Indexes of Racial Residential Segregation for 109 Cities in the United States, 1940 to 1970

Abstract

An index of racial residential segregation for a city may be calculated from census data reporting the number of white and nonwhite households resident in each city block. Such an index summarizes the dissimilarity in residential location of the two groups. Segregation indexes for 109 cities for the years 1940, 1950, and 1960 were published in Taeuber and Taeuber Negroes in Cities (1965).

Segregation indexes for 109 cities for 1970, together with the previously published indexes for the three earlier census dates, are presented in Table 1. The trend data from 1940 through 1970 refer to residential segregation of whites and nonwhites. For 1970 only, segregation indexes are also presented comparing whites and Negroes.

The trend data reveal a distinctive pattern of change during each of the three decades. From 1960 to 1970, declines in segregation prevailed among cities in each region of the country.

The indexes for 1970 were calculated from Public Use Summary Tapes issued by the Bureau of the Census. Certain difficulties were encountered in the use of these tapes. A methodological appendix describes the data source and retrieval procedure for calculation of city segregation indexes for 1970.     

Axiomatic measurement of multidimensional well-being inequality: Some distributional questions

This paper focuses on two main issues which are crucial for improving on the analysis of multidimensional inequality: the effect of both the dispersion of well-being attributes across individuals and the interaction among attributes on the measurement of multidimensional well-being. To approach these distributional questions we rely on the Atkinson, Kolm, Sen (hereafter AKS) methodology, which defines a multidimensional inequality index consistent with the Pigou–Dalton principle. This index can be decomposed into univariate indexes belonging to the class of AKS indexes, and a residual term accounting for the interaction across dimensions. The empirical application investigates the evolution of inequality in well-being across some EU countries between 1994 and 2001.Since the multidimensional index depends on the values assigned to the parameters, we test the sensitivity of the trend in well-being to the degree of inequality aversion on each dimension. Our empirical results summarize the evolution of inequality for the indicators of well-being considered both separately and jointly, over time and across countries.     

A characterization of optimal feasible tax mechanism

If the provision of public good is financed by property (wealth or endowment) taxes, what is the optimal tax mechanism when agents have private information about his own endowment? Employing the state-dependent implementation model, under incentive compatibility and feasibility constraints, we provide the full characterization of an optimal tax mechanism with two agents and its properties. Some interesting comparative statics analyses are also provided. For the general n-agent case, some partial characterization results are obtained. In addition, we fully characterize the optimal tax mechanism for the corresponding infinitely large economy.     

Poverty and time

We examine the measurement of individual poverty in an intertemporal context. Our aim is to capture the importance of persistence in a state of poverty and we characterize a corresponding individual intertemporal poverty measure. Our first axiom requires that intertemporal poverty is identical to static poverty in the degenerate single-period case. The remaining two properties express decomposability requirements within poverty spells and across spells in order to reflect the persistence issue. In addition, we axiomatize an aggregation procedure to obtain an intertemporal poverty measure for societies and we illustrate our new index with an application to EU countries.     

Three Likelihood-Based Methods For Mean and Covariance Structure Analysis With Nonnormal Missing Data

Survey and longitudinal studies in the social and behavioral sciences generally contain missing data. Mean and covariance structure models play an important role in analyzing such data. Two promising methods for dealing with missing data are a direct maximum-likelihood and a two-stage approach based on the unstructured mean and covariance estimates obtained by the EM-algorithm. Typical assumptions under these two methods are ignorable nonresponse and normality of data. However, data sets in social and behavioral sciences are seldom normal, and experience with these procedures indicates that normal theory based methods for nonnormal data very often lead to incorrect model evaluations. By dropping the normal distribution assumption, we develop more accurate procedures for model inference. Based on the theory of generalized estimating equations, a way to obtain consistent standard errors of the two-stage estimates is given. The asymptotic efficiencies of different estimators are compared under various assumptions. We also propose a minimum chi-square approach and show that the estimator obtained by this approach is asymptotically at least as efficient as the two likelihood-based estimators for either normal or nonnormal data. The major contribution of this paper is that for each estimator, we give a test statistic whose asymptotic distribution is chi-square as long as the underlying sampling distribution enjoys finite fourth-order moments. We also give a characterization for each of the two likelihood ratio test statistics when the underlying distribution is nonnormal. Modifications to the likelihood ratio statistics are also given. Our working assumption is that the missing data mechanism is missing completely at random. Examples and Monte Carlo studies indicate that, for commonly encountered nonnormal distributions, the procedures developed in this paper are quite reliable even for samples with missing data that are missing at random.     

Patterns of gay and lesbian partnering in the larger metropolitan areas of the United States

This paper had two objectives. First, we developed for each large metropolitan area of the United States with a population of 500,000 or more in 1990 four indexes of gay partnering and four indexes of lesbian partnering. We compared and related these indexes and their variable measurements with one another. Second, using what we argue is the statistically and demographically preferred set of gay and lesbian partnering rates, we proposed and tested an assortment of ecological hypotheses relating characteristics of the metropolitan areas with the gay and lesbian partnering rates. Rates of gay and lesbian partnering, we show, are more influenced by such metropolitan characteristics as physical climate and the crime rate than by a religious characteristic such as the number of Southern Baptist adherents. Among the conclusions of the paper is our claim that there needs to be greater consideration of the methodological issues related to the use of government data for the development of rates of gay and lesbian partnering.     

