Article

Long-Run Equilibrium in a Keynesian Model of a Small Open Economy

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1986
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Although 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 yi and Li 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, L¯ is the “natural” level of employment, 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 LT + LN even if this demand exceeds the “natural” level of employment L¯.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 PT, derived from the world price PTF 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′(LT) = wT, where wT = W/PT 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 PN,

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 PN 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 L˜N, is therefore found by inverting the production function (1b):

The markup equation (5) determines the wage measured in terms of nontraded goods, wN. Because wN = W/PN, equation (5) implies wN = 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′(LN) depicts the marginal product of labor. At the product wage wN0, the profit-maximizing level of employment is L0N, which satisfies N'(L0N)=wN0 (at point A) and corresponds to a notional supply of output equal to y0N=N(L0N). If demand for nontraded goods is deficient—say, yN<y0N—the firm will operate at B with employment equal to L1N=N1(y1N)<L0N. Because the marginal product of labor exceeds the real wage by the amount DB when L1N workers are employed, the firm could increase its profits—if the additional output could be sold—by expanding employment beyond L1N. Similarly, when demand is excessive— say, at the level y2N>y0N—the firm operates at a point such as 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 wN (increasing PN) when the level of employment LN(yN) exceeds the firm’s notional demand for labor LN(wN) (that is, at a point such as C in Figure 1) and to increasing the product wage (reducing PN) 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 FB) and of credit extended to the private (DP ) and public (DG ) sectors. The central bank’s balance sheet is thus

where D = DG + DP is total domestic credit. The central bank exercises direct control over DG and DP. To defend the exchange parity, it stands ready to trade M and FB 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 FP. Net private financial wealth, denoted NP, is therefore

The private sector must allocate its portfolio among M, FP, and Dp subject to the balance-sheet constraint (12). It considers domestic credit and foreign securities to be perfect substitutes. Thus, if rF is the external nominal interest rate and r is the interest rate on domestic credit, the interest parity condition r = rF 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 BOPeḞB, differentiating equations (11), (13), and (16) with respect to time, and making the appropriate substitutions yields where rF 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 = FB + FP + FG.

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 tP 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 (NP - 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 c3>rFP^ will also be imposed.

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 (cT) and nontraded goods (cN) must be

With g representing real government purchases of goods and tB 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 (gT) and nontraded (gN) 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 eR as

Thus eR 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 eR = 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 P^, and the level of output of nontraded goods, yN. 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 nPT is real private financial wealth measured in terms of traded goods.

Real GDP, y, the domestic rate of inflation, P^, and the level of output of nontraded goods, yN, 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 gN and tP, the external variables rF and P^T, and the state variables nPT (real private financial wealth), eR (the real exchange rate), and wT (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 ρF=rFP^T is the external real interest rate. The signs of the partial derivatives are indicated under the respective variables in each equation.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 eR 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 nPT, eR, and wT 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, P^, and yN. Because y, P^, and yN 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) PT, ėR, or 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 PT = ėR = T = 0. The particular configuration of (nPT, eR, wT) 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 PT = ėR = 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 ėR = 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 L˜N, one has

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 yN* yields

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

Proposition2. Relative purchasing power parity holds in the long run.

This proposition follows directly from the long-run constancy of the real exchange rate (ėR = 0). Equation (9b) can be written in the form

Since P^T=e^+P^TF,

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 ηLY 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 P^,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 P^T=0, nonzero values of P^ and ŷ can be observed only in the short run. In the long run, PT = ėR = T = 0 implies that P^ = ŷ = 0 if P^T=0. If in addition = 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 P^T=D^=0. Now suppose that there is an increase in the flow of domestic credit either to the private sector or to the government—in the latter case, for financing purchases of traded goods. From equations (34)-(36), the economy’s short-run equilibrium is unaffected. Thus P^ = ŷ = 0 holds continuously. From equation (17), the increase in causes an exactly offsetting balance of payments deficit for as long as that increase lasts. When 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 gN or tP affect the economy’s short-run equilibrium (equations (34)-(36)), and thus P^ and ŷ will not remain at zero. Because the changes in gN, tP, 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 eFB.

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 PT = ePTF. Thus the economy will return to its initial long-run real configuration (nPT*,eR*,wT*) after a devaluation. Because the real exchange rate is unaffected, the domestic price level will rise in proportion to the devaluation. Given that the original level of real GDP (y)—and thus the original real demand for money—will be restored, the nominal demand for money will increase in proportion to the devaluation. To the extent that the central bank does not meet this increased demand for money through an expansion of credit, the private sector will be able to add to its money balances only by selling foreign exchange to the central bank, thereby augmenting exchange reserves. Using the subscripts 0 and 1 to denote pre- and postdevaluation values of the variables, and using equation (11), one has

After some manipulation, this expression can be written

from equation (11),

Thus, if D1 = D0, then e1(FB1 - FB0) = (e1/e0 - 1)D0 > 0 for a devaluation (e1>e0), so that reserves increase. If, however, D1 = (e1/e0)D0 (credit is expanded in proportion to the devaluation), then FB1 = FB0.

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, eR and wT would be unaffected; only nPT would diverge from its long-run equilibrium nPT*; and nPT 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 nPT 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 D^=P^TF. Then, from equation (17a), the long-run balance of payments is

using equation (11), one has

since P^=P^TF and 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 PT = G = 0, so that = 0 (where n = N/P). Now, using equations (26) and (19), one obtains

Under the conditions of this proposition F > FB, 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) FB, FP + FG, 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 (nPT*,eR*,wT*) that is in effect—that is, regardless of the values of the exogenous variables. The relationship between the exogenous variables and the model’s long-run equilibrium configuration is the subject of the next section.

