Belief consistency and trade consistency

Interpersonal consistency can be described in epistemic terms as a property of beliefs, or in economic terms as the impossibility of certain trades. The existence of a common prior from which all agentsʼ beliefs are derived is of the first kind. The non-existence of an agreeable bet, that is, a contingent zero-sum trade which is always favorable to all agents, is of the second kind. It is well established that these two notions of consistency are equivalent for finite type spaces but not for countable ones. We present three equivalences of epistemic consistency and economic consistency conditions for countable type spaces, defining in this way three levels of consistency of type spaces: weak consistency, consistency, and strong consistency. These three levels coincide in the finite case. We fully analyze the level of consistency of type spaces based on the knowledge structure of Rubinsteinʼs email game. The new notion of belief consistency introduced here helps to justify the requirement of boundedness of payoff functions in countable type spaces by showing that in a large class of spaces there exists an agreeable unbounded bet even when a common prior exists.     

Aggregation of multiple prior opinions

Experts are asked to provide their advice in a situation of uncertainty. They adopt the decision maker?s utility function, but each has a potentially different set of prior probabilities, and so does the decision maker. The decision maker and the experts maximize the minimal expected utility with respect to their sets of priors. We show that a natural Pareto condition is equivalent to the existence of a set Λ of probability vectors over the experts, interpreted as possible allocations of weights to the experts, such that (i) the decision maker?s set of priors is precisely all the weighted-averages of priors, where an expert?s prior is taken from her set and the weight vector is taken from Λ; (ii) the decision maker?s valuation of an act is the minimal weighted valuation, over all weight vectors in Λ, of the experts? valuations.     

Robust equilibria under non-common priors

This paper considers the robustness of equilibria to a small amount of incomplete information, where players are allowed to have heterogeneous priors. An equilibrium of a complete information game is robust to incomplete information under non-common priors if for every incomplete information game where each player's prior assigns high probability on the event that the players know at arbitrarily high order that the payoffs are given by the complete information game, there exists a Bayesian Nash equilibrium that generates behavior close to the equilibrium in consideration. It is shown that for generic games, an equilibrium is robust under non-common priors if and only if it is the unique rationalizable action profile. Set-valued concepts are also introduced, and for generic games, a smallest robust set is shown to exist and coincide with the set of a posteriori equilibria.     

Ambiguous events and maxmin expected utility

We study the properties associated to various definitions of ambiguity [L.G. Epstein, J. Zhang, Subjective probabilities on subjectively unambiguous events, Econometrica 69 (2001) 265-306; P. Ghirardato et al., Differentiating ambiguity and ambiguity attitude, J. Econ. Theory 118 (2004) 133-173; K. Nehring, Capacities and probabilistic beliefs: a precarious coexistence, Math. Soc. Sci. 38 (1999) 197-213; J. Zhang, Subjective, ambiguity, expected utility and Choquet expected utility, Econ. Theory 20 (2002) 159-181] in the context of Maximin Expected Utility (MEU). We show that each definition of unambiguous events produces certain restrictions on the set of priors, and completely characterize each definition in terms of the properties it imposes on the MEU functional. We apply our results to two open problems. First, in the context of MEU, we show the existence of a fundamental incompatibility between the axiom of “Small unambiguous event continuity” (Epstein and Zhang, 2001) and the notions of unambiguous event due to Zhang (2002) and Epstein and Zhang (2001). Second, we show that, in the context of MEU, the classes of unambiguous events according to either Zhang (2002) or Epstein and Zhang (2001) are always λ-systems. Finally, we reconsider the various definitions in light of our findings, and identify some new objects (Z-filters and EZ-filters) corresponding to properties which, while neglected in the current literature, seem relevant to us.     

Rational preferences under ambiguity

This paper analyzes preferences in the presence of ambiguity that are rational in the sense of satisfying the classical ordering condition as well as monotonicity. Under technical conditions that are natural in an Anscombe?CAumann environment, we show that even for such a general preference model, it is possible to identify a set of priors, as first envisioned by Ellsberg (Q J Econ 75:643?C669, 1961). We then discuss ambiguity attitudes, as well as unambiguous acts and events, for the class of rational preferences we consider.     

Existence of equilibrium in the Helpman–Krugman model of international trade with imperfect competition

Helpman and Krugman (Market structure and foreign trade. Increasing returns, imperfect competition, and the international economy. MIT Press, Cambridge, 1985) provide a synthesis of the traditional factor proportions theory of international trade and the theory of international trade due to the exploitation of scale economies in imperfectly competitive markets. They derive illuminating results about trade patterns and gains from trade, among other things, leaving unanswered the question of existence of equilibrium, however. The central significance of their characterization of properties of free trade equilibria with inter-industry and intra-industry trade calls for an analysis of existence of equilibrium. This is the object of the present paper. We prove the existence of equilibrium for the integrated multi-sector multi-factor Helpman–Krugman economy without national borders. Well-known conditions ensure that the world economy under free trade reproduces this equilibrium and thus establishes existence of a free trade equilibrium. Since an equilibrium of the integrated economy is not necessarily unique, the same holds true for a free trade equilibrium.     

