**A**lthough the seminal papers that introduced the monetary approach to the balance of payments are now more than a decade old, a workable synthesis between this approach and its “Keynesian” predecessor has not yet emerged. Many theoretical expositions of the monetary approach employ “global monetarist” structural models, and empirical implementations of the approach have been limited almost exclusively to testing the global monetarist variant. Under fixed exchange rates, these models are designed to explain the domestic rate of inflation and the overall balance of payments. As recent experience with stabilization efforts in developing countries has emphasized, however, policymakers also tend to be concerned with deviations of output from capacity. Casual empiricism suggests that underutilization of resources tends to be an important component of the adjustment process, at least in the short run. These temporary deviations of output from capacity constitute the analytical focus of Keynesian models. Thus, the analysis of stabilization policies in small open economies under fixed exchange rates would benefit from the construction of tractable models that reconcile the insights of the monetary approach with regard to the determination of the domestic rate of inflation and the overall balance of payments with Keynesian features that allow for the possible short-run underutilization of resources.

There are several analytical models in the tradition of the monetary approach that embody Keynesian features—early examples include Mussa (1976) and Rodriguez (1976)—but these tend to be very simple models that have limited usefulness for policy purposes. More recently, an important paper by Frenkel, Gylfason, and Helliwell (1980) explicitly proposed a synthesis of the Keynesian and monetary approaches. As these authors put it, however,

The model we . . . use is short run in nature, and suppresses many elements of behaviour that are potentially relevant. In particular, the wealth, portfolio balance, aggregate supply, and current account consequences of government debt issue, foreign capital flows, and domestic investment are all ignored. . . . We thus bypass the important question of whether a short-run analysis can be made meaningful without an explicit incorporation of longer run considerations, (p. 587)

Other limitations of their model cited by the authors are the dependence of capital flows on the *levels* of interest rates and the absence of a role for expectations. In addition, they retained the traditional Mundell-Fleming structure of production in which the domestic economy is completely specialized in its exportable commodity and has monopolistic power over its price while simultaneously being small in the market for its importable good (Mundell (1968) and Fleming (1962)).

A more general model that avoids many of these limitations was presented in Montiel (1985). The purpose of that paper was to conduct a “monetary” analysis of the balance of payments for a small open economy—an analysis organized around the “reserve-flow” equation of the monetary approach—in the context of a Keynesian structural model in which both the level of real output and the domestic rate of inflation are endogenous. The short-run consequences of stabilization policies and of a variety of external shocks for the level of real output, the domestic rate of inflation, and the balance of payments were examined. The dynamic considerations called for by Frenkel, Gylfason, and Helliwell, however, did not receive explicit treatment.

This paper extends the earlier analysis by making explicit the dynamic structure of the 1985 model and by examining the properties of its long-run equilibrium. The purpose is both to gain some insight into the path that the economy is likely to follow from its short-run equilibrium and to render the short-run analysis more meaningful by demonstrating that the model exhibits reasonable behavior in the long run. As we shall see, the model’s short-run Keynesian flavor is consistent with long-run characteristics common to many “monetary” models of the balance of payments.

The remainder of the paper is organized in four sections. After the model is presented in Section I, its dynamic structure is discussed in detail in Section II. The model’s long-run equilibrium is derived, and its properties are compared with those of familiar global monetarist models. Section III examines the effects on long-run equilibrium of certain policy and external disturbances. The final section presents a brief summary and some conclusions.

## I. A Keynesian Model of a Small Open Economy

This section will present a slightly modified version of the model described in Montiel (1985). The model is modified in two respects: a variable markup is introduced, and portfolio equilibrium holds continuously. Both alterations are associated with the extension of the analysis to the long run, but neither change affects the essential conclusions of the previous paper. The section is organized into three subsections that describe in turn the determination of wages and prices, asset markets, and goods markets.

### Wages and Prices

In the model there are two production sectors, producing traded and nontraded goods. A single variable input—labor—is employed in each sector, under conditions of diminishing marginal productivity. The sectoral production functions are

where *y*^{i} and *L*^{i} denote real output and total employment, respectively, in sector *i*. Labor is homogeneous and mobile between sectors. Thus workers in both sectors receive the same nominal wage *W*.

It is the behavior of the nominal wage that identifies the model as Keynesian. The wage is assumed to be sticky in the sense that it is a continuous function of time. Specifically, it adjusts only gradually over time in response to labor market disequilibrium, according to the Phillips-curve relationship:

where *Ŵ* is the rate of change of the nominal wage, *π* is the expected rate of inflation, and a circumflex (ˆ) denotes a proportional rate of change. As is conventional in Keynesian models, the level of employment is demand determined in the short run. In other words, firms can satisfy their total labor demand *L*^{T} + *L*^{N} even if this demand exceeds the “natural” level of employment ^{1} As long as this is the case, however, according to equation (2) the nominal wage will rise faster than the expected rate of inflation.

