The Role of Fiscal Policy in an Incomplete Markets Framework

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 451 September 1993

THE ROLE OF FISCAL POLICY IN AN INCOMPLETE MARKETS FRAMEWORK

Charles P. Thomas

Note: International Finance Discussion Papers are preliminary marerials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.

Abstract

A general-equilibrium model is developed to highlight the link between neo-Keynesian models of unemployment and recent results on the constrained suboptimality of competitive economies with incomplete asset markets. Although the model deviates from the Arrow-Debreu paradigm only by the absence of some contingent claims, the competitive equilibrium exhibits under-

employment and balanced-budget fiscal policies have Keynesian effects which are Pareto

improving.

The Role of Fiscal Policy in an Incomplete Markets Framework

Charles P. Thomas!

I. Introduction

Will a market economy, left to itself, fully employ its resources? In The General Theory, Keynes exploited several mechanisms through which real economies differ from the classical paradigm where unemployment is either voluntary or non-existent. A common characteristic of these mechanisms is the difficulty of coordinating production and consumption plans in a decentralized economy. In recent years neo-Keynesians have sought to develop generalequilibrium models from micro foundations where this coordination problem can be analyzed. These efforts are of interest for two reasons. First, as an intellectual exercise it is of interest to explore which deviations from the classical paradigm are necessary and/or sufficient to generate Keynesian effects. Second, from a policy perspective, it is important to start from micro foundations to verify the welfare implications of policy.

The neo-Keynesian literature has gone in several directions. We will not review them here.” At this point it is sufficient to note that the argument developed below is based on incomplete financial markets and thus is related to the asymmetric information models of Greenwald and Stiglitz.’

The main contribution of this paper is the development of a model where we can make the following three points: 1) The Keynesian coordination problem can arise naturally ina competitive system with perfectly flexible prices and rational expectations. 2) The mechanism underlying the coordination problem is related to recent work on the constrained suboptimality of competitive equilibria with incomplete markets. As such, the coordination problem is generic to this and cther models with incomplete financial markets. 3) Familiar, and feasible, policies

can be welfare improving even though they do not directly address the fundamental

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~ microeconomic causes of the coordination failure. We study in detail the welfare effects of two fiscal policies and discuss briefly how other policies can be studied within this model.

The paper is organized as follows: The rest of the introduction contairis a review of recent results on the constrained suboptimality of economies with incomplete markets along with an overview of the model and argument. Section II lays out the formal model and computes its equilibrium. Section III discusses why the constrained suboptimality takes the form of underemployment and why agents do not act to alleviate the underemployment. Section 1V looks at the welfare effects of two balanced-budget fiscal policies and shows they can be Pareto improv-

ing. Section V outlines how other policies can be studied within this framework and concludes.

Constrained Suboptimality | In 1986 Geanakoplos and Polemarchakis (GP) established that with incomplete

financial markets the competitive allocation is constrained suboptimal (CS) in the following sense: If we consider the set of allocations that can be obtained by arbitrary trades in the existing (incomplete) assets and competitive trades in the goods markets, the competitive allocation is Pareto dominated by some other allocation in this set. It is important to note that we are not ranking the competitive allocation against those that could be obtained in a complete-market setting. Instead we are ranking it against those that can be obtained with the existing markets. That is, competitive agents do not efficiently use the markets they have. GP (1986) showed that this inefficiency is generic for exchange economies with two or more agents and two or more goods in each state. A similar result for production economies with stock markets was obtained by Geanakoplos, Magill, Quinzii and Dreze (1990).

The intuition behind this suboptimality is straightforward, but focuses on a channel often ignored by macro economists.

"...[Flor generic utilities (for which different agents have different marginal propensities to consume), a redistribution of assets redistributes wealth in any given state, leading to a change in relative prices. This relative price change yields yet another redistribution of wealth

which is not necessarily achievable through the [asset] market. By judiciously choosing the right

portfolio adjustments, the government can use the pecuniary externality to make everyone better off."

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Since this suboptimality is generic, it would appear to provide a wide avenue for policy. Its policy relevance can be challenged on two, so far unanswered, grounds, however. First, there is the information-based question of how the policy maker could learn enough about preferences to devise a useful policy. GP (1990) show that existing asset and goods prices do not reveal enough information about preferences to construct the Pareto improving trades. Second, even if the preferable trades could be discerned, there is a "feasability" question, since the direct application of the suboptimality result would suggest that a market be closed and agents be forced to make trades that they choose not to make on their own.

The model developed below addresses both of these questions. The first is addressed by showing that, for standard preferences, the suboptimality can manifest itself in terms of underemployment and the mechanism behind this underemployment can be understood with the more familiar intuition from neo-Keynesian models. As such, policy makers are able to consider policies that use this mechanism even though they cannot know everyone’s preferences. The second issue, that it is infeasible to close some markets and force trades on people, is addressed more directly. We show that without closing any markets or imposing any trades two standard fiscal policies can alleviate some of the inefficiency introduced by incomplete asset markets.

The strategy of what follows is to develop a static two-period economy with incomplete asset markets where the constrained suboptimality has a clean, macro interpretation in terms of equilibrium underemployment. We then show how balanced-budget fiscal policies,

within the given market structure, have Keynesian effects and can be welfare improving.

Overview of the Argument

Before presenting the formal model, it is useful to have an overview of the model structure and the argument. The setting is a two-period production economy with demand uncertainty arising from a random element in preferences. Production takes time which forces

producers to hire labor, and thus commit themselves to a wage bill, before they learn what the

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demand for their product is. Bankruptcy is prohibited, so we require that the revenue: from sales in each state be sufficient to meet the pre-committed wage bill. The producer does not consume the good he produces nor does he derive any direct (dis)utility from the production process. Consumers provide the labor in the production process.

The only financial asset is a riskless bond that producers issue in exchange for labor services. As such, there are no assets for trading demand risk. From the constrained suboptimality results we know that the competitive trade in the existing asset will not be efficient. That is, if the competitive trade of bonds for labor were replaced with another, using the same bonds, the allocation from subsequent clearing of competitive markets would Pareto dominate the allocation from competitive trades in both the labor and goods markets. In this model, the superior trade includes a higher level of employment. Thus we can interpret the inefficiency as a form of equilibrium underemployment.

The underemployment arises in a straightforward way. The asset structure does not allow producers to insure against the demand shocks, which leads to uncertainty in revenue and profits. When producers are risk averse, this revenue uncertainty induces them to limit production to a level below the benchmark level where marginal cost equals expected price. Even if they are risk neutral, the possibility that revenues can fall short of the wage bill can limit production to a level below this benchmark level.

