The testable implications of competitive equilibrium in economies with externalities

Suppose that one has a data set consisting of prices and individual endowments for some economy. Brown and Matzkin (Econometrica 64:1249–1262, 1996) have shown that there are conditions that the data have to satisfy, if the observed prices are determined by the competitive equilibrium process, given the observed endowments, when there are no external effects in the economy’s interactions. The results here show that the same conclusion does not apply, in general, if the economy exhibits externalities. On the other hand: (i) some restrictions exist if there exist at least two commodities on which the individuals’ preferences are weakly separable; (ii) although extremely mild, restrictions exist too if one observed individual consumption for the economy that causes the external effects; and (iii) importantly, even if the previous two cases do not apply, restrictions exist when the externalities that exist are in the form of a public good.     

Theory of negative consumption externalities with applications to the economics of happiness

This paper investigates the problem of obtaining Pareto efficient allocations in the presence of negative consumption externalities. In contrast to the conventional wisdom, we show that even if consumers’ preferences are monotonically increasing in their own consumption, one may have to dispose of resources to achieve Pareto efficiency when negative consumption externalities exist. We provide characterization results on destruction both for pure exchange economies and for production economies. As an application, our results provide an explanation to Easterlin’s paradox: average happiness levels do not increase as countries grow wealthier. We thank an anonymous referee, Xiaoyong Cao, Li Gan, and Tapan Mitra for helpful comments and suggestions that improved the exposition of the paper. The first author thanks the National Natural Science Foundation of China and Private Enterprise Research Center at Texas A&M University for financial support.     

Externalities, consumption constraints and regular economies

We consider a general model of pure exchange economies with consumption externalities. Households may have different consumption sets and each consumption set is described by a function called the possibility function. Utility and possibility functions depend on the consumptions of all households. Showing by means of an example that basic assumptions are not enough to guarantee generic regularity, we provide sufficient conditions for generic regularity in the space of endowments and possibility functions.     

An Afriat Theorem for the collective model of household consumption

We provide a nonparametric ‘revealed preference’ characterization of rational household behavior in terms of the collective consumption model, while accounting for general individual preferences that can be non-convex. Our main result is the Collective Afriat Theorem, which parallels the well-known Afriat Theorem for the unitary model. First, it provides a characterization of collectively rational consumption behavior in terms of collective Afriat inequalities. Next, it implies the Collective Axiom of Revealed Preference (CARP) as a testable necessary and sufficient condition for data consistency with collective rationality. Finally, the theorem has some interesting testability implications. With only a finite set of observations, the nature of consumption externalities (positive or negative) in the intra-household allocation process is non-testable. The same non-testability conclusion holds for privateness (with or without externalities) or publicness of consumption. By contrast, concavity of individual utility functions (representing convex preferences) turns out to be testable. In addition, monotonicity is testable for the model that assumes all household consumption is public.     

Relative consumption, economic growth, and taxation

This paper studies the influence of consumption externalities in the Ramsey model. In contrast to the recent literature, a quite general specification of preferences is used and the concept of the effective intertemporal elasticity of substitution is introduced. We give conditions for the observational equivalence between economies with consumption externalities and externality-free economies. An additional key result is that there exist several types of instantaneous utility functions in which the decentralized solution coincides with the socially planned one in spite of the presence of consumption externalities. The conditions for optimal taxation are also derived.     

Convergence of the Aumann–Davis–Maschler and Geanakoplos bargaining sets

Summary. Geanakoplos [17] defined a notion of bargaining set, and proved that his bargaining set is approximately competitive in large finite transferable utility (TU) exchange economies with smooth preferences. Shapley and Shubik [26] showed that the Aumann–Davis–Maschler bargaining set is approximately competitive in replica sequences of TU exchange economies with smooth preferences. We extend Geanakoplos result to nontransferable utility (NTU) exchange economies without smooth preferences, and we extend the Shapley and Shubik result to non-replica sequences of NTU exchange economies with smooth preferences.Received: November 11, 1996This revised version was published online in February 2005 with corrections to the cover date.     

General equilibrium with nonconvexities and money

In a general-equilibrium economy with nonconvexities, there are sunspot equilibria with good welfare properties; sunspots can ameliorate the effects of the nonconvexities. For these economies, we show that agents act as if they have quasi-linear utility functions. We use this result to construct a new model of monetary exchange along the lines of Lagos and Wright, where trade occurs in both centralized and decentralized markets, but instead of quasi-linear preferences we assume general preferences but with indivisible labor. This suggests that modern monetary theory is more robust than one might have thought. It also constitutes progress on the classic problem of integrating monetary economics and general-equilibrium theory.     

