Arbitrage and equilibrium in unbounded exchange economies with satiation

In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner’s existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations. Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. First, we show that in unbounded exchange economies, even if some agents’ preferences are satiated, the absence of arbitrage is sufficient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades– that is, as long as agents’ preferences satisfy weak nonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation – a condition considerably weaker than local or global nonsatiation – that makes possible this transformation.     

Erratum to “Walras and dividends equilibrium with possibly satiated consumers”

The main contribution of the paper is to provide a weaker nonsatiation assumption than the one commonly used in the literature to ensure the existence of competitive equilibrium. Our assumption allows for satiation points in the set of individually feasible consumptions, provided that the consumer has satiation points available to him outside this set. As a result, we show the concept of equilibrium with dividends (see Aumann, R.J., Drèze, J.H., 1986. Values of markets with satiation or fixed prices. Econometrica 54, 1271–1318; Mas-Collel, A., 1992. Equilibrium theory with possibly satiated preferences. In: Majumdar, M. (Ed.), Equilibrium and Dynamics: Proceedings of the Essays in Honour of David Gale. MacMillan, London, pp. 201–213) is pertinent only when the set of satiation points is included in the set of individually feasible consumptions. Our economic motivation stems from the fact that in decentralized markets, increasing the incomes of consumers through dividends, if it is possible, is costly since it involves the intervention of a social planner. Then, we show, in particular, how in securities markets our weak nonsatiation assumption is satisfied by Werner’s (1987) assumption.     

Hierarchic competitive equilibria

Without an interiority or strong survival assumption, an equilibrium may not exist in the standard Arrow–Debreu model. We propose a generalized concept of competitive equilibrium, called hierarchic equilibrium. Instead of using standard prices we use hierarchic prices. Existence will be shown without a strong survival assumption and without a non-satiation condition on the preferences. Under standard assumptions this reduces to the Walras equilibrium. Hierarchic equilibria are weakly Pareto optimal and any Pareto optimum can be decentralized without a border condition. We prove the existence of a Pareto optimal hierarchic equilibrium under additional assumptions. Later, we establish a core equivalence result.     

Multi-lateral strategic bargaining without stationarity

This paper establishes existence of subgame perfect equilibrium in pure strategies for a general class of sequential multi-lateral bargaining games, without assuming a stationary setting. The only required hypothesis is that utility functions are continuous on the space of economic outcomes. In particular, no assumption on the space of feasible payoffs is needed. The result covers arbitrary and even time-varying bargaining protocols (acceptance rules), externalities, and other-regarding preferences. As a side result, we clarify the meaning of assumptions on “continuity at infinity.”     

Double implementation of the Lindahl equilibrium by a continuous mechanism

We consider a class of economies with public goods that have the following properties: (i) The preferences of the agents are convex, interior, and strictly increasing. (ii) The technology for production of public goods is a closed convex cone that satisfies free disposal and an additional mild assumption. No assumptions are made on continuity, completeness or transitivity of preferences. We provide a continuous and feasible mechanism that implements the Lindahl equilibrium by Nash equilibria, and has the following property: For every economy in our class every Nash equilibrium of the game induced by the mechanism is a strong Nash equilibrium.     

An existence theorem for Cournot–Walras equilibria in a monopolistically competitive economy

We establish an existence theorem for Cournot–Walras equilibria in a monopolistically competitive economy. Instead of the traditional approach which depends on Kakutani’s fixed point theorem, we employ the theories of aggregative games and best reply potential games. We show that, if there exists a representative consumer, under some conditions on preferences and production technologies, the profit maximization game is a (pseudo) best reply potential game. Hence, the existence of the equilibria is proved independently of the well known convex-valued assumption on the best responses. Although our assumptions result in the additive separability on a utility function of a representative consumer, the existence of increasing returns and indivisible productions can be allowed. In our model, it is shown that the game played by firms exhibits strategic substitutes whether the products of firms are substitutes or complements, and this plays an important role for the existence of the equilibria.     

ML– and semiparametric estimation in logistic models with incomplete covariate data

ML–estimation of regression parameters with incomplete covariate information usually requires a distributional assumption regarding the concerned covariates that implies a source of misspecification. Semiparametric procedures avoid such assumptions at the expense of efficiency. In this paper a simulation study with small sample size is carried out to get an idea of the performance of the ML–estimator under misspecification and to compare it with the semiparametric procedures when the former is based on a correct assumption. The results show that there is only a little gain by correct parametric assumptions, which does not justify the possibly large bias when the assumptions are not met. Additionally, a simple modification of the complete case estimator appears to be nearly semiparametric efficient.     

