}^{*} & I M_{t}^{*} - {\bar{a}}^{*} H \\ \bar{\begin{matrix} a \end{matrix}} & - e_{t} ({\bar{s}}^{*} + {\bar{a}}^{*}) & - I M_{t} - (1 - {\bar{s}}^{*} - {\bar{a}}^{*}) H \\ M_{y} / M_{r} & - M_{y}^{*} . / M_{r}^{*} & H M_{y}^{*} . / e_{t} M_{r}^{*} . \end{matrix}] [\begin{matrix} d Y_{t} \\ d Y_{t}^{*} \\ d e_{t} \end{matrix}] = - [\begin{matrix} 1 - a^{g} \\ a^{g} \\ 0 \end{matrix}] d G + [\begin{matrix} 1 - \bar{s} - \bar{a} \\ a \\ M_{y} / M_{r} \end{matrix}] d T_{t} . (91)

By solving equation (91), we find that the short-run effects of a debt-financed rise in government spending are

\frac{d Y_{t}}{d G} = \frac{M_{y}^{*} .}{Δ M \frac{*}{r}} [I M_{t} (1 - a^{g}) + I M_{t}^{*} a^{g} + (1 - a^{g}) H], f o r d T_{t} = 0 (92)

\frac{d Y_{t}^{*}}{d G} = \frac{M_{y}}{Δ M_{r}} [I M_{t} + a^{g} (I M_{t}^{*} - I M_{t})] + \frac{t}{Δ} {\frac{M_{y}^{*} .}{M_{r}^{*}} (\bar{a} + \bar{s} a^{g}) + \frac{M_{y}}{M_{r}} [(1 - a^{g}) (1 - {\bar{s}}^{*}) - {\bar{a}}^{*}]] H, f o r d T_{t} = 0 (93)

\frac{d e_{t}}{d G} = \frac{1}{Δ} {\frac{M_{y}^{*} .}{M_{r}^{*}} (\bar{a} + \bar{s} a^{g}) - \frac{e_{t} M_{y}}{M_{r}} [{\bar{a}}^{*} + {\bar{s}}^{*} (1 - a^{g})]}, f o r d T_{t} = 0 (94)

where

Δ = \frac{M_{y}^{*} .}{{M_{r}}^{*}} [(\bar{s} + \bar{a}) I M_{t} - \bar{a} I M_{t}^{*}] + \frac{e_{t} M_{y}}{M_{r}} [({\bar{s}}^{*} + {\bar{a}}^{*}) I M_{t}^{*} - a^{*} I M_{t}] + [(\bar{s} + \bar{a}) \frac{M_{y}^{*} .}{M_{r}^{*}} - e_{t} {\bar{a}}^{*} \frac{M_{y}}{M_{r}}] H .

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:

\frac{d r_{t}}{d G} = - \frac{M_{y} M_{y}^{*} .}{M_{r} M_{r}^{*} Δ} [I M_{t} + a^{g} (I M_{t}^{*} - I M_{t}) + (1 - a^{g}) H], f o r d T_{t} = 0 (95)

Similarly, the short-run effects of a tax-financed rise in government spending are

\frac{d Y_{t}}{d G} = \frac{1}{Δ} {\frac{M_{y}^{*} .}{M_{r}^{*}} [\bar{s} I M_{t} + (\bar{a} - a^{g}) (I M_{t} - I M_{t}^{*})] + \frac{e_{t} M_{y}}{M_{r}} [{\bar{s}}^{*} I M_{t}^{*} + {\bar{a}}^{*} (I M_{t}^{*} - I M_{t})] + [\frac{M_{y}^{*} .}{M_{r}^{*}} (\bar{s} + \bar{a} - a^{g}) - \frac{e_{t} M_{y}}{M_{r}} {\bar{a}}^{*}] H}, f o r d G = d T_{t} (96)

\frac{d Y_{t}^{*}}{d G} = \frac{a^{g}}{Δ} {\frac{M_{y}}{M_{r}} (I M_{t}^{*} - I M_{t}) - [\frac{M_{y}}{M_{r}} (1 - {\bar{s}}^{*}) - \frac{M_{y}^{*}}{M_{r}^{*}} \bar{s}] H}, f o r d G = d T_{t} (97)

\frac{d e_{t}}{d G} = \frac{a^{g}}{Δ} (\frac{e_{t} M_{y}}{M_{r}} {\bar{s}}^{*} + \frac{M_{y}^{*}}{M_{r}^{*}} \bar{s}), f o r d G = d_{T_{t} . (98)}

