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Devaluation and Monetary Policy in Developing Countries: A General Equilibrium Model for Economies Facing Financial Constraints

Author(s):
International Monetary Fund. Research Dept.
Published Date:
January 1987
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THE CENTRAL THEME OF THIS PAPER is that financial constraints faced by developing countries play a crucial role in the short-run responses of output, prices, and the level of foreign reserves to devaluations and monetary shocks. Specifically, this paper shows that in an economy where firms are constrained to finance in advance their working capital by borrowing solely from a domestic banking sector, the output of tradable and nontradable goods depends positively on the equilibrium real monetary base (the financial constraint effect). In addition, the supply of nontradables (tradables) depends negatively (positively) on the price of tradable goods relative to the price of nontradable goods. Therefore, the response of aggregate output to exogenous shocks (devaluation and monetary shocks) depends on the relative strengths of the financial constraint effect and the relative price effects.

Traditional models that attempt to explain the short-run behavior of output and prices in small open economies facing a fixed exchange rate usually conclude that a devaluation or a monetary increase will either be expansionary (if prices are not perfectly flexible) or have no effect on the short-run level of output (if prices are fully flexible).1 In contrast with the traditional results, but in accordance with recent theoretical and empirical work on developing countries, this paper shows that if proper account is taken of the limitations in financial markets faced by developing countries, anticipated (permanent or transitory) increases in the level of the exogenous component of money might be expansionary even under complete price flexibility. Moreover, this paper establishes that an anticipated devaluation might result in a contraction in the short-run level of output. These results are demonstrated by constructing a model in which an expected increase in domestic inflation leads to a reduction in the equilibrium level of the real monetary base and in the real amount of domestic credit available to finance output production.2 Thus, any variation in an exogenous variable which leads to an increase in expected inflation causes a “tightening up” of the financial constraint, with negative effects on the output levels of both tradable and nontradable goods. Even in the presence of a favorable relative price effect, therefore, the supply of a component of output might decrease if the relative price effect is outweighed by a negative financial constraint effect. In this model, either a decrease in the anticipated level of the exogenous component of money or a devaluation leads to an increase in the expected inflation rate. Therefore, they lead to a negative financial constraint effect, which, if strong enough, results in a short-run contraction of aggregate output.

The idea that a devaluation might be contractionary in the short run is not new. At the empirical level, studies by Edwards (1985) and Gomez-Oliver (1985) found that devaluations have generated a shortrun decline in aggregate output in some developing countries. There are several theoretical arguments that attempt to explain such a result. Some, such as those by Diaz-Alejandro (1963) and Krugman and Taylor (1978), among others, argue that a devaluation is contractionary because of its effects on demand, which range from negative real balance effects to income distribution toward economic agents with a high marginal propensity to save. Other models advance supply-side arguments of the kind used in this paper to explain the contractionary effects of a devaluation. In particular, Taylor (1981) and van Wijnbergen (1986) construct models in which the need to finance working capital requirements provide a channel via which a devaluation leads to a reduction in the level of output. However, those models use a nonstochastic disequilibrium framework where either output is supply determined (as in van Wijnbergen) or prices are determined by fixed markups over variable costs (especially the interest rate as in Taylor (1981)). The model used in this paper shows that the introduction of a financial constraint might lead to a short-run output contraction following a devaluation even in a stochastic general equilibrium model where agents are assumed to be fully rational and where prices adjust to clear markets.

Financial constraints have also been advocated as a channel via which reductions in the level of the exogenous component of money has a contractionary effect on output in the short run (see, for example, Cavallo (1981), Bruno (1979), Taylor (1981), van Wijnbergen (1982), and Buffie (1984)).3 However, in that literature restrictive monetary policies not only reduce output but also increase inflation in the short run. That last result does not follow, however, from financial constraints but from wage and price rigidities assumed in the models. In contrast, in the model of this paper, the assumption of full equilibrium implies that a restrictive monetary policy unambiguously decreases the price level. This classical result holds even when a strong enough financial constraint effect leads to a short-run contraction in aggregate output.

This paper follows a choice-theoretic approach. A macromodel is fully derived from the decision rules followed by rational agents who maximize utility or profits subject to the constraints imposed by the environment in which they live (which will be defined below). The model is then solved in a general equilibrium, rational expectations, stochastic framework.

The rest of the paper is organized as follows: Section I describes the basic characteristics of the model, with special emphasis on the assumptions regarding the organization of markets and the timing of transactions. Section II derives the optimal decision rules implied by the maximizing behavior of economic agents, while the next section derives the domestic aggregate supply and demand functions for tradable and nontradable commodities. Section IV sets out the complete macromodel to be solved in this fixed exchange rate economy. Under the assumption of complete current information, Section V then solves for the equilibrium levels of the outputs of tradable and nontradable goods, the stock of foreign exchange reserves, and the price of the nontradable good. This section also discusses the implications for the economy of a devaluation, a change in the foreign price of tradables, and a change in the exogenous component of the monetary base. Section VI then briefly discusses the implications of relaxing the assumption of full current information. Finally, Section VII summarizes the main conclusions.

I. Basic Model

Consider an economy with four agents—firms, households, banks, and the government—and five markets: money, tradable commodities, nontradable commodities, (domestic) labor, and (domestic) credit.

