Private Value Allocations in Large Economies with Differential Information

We consider a Radner-type (e.g., Radner, 1968, Econometrica36, 31–58) pure exchange economy with differential information and a continuum of agents. We show that under appropriate assumptions the set of Aumann–Shapley private value allocations in such an economy coincides with the set of Radner competitive equilibrium allocations. Journal of Economic Literature Classification Numbers: C71, D51, D82.     

Intertemporal consumption with directly measured welfare functions and subjective expectations

Euler equation estimation of intertemporal consumption models requires many, often unverifiable assumptions. These include assumptions on expectations and preferences. We aim at reducing some of these requirements by using direct subjective information on respondents’ preferences and expectations. The results suggest that individually measured welfare functions and expectations have predictive power for the variation in consumption across households. Furthermore, estimates of the intertemporal elasticity of substitution based on the estimated welfare functions are plausible and of a similar order of magnitude as other estimates found in the literature. The model favored by the data only requires cross-section data for estimation.     

When sunspots don't matter

Summary We show that a finite, competitive economy isimmune to sunspots if (i) preferences are strictly convex, (ii) the set of feasible allocations is convex, and (iii) the contingent-claims market is perfect. The conditions (i)–(ii) cover some, but not all, economies with nonconvex technologies. Based on an indivisible-good example, we show that even economies with strictly convex preferences and full insurance arenot in general immune from sunspots. We also show that (1) the sufficient conditions (i)–(iii) are not necessary for sunspot immunity and (2)ex-ante efficiency is not necessary for immunity from sunspots.This paper is based on an earlier paper, Indivisibilities in Production, and Sunspot Equilibrium, presented at the 1990 S.E.D.C. Meetings, Minneapolis-St. Paul, June 1990. The research support of NSF Grant SES-9012780, the Center for Analytic Economics, and the Thorne Fund is gratefully acknowledged.     

Equilibria in large economies with differentiated commodities and non-ordered preferences

Summary. The purpose of this paper is to provide an equilibrium existence result for economies with a measure space of agents, a finite set of producers and infinitely many differentiated commodities. The approach proposed in this paper, based on the discretization of measurable correspondences, allows us to extend the existence results in Ostroy and Zame (1994) and Podczeck (1997) to economies with a non-trivial production sector and with possibly non-ordered preferences. Moreover, our approach allows for more general consumption sets than the positive cone and following the direction introduced by Podczeck (1998), the uniform substitutability assumptions of Mas-Colell (1975), Jones (1983), and Ostroy and Zame (1994), are replaced by the weaker assumptions of uniform properness.Received: 11 June 2001, Revised: 6 March 2003, JEL Classification Numbers: C62, D51.Thanks to Charalambos D. Aliprantis, Erik J. Balder, Jean-Marc Bonnisseau, Bernard Cornet, Monique Florenzano, Konrad Podczeck, Rabee Tourky, Nicholas C. Yannelis and two anonymous referee for helpful discussions and suggestions.     

Subgame-perfect implementation of bargaining solutions

We study house allocation problems introduced by L. Shapley and H. Scarf (1974, J. Math. Econ.1, 23–28). We prove that a mechanism (a social choice function) is individually rational, anonymous, strategy-proof, and nonbossy (but not necessarily Pareto efficient) if and only if it is either the core mechanism or the no-trade mechanism, where the no-trade mechanism is the one that selects the initial allocation for each profile of preferences. This result confirms the intuition that even if we are willing to accept inefficiency, there exists no interesting strategy-proof mechanism other than the core mechanism. Journal of Economic Literature Classification Numbers: C71, C78, D71, D78, D89.     

Eliciting Preferences to Assign Positions and Compensation

We describe strategy-proof rules for economies where an agent is assigned a position (e.g., a job) plus some of a divisible good. For the 2-agent–2-position case we derive a robust characterization. For the multi-agent–position case, many “arbitrary” such rules exist, so we consider additional requirements. By also requiring coalitional strategy-proofness or nonbossiness, the range of a solution is restricted to the point that such rules are not more complex than those for the Shapley–Scarf housing model (no divisible good). Third, we show that essentially only constant solutions are immune to manipulations involving “bribes.” Finally, we demonstrate a conflict between efficiency and strategy-proofness. The results extend to models (without externalities) in which agents share positions. Journal of Economic Literature Classification Numbers: C72, D70.     

Extensive Form Games with Uncertainty Averse Players

Nash equilibrium presumes that the beliefs of a player are represented by a probability measure. Motivated by the Ellsberg Paradox and relevant experimental findings demonstrating that this representation of beliefs may be unrealistic, this paper generalizes Nash equilibrium in finite extensive form games to allow for preferences conforming to the multiple priors model developed by Gilboa and Schmeidler [Journal of Mathematical Economics, 18 (1989), 141–153]. The implications of this generalization for strategy choices and welfare are studied. Journal of Economic Literature Classification Numbers: C72, D81.     

