Judgment of distributional inequality in networks

Why is income inequality perceived and judged differently across a society? Following the social comparison theory, one reasonable explanation suggests that individuals are exposed to different local reference groups in social networks. We design a vignette experiment to study how income distributions are judged by individuals structured in networks. The experiment shows that perceptions of distributional inequality are high when network ties are unequally distributed across individuals, suggesting that network inequality contributes to distributional inequality. Beyond the network effect, inequality judgment is found to be driven by a mix of self-interest and other-regarding preference: people are in favor of group-beneficial income distributions wherein they rank high, but not extremely high, in the group. It shows that people care about not only their relative affluence, but also where others stand in the distribution.     

On the Utility of Robust and Resampling Procedures1

Abstract Kassab (1990) makes an important methodological contribution by urging the use of robust regression methods in the study of community economic impacts and by indicating the utility of the bootstrap in assessing standard errors in robust regression. By introducing the notion of a contaminating distribution, we reconcile differences between her claim that ordinary least squares (OLS) regression is biased when outliers are present and standard linear model theory that does not make assumptions about the shape of the residual distribution in proving OLS an unbiased estimator. The contaminating distribution provides a framework for rural sociologists to link their statistical assumptions to a substantive understanding of the phenomena being studied. We suggest an alternative regression estimation strategy that may be more robust than the technique she uses. We also discuss an approach to bootstrapping that is more appropriate for macro-level social indicator data than the one she describes. An appendix discusses the software available for implementing these methods.     

COMPETITIVE BALANCE MEASURES IN SPORTS LEAGUES: THE EFFECTS OF VARIATION IN SEASON LENGTH

Appropriate measurement of competitive balance is central to the economic analysis of professional sports leagues. We examine the distributional properties of the ratio of standard deviations (RSD) of points percentages, the most widely used measure of competitive balance in the sports economics literature, in comparison with other standard‐deviation‐based measures. Simulation methods are used to evaluate the effects of changes in season length on the distributions of competitive balance measures for different distributions of the strengths of teams in a league. The popular RSD measure performs as expected only in cases of perfect balance; if there is imbalance in team strengths, its distribution is sensitive to changes in season length. It is therefore not recommended for comparisons of competitive balance for different sports leagues with different numbers of teams and/or games played. (JEL L83, D63, C63)     

Vulnerability to poverty revisited: Flexible modeling and better predictive performance

This paper analyzes several modifications to improve a simple measure of vulnerability as expected poverty. Firstly, in order to model income, we apply distributional regression relating potentially each parameter of the conditional income distribution to the covariates. Secondly, we determine the vulnerability cutoff endogenously instead of defining a household as vulnerable if its probability of being poor in the next period is larger than 0.5. For this purpose, we employ the receiver operating characteristic curve that is able to consider prerequisites according to a particular targeting mechanism. Using long-term panel data from Germany, we build both mean and distributional regression models with the established 0.5 probability cutoff and our vulnerability cutoff. We find that our new cutoff considerably increases predictive performance. Placing the income regression model into the distributional regression framework does not improve predictions further but has the advantage of a coherent model where parameters are estimated simultaneously replacing the original three step estimation approach.     

Decomposition of Changes in Korean Wage Inequality, 1998–2007

South Korea experienced a steep increase in wage inequality between the Asian financial crisis in 1997 and the global financial crisis in 2008. This paper investigates the causes of the sharp change during that time period by looking at the contributions of changes in the distributions of schooling and unionization. The effects are estimated applying two robust distributional function based decomposition methods on Korean Labor and Panel Survey data for the time period 1998–2007. The results suggest changes in the distribution of schooling can explain about 10 % of the changes in the 90/50 percentile wage gap. The declining unionization rate does not have much impact on the upward trend of Korean wage inequality. In addition, aggregate decomposition results suggest that changes in labor force composition can explain a significant proportion of the total wage changes in the upper-tail of the distribution. Based on our findings we provide a list of policy recommendations to address the wage inequality issue in Korea.     

What is “Pro-Poor”?

Assessing whether distributional changes are “pro-poor” has become increasingly widespread in academic and policy circles. Starting from relatively general ethical axioms, this paper proposes simple graphical methods to test whether distributional changes are indeed pro-poor. Pro-poor standards are first defined. An important issue is whether these standards should be absolute or relative. Another issue is whether pro-poor judgements should put relatively more emphasis on the impact of growth upon the poorer of the poor. Having formalized the treatment of these issues, the paper describes various ways for checking whether broad classes of ethical judgements will declare a distributional change to be pro-poor. This paper was funded through a World Bank Research Support Budget and has also benefitted from the support of SSHRC, FQRSC, and the Poverty and Economic Policy research network of IDRC. I am very grateful to Quentin Wodon for his contribution to an earlier version of this paper, and to Christian Calmes, Boniface Essama-Nssah, Ashok Kotwal and two anonymous referees for very helpful comments.     

