Incomplete markets and individual risks

Summary This paper studies the incomplete markets model with financial assets when the only missing markets are for individual risks. There are no aggregate risks in the economy. Assuming the individual risks are only privately observable, the only equilibria that are implementable by anonymous mechanisms are those in which prices do not vary across states of the world. Such equilibria always exist. Generically, they are locally unique and depend continuously on the parameters of the economy, just like complete-markets equilibria. Generically, there is also an infinite-dimensional manifold of equilibria in which prices do vary across states of the world. These equilibria are isomorphic to sunspot equilibria.I am grateful to Dave Cass for several helpful discussions and to Darrell Duffie for his comments on an earlier draft.     

Incomplete Markets, Allocative Efficiency, and the Information Revealed by Prices

We compare rational expectations equilibria with different degrees of information revelation through prices. These equilibria arise in a two-period exchange economy with finitely many states and signals, multiple commodities and incomplete financial markets for nominal assets. We show that there are always equilibria where information is redundant in the sense of being of no value to the uninformed traders. We give conditions under which for a generic set of economies, parametrized by endowments and utilities, there exist open sets of equilibria for which allocative and informational efficiency are independent, with implications for monetary policy. Journal of Economic Literature Classification Numbers: D52, D60, D82, E52.     

A bargaining model in general equilibrium

The goal of the paper is to present a simple model of rational endogenous household formation in a general equilibrium framework in which Pareto optimality at the economy level is not necessarily obtained. The simplest example of household formation is the case in which pairs of individuals engage themselves in a bargaining process on the division of some wealth: if an agreement on the distribution is (not) reached, we can say that the household is (not) formed. The vast majority of existing bargaining models predicts agreements on an efficient outcome. A seminal paper by Crawford (Econometrica 50:607–637, 1982) describes a very simple game with incomplete information in which, even with rational agents, disagreement causes welfare losses. We embed that model in a general equilibrium framework and present some results on equilibria both in the bargaining game and the associated exchange economy. Crawford’s results support Schelling’s intuition on the reasons of disagreement: it may arise if players’ commitments are reversible. Crawford shows that high probabilities of reversibility tend to favor the bargaining impasse, in fact with low probability. We prove that even if those probabilities are arbitrarily close to zero, disagreement is an equilibrium outcome, with high probability. That conclusion seems to be an even stronger support to Schelling’s original viewpoint. In the exchange economy model with that noncooperative bargaining game as a first stage, we present significant examples of economies for which equilibria exist. Because of disagreement, Pareto suboptimal exchange economy equilibria exist for all elements in the utility function and endowment spaces and they may coexist with Pareto optimal equilibria even at the same competitive prices.     

Existence of Lindahl equilibria in measure theoretic economies without ordered preferences

A proof of the existence of Lindahl equilibria is given for a class of measure theoretic economies, possibly atomless, in which consumers' preferences need be neither complete nor transitive. This is done as an application of a nonstandard-analytic technique that allows for the derivation of statements concerning measure theoretic economies from analogous finite economy propositions. This approach to the problem allows use of Foley's method of working with an associated private goods economy without the dimension of the commodity space in the associated economy becoming problematic. Potential extensions of the technique used are also discussed.     

Trade,Growth, and Increasing Returns to Infrastructure: The Role of the Sophisticated Monopolist*

Equilibrium in international trade with increasing returns in infrastructure depends on whether the infrastructure provider is “naïve” or sophisticated. A monopolist produces infrastructure under decreasing cost using fixed equipment. Unlike similar work, we derive a unique closed‐economy equilibrium. In a small open economy, with “naïve” infrastructure provider(s), multiple equilibria obtain. The industrial export potential of the economy depends on unexhausted economies of scale, and equilibria are possible where manufactures are exported despite an autarky price higher than the world price. With a sophisticated infrastructure provider, even an open economy has a unique equilibrium, which, at least as long as economies of scale are unexhausted, also involves more industrialization than the “naïve” equilibria. Access to the unlimited world market is necessary for significant industrialization but is not sufficient: one may also require “Schumpeterian” entrepreneurs, monopolists with a panoramic vision of the economy and of their catalytic role in it.     

Excess supply equilibria

This paper addresses a fundamental problem in economic theory: How can there be equilibria of the economic system where some commodity is in excess supply, yet that commodity's relative price shows no tendency to fall? Of course, the principal example of such a phenomenon is an economy experiencing a prolonged period of involuntary unemployment of the labor force during which there is no significant change in the real wage.In the following pages, I shall describe a two-commodity, general equilibrium model that has a continuum of unemployment equilibria, one for any given unemployment rate. The important feature of this model is that workers establish their wage rates in an attempt to maximize expected utility. The information upon which these wage setting decisions are based is provided by actual labor market transactions.Despite the voluntary nature of the wage setting decision, I shall argue that each equilibrium of this economy exhibits involuntary unemployment in the Keynesian sense. For there will always be another equilibrium with a lower real wage, a higher level of employment, and at which (at least when workers are risk neutral) each worker achieves a higher level of expected utility.     