Using the money-market equilibrium condition together with equation (96) yields

\frac{d r_{t}}{d G} = - \frac{M_{y}}{M_{r} Δ} {a^{g} (I M_{t}^{*} - I M_{t}) + [\frac{M_{y}^{*} .}{M_{r}^{*}} (\bar{s} + \bar{a} - a^{g}) + \frac{e_{t} M_{y}}{M_{r}} {\bar{a}}^{*}] H}, f o r d G = d T_{t} . (99)

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:

(1 - β_{m}) \tilde{E} [Y - T + M - (1 + r) B^{p}, M] + (1 - β_{m}^{8}) G + e β_{x}^{*} \tilde{E} * (Y * + M * + \frac{1 + r}{e} B^{p}, M *) = Y (100)

β_{m} \tilde{E} [Y - T + M - (1 + r) B^{p}, M] + β_{m}^{8} G + e (1 - β_{x}^{*}) \tilde{E} (Y * + M * + \frac{1 + r}{e} B^{p}, M) = e Y * (101)

r [Y - T + M - (1 + r) B^{p}, M] = r * (Y * + M * + \frac{1 + r}{e} B^{p}, M *) (102)

\tilde{E} [Y - T + M - (1 + r) B^{p}, M] = Y - r B^{p} - T (103)

\tilde{E} * (Y * + M * + \frac{1 + r}{e} B^{p}, M *) = Y * + \frac{e B^{p}}{e} . (104)

This system, which determines the long-run equilibrium values of Y, Y*, e, B^p, 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

E_{t} + {\ddot{M}}_{t} - e_{t} {\ddot{B}}_{f t}^{p} = Y_{t} - T_{t} - {\bar{r}}_{f} e_{t} B_{f t}^{p}, (105)

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

E_{t} = E (Y_{t} - T_{t} - {\bar{r}}_{f} e_{t} B_{f t}^{p}, M_{t} - e_{t} B_{f t}^{p}, {\bar{r}}_{f}) (106)

E_{t} = E (Y_{t} - T_{t} - {\bar{r}}_{f} e_{t} B_{f t}^{p}, M_{t} - e_{t} B_{f t}^{p}, {\bar{r}}_{f} + \frac{{\ddot{e}}_{t}}{e_{t}}), (107)

where the demand for money is expressed as a negative function of the expected depreciation of the currency, ė_t/e_t. In what follows, we simplify the exposition by assuming that the world interest rate, r_f, is very low (zero) and that the effect of assets, $M_{t} - e_{t} B_{f t}^{p},$ , on spending is negligible. With these simplifications, the goods-market and money-market equilibrium conditions (the counterparts to equations (20a) and (22a) of the text) are

(1 - β_{m}) E (Y_{t} - T_{t}) + (1 - β_{m}^{8}) G + e_{t} \bar{e} * = Y_{t} (108)

M (Y_{t} - T_{t}, M - e_{t} B_{f t}^{p}, \frac{{\ddot{e}}_{t}}{e_{t}}) = M . (109)

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

Y_{t} = Y (e_{t}, G, T_{t}), (110)

where $\partial Y_{t} / \partial e_{t} = \bar{D} * / (s + a), \partial Y_{t} / \partial G = (1 - a^{8}) / (s + a)$ and $\partial Y_{t} / \partial T_{t} = - (1 - s - a) / (s + a)$ are the conventional foreign trade multipliers. Substituting the functional relation (110) into the money-market equilibrium condition and solving for the (actual and expected) percentage change in the exchange rate yields

\frac{{\ddot{e}}_{t}}{e_{t}} = f (e_{t}, B_{f t}^{p}, G, T_{t}, M), (111)

where

\partial f / \partial e = [- M_{y} \bar{D} * / (s + a) + M_{A} B_{f t}^{p}] / M_{r} \partial f / \partial B_{f t}^{p} = e_{t} M_{A} / M_{r} \partial f / \partial G = 1 (1 - a^{8}) / (s + a) M_{r} \partial f / \partial T_{t} = (1 - s - a) / (s + a) M_{r}

