I. Introduction

The central theme of this paper is that financial constraints faced by less developed countries (LDCs) play a crucial role in the short-run responses of output, prices, and the level of foreign reserves to devaluations and other monetary and real 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 outputs of tradable and nontradable goods depend 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 non-tradables goods. Therefore, the response of aggregate output to exogenous shocks (devaluations and other monetary and real 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 or have no effect on the short-run level of output. ^2/ However, recent empirical analysis of the short-run behavior of output in LDCs does not seem to support these traditional results. In particular, the studies by Edwards (1985) and Gomez-Oliver (1985) found that in recent years devaluations have generated a short-run decline in aggregate output in some LDCs. ^3/ In addition, the evidence with respect to the effects of changes in the actual rate of growth of 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, ^4/ 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 and Chile. ^{5/ 6/}

In contrast with the traditional theories, but in accordance with recent evidence for LDCs, this paper establishes the plausibility that either an anticipated devaluation or an anticipated increase in the rate of growth of the exogenous component of the money supply might result in a contraction in the short-run level of output. This is 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. ^7/ 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.

The idea that a devaluation might be contractionary in the short run is not new. There are several theoretical arguments that attempt to explain such a result. However, most arguments ^8/ are based on demand-related effects ^9/ generated by a devaluation, ranging from negative real balance effects on aggregate demand to income distributions towards economic agents with high marginal propensity to save. This paper advances the literature by showing that the introduction of a financial constraint in an economy where agents are fully rational and prices adjust to clear markets, adds an additional channel through which a devaluation might be contractionary. By demonstrating in addition that the channels leading to contractionary devaluations might also lead to output contraction in response to an increase in the rate of growth of the exogenous component of the money supply, the paper provides insights on a topic on which little theoretical research has been contributed. ^10/

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 II describes the basic characteristics of the model, with special emphasis on the assumptions regarding the organization of markets and the timing of transactions. Section III derives the optimal decision rules implied by the maximizing behavior of economic agents. Section IV derives the domestic aggregate supply and demand functions for tradable and nontradable commodities, and the aggregate demand for money. Section V sets out the complete macromodel to be solved in this fixed exchange rate economy. Under the assumption of complete current information, Section VI 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. In addition, it briefly analyzes how the economy responds to real shocks. Section VII then briefly discusses the implications of. relaxing the assumption of full current information. Finally, Section VIII summarizes the main conclusions.

II. The Model: Basics

Consider an economy where 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. That is, the transaction’s role of money is recognized in this paper, and money enters the model in the same way as in the models of Clower (1967), McKinnon (1973), Kapur (1976a), Mathieson (1979), Lucas (1980), Stockman (1980, 1981), and Helpman (1981).

This economy nonetheless is assumed to face a severely limited capital market. The chief limitations are the absence of a market for primary securities together with an absence of any type of financial intermediation other than commercial banking. Moreover, the only source of finance for firms is assumed to be loans from domestic commercial banks. 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 advances by demanding credit solely from the banking sector. Thus, the availability of real credit places a constraint on the level of output. Since the financial structure of this economy consists of only a banking sector and since money is the only tradable asset, the total supply of money in the economy coincides with the total supply of credit (to the government and to firms).

The monetary transactions involve four markets: tradable commodities, nontradable commodities (domestic) labor, and (domestic) credit. The economy is inhabited by four kinds of agents: firms, households, banks, and the government.

Firms supply output in a competitive environment using domestic labor services (working capital) provided by households as the only variable factor of production.

Households maximize expected utility over their lifetime. We assume the existence 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. When old, households receive profits from the firms and commercial banks (they own both kinds of businesses) and net lump-sum transfers from the government and consume these and their previous savings. They 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. ^11/ 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.

The credit market involves the banking system as the only supplier of credit and firms as the only agents demanding it. ^12/ 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 high-powered money, imposes a required reserve ratio on the commercial banks, and acts as the foreign exchange authority. In this fixed exchange rate regime, the monetary base (H_t) has two asset counterparts: the government credit (GC_t) and the 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. ^13/ It is assumed that banks incur no labor costs in providing the services of intermediation. Also, it is assumed that bank loans have a maturity length of one period.

It is assumed that households and firms keep all their money in the form of 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 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. To gain insight into the nature of the model, let us follow the activities of the economy during any given period t.

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. Given the level of banks’ reserves, at the beginning of the period, the supply of credit by the commercial banks is also determined at the beginning of the period. Finally, the old generation receive 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). 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 equals: ^14/

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

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 commodities, and 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_tY_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 just described begins again.

III. The Maximizing Behavior of the Economic Agents

The problems to be solved by a representative bank, firm, and household are now considered. Agents are rational and maximizing behavior 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 the current period price levels of the commodities at the beginning of the period, nor do they know the future period prices of the commodities 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.

1. The representative bank

As has already been said, the assumptions regarding imperfections in the capital market and barriers of entry imposed by government’s regulations imply that the banking sector holds a monopolistic position such that demand deposits are noninterest bearing but bank loans to firms are interest bearing one period loans. Thus, the representative bank chooses its supply of credit to maximize:

$\begin{array}{cc}\mathrm{\left(}\mathrm{3}\mathrm{\right)}& \underset{\mathrm{\left\{}{\mathrm{C}}_{\mathrm{t}}^{\mathrm{s}}\mathrm{\right\}}}{\begin{array}{c}\mathrm{M}\mathrm{ax}\end{array}}{\mathrm{at}}^{\mathrm{E}}\mathrm{\left[}\frac{{{}^{\mathrm{b}}\mathrm{\pi }}_{\mathrm{t}}}{{\mathrm{PI}}_{\mathrm{t}\mathrm{+}\mathrm{1}}}\mathrm{\right]}\mathrm{=}{\mathrm{at}}^{\mathrm{E}}\mathrm{\left[}\frac{{\mathrm{i}}_{\mathrm{t}}}{{\mathrm{PI}}_{\mathrm{t}\mathrm{+}\mathrm{1}}}{\mathrm{C}}_{\mathrm{t}}^{\mathrm{s}}\mathrm{\right]}\end{array}$

where:	E	=	the expectations operator; atE(X) refers to “beginning-of-period t expectations” of a variable X; btE(X) will refer to “end-of-period t expectations” of a variable X;
	bπt	=	nominal profits realized by the bank at the beginning of period t;
	${\mathrm{C}}_{\mathrm{t}}^{\mathrm{s}}$	=	nominal amount of credit (loans) supplied by the representative bank;
	it	=	nominal interest rate; and
	PI t+1	=	domestic price index during period t+1.

