ω‐Homothetic Preferences: Theory and Applications

This paper develops a new class of homothetic preferences which generate Marshallian demand curves for individual goods which can be concave, convex or linear in own price under the assumption that agents treat aggregate price indices as given (as in Dixit‐Stiglitz, 1977). The preferences are represented by a cost function which has two parameters: one determining the curvature of the Marshallian demand; the other determining the elasticity of demand when all prices are equal. The elasticity of demand varies with relative prices. Illustrative examples are given of Cournot duopoly and exchange rate pass‐through.     

Contracting with Diversely Naive Agents

In standard contract-theoretic models, the underlying assumption is that agent types differ in their preference or cost parameters, and the principal's objective is to design contracts in order to screen this type. We study a contract-theoretic model in which the heterogeneity among agent types is of a "cognitive" nature. In our model, the agent has dynamically inconsistent preferences. Agent types differ only in their degree of "sophistication", that is, their ability to forecast the change in their future tastes. We fully characterize the menu of contracts which the principal offers in order to screen the agent's sophistication. The menu does not exclude any type: it provides a perfect commitment device for relatively sophisticated types, and "exploitative" contracts which involve speculation with relatively naive types. More naive types are more heavily exploited and generate a greater profit for the principal. Our results allow us to interpret real-life contractual arrangements in a variety of industries.     

Naive traders and mispricing in prediction markets

This paper studies pricing patterns in a speculative market with asymmetric information populated by both sophisticated and naive traders. Three pricing regimes arise in equilibrium: perfect pricing, with prices equalling asset values, partial mispricing and complete mispricing. Perfect pricing obtains when the presence of naive traders is small although not necessarily zero. When the fraction of naive traders is moderate prices are correct for some values but not for others. Finally, complete mispricing typically arises when the presence of naive traders is sufficiently high. Mispricing exhibits a systematic pattern of overpricing low values and underpricing high values.     

Existence and fairness of value allocation without convex preferences

Shafer (Econometrica, 48 (1980), 467–476) proved that in a finite exchange economy value allocations exist, provided that each agent has convex, complete, transitive, compact and monotone preferences. However, if preferences are not convex, then value allocations may not exist. To remedy this difficulty we enlarge the set of value allocations by introducing the concept of approximate value allocations, and show that in a finite exchange economy approximate value allocations exist, even if preferences are not convex, or compact, or monotone. This value existence result can be used to provide a very general value existence theorem for a sequence of finite economies. Further, we show that value allocations may discriminate in favor of or against a coalition of agents.     

Work costs and nonconvex preferences in the estimation of labor supply models

Works costs have not been adequately handled in labor supply estimation, likely due to their complexity. We show that, if work costs are not accounted for in the budget and time constraints in a structural labor supply model, they will be subsumed into the data generating preferences. Even if underlying preferences over consumption and leisure are convex, the presence of unobservable work costs can make these preferences appear nonconvex. However, we show that, under plausible conditions, policy relevant calculations, such as estimates of the effect of tax changes on labor supply and deadweight loss measures, are not affected by the fact that estimated preferences incorporate work costs.     

A tangent cone analysis of smooth preferences on a topological vector space

Summary. A theory of smooth preferences on a locally convex, topological vector space is developed by characterizing the existence of a unique supporting hyperplane to a convex set at a given point. The results are expressed in terms of the tangent cone. A new concept of properness, called strict properness, is also proposed to characterize the existence of a strictly supporting hyperplane to a convex set at a given point. We say that strict preferences are properly smooth at a given point provided that they are smooth, strictly proper, and the secant cone has a non-empty interior. Proper smoothness is broadly consistent with Gâteaux-differentiable utility even when the preference domain has an empty interior. Yet proper smoothness also allows the possibility of incomplete or intransitive preferences. This concept has immediate applications to optimization and equilibrium theory. For example, we demonstrate a version of the Second Welfare Theorem for agents with properly smooth preferences.Received: 25 September 2002; revised version: February 5, 2003, Revised: 5 February 2003, JEL Classification Numbers: D46, D51.     

An experimental investigation of the explosive effect in almost common value auctions

With only two bidders, a slight private value advantage in a common value auction is predicted to have an explosive effect on the allocation and revenue of the auction when using a second price and/or English clock mechanism. This paper uses the “wallet game” in an English clock mechanism with two players to test these predictions. The results show that the effect is proportional, not explosive, confirming the results of past experiments. A behavioral model with two types of players, naive and sophisticated, is developed and tested against the experimental data. In the model, naive players use a rule of thumb bidding function, while the sophisticated players are fully rational and, when forming their strategy (choosing the best response), correctly account for the probability that a rival is naive or sophisticated. We use cluster analysis to classify the players in the symmetric auctions as naive or sophisticated and a strict win/lose criteria to classify players in the asymmetric auctions. We find that those players classified as sophisticated are more aggressive in responding to high signals or advantaged status than their naive counterparts, but do not lower their bids relative to the naive players when receiving low signals or when regular.     