This benchmark level of production--where marginal cost equals expected price--is of interest because it represents the point at which the incremental disutility to the consumer from the labor required to produce a marginal unit of production (the incremental wage bill) equals the expected utility from having a marginal unit of the produced good available for consumption (expected price). Since the consumer is the only agent who derives direct disutility from the production process and he is also the only agent who derives direct utility from consuming the produced good, it is clear that a higher level of production would make him better off whenever expected marginal profit is positive.

Without the constrained suboptimality results we might be inclined to attribute this

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to the general inefficiencies arising from incomplete asset markets: Agents are unable to transfer tisk fully which has general equilibrium effects and the lower level of employment is one manifestation of them. But the CS results indicate that agents could do better with the assets they have. In this setting better includes a higher level of employment. In particular, the consumer would be better off if the competitive bond-for-labor trade were replaced with one where more labor is traded for the same number of, or slightly fewer, bonds.

From a policy perspective this may seem to be a useless result since there is no apparatus for closing the labor market and forcing workers to supply more labor than they want at an "official" wage rate. There are, however, feasible policies which have much the same effect. In particular an ex-ante transfer from the consumer to the producer or a balanced-budget fiscalspending policy which is financed by a lump-sum tax on the consumer can be Pareto improving

by exploiting these same inefficiencies. Two such policies are explored below.

I]. Formal Model

Basic Structure

Consider a two-period, two-agent production economy with an aggregate producer and an aggregate consumer. In the first period, labor/leisure is the only factor or good. In the second period, there are two goods -- a produced good (G) and a non-produced good (N).° There are S second-period states of nature which correspond to a random element of the consumer’s preferences. This is the only exogenous random element in the model.

The Consumer

The consumer is endowed with one unit of leisure and e, units of N. His preferences, which are intertemporally separable and stochastic, are described by the following

two-period utility function:

u IL, Cog? Xal = In[I-L] + p- ((-a.,) . Infe. J +O. Infx,.))

-6where 1-L = First-period leisure; a. = A random variable where se S = {1,2,...,8} and O.€ [a., a,],0<a <a, < 1; Cog Consumption of N in state s;

Cc

Kost Consumption of G in state s; p = A positive time discount factor.

State s occurs with probability T.

The realization of o is learned at the beginning of the second period. The consumer knows the true state probabilities and satisfies the expected utility hypothesis.

The Producer

. The producer is endowed with ey units of N and no leisure. His preferences are

described by the one-period utility function Uteps! where Cos is his consumption of N. We assume that U5 > 0, Up < O, and that U5 and Up are continuous. He derives no utility from the consumption of G. He is the sole owner and manager of a firm which produces G; there is no stock market. He hires labor in the first period to produce G which he sells in the second period. The firm is useful to him only to the extent that it generates income in terms of the non-produced good.

The Technology

G is produced by the following technology: qd, = q{L] = Lia

,a>1. That is, production is non-stochastic, labor is the only factor, and there are diminishing marginal returas.

The Market Structure

In the first period the sole financial asset is a risk-free bond that pays one unit of N in the second period regardless of the state. It is traded against the other first-period good, labor. The bond’s price is normalized to one and the wage rate, in terms of the bond, is w. There is no exogenous supply of the bonds and in equilibrium the producer issues them to the consumer in

exchange for labor services.

In the second period there is a spot market where N is traded for G. The price of N

-7is normalized to one in each state and the price of G in state s is denoted by Py Some additional notation is helpful. Let p = [Py ++ Poo+Po] Vector of state-specific G prices; a = Efa]= XO, Expectation of « over states; ® = w-L Wage bill in terms of N;

“Tl = @t+ e, Consumer second-period income in terms of N;

Y, = Po q-@+ ey Producer income in terms of N.

Consumer Behavior

The consumer acts to maximize expected utility of the form: Vo = Efu.{L, Cog Xoo] =E{In[1-L] + p- (a) . Infe,.] + O. In{x..)}

subject to: 0 <L<1; I=w-Lte; Cc

>

0 <I-py-x,o-¢ 5 VseS;

c

0 C46 > O<x. VseS.

When the budget constraints are inserted into the objective function, it becomes: (C1) V, =E{In[I-L] + p- ((-o.,) -In{I - Ps Cog] + Q- In[x,.)}. This is a two-period dynamic-programming problem. The FOCs yield

(C2) Keg =I -a yp,

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as the consumer’s demand for G. Substituting this Xos into the first-period problem and maximiz-

ing with respect to L yields the following labor-supply schedule: (C3) L* = (wp - e)/lw- (+p)].

This can be expressed as a function of the wage bill alone: (C4) L*[o] =p -a/fo- (1 +p) +e].

Producer Behavior

In the second period the producer sells all of the produced good at price Py and spends all of his income on N. In the first period, he chooses the level of production, q -- a choice which depends on the the wage rate, his preferences, and the distribution of prices. His

first-period problem is to choose q to maximize

Vp = Etule nc} subject to

(PBC) Osc. <poq-wL+e, VseS,0<qsLi"

(PBC) is a sequence of budget constraints. The first inequality says that consumption cannot be negative. The second is the usual budget constraint with uncertain prices. Taken together, they form a bankruptcy constraint (BC) which insures that the producer will be able to meet his wage obligations in all states.’ Later it is shown that in equilibrium min [p.| is well defined, so there is a production/consumption plan that satisfies (PBC). The third and fourth ine-

qualities represent the technology.

When BC is not binding, the producer’s FOCs imply

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(P1) [q;p,w] = MuALY ] “(Py - wea: g*)) =o, The expression in parentheses is the difference between the price of G in state s and its marginal cost, 1.e., perceived, state-specific marginal profit. S[q;p,w] is the expected marginal utility from an incremental unit of production for given wages and state-specific prices. Although ® is used to characterize interior solutions (BC not binding), it is convenient for it to be defined when income is negative for some states; let ulY J = u[0] + u’[0] - Y, when Y. <0. The solution to (P1) is unique, so we can define q[p,w] to be the zero of &[q;p,w].® When BC is binding, the producer’s net income is zero in some state, which means the level of production is determined by his ability to meet the wage bill in that state. This

choice is characterized by (P2) Pqsp.w] = min.[p.]-q-w-q' +e, =0.

In the minimum-price state, the incremental revenue from production is less than the incremental wage bill, so any further production would violate the bankruptcy constraint. Since the solution to (P2) is also unique, we can define q[p,w] to be the zero of

®[q;p,w] and characterize the solution to the producer’s problem as * so - (P3) qip,w] = min{q[p,w], q[p,w]}.

