Liquidity provision vs. deposit insurance: preventing bank panics without moral hazard

Equilibrium bidding strategies under most multi-unit auction rules cannot be obtained as closed form expressions. Research in multi-unit auctions has, therefore, depended on implicit characterization of equilibrium strategies using the first-order conditions of the bidders’ expected payoff maximization problem. In this paper we consider the pay-as-bid auction with diminishing marginal values for two units and show that any symmetric equilibrium in continuous strategies has the necessary properties to allow such a characterization. Moreover, any increasing solution to the system of differential equations that is used to characterize the equilibrium strategies describes an equilibrium strategy.Generous suggestions and comments from Richard Engelbrecht-Wiggans, Charles M. Kahn, and an anonymous referee are gratefully acknowledged.     

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.     

Orthogonal Parameters and Panel Data

This paper describes a class of consistent estimators for short panels with fixed effects. The method is to find an orthogonal reparametrization of the fixed effects and then to integrate the new effects from the likelihood with respect to an appropriately chosen prior density. The resulting marginal posterior densities of the common parameters have modes that are shown to be consistent in the models examined here. The main result concerns the first-order autoregressive model with agent specific intercepts where the likelihood is conditional on the set of initial observations. This paper provides a consistent likelihood-based estimator for this model. Some numerical illustrations are given. The first-order conditions for the posterior mode can also be thought of as new moment conditions for GMM estimation.     

The first-order approach in rank-order tournaments

The first-order approach in rank-order tournaments is addressed. It is demonstrated that the conditions given in the literature are not sufficient to guarantee concavity of agents' objective functions. Additional conditions are provided that ensure validity of the first-order approach.     

Monotone imitation

We analyze the social learning process of a group of individuals who have limited information about the payoff distributions of each action. We say that a behavioral rule is first-order monotone (FOM) if the number of individuals who play actions with first-order stochastic dominant payoff distributions is expected to increase in any environment. We provide a characterization of FOM rules. Both Imitate if Better and Schlag’s (J Econ Theory 78:130–156, 1998) Proportional Imitation rule are FOM. No FOM rule is dominant in the sense of having the best performance in every environment.     

On the first-order approach in principal-agent models with hidden borrowing and lending

We provide sufficient conditions for the validity of the first-order approach for two-period dynamic moral hazard problems where the agent can save and borrow secretly. The first-order approach is valid if the following conditions hold: (i) the agent has non-increasing absolute risk aversion utility (NIARA), (ii) the output technology has monotone likelihood ratios (MLR), and (iii) the distribution function of output is log-convex in effort (LCDF). Moreover, under these three conditions, the optimal contract is monotone in output. We also investigate a few possibilities of relaxing these requirements.     

Bias correcting adjustment coefficients in a cointegrated VAR with known cointegrating vectors

The maximum likelihood estimator of the adjustment coefficient in a cointegrated vector autoregressive model (CVAR) is generally biased. For the case where the cointegrating vector is known in a first-order CVAR with no intercept, we derive a condition for the unbiasedness of the maximum likelihood estimator of the adjustment coefficients, and provide a simple characterization of the bias in case this condition is violated. A feasible bias correction method is shown to virtually eliminate the bias over a large part of the parameter space.     

Distributions for the first-order approach to principal-agent problems

Summary. The first-order approach is a technical shortcut widely used in agency problems. The best known set of sufficient conditions for its validity are due to Mirrlees and Rogerson and require that the distribution function is convex in effort and has a likelihood ratio increasing in output. Only one nontrivial example was so far known to satisfy both properties. This note provides two rich families of examples displaying both properties. Received: December 4, 2000; revised version: December 10, 2001     

Limited knowledge of demand and oligopoly equilibria

In a standard model of oligopoly with differentiated products, the existence of an equilibrium at which the first-order conditions for profit maximisation are simultaneously satisfied for all firms is proved and this is done without imposing any restrictions on the demand functions. This is an equilibrium in the following sense: although some firms may not necessarily be maximising their profits, nevertheless if each firm's knowledge of demand is limited to the linear approximation of its own demand curve, then it will believe that it is indeed maximising its profits.     

Quality adjusted life years as expected utilities

Abstract. This article is intended to systematicaly show all the conditions that the Quality Adjusted Life Year (QALY) must satisfy so that it can be interpreted as a von Newman-Morgenstern utility. Such conditions cover two cases. When health states are chronic, we shall be referring to the conditions inferred by Pliskin, Shepard and Weinstein (1980). Likewise, we will devote our attention to commenting on the characterization of Bleichrodt (1996), pointing out that its condition 0 is a bit artificial. In turn, for temporary health states, we will remark that the characterization of Bleichrodt (1995) appears to be incomplete. We shall provide a complete derivation of QALYs. In this way, QALYs can be derived from an individual's preference relation that satisfies the von Newman-Morgenstern axioms by imposing additive independence, absence of contradictory trade-offs and partial symmetry. Moreover, the two last conditions conditions can be replaced by a single condition that we call general symmetry.     

