Regional economic growth disparities: A political economy perspective

Regional differences in economic growth have been observed within many countries. Our story emphasises three region-specific factors driving growth—capital, labour and political factors. Conditional on differences in production factor (i.e., labour and capital) variations across democratic states, what role do differences in underlying “political factors” across regions play in accounting for regional growth disparities? We build a political economy model of endogenous growth where regions have the same political institutions, but experience different (and estimable) distributions over voter political biases (i.e., our “political factors”). In our model, political factors affect regional productivity as a consequence of politico-economic equilibrium. We discipline our regional growth accounting exercises by calibrating/estimating each model to American state-level economic and political-survey data. We show that the capital factor is the predominant driving force behind growth in American states. Nevertheless, regional variations in distributions of voter's political biases also account a great deal for regional growth disparities. We also evaluate how much politics would have distorted agents' welfare and regional growth, were regional economies given the opportunity to live under an efficient social planner's allocation system; and, if agents were to live under the same democratic system but where all voters have equal voting influence.     

Preference aggregation with randomized social orderings

We show that every binary and Paretian method for passing from preference profiles to lotteries over preferences is associated with a subadditive function on the set of coalitions of individuals. This function gives the power of each coalition to secure its preference for any x over any y.     

INEQUALITY OF OPPORTUNITIES VS. INEQUALITY OF OUTCOMES: ARE WESTERN SOCIETIES ALL ALIKE?

This paper analyzes the relationship between income inequality and inequality of opportunities for income acquisition in nine developed countries during the 1990s. Equality of opportunity is defined as the situation where income distributions conditional on social origin cannot be ranked according to stochastic dominance criteria. We measure social origin by parental education and occupation and use the database built by Roemer et al. (2003 ). Stochastic dominance is assessed using nonparametric statistical tests. Our results indicate strong disparities in the degree of equality of opportunity across countries and a strong correlation between inequality of outcomes and inequality of opportunity. The U.S. and Italy show up as the most unequal countries in terms of both outcome and opportunity. At the opposite extreme, income distributions conditional on social origin are almost the same in Scandinavian countries even before any redistributive policy. We complement the ordinal comparison by resorting to an original scalar “Gini” index of opportunities, which can be decomposed into a risk and a return component. In our sample, inequality of opportunity is mostly driven by differences in mean income conditional on social origin, and differences in risk compensate the return element in most countries.     

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.     

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.     

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.     

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.     

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.     

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     

Core allocations and the dimension of the cone of efficiency price vectors

Let (R₁,…,R_k) be an arbitrary partition of the grand coalition in an atomless exchange economy with k “large enough.” We prove that an optimal allocation x belongs to the core if and only if x cannot be improved upon by any coalition that includes at least one of the R_i's. K is “large enough” if k ? r + 1, where r is the linear dimension of the cone P of the efficiency price vectors for x. Recall that it is always true that r ? n, when n is the number of commodities in the market, and that under differentiability and interiority r = 1; thus k can be chosen to be 2 (i.e., for any coalition R, an allocation x belongs to the core of the market if and only if x is not blocked by any coalition that either contains R or contains its complement).     

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.     

Characterization of the private alternatives domains admitting arrow social welfare functions

An n-person social choice problem is considered in which the alternatives are n dimensional vectors with the ith component of such a vector being the part of the alternative effecting individual i alone. Assuming that individuals are selfish (i is indifferent between any two alternatives that have the same ith component) we characterize all the families of permissible individual preferences that admit nondictatorial Arrow-type social welfare functions. We also show that the existence of such a function for a given family of preferences is independent of n provided that is greater than one.     

On choosing which game to play when ignorant of the rules

This paper suggests a theory of choice among strategic situations when the rules of play are not properly specified. We take the view that a “strategic situation” is adequately described by a TU game since it specifies what is feasible for each coalition but is silent on the procedures that are used to allocate the surplus. We model the choice problem facing a decision maker (DM) as having to choose from finitely many “actions”. The known “consequence” of the ith action is a coalition from game f _i over a fixed set of players \(N_i\cup\{d\}\) (where d stands for the DM). Axioms are imposed on her choice as the list of consequences (f ₁,..., f _m ) from the m actions varies. We characterize choice rules that are based on marginal contributions of the DM in general and on the Shapley Value in particular.     

