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 (H_t) has two asset counterparts: government credit (GC_t) and foreign exchange reserves (F_t).

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 (Tr_t) is assumed to be equal to the increase in government credit (ΔGC_t).

In this system of fixed exchange rates, the beginning-of-period monetary base (_aH_t) differs from the end-of-period monetary base (_bH_t) if there is any net change in the economy’s stock of foreign reserves (F_t). (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 (GC_t) 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 $\left(C_t^s\right)$ 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 (M_t), which in this economy equals the monetary base (_bH_t) plus the supply of bank credit $\left(C_t^s\right)$, 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 (P_t Y_t) 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.

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 i_t, 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:

$\begin{array}{cc}{l}_t^d={\alpha }_0+{\alpha }_1[{}_{bt}E\left({pi}_t\right)-w_t+i_t]+u_t,& \left(20\right)\end{array}$

where $u_t=\log {\phi }_t\sim N(0,{\sigma }_u^2),u_t$ is independent of the other disturbances in the model, and $p{i}_t\equiv \tau p_t+(1-\tau )(p_t^{*}+s_t)\mathrm{.}$

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

$\begin{array}{cc}{c}_t^d={\beta }_0+{\alpha }_1\left[{}_{at}E\left(p{i}_t\right)-i_t\right]+(1-{\alpha }_1)w_t+u_t\mathrm{.}& \left(21\right)\end{array}$

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

$\begin{array}{cc}{l}_t^s={\gamma }_0+{\gamma }_1\left[w_{t-}{}_{at}E\left(p{i}_{t+1}\right)\right],& \left(22\right)\end{array}$

$\begin{array}{cc}{c}_t^s=k+{}_a{h}_t\mathrm{.}& \left(23\right)\end{array}$

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:

$\begin{array}{cc}{y}_t^s=-w_t-i_t+{}_{at}E\left(p_t\right)+u_t,& \left(24\right)\end{array}$

$\begin{array}{cc}{y^{*}}_t^s=-w_t-i_t+{}_{at}E\left(P_t^{*}\right)+{}_{at}E\left(s_t\right)+u_t\mathrm{.}& \left(25\right)\end{array}$

The unitary coefficients (in absolute value terms) accompanying the arguments of $y_t^{s}and{y^{*}}_t^s$ 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 $l_t^d=l_t^{s}and{c}_t^d=c_t^s,$ the aggregate supply functions of outputs are obtained:

$\begin{array}{ccc}{y}_t^s& =& a_0+a_1[{}_a{h}_t-{}_{at}E\left(p{i}_{t+1}\right)]\hfill \\ & & +(1-\tau )\left[{}_{at}E(p_t-P_t^{*}-s_t)\right]+a_2{u}_t,\left(26\right)\hfill \end{array}$

$\begin{array}{cc}{y^{*}}_t^s=a_0+a_1[{}_a{h}_t-{}_{at}E\left(p{i}_{t+1}\right)]-\tau \left[{}_{at}E(p_t-p_t^{*}-s_t)\right]+a_2{u}_t,& \left(27\right)\end{array}$

where:

$\begin{array}{cc}\begin{array}{cc}{a}_0=-({\beta }_0+{{\gamma }_0}^{\prime }),& a_1=\frac{{\gamma }_1}{{\alpha }_1+{\alpha }_1{\gamma }_1},\end{array}& a_2=1-{{\gamma }_3}^{\prime }\end{array}\mathrm{.}$

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:$\left[{}_{at}E(p_t-p_t^{*}-s_t)\right]$—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 u_t 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 $c_t^d=c_t^s,$ CC in Figure 1 represents the credit market equilibrium locus:¹⁰

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Determinants of the Aggregate Supply Function

Citation: IMF Staff Papers 1987, 002; 10.5089/9781451972931.024.A002

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$\begin{array}{cc}{i}_t=\frac{{\beta }_0-k}{{\alpha }_1}-\frac{{}_a{h}_t}{{\alpha }_1}+{}_{at}E\left(p{i}_t\right)+\left(\frac{1-{\alpha }_1}{{\alpha }_1}\right)w_t+u_{\mathrm{t.}}& \left(28\right)\end{array}$

In addition, using equations (20) and (22) and the equilibrium condition $l_t^s=l_t^d,$ LL in Figure 1 represents the labor market equilibrium locus.

That is, LL represents:

$\begin{array}{cc}{i}_t=\left(\frac{{\alpha }_0-{\gamma }_0}{{\alpha }_1}\right)+{}_{at}E\left({pi}_t\right)+\frac{{\gamma }_1}{{\alpha }_1}{}_{at}E\left({pi}_{t+1}\right)-\left(\frac{1+{\gamma }_1}{{\alpha }_1}\right)w_t+u_t\mathrm{.}& \left(29\right)\end{array}$

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:

$\begin{array}{cc}{i}_t=-w_t+{}_{at}E\left({pi}_t\right)+(1-\tau ){}_{at}E(p_t-p_t^{*}-s_t)-y_t^s+u_t,& \left(30\right)\end{array}$

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

$\begin{array}{cc}{i}_t=-w_t+{}_{at}E\left({pi}_t\right)-{\tau }_{at}E(p_t-p_t^{*}-s_t)-{y^{*}}_t^s+u_t\mathrm{.}& \left(31\right)\end{array}$

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(pi_t) enters all the curves with a unit coefficient, an increase in _atE(pi_t) 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.

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 ε_t 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 (gc_t) 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 (f_t-1) enters into the structural supply and demand equations in the same way as does the current level of government credit (gc_t).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 ξ_t (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 ξ_t, 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 (v_t) and temporary (x_t). Hence, gc_t is generated in accordance with:¹⁵

The two random terms v_t and x_t are generated by white noise processes, that is:$v_t\sim N(0,{\sigma }_v^2);x_t\sim N(0,{\sigma }_x^2)$ and both v_t and x_t are serially independently distributed.

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