EXCESSIVE COMPETITION ON HEADLINE PRICES

In a variety of purchasing situations, consumers may focus primarily on headline prices, disregarding the full costs associated with acquiring and maintaining a product or service contract. Even when this is the case, the literature has delineated various circumstances where intense competition can protect consumers through the so-called “waterbed effect.” In this article, we however show that when consumers have context-dependent preferences, competition may rather exacerbate their and society's harm by distorting product choice and provision. Then, consumer protection policy must sufficiently constrain hidden fees so that competition, along with high-quality firms' incentives to educate consumers, can restore efficiency.     

Selection in asset markets: the good, the bad, and the unknown

In this paper, we use a series of simple examples to illustrate how wealth-driven selection works in a market for Arrow securities. Our analysis delivers both a good and a bad message. The good message is that, when traders invest constant fractions of their wealth in each asset and have equal consumption rates, markets are informationally efficient: the best informed agent is rewarded and asset prices eventually reflect this information. However, and this is the bad message, when asset demands are not constant fractions of wealth but dependent upon prices, markets might behave sub-optimally. In this case, asymptotic prices depend on preferences and beliefs of the whole ecology of traders and do not, in general, reflect the best available information. We show that the key difference between the two cases lies in the local, i.e. price dependent, versus global nature of wealth-driven selection.     

Accounting for Preference and Scale Heterogeneity in Establishing Whether it Matters Who is Interviewed to Reveal Household Automobile Purchase Preferences

The choice of automobile purchases in households often involves participation of more than one household member, each of which exerts some degree of influence on the final choice outcome. The influence of more than one agent has been recognised for many years, and yet the majority of automobile choice studies develop choice models as if a single agent is involved in the preference revelation process. What is not clear is whether it makes any substantive difference in preference revelation according to who is interviewed in a household. Using a generalised mixed logit framework that accounts for preference and scale heterogeneity, we estimate a series of models to investigate whether there are significant differences between the preferences of each individual in a household when assessed in isolation from other household members, as well as their joint preferences when expressing their preferences through a group choice task. The context is choosing amongst petrol, diesel and hybrid fuelled vehicles (associated with specific levels of fuel efficiency and engine capacity) when faced with a mix of vehicle prices, fuel prices, fixed annual registration fees, annual emission surcharges and vehicle kilometre emission surcharges. Using a stated choice experiment, we find that sampling a single individual as a representative of the household’s preferences is less appropriate than utilising preference information from the relevant group of decision makers in the household.     

Arbitrage and equilibrium with portfolio constraints

We consider a multiperiod financial exchange economy with nominal assets and restricted participation, where each agent’s portfolio choice is restricted to a closed, convex set containing zero, as in Siconolfi (Non-linear Dynamics in Economics and Social Sciences, 1989). Using an approach that dates back to Cass (CARESS Working Paper, 1984; J Math Econ 42:384–405, 2006) in the unconstrained case, we seek to isolate arbitrage-free asset prices that are also quasi-equilibrium or equilibrium asset prices. In the presence of such portfolio restrictions, we need to confine our attention to aggregate arbitrage-free asset prices, i.e., for which there is no arbitrage in the space of marketed portfolios. Our main result states that such asset prices are quasi-equilibrium prices under standard assumptions and then deduces that they are equilibrium prices under a suitable condition on the accessibility of payoffs by agents, i.e., every payoff that is attainable in the aggregate can be marketed through some agent’s portfolio set. This latter result extends previous work by Martins-da-Rocha and Triki (Working Paper, University of Paris 1, 2005).     

Uniqueness of equilibrium in sealed high-bid auctions

For the case of two buyers we show that equilibrium in the sealed high-bid auction is unique when (i) buyers' reservations prices are drawn independently from distributions with finite support and positive mass at the lower endpoint; (ii) buyers have private values; and (iii) buyers' preferences are log supermodular. For more than two buyers, we obtain the same result under the additional assumptions that (iv) buyers with the same reservation price have the same preferences; (v) buyers are risk neutral or risk averse with non-increasing absolute risk aversion; and (vi) the supports of the different buyers' distributions of reservation prices have the same upper endpoint.     