The small-country assumption ensures that firms are unconstrained in the market for traded goods—that is, firms face an infinitely elastic demand for their output at the domestic currency price *P*_{T}, derived from the world price *P*_{TF} through the law of one price:

where *e* is the nominal exchange rate defined as the domestic currency price of foreign exchange. Under these circumstances, the demand for labor by firms in the traded-goods sector is derived by solving the first-order condition for profit maximization, *T′*(*L*^{T}) = *w*_{T}, where *w*_{T} = *W/P*_{T} is the product wage in the traded goods sector (that is, the real wage measured in terms of traded goods). This solution yields

Firms in the nontraded-goods sector set prices by applying a markup a to nominal wages. With the price of nontraded goods denoted as *P*_{N},

If the markup is itself sticky, the stickiness of the nominal wage will cause the price of nontraded goods to behave in similar fashion. Thus *P*_{N} will not instantaneously clear the market for non-traded goods. Output in this sector is determined by aggregate demand for nontraded goods. The effective demand for labor in the nontraded goods sector, denoted

The markup equation (5) determines the wage measured in terms of nontraded goods, *w*_{N}. Because *w*_{N} = *W/P*_{N}, equation (5) implies *w*_{N} = α^{-1}. Since output is demand determined, firms in the nontraded-goods sector will be off their demand curves for labor whenever the nontraded-goods market fails to clear—that is, firms will not be selling their profit-maximizing level of output, which represents their “notional” supply (Barro and Grossman (1971)). This set of relationships is illustrated in Figure 1. The curve *N′*(*L*^{N}) depicts the marginal product of labor. At the product wage *w*_{N0}, the profit-maximizing level of employment is *A*) and corresponds to a notional supply of output equal to *B* with employment equal to *DB* when *C*, where the real wage exceeds the marginal product of labor (by *CE*), so that profits could be increased by reducing employment.

Figure 1. Employment and Notional Labor Demand in the Short Run

Although the firm may temporarily operate at points such as *B* or *C*, it is unreasonable to expect it to continue to do so in the long run. Thus, the model in Montiel (1985), which assumed a fixed short-run markup, must be modified to permit the markup to respond to changes in demand in the long run. Firms will be assumed to increase the markup when demand exceeds their notional supply and to reduce it when demand falls short of notional supply. From the discussion of Figure 1, and recalling that the product wage in the nontraded-goods sector is determined by the markup, this behavior is equivalent to reducing the product wage *w*_{N} (increasing *P*_{N}) when the level of employment *L*^{N}(*y*^{N}) exceeds the firm’s notional demand for labor *L*^{N}(*w*_{N}) (that is, at a point such as C in Figure 1) and to increasing the product wage (reducing *P*_{N}) when employment falls short of the notional demand for labor (point *B*). In other words,

In the context of Figure 1, equation (7) means that the product wage will always be moving toward the marginal product of labor (that is, toward points such as *D* or *E*).

Applying equation (5) to equation (7) produces the conventional price equation:

The weight of the empirical evidence on price equations (see Gordon (1971), Nordhaus (1972), Montiel (1976), and Parkin (1975)) indicates that the effects of changes in demand on the markup are weak at best. It is convenient to incorporate the relative weakness of these effects in the model by means of an inequality that compares the derivative of *h* ( ) to the slope of the short-run Phillips curve:^{2}

*h′*<*g′*.

The domestic price level is given by

where θ is the share of nontraded goods in private consumption. Therefore the domestic rate of inflation is

Price expectations are assumed to be formed with perfect myopic foresight, so that

### Asset Markets

The model contains a simple financial structure. The central bank is the only financial institution. Its liabilities consist of non-interest-paying money (*M*), which is held by the private sector. Its assets consist of foreign exchange reserves held in the form of foreign securities (with a foreign currency value of *F*_{B}) and of credit extended to the private (*D*_{P} ) and public (*D*_{G} ) sectors. The central bank’s balance sheet is thus

where *D* = *D*_{G} + *D*_{P} is total domestic credit. The central bank exercises direct control over *D*_{G} and *D*_{P}. To defend the exchange parity, it stands ready to trade *M* and *F*_{B} with the private sector at price *e*.

In addition to holding money and credit, the private sector also holds foreign securities with foreign currency values *F*_{P}. Net private financial wealth, denoted *N*_{P}, is therefore

The private sector must allocate its portfolio among *M*, *F*_{P}, and *D*_{p} subject to the balance-sheet constraint (12). It considers domestic credit and foreign securities to be perfect substitutes. Thus, if *r*_{F} is the external nominal interest rate and *r* is the interest rate on domestic credit, the interest parity condition *r* = *r*_{F} must hold continuously under fixed exchange rates. The private sector’s portfolio-allocation decision is summarized by its demand for money, which takes the form

where *y* represents real gross domestic product (GDP) and is defined as:

The demand for foreign securities then follows from the balance-sheet constraint (12):

In a second departure from the previous version of this model, it is assumed that portfolio equilibrium is instantaneously achieved—that is,

The purpose of this modification is to simplify the stability analysis slightly. Neither the model’s short-run internal equilibrium nor its long-run equilibrium will be affected. Because the speed of adjustment in asset markets will affect capital flows, however, the expression for the balance of payments will differ from that in Montiel (1985). Defining the balance of payments in domestic currency as *BOP* ≡ *eḞ*_{B}, differentiating equations (11), (13), and (16) with respect to time, and making the appropriate substitutions yields where *r*_{F} has been assumed to be constant, and a dot (•) indicates a time derivative. As before, this is the “reserve-flow” equation familiar from the monetary approach to the balance of payments. The first term on the right-hand side is the flow demand for money, or “hoarding,” and the second is the flow supply of domestic credit.

