Decomposition of inequality measures and a comparative analysis

The main objectives of the paper are to decompose Atkinson's measure into within-group and between-group inequality and to compare it with decompositions of inequality measures, like the Gini coefficient, variance of logarithms, Theil's entropy index and the square of the coefficient of variation. Atkinson's inequality index is given an interpretation of mean order β and then it is decomposed for population subgroups. Various other measures are considered for decompositions and a variety of decomposition schemes for Gini coefficient and other measures in the literature is reviewed and commented upon. Empirical analysis using U.S.A. and U.K. data are performed on the basis of income distribution data classified by family size. For various decomposition schemes, contribution to between size-group and within size-group inequalities are compared in percentage terms. Comparisons are also made over time for the years 1964 and 1974 both for U.S.A. and U.K. and the result indicates that within size-group income inequality has declined while between size group and total income inequality shows an increase. Three important properties of Atkinson's inequality index are proved in the appendix.     

QUADRATIC PEN'S PARADE AND THE COMPUTATION OF THE GINI INDEX

Following Milanovic's (1997) paper, we propose a simple way to compute the Gini index when income y is a quadratic function of its rank among n individuals.     

Public Pensions: To What Extent Do They Account for Swedish Wealth Inequality?

Sweden's distribution of disposable income is very even, with a Gini coefficient of just 0.31. Yet its wealth distribution is extremely unequal, with a Gini coefficient of 0.79. Moreover, Swedish wealth inequality is, to a large extent, driven by the large fraction of households with zero or negative wealth. In this paper, we investigate to what extent the redistributive public pension scheme is responsible for these features of the data. To address this problem, we study the properties of two overlapping generations economies with uninsurable idiosyncratic risk. The first has a pension system modeled on the actual system; the second has no public pension scheme at all. Our findings support the view that the public pension scheme is, to a large extent, responsible for the features of the data that we focus on. Journal of Economic Literature Classification Numbers: E13, D31, H55.     

Income distribution and economic development: Insights from machine learning

We draw upon recent advances that combine causal inferences with machine learning, to show that poverty is the key income distribution measure that matters for development outcomes. In a predictive framework, we first show that LASSO chooses only the headcount measure of poverty from 37 income distribution measures in predicting schooling, institutional quality, and per capita income. Next, causal inferences with post‐LASSO models indicate that poverty matters more strongly for development outcomes than does the Gini coefficient. Finally, instrumental variable estimates in conjunction with post‐LASSO models show that compared to Gini, poverty is more strongly causally associated with schooling and per capita income, but not institutional quality. Our results question the literature's overwhelming focus on the Gini coefficient. At the least, our results imply that the causal link from inequality (as measured by Gini) to development outcomes is tenuous.     

Simple Markovian equilibria in dynamic spatial legislative bargaining

The paper proves, by construction, the existence of Markovian equilibria in a dynamic spatial legislative bargaining model. Players bargain over policies in an infinite horizon. In each period, a sequential protocol of proposal-making and voting, with random proposer recognitions and a simple majority, produces a policy that becomes the next period's status-quo; the status-quo is endogenous. The construction relies on simple strategies determined by strategic bliss points computed by the algorithm we provide. A strategic bliss point, the dynamic utility ideal, is a moderate policy relative to a bliss point, the static utility ideal. Moderation is strategic and germane to the dynamic environment; players moderate in order to constrain the future proposals of opponents. Moderation is a strategic substitute; when a player's opponents do moderate, she does not, and when they do not moderate, she does. We provide conditions under which the simple strategies induced by the strategic bliss points computed by the algorithm deliver a Stationary Markov Perfect equilibrium, and we prove its existence in generic games with impatient players and in symmetric games. Because the algorithm constructs all equilibria in simple strategies, we provide their general characterization, and we show their generic uniqueness.     

Status Aspirations, Wealth Inequality, and Economic Growth

This paper argues that an increase in the inequality of wealth prompts a stronger quest for status that in turn fosters the accumulation of wealth. It proposes a measure for an individual's want of social status. For a given level of a population's wealth, the corresponding aggregate measure of want of social status is shown to be positively related to the Gini coefficient of wealth inequality. Hence, the Gini coefficient and growth are positively correlated, holding the population's wealth constant.     

