On the income dependence of equivalence scales

Household consumption exhibits economies of scale as the number of household members increases. We collect survey data from two countries, Germany and France, in order to obtain direct subjective estimates of household consumption economies of scale, and, in particular, to examine an additional dimension: whether household consumption economies of scale change as living standards go up. Our data from both countries indicate strongly that household economies of scale increase as the living standard goes up. We discuss the robustness of our survey method and compare our results to these of alternative estimation methods in the literature.     

Can PIGLOG preferences identify equivalence scales?

This paper clarifies the conditions under which PIGLOG and extended PIGLOG preferences can identify household equivalence scales. The results are of interest to practitioners who have to elect preferences suitable for welfare analysis. It also shows that independent of the base utility equivalence scales are the same whether the budget shares of the demand systems are linear or quadratic in log income. (JEL: D11, D13) The author is grateful to an anonymous referee for several helpful suggestions.     

A nested test of the Barten model of equivalence scales

The Barten model, as the principal equivalence scale model, has considerable policy importance. It has, however, never been subjected to a statistically satisfactory test. This note proposes a simple modelling artefact that allows the Barten model to be nested and tested in the conventional way. Illustrative estimation is, then, carried out on U.K. budget data.     

Equity-regarding poverty measures: differences in needs and the role of equivalence scales

Abstract .  The paper investigates the definition of equity-regarding poverty measures when there are different household types in the population. It demonstrates the implications of a between-type regressive transfer principle for poverty measures, for the choice of poverty lines, and for the measurement of living standard. The role of equivalence scales, which are popular in empirical work on poverty measurement, is clarified.     

A test of McClements' method for the estimation of equivalence scales

An attempt was made to determine equivalence scales for children by using the McClements technique to estimate the Prais-Houthakker expenditure model using Australian data. It was found that the method was used by McClements to identify the system introduced an unacceptable degree of subjective bias.     

Adult equivalence scales and food expenditures: an application to Mexican beef and pork purchases

In the analysis of food expenditures, the use of a simple count of household members as an estimate of household size implicitly assumes each household member has the same marginal impact. In this analysis of Mexican food expenditures, endogenously determined adult equivalence scales are estimated in such a way that these marginal impacts are allowed to vary by household member age and gender. The results of a series of hypothesis tests indicate a rejection of the implied null hypothesis of equal marginal expenditure impacts associated with the use of the traditional count based household size variable. This study also rejects the null hypothesis of the equality of adult equivalent scales across the commodities included in this analysis.     

Semi-core equivalence

Summary. The main requirements for equivalence of the core of an economy and the Walrasian equilibrium allocations are largeness and the freedom to form almost arbitrary coalitions in the Edgeworthian barter processes. We investigate whether constraints on coalition formation and coalitional barter alter these insights. Our notion of the semi-core imposes a restriction on the collection of formable coalitions that does not affect the fundamental equivalence property. Using our concept of the contract-core we show that additional constraints on coalitional barter can only be alleviated within an environment with sufficiently many formable coalitions: besides a contract-core equivalence theorem we show certain non-equivalence results.Received: December 11, 1995; revised version: September 17, 1996This revised version was published online in February 2005 with corrections to the cover date.     

Best response equivalence

Two games are best-response equivalent if they have the same best-response correspondence. We provide a characterization of when two games are best-response equivalent. The characterizations exploit a dual relationship between payoff differences and beliefs. Some “potential game” arguments [Games Econ. Behav. 14 (1996) 124] rely only on the property that potential games are best-response equivalent to identical interest games. Our results show that a large class of games are best-response equivalent to identical interest games, but are not potential games. Thus we show how some existing potential game arguments can be extended.     

Revealed smooth nontransitive preferences

In the present paper, we are concerned with the behavioural consequences of consumers having nontransitive preference relations. Data sets consist of finitely many observations of price vectors and consumption bundles. A preference relation rationalizes a data set provided that for every observed consumption bundle, all strictly preferred bundles are more expensive than the observed bundle. Our main result is that data sets can be rationalized by a smooth nontransitive preference relation if and only if prices can normalized such that the law of demand is satisfied. Market data sets consist of finitely many observations of price vectors, lists of individual incomes and aggregate demands. We apply our main result to characterize market data sets consistent with equilibrium behaviour of pure-exchange economies with smooth nontransitive consumers.     

A three way equivalence

In view of the well known core equivalence results in atomless economies, coincidence of market game equilibrium allocations with competitive allocations is tantamount to a three way equivalence between market game mechanisms, competitive equilibria and the core. Based on this idea we study equilibrium refinements of market games, which allow us to use the core equivalence machinery in order to provide an exact market game characterization of competitive equilibria.     

Revealed preference and differentiable demand

Summary. We prove that, for finitely many demand observations, the Strong Axiom of Revealed Preference tests not only the existence of a strictly concave, strictly monotone and continuous utility generator, but also one that generates an infinitely differentiable demand function. Our results extend those of previous related results (Matzkin and Richter, 1991; Chiappori and Rochet, 1987), yielding differentiable demand functions but without requiring differentiable utility functions.Received: 1 November 2001, Revised: 5 February 2004, JEL Classification Numbers: D11, D12. Correspondence to: Kam-Chau WongThis is a much revised version of Lee and Wong (2001). We are grateful to the Referee for valuable suggestions. We also thank Professor Marcel K. Richter for his comments.     

On the equivalence of preferences

Preference relations that agree on the ranking of elements of the space on which they are defined necessarily agree on all the conditional rankings of pairs of components of these elements. In this note we show the converse statement is also true.     

Core equivalence theorem with production

In production economies, the extent to which non-equilibria are blocked depends on the allocation of control rights among shareholders, because a blocking coalition's resources are affected by the firms it jointly owns with outsiders. We formulate a notion of blocking that takes such interdependency problem into account, and we prove an analog of the Debreu-Scarf theorem for replica production economies. Our theorem differs from theirs in using an additional assumption, which we argue is indispensable and is driven by the interdependency problem.     

An inner core equivalence theorem

Summary We extend the notion of the inner core of a finite economy to a large economy. We prove that competitive allocations and the core coincide with the inner core.This is based on Chapter 5 of my Ph.D thesis. I am indebted to my thesis advisor, Lloyd S. Shapley, for his guidance. Discussions with Michael Balch are gratefully acknowledged. I also thank Charles Stuart, Nicholas C. Yannelis and an anonymous referee for comments and suggestions that greatly improved the paper.     

Tax evasion and Ricardian equivalence

This paper studies whether the Ricardian equivalence holds in a context with tax evasion. In such a context, the degree of uncertainty becomes endogenous since agents control the distribution of their future income through their income report. We find that Ricardian equivalence holds when proportional fines are imposed on evaded taxes, but does not hold when the fines are on the amount of unreported income. We also show that it is possible to explain the empirical negative relation between tax rates and declared income when the path of government spending remains unchanged.     

Headquarter Services and Revealed Factor Abundance

This paper analyzes how usual measures of revealed factor abundance (RFA), based on trade in merchandise, are affected by the existence of trade in services of intangible assets; trade that is mainly associated with multinational firms. It presents empirical estimates of both usual measures of RFA and new measures that take account of trade in headquarter services for the United States, a country that has a substantial surplus in the recorded components of such trade. It is found that the usual measures underestimate the abundance of highly skilled labor and technological knowledge, and overestimate the abundance of physical capital.