Constrained suboptimality in incomplete markets: a general approach and two applications

Summary. In this paper we re-examine generic constrained suboptimality of equilibrium allocations with incomplete numeraire asset markets. We provide a general framework which is capable of resolving some issues left open by the previous literature, and encompasses many kinds of intervention in partially controlled market economies. In particular, we establish generic constrained suboptimality, as studied by Geanakoplos and Polemarchakis, even without an upper bound on the number of households. Moreover, we consider the case where asset markets are left open, and the planner can make lump-sum transfers in a limited number of goods. We show that such a perfectly anticipated wealth redistribution policy, though consistent with the assumed incomplete financial structure, is typically effective. Received: August 14, 1995; revised version: April 11, 1997     

Which improves welfare more: A nominal or an indexed bond?

Summary. Economists have long argued that loan contracts should be indexed to remove the risks arising from fluctuations in the purchasing power of money: indexation however while eliminating one risk, substitutes another, arising from fluctuations in relative prices of goods. We present a theoretical framework which permits the relative merits of a nominal versus an indexed bond to be assessed in a general equilibrium setting. Received: July 31, 1995; revised version August 7, 1996     

Recursive utility and preferences for information

Summary. This paper presents an axiomatic foundation for recursive utility that captures the role of the timing of resolution of uncertainty without relying on exogenously specified objective beliefs. Two main representation results are proved. In the first one, future utility enters the recursion through the type of general aggregators considered in Skiadas (1997a), and as a result the formulation is purely ordinal and free of any probabilities. In the second representation these aggregators are conditional expectations relative to subjective beliefs. A new recursive representation incorporating disappointment aversion is also suggested. The main methodological innovation of the paper derives from the fact that the basic objects of choice are taken to be pairs of state-contingent consumption plans and information filtrations, rather than the temporal (objective) lotteries of the existing literature. It is shown that this approach has the additional benefit of being directly applicable to the continuous-time version of recursive utility developed by Duffie and Epstein (1992). Received: February 18, 1997; revised version: July 18, 1997     

Options and sunspots in a simple monetary economy

Summary. We study sunspot immunity in a dynamic monetary economy in which consumers are allowed to trade put and call option contracts on the general price level. We define the concept of strong sunspot immunity to characterize economies that have no sunspot equilibria regardless of the number of extrinsic states and their probabilities of occurrence. We show that a small number of option contracts can make an economy strongly sunspot immune. In addition, we demonstrate how asset re-trading opportunities, and the associated capital gains and losses, reduce the number of options needed for this result to obtain. Received: August 13, 1996; revised version: January 20, 1997     

Ranking agencies under moral hazard

Summary. We provide rankings across uncertain outputs generated by agents functioning within the Principal-Agent paradigm. For agents who are identical except for their productivity, a necessary (but not sufficient) condition for an agent to be preferred is that her output dominates that of lower agents in the sense of First Degree Stochastic Dominance (FDSD) at every level of effort. Sufficient conditions are based on Blackwells ranking of information systems and involves a characterization of FDSD using stochastic matrices. Our conditions for ranking outputs extends earlier results concerning the value of information within the agency framework. We also show how our techniques can be adapted to rank agents even if the first-order approach for determining optimal contracts fails to hold.Received: April 2, 1996; revised version: October 30, 1996This revised version was published online in February 2005 with corrections to the cover date.     

Excess demand functions, equilibrium prices, and existence of equilibrium

Summary. For continuous aggregate excess demand functions of economies, the existing literature (e.g. Sonnenschein (1972, 1973), Mantel (1974), Debreu (1974), Mas-Colell (1977), etc.) achieves a complete characterization only when the functions are defined on special subsets of positive prices. In this paper, we allow the functions to be defined on a larger class of price sets, (allowing, for example the closed unit simplex, including its boundary). Besides characterizing excess demands for a larger class of economies, our extension provides a useful tool for proving other results. It allows us to characterize the equilibrium price set for a larger class of economies. It also permits extending Uzawa's observation (1962), by showing that Brouwer's Fixed-Point Theorem is implied by the Arrow-Debreu Equilibrium Existence Theorem (1954, Theorem I). Received: October 18, 1995; revised version June 28, 1996     

On the uniqueness of competitive equilibrium

Summary . The paper is concerned with the following question: in addition to local uniqueness, what other conditions must be imposed to ensure global uniqueness of competitive equilibrium? The answer is provided within a standard framework involving excess demand functions. Conditions are identified which have the nice property that they are true close to a regular equilibrium. Uniqueness is established by considering an adjustment process and showing that under the mentioned conditions, every equilibrium is locally asymptotically stable and moreover the process itself is globally stable; uniqueness follows from an Arrow and Hahn (1971) result. Alternatively, the paper may be seen as identifying conditions under which there is a vectorfield satisfying the requirements of an uniqueness result due to Dierker (1974). Received: July 1, 1996; revised version October 7, 1996     