Statistical Equilibrium Wealth Distributions in an Exchange Economy with Stochastic Preferences

We describe an exchange market consisting of many agents with stochastic preferences for two goods. When individuals are indifferent between goods, statistical mechanics predicts that goods and wealth will have steady-state gamma distributions. Simulation studies show that gamma distributions arise for a broader class of preference distributions. We demonstrate this mathematically in the limit of large numbers of individual agents. These studies illustrate the potential power of a statistical mechanical approach to stochastic models in economics and suggest that gamma distributions will describe steady-state wealths for a class of stochastic models with periodic redistribution of conserved quantities. Journal of Economic Literature Classification Numbers: C15, C62, C73, D3, D5.     

Transfer principles in income redistribution

Dalton's principle of transfer for income redistribution says that society will be better off when a unit of income in transferred from a richer to a poorer individual. This paper investigates the conjunction of a natural extension of Dalton's principle — which says that any combination of a socially desirable transfer with its inverse at uniformly higher levels of income will have positive social benefit — and a traditional utilitarian-egalitarian formulation of social welfare. The transfer principles involved in the extension of Dalton's rule correspond to stochastic dominance relations between income distributions with a common mean, and lead to the conclusion that, when ? and g are income distributions, the social welfare of ? is larger than that of g if $\text{Σe}{}^{\mathrm{-ax}}\text{?(x)<Σe}{}^{\mathrm{-ax}}\text{g(x)}$ for all positive a. This conclusion is intimately connected with a measure of income inequality studied by Kolm.     

Manipulation and the Pareto rule

This paper examines rules that map preference profiles into choice sets. There are no agendas other than the entire set of alternatives. A rule is said to be “manipulable” if there is a person i, and a preference profile, such that i prefers the choice set obtained when he is dishonest to the one obtained when he is honest. It is “nonmanipulable” if this can never happen. The paper indicates how preferences over choice sets might be sensibly derived from preferences over alternatives, and discusses seven different notions of manipulability associated with seven different assumptions about preferences over sets of alternatives. The paper has two sections of results. In the first I show that the Pareto rule, that is, the rule that maps preference profiles into corresponding sets of Pareto optima, is nonmanipulable in four of the seven senses of manipulability, and manipulable in three of them. In the second section, I examine this conjecture: If an arbitrary rule is nonmanipulable and nonimposed, and if indifference is disallowed, then every choice set must be contained in the set of Pareto optima. The conjecture is true under the strongest definition of nonmanipulability.     

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.     

Fuzzy revealed preference theory

Rationality has traditionally been defined as choice behaviour which can be explained in terms of some implicit binary preference. The point of departure of this paper lies in permitting the binary preference relation to be “fuzzy.” Concepts from fuzzy set theory are used to formalise different notions of rationality, including degrees of rationality. The relation between these and traditional concepts is formally explored. In welfare economics, quasi-orderings have often been used to capture the inherent imprecisions of human value judgements. It is argued here that, in many situations, a more appropriate tool for this may be fuzzy orderings.     

Beliefs and rationalizability in games with complementarities

We propose two characteristics of beliefs and study their role in shaping the set of rationalizable strategy profiles in games with incomplete information. The first characteristic, type-sensitivity, is related to how informative a player thinks his type is. The second characteristic, optimism, is related to how “favorable” a player expects the outcome of the game to be. The paper has two main results: the first result provides an upper bound on the size of the set of rationalizable strategy profiles; the second gives a lower bound on the change of location of this set. These bounds are explicit expressions that involve type-sensitivity, optimism, and payoff characteristics. Our results generalize and clarify the well-known uniqueness result of global games (Carlsson and van Damme, 1993). They also imply new uniqueness results and allow us to study rationalizability in new environments. We provide applications to supermodular mechanism design (Mathevet, 2010b) and information processing errors.