Greater prudence and greater downside risk aversion

Variation in the degree of downside risk aversion across decision makers has implications for efficient risk sharing. However, except for small differences in risk preferences, there is no index, analogous to the Arrow-Pratt index of risk aversion, that depends only on local properties of the utility function and indicates the degree of aversion to downside risk. A measure that does depend only on local properties of the utility function u, the index of prudence p=−u^?/u^″, is related to downside risk aversion, which is indicated by a positive value for u^?. Although we show that the degree of prudence is not an accurate indicator of the degree of downside risk aversion, we nonetheless demonstrate that a uniform increase in prudence accompanied by a uniform increase (decrease) in risk aversion is sufficient to indicate greater downside risk aversion, provided prudence is greater (less) than three times the degree of risk aversion.     

Comparative statics for oligopoly: A generalized result

We perform comparative statics for a general model of asymmetric oligopoly and derive a concise formula for the response of one firm to a marginal change in its rival’s strategic variable, taking into account the responses of all other firms. We obtain the conditions under which the sign of this response coincides with that of the mixed second-order partial derivative of the firm’s payoff function. We then propose a distinction between gross and net strategic relationships (i.e., strategic substitute and complement).     

The Impact of Payoff Interdependence on Trust and Trustworthiness

Abstract. In one‐shot investment games where each player's payoff is a convex combination of own and other's profit, we measure trust by the amount given to the trustee and trustworthiness by the amount returned to the trustor by the trustee. Does the degree of payoff interdependence increase both trust and trustworthiness or one but not the other or neither of them? According to our experimental data, trust remains unaffected by the extent of interdependence whereas trustworthiness reacts positively to it.     

The measurement of rank mobility

In this paper we investigate the problem of measuring social mobility when the social status of individuals is given by their rank. In order to sensibly represent the rank mobility of subgroups within a given society, we address the problem in terms of partial permutation matrices which include standard (“global”) matrices as a special case. We first provide a characterization of a partial ordering on partial matrices which, in the standard case of global matrices, coincides with the well-known “concordance” ordering. We then provide a characterization of an index of rank mobility based on partial matrices and show that, in the standard case of comparing global matrices, it is equivalent to Spearman's ρ index.     

The micro economics of group behavior: General characterization

We study the demand function of a group of S members facing a global budget constraint. Any vector belonging to the budget set can be consumed within the group, with no restriction on the form of individual preferences, the nature of individual consumptions or the form of the decision process beyond efficiency. Moreover, only the group aggregate behavior, summarized by its demand function, is observable. We provide necessary and (locally) sufficient restrictions that fully characterize the group's demand function, with and without distribution factors. We show that the private or public nature of consumption within the group is not testable from aggregate data on group behavior.     

Improving consumption measurement and other survey data through CAPI: Evidence from a randomized experiment

This paper reports on a randomized survey experiment among 1840 households, designed to compare pen-and-paper interviewing (PAPI) to computer-assisted personal interviewing (CAPI). We find that PAPI data contain a large number of errors, which can be avoided in CAPI. Error counts are not randomly distributed across the sample, but are correlated with household characteristics, potentially introducing sample bias if dubious observations need to be dropped. We demonstrate a tendency for the spread of total measured consumption to be higher on paper compared to CAPI, translating into significantly higher measured inequality. Investigating further the nature of PAPI's measurement error for consumption, we fail to reject the hypothesis that it is classical: it attenuates the coefficient on consumption when used as explanatory variable and we find no evidence of bias when consumption is used as dependent variable. Finally, CAPI and PAPI are compared in terms of interview length, costs and respondents' perceptions.     

A Note on α‐Gini Measures

This note provides a characterization of α‐Gini inequality measures. These measures generalize the standard Gini index by including one sensitivity parameter α, which captures different value judgments. The α‐Gini measures are shown to be weakly decomposable and unit consistent. Weak decomposition provides within‐group and between‐group inequalities. Unit consistency keeps unchanged the ranking of two income distributions when the income units vary. It is shown that the α‐Gini measures are relevant with either “leftist” or“rightist” views.     