Money is the only tradable asset and serves both as a medium of transactions and as a store of value. The liquidity constraint associated with Clower (1967) and used by Lucas (1980), Stockman (1980), and Helpman (1981), among others, motivates the transactions demand for money. All transactions are carried out with money. Households need money in advance to purchase commodities and firms need money in advance to finance their production process. To motivate the demand for money as a store of value, the existence is assumed of overlapping generations at each moment, as in Samuelson (1958). Each generation lives for two periods. When young, households supply labor and demand commodities and money. Money is held to buy commodities at the end of this first period or to be carried over into the second period as a store of value with which to pay for consumption during retirement.4

This economy is assumed to face a severely limited capital market; there is no market for primary securities nor any financial intermediation other than commercial banking. The only source of finance for firms is assumed to be loans from domestic commercial banks since sales of equities or bonds to domestic households or foreigners are ruled out. In this context, firms face the following “financial constraint”: they need to finance their monetary advances by demanding credit solely from the banking sector. Thus, the availability of real credit constrains the level of output. It is also assumed that imperfections in the capital market prevent households from obtaining bank loans.

The credit market therefore involves the banking system as the only supplier of credit and firms as the only agents demanding it. The banking system is made up of a central bank and commercial banks. The central bank has three functions: it finances the government (whose only function is to provide transfers to households) through the issuance of highpowered money; it imposes a required reserve ratio on the commercial banks; and it acts as the foreign exchange authority. In this fixed exchange rate regime, the monetary base (Ht) has two asset counterparts: government credit (GCt) and foreign exchange reserves (Ft).

Commercial banks hold reserves, supply credit to firms, and issue only one kind of deposit: demand deposits that do not pay interest.5 It is assumed that banks incur no labor costs in providing the services of intermediation and that bank loans have a maturity length of one period.

It is assumed that households and firms keep all their money as demand deposits issued by the commercial banks; that is, that their currency-deposit ratio is equal to zero. Hence, the entire monetary base is held as reserves by the banks. Domestic residents do not hold foreign exchange. It is also assumed that they buy foreign money at the end of the period when they decide to import the tradable good. Finally, only domestic residents hold domestic demand deposits.

Time is divided into discrete, uniform intervals. A sequential trading arrangement in which labor and credit markets open and clear at the beginning of the period and the commodities (tradable and nontradable) and money markets at the end of the period is assumed. At the beginning of period t, firms and banks distribute profits realized at the end of period t - 1 to households (the old generation), firms pay back past loans to the commercial banks, demand labor from households (the young generation), and loans from the banking system. Also, the old generation receives a lump sum net transfer from the government. The net governmental transfer (Trt) is assumed to be equal to the increase in government credit (ΔGCt).

In this system of fixed exchange rates, the beginning-of-period monetary base (aHt) differs from the end-of-period monetary base (bHt) if there is any net change in the economy’s stock of foreign reserves (Ft). (In general, the subscript a refers to the beginning of a period and the subscript b refers to the end of a period.) While the component of the monetary base corresponding to the government credit (GCt) is determined at the beginning of the period, changes in foreign exchange reserves occur at the end of the period when transactions in tradable commodities take place.

Hence, the beginning-of-period monetary base of the central bank is:

while the monetary base at the end of the period is equal to:

At the beginning of the period, the central bank imposes the reserve requirement ratio (K). Since the nonbanking sector is assumed to hold its money only in the form of non-interest-bearing demand deposits, the beginning-of-period bank reserves equal the beginning-of-period monetary base. Therefore, the commercial bank’s decision rule to supply credit (Cts) is:

The commercial bank’s supply of credit implies that the bank finds it optimal to supply as much credit as possible given the reserve requirement ratio. Hence the optimal decision rule for the bank is to hold zero excess reserves. This result follows obviously from the assumption that the bank pays no interest on demand deposits, but it will also and equally obviously hold zero excess reserves as long as the interest payments on deposits are lower than the interest charged on credit.

Once the credit and labor markets clear, production takes place and no further transactions occur until the end of the period when the markets for tradable and nontradable commodities open. At this moment, the young generation decides on its current and future consumption plan and thus, on its demand for money. Both generations demand commodi ties. Therefore, given the end-of-period supply of money (Mt), which in this economy equals the monetary base (bHt) plus the supply of bank credit (Cts), the price of the nontradable good and the equilibrium level of foreign reserves are determined. Firms also carry over money in an amount equal to the value of the total output (Pt Yt) in order to pay back banking loans and distribute profits. The old generation dies between periods and it is assumed that it has depleted its money balances on consumption before dying. At the start of t + 1, a new generation is born and the whole process begins again.

II. Maximizing Behavior of Economic Agents

The problems to be solved by a representative firm and household will now be considered. Rational and maximizing behavior for agents implies that they use all the available information relevant for their decisions. However, they do not have perfect foresight. Specifically, in this section it is assumed that agents do not observe current prices of commodities at the beginning of the period, nor do they know future prices at the end of the period. Hence, they have to form expectations about these variables. In addition, agents have to form beginning-of-period expectations about the exchange rate.

Representative Firm

The objective of the firm is to maximize expected profits. The representative domestic firm is assumed to produce both tradable (Yt*) and nontradable (Yt) commodities. The firm engages in a production process that yields joint products. In addition, a single input, domestic labor supply (Lt), is used in the production of the two outputs. Specifically, in order to obtain explicit results, the following product transformation curve is assumed:

Equation (4) states costs of production in terms of labor units. φt is a productivity shock and is assumed to affect both outputs equally.6

The total cost faced by the firm is the total wage bill plus the interest payments made on bank loans needed to pay labor in advance. Therefore, the maximization problem for the representative firm becomes:

where:

E = the expectations operator; atE(X) refers to expectations at beginning of period t about a variable X; btE(Xt) refers to expectations about X at the end of period t;

πt = nominal profits realized by the firm;

Yts = domestic supply of the nontradable good;

Y*ts = domestic supply of the tradable good;

Pt = price level of the nontradable good;

Pt* = price level of the tradable good;

St = nominal exchange rate: the domestic currency price of foreign exchange; and

it = nominal interest rate.

The superscripts “s” and “d” refer to the quantity supplied or demanded respectively, of the attached variable.