and where M_A and M_r denote, respectively, the derivatives of the demand for money with respect to assets $(M - e_{t} B_{f t}^{p})$ and the rate of interest. The former is positive, the latter negative. The interpretation of the dependence of the percentage change in the exchange rate, which represents the money-market-clearing interest rate, on the various variables follows. A rise in the exchange rate raises the goods-market-clearing level of output and raises the demand for money. To restore money-market equilibrium, the rate of interest must rise; that is, è_t/e_t, must rise. The rise in e, however, raises the domestic currency value of the debt, B^p_ft If the private sector is a net creditor, the depreciation of the currency raises the domestic currency value of assets and raises the demand for money. This in turn also contributes to the rise in the rate of interest. If, however, the private sector is a net debtor, then the value of assets falls and the demand for money is reduced, thereby contributing to a downward pressure on the rate of interest. The net effect on the rate of interest depends, therefore, on the net debtor position of the private sector; if, however, B^p_ft is zero, then the rate of interest must rise so that ∂f/ ∂e_t > 0. Analogous interpretations apply to the other derivatives, for which it is evident that $\partial f / \partial B_{f t}^{p} < 0, \partial f / \partial G \geq 0,$ and ∂f / ∂T_t > 0.

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 M_t = 0, we can solve for the dynamics of private sector debt:

{\ddot{B}}_{f t}^{p} = \frac{1}{e_{t}} h (e_{t}, G, T_{t}) = \frac{1}{e_{t}} {E_{t} [Y (e_{t}, G, T_{t}) - T_{t}] - Y (e_{t}, G, T_{t}) + T_{t}} . (112)

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 $\partial h / \partial e_{t} = - \bar{D} * s / (s + a) < 0, \partial h / \partial G = - (1 - a^{8}) s / (s + a) \leq 0, a n d \partial h / \partial T_{t} = s / (s + a) > 0.$

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 e_t=0 schedule shows combinations of the exchange rate and private sector debt that maintain an unchanged exchange rate. The schedule represents equation (111) for e_t — 0. Its slope is positive around a zero level of private sector debt, and its position depends on the policy variables G, T_t, and M. Similarly, the ${\ddot{B}}_{f t}^{p} = 0$ locus represents equation (112) for ${\ddot{B}}_{f t}^{p} = 0.$ It is horizontal because, as specified, the rate of change of private sector debt does not depend on the value of debt. The arrows around the schedules indicate the directions in which the variables tend to move, and the solid curve with arrows shows the unique saddle path converging toward a stationary state. As is customary in this type of analysis, we associate this saddle path with the equilibrium path. The long-run equilibrium of the system is shown by point A in Figure 12, by which, for convenience, we show a case in which the long-run value of private sector debt is zero.

Figure 12.

Equilibrium Exchange Rate Dynamics and Debt Accumulation

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A001

Figure 13.

Effects of a Debt-Financed Rise in Government Spending on the Paths of the Exchange Rate and Private Sector Debt

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A001

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 ${\dot{B}}_{ft}^{p}$ schedule from point A downward by $- 1 (1 - a^{8}) / \bar{D} *,$ and it also shifts the e = 0 schedule from point A downward by $- 1 (1 - a^{8}) / M_{y} D *,$ For M_y<l, the vertical displacement of the e = 0 schedule exceeds the corresponding displacement of the ${\ddot{B}}_{f t}^{p} = 0$ schedule, and the new long-run equilibrium obtains at point C, at which the domestic currency has appreciated and private sector debt has risen. The short-run equilibrium obtains at point B along the new saddle path, and transition toward the long-run equilibrium follows along the path connecting points B and C. As is evident, the initial appreciation of the currency overshoots the long-run appreciation.

The effects of a unit tax-financed rise in government spending are shown in Figure 14. With dG – dT, the ${\ddot{B}}_{f t}^{p} = 0$ schedule shifts upward by $a^{8} / \bar{D} *,$ whereas the e = 0 schedule shifts vertically by $(s + a - a^{8}) / M_{y} \bar{D} * .$ The benchmark case shown in Figure 14 corresponds to the situation in which the private sector and the government have the same marginal propensities to spend on domestic goods (that is, s + a = a⁸). In that case, the e = 0 remains intact, the short-run equilibrium is at point B, and the long-run equilibrium is at point C. As can be seen in this case, the domestic currency depreciates, and the short-run depreciation undershoots the long-run depreciation. These results are sensitive, however, to alternative assumptions about the relative magnitudes of (s + a) and a⁸.

Figure 14.

Effects of a Tax-Financed Rise in Government Spending on the Paths of the Exchange Rate and Private Sector Debt

Citation: IMF Staff Papers 1987, 003; 10.5089/9781451930719.024.A001

Note: (s + a) and a⁸

References

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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.

