A MARKET WITH A SOCIAL CONSUMPTION EXTERNALITY*

We model a spatial market in which the utility of each consumer is affected by the consumers who buy precisely the same product. The marginal contribution of consumers x's purchase on consumer y depends on |x–y|, which declines as |x–y| increases. Such modelling of preferences fits goods that signal a consumer's place in society—clothing styles, automobiles and jewellry are examples. For 2n + 1 firms we find the unique symmetric equilibrium and derive comparative statics on the optimal number of firms, the largest number of firms the market can support, and the behaviour of profits per firm as n increases.     

Measuring Beliefs in an Experimental Lost Wallet Game

We measure beliefs in an experimental game. Player 1 may take x < 20 Dutch guilders, or leave it and let player 2 split 20 guilders between the players. We find that the higher is x (our treatment variable), the more likely is player 1 to take the x. Out of those who leave the x, many expect to get back less than x. There is no positive correlation between x and the amount y that 2 allocates to 1. However, there is positive correlation between y and 2's expectation of 1's expectation of y. Journal of Economic Literature Classification Numbers: C72, C92.     

Paying the expected externality for a price quote achieves bargaining efficiency

A seller and buyer have reservation prices x and y. Each has a subjective distribution on the other's reservation price. Paying an offer or the expected benefit the other participant receives from his offer induces honest price quotations, hence efficiency: sale iff y> x.     

When is multidimensional screening a convex program?

A principal wishes to transact business with a multidimensional distribution of agents whose preferences are known only in the aggregate. Assuming a twist (= generalized Spence-Mirrlees single-crossing) hypothesis, quasi-linear utilities, and that agents can choose only pure strategies, we identify a structural condition on the value b(x,y) of product type y to agent type x — and on the principal?s costs c(y) — which is necessary and sufficient for reducing the profit maximization problem faced by the principal to a convex program. This is a key step toward making the principal?s problem theoretically and computationally tractable; in particular, it allows us to derive uniqueness and stability of the principal?s optimal strategy — and similarly of the strategy maximizing the expected welfare of the agents when the principal?s profitability is constrained. We call this condition non-negative cross-curvature: it is also (i) necessary and sufficient to guarantee convexity of the set of b-convex functions, (ii) invariant under reparametrization of agent and/or product types by diffeomorphisms, and (iii) a strengthening of Ma, Trudinger and Wang?s necessary and sufficient condition (A3w) for continuity of the correspondence between an exogenously prescribed distribution of agents and of products. We derive the persistence of economic effects such as the desirability for a monopoly to establish prices so high they effectively exclude a positive fraction of its potential customers, in nearly the full range of non-negatively cross-curved models.     

A strategy-proofness characterization of majority rule

Summary. A feasible alternative x is a strong Condorcet winner if for every other feasible alternative y there is some majority coalition that prefers x to y. Let (resp., denote the set of all profiles of linear (resp., merely asymmetric) individual preference relations for which a strong Condorcet winner exists. Majority rule is the only non-dictatorial and strategy-proof social choice rule with domain , and majority rule is the only strategy-proof rule with domain . Received: August 29, 2000; revised version: November 13, 2002 RID="*" ID="*"We are grateful to Wulf Gaertner and our two referees for insightful comments on a previous draft. Correspondence to: D. E. Campbell     

Efficiency First or Equity First? Two Principles and Rationality of Social Choice

This paper formalizes two different principles to socially rank allocations under efficiency-equity trade off. The efficiency-first social preference relation ranks an allocation x higher than an allocation y if and only if (i) x is Pareto-superior to y or (ii) x and y are Pareto-noncomparable and x is equity-superior to y. The equity-first social preference relation reverses the order of application of the two criteria. We show that the efficiency-first relation may have a cycle, whereas the equity-first relation is transitive. We also characterize and compare the sets of maximal elements for these social preference relations in the Edgeworth box and examine the nonemptiness of the sets. Journal of Economic Literature Classification Numbers: D71, D63, D61.     