Finally, the government also borrows from the domestic banking system and purchases foreign securities. The government’s net worth is

Note from equations (11), (12), and (18) that national wealth, denoted *N*, is

where *F* = *F*_{B} + *F*_{P} + *F*_{G}.

### Goods Markets

Private and government financial wealth represent the cumulative savings of households and the government. Private saving is the difference between private disposable income and private consumption:

where *t*_{P} is real taxes paid by the private sector, and *c* is real private consumption. Real private consumption is in turn determined by

The signs of the partial derivatives of *c*( ) are conventional. If holdings of net nonmonetary assets are positive (*N*_{P} - *M* > 0)— which shall be taken to be the standard case here—an increase in net financial wealth increases both disposable income (equation (20)) and consumption. To ensure that the net effect on saving is negative—that is, that an increase in household wealth reduces saving—the restriction

The expenditure shares θ and 1-θ from equation (9a) will be assumed to be constant. (Thus the representative consumer’s utility function is Cobb-Douglas in form.) Consequently, consumption of traded (*c*^{T}) and nontraded goods (*c*^{N}) must be

With *g* representing real government purchases of goods and *t*_{B} denoting real profits of the central bank (assumed to be transferred to the government), government saving is

The government’s real net worth will be assumed to be constant in the long run. That is, only temporary changes in the fiscal deficit will be contemplated below.

Real government spending is divided into spending on traded (*g*^{T}) and nontraded (*g*^{N}) goods, so that

It is assumed that the government initially devotes a fraction θ of its spending to nontraded goods. Central bank profits are given by

Summing the private and public budget constraints (20) and (23) and using equations (11) and (25) allows one to derive the expression for the real value of the current account (*ca*):

This is, of course, the familiar income-minus-absorption identity. The real balance of trade *b* is

or, from the assumption that output in the nontraded-goods sector is demand determined,

one has from equations (14), (22), and (24) that

That is, the trade balance is the difference between domestic production of traded goods and domestic demand for traded goods.

## II. Long-Run Equilibrium

The model in the previous section can be solved for a short-run equilibrium that expresses the endogenous variables as functions of the exogenous variables for given values of the “state” variables (that is, those endogenous variables that are continuous functions of time). The system will also generate a set of dynamic equations that determines the rate at which the state variables are evolving in a given short-run equilibrium. Unless the economy’s configuration is such that the dynamic equations imply stable values for the state variables, the short-run equilibrium will be temporary—that is, evolution of the state variables will produce a succession of new short-run equilibria over time, even if the exogenous variables are unchanged. If the system is stable, it will converge to a short-run equilibrium that is consistent with no further change in the state variables. In the absence of further shocks, this will represent the economy’s long-run equilibrium. This section carries out such dynamic analysis for the model of Section I and describes some familiar properties of the model’s long-run equilibrium. Less familiar properties—involving the effects on this equilibrium of changes in exogenous variables—are analyzed in Section III.

### Derivation of Long-Run Equilibrium

It is useful to define the real exchange rate *e*_{R} as

Thus *e*_{R} is the relative price of traded goods in terms of nontraded goods. Using equation (9a) obtains

Without loss of generality, units are chosen so that initially *e*_{R} = 1.

The economy’s short-run equilibrium can be described in terms of equations that determine the level of real output *y*, the domestic rate of inflation *y*^{N}. Substituting equation (4) in equation (la) and using the result together with equations (30a) and (30b) in equation (14) allows *y* to be expressed as

The domestic rate of inflation is determined by equation (9b). Substituting into this equation from equation (8), and using equations (2), (4), (6), and (10) along with the definitions (30a) and (30b), produces

Finally, to solve for the level of output of nontraded goods, substitute equation (21) into equation (22b), and the result into equation (28). Once again, making use of the definitions (30a) and (30b), one has

where *n*_{PT} is real private financial wealth measured *in terms of traded goods*.

