Paths of efficient self-enforcing trade agreements

This paper characterizes the efficient payoff frontier in a three country model where countries face one time adjustment costs of forming trade agreements, and compares it with the constrained efficient frontier when agreements must be self-enforcing. The presence of self-enforcement constraints puts a limit on the magnitude of transfers that can be made between countries, and makes it more likely that bilateral agreements are observed on the constrained efficient frontier. The existence of adjustment costs leads to the possibility that payoffs under a two step agreement, in which an initial bilateral agreement is expanded to include the third country, may Pareto dominate the payoffs from immediate formation of an agreement among all three countries. However, the condition that a two step agreement be efficient in the absence of self-enforcing constraints is neither necessary nor sufficient for the gradual approach to have a lower minimum discount factor. This paper was prepared for the conference “New Directions in International Trade Theory” held at the University of Nottingham. I thank Andres Rodriguez-Clare, Rod Falvey, conference participants, and anonymous referees for helpful comments on an earlier draft.     

Endogenous market incompleteness without market frictions: Dynamic suboptimality of competitive equilibrium in multiperiod overlapping generations economies

In this paper, we show that within the set of stochastic three-period-lived OLG economies with productive assets (such as land), markets are necessarily sequentially incomplete, and agents in the model do not share risk optimally. We start by characterizing perfect risk-sharing and find that it requires state-dependent consumption claims which depend only on the exogenous shock realizations. We show then that the recursive competitive equilibrium of any overlapping generations economy with weakly more than three generations is not strongly stationary. This then allows us to show directly that there are short-run Pareto improvements possible in terms of risk-sharing and hence, that the recursive competitive equilibrium is not Pareto optimal. We then show that a financial reform which eliminates the equity asset and replaces it with zero net supply insurance contracts (Arrow securities) will implement to Pareto optimal stochastic steady-state known to exist in the model. Finally, we also show via numerical simulations that a system of government taxes and transfers can lead to a Pareto improvement over the competitive equilibrium in the model.     

Revealed group preferences on non-convex choice problems

Summary. This paper studies the conditions under which the basic results of the revealed preference theory can be established on the domain of choice problems which include non-convex feasible sets; the exercise is closely related to the works of Peters and Wakker (1991) and Bossert (1994). We show that while no continuous choice function can satisfy strong Pareto optimality over the class of all compact and comprehensive choice problems, strong Pareto optimality, Arrow's choice axiom, upper hemicontinuity and a weak compromisation postulate turn out to be necessary and sufficient to represent choice correspondences by continuous, strictly increasing and quasiconcave real-valued functions. Some applications of our main findings to axiomatic bargaining theory are also studied. Received: December 2, 1996; revised version: February 27, 1998     

Specialization and Dynamics in a Trade Model*

An economy which can produce two tradeable goods, and an investment good which augments capital stocks, is shown to specialize in an optimal stationary state unless it is in the interior of a continuum from which no change is ever needed. On the traverse to a stationary state, non-specialization occurs if at all for only a finite time. Although the instantaneous production frontier is concave, the long-run frontier is linear, but the long-run rate of product transformation differs from the supply price ratio with positive time-preference. Long-run specialization may differ from that predicted by long-run comparative advantage.     

Private information,Coasian bargaining,and the second welfare theorem

Most of the debate about Coasian bargaining in the presence of externalities relates to the First Welfare Theorem: is the outcome under bargaining efficient? This debate has involved the definition and importance of transaction costs, the significance of private information, and the effect of entry. There has been little analysis of how Coasian bargaining relates to the Second Welfare Theorem: even if the bargaining outcome is efficient, does the process limit the set of Pareto optimal allocations which can be achieved?We consider a model in which individuals utilize a common resource and may affect each other's output. The individuals differ in their productivities or tastes and this information is private to each of them. The government can manage the common resource and use nonlinear taxes to correct for the externality or it can turn the common resource over to a private owner who can charge individuals to utilize it with a nonlinear fee schedule. The government and the owner have the same information about tastes and productivities of the individuals. Except for the private information, there are no bargaining or administrative costs for collecting the taxes or fees. Whether there is public or private ownership, the government desires to redistribute, but it faces self-selection constraints.We show that the outcome of Coasian bargaining is constrained Pareto efficient. That is, given the information constraints, no Pareto improvement is possible. However, private ownership may limit what Pareto optimal allocations the government can achieve. The private owner in seeking to maximize profits always proposes contracts which counteract the government's attempts to redistribute across individuals with different characteristics. Under public management, any Pareto optimum can be sustained. In this context, private ownership, while not inefficient, does limit the government's ability to redistribute.     