Computation of the Equilibrium

A perfect stochastic foresight (PSF) equilibrium is an S+1 price vector (wp) such that the wage rate w. clears the first-period labor market when agents condition on second-period prices p , p clears the second-period goods markets with the income and level of production determined in the first period, and agents know the true state probabilities.

Note that w, L, q, and I are determined in the first period, so they are independent

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of the realization of «. For the G market to clear Kus =4 for each s. From (C2),

(El) P, = (iq) 0,

which is unique for each s, given the levels of income and production. Substituting for P. in

®[q;p,w] and &[q;p,w] yields

(E2) ®[q;I,w] = Lnu {la -w- Liq] + ey) “(I-a.-a-w- L{q)/q ;

(E3) ®[q;I,w] = min {I . a] -w-L[q] + ep

Since L is monotonic in the wage bill, , (see (C4)) and q is monotonic in L, q can

be written as a function of w alone. The wage rate enters (E2) and (E3) through the wage bill

alone and consumer income is the wage bill plus endowment. Therefore, ®[q;I,w] and ®[q;I,w] can be written as functions of @ alone.

(E4) ®[w] = Lruw{o- (a1) +a.-e + e,) “(@-(a,-a) + a, e /qlo].

(E5) Po] =o0- (min {oJ -1)+ min [oJ e, +e =o: (a -l)+a- et ey The zeros of (E4) and (ES) are used to characterize the equilibria of the system.

Although the producer’s choice is unique -- (P1) has a single zero in q -- (E4) can have several

zeros. (This is the familiar "third derivative" problem; see Rothschild and Sti glitz (1971).)

{: ®[w@] =0} and

Let (@ : B[@] = 0) =(a_- e,t eM(1-a).

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QQ is the set of of wage bills that satisfy the equilibrium conditions without regard for the bankruptcy constraint. w is the wage bill at which the bankruptcy constraint is just binding.

Finally, let

={meQ:a<o} if Of } <0

= {we QD: <a JU{o } otherwise.

This is the set of wage bills that satisfy the bankruptcy constraint as well as the FOC for bo:h consumer and producer maximization. The existence of the equilibrium is given

by the following claim:

Claim 1: (Existence of PSF Equilibrium) i * Q is non-empty; each element of Q fully characterizes an equilibrium of the sys- * tem and every equilibrium is characterized by an element of Q .

Proof: (See Appendix for details.)

* ~, . . . . That Q is non-empty is proved by showing that ®[q] is a continuous function that is positive for low values of w and is negative for high values of w. That this is an equilibrium

. . * drops out directly from the construction of Q .

The argument that follows does not depend on the multiplicity of equilibria, so we ; * will deal with the equilibrium that corresponds to the highest level of employment. Let =

* max{@e Q ],.

Benchmark Case: Risk-Neutral Producers with BC not Binding

Before looking at the properties of this equilibrium, it is useful to have a benchmark «ase where the producer is risk neutral and the bankruptcy constraint is not binding.

It is against the level of employment for this benchmark economy that we measure the equi-

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librium underemployment. In this special case (E4) becomes 4’ A ; (E4 ) P[o] = ull “UT. (W-(a.,-a) + a, -e /qlo]. A A Solving for@ =(@: [a] =0) yields A A - - (E5 ) ®O =a: e /a-a) Using (C4), the level of employment is given by A A - - (E6 ) L =p-o/f(a+p-a).

Note that this level of employment is independent of the producer’s preferences and both agents’ endowments. It can be shown that this is also the level of employment when there is a complete set of financial markets, which implies it is the level of employment at a fully Pareto efficient allocation.’ It is understandable that only the consumer’s preferences enter into the determination of the fully Pareto efficient level of production, since the consumer is the only agent who is made worse off by not consuming more of the factor of production and he is also the only agent who derives utility from the consumption of the produced good.

It is a straight-forward calculation to show that at LEIp] =a-w gt! That is, expected price equals marginal cost when the producer is risk neutral (RN) and the BC is not

binding.

Level of Employment Relative to Benchmark The significance of the benchmark level of employment is discussed in the next subsection. At this point it is useful to establish that in general the equilibrium level of employ-

ment will be less than that of the benchmark case. This is done in claim 2. Part (i) of Claim 2 is

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that producer risk-aversion is sufficient to yield employment below L’. part (ii) is that riskaversion is not necessary, because of the bankruptcy constraint.

Claim 2: (Employment is Below the Benchmark Level)

i) When the producer is risk-averse, o is less than o and Llo |] < L. ii) When the producer iS risk neutral, there are endowments and consumer a.’s such that the bankruptcy constraint is binding and L[w’] < L.

Proof: (See Appendix details)

Parti: At o, expected price equals marginal cost. For a risk-averse producer this implies that B[w] is negative at o, Since a risk-averse agent will avoid what he perceives as a fair bet when it increases the volatility of his income. Since @[] is negative at @ , Po] crosses through zero to the left of o , and max[@ e Q"| is less than o. Since labor-supply is monotonic in the wage bill, the level of employment at this wage bill is below the level of employment at o.

Part ii: The wage bill where the bankruptcy constraint binds, (a, e+ ey 1-@ ), is independent of producer preferences. Even if the producer is risk neutral, if (a_- et e(1-a ) <a: e,/(a-a), the bankruptcy constraint will bind and employment will be below L By choosing endowments and consumer preferences appropriately we can clearly make this hold.’ °

Labor Market

The wage bill o represents the employment/wage combinations consistent with the producer’s maximization. It is, then, a hyperbolic labor-demand schedule. Equation (C3) is a labor-supply schedule. Figure 1 depicts the labor market for the benchmark and general cases.

. * Ak, A Since @ is less than@ ,L is to the left of L .

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Figure |

Labor Market Benchmark and General Cases

L“ Benchmark

[— n

d L : General

Wage Rate

II: Underemployment and Constrained Suboptimality in the Model

The fact that the level of employment is higher when the producer is risk neutral and BC is not binding than it is when the producer is risk averse or the BC is binding is not, in itself, any indication of inefficiency. It could reflect the best agents can do with the markets they have. In this section we show why a level of employment below L’ is indeed an indication of inefficiency. In particular, we show that there are trades other than the competitive ones that the agents could make with the existing assets that yield allocations that Pareto dominate those of the competitive equilibrium. Claim 3 establishes the constrained suboptimality of the equilibrium.

Claim 3: (The Equilibrium is Constrained Suboptimal)

BS ok LetL and _ be the level of employment and the wage bill in the above economy.

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When the producer is risk averse or BC is bindin g, there is a first-period trade (L* on") such that the allocation which results from the competitive clearing of subsequent markets Pareto dominates the allocation arising from (Lo) and subsequent market clearing.