Real GDP, *y*, the domestic rate of inflation, *y*^{N}, are all endogenous in the short run. Using equations (31)—(33), one can express these variables in terms of the exogenous variables—the policy variables *g*^{N} and *t*_{P}, the external variables *r*_{F} and *n*_{PT} (real private financial wealth), *e*_{R} (the real exchange rate), and *w*_{T} (the real wage measured in terms of traded goods). The model’s short-run equilibrium was discussed in detail in Montiel (1985, pp. 188-96), and that analysis will not be repeated here. The properties of the short-run equilibrium can usefully be summarized as

where ^{3}

The next step is to derive the dynamic equations for the state variables. Substituting equations (13) and (21) into the private saving function (20) yields

To derive the dynamic equation for the real exchange rate, differentiate equation (30) with respect to time. Dividing the result by *e*_{R} yields

Using equation (9b), one obtains

Finally, substituting from equation (32), one has

The final dynamic equation describes the behavior over time of the real wage measured in terms of traded goods. Substituting equations (4), (6), and (10) in equation (2), using equation (32), and simplifying produce

Equations (37), (39), and (40) describe the evolution over time of real private financial wealth, the real exchange rate, and the real wage in terms of traded goods. Changes in *n*_{PT}, *e*_{R}, and *w*_{T} depend on the current values of these variables (the “state” of the system, consisting of equations (37), (39), and (40)), on the exogenous variables, and on the economy’s current short-run equilibrium configuration, as summarized by *y*, *y*^{N}. Because *y*, *y*^{N} in turn depend on the exogenous and state variables (through equations (34)-(36)), the current rates of change of the state variables ultimately depend on the exogenous variables and on the state of the system.

As long as (at least one of) *ṅ*_{PT}, *ė*_{R}, or *ẇ*_{T} is nonzero, one or more of the state variables will be changing, and the economy will be moving through a succession of different short-run equilibria. Long-run equilibrium thus implies *ṅ*_{PT} = *ė*_{R} = *ẇ*_{T} = 0. The particular configuration of (*n*_{PT}, *e*_{R}, *w*_{T}) that satisfies these conditions depends on the values assumed by the exogenous variables. This relationship will be investigated in Section III.

### Properties of the Long-Run Equilibrium

An examination of the properties of the model in long-run equilibrium (that is, when *ṅ*_{PT} = *ė*_{R} = *ẇ*_{T} = 0) yields, among other observations, the following propositions.

Proposition 1. *In the long run, employment will be at its “natural” (full-employment) level, and the market for nontraded goods will be in equilibrium—that is, all firms will be on their “notional” supply curves*.

This proposition states that the model’s long-run equilibrium is Walrasian. To see that the proposition must be true, set *ė*_{R} = *ẇ*_{T} = 0 in equations (39) and (40). This property implies that

0=g( )+h( )

0=g( )+θh( ).

Since θ is a constant, these conditions can hold simultaneously only if *g*( ) = *h*( ) = 0. But *h*( ) = 0 implies that

where asterisks (*) denote the long-run values of the relevant variables. That is, the actual level of employment equals its desired (profit-maximizing) level, and firms are on their labor demand curves. Inverting

that is, demand for nontraded-goods output equals notional supply, and firms are on their “notional” supply curves. Similarly, *g*( ) = 0 implies that

Applying the previous result to substitute for *y*^{N*} yields

Thus the level of employment is at its “natural” full-employment level.

Proposition*2. Relative purchasing power parity holds in the long run*.

This proposition follows directly from the long-run constancy of the real exchange rate (*ė*_{R} = 0). Equation (9b) can be written in the form

Since

that is, the rate of depreciation of the exchange rate is equal to the difference between the domestic and foreign inflation rates— simply a statement of “relative” purchasing power parity (see Officer (1976)). Note that causation runs from the rate of depreciation (a policy variable) to the domestic inflation rate, as is conventional in the tradition of the monetary approach.

Indeed, the model has a decidedly global monetarist flavor in its long-run configuration. Whitman (1975) characterized global monetarist models by their assumptions of full employment, purchasing power parity, and uncovered interest parity. Although the model presented here does not necessarily satisfy the first two of these properties in the short run, propositions 1 and 2 have established that both properties hold in the long run. Because uncovered interest parity is assumed to hold continuously through the assumptions of perfect capital mobility and the perfect substitutability of domestic credit and foreign securities, all three global monetarist properties hold for the model of Section I in the long run. It is therefore not surprising that the long-run model exhibits some familiar global monetarist properties. For example, equation (17) can be written in the familiar global monetarist form:

where η_{LY} is the income elasticity of the demand for money (see, for example, Johnson (1976)). Although equation (17a) holds continuously in the model, the endogenous variables *ŷ*, and *M* can only be treated as constant, in global monetarist fashion, in the long run. This equation permits one to establish some familiar global monetarist results.

Proposition 3. *Under fixed exchange rates, and in the absence of external inflation and domestic credit creation, balance of payments deficits are inherently temporary*.

With *ŷ* can be observed only in the short run. In the long run, *ṅ*_{PT} = *ė*_{R} = *ẇ*_{T} = 0 implies that *ŷ* = 0 if *Ḋ* = 0, this means that *BOP* = 0.

Proposition 4. *Changes in the stock of domestic credit are exactly offset by changes in the stock of foreign exchange reserves*.

