Pareto improving financial innovation in incomplete markets

Summary. In this paper we develop a differential technique for investigating the welfare effects of financial innovation in incomplete markets. Utilizing this technique, and after parametrizing the standard competitive, pure-exchange economy by both endowments and utility functions, we establish the following (weakly) generic property: Let S be the number of states, I be the number of assets and H be the number of households, and consider a particular financial equilibrium. Then, provided that the degree of market incompleteness is sufficiently larger than the extent of household heterogeneity, S−I≥2H−1 [resp. S−I≥H+1], there is an open set of single assets [resp. pairs of assets] whose introduction can make every household better off (and, symmetrically, an open set of single assets [resp. pairs of assets] whose introduction can make them all worse off ). We also devise a very simple nonparametric procedure for reducing extensive household heterogeneity to manageable size, a procedure which not only makes our restrictions on market incompleteness more palatable, but could also prove to be quite useful in other applications involving smooth analysis. Received: August 14, 1995; revised version: April 14, 1997     

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     

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     

Reallocation of an infinitely divisible good

Summary. We consider the problem of reallocating the total initial endowments of an infinitely divisible commodity among agents with single-peaked preferences. With the uniform reallocation rule we propose a solution which satisfies many appealing properties, describing the effect of population and endowment variations on the outcome. The central properties which are studied in this context are population monotonicity, bilateral consistency, (endowment) monotonicity and (endowment) strategy-proofness. Furthermore, the uniform reallocation rule is Pareto optimal and satisfies several equity conditions, e.g., equal-treatment and envy-freeness. We study the trade-off between properties concerning variation and properties concerning equity. Furthermore, we provide several characterizations of the uniform reallocation rule based on these properties. Received: August 29, 1995; revised version June 26, 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 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     

Consumption choice and asset pricing with a non-price-taking agent

Summary. This paper develops a pure-exchange model to study the consumption-portfolio problem of an agent who acts as a non-price-taker, and to analyze the implications of his behavior on equilibrium security prices. The non-price-taker is modeled as a price leader in all markets; his price impact is then recast as a dependence of the Arrow-Debreu prices on his consumption, allowing a tractable formulation. Besides the aggregate consumption, the endowment of the non-price-taker appears as an additional factor in driving equilibrium allocations and prices. Comparisons of equilibria between a price-taking and a non-price-taking economy are carried out. Received: March 29, 1996; revised version October 29, 1996     

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     

Coinage, debasements, and Gresham's laws

Summary. This paper formulates a model of commodity money that circulates by tale, and applies it to a variety of situations, some of which seem to confirm, and others to contradict, `Gresham's Law'. We analyze how debasements could prompt decisions of citizens voluntarily to participate in recoinages that subjected them to seigniorage taxes. Received: December 19, 1994; revised version August 1, 1996     

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     

Edgeworth's conjecture with infinitely many commodities: commodity differentiation

Summary. Convergence of the cores of finite economies to the set of Walrasian allocations as the number of agents grows has long been taken as one of the basic tests of perfect competition. The present paper examines this test in the most natural model of commodity differentiation: the commodity space is the space of nonnegative measures, endowed with the topology of weak convergence. In Anderson and Zame [12], we gave counterexamples to core convergence in L ¹, a space in which core convergence holds for replica economies and core equivalence holds for continuum economies; in addition, we gave a core convergence theorem under the assumption that traders' utility functions exhibit uniformly vanishing marginal utility at infinity. In this paper, we provide two core convergence results for the commodity differentiation model. A key technical virtue of this space is that relatively large sets (in particular, closed norm-bounded sets) are compact. This permits us to invoke a version of the Shapley-Folkman Theorem for compact subsets of an infinite-dimensional space. We show that, for sufficiently large economies in which endowments come from a norm bounded set, preferences satisfy an equidesirability condition, and either (i) preferences exhibit uniformly bounded marginal rates of substitution or (ii) endowments come from an order-bounded set, core allocations can be approximately decentralized by prices. Received: July 29, 1996; revised version: January 14, 1997     

Unawareness and bankruptcy: A general equilibrium model

Summary. We present a consistent pure-exchange general equilibrium model where agents may not be able to foresee all possible future contingencies. In this context, even with nominal assets and complete asset markets, an equilibrium may not exist without appropriate assumptions. Specific examples are provided. An existence result is proved under the main assumption that there are sufficiently many states that all the agents foresee. An intrinsic feature of the model is bankruptcy, which agents may involuntarily experience in the unforeseen states. Received: April 23, 1997; revised version: May 19, 1997     

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     

On capital accumulation paths in a neoclassical stochastic growth model

Summary. Boldrin and Montrucchio [2] showed that any twice continuously differentiable function could be obtained as the optimal policy function for some value of the discount parameter in a deterministic neoclassical growth model. I extend their result to the stochastic growth model with non-degenerate shocks to preferences or technology. This indicates that one can obtain complex dynamics endogenously in a wide variety of economic models, both under certainty and uncertainty. Further, this result motivates the analysis of convergence of adaptive learning mechanisms to rational expectations in economic models with (potentially) complicated dynamics. Received: June 21, 1996; revised version: October 31, 1996     

Firm reputation with hidden information

Summary. An adverse selection model of firm reputation is developed in which short-lived clients purchase services from firms operated by overlapping generations of agents. A firm's only asset is its name, or reputation, and trade of names is not observed by clients. As a result, names are traded in all equilibria regardless of the economy's horizon The general equilibrium analysis links the value of a name to the market for services. This causes a non-monotonicity that precludes higher types from sorting themselves through the market for names, and leads to “sensible” dynamics: reputations, and name prices, increase after success and decrease after failure. Received: July 31, 2001; revised version: December 20, 2001 RID="*" ID="*" I thank Jon Levin, Eric Maskin and Drew Fudenberg for valuable discussions, and Heski Bar-Isaac for comments on an earlier draft. Financial support from the National Science Foundation (NSF grants SBR-9818981 and SES-0079876) is gratefully acknowledged. This paper replaces an older (and incomplete) working paper titled “Reputation with Hidden Information”.     

Translation homotheticity

Summary. The concept of translation homotheticity is introduced and defined. It is demonstrated that translation homotheticity is necessary and sufficient for: disposable surplus to be independent of the reference utility, Luenberger's compensating and equivalent benefits to be independent of the reference utility and always equal to one another, the risk premium to be independent of reference-level utility, absolute indexes of income inequality to be reference free, and social-welfare functionals to satisfy invariance with respect to the choice of a common origin. Translation homotheticity is also sufficient for Hicks' many-market consumer surplus measure to be a second-order approximation to disposable surplus, compensating benefit, and equivalent benefit. If preferences are translation homothetic and appropriately quadratic, Hicks, many-market consumer surplus measure is exact for these welfare measures. Received: October 24, 1996; revised version: March 3, 1997     

Contract renegotiation in a continuous state space

Summary. When players are unable to write complete state contingent contracts it is shown, within the context of a non-cooperative contracting-renegotiation game, that the only subgame perfect equilibrium allocations are those that correspond to the set of first-best allocations. Players are able to implement this set of allocations by signing an initial contract that is subsequently renegotiated in all states of the world. The contracting-renegotiation problem is complicated in an interesting way by assuming that the state space is continuous. The issue of the existence of an initial contract, that is subsequently renegotiated to the set of first-best allocations, must be resolved. Unlike Aghion, Dewatripont and Rey [1994], the results here do not require nor depend upon the comonotonicity of the objective functions. Received: January 27, 1995; revised version July 1, 1996     

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