Existence of equilibria for economies with externalities and a measure space of consumers

Summary. This paper considers an exchange economy with a measure space of agents and consumption externalities, which take into account two possible external effects on consumers preferences: dependence upon prices and dependence upon other agents consumption. We first consider a model with a general externality mapping and we then treat the particular case of reference coalition externalities, in which the preferences of each agent a are influenced by prices and by the global or the mean consumption of the agents in finitely many (exogenously given) reference coalitions associated with agent a. Our paper provides existence results of equilibria in both models when consumers have transitive preferences. It extends in exchange economies the standard results by Aumann [2], Schmeidler [16], Hildenbrand [12], and previous results by Greenberg et al. [11] for price dependent preferences, Schmeidler [17] for fixed reference coalitions and Noguchi [15] for a more particular concept of reference coalitions. We also mention related results obtained independently by Balder [4].Received: 25 May 2004, Revised: 19 October 2004, JEL Classification Numbers: D62, D51, H23. Correspondence to: Bernard CornetThis paper has benefited from comments and valuable discussions with Erik Balder, Stefan Balint, Jean-Marc Bonnisseau, Alessandro Citanna, Gael Giraud, Filipe Martins-da-Rocha, Jean-Philippe Médecin, Jean-François Mertens, Nicholas Yannelis and an anonymous referee.     

Consumption externalities,production externalities,and long-run macroeconomic efficiency

We analyze the effects of consumption and production externalities on capital accumulation. We show that the importance of consumption externalities depends upon the elasticity of labor supply. If the labor supply is inelastic, consumption externalities cause no long-run distortions. Whether there are distortions along the transitional path depends upon consumer preferences. The effects of production externalities are more pervasive; they exert long-run distortionary effects irrespective of labor supply. The optimal taxation to correct for the distortions created by the externalities is characterized. We analyze both stationary and endogenously growing economies, and while there are many parallels in how externalities impact, there are also important differences.     

A complete characterization of Pareto optimality for general OLG economies

In the context of general pure exchange OLG economies where agents can have heterogeneous longevities, we provide both sufficient and necessary conditions for Pareto optimality of competitive equilibria. For the case in which all agents live for the same number of periods, we find that these conditions are equivalent. We also find this equivalence when agents can have different lifetimes, but in this case we need to impose particular restrictions on relative equilibrium prices. Moreover, we show that without these conditions on prices the equivalence, and hence a full characterization, is not necessarily obtained.     

WELFARE IMPLICATIONS OF THE INTERACTION BETWEEN HABITS AND CONSUMPTION EXTERNALITIES*

We analyze the welfare properties of the equilibrium path of a growth model where both habits and consumption externalities affect the utility of consumers. Our analysis highlights the crucial role played by complementarities between externalities and habits in order to generate an inefficient dynamic equilibrium. In particular, we show that the competitive equilibrium is inefficient when consumption externalities and habit‐adjusted consumption are not perfect substitutes.     

Identification of consumers’ preferences when their choices are unobservable

Summary. We provide conditions under which the heterogenous, deterministic preferences of consumers in a pure exchange economy can be identified from the equilibrium manifold of the economy. We extend those conditions to consider exchange economies, with two commodities, where consumers preferences are random. For the latter, we provide conditions under which consumers heterogenous random preferences can be identified from the joint distribution of equilibrium prices and endowments. The results can be applied to infer consumers preferences when their demands are unobservable.Received: 8 May 2003, Revised: 14 September 2004, JEL Classification Numbers: D12, D51.I am very grateful to an anonymous referee, Donald Brown, and Daniel McFadden for their detailed comments and insightful suggestions. Section 2 of this paper is joint work with Donald J. Brown; it is included here for publication with his permission. Those results were presented at the 1990 Workshop on Mathematical Economics at the University of Bonn, the 1992 SITE Workshop on Empirical Implications of General Equilibrium Models at Stanford University, and, more recently, at the June 2000 Conference in Honor of Rolf Mantel, in Buenos Aires, Argentina. The comments of the participants at those conferences and workshops are much appreciated. The research presented in this paper was supported by NSF Grants SES-8900291, SBR-9410182, and SES-0241858. This paper is dedicated to Marcel K. Richter, who has inspired much of my research.     

State-uncertainty preferences and the risk premium in the exchange rate market

This paper shows that state-uncertainty preferences help to explain the observed exchange rate risk premium. In the framework of Lucas (1982) economy, state-uncertainty preferences amount to assuming that a given level of consumption will yield a higher level of utility the lower is the level of uncertainty perceived by consumers. Under these preferences we can distinguish between two factors driving the exchange rate risk premium: “macroeconomic risk” and “the risk associated with variation in the private agents' perception on the level of uncertainty”. Empirical evidence from three main European economies in the transition period to the euro provides empirical support for the model. The model is more successful in accounting for the observed currency risk premium than models with more standard preferences, and the general perception of risk by private agents is shown to be a more important determinant of risk premium than macroeconomic uncertainty.     