Proof:

To prove this, we compute the ex-ante welfare of the agents in terms of employment and income -- claims to N -- when period-two markets clear competitively. We then show that for unchanged claims to N, an increase in the level of production makes the consumer better off whenever L < L It is then shown that for the risk-averse or BC cases, there is a first period trade Lt, w ) with L < Lt < L which makes the consumer better off without changing the producer’s welfare. Finally, it is argued that a small decrease in w allows the producer to share in this increase in welfare while keeping the consumer’s welfare above the competitive level.

Consumer Welfare

Consumer ex-ante welfare is given by

(W1) Ww. = In[1-L] + p “E{(1-a.) In[c,.J +a.- In{x, 1}

When the second-period allocations are determined by market clearing, the follow-

V/A Substituting these into (W1) yields

ing obtain: Cost I. (1-o.) and X ag L

(W2) W, = In[1-L] + p -E{(1-a.,) -In{I-(1-a)] +o. int !/4y).

This is an expression for the consumer’s welfare in terms of his claims to N and the amount of

labor supplied. Taking the total differential of W2 yields (W3) dW. = OW /oL -db + dW Jal - dl where

dW /oL =-I/(1-L)+p-a/(a-L) =0;

VIIA

dW /al= p-(1-a) A >0.

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With a little algebra it is easily seen that (W4) (L<p-a/(a+p-a))= (dW /dL >0).

A The key to the suboptimality result is to note that the critical value of L in (W4) is the L_ from the benchmark case where the producer is risk neutral and the BC is not binding. Producer Welfare

Ex-ante producer welfare, when the period-two markets clear, is given by (WS) Wy = Efu,fY I] = E{u,[o- (a.,-1) + ae, + e)) Taking the total differential yields

dW /9@ = E{u[Y J] . (a.- 1}<0O dW /8e, = E{u'[Y ] . a} >0 OW /9e, = E{u [TY J} > 0.

Suboptimality

From claim 2, we know that if the producer is risk averse or the BC is binding, then L is less than L Let L® be any value between L and L Since L < L’ implies that dW J/AL is positive, the consumer is made better off if the competitive trade in period one is replaced by (L*, o). Since L does not enter directly into Wo and «, eo and ey are unchanged, the producer’s utility is unchanged. From the continuity of the utility functions, there is some positive € such that ct @ -e) yields an allocation which both the consumer and producer prefer to the competitive allocation. This proves the constrained suboptimality of the competitive trades.

Figure 2 depicts the weakly-Pareto superior trade.

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Constrained Suboptimality

d L : Benchmark

d L : General

Wage Rate

Competitive

Interpretation of Underemployment

One interpretation of this suboptimality is that the consumer’s wage schedule is too high -- he demands too high a wage for any given amount of labor supplied. For the weakly Pareto improving trade of a, o ), the "wage rate" is wit = o ML", which is less than the wage under competitive market clearing. Even so, consumer welfare is higher under the alternative labor agreement.

The microeconomic intuition for this is clear. When the worker supplies more labor for an unchanged wage bill, the level of production rises and consumer income, in terms of N, is unchanged. The Cobb-Douglas preferences imply that the shares of income spent on G and

N will remairi unchanged, so the price of G falls in proportion to the increase in production. The

-18net effect for the consumer is less leisure, more consumption of G, and unchanged consumption of N. So long as L is less than L. consumer welfare is improved by giving up more labor in exchange for its marginal physical product in G. For the producer, the wage bill and all statespecific revenues are unchanged, so producer profit and welfare are unchanged in each state. The macroeconomic intuition is also clear and echoes many of the neo-Keynesian arguments. In a decentralized economy, production and consumption decisions are made by different people at different times. Production decisions require a commitment of resources and are made in anticipation of the future consumption decisions to be made by others. Without a mechanism by which employees can, at the production stage, commit to later consumption, the direct link between productive activity and future consumption opportunities is broken. Once this link is broken, financial market imperfections, either in the form of financing constraints or inadequate vehicles for risk sharing, drive a wedge between the wage rate and the value of

productive activity. The result is a level of activity below that which agents would prefer.

Persistence of Underemployment

Why do agents not make the Pareto-superior trade themselves and eliminate the underemployment? There are at least two reasons for this. The first is the usual competitive assumption that agents do not know how their actions affect prices. The consumer will voluntarily supply the requisite labor at the lower wage only if he believes that the amount he works affects the second-period price.

The second reason is that even if the consumer knew how his labor supply affected second-period prices, the Pareto-superior trades will not be stable when the economy is replicated to include many identical consumers and producers. Bester (1984) and Repullo (1988) have shown that in exchange economies with incomplete securities markets the competitive equilibrium will coincide with the core after sufficient replication. If this economy were replicated many times, the first-period trade of a, @ ) would not be stable. A coalition of workers and (a

* * smaller number of) producers could defect from the rest and make a trade closer to (L_,@ ). By

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choosing the proportion of consumers and producers in the coalition appropriately we can leave each producer’s level of production and wage bill the same as it would have been at cL @ ), but at the same time give the workers the w" wage rate with less than the L* labor supply. From the labor supply curve, we know that the workers would prefer this trade to , ). Thus the a @ ) trade is not stable to free coalition formation.

“This argument is similar to the one Keynes (1936, Chapt. 19) gives as to why workers who negotiate their contracts at different times cannot change the real wage when it is

an effective way to increase employment.

Policy Relevance

Since constrained suboptimality is a generic result, we can expect that the kind of inefficiency described above is pervasive. Itis a Separate question as to whether this insight is useful for policy. It would seem not for two reasons. First, itis not clear how the planner could learn of this superior trade. Second, the direct implementation of the superior trade would require that the labor market be closed and that people be forced to work beyond their will.

To show that the competitive trades were suboptimal we used the individual utility functions. In practice the planner cannot know these functions and, as discussed earlier, the planner cannot learn enough about preferences from the observed asset demands to discern what the superior trades in the asset market are. But this same objection can be raised about any macroeconomic policy analysis that starts with individual utility. Economists presume to have some understanding of the structure of the economy and develop models to hi ghlight certain aspects of it. The individual utility is used both to motivate individual actions and to verify that welfare gains from policy are possible. If the analysis is relevant, in that it highlights important problems with the economy, then the usefulness of policy will be robust to errors in the specification of individual utility. As is shown below, a general understanding of the source of inefficiency can be sufficient to find an improving policy even if it is not sufficient to find an optimal one.

