Wealth inequality, preference heterogeneity and macroeconomic volatility in two-sector economies

We explore the link between wealth inequality, preference heterogeneity and macroeconomic volatility in a two-sector neoclassical growth model. First we prove that, if agents have homogeneous preferences, when the absolute risk tolerance is a strictly convex (concave) function, sufficiently high (low) levels of wealth inequality may lead to endogenous fluctuations in the neighborhood of the steady state. Second, we consider the effects of preference heterogeneity when agents are homogeneous with respect to their wealth. We show that when the utility function belongs to the HARA class, sufficiently high levels of preference heterogeneity may lead to endogenous fluctuations in the neighborhood of the steady state if the elasticity of intertemporal substitution in consumption is greater than one.     

Wealth distribution and output fluctuations

We explore the link between wealth inequality and output fluctuations in a general two-sector neoclassical growth model with endogenous labor and heterogeneous agents. When agents have homogeneous CRRA preferences and individual wealth is Pareto distributed, a sufficiently large rise in the Gini index typically leads to an increase in endogenous fluctuations of output. For general economies, we show that under plausible conditions on the fundamentals, wealth inequality is still a destabilizing factor.     

Strategy-proof assignment on the full preference domain

We consider the problem of efficiently allocating several indivisible objects between agents who are to receive at most one object and whose preferences are private information. We examine this standard “assignment” problem from the perspective of mechanism design giving up the usual assumption of linear preferences and instead using a full preference domain (with indifferences permitted). We characterize two classes of mechanisms: (i) Bi-polar Serially Dictatorial Rules by Essential Single-Valuedness, Pareto Indifference, Strategy-Proofness and Non-Bossiness; and (ii) all selections from Bi-polar Serially Dictatorial Rules by Single-Valuedness, Efficiency, Strategy-Proofness and Weak Non-Bossiness. We compare the outcomes from the (Bi-polar) Serially Dictatorial Rules with the outcomes obtained using a market based approach, namely the “core” of the market. We show that all strongly efficient outcomes in the core can be generated using Serially Dictatorial Rules. Moreover, we argue that Serially Dictatorial Rules have an advantage over the market based approach in that they yield strongly efficient solutions for all preference profiles, making it possible to use randomization to restore equity. When preferences are private information, this type of ex ante equity cannot be implemented using the market based approach.     

The veil of public ignorance

A theory of cooperative choice under incomplete information is developed in which agents possess private information at the time of contracting and have agreed on a utilitarian “standard of evaluation” governing choices under complete information. The task is to extend this standard to situations of incomplete information. Our first main result generalizes Harsanyi's (J. Polit. Econ. 63 (1955) 309) classical result to situations of incomplete information, assuming that group preferences satisfy Bayesian Coherence and Interim Pareto Dominance. These axioms are mutually compatible if and only if a common prior exists. We argue that this result partly resolves the impossibility of Bayesian preference aggregation under complete information.     

Efficiency and equilibrium when preferences are time-inconsistent

We consider an exchange economy with time-inconsistent consumers whose preferences are additively separable. If consumers have identical discount factors, then allocations that are Pareto efficient at the initial date are also renegotiation-proof. In an economy with a sequence of markets, competitive equilibria are Pareto efficient in this sense, and for generic endowments, only if preferences are locally homothetic.     

Intertemporal equilibria with Knightian uncertainty

We study a dynamic and infinite-dimensional model with incomplete multiple prior preferences. In interior efficient allocations, agents share a common risk-adjusted prior and subjective interest rate. Interior efficient allocations and equilibria coincide with those of economies with subjective expected utility and priors from the agents? multiple prior sets. A specific model with neither risk nor uncertainty at the aggregate level is considered. Risk is always fully insured. For small levels of ambiguity, there exists an equilibrium with inertia where agents also insure fully against Knightian uncertainty. When the level of ambiguity exceeds a critical threshold, full insurance no longer prevails and there exist equilibria with inertia where agents do not insure against uncertainty at all. We also show that equilibria with inertia are indeterminate.     