Inference for the measurement of poverty in the presence of a stochastic weighting variable

Empirical applications of poverty measurement often have to deal with a stochastic weighting variable such as household size. Within the framework of a bivariate distribution function defined over income and weight, I derive the limiting distributions of the decomposable poverty measures and of the ordinates of stochastic dominance curves. The poverty line is allowed to depend on the income distribution. It is shown how the results can be used to test hypotheses concerning changes in poverty. The inference procedures are briefly illustrated using Belgian data. An erratum to this article can be found at     

AN EXPLORATORY MODEL OF THE SIZE DISTRIBUTION OF INCOME

Through a specific model, this paper explores a promising general framework for unified modelling of the size distribution of income and wealth. The specific model includes physical and human capital accumulation, factoral and size distribution effects, redistributive taxation, economic growth, and other distribution-related mechanisms. The main conclusion is that the general framework can accommodate a wide range of distributional phenomena and still remain analytically tractable. Specifically, the framework allows closed form analytic solution for the first two moments (mean vector and variance-covariance matrix) of the joint distribution over individuals of income, wealth, and other variables.     

Survey mode effects on measured income inequality

We study the effect of interview modes on estimates of economic inequality which are based on survey data. We exploit variation in interview modes in the Austrian EU-SILC panel, where between 2007 and 2008 the interview mode was switched from personal interviews to telephone interviews for some but not all participants. We combine methods from the program evaluation literature with methods from the distributional decomposition literature to obtain causal estimates of the effect of interview mode on estimated inequality. We find that the interview mode has a large effect on estimated inequality, where telephone interviews lead to a larger downward bias. The effect of the mode is much smaller for robust inequality measures such as interquantile ranges, as these are not sensitive to the tails of the distribution. The magnitude of effects we find are of a similar order as the differences in many international and intertemporal comparisons of inequality.     

New approaches to the estimation of migration flows from census and administrative data sources

Census data represent an important source of information about migration flows. However, existing estimation procedures based on intercensal projection are often inconvenient to apply and are sensitive to even quite small changes in enumeration completeness. 2 new estimation procedures applicable to data from 2 censuses are developed and illustrated using US data. The 1st method is essentially a modification of traditional intercensal projection techniques, but as a result of working with age groups rather than cohorts, it is simpler to apply and allows mortality of the migrants to be incorporated over the intercensal period. The 2nd method also uses information from 2 censuses, but also uses independent information on the age pattern of migration from administrative sources or from other census questions. The method uses the fact that the age pattern of recent migration is likely to be different from the age distribution of the overall population to distinguish between intercensal change due to migration and apparent intercensal change due to changes in enumeration completeness. If the method's assumptions are met, it is possible to estimate the relative coverage of the 2 censuses as well as the scale of the independent age pattern of migration relative to the coverage of 1 or other of the censuses. The illustrative applications of the methods to US data suggest that both can work reasonably well.     

Poverty, income distribution and CGE micro-simulation modeling: Does the functional form of distribution matter?

This paper explores income distribution modeling approaches for poverty analysis in a CGE micro-simulation context. Income distribution functional forms such as the lognormal, Pareto, beta distribution and empirical methods are currently used in CGE models in parallel with the estimation of FGT poverty indices. The particular methods or functional forms used in this context are not always clearly defined and justified. In this paper, we investigate and provide better criteria for selecting a functional distribution for poverty analysis. To achieve this, we apply parametric estimation to seven functional forms and compare the results to a purely “empirical” method. The results showed that no single form is more appropriate in all instances or for all household subgroups. The choice of a modeling approach should be motivated by a search for best fit and should be based on appropriate statistical tests. Selecting inappropriate distributional forms can lead to biased results in terms of poverty analysis. Introducing functional forms in the empirical approach can also provide greater confidence in the results obtained.

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An erratum to this article can be found at     

A dwindling middle class? Italian evidence in the 2000s

In recent years, increasing attention has been paid to household impoverishment in Italy. Most of previous analyses dealing with this issue are based on summary statistics, which may not capture the whole income distribution. This paper employs a non-parametric tool, the “relative distribution”, to describe patterns of changes in the entire Italian household income distribution over the period 2000–2004. This approach also allows for a decomposition of the relative density to isolate changes due to differences in location from changes due to differences in shape, thus enabling deeper analysis of income polarization. During the 2000s there was a significant location effect, and also increased income polarization, which has particularly affected incomes below the median. Analyses by social groups, according to the employment status of the household head, show significant re-distribution effects within groups.     

Does the retirement consumption puzzle differ across the distribution?

Previous research has repeatedly found a puzzling one-time drop in the mean and median of consumption at retirement, contrary to the predictions of the life-cycle hypothesis. However, very little is known as to whether these effects vary across the consumption distribution. This study expands upon the previous work by examining changes in the consumption distribution between the non-retired and the retired using quantile regression techniques on pseudo-cohorts from the cross-sectional data of the 1990–2007 Consumer Expenditure Survey. The results indicate that there are insignificant changes between these groups at the lower end of the consumption distribution, while there are significant decreases at the higher end of this distribution. In addition, these changes in the distribution are gradually larger in magnitude when moving from the lower end to the higher end, which is found using several different measures of consumption. Work-related expenditures are instead shown to decrease uniformly across the consumption distribution. This evidence reveals that there is a progressive distributional component to the retirement consumption puzzle.     