In this model, changes in the stock of domestic credit are brought about through temporary changes in the flow of credit. Consider a situation in which initially *ŷ* = 0 holds continuously. From equation (17), the increase in *Ḋ* causes an exactly offsetting balance of payments deficit for as long as that increase lasts. When *Ḋ* is again equal to zero, the deficit will disappear, but foreign exchange reserves will have been reduced by the cumulative credit expansion. All other variables will remain undisturbed.^{4}

If the credit expansion finances an increase in government purchases of nontraded goods or a reduction in taxation, the dynamics are more complicated. Temporary changes in *g*^{N} or *t*_{P} affect the economy’s short-run equilibrium (equations (34)-(36)), and thus *ŷ* will not remain at zero. Because the changes in *g*^{N}, *t*_{P}, or both are temporary, however, when the original levels are restored *P* and *y* must return to their original values. Thus *M* will also return to its original value, and the stock expansion in *D* must be exactly offset by a contraction in *eF*_{B}.

Proposition 5. *An exchange rate devaluation will have no long-run effect on the balance of payments. In the absence of changes in the stock of domestic credit, the only long-run effect of devaluation will be to increase the stock of foreign exchange reserves. If the stock of domestic credit is increased in proportion to the devaluation, foreign exchange reserves will remain unchanged*.

This familiar global monetarist proposition follows from the fact that no real variables in the system (equations (37), (39), and (40)) are affected by changes in *P*_{T} = *eP*_{TF}. Thus the economy will return to its initial long-run real configuration

After some manipulation, this expression can be written

from equation (11),

Thus, if *D*_{1} = *D*_{0}, then *e*_{1}(*F*_{B1} - *F*_{B0}) = (*e*_{1}/*e*_{0} - 1)*D*_{0} > 0 for a devaluation (*e*_{1}>*e*_{0}), so that reserves increase. If, however, *D*_{1} = (*e*_{1}/*e*_{0})*D*_{0} (credit is expanded in proportion to the devaluation), then *F*_{B1} = *F*_{B0}.

The precise path the economy will follow in returning to its initial long-run equilibrium after a devaluation depends on the instantaneous response of nominal wages. If wages immediately adjust in proportion to the devaluation, the domestic price level would immediately rise in the same proportion. Initially, *e*_{R} and *w*_{T} would be unaffected; only *n*_{PT} would diverge from its long-run equilibrium *n*_{PT} would fall somewhat less than in proportion to the devaluation, which would act as a capital levy on the private sector’s financial wealth. From equation (34), domestic output would initially be depressed, causing a reduction in domestic inflation. Financial savings would initially increase, the real exchange rate would depreciate, and the product wage in the traded sector would fall. (The direction of these effects will be discussed in Section III.) If the long-run equilibrium is stable, the last two effects would eventually be reversed.

To the extent that the nominal wage rises initially by less than in proportion to the devaluation, however, the decline in *n*_{PT} will be muted, the real exchange rate will rise, and the product wage in the traded-goods sector will fall. As can be seen from equation (34), all of these effects tend to mitigate the short-run contractionary effects of devaluation.

Proposition 6. *In the presence of external inflation, the balance of payments will be in surplus in the long run if net foreign exchange reserves are positive. In this case, if the country’s nonbank sectors are net international creditors, a capital account deficit is more than offset by a surplus in the current account*.

A long-run balance of payments surplus in a small open economy is a familiar result from monetarist analyses of the optimal balance of payments deficit (see Mundell (1972)). Assume that all countries expand domestic credit at the rate

using equation (11), one has

since *ŷ* = 0 in long-run equilibrium. Note that, unlike in Mundell (1972), this surplus does not represent a seignorage payment from the home country to the rest of the world. Reserves are held in the form of securities rather than in non-interest-bearing currency. Instead, the surplus represents the “inflationary” component of the central bank’s interest receipts on its holdings of foreign reserves. To derive the long-run current account surplus, recall that in the long run *ṅ*_{PT} = *ṅ*_{G} = 0, so that *ṅ* = 0 (where *n* = *N/P*). Now, using equations (26) and (19), one obtains

Under the conditions of this proposition *F* > *F*_{B}, so the current account surplus exceeds the balance of payments surplus. Thus the capital account must be in deficit. In effect, the inflationary component of interest receipts on holdings of foreign securities by all sectors is saved and used to acquire a flow of new securities sufficient to maintain the real value of each sector’s existing stock. The total of these receipts represents the aggregate current account surplus, whereas purchases of new securities by the private sector and the government represent a capital outflow. Finally, the acquisition of new securities by the central bank constitutes the balance of payments surplus. It is clear that similar propositions could be formulated for cases in which (at least one of) *F*_{B}, *F*_{P} + *F*_{G}, or *F* is negative.

The Keynesian model of Section I therefore possesses a long-run Walrasian equilibrium characterized by full employment, profit maximization, and the usual international parity conditions in goods and asset markets. Thus the model exhibits reasonable long-run properties. Several global monetarist results follow directly from these properties. A nonzero long-run balance of payments can be observed only in the presence of external inflation, and the long-run value of the balance of payments in this case can be derived from the “reserve-flow” equation. In addition, global monetarist predictions with regard to the effects of domestic credit expansion and devaluation are upheld. Changes in the stock of domestic credit affect the stock of foreign exchange reserves with an “offset coefficient” of -1, regardless of the type of spending associated with the change in credit. Finally, the effect of devaluation depends critically on the nature of the accompanying monetary policy.

