Knightian uncertainty and moral hazard

This paper presents a principal-agent model in which the agent has imprecise beliefs. We model this situation formally by assuming the agent?s preferences are incomplete as in Bewley (1986) [2]. In this setting, incentives must be robust to Knightian uncertainty. We study the implications of robustness for the form of the resulting optimal contracts. We give conditions under which there is a unique optimal contract, and show that it must have a simple flat payment plus bonus structure. That is, output levels are divided into two sets, and the optimal contract pays the same wage for all output levels in each set. We derive this result for the case in which the agent?s utility function is linear and then show it also holds if this utility function has some limited curvature.     

Equilibrium theory with asymmetric information and with infinitely many commodities

The traditional deterministic general equilibrium theory with infinitely many commodities cannot cover economies with private information constraints on the consumption sets. We bring the level of asymmetric information equilibrium theory at par with that of the deterministic one. In particular, we establish results on equilibrium existence for exchange economies with asymmetric (differential) information and with an infinite dimensional commodity space. Our new equilibrium existence theorems include, as a special case, classical results, e.g. Bewley [Existence of equilibria in economies with infinitely many commodities, J. Econ. Theory 4 (1972) 514-540] or Mas-Colell [The price equilibrium existence problem in topological vector lattices, Econometrica 54 (1986) 1039-1053].     

Self-insurance vs. self-financing: A welfare analysis of the persistence of shocks

We study the welfare cost of market incompleteness in a generalized Bewley model where idiosyncratic risk takes the form of entrepreneurial productivity shocks. Market incompleteness in our framework has two dimensions. First, in the Bewley tradition, only a limited set of instruments for consumption smoothing is available. Second, entrepreneurs? capital rental is subject to collateral constraints. As is well known, it is harder to self-insure against more persistent shocks, and the welfare cost of missing consumption insurance increases with shock persistence. On the other hand, with collateral constraints, an increase in shock persistence leads to better allocation of production factors through entrepreneurs? self-financing, and the welfare cost of imperfect capital rental markets decreases with shock persistence. The overall welfare cost of market incompleteness can be increasing, decreasing, or even non-monotone in shock persistence, depending on the relative strengths of its two components—the cost of missing insurance and the cost of imperfect capital markets.     

Public versus private risk sharing

Can public income insurance through progressive income taxation improve the allocation of risk in an economy where private risk sharing is incomplete? The answer depends crucially on the fundamental friction that limits private risk sharing in the first place. If risk sharing is limited because insurance markets are missing for model-exogenous reasons (as in Bewley (1986) [8]) publicly provided risk sharing improves on the allocation of risk. If instead private insurance markets exist but their use is limited by limited enforcement (as in Kehoe and Levine (1993) [23]) then the provision of public insurance interacts with equilibrium private insurance, as, by providing risk sharing, the government affects the value of exclusion from private insurance markets and thus the enforcement mechanism of these contracts. We characterize consumption allocations in an economy with limited enforcement and a continuum of agents facing plausible income risk and tax systems with various degrees of progressivity (public risk sharing). We provide conditions under which more publicly provided insurance actually reduces total insurance for agents (excess crowding-out), or under which more public insurance increases total insurance (partial crowding-out).     

Incentive compatibility and differentiability: New results and classic applications

We provide several generalizations of Mailath?s (1987) [9] result that in games of asymmetric information with a continuum of types incentive compatibility plus separation implies differentiability of the informed agent?s strategy. The new results extend the theory to classic models in finance such as Leland and Pyle (1977) [8], Glosten (1989) [4], and DeMarzo and Duffie (1999) [3], that were not previously covered.     

The genericity of beliefs-determine-preferences models revisited

Barelli [P. Barelli, On the genericity of full surplus extraction in mechanism design, J. Econ. Theory 144 (2009) 1320-1332] defines beliefs-determine-preferences (BDP) models and argues that BDP models are nongeneric in a topological sense. In this note, we point out some difficulties in Barelli?s approach. Furthermore, we follow the idea of Heifetz and Neeman [A. Heifetz, Z. Neeman, On the generic (im)possibility of full surplus extraction, Econometrica 74 (2006) 213-233] to propose a more relevant notion of BDP^? model. We prove that BDP^? models are generic, which is opposite to Barelli?s conclusion.     

Justifiable preferences

We characterize preferences over acts that can be represented by a utility function and a multiple-prior, such that an act f is preferred to act g if there is a prior under which the expected utility induced by f is higher than that induced by g. These preferences are referred to as justifiable preferences. We further introduce a generalized model of ambiguity that involves a collection of multiple-priors, namely, multiple multiple-priors and incorporate Bewley?s Knightian model in justifiability: f is preferred to g if, according to at least one set of priors, f is unanimously preferred to g.     