View Table

where:	E	=	the expectations operator; atE(X) refers to “beginning-of-period t expectations” of a variable X; btE(X) will refer to “end-of-period t expectations” of a variable X;
	bπt	=	nominal profits realized by the bank at the beginning of period t;
	${\mathrm{C}}_{\mathrm{t}}^{\mathrm{s}}$	=	nominal amount of credit (loans) supplied by the representative bank;
	it	=	nominal interest rate; and
	PI t+1	=	domestic price index during period t+1.

The bank maximizes “expected real profits” because it belongs to households who will only receive bank’s profits at the beginning of the subsequent period.

It is assumed here that the central bank imposes a beginning-of-period reserve requirement ratio and hence, every period the commercial bank faces the following set of constraints:

$\begin{array}{cc}\mathrm{\left(}\mathrm{4}\mathrm{\right)}& {\mathrm{a}}^{\mathrm{R}}\mathrm{t}\mathrm{>}\mathrm{K}{\mathrm{a}}^{\mathrm{D}}\mathrm{t}\end{array}$

$\begin{array}{cc}\mathrm{\left(}5\mathrm{\right)}& {\mathrm{a}}^{\mathrm{R}}\mathrm{t}\mathrm{+}{\mathrm{C}}_{\mathrm{t}}^{\mathrm{s}}\mathrm{=}{\mathrm{a}}^{\mathrm{D}}\mathrm{t}\end{array}$

$\begin{array}{cc}\mathrm{\left(}\mathrm{6}\mathrm{\right)}& {\mathrm{a}}^{\mathrm{R}}\mathrm{t}\mathrm{\equiv }{\mathrm{RR}}_{\mathrm{t}}\mathrm{+}{\mathrm{RE}}_{\mathrm{t}}\end{array}$

$\begin{array}{cc}\mathrm{\left(}\mathrm{7}\mathrm{\right)}& {\mathrm{a}}^{\mathrm{R}}\mathrm{t}\mathrm{=}{\mathrm{GC}}_{\mathrm{t}}\mathrm{+}{\mathrm{F}}_{\mathrm{t}\mathrm{-}\mathrm{1}}\mathrm{=}{\mathrm{a}}^{\mathrm{H}}\mathrm{t}\end{array}$

where:	aRt	=	beginning-of-period reserves in the vault of the commercial bank = required reserves (RR) plus excess reserves (RE);
	aDt	=	beginning-of-period level of demand deposits; and
	K	=	reserve requirement ratio.

View Table

where:	aRt	=	beginning-of-period reserves in the vault of the commercial bank = required reserves (RR) plus excess reserves (RE);
	aDt	=	beginning-of-period level of demand deposits; and
	K	=	reserve requirement ratio.

Equation (4) is the reserve requirement constraint imposed by the central bank. Equation (5) is the bank’s balance sheet constraint, which requires that the total assets of the bank equal the total liabilities. Identity (6) defines the composition of the level of reserves, and equation (7) follows from the assumption that the nonbanking sector holds its money only in the form of demand deposits.

The maximization procedure will lead to the following commercial bank’s decision rule to supply credit:

$\begin{array}{cc}\mathrm{\left(}\mathrm{8}\mathrm{\right)}& {\mathrm{C}}_{\mathrm{t}}^{\mathrm{s}}\mathrm{=}\frac{\mathrm{1}\mathrm{-}\mathrm{K}}{\mathrm{K}}{\mathrm{a}}^{\mathrm{H}}\mathrm{t}\end{array}$

The commercial bank’s supply of credit implies that the bank finds it optimal to supply as much credit as possible. The bound is, of course, given by the reserve requirement ratio and 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 as long as the interest payments on deposits is lower than the interest charge on credit.

2. The representative firm

The objective of the firm is to maximize profits. The representative domestic firm is assumed to produce both tradable $\mathrm{\left(}{\mathrm{Y}}_{\mathrm{t}}^{\mathrm{*}}\mathrm{\right)}$ and nontradable (Y_t) commodities. The firm engages in a production process that yields joint products. In addition, a single input, domestic labor supply (L_t) is used in the production of the two outputs. Specifically, in order to obtain explicit results, the following product transformation curve is assumed:

$\begin{array}{cc}\mathrm{\left(}\mathrm{9}\mathrm{\right)}& {\mathrm{L}}_{\mathrm{t}}\mathrm{=}\frac{\mathrm{1}}{\mathrm{2}}\mathrm{\left(}{\mathrm{Y}}_{\mathrm{t}}^{\mathrm{2}}\mathrm{+}{\mathrm{\left(}\mathrm{Y}\mathrm{*}\mathrm{\right)}}_{\mathrm{t}}^{\mathrm{2}}\mathrm{\right)}\frac{\mathrm{1}}{{\mathrm{\varphi }}_{\mathrm{t}}}\end{array}$

Equation (9) states costs of production in terms of labor units. ϕ_t is a productivity shock and is assumed to affect both outputs equally. ^15/

The maximization problem for the representative firm becomes:

$\begin{array}{cc}\mathrm{\left(}\mathrm{10}\mathrm{\right)}& \underset{\mathrm{\left\{}{\mathrm{Y}}_{\mathrm{t}}^{\mathrm{s}}\mathrm{,}{\mathrm{\left(}\mathrm{Y}\mathrm{*}\mathrm{\right)}}_{\mathrm{t}}^{\mathrm{s}}\mathrm{\right\}}}{\begin{array}{c}\mathrm{M}\mathrm{ax}\end{array}}{\mathrm{at}}^{\mathrm{E}}\mathrm{\left[}\frac{{{}^{\mathrm{f}}\mathrm{\pi }}_{\mathrm{t}}}{{\mathrm{PI}}_{\mathrm{t}\mathrm{+}\mathrm{1}}}\mathrm{\right]}\mathrm{=}\underset{\mathrm{\left\{}{\mathrm{Y}}_{\mathrm{t}}^{\mathrm{s}}\mathrm{,}{\mathrm{\left(}\mathrm{Y}\mathrm{*}\mathrm{\right)}}_{\mathrm{t}}^{\mathrm{s}}\mathrm{\right\}}}{\mathrm{M}\mathrm{ax}}{\mathrm{at}}^{\mathrm{E}}\mathrm{\left\{}\frac{{\mathrm{P}}_{\mathrm{t}}}{{\mathrm{PI}}_{\mathrm{t}\mathrm{+}\mathrm{1}}}{\mathrm{Y}}_{\mathrm{t}}^{\mathrm{s}}\mathrm{+}\frac{{\mathrm{P}}_{\mathrm{t}}^{\mathrm{*}}{\mathrm{S}}_{\mathrm{t}}}{{\mathrm{PI}}_{\mathrm{t}\mathrm{+}\mathrm{1}}}{\mathrm{\left(}\mathrm{Y}\mathrm{*}\mathrm{\right)}}_{\mathrm{t}}^{\mathrm{s}}\mathrm{-}\frac{{\mathrm{W}}_{\mathrm{t}}}{{\mathrm{PI}}_{\mathrm{t}\mathrm{+}\mathrm{1}}}{\mathrm{L}}_{\mathrm{t}}^{\mathrm{d}}\mathrm{-}\frac{{\mathrm{i}}_{\mathrm{t}}}{{\mathrm{PI}}_{\mathrm{t}\mathrm{+}\mathrm{1}}}{\mathrm{C}}_{\mathrm{t}}^{\mathrm{d}}\mathrm{\right\}}\end{array}$

where:	${\mathrm{Y}}_{\mathrm{t}}^{\mathrm{s}}$	=	domestic supply of the nontradable good;
	${\mathrm{\left(}\mathrm{Y}\mathrm{*}\mathrm{\right)}}_{\mathrm{t}}^{\mathrm{s}}$	=	domestic supply of the tradable good;
	Pt	=	price level of the nontradable good;
	${\mathrm{P}}_{\mathrm{t}}^{\mathrm{*}}$	=	price level of the tradable good; and
	St	=	exchange rate: the domestic currency price of the foreign exchange.

View Table

where:	${\mathrm{Y}}_{\mathrm{t}}^{\mathrm{s}}$	=	domestic supply of the nontradable good;
	${\mathrm{\left(}\mathrm{Y}\mathrm{*}\mathrm{\right)}}_{\mathrm{t}}^{\mathrm{s}}$	=	domestic supply of the tradable good;
	Pt	=	price level of the nontradable good;
	${\mathrm{P}}_{\mathrm{t}}^{\mathrm{*}}$	=	price level of the tradable good; and
	St	=	exchange rate: the domestic currency price of the foreign exchange.

The firm maximizes expected real profits. Once more, the expected price index of period t+1 is the relevant deflator because the firm’s profits realized during period t are distributed to its owners (households) at the beginning of period t+1. 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.

Equation (10) is maximized subject to the product transformation curve (equation (9)) and to the firms’ financial constraint:

$\begin{array}{cc}\mathrm{\left(}\mathrm{11}\mathrm{\right)}& {\mathrm{C}}_{\mathrm{t}}^{\mathrm{d}}\mathrm{=}{\mathrm{W}}_{\mathrm{t}}{\mathrm{L}}_{\mathrm{t}}^{\mathrm{d}}\end{array}$

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. ^16/

The information set that the firm uses at the beginning of the period to form its expectations (Ω_at) consists of the information on variables up to period t-1, plus the current wage rate, the interest rate, and the productivity term. ^17/ Thus:

$\begin{array}{cc}\mathrm{\left(}\mathrm{12}\mathrm{\right)}& {\mathrm{\Omega }}_{\mathrm{at}}\mathrm{=}\mathrm{\left\{}{\mathrm{\Omega }}_{\mathrm{t}\mathrm{-}\mathrm{1}}\mathrm{,}{\mathrm{W}}_{\mathrm{t}}\mathrm{,}{\mathrm{i}}_{\mathrm{t}}\mathrm{,}{\mathrm{\varphi }}_{\mathrm{t}}\mathrm{,}{\mathrm{\mu }}_{\mathrm{t}}\mathrm{\right\}}\end{array}$

The maximization procedure leads to the following supply function for the nontradable good:

$\begin{array}{cc}\mathrm{\left(}\mathrm{13}\mathrm{\right)}& {\mathrm{Y}}_{\mathrm{t}}^{\mathrm{s}}\mathrm{=}\frac{{\mathrm{at}}^{\mathrm{E}}\mathrm{\left(}{\mathrm{P}}_{\mathrm{t}}\mathrm{\right)}}{{\mathrm{W}}_{\mathrm{t}}\mathrm{\left(}\mathrm{1}\mathrm{+}{\mathrm{i}}_{\mathrm{t}}\mathrm{\right)}}{\mathrm{\varphi }}_{\mathrm{t}}\end{array}$

and to the following supply function for the tradable commodity:

$\begin{array}{cc}\mathrm{\left(}\mathrm{14}\mathrm{\right)}& {\mathrm{\left(}\mathrm{Y}\mathrm{*}\mathrm{\right)}}_{\mathrm{t}}^{\mathrm{s}}\mathrm{=}\frac{{\mathrm{at}}^{\mathrm{E}}\mathrm{\left(}{\mathrm{P}}_{\mathrm{t}}^{\mathrm{*}}{\mathrm{S}}_{\mathrm{t}}\mathrm{\right)}}{{\mathrm{W}}_{\mathrm{t}}\mathrm{\left(}\mathrm{1}\mathrm{+}{\mathrm{i}}_{\mathrm{t}}\mathrm{\right)}}{\mathrm{\varphi }}_{\mathrm{t}}\end{array}$

From these decisions 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: W_t(1+i_t).