The second objection, that to implement the policy requires forcing trades on some

-20agents, may seem more daunting. In the next section we show how policies which leave the labor market to clear competitively can be useful. In particular, feasible government redistribu-

tion and spending policies have Pareto improving effects because they act to mitigate the

inefficiency described above.

IV. Effectiveness of Fiscal Policy

We consider two types of fiscal policies, both of which are state independent. The first is a transfer policy implemented by an ex-ante lump-sum transfer of endowments from the consumer to the producer. The second is a balanced-budget spending policy where the government imposes a fixed lump-sum tax on the consumer, spends all of the tax revenue on the produced good, and throws its purchases away. That is, although we attach no social utility to government-consumption, the government spending is still useful.

Transfer Policy

The transfer is fully anticipated before the first-period labor market opens ar.d agents condition on the post-transfer equilibrium prices. The first effect of the transfer is purely accounting -- it lowers e and raises ey by the same amount. The decrease in e, lowers the laborsupply schedule which, cezeris paribus, increases the level of production.

In general, the transfer will also shift the labor-demand schedule. The direction and size of this shift is indeterminate, which makes the net effect on employment ambiguous. '

To sort out these effects and show how the tax can improve the welfare of both agents, we look at two cases. In the first case the BC is binding and the change in w resulting from the transfer can be computed directly. We show that whenever the BC is binding the transfer makes the consumer better off and leaves producer welfare unchanged. For the second case, where the BC is not binding, we compute an example to show that when the producer’s preferences are logarithmic, a small transfer can increase both agents’ welfare while a lare

transfer makes the consumer worse off.

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Welfare The change in consumer welfare from a change in the endowments of N can be

written as

(FI) “dWo= aWYAL - (@LS/a0) - (aa/ae cde, dolde,. de,)+ OW /dL - (AL*/de,) - de, +

dW Jal * (da/de + 1) - de, +

dW Jal (0@/de,) - de,

where aW /oL = -1/(1-L) + p -a@/(a-L) and ow JI =p -(1-a)1. The analogous expression for producer welfare is

(F2) dW, = OW /0@ ; (do/de: de, tou/de,,- de,,) +

dW ,/de, e+ Ww Pr) p/%e, ep

where OW ,/d@ = E[u’[Y |] (a, - 1)], OW fe, = Efu [TY .] : a] and OW /de, = E[w’fY J].

The policy we are considering is an ex-ante redistribution of second-period endow-

ments, 1.e., de, = “de... Inserting this equality into (F1) and (F2) and simplifying yields

= s . - - S . (F3) dW, = dW /oL - (AL*/d@ (dave, dw/de,) dL /0e,) de,, + OW Jal (do/de, - du/de, -1).- de, 3

(F4) dw. = E[w’lY J “(1 - a] -dU- dole , - dw/de.,) . de, .

-22-

Case One: Bankruptcy Constraint Binding

Claim 4: (With BC Binding, Transfer is Pareto Improving)

When the BC is binding, an ex-ante transfer of endowments from the consurner to the producer increases consumer welfare and leaves producer welfare unchanged.

Proof:

We look at marginal changes in endowments which do not move the economy off

of the BC. Ata BC equilibrium @. =@ =(a@ - e, + et - a). Therefore, (F5) dade, - dw/de, = 1/(1-a_) - a /(1-o_) = 1. Substituting (F5) into (F1) yields

(F6) dW, = aW_/aL - (AL*/dw- aL/de,) - de, Since dL*/da is positive and dL/de, is negative, the expression in parentheses is positive. Ata BC equilibrium we know 0W / dL > 0, therefore, dW Jde , >. That is, the initial shift of endowments from the consumer to the producer makes the consumer better off.

Substituting (F5) into (F4) yields dW /de p =(. Therefore, when the BC constraint is binding an ex-ante increase in producer endowment accompanied by an equal decrease in consumer endowment raises consumer welfare and leaves producer welfare unchanged. This establishes Claim 4.

By looking at the two components of the transfer, we can see what is happening to the system. The decrease ine c shifts the labor supply curve down as the consumer tries to transfer wealth into the second period to offset the tax. Lower income, for a given wage bill, means less spending on the produced good in each state which tends to decrease the demand for labor.

The increase in ep does not affect the supply of labor, but it does increase its

demand since the producer has a larger reserve out of which to pay the wage bill in the low-

-23demand states. The net effect on the demand for labor is to increase the wage bill by the amount of the trarisfer.

The increase in the labor demand alone, for an unchanged labor supply schedule, would be sufficient to increase consumer welfare. There would be an increase in production with no change in consumer income which is sufficient to make the consumer better off. As it is, however, the labor supply schedule moves down with the transfer and there is a further increase in the level of production which increases consumer welfare further. The final allocation is identical to that with the unfeasible policy of closing the labor market and requiring trades below the

labor supply schedule.

Case 2: BC not binding

Claim 5: (With BC Not Binding, Transfer Can be Pareto Improving)

At an interior equilibrium for some preferences and endowments, an ex-ante transfer of N endowments from the consumer to the producer makes both agents better off.

Proof:

An example is sufficient to prove the claim. Let technology, preferences, and

initial endowments be given as follows:

a= 1.25; Inleps] = In{c.,J: S = {1,2}; a = {.2, .8}; m= {.2, 8}; p = .9;

ey =0, eo = 1.

Figure 3 plots an index of welfare for each agent for various tax rates. The example is constructed so that a transfer from the consumer to the producer makes both agents better off for small transfers. After a point, however, further increases in the transfer make the consumer worse off while continuing to make the producer better off. Figure 4 depicts the labor

market without any tax and with the tax corresponding to that which maximizes consumer wel-

fare.

Welfare

-24-

Figure 3

Effect of Fiscal Transfer Policy elfare

Consumer Welfare

a Producer Welfare

0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 Tax Rate

-25-

Figure 4

Effect of Fiscal Transfer Policy Labor Market

Equilibrium Without Tax

Wage Rate o

-—7

0.13 0.15 017 0.19 0.21 0.23 0.25 Labor

0.05 0.07 0.09 0.11

The mechanism is essentially the same as in the BC binding case. The tax lowers the labor supply curve, which ceteris paribus increases employment and tends to make the consumer better off. There are, however, other effects of the tax which make the general characterization of the comparative statics impossible. The fall in consumer endowment can decrease the demand for labor. Similarly, the increase in producer endowment can increase the

demand for labor.

Fiscal Spending Policy:

The second policy we consider is a balanced-budget spending policy where the

government levies a constant lump-sum tax on the consumer, purchases the produced good and

-26-

throws the purchases away. This policy tends to stabilize the price of the produced good and increase production. For some preferences and endowments, the consumer’s consumption of G is higher for some states and lower for others which can lead to a welfare gain.