Equation (5) is maximized subject to the product transformation curve (equation (4)) and to the firms’ financial constraint:

Given that the only reason for a firm to demand loans is to finance labor, this constraint has to be satisfied as an equality every period.7

The information that the firm uses at the beginning of the period to form its expectations consists of information on variables up to period t – 1, plus the current wage rate, the interest rate, and the productivity term. Therefore, the maximization procedure leads to the following supply function for the nontradable good:

and to the following supply function for the tradable commodity:

From these decision rules, it is clear that the supply of each commodity depends positively on its own price and on a “common” productivity shock, and negatively on the “effective” cost of labor: Wt(1 + it).

Substituting equations (7) and (8) into equation (4) yields the demand for labor:

The demand for labor depends positively on the expected money prices of the final outputs and on the productivity shock, and negatively on the effective cost of labor.

Finally, equation (6) can be used to derive the firms’ demand for credit:

Representative Household

Each household lives two periods and maximizes expected utility. Consumption of commodities and leisure are assumed to yield positive utility. Thus, utility depends inversely on time devoted to work. For simplicity, and in order to obtain explicit results, it is assumed that the young agent maximizes the expected value of the following utility function:

where the subscript 1 is used to indicate the agent’s first period of life and 2 to indicate his second and last period. Y1, Y2 and Y1*,Y2* refer to his demand for nontradables and tradables, respectively, for the first and second periods. μ1 refers to a random shock that increases the utility derived from current consumption, and (L¯L1) is the amount of leisure available to the agent after he has supplied labor. Also β is a discount factor and 0 < β ≤ 1. In addition τ reflects each period’s share in expenditure of the nontradable good. The utility function (11) is additive, separable in consumption and leisure and shows constant marginal utility of future consumption.

In the first period of his life, the individual works, consumes, and saves money. In the beginning of the second period he receives net transfers (Tr2) from the government and profits from the firm (π1) and banks (i1 C1).

Thus, the lifetime budget constraint of the household is:

The problem for the young generation is to maximize the expected value of equation (11) subject to the budget constraint (12) and to the condition that the young agent’s demand for money be non-negative:

The inequality constraint (13) is necessary to satisfy the assumption that all transactions are carried out with money, given that the young generation starts life with no money.

The representative young agent faces a two-stage decision problem: at the beginning of the period, he chooses his labor supply, taking into account the available and relevant information at his disposal at that moment, which is the same as the information available to firms. At the end of the period, the agent decides on his demand for commodities and money, taking into account the information available at that time, which includes the information available at the beginning of the period plus knowledge of the exchange rate, the price level of the tradable good, and the price level of the nontradable good.

Appendix I shows the derivation of the agent’s decision rules. It is enough to state here that the maximization problem leads to the following decision rules for consumption in the first period:

That is, current consumption of tradable and nontradable commodities depends positively on expected inflation, where the relevant future price level is a price index, while the relevant current price level is the own commodity price. The decision rules (14) and (15) also depend positively on a random term (μt) which affects the marginal utility of (total) current consumption.

The labor supply decision rule derived in this model is:

That is, labor supply depends positively on the expected future real wage where the expected future price index is the relevant deflator. This is so because the supply of labor involves an intertemporal decision.

Equations (14) and (15) represent the consumption demands of the young generation. To obtain the total market demand for consumption goods, we have to add to these the demands of the old generation. Such demands have already been obtained in Appendix I (equations (51) and (52)), where the solution to the agent’s second period problem was presented. Hence, for every period t, the total current demand for nontradables (Ztd) and tradables (Z*td), respectively are:

Finally, the young agent’s demand for money (bMtd) can be obtained by subtracting the value of his consumption bundle from his wage earnings, and by using equations (14) and (15):

That is, the household’s demand for the real stock of money depends positively on real wage income and negatively on the expected inflation rate.

III. Aggregate Supply and Demand Functions

In Section II, domestic supply equations for the tradable and nontradable commodities were derived as functions of the wage rate and the interest rate (see equations (7) and (8)). However, the equilibrium conditions in the labor and credit markets determine both the nominal wage rate and the interest rate.

Aggregate Supply

This section will obtain the final form of the aggregate supply functions. In order to achieve this, the model will be cast in log-linear terms. Lower-case letters will be used to represent the log of a variable (with the exception of it, which stands for the observed value of the interest rate).

Based on equation (9) and assuming that the “weights” in the firm’s price index equal those in the consumer price index, a log-linear version of the demand for labor is:

where ut=logφtN(0,σu2),ut is independent of the other disturbances in the model, and pitτpt+(1τ)(pt*+st).

Similarly, based on equation (10), a log-linear approximation for the demand for credit is:

Log-linear versions for the supply of labor and credit are based on equations (16) and (3), respectively. Hence:

In addition, log-linear approximations of the supply functions for nontradable and tradable goods obtained in Section II (equations (7) and (8)) are as follows:

The unitary coefficients (in absolute value terms) accompanying the arguments of ytsandy*ts reflect the specification of the production side of the model, which implies a unitary own price elasticity and a unitary factor price elasticity for the output supplies.

By solving the system formed by equations (20) to (25), and the equilibrium conditions ltd=ltsandctd=cts, the aggregate supply functions of outputs are obtained:

where:

The most important features of equations (26) and (27) are as follows. First, the only difference between the two functions lies in the coefficient of the expected relative price term. This difference is due to the fact that, although both commodities share the input markets indistinguishably, they face separate output markets. Now, the real exchange rate in this model coincides with the relative price term. Hence, an appreciation of the expected real exchange rate—an increase of the term:[atE(ptpt*st)]—decreases the supply of tradables and increases that of nontradables. The third term of both equations will be labeled “the relative price effect.”