Interim efficient allocations under uncertainty

This paper considers an exchange economy under uncertainty with asymmetric information. Uncertainty is represented by multiple priors and posteriors of agents who have either Bewley's incomplete preferences or Gilboa-Schmeidler's maximin expected utility preferences. The main results characterize interim efficient allocations under uncertainty; that is, they provide conditions on the sets of posteriors, thus implicitly on the way how agents update the sets of priors, for non-existence of a trade which makes all agents better off at any realization of private information. For agents with the incomplete preferences, the condition is necessary and sufficient, but for agents with the maximin expected utility preferences, the condition is sufficient only. A couple of necessary conditions for the latter case are provided.     

Interim efficiency with MEU-preferences

Recently Kajii and Ui (2009) [17] proposed to characterize interim efficient allocations in an exchange economy under asymmetric information when uncertainty is represented by multiple posteriors. When agents have Bewley's incomplete preferences, Kajii and Ui (2009) [17] proposed a necessary and sufficient condition on the set of posteriors. However, when agents have Gilboa-Schmeidler's MaxMin expected utility preferences, they only propose a sufficient condition. The objective of this paper is to complete Kajii and Ui's work by proposing a necessary and sufficient condition for interim efficiency for various models of ambiguity aversion and in particular MaxMin expected utility. Our proof is based on a direct application of some results proposed by Rigotti, Shannon and Stralecki (2008) [24].     

The dynamics of environmentalism and the environment

We study the relationship between environmental preferences and the environment. Preferences are transmitted intergenerationally and through social interactions, where we assume that agents are more likely to adopt environmental preferences the larger the amount of pollution. In the basic setting we find that both converge non-monotonically towards an interior steady state. When including technical change we notice that there will be no change in the steady state level of the environment unless technical change is sufficiently strong, which stands in stark contrast to the literature. Upon introducing environmental laws we find that these may lead to a virtually pollution-free environment. This happens if environmental laws are implemented when public support is strong enough.     

A complete characterization of Pareto optimality for general OLG economies

In the context of general pure exchange OLG economies where agents can have heterogeneous longevities, we provide both sufficient and necessary conditions for Pareto optimality of competitive equilibria. For the case in which all agents live for the same number of periods, we find that these conditions are equivalent. We also find this equivalence when agents can have different lifetimes, but in this case we need to impose particular restrictions on relative equilibrium prices. Moreover, we show that without these conditions on prices the equivalence, and hence a full characterization, is not necessarily obtained.     

Wealth inequality and dynamic stability

We explore the link between wealth inequality and stability in a two-sector neoclassical growth model with heterogeneous agents. We show that when the inverse of absolute risk aversion (or risk tolerance) is a strictly convex function, wealth inequality is a factor that favors instability. In the opposite case, inequality favors stability. Our characterization also shows that whenever absolute risk tolerance is linear, as when preferences exhibit hyperbolic absolute risk aversion (HARA), wealth heterogeneity is neutral.     

Representation and aggregation of preferences under uncertainty

We axiomatize in the Anscombe-Aumann setting a wide class of preferences called rank-dependent additive preferences that includes most known models of decision under uncertainty as well as state dependent versions of these models. We prove that aggregation is possible and necessarily linear if and only if (society's) preferences are uncertainty neutral. The latter means that society cannot have a non-neutral attitude toward uncertainty on a subclass of acts. A corollary to our theorem is that it is not possible to aggregate multiple prior agents, even when they all have the same set of priors. A number of ways to restore the possibility of aggregation are then discussed.     

Information-constrained optima with retrading: An externality and its market-based solution

This paper studies the efficiency of competitive equilibria in environments with a moral hazard problem and unobserved states, both with retrading in ex post spot markets. The interaction between private information problems and the possibility of retrade creates an externality, unless preferences have special, restrictive properties. The externality is internalized by allowing agents to contract ex ante on market fundamentals determining the spot price or interest rate, over and above contracting on actions and outputs. Then competitive equilibria are equivalent with the appropriate notion of constrained Pareto optimality. Examples show that it is possible to have multiple market fundamentals or price-islands, created endogenously in equilibrium.     