Resource-envy-free and efficient allocations: A new solution for production economies with dedicated factors

I consider the problem of determining an equitable and efficient allocation of resources in production economies with factors which must be dedicated to production and cannot be consumed directly. First, I show that in such economies envy-free and efficient allocations exist under standard assumptions. However, I argue this notion of fairness is unsuitable for the present context. I then introduce a new notion of fairness, which I call resource-envy-freeness. First, I associate with each consumption bundle its resource footprint consisting of the vector of factors used to produce it. I then show that preferences over consumption bundles can be extended to preferences over factor bundles. An allocation is resource-envy-free if no agent prefers another agent’s resource footprint to its own. The analysis of resource-envy-free allocations in production is exactly analogous to the analysis of envy-free allocations in exchange. I establish that resource-envy-free and efficient allocations exist under standard assumptions, and I demonstrate that such allocations are intuitively appealing.     

Equilibrium theory with a measure space of possibly satiated consumers

Walras equilibria may not exist when consumers’ preferences are possibly satiated. To overcome this difficulty, several extended notions of equilibria have been proposed and all reduce to Walras equilibria under nonsatiation and free disposal. This includes the notions of equilibria with slack (also called dividend equilibria) as by Drèze and Müller [J. Economic Theory 23 (1980) 131], Makarov [J. Mathematical Economics 8 (1981) 87], Aumann and Drèze [Econometrica 54 (1986) 1271], Mas-Colell [Equilibrium theory with possibly satiated preferences, in: Majumdar, M. (Ed.), Proceedings of the Essays in Honour of David Gale on Equilibrium and Dynamics, Macmillan, London, pp. 201–213], monetary equilibria as by Kajii [J. Mathematical Economics 25 (1996) 75], or weak equilibria as by Polemarchakis and Siconolfi [J. Mathematical Economics 22 (1993) 85], which are all defined when there are finitely many consumers. This includes also the notion of free disposal equilibrium, when markets clear in a weak sense, allowing free disposal. Our paper considers an economy with a measure space of consumers and provides a general existence result of equilibria for the various existing notions. This result extends in particular the result by Hildenbrand [Econometrica 38 (1970) 608] on the existence of Walras equilibria.     

Inconsequential arbitrage

We introduce the concept of inconsequential arbitrage and, in the context of a model allowing short-sales and half-lines in indifference surfaces, prove that inconsequential arbitrage is sufficient for existence of equilibrium. Moreover, with a slightly stronger condition of nonsatiation than that required for existence of equilibrium and with a mild uniformity condition on arbitrage opportunities, we show that inconsequential arbitrage, the existence of a Pareto optimal allocation, and compactness of the set of utility possibilities are equivalent. Thus, when all equilibria are Pareto optimal — for example, when local nonsatiation holds — inconsequential arbitrage is necessary and sufficient for existence of an equilibrium. By further strengthening our nonsatiation condition, we obtain a second welfare theorem for exchange economies allowing short sales.Finally, we compare inconsequential arbitrage to the conditions limiting arbitrage of Hart [Hart, O.D., 1974. J. Econ. Theory 9, 293–311], Werner [Werner, J., 1987. Econometrica 55, abs1403–1418], Dana et al. [Dana, R.A., Le Van, C., Magnien, F., 1999. J. Econ. Theory 87, 169–193] and Allouch [Allouch, N., 1999. Equilibrium and no market arbitrage. CERMSEM, Universite de Paris I]. For example, we show that the condition of Hart (translated to a general equilibrium setting) and the condition of werner are equivalent. We then show that the Hart/Werner conditions imply inconsequential arbitrage. To highlight the extent to which we extend Hart and Werner, we construct an example of an exchange economy in which inconsequential arbitrage holds (and is necessary and sufficient for existence), while the Hart/Werner conditions do not hold.     

A dual approach to ambiguity aversion

In the present paper, the assumption of monotonicity of Anscombe and Aumann (1963) is replaced by an assumption of monotonicity with respect to first-order stochastic dominance. This yields a representation result where ambiguous distributions of objective beliefs are first aggregated into “equivalent unambiguous beliefs” and then risk preferences are used to compute the utility of these equivalent unambiguous beliefs. Such an approach makes it possible to disentangle uncertainty aversion, related to the processing of information, from risk aversion, related to the evaluation of the equivalent unambiguous beliefs. An application to portfolio choice shows the tractability of the framework and its intuitive appeal.     

When Do Outsider CEOs Generate Strategic Change? The Enabling Role of Corporate Stability

When academic researchers, business commentators, and boards of directors have debated the merits of hiring new CEOs from outside the firm, the implicit or explicit assumption typically made is that outsider CEOs will provide an advantage in achieving strategic change. In this study, we challenge this assumption by employing a duality perspective on stability/change, and we provide an original conceptual framework to posit that it is the presence of corporate stability (ordinary succession, a long‐tenured predecessor CEO, and good firm performance) that allows outsider CEOs to generate a greater degree of post‐succession strategic change. We use extensive longitudinal data from US airline and chemical industries between 1972 and 2010 to test our hypotheses, and we discuss how our supportive findings challenge long‐standing assumptions regarding the outsider succession–strategic change relationship, and we advocate embracing the non‐intiutive notion that stable (unstable) conditions can be enablers (barriers) of strategic change for outsider CEOs.     