Substituting equations (13) and (14) into equation (9) yields the demand for labor:

$\begin{array}{cc}\mathrm{\left(}\mathrm{15}\mathrm{\right)}& {\mathrm{L}}_{\mathrm{t}}^{\mathrm{d}}\mathrm{=}\frac{\mathrm{1}}{\mathrm{2}}{\mathrm{\varphi }}_{\mathrm{t}}\mathrm{\left[}\frac{{\mathrm{\left(}{\mathrm{at}}^{\mathrm{E}}\mathrm{\left(}{\mathrm{P}}_{\mathrm{t}}\mathrm{\right)}\mathrm{\right)}}^{\mathrm{2}}\mathrm{+}{\mathrm{\left(}{\mathrm{at}}^{\mathrm{E}}\mathrm{\left(}{\mathrm{P}}_{\mathrm{t}}^{\mathrm{*}}{\mathrm{S}}_{\mathrm{t}}\mathrm{\right)}\mathrm{\right)}}^{\mathrm{2}}}{{\mathrm{\left(}{\mathrm{W}}_{\mathrm{t}}\mathrm{\left(}\mathrm{1}\mathrm{+}{\mathrm{i}}_{\mathrm{t}}\mathrm{\right)}\mathrm{\right)}}^{\mathrm{2}}}\mathrm{\right]}\end{array}$

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 (11) can be used to derive the firms’ demand for credit:

$\begin{array}{cc}\mathrm{\left(}\mathrm{16}\mathrm{\right)}& {\mathrm{C}}_{\mathrm{t}}^{\mathrm{d}}\mathrm{=}\frac{{\mathrm{W}}_{\mathrm{t}}{\mathrm{\varphi }}_{\mathrm{t}}\mathrm{\left[}{\mathrm{\left(}{\mathrm{at}}^{\mathrm{E}}\mathrm{\left(}{\mathrm{P}}_{\mathrm{t}}\mathrm{\right)}\mathrm{\right)}}^{\mathrm{2}}\mathrm{+}{\mathrm{\left(}{\mathrm{at}}^{\mathrm{E}}\mathrm{\left(}{\mathrm{P}}_{\mathrm{t}}^{\mathrm{*}}{\mathrm{S}}_{\mathrm{t}}\mathrm{\right)}\mathrm{\right)}}^{\mathrm{2}}\mathrm{\right]}}{\mathrm{2}{\mathrm{\left[}{\mathrm{W}}_{\mathrm{t}}\mathrm{\left(}\mathrm{1}\mathrm{+}{\mathrm{i}}_{\mathrm{t}}\mathrm{\right)}\mathrm{\right]}}^{\mathrm{2}}}\end{array}$

3. The representative household

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

$\begin{array}{cc}\mathrm{\left(}\mathrm{17}\mathrm{\right)}& \mathrm{U}\mathrm{=}{\mathrm{\mu }}_{\mathrm{1}}\mathrm{1}\mathrm{n}\mathrm{\left[}{\mathrm{Y}}_{\mathrm{1}}^{\mathrm{\tau }}{\mathrm{\left(}{\mathrm{Y}}^{*}\mathrm{\right)}}_{\mathrm{1}}\mathrm{(}\mathrm{1}\mathrm{-}\mathrm{\tau }\mathrm{)}\mathrm{\right]}\mathrm{+}\mathrm{1}\mathrm{n}\mathrm{(}\overline{\mathrm{L}}\mathrm{-}{\mathrm{L}}_{\mathrm{1}}\mathrm{)}\mathrm{+}{\mathrm{\beta Y}}_{\mathrm{2}}^{\mathrm{\tau }}{\mathrm{\left(}{\mathrm{Y}}^{*}\mathrm{\right)}}_{\mathrm{2}}\mathrm{(}\mathrm{1}\mathrm{-}\mathrm{\tau }\mathrm{)}\end{array}$

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 and ${\mathrm{Y}}_{\mathrm{1}}^{\mathrm{*}}$ refer to his demand for nontradables and tradables, respectively, for his first period and Y₂ and ${\mathrm{Y}}_2^{\mathrm{*}}$ refer to his consumption demands for the second period. μ₁ refers to a random shock affecting the utility derived from current consumption, and $\mathrm{\left(}\overline{\mathrm{L}}\mathrm{-}{\mathrm{L}}_{\mathrm{1}}\mathrm{\right)}$ is the amount of leisure available to the agent after he has supplied labor. Also, 0 < β < 1. The utility function (17) is additive separable in consumption and leisure and shows constant marginal utility of future consumption. ^18/

In the first period of his life, the individual works, consumes, and saves money. In his second period, he is old and at the beginning of the period receives net transfers (Tr₂) from the government and profits from the firm (^fπ₁) and banks (i₁C₁).

Thus, the lifetime budget constraint of the agent is:

$\begin{array}{cc}\mathrm{\left(}\mathrm{18}\mathrm{\right)}& {\mathrm{P}}_{\mathrm{2}}{\mathrm{Y}}_{\mathrm{2}}^{\mathrm{d}}\mathrm{+}\mathrm{\left(}{\mathrm{P}}_{\mathrm{2}}^{\mathrm{*}}{\mathrm{S}}_{\mathrm{2}}\mathrm{\right)}{\mathrm{\left(}\mathrm{Y}\mathrm{*}\mathrm{\right)}}_{\mathrm{2}}^{\mathrm{d}}\mathrm{=}{\mathrm{W}}_{\mathrm{1}}{\mathrm{L}}_{\mathrm{1}}^{\mathrm{s}}\mathrm{+}{\mathrm{Tr}}_{\mathrm{2}}\mathrm{+}{{}^{\mathrm{h}}\mathrm{\pi }}_{\mathrm{2}}\mathrm{-}{\mathrm{P}}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{1}}^{\mathrm{d}}\mathrm{-}\mathrm{\left(}{\mathrm{P}}_{\mathrm{1}}^{\mathrm{*}}{\mathrm{S}}_{\mathrm{1}}\mathrm{\right)}{\mathrm{\left(}\mathrm{Y}\mathrm{*}\mathrm{\right)}}_{\mathrm{1}}^{\mathrm{d}}\end{array}$

where: ^hπ₂ = ^fπ₁ + i₁C₁.