Proper scoring rules for general decision models

If a decision maker whose behavior conforms to the max-min expected utility model is faced with a scoring rule for a subjective expected utility decision maker, she will always announce a probability belonging to her set of priors; moreover, for any prior in the set, there is a scoring rule inducing the agent to announce that prior. We also show that on the domain of Choquet expected utility preferences with risk neutral lottery evaluation and totally monotone capacities, proper scoring rules do not exist. This implies the non-existence of proper scoring rules for any larger class of preferences (CEU with convex capacities, multiple priors).     

Informational efficiency with ambiguous information

This paper proves the existence of fully revealing rational expectations equilibria for almost all sets of beliefs when investors are ambiguity averse and have preferences that are characterized by Choquet expected utility with a convex capacity. The result implies that strong-form efficient equilibrium prices exist even when many investors in the market make use of information in a way that is substantially different from traditional models of financial markets.     

Skewness,short interest and the efficiency of stock prices

We examine the association between return skewness, short interest and the efficiency of stock prices. Since preferences for skewness have been shown to impact asset prices, we examine how skewness relates to market efficiency. We find that stocks with positive skewness are less efficient, which might be explained by investor preferences for positive skewness. Next, we document that short interest reduces both total skewness and idiosyncratic skewness. Finally, while research has shown that short selling can improve the efficiency of markets generally, we show that short interest’s ability to improve market efficiency is strongest in stocks with the highest skewness.     

Aggregation under homogeneous ambiguity: a two-fund separation result

Contrary to the common prior model, the construction of a representative agent whose preferences follow the multiple-priors model (1989) requires strong restrictions on sets of priors and on an aggregate endowment process if we permit a large deviation among agents’ degrees of risk aversion. This paper shows that if agents’ felicity functions belong to a family of linear risk tolerance functions with the same marginal risk tolerance, the representative agent always exists at an interior equilibrium without such restrictions, and two-fund separation holdsI am grateful to a referee and to participants at the conference, Uncertainty in Economic Theory, held at Yale University (October 2004) for their valuable comments and suggestions     

Inflation,oil price volatility and monetary policy

In a fully micro-founded New Keynesian framework, we characterize an analytical relationship between average inflation and oil price volatility by solving the rational expectations equilibrium of the model up to second order of accuracy. The model shows that higher oil price volatility induces higher levels of average inflation. We also show that when oil has low substitutability in the production function, the higher the weight the central bank assigns to inflation in the policy rule, the lower the level of average inflation is. The analytical solution further indicates that, for a given level of oil price volatility, average inflation is higher when marginal costs are convex in oil prices, the Phillips Curve is convex, and the degree of relative price dispersion is higher. The evolution of inflation during the 70s and 80s is consistent with the prediction of the model.     

Privatization and Price Liberalization: Comparative Analysis

Two transition paths from a mixed to market economy are investigated: a gradual increase in state retail prices and a gradual decrease of the state sector's share of the economy. The analysis is carried out in the framework of a general equilibrium model of a mixed economy with production. It is shown that, for a representative agent, privatization is better than price liberalization during the entire transition period regardless of individual preferences. For an economy with heterogeneous agents the conclusion remains valid for rich agents, but it is indeterminate for poor agents.J. Comp. Econom.,June 1997,24(3), pp. 313–334. Central Institute of Economics and Mathematics, Moscow 117418, Russia.     

Speculative trade and the value of public information

In environments with expected utility, it has long been established that speculative trade cannot occur and that the value of public information is negative in economies with risk-sharing and no aggregate uncertainty. We show that these results are still true even if we relax expected utility, so that either Dynamic Consistency (DC) or Consequentialism is violated. We characterize no speculative trade in terms of a weakening of DC and find that Consequentialism is not required. Moreover, we show that a weakening of both DC and Consequentialism is sufficient for the value of public information to be negative. We therefore generalize these important results for convex preferences which contain several classes of ambiguity averse preferences.     

Existence, uniqueness and efficiency of equilibrium in hedonic markets with multidimensional types

We study equilibrium in hedonic markets, when consumers and suppliers have reservation utilities, and the utility functions are separable with respect to price. There is one indivisible good, which comes in different qualities; each consumer buys 0 or 1 unit, and each supplier sells 0 or 1 unit. Consumer types, supplier types and qualities can be either discrete of continuous, in which case they are allowed to be multidimensional. Prices play a double role: they keep some agents out of the market, and they match the remaining ones pairwise. We define equilibrium prices and equilibrium distributions, and we prove that equilibria exist, we investigate to what extend equilibrium prices and distributions are unique, and we prove that equilibria are efficient. In the particular case when there is a continuum of types, and a generalized Spence–Mirrlees condition is satisfied, we prove the existence of a pure equilibrium, where demand distributions are in fact demand functions, and we show to what extent it is unique. The proofs rely on convex analysis, and care has been given to illustrate the theory with examples.