Externalities and fundamental nonconvexities: A reconciliation of approaches to general equilibrium externality modeling and implications for decentralization

Starrett (1972) [33] and Boyd and Conley (1997) [7] approaches to externality modeling are unified by distinguishing between producible and nonproducible public commodities. Nonconvexities are associated with detrimental producible public commodities but not with nonproducible public commodities in Boyd and Conley (1997) [7]. Disposability properties (costly or costless) imply that producible public commodities are either by-products (e.g., pollution) or joint-products (e.g., national defense). Markets fail for both beneficial and detrimental by-products. Nonconvexities imply that price-based equilibria, e.g., Pigovian tax equilibrium, may not be Pareto-efficient. Foley's (1967, 1970) [17] and [18] “public competitive equilibrium” combines price and quantity signals with a unanimity criterion and restores the equivalence between equilibrium and efficiency.     

Uniqueness of stationary equilibrium payoffs in coalitional bargaining

We study a model of sequential bargaining in which, in each period before an agreement is reached, the proposer?s identity is randomly determined, the proposer suggests a division of a pie of size one, each other agent either approves or rejects the proposal, and the proposal is implemented if the set of approving agents is a winning coalition for the proposer. The theory of the fixed point index is used to show that stationary equilibrium expected payoffs of this coalitional bargaining game are unique. This generalizes Eraslan [34] insofar as: (a) there are no restrictions on the structure of sets of winning coalitions; (b) different proposers may have different sets of winning coalitions; (c) there may be a positive probability that no proposer is selected.     

On the optimality of optimal income taxation

The Mirrleesian model of income taxation restricts attention to simple allocation mechanism with no strategic interdependence, i.e., the optimal labor supply of any one individual does not depend on the labor supply of others. It has been argued by Piketty (2009) [12] that this restriction is substantial because more sophisticated mechanisms can reach first-best allocations that are out of reach with simple mechanisms. In this paper, we assess the validity of Piketty?s critique in an independent private values model. As a main result, we show that the optimal sophisticated mechanism is a simple mechanism, or, equivalently, a Mirrleesian income tax system.     

Comment on “Correlated information, mechanism design and informational rents” [J. Econ. Theory 123 (2) (2005) 210–217]

We amend an error in [S. Parreiras, Correlated information, mechanism design and informational rents, J. Econ. Theory 123 (2005) 210–217]. Consequently, it is in general not possible to reinterpret a mechanism design model that violates the spanning condition of Crémer and McLean [J. Crémer, R. McLean, Full extraction of the surplus in bayesian, dominant strategy auctions, Econometrica 56 (1988) 1247–1258] as one in which agents hold private information about the informativeness of their signals about other agents? types. Instead, such an interpretation is warranted only when the weights used to span an agent?s set of beliefs stand in a singular relation with the prior type distribution that is known as an alternative characterization of Blackwell dominance.     

Ambiguity aversion and trade

What is the effect of ambiguity aversion on trade? Although in a Bewley??s model, ambiguity aversion always leads to less trade; in other models, this is not always true. However, we show that if the endowments are unambiguous, then more ambiguity aversion implies less trade for a very general class of preferences. The reduction in trade caused by ambiguity aversion can be as severe as to lead to no trade. In an economy with MEU decision makers, we show that if the aggregate endowment is unanimously unambiguous, then every Pareto optima allocation is also unambiguous. We also characterize the situation in which every unanimously unambiguous allocation is Pareto optimal. Finally, we show how our results can be used to explain the home-bias effect. As a useful result for our methods, we also obtain an additivity theorem for CEU and MEU decision makers that does not require comonotonicity.     

Taxes and the Efficiency-Rent Extraction Trade-off

This paper presents an adverse selection model in which progressive taxation enhances productive efficiency by encouraging a principal (buyer) to be less aggressive in contracting with an agent (seller). Wary of padded cost budgets, the buyer employs a hurdle‐rate procurement policy. With a low cost hurdle, the buyer keeps greater profits when transactions are undertaken but trade occurs less often. While the hurdle is unaffected by a flat tax, a progressive tax tilts the buyer's preference: the buyer's benefit from a lower hurdle becomes less pronounced, since the marginal increase in his profits is muted in after‐tax terms. The result is increased trade and the possibility of Pareto improvements.     

Ironing without control

I extend Myerson?s [R. Myerson, Optimal auction design, Math. Oper. Res. 6 (1981) 58–73] ironing technique to more general objective functions. The approach is based on a generalized notion of virtual surplus which can be maximized pointwise even when the monotonicity constraint implied by incentive compatibility binds. It is applicable to quasilinear principal-agent models where the standard virtual surplus is weakly concave in the allocation or appropriately separable in the allocation and type. No assumptions on allocation rules are required beyond monotonicity.     