The problem for the young generation is to maximize the expected value of equation (17) subject to the budget constraint (18) and to the condition that the young agent’s demand for money be nonnegative:

$\begin{array}{cc}\mathrm{\left(}\mathrm{19}\mathrm{\right)}& {\mathrm{W}}_{\mathrm{1}}{\mathrm{L}}_{\mathrm{1}}^{\mathrm{s}}\mathrm{-}{\mathrm{P}}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{1}}^{\mathrm{d}}\mathrm{-}{\mathrm{P}}_{\mathrm{1}}^{\mathrm{*}}{\mathrm{S}}_{\mathrm{1}}{\mathrm{\left(}\mathrm{Y}\mathrm{*}\mathrm{\right)}}_{\mathrm{1}}^{\mathrm{d}}\mathrm{>}\mathrm{0.}\end{array}$

The inequality constraint (19) 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. 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.

The information set available to the agent at the end of period 1 is:

$\begin{array}{cc}\mathrm{\left(}\mathrm{20}\mathrm{\right)}& {\mathrm{\Omega }}_{\mathrm{b}\mathrm{1}}\mathrm{=}\mathrm{\left\{}{\mathrm{\Omega }}_{\mathrm{a}\mathrm{1}}\mathrm{,}{\mathrm{P}}_{\mathrm{1}}\mathrm{,}{\mathrm{S}}_{\mathrm{1}}\mathrm{,}{\mathrm{P}}_{\mathrm{1}}^{\mathrm{*}}\mathrm{\right\}}\end{array}$

where the information set at the beginning of period 1 (Ω_a1) is identical to the set faced by firms and is given by equation (12).

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:

$\begin{array}{cc}\mathrm{\left(}\mathrm{21}\mathrm{\right)}& {\mathrm{Y}}_{\mathrm{1}}^{\mathrm{d}}\mathrm{=}\frac{\mathrm{j}\mathrm{\tau }}{\mathrm{\beta }}{\mathrm{\mu }}_{\mathrm{1}}\frac{\mathrm{b}{\mathrm{1}}^{\mathrm{E}}\mathrm{\left(}{\mathrm{PI}}_{\mathrm{2}}\mathrm{\right)}}{{\mathrm{P}}_{\mathrm{1}}}\end{array}$

$\begin{array}{cc}\mathrm{\left(}\mathrm{22}\mathrm{\right)}& {\mathrm{\left(}\mathrm{Y}\mathrm{*}\mathrm{\right)}}_{\mathrm{1}}^{\mathrm{d}}\mathrm{=}\frac{\mathrm{j}\mathrm{\prime }\mathrm{\left(}\mathrm{1}\mathrm{-}\mathrm{\tau }\mathrm{\right)}}{\mathrm{\beta }}{\mathrm{\mu }}_{\mathrm{1}}\frac{\mathrm{b}{\mathrm{1}}^{\mathrm{E}}\mathrm{\left(}{\mathrm{PI}}_{\mathrm{2}}\mathrm{\right)}}{{\mathrm{P}}_{\mathrm{1}}^{\mathrm{*}}{\mathrm{S}}_{\mathrm{1}}}\end{array}$

where:	PI2	≡	price index in period 2
		≡	${\mathrm{P}}_{\mathrm{2}}^{\mathrm{\tau }}\mathrm{\left(}{\mathrm{P}}_{\mathrm{2}}^{\mathrm{*}}{\mathrm{S}}_{\mathrm{2}}\mathrm{\right)}\mathrm{1}\mathrm{-}\mathrm{\tau }$.

View Table

where:	PI2	≡	price index in period 2
		≡	${\mathrm{P}}_{\mathrm{2}}^{\mathrm{\tau }}\mathrm{\left(}{\mathrm{P}}_{\mathrm{2}}^{\mathrm{*}}{\mathrm{S}}_{\mathrm{2}}\mathrm{\right)}\mathrm{1}\mathrm{-}\mathrm{\tau }$.

That is, current consumption of tradable and nontradable commodities depends positively on expected inflation, where the relevant future price level is the “general” price level or “price index,” while the relevant current price level is the own commodity price. The decision rules (21) and (22) also depend positively on a random term (μ_t) which affects the marginal utility of (total) current consumption.

The labor supply decision rule derived in this model is:

$\begin{array}{cc}\mathrm{\left(}\mathrm{23}\mathrm{\right)}& {\mathrm{L}}_{\mathrm{1}}^{\mathrm{s}}\mathrm{=}\overline{\mathrm{L}}\mathrm{-}\frac{\mathrm{j}\mathrm{\prime }}{\mathrm{\beta }}\frac{\mathrm{a}{\mathrm{1}}^{\mathrm{E}}\mathrm{\left(}{\mathrm{PI}}_{\mathrm{2}}\mathrm{\right)}}{{\mathrm{W}}_{\mathrm{1}}}\mathrm{.}\end{array}$

That is, labor supply depends positively on the expected future real wage where the relevant deflator is the expected future price index.

