Collective Organizations versus Relative Performance Contracts: Inequality, Risk Sharing, and Moral Hazard

This paper studies collective economic organizations that share risk and mitigate moral hazard and compares them with relative performance contracts. Information-constrained optimal distributions of organizations and contracts are shown to be functions of the underlying primitives, in particular, the distribution of Pareto weights, and hence degree of inequality. Internal inequality of a potential, local group is a force for collective organization. That is, multi-agent organizations exist in order to extract wealth from some but not necessarily all members. The group organization is also shown to be information-constrained Pareto optimal at extremes of local wealth relative to an outsider. But the group organization is susceptible to both agents simultaneously deviating, colluding against the outsider, and this distortion makes an individualistic, relative performance contract an attractive alternative. More generally, organizations, contracts, and allocations are jointly determined. These implications could be distinguished in cross-sectional, time series data. Journal of Economic Literature Classification Numbers: D70, D82.     

Credibility and endogenous societal discounting

We consider a dynamic moral hazard economy inhabited by a planner and a population of privately informed agents. We assume that the planner and the agents share the same discount factor, but that the planner cannot commit. We show that optimal allocations in such settings solve the problems of committed planners who discount the future less heavily than agents. Thus, we provide micro-foundations for dynamic moral hazard models that assume a societal discount factor in excess of the private one. We extend the analysis to allocations that are reconsideration-proof in the sense of Kocherlakota [Kocherlakota, N., 1996. Reconsideration-proofness: A refinement for infinite horizon time inconsistency. Games and Economic Behavior 15, 33–54]. We show that these allocations solve the choice problem of a committed planner with a unit discount factor.     

Nonseparable preferences and optimal social security systems

In this paper, we consider economies in which agents are privately informed about their skills, which evolve stochastically over time. We require agents' preferences to be weakly separable between the lifetime paths of consumption and labor. However, we allow for intertemporal nonseparabilities in preferences like habit formation. In this environment, we derive a generalized version of the Inverse Euler Equation and use it to show that intertemporal wedges characterizing optimal allocations of consumption can be strictly negative. We also show that preference nonseparabilities imply that optimal differentiable asset income taxes are necessarily retrospective in nature. We show that under weak conditions, it is possible to implement a socially optimal allocation using a social security system in which taxes on wealth are linear, and taxes/transfers are history-dependent only at retirement. The average asset income tax in this system is zero.     

Existence and fairness of value allocation without convex preferences

Shafer (Econometrica, 48 (1980), 467–476) proved that in a finite exchange economy value allocations exist, provided that each agent has convex, complete, transitive, compact and monotone preferences. However, if preferences are not convex, then value allocations may not exist. To remedy this difficulty we enlarge the set of value allocations by introducing the concept of approximate value allocations, and show that in a finite exchange economy approximate value allocations exist, even if preferences are not convex, or compact, or monotone. This value existence result can be used to provide a very general value existence theorem for a sequence of finite economies. Further, we show that value allocations may discriminate in favor of or against a coalition of agents.     

Dynamic Optimal Taxation with Private Information

We study dynamic optimal taxation in a class of economies with private information. Optimal allocations in these environments are complicated and history-dependent. Yet, we show that they can be implemented as competitive equilibria in market economies supplemented with simple tax systems. The market structure in these economies is similar to that in Bewley (1986) ; agents supply labour and trade risk-free claims to future consumption, subject to a budget constraint and a debt limit. Optimal taxes are conditioned only on two observable characteristics—an agent's accumulated stock of claims, or wealth, and her current labour income. We show that optimal taxes are generally non-linear and non-separable in these variables and relate the structure of marginal wealth and income taxation to the properties of agent preferences.     