The Theory of Moral Hazard and Unobservable Behaviour: Part I

Principal-agent models are studied, in which outcomes conditional on the agent's action are uncertain, and the agent's behaviour therefore unobservable. For a model with bounded agent's utility, conditions are given under which the first-best equilibrium can be approximated arbitrarily closely by contracts relating payment to observable outcomes. For general models, it is shown that the solution may not always be obtained by using the agent's first-order conditions as constraint. General conditions of Lagrangean type are given for problems in which contracts are finite-dimensional.     

Bunching and second-order conditions: A note on optimal tax theory

We present in this note a simple non-linear taxation model in which the agents are indexed by a one-dimensional parameter. Our purpose is to propose a method of resolution and to compute the optimal solution. We point out that the solution could not always be obtained with a simple derivation of the first-order conditions of the control problem under consideration, and we show the necessity to take into account the second-order conditions.     

Two-dimensional screening: a case of monopoly regulation

This paper deals with the optimal regulatory policy of a monopolist producing two goods and with two-dimensional private information about costs. The case of perfectly and negatively correlated cost's parameters is analyzed and a complete characterization of the optimal mechanism by means of easily interpretable conditions is obtained.     

Market Power and Buffer Stocks

The first-order conditions for a monopolist inventory holder are found under more general conditions than previously. It is found that monopolist storers facing inelastic demand will carry over more stock than they would with competition unless the elasticity of demand b increasing as price decreases or is constant. The competitive stocks equilibrium is identified and found to be Pareto optimal and hence Sams' result that there will be no losers from a rent-maximizing buffer stock policy is shown to be wrong.     

Time-Consistent Public Policy

In this paper we study how a benevolent government that cannot commit to future policy should trade off the costs and benefits of public expenditure. We characterize and solve for Markov-perfect equilibria of the dynamic game between successive governments. The characterization consists of an inter-temporal first-order condition (a "generalized Euler equation") for the government, and we use it both to gain insight into the nature of the equilibrium and as a basis for computations. For a calibrated economy, we find that when the only tax base available to the government is capital income—an inelastic source of funds at any point in time—the government still refrains from taxing at confiscatory rates. We also find that when the only tax base is labour income the Markov equilibrium features less public expenditure and lower tax rates than the Ramsey equilibrium.     

Robust and secure implementation: equivalence theorems

This paper shows that in private value environments, strategy-proofness and the rectangular property are necessary conditions for (full) robust implementation (Bergemann and Morris, 2011). As corollaries, we obtain the equivalence between robust and secure implementation (Saijo et al., 2007), the revelation principle for robust implementation, and characterization of double implementation in robust and secure implementation.     

Natural Oligopolies: A Vertical Differentiation Model

This article contains a more complete characterization of conditions under which vertically differentiated markets are or are not natural oligopolies than has been found previously in the literature. Specifically, previous results on markets in which firms have cost functions with constant returns are incomplete; these results are expanded. Moreover, results are provided for markets with firms having increasing or decreasing marginal cost functions.     

A Simple Characterization of the Second‐best Two‐part and Block‐rate Tariffs Theory and Applications

The general necessary optimality conditions for second‐best discrete multipart tariffs are rather complex. In this paper, we derive a simplified characterization of these conditions for two‐part tariffs and for block‐rate tariffs for given thresholds of these tariffs. The simplified necessary optimality conditions are equivalent to the necessary conditions for a Ramsey‐optimum for goods with continuously variable individually demanded quantities. We demonstrate that this characterization of second‐best multipart tariffs can be helpful, when applying the usual regulatory mechanisms to these tariffs. In particular, we consider Vogelsang–Finsinger (1979) regulation as well as a particular form of price‐cap regulation which is related to the Laspeyres index of prices.     

Non-paternalistic Altruism and Utility Interdependence

This paper clarifies the notion of non-paternalistic altruism through the use of utility aggregators. It presents conditions for the existence of non-paternalistically altruistic utility functions and provides a complete characterization of such utility functions. The results are used to generalize the Second Theorem of Welfare Economics and to prove the existence of an equilibrium in a game of voluntary gift-giving.
JEL Classification Nos.: D11, D64.     

Restricted feedback in long term relationships

This paper studies long term relationships, modeled as repeated games, with restricted feedback. Players condition current play on summary statistics of past play rather than the entire history, as may be the case in online markets. Our state strategy equilibrium framework allows for arbitrary restrictions on strategies. We derive a recursive characterization for the set of equilibrium payoffs similar to that of Abreu, Pearce, and Stacchetti (1986, 1990) [2], [3] for perfect public equilibria and show that the set of equilibrium payoffs is the largest fixed point of a monotone operator. We use our characterization to derive necessary and sufficient conditions for efficient trade in a repeated product choice game where costumers condition their purchase decisions only on the last performance signal.