Equations (21) and (22) represent the consumption demands of the young generation. To obtain the total market demands for consumption goods, we have to add to these the old generation demands. Such demands have already been obtained in Appendix I (equations (1.3) and (1.4)), where the solution to the agent’s second period problem was presented. Hence, for every period t, the total current demand for nontradables $\mathrm{\left(}{\mathrm{Z}}_{\mathrm{t}}^{\mathrm{d}}\mathrm{\right)}$ and tradables $\mathrm{\left(}{\mathrm{\left(}\mathrm{Z}\mathrm{*}\mathrm{\right)}}_{\mathrm{t}}^{\mathrm{d}}\mathrm{\right)}$, respectively are:

$\begin{array}{cc}\mathrm{\left(}\mathrm{24}\mathrm{\right)}& {\mathrm{Z}}_{\mathrm{t}}^{\mathrm{d}}\mathrm{=}\frac{\mathrm{j}\mathrm{\prime }\mathrm{\tau }}{\mathrm{\beta }}{\mathrm{\mu }}_{\mathrm{t}}\frac{{\mathrm{bt}}^{\mathrm{E}}\mathrm{\left(}{\mathrm{PI}}_{\mathrm{t}\mathrm{+}\mathrm{1}}\mathrm{\right)}}{{\mathrm{P}}_{\mathrm{t}}}\mathrm{+}\mathrm{\tau }\frac{{{\mathrm{a}}^{\mathrm{H}}}_{\mathrm{t}}}{{\mathrm{P}}_{\mathrm{t}}}\end{array}$

$\begin{array}{cc}\mathrm{\left(}\mathrm{25}\mathrm{\right)}& {\mathrm{\left(}\mathrm{Z}\mathrm{*}\mathrm{\right)}}_{\mathrm{t}}^{\mathrm{d}}\mathrm{=}\frac{\mathrm{j}\mathrm{\prime }\mathrm{\left(}\mathrm{1}\mathrm{-}\mathrm{\tau }\mathrm{\right)}}{\mathrm{\beta }}{\mathrm{\mu }}_{\mathrm{t}}\frac{{\mathrm{bt}}^{\mathrm{E}}\mathrm{\left(}{\mathrm{PI}}_{\mathrm{t}\mathrm{+}\mathrm{1}}\mathrm{\right)}}{{\mathrm{P}}_{\mathrm{t}}^{\mathrm{*}}{\mathrm{S}}_{\mathrm{t}}}\mathrm{+}\mathrm{\left(}\mathrm{1}\mathrm{-}\mathrm{\tau }\mathrm{\right)}\frac{{\mathrm{a}}^{\mathrm{H}}\mathrm{t}}{{\mathrm{P}}_{\mathrm{t}}^{\mathrm{*}}{\mathrm{S}}_{\mathrm{t}}}\end{array}$

Finally, the young agent’s demand for money $\mathrm{\left(}{{}^{\mathrm{y}}\mathrm{D}}_{\mathrm{t}}^{\mathrm{d}}\mathrm{\right)}$ can be obtained by subtracting the value of his consumption bundle from his wage earnings.

$\begin{array}{cc}\mathrm{\left(}\mathrm{26}\mathrm{\right)}& {{}^{\mathrm{y}}\mathrm{D}}_{\mathrm{t}}^{\mathrm{d}}\mathrm{=}{\mathrm{W}}_{\mathrm{t}}{\mathrm{L}}_{\mathrm{t}}\mathrm{-}{\mathrm{P}}_{\mathrm{t}}{\mathrm{Y}}_{\mathrm{t}}^{\mathrm{d}}\mathrm{-}{\mathrm{P}}_{\mathrm{t}}^{\mathrm{*}}{\mathrm{S}}_{\mathrm{t}}{\mathrm{\left(}\mathrm{Y}\mathrm{*}\mathrm{\right)}}_{\mathrm{t}}^{\mathrm{d}}\end{array}$

and from equations (21) and (22);

$\begin{array}{cc}\mathrm{\left(}\mathrm{26}\mathrm{\prime }\mathrm{\right)}& {{}^{\mathrm{y}}\mathrm{D}}_{\mathrm{t}}^{\mathrm{d}}\mathrm{=}\frac{{\mathrm{W}}_{\mathrm{t}}}{{\mathrm{PI}}_{\mathrm{t}}}{\mathrm{L}}_{\mathrm{t}}\mathrm{-}\frac{\mathrm{j}\mathrm{\prime }}{\mathrm{\beta }}{\mathrm{\mu }}_{\mathrm{t}}\frac{{\mathrm{bt}}^{\mathrm{E}}\mathrm{\left(}{\mathrm{PI}}_{\mathrm{t}\mathrm{+}\mathrm{1}}\mathrm{\right)}}{{\mathrm{PI}}_{\mathrm{t}}}\end{array}$

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.

IV. The Aggregate Supply and Demand Functions

V. The Complete Macromodel

The results from the previous sections can now be consolidated into the macro-model 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. ^21/ The complete model consists, then, of the following set of equations (expressed in log terms):

Equations (39) and (40) are log-linear approximations of equations (24) and (25), 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 (41) and (42) are identical to equations (33) and (34), respectively, and are repeated here only for convenience. These first four equations characterize the domestic markets for tradable and non-tradable commodities.

Equation (43) is a log approximation of the price index. Equation (44) 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 II and III, 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). ^22/

The equilibrium condition in the nontradable goods market is represented by equation (45), while the equilibrium in the market for tradable goods is represented by equation (46). ^{23/ 24/}

VI. Expectations and the Behavior of Prices, Output, and the Stock of Foreign Reserves Under Complete Current Information

In the previous sections, price expectations were not treated as endogenous variables. To solve the model formed by equations (39) through (46) for the output levels, the price level of the nontradable good and the stock of foreign reserves, it will be assumed that expectations are formed rationally in the sense of Muth (1961). To proceed towards the solution of the model, 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 (as in Weber (1981)) that the monetary authority sets a target value for the exchange rate according to some known rule that is independent of the behavior of other variables in the model. For purposes of simplification, the analysis in this paper will assume that the exchange rate follows a random walk; that is:

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 the 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: ^25/

The two random terms v_t and x_t are generated by white noise processes, that is: ${\mathrm{v}}_{\mathrm{t}}\mathrm{~}\mathrm{N}\mathrm{\left(}\mathrm{0}\mathrm{,}{\mathrm{\sigma }}_{\mathrm{v}}^{\mathrm{2}}\mathrm{\right)}\mathrm{;}{\mathrm{x}}_{\mathrm{t}}\mathrm{~}\mathrm{N}\mathrm{\left(}\mathrm{0}\mathrm{,}{\mathrm{\sigma }}_{\mathrm{x}}^{\mathrm{2}}\mathrm{\right)}$ and both v_t and x_t are serially independent distributed.