Pairwise trade and coexistence of money and higher-return assets

A new theory of coexistence of money and higher-return assets is set out. It applies to any setting in which some trade involves an exchange of goods for assets and occurs between two people—a buyer and a seller. We show that there exists a function mapping the portfolios of the buyer and the seller to the trade that occurs such that (i) the trade is in the buyer-seller core and (ii) some people are induced to enter the buyer-seller meeting with money.     

Can Trade Be Good for the Environment?

We analyze the impact of trade in a differentiated good on environmental policy when there is local and transboundary pollution. In autarky, the (equivalent) pollution tax is set equal to the marginal damage from own emissions. If the strategic policy instrument is a tax, leakage occurs under trade and tends to lower the tax. The net terms of trade effect, due to the exportable and importable varieties of the differentiated good, tends to increase the tax. We derive conditions under which pollution taxes under trade are higher than the marginal damage from own emissions, i.e., higher than the Pigouvian tax and than that under autarky. Then, pollution falls under trade relative to autarky. When countries use quotas/permits to regulate pollution, there is no leakage, while the net terms of trade effect tends to make pollution policy stricter. The equivalent tax is always higher than the marginal damage from own emissions, i.e., always higher than the Pigouvian tax and than that under autarky; hence, pollution always falls under trade. Our analysis provides some insight into the findings in the empirical literature that trade might be good for the environment.     

On the uniqueness of fully informative rational expectations equilibria

Summary. This paper analyzes two equivalent equilibrium notions under asymmetric information: risk neutral rational expectations equilibria (rn-REE), and common knowledge equilibria. We show that the set of fully informative rn-REE is a singleton, and we provide necessary and sufficient conditions for the existence of partially informative rn-REE. In a companion paper (DeMarzo and Skiadas (1996)) we show that equilibrium prices for the larger class of quasi-complete economies can be characterized as rn-REE. Examples of quasi-complete economies include the type of economies for which demand aggregation in the sense of Gorman is possible (with or without asymmetric information), the setting of the Milgrom and Stokey no-trade theorem, an economy giving rise to the CAPM with asymmetric information but no normality assumptions, the simple exponential-normal model of Grossman (1976), and a case of no aggregate endowment risk. In the common-knowledge context, we provide necessary and sufficient conditions for a common knowledge posterior estimate, given common priors, to coincide with the full communication posterior estimate. Received: May 29, 1997; revised version: July 18, 1997     

Globalization and taxation: Theory and evidence

We construct a theoretical model to capture the compensation and efficiency effects of globalization in a set up where the redistributive tax rate is chosen by the median voter. The model predicts that the two alternative modes of globalization- trade liberalization and financial openness- could potentially have different effects on taxation. We then provide some empirical evidence on the relationship between taxation and the alternative modes of globalization using a large cross-country panel data set. On average, globalization is associated with lower taxation but there is some evidence that in countries with high capital-labor ratio, globalization is associated with increased taxation. We make a distinction between de jure and de facto measures of globalization and find a strong negative relationship between taxation and de jure measures of globalization. The results for de facto measures of globalization are mixed.     

On equilibrium in Hart's securities exchange model

In this paper, we use a no unbounded arbitrage condition to give a very direct proof of the existence of equilibrium in Hart's unbounded securities exchange model (J. Econ. Theory, 9 (1974), 293–311). We also examine the relationship between the no unbounded arbitrage condition and the sufficiency conditions of Hart, ibid. and Hammond (J, Econ. Theory, 31 (1983), 170–175). We present an example to show that if traders are not sufficiently risk averse, then Hammond's overlapping expectations condition is not, in general, equivalent to the no unbounded arbitrage condition or Hart's sufficiency conditions, and therefore, is not sufficient to guarantee the existence of equilibrium. We also present an example to show that it is possible for the no unbounded arbitrage condition to hold without overlapping expectations, and therefore, it is possible for equilibrium to exist without overlapping expectations.     

Pure strategy equilibria of single and double auctions with interdependent values

We prove the existence of monotonic pure strategy equilibrium for many kinds of asymmetric auctions with n bidders and unitary demands, interdependent values and independent types. The assumptions require monotonicity only in the own bidder's type. The payments can be a function of all bids. Thus, we provide a new equilibrium existence result for asymmetrical double auctions and a small number of bidders. The generality of our setting requires the use of special tie-breaking rules. We present an example of a double auction with interdependent values where all equilibria are trivial, that is, they have zero probability of trade. This is related to Akerlof's “market for lemmons” example and to the “winner's curse,” establishing a connection between them. However, we are able to provide sufficient conditions for non-trivial equilibrium existence.     