Second, the supply of both types of commodities depends positively on the expected real monetary base evaluated at the future level of the price index.8 This result is a direct consequence of the “financial constraint” assumption, and hence the second term of the output equations will be labeled “the financial constraint effect.” Third, the random term affecting productivity affects the aggregate supplies with a positive coefficient less than one because in this model ut has a nonproportional effect on the interest rate.

The system formed by equations (20) to (25) can also be represented diagrammatically.9 Using equations (21) and (23) and the equilibrium condition ctd=cts,CC in Figure 1 represents the credit market equilibrium locus:10

Figure 1.Determinants of the Aggregate Supply Function

In addition, using equations (20) and (22) and the equilibrium condition lts=ltd,LL in Figure 1 represents the labor market equilibrium locus.

That is, LL represents:

Finally, using either equation (24) or equation (25), YY or Y*Y* represents the locus of constant output (of either nontradables or tradables).

The equation for the locus YY can be written as:

while the equation for the locus Y*Y* can be written as:

For convenience, only the locus YY is presented in Figure 1.11 Notice that for given relative prices and the general price level, points above and to the right of YY correspond to lower output, while points below YY correspond to higher output. Also, since atE(pit) enters all the curves with a unit coefficient, an increase in atE(pit) shifts all curves up equally, leaving output unchanged. Figure 1 will prove very convenient to illustrate the output effects of monetary policy and devaluations analyzed in Section V.

Aggregate Demand

Equations (17) and (18) can be treated as the aggregate demand functions for nontradables and tradables, respectively. Equation (19) represents the households’ aggregate demand for money. To obtain the total demand for money (Mtd), the end-of-period demand for money by firms, fMtd (equal to the value of final output) has to be added to equation (19).

The three markets (the two commodities markets and the money market) clear at the end of every period. The equilibrium conditions for the nontradable good and money markets are:

In addition, the equilibrium condition for the tradable commodity market is:

Under the assumption of zero capital mobility and fixed exchange rates, the overall balance of payments is identical to the balance of trade, which in this model is equal to the difference between the value of the supply and demand for tradable goods; that is, only net exports can be explained in this model, but not the composition between exports and imports. Such is the nature of equation (34).

IV. Complete Macromodel

The results from the previous sections can now be consolidated into the macromodel to be analyzed in the next sections. By Walras’ law we can use only the tradable and nontradable commodity markets to represent the entire macro system.12 The complete model consists, then, of the following set of equations (expressed in log terms):

Equations (35) and (36) are log-linear approximations of equations (17) and (18), respectively, with εt being a serially independent log normal disturbance, which is also independent of the rest of disturbances of the model, where:

Equations (37) and (38) are identical to equations (26) and (27), respectively, and are repeated here only for convenience. These first four equations characterize the domestic markets for tradable and nontradable commodities.

Equation (39) is a log approximation of the price index. Equation (40) is a log-linear approximation (based on a Taylor expansion) of the identity for the beginning-of-period monetary base (equation (1)). As discussed in Sections I and II, a distinction between the beginning and the end-of-period monetary base arises in this fixed exchange rate model. The government credit (gct) is decided at the beginning of the period, but transactions leading to a change in the level of foreign reserves occur at the end of the period. This feature of the model implies that the end-of-previous-period level of the foreign reserves (ft-1) enters into the structural supply and demand equations in the same way as does the current level of government credit (gct).13

The equilibrium condition in the nontradable goods market is represented by equation (41), while the equilibrium in the market for tradable goods is represented by equation (42).14

V. Expectations and the Behavior of Prices and Output Under Complete Current Information

In the previous sections, price expectations were not treated as endogenous. To solve the model formed by equations (35)-(42) for output, nontradable goods prices, and the stock of foreign reserves, it will be assumed that expectations are formed rationally in the sense of Muth (1961). It is now necessary to specify the processes governing the behavior of the exogenous variables.

The exchange rate is assumed to be an exogenous variable in this model. It is assumed that the current exchange rate can change relative to its previous value only by a disturbance ξt (representing the amount of devaluation or revaluation), which is assumed to be known by the public. That is, the exchange rate is assumed to follow a random walk:

where ξt, is a white noise disturbance independently distributed from the other disturbances in the model.

Since the level of foreign reserves and hence, the money supply, are endogenous variables in this fixed exchange rate case, the only exogenous monetary element in the domestic economy is government credit. It is assumed that the process followed by the government credit involves a constant trend growth rate, m, in addition to stochastic elements that make the growth rate fluctuate around m. Stochastic shocks will be of two kinds: permanent (vt) and temporary (xt). Hence, gct is generated in accordance with:15

The two random terms vt and xt are generated by white noise processes, that is:vtN(0,σv2);xtN(0,σx2) and both vt and xt are serially independently distributed.

The process governing the behavior of the price of the tradable good pt* is assumed to be similar to the process followed by the exchange rate. Hence, pt* is generated in accordance with:

where nt is a stochastic permanent shock and nt is a white noise process, that is: ntN(0,σn2).

In this section, it is assumed that agents possess full current information; that is, they know (or have enough information to infer) all current values of the relevant variables that affect their decisions.

To facilitate the exposition, the derivation of the final solutions for the stock of foreign reserves and for the price and output levels of the nontradable good is presented in Appendix II. The behavioral responses of the price level of the nontradable good, the stock of foreign reserves, and the levels of output, following a change in the exogenous variablesof the model will now be analyzed.

Increase in Government Credit

Consider first an increase in the current level of government credit caused by a positive permanent monetary change (vt). The price level of the nontradable good will increase and the level of foreign reserves will decrease, because there will be a net “potential” excess demand for each commodity. These changes in pt and ft, however, will be less than proportional to the increase in government credit.16 two effects: (1) a financial constraint effect; and (2) a relative price effect. While the increase in gct generates an unambiguous relative price change favoring an increase in the output of nontradables and a decrease in that of tradables, the response of the real monetary base (deflated by the expected future general price level) needs some explanation. Since only the predetermined level of foreign reserves (ft-1) enters into the beginning-of-period monetary base, an increase in gct will unambiguously result in an increase in the nominal level of the monetary base.