Adaptive learning in extensive form games and sequential equilibrium

Summary. This paper studies adaptive learning in extensive form games and provides conditions for convergence points of adaptive learning to be sequential equilibria. Precisely, we present a set of conditions on learning sequences such that an assessment is a sequential equilibrium if and only if there is a learning sequence fulfilling the conditions, which leads to the assessment. Received: November 5, 1996; revised version: May 28, 1997     

Sealed bid auctions with uncertainty averse bidders

Summary. Traditional analysis of auctions assumes that each bidder's beliefs about opponents' valuations are represented by a probability measure. Motivated by experimental findings such as the Ellsberg Paradox, this paper examines the consequences of relaxing this assumption in the first and second price sealed bid auctions with independent private values. The multiple priors model of Gilboa and Schmeidler [Journal of Mathematical Economics, 18 (1989), 141–153] is adopted specifically to represent the bidders' (and the auctioneer's) preferences. The unique equilibrium bidding strategy in the first price auction is derived. Moreover, under an interesting parametric specialization of the model, it is shown that the first price auction Pareto dominates the second price auction. Received: December 15, 1995; revised version: February 19, 1997     

A unified treatment of finite and infinite economies: limited arbitrage is necessary and sufficient for the existence of equilibrium and the core

Summary. A single condition, limited arbitrage, is shown to be necessary and sufficient for the existence of a competitive equilibrium and the core in economies with any number of markets, finite or infinite, with or without short sales. This extends earlier results of Chichilnisky [8] for finite economies. This unification of finite and infinite economies is achieved by proving that in Hilbert spaces limited arbitrage is necessary and sufficient for the compactness of the Pareto frontier. Limited arbitrage has also been shown to be necessary and sufficient for a resolution of the social choice paradox [9], [10], [12], [13], [14]. Received: August 4, 1995; revised version: April 11, 1997     

A note on representability of consumer's behavior

Summary. We offer an alternative approach to the study of representability of choice behavior in a competitive framework that is based on recent advances in utility theory (cf. Alcantud and Rodrí guez-Palmero (1999)). Our technique enables us to tackle this classical problem efficiently in fairly general situations, thus obtaining alternative sufficient conditions as well as different proofs and generalizations of prior results. Received: July 14, 1999; revised version: February 15, 2001     

On the uniqueness of fully informative rational expectations equilibria

Summary. This paper analyzes two equivalent equilibrium notions under asymmetric information: risk neutral rational expectations equilibria (rn-REE), and common knowledge equilibria. We show that the set of fully informative rn-REE is a singleton, and we provide necessary and sufficient conditions for the existence of partially informative rn-REE. In a companion paper (DeMarzo and Skiadas (1996)) we show that equilibrium prices for the larger class of quasi-complete economies can be characterized as rn-REE. Examples of quasi-complete economies include the type of economies for which demand aggregation in the sense of Gorman is possible (with or without asymmetric information), the setting of the Milgrom and Stokey no-trade theorem, an economy giving rise to the CAPM with asymmetric information but no normality assumptions, the simple exponential-normal model of Grossman (1976), and a case of no aggregate endowment risk. In the common-knowledge context, we provide necessary and sufficient conditions for a common knowledge posterior estimate, given common priors, to coincide with the full communication posterior estimate. Received: May 29, 1997; revised version: July 18, 1997     

Serial cost sharing of excludable public goods: general cost functions

Summary. A group of individuals meet to share the cost and determine output allocations of a partial-excludable public good. We demonstrate that, for general cost functions and preferences that satisfy the Spence-Mirlees sorting condition, the serial cost-sharing formula (Moulin, 1994) has remarkable incentive properties. First, a direct economic mechanism that uses the serial formula is coalition strategy-proof, envy-free and satisfies the stand-alone property. Second, the serial mechanism involves partial exclusion, which is important for the reduction of the free-rider problem. Received: June 10, 1996; revised version; February 11, 1997     