The process governing the behavior of the price of the tradable good ${\mathrm{p}}_{\mathrm{t}}^{\mathrm{*}}$ is assumed to be similar to the process followed by gc_t. Hence, ${\mathrm{p}}_{\mathrm{t}}^{\mathrm{*}}$ is generated in accordance with:

where:

• j* is a constant trend growth rate

• n_t is a stochastic permanent shock

• t_t is a stochastic temporary shock

and n_t and t_t are white noise processes, that is: ${\mathrm{n}}_{\mathrm{t}}\mathrm{~}\mathrm{N}\mathrm{\left(}\mathrm{0}\mathrm{,}{\mathrm{\sigma }}_{\mathrm{n}}^{\mathrm{2}}\mathrm{\right)}\mathrm{;}{\mathrm{t}}_{\mathrm{t}}\mathrm{~}\mathrm{N}\mathrm{\left(}\mathrm{0}\mathrm{,}{\mathrm{\sigma }}_{\mathrm{t}}^{\mathrm{2}}\mathrm{\right)}$ and n_t and t_t are serially independent distributed.

In this section, it is assumed that agents posess 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. Based on Appendix II, Table 1 distinguishes between the “financial constraint effect” (the effects of exogenous shocks on the expected real monetary base) and the “relative price effect” (the effects of exogenous shocks on the real exchange rate) that impinge on the levels of output of both commodities following a change in the exogenous variables of the model.

Table 1.

Decomposition of the Effects Impinging on the Domestic Levels of Output in the Full Current Information Case

Source: Appendix II.

^1/A direct effect on the aggregate supply equal to a₂ should be added in order to obtain the total output effect of a productivity shock.

Table 1.

Decomposition of the Effects Impinging on the Domestic Levels of Output in the Full Current Information Case

Endogenous Variables:	yt		${\mathrm{y}}_{\mathrm{t}}^{\mathrm{*}}$
Exogenous Variables	Financial constraint effect = a1 (aht-atE(Pit+1))	Relative price effect = $\mathrm{\left(}\mathrm{1}\mathrm{-}\mathrm{\tau }\mathrm{\right)}\mathrm{\left(}{\mathrm{p}}_{\mathrm{t}}\mathrm{-}{\mathrm{p}}_{\mathrm{t}}^{\mathrm{*}}\mathrm{-}{\mathrm{s}}_{\mathrm{t}}\mathrm{\right)}$	Financial constraint effect = a1 (aht-atE(Pit+1))	Relative price effect = $\mathrm{-}\mathrm{\tau }\mathrm{\left(}{\mathrm{p}}_{\mathrm{t}}\mathrm{-}{\mathrm{p}}_{\mathrm{t}}^{\mathrm{*}}\mathrm{-}{\mathrm{s}}_{\mathrm{t}}\mathrm{\right)}$
Increase in vt	$\frac{{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\omega }}_{\mathrm{1}}\mathrm{-}\mathrm{\tau }\mathrm{\left(}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{2}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{2}}\mathrm{\right)}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)θ2	$\frac{{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\omega }}_{\mathrm{1}}\mathrm{-}\mathrm{\tau }\mathrm{\left(}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{2}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{2}}\mathrm{\right)}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τθ2
Increase in m	$\frac{{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\omega }}_{\mathrm{1}}\mathrm{-}\mathrm{\tau }\mathrm{\left(}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{2}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{2}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{3}}\mathrm{\right)}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)θ3	$\frac{{\mathrm{a}}_{\mathrm{1}}\mathrm{[}{\mathrm{\omega }}_{\mathrm{1}}\mathrm{-}\mathrm{\tau }\mathrm{(}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{2}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{2}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{3}}\left)\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τθ3
Increase in xt	$\frac{{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\omega }}_{\mathrm{1}}\mathrm{-}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{2}}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)θ5	$\frac{{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\omega }}_{\mathrm{1}}\mathrm{-}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{2}}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τθ5
Increase in nt or st	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\tau \theta }}_{\mathrm{1}}\mathrm{\left(}{\mathrm{Y}}_{\mathrm{4}}\mathrm{+}{\mathrm{Y}}_{\mathrm{5}}\mathrm{\right)}\mathrm{+}{\mathrm{\tau \theta }}_{\mathrm{7}}\mathrm{+}\mathrm{\left(}\mathrm{1}\mathrm{-}\mathrm{\tau }\mathrm{\right)}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)(θ7-1)	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\tau \theta }}_{\mathrm{1}}\mathrm{\left(}{\mathrm{Y}}_{\mathrm{4}}\mathrm{+}{\mathrm{Y}}_{\mathrm{5}}\mathrm{\right)}\mathrm{+}{\mathrm{\tau \theta }}_{\mathrm{7}}\mathrm{+}\mathrm{\left(}\mathrm{1}\mathrm{-}\mathrm{\tau }\mathrm{\right)}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τ(θ7-1)
Increase in j*	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\tau \theta }}_{\mathrm{1}}\mathrm{\left(}{\mathrm{Y}}_{\mathrm{4}}\mathrm{+}\mathrm{2}{\mathrm{Y}}_{\mathrm{5}}\mathrm{\right)}\mathrm{+}\mathrm{\tau }\mathrm{\left(}{\mathrm{\theta }}_{\mathrm{7}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{8}}\mathrm{\right)}\mathrm{+}\mathrm{2}\mathrm{\left(}\mathrm{1}\mathrm{-}\mathrm{\tau }\mathrm{\right)}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)(θ8-1)	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\tau \theta }}_{\mathrm{1}}\mathrm{\left(}{\mathrm{Y}}_{\mathrm{4}}\mathrm{+}\mathrm{2}{\mathrm{Y}}_{\mathrm{5}}\mathrm{\right)}\mathrm{+}\mathrm{\tau }\mathrm{\left(}{\mathrm{\theta }}_{\mathrm{7}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{8}}\mathrm{\right)}\mathrm{+}\mathrm{2}\mathrm{\left(}\mathrm{1}\mathrm{-}\mathrm{\tau }\mathrm{\right)}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τ (θ8-1)
Increase in tt	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{4}}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)(θ10-1)	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{4}}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τ(θ10-1)
Increase in ut 1/	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_6}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)θ12	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_6}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τθ12
Increase in εt	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_7}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)θ13	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_7}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τθ13

Source: Appendix II.