However, the response of the real monetary base can be analyzed by considering the expected inflation rate.17 By using the relevant coefficients in equations (62) and (63) of Appendix II, it is clear that:

where δ refers to a partial derivative. Equation (46) is negative and less than 1 in absolute terms. Thus, although the current price level of the nontradable good will increase, the public will also expect a deflation in the subsequent period. The intuition behind this result is straightforward: the decrease in the level of reserves which follows an increase in vt does not affect the current general price level. This is affected solely by the predetermined value of ft-1. However, the decrease in reserves will decrease the future level of the monetary base and hence will impinge negatively on the expected future general price level. Now, this decrease in the expected inflation rate generates an increase in the equilibrium level of the real monetary base (deflated by the future expected general price level) and hence an increase in the firms’ demand for labor. Thus, it generates a positive financial constraint effect tending to cause a short-run increase in the output of both commodities. As a result, the response of nontradables output will always be positive following an increase in vt, but the output of tradables may either increase or decrease. It will increase if the positive financial constraint effect is greater than the negative relative price effect; hence, a strong enough financial constraint effect will result in higher output of both goods.

Suppose now that the increase in the government credit is caused by a temporary monetary increase (xt). The relative price effect will be similar to that analyzed above, and will favor an increase in the supply of nontradable goods. It will, however, be smaller. The financial constraint effect will also be unambiguously positive in this case because there will be an unambiguous reduction in the expected inflation rate. Moreover, the financial constraint effect is larger if the monetary increase is temporary instead of permanent. The intuition behind this result is as follows: not only will government credit decrease in period t + 1, but the reduction in the current level of foreign reserves will further reduce the level of the monetary base in period t + 1. Hence, the expected value of the future general price level will be lower. As a result, and as in the case of a permanent increase in the government debt, a strong enough financial constraint effect will generate an increase in the level of aggregate output.

The output effect of an increase in the level of government credit (either permanent or temporary) is illustrated in Figure 2. From equations (62) and (67) of Appendix II, we know that this raises atE(pit) = pit, so that all three curves move up proportionally leaving output unchanged. Call this point E1 in Figure 2. Now, the increase in aht causes CC to move down. In addition, it is clear from equation (46) that the expected inflation rate decreases. Therefore, the increase in atE(pit+1) is smaller than the increase in pt, which in turn is smaller than the increase in aht.18 Therefore, LL shifts to the right, but since (aht - atE(pit+i)) increases, E2 lies below YY, implying that the financial constraint effect increases output.19 Finally, the raise in pt causes a change in relative prices that shifts the YY curve to the right. This further increases the distance between E2 and the YY locus and represents the positive relative price effect.

Figure 2.Effects of a Monetary Expansion

Notice that the analysis for the tradable goods implies an identical financial constraint effect but a negative relative price effect since the Y*Y* curve has to shift to the left, diminishing the distance between E2 and the Y*Y* locus. If this shift were large enough, E2 would lie above the new Y*Y* locus; and, in that case, the net effect of the monetary expansion may be negative for the tradable goods.

The result that an increase in government credit generates a positive financial constraint effect arises because we have considered increases in the level of that monetary aggregate. Instead, consider now an increase in the trend growth rate of government credit. In that case, while the relative price effect generated by an increase in m is similar (but bigger) than the one generated by an increase in the level of the debt, the financial constraint effect might be quite different and might even decrease the supply of both commodities. In fact, it is clear from Appendix II that when the rate of growth of the government credit increases, the effect on the inflation rate is:

This effect might be positive or negative. If it is positive, the real monetary base (deflated by either pt, or atE(pt+1)) will decrease, generating a negative financial constraint effect on the aggregate supply of both commodities. In that case, the level of output of tradable goods will unambiguously decrease and the level of output of nontradables might decrease if the negative financial constraint effect outweighs the positive relative price effect. Notice that in this case, output responses are opposite to those resulting from an increase in vt and, hence, aggregate output will decrease following the monetary expansion. This example serves to illustrate the importance of the nature of an observed increase in government credit in order to derive conclusions regarding the monetary effects on output. In particular, while a restrictive monetary policy that decreases the level of government credit might be contractionary, a decrease in the trend growth rate might be expansionary since it lowers the expected rate of inflation.

Devaluation or Increase in the Foreign Price of Tradable Good

A devaluation or an increase in the foreign price of the tradable good affects the expected general inflation rate through their effects on the domestic price levels of both produced goods. In addition, while such changes do not affect the current level of the beginning-of-period monetary base, they do affect the future level of the monetary base through their impact on the level of reserves.

Since st enters into the system of structural equations in the same way as pt* does, the economic effects of an anticipated permanent devaluation, that is, a rise in ξt, are identical to the effects generated by a permanent rise in the price level of the tradable good (nt). Thus, consider an increase in either nt or ξt. Both the price level of the nontradable good and the level of foreign reserves will rise because this kind of increase generates a “potential” excess demand for nontradables and an excess supply of tradables.20 The effect on the output levels of both commodities can, once more, be decomposed in a “relative price” effect and a “financial constraint” effect. From Appendix II, it can be seen that the relative price effect implies a depreciation of the real exchange rate that favors an increase in the supply of tradables and a decrease in the supply of nontradables (since θ< 1). Since the current nominal monetary base at the beginning of the period remains unchanged when there is a devaluation or a rise in the price of tradables, the financial constraint effect can be evaluated by analyzing the effect on the expected future general price level.21 That is, from Appendix II:

which is unambiguously positive because |Y4 | < |Y5 | and θ7 < 0. This result is straightforward. A permanent devaluation or a permanent rise in the current price level of the tradable good increases the current level of foreign reserves. This in turn increases the next-period monetary base and hence generates an increase in the expected value of the future general price level. Since the change in reserves does not affect the current beginning-of-period monetary base, the increase in the expected value of the future general price level will be larger than the increase in the current general price level; that is, the expected inflation rate will increase. As a result, the current real monetary base (deflated by atE(pit+1)) will decrease, generating a negative financial constraint effect. Thus, the supply of the nontradable good will unambiguously decrease, while the response of the supply of the tradable good depends on the importance of the relative price effect compared to the financial constraint effect. If the latter outweighs the former, the supply of tradables also decreases. In this case, and contrary to the standard result, a devaluation or an increase in the price level of the tradable good give rise to a decrease in aggregate output.