These familiar global monetarist propositions hold for the model regardless of the particular long-run equilibrium configuration

## III. Determinants of the Long-Run Equilibrium Configuration

The previous section analyzed properties that are satisfied by all possible long-run equilibria in the model. This section first investigates how the model determines the particular long-run equilibrium that is generated and then examines how the equilibrium configuration is affected by certain exogenous shocks.

### Configuration of the Economy in Long-Run Equilibrium

As indicated in Section II, equations (37), (39), and (40) imply that the evolution of the variables *n*_{PT}, *e*_{R}, and *w*_{T} at any moment in time depend on the values of these variables at that moment, on the vector of exogenous variables *y*, *y*^{N}). But the equations of short-run equilibrium, equations (34)-(36), indicate that the short-run endogenous variables themselves depend on the state variables *n*_{PT}, *e*_{R}, and *w*_{T} and on the vector of exogenous variables. Substituting equations (34)-(36) in equations (37), (39), and (40) produces a set of equations of the following form:

Thus the rate of change of the state variables depends only on the state (*n*_{PT}, *e*_{R}, *w*_{T}) of the system and the vector of exogenous variables.

A long-run equilibrium is a state *ṅ*_{PT} = *ė*_{R} = *ẇ*_{T} =0. By imposing these conditions on equations (37a), (39a), and (40a), one can solve for the economy’s long-run configuration ^{5}

As a first step, note that the conditions *ė*_{R} = 0 and *ẇ*_{T} = 0 are equivalent to the clearing of both the labor market and the market for nontraded goods, in the sense that *ė*_{R} = 0 and *ẇ*_{T} = 0 are necessary and sufficient for both of these markets to clear. The market-clearing conditions are, for the labor market,

and, for the nontraded-goods market,

Proposition 1 of the previous section established sufficiency—that is, if *ė*_{R} = *ẇ*_{T} = 0, then both the labor market and the nontraded-goods market are in equilibrium. That these conditions are also necessary follows directly by imposing the market-clearing conditions (41) and (42) on equations (39a) and (40a). Since *g*(0) = *h* (0) = 0, doing so produces *ė*_{R} = *ẇ*_{T} = 0. The characterization of long-run equilibrium *ṅ*_{PT} = *ė*_{R} = *ẇ*_{T} = 0 can therefore be replaced by the alternative one: *ṅ*_{PT} = 0, *y*^{N} = *N*(*w*_{T}*e*_{R}), and

Second, the analysis can be simplified by considering the special case in which the slopes of the labor demand curves in the traded-and nontraded-goods sectors are equal at the initial long-run equilibrium. It can be shown that in this case the level of real output must be constant in the vicinity of this equilibrium. To do so, note first that the labor-market-clearing condition (41) defines a relationship that must hold between *w*_{T} and *e*_{R} in long-run equilibrium:

The derivative of *σ* is

The last equality follows from the assumption that initially *e*_{R} = 1 and *L*^{T}*′* = *L*^{N}*′*. Next, using equations (30a) and (30b), together with the equilibrium condition (42) in the definition of real GDP given by equation (14), yields

Therefore, using equation (43), one has

The first term is equal to zero because initially both households and government devote a fraction θ of their spending to nontraded goods. The second term is shown also to be equal to zero by substituting *e*_{R} = 1, *T′* = *N′*, and *σ′* = *-w*_{T}/2. Thus the long-run value of *y*, denoted *y**, is constant.

From this restriction together with equation (43), characterization of long-run equilibrium becomes

Equation (37b) imposes the condition *ṅ*_{PT} = 0 on equation (37a) and uses equation (37) to write the function *n*( ) explicitly. The long-run equilibrium properties *y* = *y** and *y* = *y** and

These equations can be used to examine how the long-run configuration

Note that the function *n*( ) depends only on *n*_{PT}, *e*_{R}, and the exogenous variables. Substituting equation (43) into equation (44), allows one to derive a function,

that also depends only on *n*_{PT}, *e*_{R}, and exogenous variables. These equations describe a pair of loci in (*e*_{R}, *n*_{PT}) space, as depicted in Figure 2. The slopes of these loci are

Figure 2. Determination of Long-Run Equilibrium

Because (1 - θ)*c*/*c*_{3} + *N’w*_{T}/2θ*c*_{3} > 0, one also has

that is, the locus *n* = 0, along which private financial wealth is constant, is steeper than the locus ϕ = 0, along which the nontraded-goods market is in Walrasian equilibrium, as depicted in Figure 2. The long-run equilibrium configuration *A*.

### Effects of Exogenous Shocks

With this apparatus in hand, one can now establish the following propositions.