The measurement of income mobility: A partial ordering approach

Summary. Given a set of longitudinal data pertaining to two populations, a question of interest is the following: Which population has experienced a greater extent of income mobility? The aim of the present paper is to develop a systematic way of answering this question. We first put forth four axioms for income movement-mobility indices, and show that a familiar class of measures is characterized by these axioms. An unambiguous (partial) ordering is then defined as the intersection of the (complete) orderings induced by the mobility measures which belong to the characterized class; a transformation of income distributions is “more mobile” than another if, and only if, the former is ranked higher than the latter for all mobility measures which satisfy our axioms. Unfortunately, our mobility ordering depends on a parameter, and therefore, it is not readily apparent how one can apply it to panel data directly. In the second part of the paper, therefore, we derive several sets of parameter-free necessary and sufficient conditions which allow one to use the proposed mobility ordering in making unambiguous income mobility comparisons in practice. Received: July 12, 1995; revised version: May 13, 1997     

Bayesian learning and convergence to Nash equilibria without common priors

Summary. Consider an infinitely repeated game where each player is characterized by a “type” which may be unknown to the other players in the game. Suppose further that each player's belief about others is independent of that player's type. Impose an absolute continuity condition on the ex ante beliefs of players (weaker than mutual absolute continuity). Then any limit point of beliefs of players about the future of the game conditional on the past lies in the set of Nash or Subjective equilibria. Our assumption does not require common priors so is weaker than Jordan (1991); however our conclusion is weaker, we obtain convergence to subjective and not necessarily Nash equilibria. Our model is a generalization of the Kalai and Lehrer (1993) model. Our assumption is weaker than theirs. However, our conclusion is also weaker, and shows that limit points of beliefs, and not actual play, are subjective equilibria. Received: March 3, 1995; revised version: February 17, 1997     

Welfare-improving financial innovation with a single good

Summary. We show that at any equilibrium of almost every single-good incomplete markets economy, it is possible to find an asset which when introduced makes every agent better-off. Diamond (1967) has shown, however, that such economies are constrained suboptimal, so it is of course impossible to find a new asset which makes all agents worse-off. This contrasts with the case of multiple consumption goods, for which Cass and Citanna (1995) and Elul (1995) demonstrate that equilibrium utilities may be arbitrarily perturbed via financial innovation. Proving our result requires us to exploit not changes in equilibrium prices, but rather the gains to trading the new asset. In particular, we find an asset which when introduced does not change the existing asset prices even though it is traded by every agent – by a revealed preference argument it must therefore make everyone better-off. Received: May 28, 1997; revised version: July 1, 1997     

Sunspot fluctuations in dynamics with predetermined variables

Summary. In this paper, I study the existence of Sunspot Equilibria in a general framework whose dynamics allow for the presence of predetermined variables in the system. The main motivation for this research comes from the fact that previous studies did not allow for such predetermined variables which, nevertheless, appear quite naturally in economic models. I show, for a non-negligible subset of dynamics with predetermined variables verifying usual assumptions, the existence of Stationary Sunspot Equilibria fluctuating between an arbitrary finite number of states arbitrarily close to a steady state. Received: March 1, 1995; revised version September 18, 1996     

Aggregation, efficiency and mutual fund separation in incomplete markets

Summary. This paper studies the conditions for aggregation, portfolio separation and effective completeness of competitive allocations in general equilibrium models with incomplete markets where agents have general preference and endowment distributions. We show that these properties are distinct. Demands may aggregate yet may fail to exhibit fund separation and conversely. Fund separation implies effective completeness while aggregation does not. The implications of these properties for the structure of equilibria are discussed, and generalizations of the CAPM, the consumption CAPM and the CAPM with nonmarketed wealth emerge from the analysis. Received: September 12, 1996; revised version: November 7, 1996     

A note on the “size” of determinacy and indeterminacy

Summary. It is shown in this note that in an incomplete markets economy with uncountably many states of the world there may be uncountably many isolated equilibria as well as uncountably many non-isolated equilibria. Moreover, both subsets can be simultaneously of second category. Therefore, none of the subsets can be considered negligible with respect to the other, neither from a cardinality point of view nor from a topological one. Unfortunately, this fact prevents from claiming that these economies may have “typically” determinate equilibria – even though uncountably many of them – as would have been desirable for comparative statics exercises. Received: May 19, 1995; revised version: March 24, 1997     

The ratchet effect and bargaining power in a two-stage model of competitive bidding

Summary. In the model presented, a buyer uses competitive bidding to facilitate her purchase of a good (the primary good of the exchange). Not included in the original purchase is the possible procurement of a good related to the original purchase: the supplementary good. The primary and supplementary goods are closely related; knowing a bidder's cost of producing the primary good implies that the buyer can infer the bidder's cost of producing the supplementary good. I show that a bidding mechanism for the primary good will fail to ensure an efficient allocation if the buyer learns the bid of the winner and the price of the supplementary good is determined through sequential bargaining. Received: August 22, 1996; revised version: June 23, 1997