The output effect of an anticipated devaluation is illustrated in Figure 3. The devaluation raises the general price level, shifting up all three curves equally, leaving output unaffected. Once more, call this point E1, in Figure 3. While the beginning-of-period monetary base remains unchanged, and therefore, the CC curve does not shift, it is clear from equation (48) that the expected future general price level increases, shifting upwards the LL curve. Therefore, as E2 is above YY, the financial constraint effect is contractionary. In addition, the change in relative prices shifts the YY curve to the left, generating a negative relative price effect that exacerbates the output decrease of nontradables. In contrast, the relative price effect shifts the Y*Y* curve to the right, decreasing or even offsetting the output loss of tradables.

Figure 3.Effects of a Devaluation

VI. Incomplete Current Information

Relax the assumption that agents possess full current information by assuming instead that: (1) agents do not know how much of a monetary shock (a shock to government credit) is temporary and how much is permanent; and (2) at the beginning of the period, although agents know the exchange rate rule in equation (43), they do not know the value of ξt. Moreover, they do not observe the price level of the tradable good that will prevail at the end of the period. The beginning-of-period observation of the interest rate only allows agents to infer the total current value of the government credit but knowledge of gct does not convey any relevant information about the current exchange rate or the current price level of the tradable good.

The beginning- and end-of-period price level expectations are not equal under fixed rates because it is assumed that nt and ξt, are only known at the end of each period.22 This feature of our model makes its solution particularly cumbersome. Hence, rather than presenting specific solutions of the model, the remainder of this section will discuss the effects on the model’s endogenous variables of removing the assumption of full current information.

Confusion Between Permanent and Temporary Monetary Shocks

Under incomplete current information, the direction of the responses of the price level of the nontradable good and the stock of foreign reserves to an increase in government debt will be the same as in the full current information case since in the latter case the effects of both a temporary or a permanent monetary shock were qualitatively similar. They were of different magnitudes, however. Under full current information, the (positive) response of the price level of the nontradable good and the (negative) response of the level of foreign reserves were larger if they followed a permanent rather than a temporary change in the government debt. It follows that if a temporary shock is mistakenly interpreted as permanent, the increase caused in pt will be larger than in the full current information case.

In addition, under full current information, both shocks generated an increase in the real monetary base (a positive financial constraint effect) and a relative price effect favoring the supply of the nontradable good. However, while the relative price effect was larger after a permanent monetary shock, the financial constraint effect was larger after a temporary shock. Thus, while both shocks generated a definite increase in the supply of the nontradable good, it could not be determined which shock generated the greater response. Moreover, although the response of the supply of the tradable good is ambiguous, a temporary monetary shock might lead to an output expansion of the tradable good, even if a permanent shock leads to an output contraction of this good. This result obviously follows because of the larger financial constraint effect and the smaller relative price effect generated by a temporary shock.

From the above considerations, it follows that, under incomplete current information, the confusion between permanent and temporary monetary shocks cannot change the direction of the response of the supply of the nontradable good relative to the full current information case; only the magnitude of the output increase will differ between the two alternative information sets. However, the confusion between monetary shocks might change the direction of response of the supply of tradables relative to the full current information case. In particular, if under full current information, a temporary shock leads to an output expansion while a permanent shock leads to an output contraction of the tradable good, a permanent shock mistakenly viewed as temporary (when lack of complete current information is assumed) might increase the output level of the tradable commodity.

The Lack of Observation of Exchange Rate and Foreign Price of Tradable Good

In our model, output decisions are made at the beginning of every period based on the information available at the time. If the current period exchange rate and the price level of the tradable good are not known at the beginning of the period, agents must form expectations about them. In this fixed exchange rate case, agents cannot infer the value of either the exchange rate or the price level of the nontradable good by observing the beginning-of-period current level of the monetary base. Thus, the short-run supplies of both commodities no longer depend on their actual price levels; instead, they depend on their expected price levels.23 Hence, the current output levels of both commodities will remain unchanged following either an unanticipated permanent devaluation or an unanticipated shock to the price level of the tradable good.

Now, since the outputs remain unchanged following an unanticipated shock to Pt* or a change in ξt, the price level of the nontradable good and the stock of foreign reserves have to bear all the adjustment. In particular, an unanticipated positive shock (either a rise inξt or a rise in nt) will raise the demand for nontradables and will decrease the demand for tradables implying that the increase in both pt and ft will be larger than in the complete current information case and hence, the depreciation of the real exchange rate will be smaller in the incomplete current information case.24

In contrast with the full current information case, no output response will follow an unanticipated devaluation or an unanticipated foreign price shock. This result contrasts with that obtained from models which stress the effects of price misperceptions on aggregate supply. In those models an anticipated devaluation has no effect on the output level, while an unanticipated devaluation does. The opposite result arises here. This is an interesting conclusion because, to the extent that real world economies are properly described by the features of this model, we may conclude that an unanticipated current devaluation will increase the level of foreign reserves without hurting the current levels of output and employment of those economies. However, notice that in period t + 1, ξt will be part of the information set and hence the unanticipated devaluation of period t might then have the contractionary effects which an anticipated devaluation would have had in period t. That is, the short-run output effects of an unanticipated devaluation will not be eliminated, but only postponed.25