^1/A direct effect on the aggregate supply equal to a₂ should be added in order to obtain the total output effect of a productivity shock.

View Table

Table 1.

Decomposition of the Effects Impinging on the Domestic Levels of Output in the Full Current Information Case

Endogenous Variables:	yt		${\mathrm{y}}_{\mathrm{t}}^{\mathrm{*}}$
Exogenous Variables	Financial constraint effect = a1 (aht-atE(Pit+1))	Relative price effect = $\mathrm{\left(}\mathrm{1}\mathrm{-}\mathrm{\tau }\mathrm{\right)}\mathrm{\left(}{\mathrm{p}}_{\mathrm{t}}\mathrm{-}{\mathrm{p}}_{\mathrm{t}}^{\mathrm{*}}\mathrm{-}{\mathrm{s}}_{\mathrm{t}}\mathrm{\right)}$	Financial constraint effect = a1 (aht-atE(Pit+1))	Relative price effect = $\mathrm{-}\mathrm{\tau }\mathrm{\left(}{\mathrm{p}}_{\mathrm{t}}\mathrm{-}{\mathrm{p}}_{\mathrm{t}}^{\mathrm{*}}\mathrm{-}{\mathrm{s}}_{\mathrm{t}}\mathrm{\right)}$
Increase in vt	$\frac{{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\omega }}_{\mathrm{1}}\mathrm{-}\mathrm{\tau }\mathrm{\left(}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{2}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{2}}\mathrm{\right)}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)θ2	$\frac{{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\omega }}_{\mathrm{1}}\mathrm{-}\mathrm{\tau }\mathrm{\left(}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{2}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{2}}\mathrm{\right)}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τθ2
Increase in m	$\frac{{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\omega }}_{\mathrm{1}}\mathrm{-}\mathrm{\tau }\mathrm{\left(}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{2}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{2}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{3}}\mathrm{\right)}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)θ3	$\frac{{\mathrm{a}}_{\mathrm{1}}\mathrm{[}{\mathrm{\omega }}_{\mathrm{1}}\mathrm{-}\mathrm{\tau }\mathrm{(}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{2}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{2}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{3}}\left)\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τθ3
Increase in xt	$\frac{{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\omega }}_{\mathrm{1}}\mathrm{-}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{2}}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)θ5	$\frac{{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\omega }}_{\mathrm{1}}\mathrm{-}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{2}}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τθ5
Increase in nt or st	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\tau \theta }}_{\mathrm{1}}\mathrm{\left(}{\mathrm{Y}}_{\mathrm{4}}\mathrm{+}{\mathrm{Y}}_{\mathrm{5}}\mathrm{\right)}\mathrm{+}{\mathrm{\tau \theta }}_{\mathrm{7}}\mathrm{+}\mathrm{\left(}\mathrm{1}\mathrm{-}\mathrm{\tau }\mathrm{\right)}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)(θ7-1)	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\tau \theta }}_{\mathrm{1}}\mathrm{\left(}{\mathrm{Y}}_{\mathrm{4}}\mathrm{+}{\mathrm{Y}}_{\mathrm{5}}\mathrm{\right)}\mathrm{+}{\mathrm{\tau \theta }}_{\mathrm{7}}\mathrm{+}\mathrm{\left(}\mathrm{1}\mathrm{-}\mathrm{\tau }\mathrm{\right)}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τ(θ7-1)
Increase in j*	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\tau \theta }}_{\mathrm{1}}\mathrm{\left(}{\mathrm{Y}}_{\mathrm{4}}\mathrm{+}\mathrm{2}{\mathrm{Y}}_{\mathrm{5}}\mathrm{\right)}\mathrm{+}\mathrm{\tau }\mathrm{\left(}{\mathrm{\theta }}_{\mathrm{7}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{8}}\mathrm{\right)}\mathrm{+}\mathrm{2}\mathrm{\left(}\mathrm{1}\mathrm{-}\mathrm{\tau }\mathrm{\right)}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)(θ8-1)	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}\mathrm{\left[}{\mathrm{\tau \theta }}_{\mathrm{1}}\mathrm{\left(}{\mathrm{Y}}_{\mathrm{4}}\mathrm{+}\mathrm{2}{\mathrm{Y}}_{\mathrm{5}}\mathrm{\right)}\mathrm{+}\mathrm{\tau }\mathrm{\left(}{\mathrm{\theta }}_{\mathrm{7}}\mathrm{+}{\mathrm{\theta }}_{\mathrm{8}}\mathrm{\right)}\mathrm{+}\mathrm{2}\mathrm{\left(}\mathrm{1}\mathrm{-}\mathrm{\tau }\mathrm{\right)}\mathrm{\right]}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τ (θ8-1)
Increase in tt	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{4}}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)(θ10-1)	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{4}}}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τ(θ10-1)
Increase in ut 1/	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_6}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)θ12	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_6}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τθ12
Increase in εt	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_7}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	(1-τ)θ13	$\frac{\mathrm{-}{\mathrm{a}}_{\mathrm{1}}{\mathrm{\tau \theta }}_{\mathrm{1}}{\mathrm{Y}}_7}{\mathrm{1}\mathrm{-}{\mathrm{\theta }}_{\mathrm{1}}{\mathrm{Y}}_{\mathrm{3}}}$	-τθ13

Source: Appendix II.

^1/A direct effect on the aggregate supply equal to a₂ should be added in order to obtain the total output effect of a productivity shock.