Efficient strategy-proof exchange and minimum consumption guarantees

For exchange economies with classical economic preferences, it is shown that any strategy-proof social choice function that selects Pareto optimal outcomes cannot guarantee everyone a consumption bundle bounded away from the origin. This result demonstrates that there is a fundamental conflict between efficiency and distributional goals in exchange economies if the social choice rule is required to be strategy-proof.     

Rational expectations equilibria of economies with local interactions

We consider general economies in which rational agents interact locally. The local aspect of the interactions is designed to represent in a simple abstract way social interactions, that is, socioeconomic environments in which markets do not mediate all of agents’ choices, which might be in part determined, for instance, by family, peer group, or ethnic group effects. We study static as well as dynamic infinite horizon economies; we allow for economies with incomplete information, and we consider jointly global and local interactions, to integrate e.g., global externalities and markets with peer and group effects. We provide conditions under which such economies have rational expectations equilibria. We illustrate the effects of local interactions when agents are rational by studying in detail the equilibrium properties of a simple economy with quadratic preferences which captures, in turn, local preferences for conformity, habit persistence, and preferences for status or adherence to aggregate norms of behavior.     

A Unique Informationally Efficient Allocation Mechanism In Economies With Consumption Externalities*

This article investigates the informational requirements of resource allocation processes in pure exchange economies with consumption externalities. It is shown that the distributive Lindahl mechanism has a minimal informational size of the message space, and thus it is informationally the most efficient allocation process that is informationally decentralized and realizes Pareto‐efficient allocations over the class of economies that include nonmalevolent economies. Furthermore, it is shown that the distributive Lindahl mechanism is the unique informationally efficient decentralized mechanism that realizes Pareto‐efficient and individually rational allocations over a certain class of nonmalevolent economies.     

When redistribution makes personalized pricing of externalities useless

We consider a standard optimal taxation framework in which consumers' preferences are separable in consumption and labor and identical over consumption, but are affected by consumption externalities. For every nonlinear, income-dependent pricing of goods there is a linear pricing scheme, combined with an adjusted income tax schedule, that leaves all consumers equally well-off and weakly increases the government's budget. The result depends on whether a linear pricing scheme exists that keeps the aggregate amount of consumption at its initial level observed under nonlinear pricing. We provide sufficient conditions for the assumption to hold. If adjusting the income tax rate is not available, personalized prices for an externality can enhance social welfare if they are redistributive, that is, favor consumers with a larger marginal social value of income.     

Delay and information aggregation in stopping games with private information

We consider equilibrium timing decisions in a model with a large number of players and informational externalities. The players have private information about a common payoff parameter that determines the optimal time to invest. They learn from each other in real time by observing past investment decisions. We develop new methods of analysis for such large games, and we give a full characterization of symmetric equilibria. We show that the equilibrium statistical inferences are based on an exponential learning model. Although the beliefs converge to truth, learning takes place too late. Ex-ante welfare is strictly between that without observational learning and that with full information.     

Consumption externality, efficiency and optimal taxation in one-sector growth model

In an economy with consumption externalities, existing studies find that a competitive equilibrium is efficient in the long run and remains efficient in transitions if preferences are homothetic. This paper revisits the efficiency issue in an otherwise standard one-sector growth model where consumption externalities affect a utility via their effects on the time preference. We find that even if preferences are homothetic, the externality changes the marginal rate of substitution between now and future and leads to a disparity in the intertemporal elasticity of substitution between the centrally planned economy and a decentralized economy. As a result, a competitive equilibrium is inefficient in transition dynamics. We characterize an optimal tax/subsidy structure that enables the allocation in a decentralized economy to replicate the social optimum.     

Consumption externalities, production externalities, and efficient capital accumulation under time non-separable preferences

The effects of consumption and production externalities on economic performance under time non-separable preferences are examined both theoretically and numerically. We show that a consumption externality alone has long-run distortionary effects if and only if labor is supplied elastically. With fixed labor supply, it has only transitional distortionary effects. Production externalities always generate long-run distortions, irrespective of labor supply. The optimal tax structure to correct for the distortions is characterized. We compare the implications of this model with those obtained when the consumption externality is contemporaneous. While some of the long-run effects are robust, there are also important qualitative and quantitative differences, particularly along transitional paths.