Pareto-optimal Nash equilibria are competitive in a repeated economy

Consider a finite exchange economy first as a static, 1 period, economy and then as a repeated economy over T periods when the utility of each agent is the mean utility over T. A family of strategic games is defined via a set of six general properties the most distinct of which is the ability of agents to move commodities forward in time. Now consider Pareto optimal allocations in the T period economy which are also Nash equilibria in this family of strategic games. We prove that as T becomes large this set converges to the set of competitive utility allocations in the one period economy. The key idea is that a repetition of the economy when agents can move commodities forward in the time acts as a convexification of the set of individually feasible outcomes for player i holding all other strategies fixed.     

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     

Coalitional fairness in interim differential information economies

In this paper we propose a concept of coalitional fair allocation in order to solve the tension that may exist between efficiency and envy-freeness when agents are asymmetrically informed and the equity of allocations is evaluated at the interim stage.     

A revised concept of distributional equity

Recent studies have shown that in a private goods economy with production, allocations which are considered to be distributionally fair may not exist. As a solution for such cases, just allocations are introduced and examined in some detail. Such allocations are shown, by rigorous proof, to exist in general.     

Retrading in market games

When agents are not price takers, they typically cannot obtain an efficient real location of resources in one round of trade. This paper presents a non-cooperative model of imperfect competition where agents can retrade allocations, consistent with Edgeworth's idea of recontracting. We show (a) there are Pareto optimal allocations, including competitive equilibrium allocations, that can be approximated arbitrarily closely when trade is myopic, i.e., when agents play a static Nash equilibrium at every round of retrading; (b) any converging sequence of allocations generated by myopic retrading can be supported along some retrade-proof subgame perfect equilibrium path when traders anticipate future rounds of trading.     

Optimal growth with many consumers

A method is described for constructing all Pareto-optimal allocations for a dynamic economy with many heterogeneous consumers, under certainty, in which both the technology and consumer preferences are recursive but preferences need not be additively separable over time. Optimal (perfect foresight competitive equilibrium) allocations are obtained through the study of a dynamic program. For an economy with one consumption good, sufficient conditions are given for the existence of a unique interior stationary distribution of consumption and wealth. For a two-person exchange economy, sufficient conditions are given for the global asymptotic stability of the unique interior stationary point.     

Credit in a Random Matching Model with Private Information

We consider a random matching model where agents have complete access to each others' histories. Exchange is motivated by risk sharing, given random unobservable incomes. There is capital accumulation and an endogenous interest rate. The key feature of this environment is that information is mobile across locations, while there are frictions associated with transporting goods. Optimal allocations in the dynamic private information environment resemble real-world credit arrangements in that there are credit balances, credit limits, and installment payments. The steady state has the property that there is a limiting distribution of expected utility entitlements with mobility and a positive fraction of agents who are credit constrained.Journal of Economic LiteratureClassification Numbers: D8, E1.     

Rational expectations in the overlapping generations model

This paper reports results on the character of the rational expectations equilibria of a stochastic overlapping generations model with heterogenous markets. The model considered is a stationary overlapping generations model in which the endowments of young agents are subject to i.i.d. random shocks. The main result shown is that if there are l > 1 commodities traded in every period, then for most preferences, the rational expectations equilibrium stochastic process of prices and allocations necessarily exhibits serial correlation. This is in marked contrast to the one commodity model in which there always exists an equilibrium which is measure isomorphic to the endowment process.     

Complete and incomplete markets with short-sale constraints

Summary. This paper argues that the introduction of a short-sale constraint in the Arrow-Radner framework invalidates standard definitions of complete and incomplete markets. Two threshold values with familiar properties arise in this constrained set-up. If short sales are not allowed on some security, then financial markets will be incomplete in the standard sense. Beyond a particular level of the short-sale bound, financial markets are “complete”, since the short-sale constraint is not effective. For intermediate bounds the distinction between complete and incomplete financial markets is blurred. Although some technical definitions hold, agents can not fully transfer wealth among states. These intermediate cases, called “technically incomplete markets”, exhibit interesting welfare properties. For instance, the resulting equilibrium allocations may not be Pareto-dominated by those of the non-restricted complete markets equilibrium. Received: November 28, 2000; / revised version: November 9, 2001     

Will Self‐Managed Superannuation Fund Investors Survive?