Reference distributions and inequality measurement

We investigate a general problem of comparing pairs of distributions which includes approaches to inequality measurement, the evaluation of “unfair” income inequality, evaluation of inequality relative to norm incomes, and goodness of fit. We show how to represent the generic problem simply using (1) a class of divergence measures derived from a parsimonious set of axioms and (2) alternative types of “reference distributions.” The problems of appropriate statistical implementation are discussed and empirical illustrations of the technique are provided using a variety of reference distributions.     

Improvements in children’s health: Does inequality matter?

The literature on the contributions to poverty reduction of average improvements in living standards vs. distributional changes uses only one measure of well-being – income or expenditure. Given that poverty is defined by deprivation over different dimensions, we explore the role of average improvements and distributional changes in children’s health and nutrition using the height of young children as our measure of well-being. Similar to the income literature, we find that shifts in the mean level of heights, not changes in distribution, account for most improvements in heights. Unlike the literature on income inequality, however, there is a positive association between improvements in average heights and reduced dispersion of those heights.     

Quantifying the Muslim population in Europe: Conceptual and data issues

A review of the growing literature on the Muslim population in Europe shows that it remains poorly captured in official statistics. There is no authoritative map of the distribution of Muslims in Europe, and little quantitative evidence on their demographic, social or economic characteristics. This paper undertakes a systematic review of the conceptual and methodological issues surrounding the quantification of Muslim populations. With few countries routinely collecting data on religious affiliation, this is generally based on an estimation of the association between religion and some other measure of identity, such as country of birth or nationality. The rationale for the various 'religiousproxy' methods, and their limitations, is discussed in relation to the range of different data regimes observed across the region. The paper argues that changes in the political status of Muslim populations (following naturalization) and the manner of their growth (increasingly driven by natural increase) have meant that in statistical terms, they represent a disappearing target. The paper concludes that meaningful statistics on the Muslims in Europe will increasingly depend on the direct measurement of religious affiliation.     

Income Comparison as a Determining Mechanism of Class Identification: A Quantitative and Simulation Study Using Japanese Survey Data

This paper questions whether personal income comparison explains the distributive gap between income and class identification by exploring the following two issues: empirical validity of income comparison as the determinant of class identification, and theoretical validity of income comparison for the distributive gap. For the first issue, we conduct a statistical analysis using data from the Social Stratification and Social Mobility surveys (1975–2005), and the Stratification and Social Psychology-I survey (2010). We find that the criteria for choosing reference groups changed historically from residential proximity to occupational equality. In addition, income comparison with sensitive to lower-income possessors and a distorted perception of income difference significantly affected class identification, except for the year of 1985. The simulation analysis employed to examine the second issue clarified that income comparison with the above-mentioned features yields a less skewed distribution compared to that of class identification. The data also indicates that the empirical conditions of income are satisfied for realization of this result. Thus, we could ascertain empirical and theoretical validity of income comparison as explanation for the distributive gap between income and class identification.     

Unemployment duration and the measurement of unemployment

We propose a framework in which the welfare bases of various unemployment measures available in the literature can be analyzed and a decomposition of these measures can be made into aggregate unemployment and the concentration of its distribution. A set of axioms for an unemployment measure is then introduced, which relate to the sensitivity of an unemployment measure to the inequality in the distribution of the unemployment. An unemployment measure is derived on the basis of these axioms that captures the distributional considerations in the measurement of unemployment.      

Explaining the Decline in Women's Household Labor: Individual Change and Cohort Differences

Women's hours of housework have declined, but does this change represent shifts in the behavior of individuals or differences across cohorts? Using data from the National Longitudinal Surveys, individual and cohort change in housework are examined over a 13‐year period. Responsibility for household tasks declined 10% from 1974–75 to 1987–88. For individual women, changes in housework are associated with life course shifts in time availability as well as with changes in gender attitudes and marital status, but are not related to changes in relative earnings. Cohort differences exist in responsibility for housework in the mid‐1970s and they persist over the 13‐year period. Overall, these findings suggest that aggregate changes in women's household labor reflect both individual change and cohort differences.     

Evaluating vehicle inspection/maintenance programs using on-road emissions data. The Atlanta Reference Method

On-road remote sensing data is an increasingly popular source of evaluation information for vehicle inspection/maintenance (I/M) programs. This article conducts one such remote sensing data evaluation for the Atlanta, Georgia, I/M program. The reference method involves comparing emissions differences in I/M and non-I/M fleet vehicles with those predicted by a regulatory computer model. Assuming that on-road emissions differences represent observed effectiveness and model-predicted emissions differences represent effectiveness goals, the Atlanta enhanced I/M program appears to be achieving 83% of its targeted emissions reductions. The method compares favorably with other remote sensing evaluation methods in its ability to be applied over time and its relatively small sample size requirement. The chief limitation to the approach is its reliance on a representative non-I/M fleet, which may differ in characteristics for which controls are difficult to locate. Such potential confounding factors include discrepancies in maintenance trends, socioeconomic conditions, and vehicle quality.