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 nPT, eR, and wT at any moment in time depend on the values of these variables at that moment, on the vector of exogenous variables (gN,tP,ρF,P^T), and on the short-run endogenous variables (y, P^,yN). But the equations of short-run equilibrium, equations (34)-(36), indicate that the short-run endogenous variables themselves depend on the state variables nPT, eR, and wT 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 (nPT, eR, wT) of the system and the vector of exogenous variables.

A long-run equilibrium is a state (nPT*,eR*,wT*) that satisfies PT = ėR = T =0. By imposing these conditions on equations (37a), (39a), and (40a), one can solve for the economy’s long-run configuration (nPT*,eR*,wT*) as a function of the vector of exogenous variables (gN,tP,ρF,P^T). The purpose of this section is to investigate how each of the exogenous variables affects the configuration of the economy’s long-run equilibrium, under the assumption that the equilibrium is stable.5

As a first step, note that the conditions ėR = 0 and T = 0 are equivalent to the clearing of both the labor market and the market for nontraded goods, in the sense that ėR = 0 and 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 ėR = 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 ėR = T = 0. The characterization of long-run equilibrium PT = ėR = T = 0 can therefore be replaced by the alternative one: PT = 0, yN = N(wTeR), and LT+LN=L¯.

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 wT and eR in long-run equilibrium:

The derivative of σ is

The last equality follows from the assumption that initially eR = 1 and LT = LN. 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 eR = 1, T′ = N′, and σ′ = -wT/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 PT = 0 on equation (37a) and uses equation (37) to write the function n( ) explicitly. The long-run equilibrium properties y = y* and P^P^T=0 (for the latter, see proposition 2 in Section II) are incorporated into equation (37) to produce equation (37b). Equation (44) is the Walrasian equilibrium condition in the market for nontraded goods—that is, the condition yN=yN(wT*eR*). It is derived by substituting equation (21) into equation (28), and the result into equation (42). Use of the long-run equilibrium properties y = y* and P^P^T=0 yields equation (44). Equations (37b), (43), and (44) thus state that, in long-run equilibrium, private wealth must be constant, the market for nontraded goods must clear, and the economy must be at full employment.

These equations can be used to examine how the long-run configuration (nPT*,eR*,wT*) is affected by changes in the exogenous variables under the assumption that the long-run equilibrium is stable (see the Appendix).

Note that the function n( ) depends only on nPT, eR, and the exogenous variables. Substituting equation (43) into equation (44), allows one to derive a function,

that also depends only on nPT, eR, and exogenous variables. These equations describe a pair of loci in (eR, nPT) space, as depicted in Figure 2. The slopes of these loci are

Figure 2.Determination of Long-Run Equilibrium

Because (1 - θ)c/c3 + N’wT/2θc3 > 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 (nPT*,eR*) is determined by the intersection of these loci at 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 ϕ˜=0 in Figure 3. As the figure shows, the effect is to appreciate the real exchange rate, thus shifting private excess demand away from nontraded goods and thereby making room for the additional government demand. Because under the assumption that c3 > ρF this real appreciation increases private saving, private wealth must rise to satisfy 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 eR 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 ϕ˜=0 in Figure 4. The long-run equilibrium moves from 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

Proposition9. 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 eR* and nPT* are ambiguous. It can be shown, however, that the rightward shift in 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 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 c4 < 0. If -c4 > L + rFL2, 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 rF=ρF+P^T have been imposed, and in the balance of payments expression D^ has been set to zero.

From these expressions it follows that both the long-run balance of payments (except when P^T=0) and the long-run stock of reserves depend on the composition of the government’s budget. Reductions in taxes on the private sector or increases in government spending on nontraded goods reduce eR*, as demonstrated in this section. In turn, a reduction in eR* increases the domestic price level, given the domestic currency price of traded goods. This increases both the long-run balance of payments surplus and the long-run stock of foreign exchange reserves. An interesting further implication of the model is that an increase in the external real interest rate may not reduce the stock of foreign exchange reserves in the long run—a proposition associated with global monetarist models—since an appreciation of the long-run equilibrium real exchange rate will be induced that will increase the domestic price level and thereby 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.

APPENDIX: Stability Conditions

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

where

and where η=1-c1+c2P3-rFL1 is the marginal propensity to save. The signs of n1 and n2 are ambiguous on the basis of assumptions in the text.

The Routh-Hurwicz necessary and sufficient conditions for stability in the neighborhood of (nPT*,eR*,wT*) are

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

It can also be shown that, if n1 is negative, the expression (n2e1 -n1e2) must also be negative. Applying these results, together with the partial derivatives derived previously, to the Routh-Hurwicz conditions above, it follows that n1<0 and n2 > 0 are jointly sufficient to guarantee the local stability of the system (45). In substituting for ϕ5 in the expressions for n1 and n2, one finds that these signs will hold if

where β = 1 - θc1 + θc2 P3 > 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 eR) will increase private saving. With the assumption of constant expenditure shares and initial eR = 1, this substitution effect is given by (1 - θ)θc, or (1 - θ)cN. This increase in consumption of nontraded goods increases real saving by ηβ-1(1-θ)cN. Inequality (46b) requires that this positive effect on saving exceed negative effects because of an increase in real wealth given by θnPT and a decrease in the domestic real interest rate equal to P1.

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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 P^NyN space—that is, they increase the sensitivity of the domestic rate of inflation to changes in the rate of capacity utilization. This effect can be directly verified through equation (8). The variable markup simply magnifies the short-run effects of stabilization policies and external shocks on domestic inflation and, through inflation, on the output of nontraded goods.

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 gT, 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.

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