Model with Government Spending

Let a and t represent the consumer’s disposable income and a lump-sum tax on consumers. When bankruptcy is prohibited, (4 is a constant equal to w + et. Consumer maximization again yields Xog = fap, and LS = (p-w- (e, -t))/(w-(1 + p)).

The producer’s FOC are again ®[q;p,w] = 0, Y, 2 0 Vs e S where Y, and ®[q:p,w] = Oif Y,>0 vse S, where Y and ®[q;p,w] are the same as above.

The government spends all of its tax revenue on the produced good, so its demand is X 9s = U/p..

Equilibrium

; _ ad oy 4x =n Total demand for G is Xog t Kas =(] a. + U/P.- For market clearing Xog t Kos =q, so

market clearing prices are (F7) p,= Ua, + t/q =[o+ e.) 0, + (1-0) t/a.

To compute the equilibria, we substitute for P. in ®[q;p,w] to obtain (F8) @[;t] = LT {Y [o.t}} fe, a, + (1-a,)-t + (o.-a)-o] where

Y [;t] =e, a5 + (1-a,.) “t+ (a.-1) -O+ ep:

The zero of ©[;t] is the wage bill consistent with market clearing and producer

maximization. Let @ [t] = (@: Pot] = 0). The maximal consistent with the BC is

(F9) w [t] = (a: min.[p.] -q-@+ cy =0)= (e, “Oo + & /(1-o ) +t.

-27-

The equilibrium is characterized by @ = min[ [t], o [t]].

Comparative Statics

From the price equation, we see that for given q and @, an increase in t increases the price of Gi in all states. From the labor-supply equation, we see an increase in t shifts the labor- -Sup ply: schedule down. The effect of the tax on the wage bill is ambiguous. When the BC is binding, de/dt equals one. For the interior case, over the range of policy interest, dw/dt switches from being positive for small tax rates to bein g negative for large tax rates. As a result, employment is increasing as the policy begins, but later falls as the policy is expanded. The rise in q induced by the increase in t tends to lower prices and we cannot, in general, put a sign on the net change to prices.

The difficulties in signing the effects of this policy are similar to those encountered with the redistribution policy. As with the redistribution policy, we study the effects analytically for the case where the BC is binding and look at simulations for the interior case.

Consumer Welfare

The consumer’s ex-ante welfare is (F10) Ww. = E{In{1-L] + p- Q. “In[x, 5! +p “(1-a,) . Infe J}. Substituting the maximizing X,, and Cos yields (F11) Ww. = Inf{l-L]+p- Inf] -p- E{a, In{p.]} +p “Ela, . Info] + (1-a,) : In[1-o.,]}

The policy is useful to the extent that the induced increase in q lowers the weighted

geometric average of prices in the third term. Substitutin g for p yields

(F12) W.= InfI-L]+p-InfI4]- p- E(a, An{I"-o, +t} +p-Efa,-Infq]} + p Efa, Info] + (1-a,) . In[1-o.,J}.

-28-

Taking the total derivative w.r.t. the tax yields

(F13) dW Jat = -1/A-L) +p a/(a-L)) - dL/at + pt? - atYat p-Ela, (a, - atfyat + yyad a+}.

At t= 0 this becomes (F14) dW Jdt = (-I/(-L) + p-@/(a-L)) - dL/dt+p- (1-04 . at4at-p an

Producer Welfare Producer welfare is given by (F15) Wo = E{u,fY J = E{u lo. (a.-1) FO e+ (1-a.) -tt+ el) hence

(F16) dW), = AW, /d@- deo + dW ,/0e, “de, + dW /de, de, + ow ,/at -dt where

aW_/dw =E{u [YJ (a, -1)} <0;

so}

oW [de = Eu [TY] . a.) >0;

no]

oW joe, =E{u[Y J} >0;

so}

aW /ot =E{w’[Y.]-(1-o,)} >0.

ao)

Case 1: BC Binding When the BC is binding, dw /dt = 1, so the spending policy does not change the

consumer’s disposable income. It does, however increase the level of production as the labor supply schedule shifts down and the labor-demand schedule, w , shifts out. The policy’s effect

on consumer welfare is given by

(F17) dW /dt =[-1/C1-L) + p -a/(a-L)]-dL/dt - p- ol?

-29-

The policy has no effect on producer welfare since ow! 0 = “oW ot and do /dt = 1.

Claim 6:

There are endowments and preferences such that the BC will bind and a balancedbudget spending policy financed by a tax on the consumer will increase consumer welfare without changing producer welfare.

Proof:

For eo Q, there is an a such that the BC binds. From this point, as a~0,o@-0 and L +0. Provided « does not go to zero, the first term in dW [dt goes to positive infinity. The second term is bounded, so the derivative on consumer welfare becomes positive for some a. As shown above, the policy has no effect on producer welfare. Which completes the proof.

The economic interpretation of this is clear. When the BC is binding, the level of production is determined by the level of demand in the state when the consumer desires the produced good the least. Demand in this state does not reflect his average preference for it. The fiscal policy raises the floor on prices which enables the producer to honor a larger wage bill. The larger wage bill, coupled with the shifted labor-supply schedule, means that production is increased. ‘The shift in the wage bill just offsets the tax to leave disposable income unchanged.

If the consumer were to enjoy the full product of his increased labor, the argument would be :he same as with the transfer policy. However, with the spending policy, the government buys some of the produced good and the amount that the consumer enjoys depends on the state. In the low-demand states, x es is lower with the policy, but in the high demand states, it is higher. Since it is in the high-demand states that the consumer most enjoys the produced good, the greater consumption of it in these states can outweigh the disutility from less leisure and the

lower consumption in the low-demand states to make him better off.

Case 2: Interior equilibrium

Claim 7:

-30- At an interior equilibrium, for some preferences and endowments, a balanced budget fiscal spending policy is Pareto improving.

Proof:

An example is sufficient to prove the claim. Let technology, preferences and endowments be the same as in the example used to prove claim 5. Figure 5 depicts the indexes of welfare. Again, producer welfare is increasing monotonically in the tax rate while consumer welfare improves for small tax rates and decreases for large tax rates. Figure 6 depicts the labor

market without any tax and with the tax that maximizes consumer welfare.