The impact of referendums on the centralisation of public goods provision: a political economy approach

The paper compares decision-making on the centralisation of public goods provision in the presence of regional externalities under representative and direct democratic institutions. A model with two regions, two public goods and regional spillovers is developed in which uncertainty over the true preferences of candidates makes strategic delegation impossible. The political economy argument against centralisation of Besley and Coate (J Public Econ 87:2611–2637, 2003) does therefore not apply. Instead, it is shown that the existence of rent extraction by delegates alone suffices to make cooperative centralisation more likely through representative democracy under reasonable assumptions. In the case of non-cooperative centralisation, the more extensive possibilities for institutional design under representative democracy increase the likelihood of centralisation. Direct democracy may thus be interpreted as a federalism-preserving institution.     

Existence of marginal pricing equilibria in economies with externalities and non-convexities

We consider a general equilibrium model with externalities and non-convexities in production. The consumption sets, the preferences of the consumers and the production possibilities are represented by set-valued mappings to take into account possibility of external effects. There is no convexity assumption on the correspondences of production. We propose a definition of the marginal pricing rule, which generalizes the one used in the model without externality and, which satisfies a continuity assumption with respect to the external effect.We prove the existence of general equilibria under assumptions which allow us to encompass together the works on economies with externalities and convex conditional production sets, and those on marginal pricing equilibria in economies without externalities. We provide examples to illustrate the definition of the marginal pricing rule and to show the difference with the standard case.     

Intertemporal choice with different short-term and long-term discount factors

This paper proposes a new axiomatic model of intertemporal choice that allows for dynamic inconsistency. We weaken the classical assumption of stationarity into two related axioms: stationarity in the short-term and stationarity in the long-term. We obtain a model with two independent discount factors, which is flexible enough to capture different time preferences, including a greater impatience for more immediate outcomes (when a long-term discount factor exceeds a compounded short-term discount factor). Our proposed model can accommodate some experimental results that cannot be rationalized by other existing models of dynamic inconsistency (such as quasi-hyperbolic discounting and generalized hyperbolic discounting).     

Fuzzy Pair-wise Dominance and Implications for Technical Efficiency Performance Assessment

Classically, the concept of efficiency measurement is based on the definition of a frontier that envelops the observed production plans. The efficiency score itself is based on the distance of an observed production plan from this frontier. The frontier along with the required technological assumptions (such as convexity) needed for its definition may be replaced with the concept of pair-wise dominance. This concept leads to a classification scheme for all production plans instead of a ranking based on efficiency scores. Also, the traditional assumption of deterministic or crisp production plans may be substituted with the weaker assumption of fuzzy production plans as proposed by fuzzy set theory. This paper merges these two concepts and defines a new classification scheme based on fuzzy dominance.     

Trading Partners and Trading Volumes: Implementing the Helpman–Melitz–Rubinstein Model Empirically

Helpman, Melitz and Rubinstein [Quarterly Journal of Economics (2008) Vol. 123, pp. 441–487] (HMR) present a rich theoretical model to study the determinants of bilateral trade flows across countries. The model is then empirically implemented through a two‐stage estimation procedure. We argue that this estimation procedure is only valid under the strong distributional assumptions maintained in the article. Statistical tests using the HMR sample, however, clearly reject such assumptions. Moreover, we perform numerical experiments which show that the HMR two‐stage estimator is very sensitive to departures from the assumption of homoskedasticity. These findings cast doubts on any inference drawn from the empirical implementation of the HMR model.     

Equilibria in vector lattices without ordered preferences or uniform properness

This paper extends a result by Mas-Colell and Richard (Journal of Economic Theory, 1991, 53, 1–11) on the existence of an equilibrium for exchange economies over a vector lattice to cover non-ordered preferences. Moreover, it is shown that the uniformity requirement in the properness assumption made by these authors can be weakened. Furthermore, it is shown that, as a consequence of properness, an equilibrium allocation which is supported by a discontinuous prices can also be supported by continuous prices.     

Robustness issues in structural equation modeling: a review of recent developments

In structural equation modeling the statistician needs assumptions inorder (1) to guarantee that the estimates are consistent for the parameters of interest, and (2) to evaluate precision of the estimates and significance level of test statistics. With respect to purpose (1), the typical type of analyses (ML and WLS) are robust against violation of distributional assumptions; i.e., estimates remain consistent or any type of WLS analysis and distribution of z. (It should be noted, however, that (1) is sensitive to structural misspecification.) A typical assumption used for purpose (2), is the assumption that the vector z of observable follows a multivariate normal distribution.In relation to purpose (2), distributional misspecification may have consequences for efficiency, as well as power of test statistics (see Satorra, 1989a); that is, some estimation methods may bemore precise than others for a given specific distribution of z. For instance, ADF-WLS is asymptotically optimal under a variety of distributions of z, while the asymptotic optimality of NT-WLS may be lost when the data is non-normal