Compatibility of expected utility and <Emphasis Type="Italic">μ/σ</Emphasis> approaches to risk for a class of non location–scale distributions

Proofs of compatibility of the expected utility and μ/σ approaches to incorporating uncertainty in decision making exist for at least some utility functions and location–scale distributions. But there are severe constraints and it is desirable to investigate compatibility more widely. We do so for the class of distributions that are transformable to location–scale form by concave transformation and where the utility functions remain concave under transformation. The class is important, containing distributions such as the lognormal and Pareto, usually considered more appropriate for modelling income or wealth than those in the location–scale family. We are grateful to Jack Meyer for very helpful comments and discussions and also to an anonymous referee for useful remarks.     

Gradualism in Trade Agreements with Asymmetric Countries

This paper uses recursive methods to characterize the payoff frontier of self–enforcing trade agreements between countries of asymmetric size. We show that at points on the frontier where only one country&'s incentive constraint binds, the efficient agreement will be a non–stationary one that starts with a positive trade distortion but eventually reaches free trade. Our analysis illustrates how (i) relative country size, (ii) consumption smoothing incentives, and (iii) sunk investments affect the form of efficient trade agreements. In contrast to previous work on gradualism, our results are obtained from a model in which the economic environment is stationary.     

On the Coalition-Proofness of the Pareto Frontier of the Set of Nash Equilibria

This article shows that the Pareto efficient frontier of the Nash equilibrium set of games with strategic substitutes is coalition-proof under the following conditions: (1) the game has three players, or, alternatively, a player's payoff depends on her own strategy and on the sum (but not on the composition) of other players' strategies; (2) an increase in a player's strategy either raises all other players' payoffs monotonically or reduces them monotonically; and (3) each player's payoff is strictly concave in her own strategy. Under these conditions, the Pareto dominance refinement is equivalent to the coalition-proof Nash equilibrium refinement.Journal of Economic LiteratureClassification Number: C72.     

Social welfare orderings for ratio-scale measurable utilities

Summary. This article characterizes all of the continuous social welfare orderings which satisfy the Weak (resp. Strong) Pareto principle when utilities are ratio-scale measurable. With Weak Pareto, on both the nonnegative and positive orthants the social welfare ordering must be representable by a weakly increasing Cobb-Douglas social welfare function while on the whole Euclidean space the social welfare ordering must be strongly dictatorial. With Strong Pareto, on the positive orthant the social welfare ordering must be representable by a strictly increasing Cobb-Douglas social welfare function but on the other two domains an impossibility theorem is obtained. Received: July 31, 1995; revised version August 7, 1996     

UNIQUE MARKOV EQUILIBRIUM UNDER LIMITED COMMITMENT

I develop a recursive method for the characterization of competitive equilibrium under limited commitment with not-too-tight solvency constraints. The reputational mechanism is fragile, as it sustains constrained efficiency as well as a large set of constrained inefficient equilibria. However, I establish that the only strongly ergodic Markov equilibrium with trade is constrained efficient. The method relies on a planning program along with the theory of monotone concave operators. It is suitable for other applications to macroeconomics and dynamic contracts.     

Folk Theorem For Bilateral Bargaining with Vector Endowments

We analyse a bargaining game of two players on the division of the sum of their vector endowments, with alternating proposals and discounting of single period utilities. The pair of endowments is not weakly Pareto‐efficient. Until they reach an agreement, each of the parties can withdraw from bargaining and keep their endowments. Any strictly individually rational division of the sum of endowments can emerge in some subgame perfect equilibrium if discount factors are close enough to one. Each subgame perfect equilibrium, in which the parties’ decisions do not depend on past rejected proposals, leads to a weakly Pareto‐efficient agreement in the first period.     

A near Pareto optimal auction with budget constraints

In a setup where a divisible good is to be allocated to a set of bidders with budget constraints, we introduce a mechanism in the spirit of the Vickrey auction. In the mechanism we propose, understating budgets or values is weakly dominated. Since the revenue is increasing in budgets and values, all kinds of equilibrium deviations from true valuations turn out to be beneficial to the auctioneer. We also show that ex-post Nash equilibrium of our mechanism is near Pareto optimal in the sense that all full winners? values are above all full losers? values.     

Efficient allocations with moral hazard and hidden borrowing and lending: A recursive formulation

We propose a tractable recursive framework to study the optimal allocation of consumption and effort in a dynamic setting with moral hazard where agents have secret access to the credit market or to storage. The recursive structure is based on a generalized first-order approach, whose validity must be verified ex post. Thanks to the recursive formulation of the optimal contract, the verification procedure turns out to be numerically parsimonious as it can be performed using standard dynamic programming techniques with only one endogenous state variable: The agent's level of assets. We study the performance of our ex post verification test in practice by solving numerically three representative infinite horizon examples.     