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IMF Staff papers: Volume 34 No. 4

Author:

International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1987: Issue 003

Publisher:: International Monetary Fund

ISBN:: 9781451930719

ISSN:: 1020-7635

Pages:: 228

DOI:: https://doi.org/10.5089/9781451930719.024

Keywords
I. The Analytical Framework
II. Capital Mobility Under Fixed Exchange Rates
- Fiscal Policies in a Small Country
- Fiscal Policies in a Two-Country World
III. Capital Mobility Under Flexible Exchange Rates
- Fiscal Policies in a Small Country
- Fiscal Policies in a Two-Country World
IV. Summary and Overview
APPENDIX I
References

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Figure 1.

Short-Run Effects of Fiscal Policy Under Fixed Exchange Rates: The Small-Country Case

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Figure 2.

Long-Run Effects of a Unit Debt-Financed Rise in Government Spending Under Fixed Exchange Rates: The Small-Country Case

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Figure 3.

Long-Run Effects of a Unit Balanced-Budget Rise in Government Spending Under Fixed Exchange Rates: The Small-Country Case

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Figure 4.

A Unit Debt-Financed Rise in Government Spending Under Fixed Exchange Rates: The Two-Country Case

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Figure 5.

A Unit Debt-Financed Rise in Government Spending Under Fixed Exchange Rates: The Two-Country Case

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Figure 6.

Short-Run Effects of a Unit Debt-Financed Rise in Government Spending Under Flexible Exchange Rates: The Small-Country Case

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Figure 7.

Short-Run Effects of a Unit Tax-Financed Rise in Government Spending Under Flexible Exchange Rates: The Small-Country Case

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Figure 8.

Short-Run Effects of a Unit Debt-Financed Rise in Government Spending Under Flexible Exchange Rates: The Debt-Revaluation Effect

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Figure 9.

Long-Run Effects of a Unit Rise in Government Spending Under Flexible Exchange Rates: The Small-Country Case

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Figure 10.

A Debt-Financed Unit Rise in Government Spending Under Flexible Exchange Rates: The Two-Country Case

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Figure 11.

A Tax-Financed Unit Rise in Government Spending Under Flexible Exchange Rates: The Two-Country Case

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Figure 12.

Equilibrium Exchange Rate Dynamics and Debt Accumulation

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Figure 13.

Effects of a Debt-Financed Rise in Government Spending on the Paths of the Exchange Rate and Private Sector Debt

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Figure 14.

Effects of a Tax-Financed Rise in Government Spending on the Paths of the Exchange Rate and Private Sector Debt

Table 2.

Direction of Short-Run Effects of a Rise in Government Spending Under Fixed and Flexible Exchange Rates: The Two-Country World

	Expected Sign of Short-Run Effect
Affected Variable	Debt-financed rise	Tax-financed rise
	Fixed Exchange Rates
Y	+ (for small H_r)	+ (for a^g≤a)
Y^*	+ (for small F_r)	+
r	+	+ (for A > 0)M –(for A < 0)
M	+ (for B + C < 0) (for B + C > 0)	–
	Fixed Exchange Rates
Y	+	+
Y^*	+	0
r	+	0
e	+(for B > 0)	+
	+(for B < 0)

A = s / M_{y} - s^{*} / M_{y} .;

B = \bar{e} (M_{y} / M_{r}) [a^{*} + s^{*} (1 - a^{g})] - (M_{y}^{*} . / M_{r}^{*}) (a + s a^{g});

and

C = M_{y} M_{y}^{*} \cdot M_{r} M_{r}^{*}

[F_{r} (1 - a^{g}) - H_{r} a^{g}]

For the flexible exchange rate regime,

B = e_{t} (M_{y} / M_{r})

[a^{*} + {\bar{s}}^{*} (1 - a^{g})] - (M_{y}^{*} \cdot / M_{r}^{*}) (\bar{a} + \bar{s} a^{g}) .

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Abstract

I. The Analytical Framework

II. Capital Mobility Under Fixed Exchange Rates

Fiscal Policies in a Small Country

Fiscal Policies in a Two-Country World

III. Capital Mobility Under Flexible Exchange Rates

Fiscal Policies in a Small Country

Fiscal Policies in a Two-Country World

IV. Summary and Overview

APPENDIX I

Fixed Exchange Rates

APPENDIX II: Flexible Exchange Rates

Exchange Rate Expectations

References

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