The measurement of income mobility: A partial ordering approach

Summary. Given a set of longitudinal data pertaining to two populations, a question of interest is the following: Which population has experienced a greater extent of income mobility? The aim of the present paper is to develop a systematic way of answering this question. We first put forth four axioms for income movement-mobility indices, and show that a familiar class of measures is characterized by these axioms. An unambiguous (partial) ordering is then defined as the intersection of the (complete) orderings induced by the mobility measures which belong to the characterized class; a transformation of income distributions is “more mobile” than another if, and only if, the former is ranked higher than the latter for all mobility measures which satisfy our axioms. Unfortunately, our mobility ordering depends on a parameter, and therefore, it is not readily apparent how one can apply it to panel data directly. In the second part of the paper, therefore, we derive several sets of parameter-free necessary and sufficient conditions which allow one to use the proposed mobility ordering in making unambiguous income mobility comparisons in practice. Received: July 12, 1995; revised version: May 13, 1997     

Bivariate income distributions for assessing inequality and poverty under dependent samples

As indicators of social welfare, the incidence of inequality and poverty is of ongoing concern to policy makers and researchers alike. Of particular interest are the changes in inequality and poverty over time, which are typically assessed through the estimation of income distributions. From this, income inequality and poverty measures, along with their differences and standard errors, can be derived and compared. With panel data becoming more frequently used to make such comparisons, traditional methods which treat income distributions from different years independently and estimate them on a univariate basis, fail to capture the dependence inherent in a sample taken from a panel study. Consequently, parameter estimates are likely to be less efficient, and the standard errors for between-year differences in various inequality and poverty measures will be incorrect. This paper addresses the issue of sample dependence by suggesting a number of bivariate distributions, with Singh–Maddala or Dagum marginals, for a partially dependent sample of household income for two years. Specifically, the distributions considered are the bivariate Singh–Maddala distribution, proposed by Takahasi (1965), and bivariate distributions belonging to the copula class of multivariate distributions, which are an increasingly popular approach to modelling joint distributions. Each bivariate income distribution is estimated via full information maximum likelihood using data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey for 2001 and 2005. Parameter estimates for each bivariate income distribution are used to obtain values for mean income and modal income, the Gini inequality coefficient and the headcount ratio poverty measure, along with their differences, enabling the assessment of changes in such measures over time. In addition, the standard errors of each summary measure and their differences, which are of particular interest in this analysis, are calculated using the delta method.     

Fiscal rules of income transformation

Summary. The purpose of this paper is to characterize the class of fiscal rules of income transformation which are equity improving and, at the same time, preserve the ranking of existing distributions. Contrary to the related literature individual well-being depends not just on income but also on prices. We show that, when the environment is restricted such that a general transformation class still can be defined, the only “desirable” fiscal rule is the simple redistributive linear taxation schedule, of the same type that is the rule in practice in most economies. Received: May 8, 1997; revised version: September 15, 1997     

Welfare-improving changes in size distributions of income

We address the question: given a parameterised welfare function defined over income (via utility), for what values of the parameters do observed changes in U.K. income distribution, over time or as a result of taxes and benefits, constitute an improvement?     

Dynamic mechanism design with hidden income and hidden actions

We develop general recursive methods to solve for optimal contracts in dynamic principal-agent environments with hidden states and hidden actions. Starting from a general mechanism with arbitrary communication, randomization, full history dependence, and without restrictions on preferences or technology, we show that the optimal contract can be implemented as a recursive direct mechanism. A curse of dimensionality which arises from the interaction of hidden income and hidden actions can be overcome by introducing utility bounds for behavior off the equilibrium path. Environments with multiple actions are implemented using multiple layers of such off-path utility bounds.     

Income distributions and decomposable divergence measures

Inequality indices evaluate the divergence between the income distribution and the hypothetical situation where all individuals receive the mean income, and are unambiguously reduced by a Pigou–Dalton progressive transfer. This paper proposes a new approach to evaluate the divergence between any two income distributions, where the latter can be a reference distribution for the former. In the case where the reference distribution is perfectly egalitarian – and uniquely in this case – we assume that any progressive transfer reduces the divergence, and that the divergence can be additively separated into inequality and efficiency loss. We characterize the unique class of decomposable divergence measures consistent with these views. We derive the associated relative and absolute subclasses, and we illustrate the applicability of our results. This approach extends the generalized entropy studied in inequality measurement.     

Income inequality and income bias in voter turnout

In the era of growing income inequality around the world, it remains inconclusive how higher income inequality affects income bias in turnout (i.e., high-income citizens vote more likely than low-income citizens). Using large-scale cross-national survey data, we show that (1) strong income bias in turnout exists in many parts of the world, (2) higher income inequality is related to lower income bias in turnout by demobilizing high-income citizens and mobilizing low-income citizens, and (3) this relationship is partly explained by the pattern that vote buying is more common in societies with higher income inequality and thus mobilizes low-income citizens but decreases political efficacy among high-income citizens. Ultimately, this study suggests that growing income inequality may not exaggerate political inequality, but may challenge the legitimacy of democratic elections.     

Social orderings for the assignment of indivisible objects

In the assignment problem of indivisible objects with money, we study social ordering functions which satisfy the requirement that social orderings should be independent of changes in preferences over infeasible bundles. We combine this axiom with efficiency, consistency and equity axioms. Our result is that the only social ordering function satisfying those axioms is the leximin function in money utility.     