Figure 5 Effect of Fiscal Spending Policy

Welfare 0.14

Consumer Welfare

0.14

0.05+

Welfare

J

a I ON a Se Se ee ee eee Sees Eee ee

O 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Tax Rate

-31-

Figure 6

Effect of Fiscal Spending Policy The Labor Market

2 2 t O a @ 1.54 1@)) = 7 Equilibrium without Spending Policy Equilibhum with 0.5- Spending Policy

I

Oe 0.05 0.07 0.09 0.11 0.13 0.15 017 0.19 0.21 0.23 0.25 Labor

V. Conclusion

This paper presents a small general-equilibrium model to highlight the link between neo-Keynesian models of unemployment and recent work on incomplete financial markets. We show how the constrained suboptimality of the competitive equilibrium, which is generic with two or more agents and two or more goods, can take the form of underemployment.

The direct application of the suboptimality results would imply that policies to improve on the competitive equilibrium would likely be infeasible as they would involve closing a market and forcing agents to make trades which they choose not to make on their own.

The economic intuition behind the underemployment is clear in this small model, however, ancl allows us to construct feasible fiscal policies that are welfare improving.

The model also provides a framework for analyzing other types of policies, two of

-32-

which we briefly discuss. Since the inefficiency arises because of a lack of securities markets, it is natural to ask what effect the introduction of another asset would have and if there is a role for policy in introducing or supporting this new market. In Thomas (1986b) use this model to show that the introduction of a financial futures market--linked to the produced good’s price--can be Pareto improving even if the worker/consumer does not trade in (or even know of) the new market. In that model, a lump-sum tax on the consumer is used to finance a government "speculator" who trades futures with the producer. This example demonstrates why there can be externalities to financial assets that drive a wedge between the private and public incentives for their introduction. It also provides a rationale for some price stabilization policies.

In discussing the persistence of underemployment above, we argued that the Paretosuperior trade will not be robust to the free formation of coalitions. It has been suggested that the model developed here could be used to explain the national wage-bargaining schemes used in

some countries.

-33-

References

Bester, Helmut (1984), "Core and Equilibrium in Incomplete Markets", Zeitschrift fiir National6konomie, 44(3):255-266.

Gale, Douglas and M. Hellwig (1984), "Incentive-Compatible Debt Contracts: The One-Period Preblem", Theoretical Economics Discussion Paper no 84/97, L.C.E.R.D., London School of Economics.

Geanakoplos, John D. (1990), "An Introduction to General Equilibrium With Incomplete Asset

Markets", Journal of Mathematical Economics 19:1-38.

Geanakoplos, John, M. Magill, M. Quinzii and J. Dreze (1990), "Generic Inefficiency of Stock Market Equilibrium when Markets Are Incomplete", Journal of Mathematical Economics 19:113-151.

Geanakoplos, John D. and H. M. Polemarchakis (1986), "Existence, Regularity and Constrained Suboptimality of Competitive Allocations when the Asset Market is Incomplete", in ncertainty, Information and Communication, Essays in Honor of Kenneth J. Arrow, vol. 3, W. Heller, R. Starr and D. Starret eds. (Cambridge: Cambridge University Press, 1986).

Geanakoplos, John D. and H. M. Polemarchakis (1990), "Observability and Optimality", Journal of Mathematical Economics 19:107-112. oa

Greenwald, Bruce and J. Stiglitz (1993), "New and Old Keynesians", Journal of Economic Perspectives, 7(1):23-44.

Keynes, John M. (1936), The General Theory of Employment, Interest and Money, Harcort Brace World, New York, New York.

Repullo, Rafael (1988), "The Core of an Economy with Transaction Costs", Review of Economic Studies, 40(55):447-458.

Romer, David (1993), "The New Keynesian Synthesis", Journal of Economic Perspectives, 7(1):5-22.

Rothschild, Michael and J.E. Stiglitz (1971), "Increasing Risk II", Journal of Economic Theory, ~ -3:66-84. . .

Thomas, Charles P. (1986a), Asset Structure and Underemployment, Ph.D.Dissertation, . Columbia University Department of Economics. Available from University Microfilms; Ann Arbor, Michigan.

Thomas, Charles P. (1986b), "The Effect of Financial Innovation on Non-Traders: A Macroeconomic Example", Center for the Study of Futures Markets Working Paper No. 144, Columbia University School of Business.

-34-

Appendix

Proof of Claim 1:

That w exists is proved by showing that S[a] has a zero. &[«] is a continuous function that is positive for low values of and is negative for high values of w. When q is low (high) enough, the price of G in each state is above (below) marginal cost which makes each term of ®[] positive (negative). We call the largest (smallest) where this is true @_ («,). For less (greater) than this critical value, @[«] is positive (negative) and the producer will want to increase (decrease) production. @[] is continuous in o (for Y.? 0), so there is at least one point between m and w, where it equals zero. At this zero, the producer has no incentive to change the level of production.

Since producer income is equal to @- (a.,-1) Fae,+ ey and 0. is always less than one, producer income is falling in q for all states. @ , then, represents the maximal @ consistent with non-negative income in all states, i.e., the no-bankruptcy constraint.

"When is greater than or equal to @ , the no-bankruptcy constraint does not affect the equilibrium. When @ is less than « , the producer would like to increase production, but cannot because of the constraint. He has no incentive to decrease production, so w becomes an equilibrium.

That o fully characterizes an equilibrium follows directly from (C2), (C4) and the consumer’s income identity. That there is no equilibrium other than o follows from the con-

* struction of @ and the concavity of the agents’ objective functions.

Proof of Claim 2:

The proof has four steps. The first step is to show that at o expected price equals marginal cost. The second step is to show that if marginal cost equals expected price, a risk averse producer i is not maximizing and Blo. ]<0. The third step is to show that if @|w | is negative there isan @ less than o such that [wm ]=0. The fourth step is to note that L[o] is a monotonically increasing function, so L[@ ] is less than Llo' |}.

Step One: At o, marginal cost equals expected price. From n equation ES, o =a-e o[a-a), which implies

(Al) Py [o J=a, Va(L{o" =o, or +e allio” ]). Substituting a-e Ma a) for o in AL yields (A2) Py [a J=a, (a-e,+ (a -1) -€ Ma a) - qlo. ]

= =o, a-e Ha a) - alo” }). Taking expectations over states yields

-35-

(A3) Ep, {o']] = @-a-e f((a-8) -qlo")) =a- 0 Valo")

Since labor is the only Productive factor, total cost is the wage bill: ws L=w.- q@ and marginal Cost is given by MC =a-w- q@ . Since L = q’, we have MC = a- w-L/q=a- aq forall. In particular, at o, this is the same expression as that for expected price in (A3). This completes step One.

Step Two: If the wage bill equals o a risk averse producer is not optimizing and ~ A Ro@)]<0. ~

(A4) @fo"] = Elu'lY fol] -(@fo"-a- wo") glo’) Since at @ » Elp, J= = MC, we can | write (Ad as

(A5) Ba" }=Efu’[Y lo N-@, [o }- E[p, [o I).