Nonparametric Tests of Differences in Medians: Comparison of the Wilcoxon–Mann–Whitney and Robust Rank-Order Tests

The nonparametric Wilcoxon–Mann–Whitney test is commonly used by experimental economists for detecting differences in central tendency between two samples. This test is only theoretically appropriate under certain assumptions concerning the population distributions from which the samples are drawn, and is often used in cases where it is unclear whether these assumptions hold, and even when they clearly do not hold. Fligner and Pollicello's (1981, Journal of the American Statistical Association. 76, 162–168) robust rank-order test is a modification of the Wilcoxon–Mann–Whitney test, designed to be appropriate in more situations than Wilcoxon–Mann–Whitney. This paper uses simulations to compare the performance of the two tests under a variety of distributional assumptions. The results are mixed. The robust rank-order test tends to yield too many false positive results for medium-sized samples, but this liberalness is relatively invariant across distributional assumptions, and seems to be due to a deficiency of the normal approximation to its test statistic's distribution, rather than the test itself. The performance of the Wilcoxon–Mann–Whitney test varies hugely, depending on the distributional assumptions; in some cases, it is conservative, in others, extremely liberal. The tests have roughly similar power. Overall, the robust rank-order test performs better than Wilcoxon–Mann–Whitney, though when critical values for the robust rank-order test are not available, so that the normal approximation must be used, their relative performance depends on the underlying distributions, the sample sizes, and the level of significance used.     

On the Uniqueness of Equilibrium in Cournot Oligopoly and Other Games

In an average surplus sharing game, such as a Cournot oligopoly, a group of agents share a production process. Each contributes an amount of input to the process, and output is divided in proportion to the amount of input contributed. Uniqueness of the equilibrium is needed for any type of comparative static analysis. However, general uniqueness results for concave games have restrictive assumptions on preferences and technology; specifically, the conditions needed for uniqueness become more difficult to meet as the number of players increases. A new theorem for uniqueness with easily interpretable conditions is given which is independent of the number of players.Journal of Economic LiteratureClassification Numbers: C70, C72, D43.     

Subjective states: A more robust model

We study the demand for flexibility and what it reveals about subjective uncertainty. As in Kreps [D. Kreps, 1979. A representation theorem for ‘preference for flexibility’. Econometrica 47, 565–577], Nehring [K. Nehring, 1996. Preference for flexibility and freedom of choice in a Savage framework. UC Davis Working Paper; K. Nehring, 1999. Preference for flexibility in a Savage framework. Econometrica 67, 101–119] and Dekel et al. [E. Dekel, B. Lipman, A. Rustichini, 2001. Representing preferences with a unique subjective state space. Econometrica 69, 891–934], the latter is represented by a subjective state space consisting of possible future preferences over actions to be chosen ex post. One contribution is to provide axiomatic foundations for a range of alternative hypotheses about the nature of these ex post preferences. Secondly, we establish a sense in which the subjective state space is uniquely pinned down by the ex ante ranking of (random) menus. Finally, we demonstrate the tractability of our representation by showing that it can model the two comparative notions “2 desires more flexibility than 1” and “2 is more averse to flexibility-risk than is 1.”     

Equilibrium without prices: A central issue in pareto’smanuale

Pareto in hisManuale asserts that the price concept is inessential for the notion of equilibrium. This view deeply contrasts with the Arrow-Debreu’s dominant approach of Walrasian derivation. This identifies general equilibrium with a system of prices at which the decentralized choices of economic agents match. In this paper the author justifies and gives substance to the Paretian point of view. The differential merit of the Paretian approach is its independence of assumptions of price taking and of convexity in preferences and in production possibility sets. These assumptions are necessary, in the walrasian framework, only to maintain the centrality of prices, but they clash against the request of realism. (JEL:BOO, D51, D60)     

On the Existence of Stable Roommate Matchings

This paper identifies a condition called “no odd rings” that is sufficient for the existence of stable roommate matchings in the weak preferences case. It shows that the process of allowing randomly chosen blocking pairs to match converges to a stable roommate matching with probability one as long as there are no odd rings. This random-paths-to-stability result generalizes that of Roth and Vande Vate (1990, Econometrica58, 1475–1480) and may not hold if there are odd rings. The “no odd rings” condition can also be used to prove a number of other sufficient conditions that are more economically interpretable. Journal of Economic Literature Classification Numbers: C78, D71.     

House Allocation with Transfers

We consider the Shapley–Scarf house allocation problem where monetary transfers are allowed. We characterize the class of mechanisms that are strategy-proof, ex post individually rational, ex post budget-balanced, and “collusion-proof.” In these mechanisms, the price of each object is fixed in advance, and the objects are reallocated according to the (unique) core assignment of the Shapley–Scarf economy associated with the prices. The special case in which all prices are zero is the core mechanism studied by Shapley and Scarf. Our mechanisms are compelling alternatives to the Groves mechanisms, which satisfy neither budget balance nor our condition of collusion-proofness. Journal of Economic Literature Classification Numbers: C71, C78, D71, D78, D89.     