VII. Conclusions

This study has set up a model for a small open economy under a fixed exchange rate regime to analyze the short-run output responses to devaluations and monetary policies in developing countries. Specific considerations have been the effects of changes in the exogenous component of the money supply (which in this model is the level of government credit), the price of the tradable goods, and the exchange rate (a devaluation) on the output of the domestically produced commodities, the price of the nontradable good, and the level of foreign reserves. It has been shown that the need of domestic firms to finance in advance their working capital from a domestic banking sector (the financial constraint) has important implications for the economy’s response to such exogenous shocks.

In particular, it has been shown that if the financial constraint effect is strong enough, an anticipated rise in the level of government credit will be expansionary since it increases the short-run level of the real monetary base, while an anticipated rise in the trend growth rate of government credit might be contractionary if it decreases the real monetary base. Moreover, an anticipated rise in the foreign price of the tradable good or an anticipated devaluation will be contractionary in the short run.

In addition, a permanent increase in the money supply (that is, government credit) might generate higher output of both commodities if it is mistakenly viewed as temporary, even in situations where a fully anticipated permanent monetary change would lead to a reduction in the output of the tradable good.

Finally, an unanticipated devaluation, or an unanticipated rise in the foreign price of the tradable good, will result in a short-run depreciation of the real exchange rate, but will have no contemporaneous effects on output. However, it might lead to lower output of both goods in the subsequent periods. This result differs from that arising in models where price misperceptions enter output supply functions; in those models, an unanticipated devaluation leads to an immediate, albeit short-run, output expansion.

In summary, this study has shown that for small open economies facing severe financial constraints under a fixed exchange rate regime, the direction of the output response to exogenous shocks depends crucially on the nature of the exogenous shock impinging on the economy and on the importance of the financial constraint effect compared with the relative price effect.

Derivation of Household’s Decision Rules

To illustrate the agent’s maximization problem, first consider the end of the period when the agent’s labor supply is known.

At the end of period 1, the agent will choose his current and future consumption levels of tradable and nontradable goods. He knows that in period 2 he will have nominal wealth A2 and will have to choose Y2 and Y2* in order

subject to:

From equations (49) and (50), the demand functions for the agent’s second period of life are obtained:

These demand functions show a unitary elasticity of demand with respect to expenditure on future consumption (A).

Given equations (51) and (52), the maximized value of Y2τY2*(1τ) is:

where:

The price index PI is homogeneous of degree one, due to the Cobb-Douglas specification of the utility function. Substituting equation (53) into equation (11) of the main text and noticing that the budget constraint (equation (12) in themain text) requires:

The first period problem is obtained.26 This requires the agent to choose Ytd,Y*td to:

where λ is the Kuhn-Tucker multiplier associated with the constraint in equation (13) in the main text.

Imposing the restrictions that consumption of both commodities be positive every period and that the young individual’s demand for money be positive, the maximization procedure leads to the following decision rules:

Now, we can turn to the young agent’s maximization problem at the beginning of the period. At that time, the individual’s demands for commodities are stochastic variables. The agent’s problem is:

where the tilde (∼) is used to indicate stochastic variables.

Notice that the inequality constraint in equation (13) in the main text does not apply at the beginning of the period, because the demands for consumption goods and money are made effective at the end of the period. The maximization procedure leads to the following labor supply decision rule:

Derivation of Final Solutions for Price and Output Levels of Nontradable Good and Level of Foreign Reserves

The macromodel of Section IV can be solved to yield the following set of semi-reduced forms for the price level of the nontradable good and the end-of-period level of foreign exchange reserves:

where the Xs and Ys are functions of the structural parameters of the model.

From equations (37) and (38) of the main text, it is clear that for stability purposes, it is necessary that δ2>a2 and b2>a1. Those conditions will be assumed here. In addition, the parameters of the model imply that (leaving aside the constant d3) the effects of gct and ft-1 on the level of foreign reserves are similar. That is, Y1 and Y2 in equation (61) are related. This is, of course, due to the fact that both variables are components of the beginning-of-period monetary base. Hence, the usual requirement for the stability of equation (61): |δft/δft-1|<1 is related to the value of |δft/δgct|. In general, in this model |δft/δgct| < 1 and, 1 > (δft/δft-1) > 0. Hence the model will be stable.

In order to proceed toward a final solution of the model, that is, taking into account the endogenous property of price expectations, it is important to realize that equations (60) and (61) are not independent from each other. The method of undetermined coefficients is used here to obtain the final solution of the model (see Lucas (1973), Barro (1976,1978)). Following McCallum (1983), notice that the solution for the price level of nontradables can be written as a linear function of the predetermined state variables ft-1, gct-1, m, vt, xt-1,Pt1*, nt, st-1t, utt, and the constant 1. Hence:

where the θs are the unknown coefficients.

Leading equation (62) once, taking beginning-of-period t expectations, and using equation (61), we obtain:

Using the method of undetermined coefficients, the solution for the θs is obtained. In particular:

There are two possible solutions for θ1. 27 To choose between them, we will follow McCallum (1983) by imposing the requirement that the solution for θ1 must be valid for all admissible values of the structural parameters. In particular, ft-1 appears in the solution for pt because it forms part of the system (equation (60)). In the special case in which X1 = 0, ft-1 would not be an argument for pt and hence, would not be included in the “minimal set of state variables.” Thus, θ1 would be equal to zero. But from equation (64) it is clear that θ1 = 0 would be obtained (under the assumption X1 = 0) only if the negative root is used.