A dynamic two country Heckscher–Ohlin model with non-homothetic preferences

We examine the properties of a two-country dynamic Heckscher–Ohlin model that allows for preferences to be non-homothetic. We show that the model has a continuum of steady state equilibria under free trade, with the initial conditions determining which equilibrium will be attained. We establish conditions under which a static Heckscher–Ohlin theorem will hold in the steady state, and also conditions for a dynamic Heckscher–Ohlin theorem to hold. If both goods are normal, each country will have a unique autarkic steady state, and all steady state equilibria are saddle points. We also consider the case in which one good is inferior, and show that this can lead to multiple autarkic steady states, violations of the static Heckscher–Ohlin theorem in the steady state. Furthermore, there may exist steady state equilibria that Pareto dominate other steady states. These steady states will be unstable if discount factors are the same in each country, although they may exhibit dynamic indeterminacy if discount factors differ.     

Weak Independence and Social Semi‐Orders

This paper provides variants of Arrow's impossibility theorem, which states that there exists no non‐dictatorial aggregation rule satisfying weak Pareto, independence of irrelevant alternatives and collective rationality. In this paper, independence of irrelevant alternatives and collective rationality are simultaneously relaxed. Weak independence is imposed instead of independence of irrelevant alternatives. Social preferences are assumed to satisfy the semi‐order properties of semi‐transitivity and the interval‐order property. We prove that there exists a vetoer when the number of alternatives is greater than or equal to six.     

Coalitional manipulation and the Pareto rule

This paper examines aggregation procedures that map profiles of individual preferences into choice sets. An aggregation procedure is said to be “manipulable by a coalition” if there is a group of individuals, and a preference profile, such that every member of the group prefers the choice set obtained when they are misrepresenting their preferences, to the one obtained when they are honest. We show that the Pareto rule, which is an aggregation procedure that maps profiles of individual preferences into corresponding sets of Pareto optima, is not manipulable by any coalition of individuals under various behavioural assumptions which relate preferences over choice sets to preferences over alternatives. The non-manipulability of the Pareto rule by a single individual follows as a special case under these behavioural assumptions.     

A uniqueness proof for monetary steady state

The framework in Lagos and Wright (2005) [20] combining decentralized and centralized markets is used extensively in monetary economics. Much is known about that model, but there is a loose end: only under special assumptions about bargaining power or decentralized market preferences has it been shown that the monetary steady state is unique. For general decentralized market utility and bargaining, I prove uniqueness for generic parameters with fiat money, and for all parameters with commodity money. As a corollary, I get monotone comparative statics.     

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.     

On the second optimality theorem of welfare economics

To what extent does the second optimality theorem of welfare economics (every Pareto optimal allocation can be repesented as a Walras equilibrium allocation) remain valid when preferences are allowed to be locally satiated? It is always valid for an exchange economy, and is valid for a production economy if there is a consumer who is not locally satiated, but not in general for a production economy where all consumers are locally satiated. A generalized equilibrium is defined, which includes the Walras equilibrium as a special case. Every Pareto optimum can be represented as a generalized equilibrium allocation. Furthermore, every Pareto optimal utility distribution can be realized by a Walras equilibrium allocation.     

On the robustness of laissez-faire

This paper considers a model economy in which agents are privately informed about their type: their endowments of various goods and their preferences over these goods. While preference orderings over observable choices are allowed to be correlated with an agent's private type, we assume that the planner/government is both uncertain about the nature of this joint distribution and unable to choose among multiple equilibria of any given social mechanism. We model the planner/government as having a maxmin objective in the face of this uncertainty.Our main theorem is as follows: Once we allow for this kind of uncertainty and assume no wealth effects in preferences, the uniquely optimal social contract is laissez-faire, in which agents trade in unfettered markets with no government intervention of any kind.