Cost Sharing under Increasing Returns: A Comparison of Simple Mechanisms

A technology with decreasing marginal costs is used by agents with equal rights. Each agent demands a quantity of output and costs are divided by means of a fixed formula. Several such mechanisms are compared for the existence of Nash equilibrium demand profiles and for the equity properties of these equilibria. Among three mechanisms, average cost pricing, the Shapley–Shubik cost sharing, and serial cost-sharing, only the latter two possess at least one Nash equilibrium on a reasonable domain of individual preferences. Only the serial cost sharing equilibria pass the equity tests of No Envy and Stand Alone cost.Journal of Economic LiteratureClassification Numbers: C72, D63.     

Determinacy of Equilibrium in an Overlapping Generations Model with Heterogeneous Agents

We study the determinacy of perfect foresight equilibrium near a steady state in an overlapping generations model with production and both altruistic and non-altruistic agents having distinct utility functions. The proportion of each type of consumer is exogenously given. Our main results show that when there are positive stationary bequests, some standard assumptions on preferences and technology rule out local indeterminacy for any positive value of the proportions. In the particular case of a separable utility function for altruistic agents, we prove that the determinacy property does not depend on the size of the “infinite lived” altruistic dynasties. Journal of Economic Literature Classification Numbers: C62, D91, O21, O41.     

Group incentive compatibility for matching with contracts

Hatfield and Milgrom [Hatfield, John William, Milgrom, Paul R., 2005. Matching with contracts. Amer. Econ. Rev. 95, 913–935] present a unified model of matching with contracts, which includes the standard two-sided matching and some package auction models as special cases. They show that the doctor-optimal stable mechanism is strategy-proof for doctors if hospitals' preferences satisfy substitutes and the law of aggregate demand. We show that the doctor-optimal stable mechanism is group strategy-proof for doctors under these same conditions. That is, no group of doctors can make each of its members strictly better off by jointly misreporting their preferences. We derive as a corollary of this result that no individually rational allocation is preferred by all the doctors to the doctor-optimal stable allocation.     

σ: The long and short of it

Research on the elasticity of substitution between capital and labor – σ – has been proceeding for 75 years. While there is clearly a strong case for the importance of σ in the analysis of growth and other economic issues, much less agreement exists on the value of σ. This paper offers some perspectives on prior estimates of σ, emphasizing the fundamental tension between the short-run data that are available and the long-run parameter that is required. Estimates of σ based on various short-run and long-run models are discussed and, while the estimates range widely, the weight of the evidence suggests a value of σ in the range of 0.40–0.60. There is little evidence to sustain the assumption of a Cobb–Douglas production function.     

Negative externalities and Sen’s liberalism theorem

Summary. Sen’s seminal, negative theorem about minimal liberalism has had a profound effect on economics, philosophy, and the social sciences. To address concerns raised by his result, we show how Sen’s assumptions must be modified to obtain positive conclusions; e.g., one resolution allows an agent to be decisive only if his choice does not impose “strong negative externalities” on others. We also uncover a significantly different interpretation of Sen’s societal cycles: rather than describing the rights of individuals to choose, the cycles identify when these choices impose difficulties on others. Other ways to address Sen’s difficulties come from game theory.Received: 14 October 2004, Revised: 7 March 2005, JEL Classification Numbers: D71, C70, D62.Donald G. Saari: Correspondenc toThe research of D. Saari was supported by NSF grant DMI-0233798. Our thanks to P. Hammond for suggesting some useful references. Some of our joint results were reported in Brunel (now Petron) (1998).     

The income–pollution relationship and the role of income distribution: An analysis of Swedish household data

The main purpose of this study is to analyze the relationship between pollution and income at household level. The study is motivated by the recent literature emphasizing the importance of income distribution for the aggregate relation between pollution and income. The main findings from previous studies are that if the individual pollution–income relationship is non-linear, then aggregate pollution for, say, a whole country, will depend not only on average income, but also on how income is distributed. To achieve our objective we formulate a model for determining the choice of consumption of goods in different types of household. Furthermore we link the demand model to emission functions for various goods. The theoretical analysis shows that without imposing very restrictive assumptions on preferences and the emission functions, it is not possible to determine a priori the slope or the curvature of the pollution–income relation. The empirical analysis shows that, given the model used, the pollution–income relation has a positive slope in Sweden and is strictly concave for all three pollutants under study (CO₂, SO₂, NO_x), at least in the neighbourhood of the observed income for an average household. We also show that altering the prevailing income distribution, holding average income constant, will affect aggregate emissions in the sense that an equalization of incomes will give rise to an increase in emissions. One implication is then that the development of aggregate pollution due to growth depends not only on the income level, but also on how growth is distributed.     

Subjective Expected Utility Theory with State-Dependent Preferences

This paper extends Savage′s subjective expected utility theory to include state-dependent preferences. The dependence of the decision maker′s preferences over consequences on the states of nature is represented by state-specific mappings of the set of consequences onto itself. Within this framework Savage′s postulates are reformulated and it is shown that there exist subjective expected utility representations of the preference relation over acts with unique, nonatomic, probability measure on the algebra of all events, and a state-dependent utility function over the set of consequences. Journal of Economic Literature Classification Number: D81.