Health care utilization and self-assessed health: specification of bivariate models using copulas

The discernment of relevant factors driving health care utilization constitutes one important research topic in health economics. This issue is frequently addressed through specification of regression models for health care use (y—often measured by number of doctor visits) including, among other covariates, a measure of self-assessed health (sah). However, the exogeneity of sah within those models has been questioned, due to the possible presence of unobservables influencing both y and sah, and because individuals’ health assessments may depend on the quantity of medical care received. This article addresses the possible simultaneity of (sah, y) by adopting a full information approach, through specification of the bivariate probability function (p.f.) of these discrete variables, conditional on a set of exogenous covariates (x). The approach is implemented with copula functions, which afford separate consideration of each variable margin and their dependence structure. The specification of the joint p.f. of (sah, y) enables estimation of several quantities of potential economic interest, namely features of the conditional p.f. of y given sah and x. The adopted models are estimated through maximum likelihood, with cross-sectional data from the Portuguese National Health Survey of 1998–1999. Estimates of the margins’ parameters do not vary much among different copula models, while, in accordance with theoretical expectations, the dependence parameter is estimated to be negative across the various joint models.     

Recursive preferences and balanced growth

We study a class of utility functions that are defined recursively by an aggregator W(x,y) where u_t=W(c_t,u_t+1). In single-agent economies it is known that a sufficient condition for the existence of a balanced growth path is that utility should be homogenous of degree γ. In the context of a multi-agent economy we show that this restriction implies that either a balanced growth equilibrium fails to exist or all agents have the same constant discount factor. We suggest a generalization of recursive preferences wherein the intertemporal utility function is time dependent. Within this class we establish that there may exist a balanced growth equilibrium even if agents are different.     

Choice and individual welfare

We propose an abstract method of systematically assigning a “rational” ranking to non-rationalizable choice data. Our main idea is that any method of ascribing welfare to an individual as a function of choice is subjective, and depends on the economist undertaking the analysis. We provide a simple example of the type of exercise we propose. Namely, we define an individual welfare functional as a mapping from stochastic choice functions into weak orders. A stochastic choice function (or choice distribution) gives the empirical frequency of choices for any possible opportunity set (framing factors may also be incorporated into the model). We require that for any two alternatives x and y, if our individual welfare functional recommends x over y given two distinct choice distributions, then it also recommends x over y for any mixture of the two choice distributions. Together with some mild technical requirements, such an individual welfare functional must weight every opportunity set and assign a utility to each alternative x which is the sum across all opportunity sets of the weighted probability of x being chosen from the set. It therefore requires us to have a “prior view” about how important or representative a choice of x at a given situation is.     

On relationships between numerical representations of interval orders and semiorders

The extent to which continuous numerical representations of interval orders are unique is considered. Apair of continuous, real-valued functions, <u, v>, represents an interval order, <X, >>, provided that for x, y ϵ X, x > y if and only if u(x) > v(y). Relationships which necessarily hold between any two such numerical representations are presented and a method by which one continuous representation can be derived from another is described. Similar considerations are made for special forms of continuous numerical representations of semiorders.     

Resource egalitarianism with a dash of efficiency

We study the problem of defining inequality-averse social orderings over allocations of commodities when individuals have different preferences. We formulate a notion of egalitarianism based on the axiom that any dominance between consumption bundles should be reduced. This Dominance Aversion requirement is compatible with Consensus, a version of the Pareto principle saying that an allocation y is better than x whenever everybody finds that everyone?s bundle at y is better than at x. We characterize a family of multidimensional leximin orderings satisfying Dominance Aversion and Consensus.     

Numerical representation of intransitive preferences on a countable set

Let > be a preference relation on a countable set X. We prove that if > is acyclic (that is, has irreflexive transitive closure), then there exists a mapping u of X into $\text{R}$ such that x > y entails u(x)>u(y). We also give a simple proof of a representation theorem of Fishburn when > is an interval order.     

Undominated directions of tax reform

This article considers the reform of a commodity tax system. Consumers' preferences over directions of tax reform are constructed from indirect utility functions. A Wicksellian decision procedure is used to define a dominance relation on the set of directions of change; direction x dominates direction y if and only if (a) everybody prefers x to y or (b) x is the status quo and at least one person prefers x to y. A number of characterizations of undominated directions of change are provided. A related unanimity rule procedure, which does not single out the status quo for special treatment, is also considered. Particular attention is paid to the issue of whether Wicksellian reforms preserve production efficiency. Remarks on the relationship between this work, previous work in optimal taxation theory, and social choice theory are also provided.     