The relative risk aversion coefficient that characterises the representative self‐managed superannuation fund (SMSF) investor reveals not only how much that investor dislikes risk but also other information about the investor's economic characteristics, including how his or her allocations to risky assets change as his or her wealth changes. Determination of the relative risk aversion coefficient for the average SMSF investor reveals a value of 5.05. This value is too high to be consistent with logarithmic utility. This is significant because it implies that SMSF investors may be too risk averse to maximise the expected growth rate of wealth share accumulation. We are left to consider a very important question: Will SMSF investors survive?     

Mechanism design with partial state verifiability

We study implementation in environments where agents have limited ability to imitate others. Agents are randomly and privately endowed with type-dependent sets of messages. So sending a message becomes a partial proof regarding type. For environments where agents can send any combination of available messages, we develop an Extended Revelation Principle and characterize the incentive constraints which implementable allocations must satisfy. When not all message combinations are feasible, static mechanisms no longer suffice. If a ‘punishment’ allocation exists for each agent, then implementable allocations can be characterized as equilibria of a “Revelation Game,” in which agents first select from the menus of allocation rules, then the mediator requests each agent to send some verifying messages. When a punishment allocation fails to exist for some agent, dynamic games in which agents gradually reveal their evidence implement a larger set of outcomes. The latter result provides a foundation for a theory of debate.     

Reclaim-proof allocation of indivisible objects

We study desirability axioms imposed on allocations in indivisible object allocation problems. The existing axioms in the literature are various conditions of robustness to blocking coalitions with respect to agentsʼ ex ante (individual rationality and group rationality) and ex post (Pareto efficiency) endowments. We introduce a stringent axiom that encompasses and strengthens the existing ones. An allocation is reclaim-proof if it is robust to blocking coalitions with respect to any conceivable interim endowments of agents. This is an appealing property in dynamic settings, where the assignments prescribed by an allocation to be implemented need to be made in multiple rounds rather than all in one shot. We show that an allocation is reclaim-proof if and only if it is induced by a YRMH–IGYT mechanism (introduced by Abdulkadiroğlu and Sönmez, 1999) and if and only if it is a competitive allocation.     

The Effectiveness of Distributive Policy in a Competitive Economy

I consider an abstract social system made of individual owners endowed with nonpaternalistic interdependent preferences, who interact by means of individual gifts and by exchanges on competitive markets. The existence of equilibrium is established. I identify the set of allocations that are decentralizable in the sense that they are general equilibria for some vectors of market prices and initial endowments. This set is characterized in a simple way from the social endowment and individual market and distributive preferences. Decentralizable allocations are all accessible to distributive policy, unless public transfers are confined to some neighborhood of 0. In the latter case, distributive policy remains free to perform local redistributions of wealth across the components of the graph of equilibrium gifts.     

Double implementation in economies with production technologies unknown to the designer

Summary. This paper considers double implementation of Walrasian allocations and Lindahl allocations in Nash and strong Nash equilibria for both private and public goods economies when preferences, initial endowments, production technologies, and coalition patterns are all unknown to the designer. It will be noted that the mechanisms presented here are feasible and continuous. In addition, unlike most mechanisms proposed in the literature, our mechanism works not only for three or more agents, but also for two-agent economies, and thus it is a unified mechanism which is irrespective of the number of agents. Received: March 12, 1998; revised version: March 12, 1998     

Pareto optima and equilibria when preferences are incompletely known

An exchange economy in which agents have convex incomplete preferences defined by families of concave utility functions is considered. Sufficient conditions for the set of efficient allocations and equilibria to coincide with the set of efficient allocations and equilibria that result when each agent has a utility in her family are provided. Welfare theorems in an incomplete preferences framework therefore hold under these conditions and efficient allocations and equilibria are characterized by first order conditions.