Consumption dynamics in general equilibrium: A characterisation when markets are incomplete

We introduce a methodology for analysing infinite horizon economies with two agents, one good, and incomplete markets. We provide an example in which an agent's equilibrium consumption is zero eventually with probability one even if she has correct beliefs and is marginally more patient. We then prove the following general result: if markets are effectively incomplete forever then on any equilibrium path on which some agent's consumption is bounded away from zero eventually, the other agent's consumption is zero eventually—so either some agent vanishes, in that she consumes zero eventually, or the consumption of both agents is arbitrarily close to zero infinitely often. Later we show that (a) for most economies in which individual endowments are finite state time homogeneous Markov processes, the consumption of an agent who has a uniformly positive endowment cannot converge to zero and (b) the possibility that an agent vanishes is a robust outcome since for a wide class of economies with incomplete markets, there are equilibria in which an agent's consumption is zero eventually with probability one even though she has correct beliefs as in the example. In sharp contrast to the results in the case studied by Sandroni (2000) [29] and Blume and Easley (2006) [8] where markets are complete, our results show that when markets are incomplete not only can the more patient agent (or the one with more accurate beliefs) be eliminated but there are situations in which neither agent is eliminated.     

The Cass criterion, the net dividend criterion, and optimality

Abel, Mankiw, Summers, and Zeckhauser [Assessing dynamic efficiency: theory and evidence, Rev. Econ. Stud. 56 (1989) 1-20] propose the net dividend criterion as an easy to use sufficient condition for optimality in general stochastic overlapping generations economies with production. We provide examples based on the criterion due to Cass [On capital overaccumulation in the aggregative neoclassical model of economic growth: a complete characterization, J. Econ. Theory 4 (1972) 200-223] and its extensions, the usual tools for such problems, to show that the net dividend criterion need not give the right answer. We identify the flaw in their proof. We also provide an alternative condition which, by an argument unrelated to theirs, is a sufficient condition for optimality when dividends are nonnegative and then argue that the condition is not innocuous since it cannot be verified in actual economies.     

Optimal use of correlated information in mechanism design when full surplus extraction may be impossible

We study the mechanism design problem when the principal can condition the agent's transfers on the realization of ex post signals that are correlated with the agent's types. Crémer and McLean [Econometrica 53(1985) 345-361; 56(1988) 1247-1257], McAfee and Reny [Econometrica 60(2)(1992) 395-421], and Riordan and Sappington [J. Econ. Theory, 45(1988) 189-199] studied situations where the signals are such that full surplus can be extracted from every agent type. We study optimal utilization of the signals when there are fewer signals than types and the Riordan and Sappington conditions do not always hold. For some special cases, we show the level of surplus that can be extracted, and identify the agent types who obtain rent.     

When are stabilizations delayed? Alesina-Drazen revisited

In an influential article, Alesina and Drazen [1991. Why are Stabilizations Delayed? American Economic Review 81, 1170-1188] model delay of stabilization as the result of a struggle between political groups supporting reform plans with different distributional implications. In this paper we show that ex ante asymmetries in the costs of delay for the groups will reduce the probability of conflict and will lead to a shorter expected delay. Accurate common information about the cost of delay may lead to no delay at all. In an asymmetric conflict, a wider divergence in the distributional implications of reform will reduce the probability of conflict but will lead to a longer expected delay. We motivate the asymmetric model of delay by reference to Latin American episodes of the 1980s.     

Bank incentives, contract design and bank runs

We study the Diamond-Dybvig [Bank runs, deposit insurance, and liquidity, J. Polit. Econ. 91 (1983) 401-419] model as developed in Green and Lin [Implementing efficient allocations in a model of financial intermediation, J. Econ. Theory 109 (2003) 1-23] and Peck and Shell [Equilibrium bank runs, J. Polit. Econ. 111 (2003) 103-123]. We dispense with the notion of a bank as a coalition of depositors. Instead, our bank is a self-interested agent with a technological advantage in record-keeping. We examine the implications of the resulting agency problem for the design of bank contracts and the possibility of bank-run equilibria. For a special case, we discover that the agency problem may or may not simplify the qualitative structure of bank liabilities. We also find that the uniqueness result in Green and Lin [Implementing efficient allocations in a model of financial intermediation, J. Econ. Theory 109 (2003) 1-23] is robust to our form of agency, but that the non-uniqueness result in Peck and Shell [Equilibrium bank runs, J. Polit. Econ. 111 (2003) 103-123] is not.     

Subjective probability over a subjective decision tree

A state space has been assumed as a primitive for modeling uncertainty, which presumes that the analyst knows all the uncertainties a decision maker (DM) perceives. This is problematic because states are private information of the DM, and hence are not directly observable to the analyst. Dekel et al. [Representing preferences with a unique subjective state space, Econometrica 69 (2001) 891-934] derive, rather than assume, the subjective state space from preference over suitable choice objects.In a dynamic setting, a decision tree, that is, a pair consisting of a state space and a filtration, has been taken as a primitive. This assumption is also problematic—a decision tree should be derived rather than assumed as a primitive. We formulate a three-stage extension of the above literature in order to model a DM who anticipates subjective uncertainty to be resolved gradually over time. We identify also subjective beliefs on the subjective state space.