COHERENCY AND COMPLETENESS OF STRUCTURAL MODELS CONTAINING A DUMMY ENDOGENOUS VARIABLE*

Let y be a vector of endogenous variables and let w be a vector of covariates, parameters, and errors or unobservables that together are assumed to determine y. A structural model y=H(y, w) is complete and coherent if it has a well‐defined reduced form, meaning that for any value of w there exists a unique value for y. Coherence and completeness simplifies identification and is required for many estimators and many model applications. Incoherency or incompleteness can arise in models with multiple decision makers, such as games, or when the decision making of individuals is either incorrectly or incompletely specified. This article provides necessary and sufficient conditions for the coherence and completeness of simultaneous equation systems where one equation is a binomial response. Examples are dummy endogenous regressor models, regime switching regressions, treatment response models, sample selection models, endogenous choice systems, and determining if a pair of binary choices are substitutes or complements.     

Algebra of Integrated Time Series: Evidence from Unit Root Analysis

It is argued if x_t ~ I(1) and y_t ~ I(1), then running a regression x_t on y_t would produce spurious results because e _t would generally be I(1). However, there may exist a ‘b’ such that e _t  = x _t - by _t is I(0), then running a regression x _t on y _t would not produce spurious results. This special case of two integrated time series is known in the literature as cointegration. In this particular case, x _t and y _t are said to be cointegrated. In our review of the development of the concept of cointegration, we identified that the underlying reason for this special case to arise is the proposition that if x _t  ~ I(d _x ), y _t  ~ I(d _y ), then z _t  = bx _t  + cy _t  ~ I(max(d _x ,d _y )). In this research, we offer evidence against this proposition.     

Estimation of Binary Response Models With Endogenous Regressors

This paper reviews six approaches to binary response (y₁) structural forms with an endogenous regressor y₂: (i) the two‐stage least squares estimator‐like substitution approach, (ii) the control function approach, (iii) the system reduced‐form approach, (iv) the artificial instrumental regressor approach, (v) the transformed‐response instrumental variable estimator approach and (vi) the classical maximum likelihood estimator approach. The applicability of the six methods differs greatly, depending on whether y₂ is a continuously distributed random variable or a discrete transformation of a latent . We conduct a real‐data‐based simulation study, and provide an empirical illustration. Our overall recommendation is using (i) and (ii), as the others have undesirable features such as analytic complexity in (iii), computational difficulty in (iv) and (vi), and poor finite‐sample performance in (v).     

A note on asymmetric and mixed strategy equilibria in the search-theoretic model of fiat money

Summary. The simple search-theoretic model of fiat money has three symmetric Nash equilibria: all agents accept money with probability 1; all agents accept money with probability 0; and all agents accept money with probability y in (0,1). Here I construct an asymmetric pure strategy equilibrium, payoff-equivalent to the symmetric mixed strategy equilibrium, where a fraction N in (0,1) of agents always accept money and 1-N never accept money. Counter to what has been conjectured previously, I find N > y. I also introduce evolutionary dynamics, and show that the economy converges to monetary exchange iff the initial proportion of agents accepting money exceeds N. Received: September 10, 1997; revised version: April 24, 1998     

Lebesgue measure and social choice trade-offs

Summary An Arrovian social choice rule is a social welfare function satisfying independence of irrelevant alternatives and transitivity of social preference. Assume a measurable outcome spaceX with its (Lebesgue) measure normalized to unity. For any Arrovian rule and any fractiont, either some individual dictates over a subset ofX of measuret or more, or at least a fraction 1–t of the pairs of distinct alternatives have their social ordering fixed independently of individual preferences. Also, for any positive integer (less than the total number of individuals), there is some subsetH of society consisting of all but persons such that the fraction of outcome pairs (x, y) that are social ranked without consulting the preferences of anyone inH, whenever no individual is indifferent betweenx andy, is at least 1–1/4.We are grateful to Roy Mathias and Daniel Waterman for help with some technical matters, and to chairman Jim Follain and the Syracuse University Economics Department for financing the exchange that launched this project. Campbell's research was funded by National Science Foundation grants, SES 9007953 and SES 9209039.     

Representing interval orders by a single real-valued function

Let > be an interval order on a topological space X, and let $\text{x > 1 y}$ if and only if there exists x′ with $\text{x?x′>y}$. Then >1 is a preference relation with transitive indifference, which, under suitable conditions, can be represented by a utility function v of the usual sort. In that case, maximisation of v (subject to contraints) leads to a most preferred point relative to >. Following both the Debreu-Rader and the Arrow-Hahn approaches, we discuss the existence and continuity of such a function v.