中国区域人才集聚合理性及其评价——中美500强企业地区分布的对比视角

本文采用中美500强企业地区分布统计数据,根据企业分布曲线,计算了中美500强企业的地区分布系数,并将此系数作为中美人才集聚度的测量指标。研究发现,我国500强企业的地区分布系数为0．58,远远高于可接受的国民收入分布（基尼）系数,但低于美国500强企业的地区分布系数。本文分析了产生此种状况的原因,展望了我国人才聚集的发展趋势,并提出了相对应的建议。     

Viewpoint: Measuring the well‐being of the poor with income or consumption: a Canadian perspective

Abstract There is a long tradition of using consumption measures derived from Statistics Canada's household expenditures surveys to study material well‐being, inequality, and poverty. We offer an introduction to this research. Income and consumption measures give different pictures of the patterns of material well‐being in Canada, but the differences are not as large as in the US. We also provide a comparison to Meyer and Sullivan's results on data quality. Canadian expenditure surveys are of high quality. Unique aspects of these surveys (variation in quality control measures over time and the possibility of comparing to income tax data) provide important insights into the quality of survey data on income and consumption.     

中国农村地区间居民收入差距及构成变化:1995—2008年——基于基尼系数的分解

本文采用分省的面板数据对农村地区间基尼系数分解结果表明,1995—2008年,中国农村地区间收入差距总体上仍然呈现上升趋势,基尼系数上升了0.0639,但增幅出现明显减弱趋势。基尼系数变化及农村居民工资性收入对基尼系数的贡献变化显示出与经济发展阶段变化一致的含义;结构性效应已不再是农村地区间收入差异的唯一构成来源,收入集中效应对基尼系数起了明显的增加作用,工资性收入的集中效应超过了其他收入来源。这些构成来源的变化蕴含着中国面临调节地区间农村收入差距的政策机遇。     

Group play in games and the role of consent in network formation

We study games played between groups of players, where a given group decides which strategy it will play through a vote by its members. When groups consist of two voting players, our games can also be interpreted as network-formation games. In experiments on Stag Hunt games, we find a stark contrast between how groups and individuals play, with payoffs playing a primary role in equilibrium selection when individuals play, but the structure of the voting rule playing the primary role when groups play. We develop a new solution concept, robust-belief equilibrium, which explains the data that we observe. We provide results showing that this solution concept has application beyond the particular games in our experiments.     

Ethically flexible gini indices for income distributions in the continuum

A single-parameter generalization of the Gini coefficient (S-Gini) is presented for income distributions defined in the continuum. Special cases are Dorfman's formula for the Gini, and the authors' S-Ginis for finite populations. We exploit the duality between indices of relative inequality and homothetic social-evaluation functions to construct these new indices.     

Improving forecast accuracy of financial vulnerability: PLS factor model approach

We present a factor augmented forecasting model for assessing the financial vulnerability in Korea. Dynamic factor models often extract latent common factors from a large panel of time series data via the method of the principal components (PC). Instead, we employ the partial least squares (PLS) method that estimates target specific common factors, utilizing covariances between predictors and the target variable. Applying PLS to 198 monthly frequency macroeconomic time series variables and the Bank of Korea's Financial Stress Index (KFSTI), our PLS factor augmented forecasting models consistently outperformed the random walk benchmark model in out-of-sample prediction exercises in all forecast horizons we considered. Our models also outperformed the autoregressive benchmark model in short-term forecast horizons. We expect our models would provide useful early warning signs of the emergence of systemic risks in Korea's financial markets.     

长三角区域创新差异和位序规模体系研究

从经济地理学的角度出发,运用区域经济发展差异的相关指标,采用长江三角洲16个城市(2003—2008年)的专利申请授权和专利申请受理量作为创新变量对创新活动进行分析。通过计算变差系数、基尼系数和赫芬达尔系数,发现长三角地区各城市在两个专利变量上的相对差异变化均呈下降趋势,首位度指标则显示创新第二高城市距离创新最高城市——上海的差距在逐年减小;然后基于位序—规模分布理论研究长三角区域创新活动规模的发展趋势,发现其模式呈分散均衡型分布。最后,归纳出促使长三角区域创新差异缩小的重要因素,并提出了若干建议。