Since P.= O, -T/q, E[p, J=a.- Va and (A5) can be written as

(M6) ®o"]=E = Ew’ [Yo J] -(a,-&) -(@ +e )/q]. Substituting for Y lo Jin (A6) yields

(A7) Po ]=E[w’ lo +e : a Oo +e pl (a, -Q)- (o- +e /a).

Since E/u’[(@ +e o a sO be pl (a, ey equals zero, we can subtract it from each term on the RHS of (A7) to yield (A8) Go }=E =E{(w’ ((o +e ae a.-0 te J-u (a +e o a- 0 +e p) (a. -a)} -(@ +e a Under the assumption that u’<0,u lay -]<u’[a; - ] iff a> a. Therefore, each term in the {} is non positive and must be negative for all s such that O. tt Thus Flo ]<0. Thr In the proof to claim 1, we showed there is an @ such that ®[] > 0 for all O<@. Since ®[] is a continuous function and @[@ ‘ <0 there must be an w between @ and o such that Pa ]=0. Finally, since L[a] is monotonically increasing, L[w ] < L{o ]. QED

-36-

Endnotes " The author is a staff economist in the Division of International Finance. This paper represents the views of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or other members of its staff. I would like to thank Herakles Polemarchakis, Ed Green, Guy Stevens, and Jon Faust for their helpful comments.

? For an overview see Romer(1993) and the related articles in that volume.

> In a series of papers, Greenwald and Stiglitz have shown how asymmetric information can give rise to capital market imperfections. The imperfections generally take the form of missing contingent claims markets. In the presence of these imperfections, firms will behave as though they were risk averse or facing financing constraints. They further show how the competitive equilibrium will not use the existing markets efficiently, which leads to a role for policy. See Greenwald and Stiglitz (1993) for a review of these arguments.

4 See Geanakoplos (1990) for a review of the literature. > J. Geanakoplos (1990) p. 26.

° N can be considered manna, a Hicksian composite good or money claims on production from the rest of the economy.

” If we allow bankruptcy, the welfare arguments that follow go through (although existence of an equilibrium is not assured), provided the contract takes the following form: If possible, the wage bill is met; if not, the worker receives all of the firm's revenue plus the producer’s endowment. Gale and Hellwig (1984) derive this as an optimal contract when it is costly for the bond holder to observe the state. See Thomas (1986a) Chapter II Section Four.

8 It is straight-forward to show that © is always falling ing. The difficulty comes from making sure u’(Y) is defined over the relevant range. This is where the definition that for Y. <Q), u(Y ) = u[O]+u’[0] - Y. is used.

* See Thomas (1986) Chapter I.

'° Asa trivial case, if o = 0, then BC will be binding for RN producers if ee, < o/(a-a). For ep

Q, this is clearly true.

-37-

'! This is another example of the "third derivative" problem discussed in Rothschild-Stiglitz (1971).

IFDP

Number

45]

450 449

448

447

446

445

444

443

442

441

440

439

438

- 38 -

International Finance Discussion Papers

Titles 1993

The Role of Fiscal Policy in an Incomplete Markets Framework

Internal Funds and the Investment Function

Measuring International Economic Linkagewith Stock Data

Macroeconomic Risk and Asset Pricing: Estimating the APT with Observable Factors

Near observational equivalence and unit root processes: formal concepts and implications

Market Share and Exchange Rate Pass-Through in World Automobile Trade

Industry Restructuring and Export Performance: Evidence on the Transition in Hungary

Exchange Rates and Foreign Direct Investment: A Note

Global versus Country-Specific Productivity Shocks and the Current Account

The GATT’s Contribution to Economic Recovery in Post-War Western Europe

A Utility Based Comparison of Some Models of Exchange Rate Volatility

Cointegration Tests in the Presence of Structural Breaks

1992

Life Expectancy of International Cartels: An Empirical Analysis

Daily Bundesbank and Federal Reserve Intervention and the Conditional Variance Tale in DM/$-Returns

Author(s)

Charles P. Thomas

Guy V.G. Stevens

John Arnmer Jianping Mei

John Arnmer

Jon Faust

Robert (C. Feenstra Joseph E. Gagnon Michael M. Knetter

Valerie J. Chang Catherine L. Mann

Guy V.G. Stevens Reuven Glick Kenneth Rogoff Douglas A. Irwin Kenneth D. West Hali J. Edison Dongchul Cho Julia Campos

Neil R. Ericsson David F.. Hendry

Jaime Marquez

Geert J. Almekinders Sylvester C.W. Eijffinger

Please address requests for copies to International Finance Discussion Papers, Division of International Finance, Stop 24, Board of Governors of the Federal Reserve System, Washington, D.C. 20551.

IFDP Number

437

436 435 434 433

432 43] 430

429 428 427 426 425 424

423

- 39-

International Finance Discussion Papers

Titles

1992

War and Peace: Recovering the Market’s Probability Distribution of Crude Oil Futures Prices Durin g

a the Gulf Crisis

Growth, Political Instability, and the Defense Burden

Foreign Exchange Policy, Monetary Policy, and Capital Market Liberalization in Korea

The Political Economy of the Won: U.S.-Korean Bilateral Negotiations on Exchange Rates

Import Demand and Supply with Relatively Few Theoretical or Empirical Puzzles

The Liquidity Premium in Average Interest Rates The Power of Cointegration Tests

The Adequacy of the Data on U.S. International Financial Transactions: A Federal Reserve Perspective

Whom can we trust to run the Fed? Theoretical support for the founders views

Stochastic Behavior of the World Economy under Alternative Policy Regimes

Real Exchange Rates: Measurement and Implications for Predicting U.S. External Imbalances

Central Banks’ Use in East Asia of Money Market Instruments in the Conduct of Monetary Policy

Purchasing Power Parity and Uncovered Interest Rate Parity: The United States 1974 - 1990

Fiscal Implications of the Transition from Planned to Market Economy

Does World Investment Demand Determine U.S. Exports?

Author(s)

William R. Melick Charles P. Thomas

Stephen Brock Blomberg Deborah J. Lindner Deborah J. Lindner Andrew M. Warner

Wilbur John Coleman II Christian Gilles Pamela Labadie Jeroen J.M. Kremers Neil R. Ericsson Juan J. Dolado

Lois E. Stekler Edwin M. Truman Jon Faust

Joseph E. Gagnon Ralph W. Tryon

Jaime Marquez Robert F. Emery Hali J. Edison

William R. Melick

R. Sean Craig Catherine L. Mann

Andrew M. Warner