Proposition 7. *A switch in government spending from traded to nontraded goods leads in the long run to an appreciation of the real exchange rate, an increase in real private financial wealth, and an increase in the product wage in the traded-goods sector*.

A switch of government spending from traded to nontraded goods has no effect on private saving but shifts the locus ϕ = 0 downward by the amount

This shift is shown as the new locus *c*_{3} > *ρ*_{F} this real appreciation increases private saving, private wealth must rise to satisfy *ṅ*_{PT} = 0. Thus the real appreciation must be sufficiently large to reduce private excess demand despite the positive effects on private demand arising from the increase in wealth. The effect on the product wage in the traded-goods sector follows directly from the decline in *e*_{R} and from equation (43).

Figure 3. Effects on Long-Run Equilibrium of an Increase in Government Spending on Nontraded Goods

Proposition 8. *An increase in government spending on traded goods, financed by an increase in taxation on the private sector, results in a real depreciation and in a reduction in real private financial wealth*.

An increase in taxation reduces private saving. The locus *n* = 0 shifts to the left by

Because private demand for nontraded goods decreases, however, the locus ϕ = 0 shifts up by

The new loci are labeled *ñ* = 0 and *A* to *B*. A reduction in private wealth and a real devaluation are required to restore simultaneously the level of private saving and equilibrium in the market for nontraded goods.

Figure 4. Effects on Long-Run Equilibrium of an Increase in Taxes

Proposition*9. With respect to external disturbances, the effects of an increase in the foreign real interest rate are a long-run real exchange appreciation together with an increase in real private financial wealth*.

An increase in the external real interest rate reduces private consumption and thus private demand for nontraded goods. At the same time, the increase in real interest rates increases private disposable income both by increasing interest receipts on existing asset holdings (as long as private net worth exceeds the demand for real cash balances, which has been assumed to be the case) and by causing a portfolio reallocation from money to interest-bearing assets. Thus the *n* = 0 locus shifts rightward by the amount

The locus ϕ = 0 shifts upward by

Because both *n* = 0 and ϕ = 0 shift to the right in Figure 5, it may appear that the final effects on *n* = 0 to *ñ* = 0 must exceed the shift from ϕ = 0 to ϕ = 0. The rightward shift in *n* = 0 was given above. The shift in ϕ = 0 is

Figure 5. Effects on Long-Run Equilibrium of an Increase in External Real Interest Rate

Thus a real appreciation and an increase in private wealth combine to restore equilibrium in the market for nontraded goods while maintaining *ṅ*_{PT} = 0.

Proposition 10. *Finally, if the real return on cash balances affects consumption directly, an increase in the external rate of inflation results in a long-run real depreciation and in a reduction in real private financial wealth*.

Allowing for the real return on cash balances to affect consumption directly means that the consumption function (21) is modified to

with *c*_{4} < 0. If *-c*_{4} > *L* + *r*_{F}*L*_{2}, an increase in inflation will reduce saving.^{6} Under these conditions, an increase in external inflation will increase consumption and thus increase demand for non-traded goods, causing a downward shift in the ϕ = 0 locus. At the same time, the reduced saving resulting from an increase in the long-run equilibrium inflation rate shifts the *n* = 0 locus to the left. As in proposition 9, it is possible to show that the shift in *n* = 0 is dominant, leading to the results claimed above.

This analysis has focused on the effects of the various disturbances considered here on the economy’s internal equilibrium. To conclude this section, it may be useful to examine the implications of these results for the balance of payments and the stock of reserves in the long run. Using equations (17a) and (33a), the long-run balance of payments is

The long-run stock of reserves can be derived from equations (11), (13), and (33a):

In both cases the conditions *y* = *y** and

From these expressions it follows that both the long-run balance of payments (except when *increase* the stock of foreign exchange reserves. These results are all consequences of the failure of absolute purchasing power parity—that is, of the long-run endogeneity of the real exchange rate—in the model of Section I.

## IV. Conclusions

To the extent that applying the monetary approach to the balance of payments involves the use of the “reserve-flow” equation, a previous paper (Montiel (1985)) showed that the model of Section I reconciles the monetary approach with the use of a fairly conventional Keynesian structural model *in the short run*. Thus, reconciling monetary and Keynesian approaches does *not* require extending the analysis to the economy’s long-run equilibrium.

This paper has gone one step further by showing that the Keynesian model of Section I can be reconciled not only with the monetary *approach* per se in the form of the reserve-flow equation, but also with the particular *structural model* most commonly associated with that approach—that is, the “global monetarist” model. This does require extending the analysis to the long run, since the reconciliation takes the form of demonstrating that the Keynesian model of Section I has global monetarist properties in the long run. That is, it is characterized in the long run by full employment, purchasing power parity, and uncovered interest parity. It is therefore not surprising that, as demonstrated in Section II, familiar global monetarist results are produced by the long-run configuration of the Keynesian model. These include the temporary nature of balance of payments deficits in the absence of inflation, an “offset coefficient” of -1 on changes in the stock of domestic credit, and the dependence of the effects of devaluation on the nature of the accompanying monetary policy. These properties characterize the model’s long-run equilibrium regardless of which long-run configuration the economy settles into— that is, regardless of the values of the exogenous variables. The actual long-run configuration, in turn, depends on the values taken by policy variables and by variables that describe the external environment.