Modern slavery,corruption, and hysteresis

We develop a model where firms profit from coercing workers into employment under conditions violating national law and international conventions and where corrupt public servants prosecuting violations of the rules are willing to turn cases down if bribed. Firms and public servants are heterogeneous. Firms benefit differently from the use of coerced labour whereas public servants have differing intrinsic motivations to behave honestly. Moreover, there is a socially determined warm-glow effect: honest public servants feel better if their colleagues are honest too. The determination of bribes is modelled via Nash bargaining between the firm and the corrupt civil servant. It is shown that multiple equilibria and hysteresis are possible. Depending on history, an economy may be trapped in a locally stable high-corruption, high-slavery equilibrium and major changes in government policies may be necessary to move the economy out of this equilibrium. Moreover, we show that trade bans that are effective in reducing slavery in the export industry tend to raise slavery in the remainder of the economy. It is possible that this leakage effect dominates the reduction of slavery in the export sector.     

The Structure of Sunspot Equilibria: The Role of Multiplicity

This paper examines the structure of sunspot equilibria in a standard two period exchange economy with real assets. We show that for a generic choice of utility functions and endowments, there exists an open set of real asset structures whose payoffs are independent of sunspots such that the economy with this asset structure has a regular sunspot equilibrium. An important implication of our result is that the multiplicity of non-sunspot equilibria is not necessary for the existence of sunspot equilibria. Our technique is general and can be applied to show the existence of sunspot equilibria in other frameworks.     

Lotteries, Sunspots, and Incentive Constraints

We study a prototypical class of exchange economies with private information and indivisibilities. We establish an equivalence between lottery equilibria and sunspot equilibria and show that the welfare and existence theorems hold. To establish these results, we introduce the concept of the stand-in consumer economy, which is a standard, convex, finite consumer, finite good, pure exchange economy. With decreasing absolute risk aversion and no indivisibilities, we prove that no lotteries are actually used in equilibrium. We provide a simple numerical example with increasing absolute risk aversion in which lotteries are necessarily used in equilibrium. We also show how the equilibrium allocation in this example can be implemented in a sunspot equilibrium. Journal of Economic Literature Classification Numbers: D11, D50, D82.     

WELFARE GAINS AND LOSSES IN SUNSPOT EQUILIBRIA*

We study a standard two period exchange economy with one nominal asset. As is well known, there is a continuum of sunspot equilibria around each efficient equilibrium. A sunspot equilibrium is inefficient but some households may gain in sunspot equilibria relative to the efficient equilibrium. We show that a household's equilibrium utility level is either locally maximized or locally minimized at the efficient equilibrium, and derive a condition which identifies whether or not a household's utility is locally minimized or maximized.     

Parametric persistence of multiple equilibria in an economy directly calibrated to 5 equilibria

In existing literature, there are few concrete examples of multiple equilibria and the only ones known to us have 3 equilibria, but multiplicity remains a major concern for applied models used in policy work. Here, we report numerical examples for a 3 individual 2 good CES/LES pure exchange economy directly calibrated to 5 equilibria. We are able to use analytical methods of the model to show that for certain parameterizations there are no more than 5 equilibria (given the parameter values). We are also able to explore the size of the regions of the parameter space for which 5 equilibria persist, and show these ranges to be very small. Other features of the equilibrium manifolds are explored. Findings are only suggestive and indicative for the special cases we consider rather than definitive, but informative relative to existing work.     

Welfare and excess volatility of exchange rates

We study the properties of a GEI model with nominal assets, outside money (injected into the economy as in Magill and Quinzii (J Math Econ 21:301–342, 1992)), and multiple currencies. We analyze the existence of monetary equilibria and the structure of the equilibrium set under two different assumptions on the determination of the exchange rates. If currencies are perfect substitutes, equilibrium allocations are indeterminate and, generically, sunspot equilibria exist. Generically, given a nonsunspot equilibrium, there are Pareto improving (and Pareto worsening) sunspot equilibria associated with an increase in the volatility of the future exchange rates. We interpret this property as showing that, in general, there is no clear-cut effect on welfare of the excess volatility of exchange rates, even when due to purely extrinsic phenomena.     

When Borch's Theorem Does Not Apply: Some Key Implications of Market Incompleteness,with Policy Relevance Today

Markets are incomplete when the assets available to the agents do not span the space of future contingencies. In that case, competitive equilibria on the markets for assets and commodities fail (generically) to be constrained efficient. Pareto‐superior allocations can be implemented through price/wage rigidities and quantity constraints. However, nominal rigidities are conducive to multiple equilibria, implying endogenous macroeconomic uncertainties that compound the primitive (exogenous) uncertainties. This paper defines a temporary general equilibrium for which there exists a set of equilibria defining an inflation – unemployment locus. Various policy implications are drawn, with relevance to the current crisis.     