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.     

Characterizing C2 aggregate excess demand functions

Summary. We integrate and sharpen two characterizations of aggregate excess demand functions: we obtain Mas-Colell's (1977) equilibrium invariance, and strengthen Geanakoplos' (1984) weakly concave utility functions to strictly concave ones. Our proofs modify and extend Geanakoplos' utility-construction. We note two applications: a sharper characterization of equilibrium price sets (cf. Mas-Colell (1977)), and a basis for the studies of computable economies (Richter and Wong (1996)). Received: July 29, 1996; revised version: February 20, 1997     

Political preference functions,trade wars,and trade negotiations

The integration of elementary political considerations into computable general equilibrium models is considered, and an extended illustration to agricultural trade negotiations provided. The application involves an evaluation of the payoffs of alternative support levels to agricultural and non-agricultural interests in the EC and the US. A government political preference function for each region is calibrated as a CES aggregation of the payoffs to the two interest groups, with weights corresponding to their benchmark political influence. The political preference function is presumed to be employed by each government to determine the level of agricultural support. The analysis illustrates how sensitive such computable general equilibrium models can be to elementary political considerations, mainly due to the flatness of the implied Pareto frontier. It also illustrates how one can modify the traditional political preference function approach to accommodate possible convexities of the Pareto frontier in empirical models.     

A simple and efficient test for the Pareto law

This note presents a simple and locally optimal test statistic for the Pareto law. The test is based on the Lagrange multiplier principle and can be computed easily once the maximum likelihood estimator of the scale parameter of the Pareto density has been obtained. A Monte Carlo exercise shows the good small sample properties of the test under the null of the Pareto law and also its power against some sensible and interesting alternatives. In addition, the proposed test is compared to a goodness of fit test which is powerful against more or less all alternatives. Eventually, a simple application to urban economics is performed.     

Production Efficiency and the Direct-Indirect Tax Mix

In the design of the optimal direct/indirect tax mix, the canonical view was laid by Atkinson and Stiglitz (1976) who showed that commodity taxes are unnecessary in an economy in which there is an optimal nonlinear income tax provided that commodities are separable from labor in the utility functions of all taxpayers, that the aggregators over these commodities are ordinally equivalent and that wages are fixed. When wages are endogenous, Naito (1999) showed that this result may not hold and in addition that production efficiency may not be Pareto optimal. Given an optimal nonlinear income tax, we show that production inefficiency is Pareto optimal if the aggregate technology set is strictly concave. The Atkinson–Stiglitz condition is neither necessary nor sufficient for zero commodity taxation and commodity taxes are part of almost all Pareto optima.     

Positive- versus zero-sum majoritarian ultimatum games: An experimental study

Politics can involve a movement from a position off the Pareto frontier to a point on it (a positive-sum game as exemplified in the classic [Buchanan, J.M., Tullock, G., 1962. The Calculus of Consent. University of Michigan Press, Ann Arbor] work), or a movement along the Pareto frontier (a zero-sum game as exemplified in the classic [Riker, W., 1962. The theory of political coalitions. Yale University Press, New Haven] work). In this paper we shed light on their differentiation experimentally by making a comparison between a positive-sum and a zero-sum majoritarian ultimatum game. Our main findings include (i) the fraction of subjects who adopted minimum winning rather than oversized coalitions increases significantly as the game form varies from positive-sum to zero-sum, (ii) oversized coalitions are attributable to non-strategic considerations, and (iii) subjects who choose to adopt the minimum winning coalition have a tendency to seek cheaper responders as their partners in the zero-sum game, but there is no evidence of such a tendency in the positive-sum game. Overall, the weight of the evidence revealed by our experimental data indicates that relative scarcity (embodied in the zero-sum game) promotes behavior more in line with the predictions of economics.     

A top dog tale with preference complementarities

The emergence of a winner-take-all (top dog) outcome is generally due to political or institutional constraints or to specific technological features which favour the performance of just one individual. In this paper we provide a different explanation for the occurrence of a top-dog equilibrium in exchange economies. We show that once heterogeneous complementarities (i.e. Scarf’s preferences) are analysed with general endowment distributions, a variety of equilibria different from the well-known symmetric outcome with full utilisation of resources can emerge. Specifically, we show that stable corner equilibria with a winner-take-all (top dog) individual arise that are Pareto optima although the remaining individuals are no better off than with zero consumption and resources can be unused. Because of heterogenous complementarities, market mechanisms are weak and cannot overcome the top dog’s power. Voting mechanisms or taxation policies can reduce the top dog’s privileged position.