The parameters of the model implies that θ1 has a positive value and hence allow us to sign the rest of θs since they are functions of θ1. Thus:

The final solution for the levels of output of both commodities can be found by substituting equations (62) and (63) and equations (64) to (73) into equations (37) and (38) of the text.28

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*

* Ms. Rojas-Suarez, an economist in the Research Department, is a graduate of the University of Western Ontario.

The author wants to thank Peter Howitt, David Laidler, Michael Parkin, and Fund colleagues for their contributions to this paper.

1

Traditional models conclude that, in the short run, a devaluation will lower the real exchange rate (defined here as the price of nontradable goods relative to the domestic price of tradable goods) and both domestic demand for nontradables and production of tradables will increase. With unutilized capacity, aggregate output will rise (see Mundell (1962) and Fleming (1962)); with full employment (as in Dornbusch (1973)), a devaluation will temporarily shift resources from the production of nontradables to that of tradables with no change in the aggregate level of output and employment. Regarding the analysis of expansions in the exogenous component of the money supply, models that assume price stickiness in the short run conclude that the consequent initial increase in aggregate demand will stimulate economic activity, while those models that assume price flexibility conclude that the resulting increase in the relative price of nontradables will temporarily shift resources from the production of tradables toward the production of nontradables with no change in the aggregate level of output.

2

It is important to note that the positive relationship between output and real money in this model does not arise from introducing money as a wealth variable. Instead, it is due to the financial constraint assumption which in turn is closely related to the standard cash-in-advance assumption used in the open economy models of Stockman (1980), Helpman (1981), and Aschauer and Greenwood (1983).

3

The evidence on the effects of changes in money on the level of output is mixed. While Barro (1979) found that the actual rate of growth of money had significant and positive explanatory power with respect to the level of the Mexican output (during the period 1959-74), some of the evidence reported in Hanson (1980) seems to indicate the presence of a negative effect of money growth on the output levels of Brazil (during the period 1952-74) and Chile (during the period 1952-70).

4

Households hold money during the second period, but not at the end of it. There is no market for property rights and the only alternative left to the old generation is to pass them over to the next generation before dying. Inheritances of money, however, are ruled out; and, hence, it is in the best interest of the old generation to spend all their money balances during the period.

5

It is assumed here that government regulations prevent perfect competition in the banking system. Fry (1982) argues that this is a mechanism through which

6

The productivity term in the denominator means that a positive random increase in productivity will result in a lower amount of labor required to produce a given amount of output. The sequence {φt} is assumed to be a strictly positive stationary stochastic process and its distribution will be specified in Section III.

7

The assumption of joint production allows the demand for credit to be treated as a single variable without having to decompose it according to its uses (the production of tradable or nontradable goods).

8

The future price level of the price index is the relevant deflator for the monetary base because of the intertemporal substitution effect embodied in the supply of labor (see equation (22)).

9

This diagram was suggested by Ranjit Teja.

10

The CC slope is positive because it is assumed that α1 < 1. If instead, α1 < 1, then the CC locus slopes downwards but will be flatter than the YY locus. The rest of the diagrammatic analysis will concentrate on the case of α1 < 1.

11

Notice that the YY locus (or the Y*Y* locus) is a 45 line, while the LL locus is steeper.

12

Imposing equilibrium in the markets for tradable and nontradable commodities implies equilibrium in the money market.

13

With the obvious allowance made for the constant of linearization: ω1.

14

Equation (42) is a log approximation of equation (34). In the remainder of this paper, ft will always stand for the end-of-period level of foreign reserves since that is the relevant endogenous variable. In addition, the predetermined level of reserves at the beginning of every period, atft , equals the end-of-the-previousperiod level of reserves, ft-1.

15

This process is identical to the one presented in Barro (1978).

16

This is so because (from Appendix II): θ2<1 and (in equation (74) of Appendix II): |δft /δgct-1| < 1 since |Y2| < 1.

17

Since Pt* is an exogenous variable, the analysis of the expected general inflation rate can be conducted by solely considering the expected inflation rate of the nontradable good.

18

This is so because θ2 is <1. See equation (65) of Appendix II.

19

The parameters of the model imply that Y2 <0. Therefore, from equation (46) it is clear that if |θ2| < |θ1 Y2|, atE(pit+1) will fall following an increase in gct. In that case, the LL curve shifts to the left increasing the stimulative effect of the financial constraint effect.

20

From Appendix II: θ7<0 and (in equation (74) of Appendix II):

because |Y4 | < |Y5 + Y3| and θ7 < 1.

21

Since Pt+1* is a component of Pt+1*, it is no longer possible to solely concentrate on the effects of a rise in pt* on the inflation rate of the nontradable good.

22

The confusion between vt and xt does not generate a discrepancy between beginning- and end-of-period expectations because the distinction between the shocks is only known with a one-period lag.

23

It is important to recall that, in this model, price misperceptions of the Lucas type are not an argument in the supply functions.

24

The demand for yt will increase because of a rise in btE(Pt+1*), while the demand for y*f will decrease because of a rise in pt*.

25

It is important to notice that this study has only concentrated on the shortrun effects of a devaluation. It can easily be shown that in the long run the model converges to the classical monetary approach to the balance of payments, and devaluation has no long-run real effects.

26

The identity A2 = aH2 is obtained by recalling that the beginning-of-period monetary base in period t + 1 equals the total demand for money (by households and firms) during period t minus the amount of bank credit during period t plus government transfers during period t + 1.

27

The roots from equation (64) are real since the term inside the square root is always positive. This is so because Y3 < 0 and X1 < 0. The fact that the roots are real is an indication that the model possesses an economically sensible solution.

28

These solutions and a step-by-step derivation of all the solutions in the model are available from the author on request.

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