Bayesian consistent belief selection

A subjective expected utility agent is given information about the state of the world in the form of a set of possible priors. She is assumed to form her beliefs given this information. A set of priors may be updated according to Bayes' rule, prior-by-prior, upon learning that some state of the world has not obtained. In a model in which information is completely summarized by this set of priors, we show that there exists no decision maker who obeys Bayes' rule, conditions her prior only on the available information (by selecting a belief in the announced set), and who updates the information prior-by-prior using Bayes' rule.     

A behavioral characterization of plausible priors

Recent decision theories represent ambiguity via multiple priors, interpreted as alternative probabilistic models of the relevant uncertainty. This paper provides a robust behavioral foundation for this interpretation. A prior P is “plausible” if preferences over some subset of acts admit an expected utility representation with prior P, but not with any other prior Q≠P. Under suitable axioms, plausible priors can be elicited from preferences, and fully characterize them; also, probabilistic sophistication implies that there exists only one plausible prior; finally, “plausible posteriors” can be derived via Bayesian updating. Several familiar decision models are consistent with the proposed axioms.     

On `indirect' trade-related R&D spillovers

An influential literature argues that trade promotes knowledge flows and technology transmission between trading partners. This literature focuses on `direct' research and development (R&D) spillovers which are related to the levels of R&D produced by the trading partners. In this paper, we argue that `indirect' trade-related R&D spillovers also take place between countries, even if they do not trade with each other. These `indirect' spillovers are associated with available rather than with produced levels of R&D. Our empirical results suggest that these `indirect' trade-related spillovers are at least as important as the `direct' ones, and strengthen the view that trade does matter for the international transmission of R&D. They also suggest that, due to the existence of these `indirect' effects, bilateral trade patterns are relatively less important determinants of the level of foreign R&D spillovers acquired through trade.     

Majority committees

Suppose an m-member committee is to be selected by a set of voters from a set X of M > m nominees. If A is an m-member committee, and if as many voters prefer A to B as prefer B to A for every other committee B of m nominees, then A is a majority committee of size m. Although the existence of majority nominees (m = 1) has been extensively analyzed, little attention has been given to conditions that imply the existence of majority committees of size m ? 2. Known restrictions on voters' preferences on X that guarntee the existence of a majority nominee could be applied directly to voters' preferences on m-member committees. However, this definitional exercise lacks intuitive appeal, and a different approach is taken in this paper. The paper presumes that profiles of voters' preferences on X are either dichotomous or single peaked. Both cases ensure the existence of a majority nominee. Independence-monotonicity assumptions are then used to connect voters' preferences on X to their preferences on committees of equal size. Although these assumptions guarantee the existence of majority committees when m = 1 and when m = M ? 1, they do not generally do so when 1 < m < M ? 1. The latter observation motivates additional restrictions on profiles. In the dichotomous case, we consider profiles in which all voters have the same number k of nominees in their preferred subsets, and show that this restriction guarantees the existence of a majority committee of size m for 1 < m < M ? 1 only when k = 1 or k = M ? 1. In the single-peaked case, we consider profiles in which all voters have the same most-preferred (peak) nominee, and prove that this guarantees the existence of a majority committee of size m for every m between 1 and M ? 1.     

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.     

A note on the existence of Pareto optima in topological vector spaces

In a previous paper we have shown that in l_∞ the existence of Pareto optima and equilibria are essentially equivalent to impatience behaviour on the part of agents. In this note we prove a result showing that in general spaces we need agents to be continuous with respect to a topology that makes the commodity space sub-reflexive.     

General equilibrium in economies with uncertain delivery

We consider a general equilibrium model of trade ex ante with differential information in which agents choose plans of state-contingent lists of bundles. Being unable to verify that the state of nature is s and not t, an agent has to accept the delivery of any bundle in the list for delivery in state s or in the list for delivery in state t. Under the assumption that each state of nature can be verified by at least one agent, we establish existence of equilibrium and we show that the equilibrium allocation satisfies a notion of coalitional incentive compatibility.     

Saddle point property and Hopf bifurcation in continuous optimal growth models: a Lagrangian approach

Conditions for saddle point property, and the loss of it, have been widely studied. Generally these properties are established by means of a Hamiltonian formalism; we propose here to work without reference to any Hamiltonian system, and to use only the Lagrangian.Our study is local; it may seem that no new result can be obtained in this setting; nevertheless we establish sufficient conditions for the loss of saddle point property and for the existence of periodic orbits which, to our knowledge, are not found in the literature.We take the standard assumption that the Lagrangian is concave. It is well known that the cross derivatives of the Hamiltonian (i.e. H_xp(x, p)) are important in these problems, but the concavity-convexity property of the Hamiltonian does not easily give any information on these derivatives. On the other hand, we obtain such information directly in the Lagrangian version, because the Lagrangian is concave on its two arguments.We give here a self-contained version of our results and we do not hesitate to re-establish some well-known results, because we believe it is interesting to underline the straightforward aspect of the Lagrangian approach.