Citizen-candidates,lobbies, and strategic campaigning

We study a spatial model of political competition in which potential candidates need a fixed amount of money from lobbies to enter an election. We show that the set of pure strategy Nash equilibria in which lobbies finance candidates whose policies they prefer among the set of entrants coincides with the set of Nash equilibria with weakly less than two entering candidates. Fixing lobbies’ preferences, if the total amount of money held by lobbies is finite, there exists some minimal distance between the two candidates’ positions. This minimal distance is a bound for all such Nash equilibria and is independent of the distribution of voters’ preferences. I would like to thank John Duggan, Al Slivinski, and William Thomson for useful comments and suggestions. Dan Kovenock and two anonymous referees also provided detailed comments and pointed out several errors. All errors are my own.     

Note on the non-existence of sunspot equilibrium

In this note, we emphasize the role of consumers’ risk aversion in the non-existence of sunspot equilibria in incomplete market economies. We prove that there are no sunspot equilibria if the fundamentals of the underlying economy admit a unique equilibrium for any distribution of endowments. This substantiates Mas-Colell’s (Economic analysis of markets and games: essays in honor of Frank Hahn. MIT, Cambridge, 1992) conjecture. We also prove that, in a two-consumer economy, no sunspot equilibrium exists under the more relaxed condition that the underlying economy admits a unique equilibrium for the initial endowment. This is a generalization of Corollaries 1 and 2 of Hens and Pilgrim (Econ Theory 24:583–602, 2004).      

Voting on public goods in multi-jurisdictional systems

This paper studies an economy with multiple jurisdictions, each producing a (pure) public good. Decisions are taken by means of a centralized voting procedure, to which individual agents participate and whose rules are defined with respect to the jurisdictional structure. In particular, a winning alternative must gain the support of a given number of jurisdictions. A well-known example is qualified majority rules. We establish condition on voting rules for the set of voting equilibria to coincide with the set of ratio equilibria of the economy, under alternative assumptions on the possibility of transfers across jurisdictions. We employ the obtained results to characterize the equilibria of two-stage voting situations, in which jurisdictional delegates vote instructed by internal committees.     

Status Preference, Wealth and Dynamics in the Open Economy

Abstract. The implications of status preference in a simple open economy model are investigated in this paper. The open economy is modeled as a continuum of identical representative agents who have preferences over consumption and status. In the paper status is identified as relative wealth, which takes the form of relative holdings international financial assets. A symmetric macroeconomic equilibrium is derived in which status is the source of transitional dynamics for domestic consumption and the current account balance. This result illustrates another way to combine transitional dynamics with interior equilibria in the small open economy Ramsey model with perfect capital mobility. We also show that status preference plays a critical role in influencing the open economy's adjustment to government expenditure and world interest rate shocks.     

Reconsideration of Some Paradoxes in the Theory of Optimal Foreign Investment*

The paper re-examines some ‘paradoxical’ propositions on optimal foreign investment discussed by Negishi and Long in the context of growing international economies. It demonstrates the following rather critical conclusions:first, the unusual message of the Negishi-Long paradoxes derives essentially from the requirement of growth equilibria rather than that of optimality; second, one of the paradoxes, attributable to Long, is at best a characterization of local optimum and, therefore, completely misleading as a policy recommendation:and thirdly, an appropriate change of standard of references would dissolve the Negishi-Long paradoxes and reveal a neglected true paradox of the model.     

Walrasian analysis via two-player games

We associate to any pure exchange economy a game with only two players, regardless of the number of consumers. In this two-player game, each player represents a different role of the society, formed by all the individuals in the economy. Player 1 selects feasible allocations trying to make Pareto improvements. Player 2 chooses an alternative from the wider range of allocations that are feasible in the sense of Aubin. The set of Nash equilibria of our game is non-empty and our main result provides a characterization of Walrasian equilibria allocations as strong Nash equilibria of the associated society game.     

Buyer investment, export variety, and intrafirm trade

This paper studies a model of buyer investment and its effect on the variety and vertical structure of international trade. A distinction is made between two types of buyer investment: “Flexible” and “specific”, which differ in the ability of a buyer to match with a seller. The interaction of buyer investment with the entry and pricing incentives of suppliers are analyzed. It is shown that (i) there can be multiple equilibria in the variety of products traded, and (ii) less product variety is associated with more intrafirm trade. The possibility of multiple equilibria is consistent with the observation that some similar economies, such as Taiwan and South Korea, differ substantially in their export varieties to the U.S. A cross-country empirical analysis confirms the negative correlation between export variety and intrafirm trade.