Corrigendum to “Reserve price signaling” [J. Econ. Theory 135 (1) (2007) 253-268]

We find an error in [H. Cai, J. Riley, L. Ye, Reserve price signaling, J. Econ. Theory 135 (1) (2007) 253-268]. The existence of the separating signaling equilibrium is not challenged, but the related comparative statics, while valid in the case without informational externalities between bidders, do not generalize to the case with informational externalities as claimed by the authors. General results on the influence of the number of bidders are obtained in a linear specification of the informational externalities.     

Migration,self‐selection and income distributions

Self‐selection in rural–urban migration is examined using three datasets from rural and urban China in 2002. We construct a migrant sample including both migrants who converted their hukou status from rural to urban (permanent migrants) and those who did not (temporary migrants). We find a strong positive selection for permanent migrants, but the selection for temporary migrants is ambiguous. We reach these conclusions by comparing migrants' counterfactual wage densities, assuming they are paid as rural local workers, to actual wage densities of rural local workers. Our results imply that permanent migration has negative effects on rural human capital accumulation and income levels.     

On the effect of income and relative price on demand for health care: EC evidence

This paper demonstrates that the relative price of health care could be used to explain the conflicting results of the empirical studies which attempt to measure the income elasticity of demand. Our empirical results, based on a conventional model and cross-national data set for the EC, show that whereas health care may be labelled as a luxury good, the large income effect can be interpreted as merely offsetting the price effect.     

A characterization of the Shapley value in queueing problems

A set of agents stand to receive a service. No two agents can be served simultaneously. A queue has to be organized, and agents having to wait should receive monetary compensations. We characterize the rule assigning positions in the queue and compensations corresponding to the payoffs recommended by the Shapley value of the associated cooperative game. We use a property of independence with respect to increase in some agents’ impatience, and an equal responsibility property.     

Decomposition of s‐concentration curves

Abstract. For any given order of inverse stochastic dominance, standard concentration curves are decomposed into three components, called contribution curves. Those components correspond to within‐group inequalities, between‐group inequalities, and transvariational inequalities. We prove, for all orders, that contribution curve dominance implies systematically welfare‐improving tax reforms and conversely. Accordingly, as welfare expansions may be costly in terms of particular inequalities, we propose targeted fiscal reforms.     

Fixing income and price targets for the poor in india

The poverty line, generally defined as the minimum income level necessary to enable a person to consume a normatively stipulated basket of goods, is widely used to set income target for the poor. But mere provision of this target income will not lead the poor to adopt the normative consumption pattern. In order to induce them to do so, it is necessary to set suitable price targets along with the income target. An attempt has been made here to fix these targets assuming that the consumers' demand pattern can be represented by the linear expenditure system. A numerical exercise has been worked out for rural India.     

Operators for the adjudication of conflicting claims

We consider the problem of allocating some amount of an infinitely divisible and homogeneous resource among agents having claims on this resource that cannot be jointly honored. A “rule” associates with each such problem a feasible division. Our goal is to uncover the structure of the space of rules. For that purpose, we study “operators” on the space, that is, mappings that associate to each rule another one. Duality, claims truncation, and attribution of minimal rights are the operators we consider. We first establish a number of results linking them. Then, we determine which properties of rules are preserved under each of these operators, and which are not.     

Income comparison and happiness: The role of fair income distribution

Relative income gap is one of the most popular approaches for explaining the income–happiness relationship. We argue in this article that when people compare their incomes, they care about distributional fairness more than relative income disparity. It is difficult for us to explain China's income–happiness paradox if we simply compare the income gap and do not explore the income‐generation process leading to income inequality. We therefore employ an approach based on a responsibility‐sensitive theory of justice that decomposes individual income into fair and unfair components. As a proxy for distributional unfairness, unfair income is considered the main source of unhappiness. Using data from the Chinese Household Income Project survey, we find strong support for the negative relationship between income unfairness and happiness. We also find a significantly positive relationship between the relative income gap and income unfairness, which leads us to consider the income comparison hypothesis as the explanation for the income–happiness paradox in a new light. Sensitivity analyses confirm the robustness of our results.     

A little fairness may induce a lot of redistribution in democracy

We use a model of self-centered inequality aversion suggested by Fehr and Schmidt (Quart. J. Econom. 114 (3) (1999) 817) to study voting on redistribution. We theoretically identify two classes of conditions when an empirically plausible amount of fairness preferences induces redistribution through referenda. We test the predictions of the adapted inequality aversion model in a simple redistribution experiment and find that it predicts voting outcomes far better than the standard model of voting assuming rationality and strict self-interest.     

The measurement of income and price elasticities

In a complete system of disaggregated demand equations, the econometrician must limit himself to the measurement of a small number of parameters for each commodity. Since interest often focuses on the income and own-price elasticities for each good, it is natural to look for models which allow independent measurement of these while providing plausible assumptions about the less essential responses. This paper surveys a number of common theoretical specifications which purport to do this, and argues that these are unsatisfactory. The conclusions are supported by an empirical comparison on British data of the results of three models, one of which is new and is designed to remedy some of the deficiencies of standard practice.