The operational content of this model depends on the empirical relevance of its dynamic structure. As long as changes in production and employment are rapid in the real world relative to changes in aggregate wage and price levels, short-run stabilization policy in small open economies may best be formulated within a Keynesian framework. A recent paper by Chopra (1985) supports the empirical relevance of gradual price adjustment—that is, of “Keynesian” dynamics—for several developing countries. Earlier analysis demonstrated that adopting such a Keynesian view of the structure of the economy need not require eschewing the reserve-flow equation characteristic of the monetary approach. This paper has demonstrated that such a view is also not in contradiction with the intuitively appealing market-clearing and parity conditions underlying global monetarist models, nor with the fundamental conclusions of such models, as long as their relevant domain is understood to be the long run.

The stability of the model in the vicinity of the long-run equilibrium can be examined by linearizing equations (37a), (39a), and (40a) around

where

and where η=1-c_{1}+c_{2}P_{3}-r_{F}L_{1} is the marginal propensity to save. The signs of *n*_{1} and *n*_{2} are ambiguous on the basis of assumptions in the text.

The Routh-Hurwicz necessary and sufficient conditions for stability in the neighborhood of

On the basis of assumptions made in the text, it can be shown that

It can also be shown that, if n_{1} is negative, the expression (n_{2}e_{1} -n_{1}e_{2}) must also be negative. Applying these results, together with the partial derivatives derived previously, to the Routh-Hurwicz conditions above, it follows that *n*_{1}<0 and *n*_{2} > 0 are jointly sufficient to guarantee the local stability of the system (45). In substituting for ϕ_{5} in the expressions for *n*_{1} and *n*_{2}, one finds that these signs will hold if

where β = 1 - θc_{1} + θc_{2} P_{3} > 0 is the inverse of the Keynesian multiplier for this model. The first expression stipulates that wealth effects on consumption are sufficiently strong that an increase in real wealth reduces saving. The second requires substitution effects on consumption to exceed a threshold value to ensure that a reduction in the price of nontraded goods (an increase in *e _{R}*) will increase private saving. With the assumption of constant expenditure shares and initial

*e*

_{R}= 1, this substitution effect is given by (1 - θ)θc, or (1 - θ)c

^{N}. This increase in consumption of nontraded goods increases real saving by ηβ

^{-1}(1-θ)c

^{N}. Inequality (46b) requires that this positive effect on saving exceed negative effects because of an increase in real wealth given by θ

*n*and a decrease in the domestic real interest rate equal to

_{PT}*P*.

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JohnsonHarry G. “The Monetary Approach to Balance-of-Payments Theory,” in The Monetary Approach to the Balance of Paymentsed. byJacob A.Frenkel and Harry G.Johnson (London: Allen & Unwin1976) pp. 147-67.

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As will be seen below, the assumption that quantities are demand determined when markets fail to clear also characterizes the market for nontraded goods. A more reasonable assumption in both cases would be that, in the presence of disequilibrium, quantities are determined by the short side of the market. This assumption will be inconsistent with the approach adopted here when excess demand exists in either the labor market or the market for nontraded goods. The recognition of such cases has given rise to an extensive literature on closed-economy general disequilibrium models (for example, Barro and Grossman (1976) and Malinvaud (1977)). Research on disequilibrium models for open economies, however, is in its infancy. The state of the art can be examined in Cuddington, Johansson, and Löfgren (1984). The assumption of demand determination made here is traditional in conventional Keynesian models. It simplifies the analysis by assuming essentially that behavior characteristic of the “Keynesian” region of wage-price space carries over into the “classical” and “repressed inflation” regions as well (see Malinvaud (1977)), thus obviating the need for separate analyses of those cases. Of course, to the extent that the deviations from long-run equilibrium that are of interest here involve short-run Keynesian unemployment, the assumption that quantities are demand determined will be appropriate. In any case, since the model’s long-run equilibrium is Walrasian (as shown in Section II), its long-run properties are not affected by this assumption.

Allowing for a variable markup has no effect on the qualitative conclusions in Montiel (1985). As is intuitively clear, adjustments in the markup increase the slope of the economy’s short-run Phillips curve in

The partial derivatives rely on the assumption that the marginal propensity to save is positive. This assumption ensures that an increase in the supply of nontraded goods reduces excess demand in that market.

It can easily be shown that, if the credit expansion finances an increase in *g*^{T}, the balance of payments deterioration will occur in the trade balance; if the expansion is directed toward the private sector, the capital account will deteriorate.

The Appendix derives a set of conditions that are sufficient to guarantee local stability. These conditions involve strong wealth and substitution effects on consumption.

Note that, since a positive effect of inflation on consumption was already operative in the model through the real interest rate, no previous results are qualitatively affected by this modification.