Probabilistic spatial power indexes

In this study, we present a generalization of spatial power indexes able to overcome their main limitations, namely (i) the excessive concentration of power measures; (ii) the too high sensitivity to players’ location in the ideological space. Voters’ propensity to support an issue is modeled via a random utility function with two additive terms: the deterministic term accounts for voters’ preference-driven/predictable behavior; the random one is a catch-all term that accounts for all the idiosyncratic/unpredictable factors. The relative strength of the two terms gives rise to a continuum of cases ranging from the Shapley value, where all aggregation patterns are equally probable, to a standard spatial value, like the Owen–Shapley index, where instead the conditional order is fully deterministic. As an illustrative application, we analyze the distribution of power in the Council of Ministers under three different scenarios: (i) EU15 Pre-Nice; (ii) EU27 Nice Treaty; (iii) EU27 Lisbon Treaty.     

Measuring influence in command games

In the paper, we study a relation between command games proposed by Hu and Shapley and an influence model. We show that our framework of influence is more general than the framework of the command games. We define several influence functions which capture the command structure. These functions are compatible with the command games, in the sense that each commandable player for a coalition in the command game is a follower of the coalition under the command influence function. Some of the presented influence functions are equivalent to the command games, that is, they are compatible with the command games, and additionally each follower of a coalition under the command influence function is also a commandable player for that coalition in the command games. For some influence functions we define the equivalent command games. We show that not for all influence functions the compatible command games exist. Moreover, we propose a more general definition of the influence index and show that under some assumptions, some power indices, which can be used in the command games, coincide with some expressions of the weighted influence indices. Both the Shapley–Shubik index and the Banzhaf index are equal to a difference between the weighted influence indices under some influence functions, and the only difference between these two power indices lies in the weights for the influence indices. An example of the Confucian model of society is broadly examined. The authors wish to gratefully thank two anonymous referees for useful suggestions concerning this paper.     

A general class of inequality elasticities of poverty

Many authors have recently emphasized the crucial role of income inequalities in the design of efficient policies aimed at reducing poverty. However, the link between variations in the degree of inequality and variations in poverty is not well documented. The literature, for instance, does not provide any satisfying tool for predicting how a small relative variation in the Gini index may be associated with a variation in the headcount index. In the present paper, we define a family of Lorenz curve transformations that can directly be interpreted in terms of relative variations of known inequality measures. Then, we extend Kakwani’s (Rev Income Wealth 39(2):121–139, 1993) methodology for the calculation of inequality elasticities of poverty. Improvements are threefold with respect to Kakwani’s work. First, our formulas are not confined to the sole Gini index. Secondly, they embrace the uncertainty and the complexity of the mechanical link between inequality and poverty. Third, using some flexible functional form, one can easily perform an accurate estimation of the point inequality elasticities of poverty corresponding to observed variations of a given income distribution. We also propose a simple measure that may be helpful to assess how “pro-poor” are inequality variations by comparing the observed elasticities with the set of theoretical elasticities that could be obtained from the initial income distribution.     

ON THE ASSIGNMENT OF INDIVIDUALS TO LATENT CLASSES

Consider an m-way cross-classification table (for m = 3, 4, … ) of m dichotomous variables that describes (1) the 2 ^m possible response patterns to a set of m questions (where the response to each question is binary), and (2) the number of individuals whose responses to the m questions can be described by a particular response pattern, for each of the 2 ^m possible response patterns. Consider the situation where the data in the cross-classification table are analyzed using a particular latent class model having T latent classes (for T = 2, 3, …), and where this model fits the data well. With this latent class model, it is possible to estimate, for an individual who has a particular response pattern, what is the conditional probability that this individual is in a particular latent class, for each of the T latent classes. In this article, the following question is considered: For an individual who has a particular response pattern, can we use the corresponding estimated conditional probabilities to assign this individual to one of the T latent classes? Two different assignment procedures are considered here, and for each of these procedures, two different criteria are introduced to help assess when the assignment procedure is satisfactory and when it is not. In addition, we describe here the particular framework and context in which the two assignment procedures, and the two criteria, are considered. For illustrative purposes, the latent class analysis of a classic set of data, a four-way cross-classification of some survey data, obtained in a two-wave panel study, is discussed; and the two different criteria introduced herein are applied in this analysis to each of the two assignment procedures .     

On monotonicity in economies with indivisible goods

We consider the problem of fair allocation in economies with indivisible objects that may or may not be desirable (for instance, activities that may or may not be pleasurable but have to be carried out unless there are not enough agents for that). We search for efficient solutions satisfying two additional properties. First, each agent should find his bundle at least as desirable as the bundle that would be assigned to him in the hypothetical economy in which all agents have preferences identical to his, under equal treatment of equals and efficiency. In a preliminary step, we show that there is no logical relation between this requirement and no-envy, and between it and egalitarian-equivalence. We also establish the existence of efficient allocations satisfying it. The second property, object monotonicity, says that the availability of additional objects either has a negative impact on everyone's welfare, or it has a positive impact on everyone's welfare. We show that there is no object-monotonic selection from the correspondence that associates with each economy its set of efficient allocations meeting an even weaker version of the bound.I am grateful to Atila Abdulkadiroglu, Koichi Tadenuma, and a referee for their very helpful comments.     

Egalitarian property for power indices

In this study, we introduce and examine the Egalitarian property for some power indices on the class of simple games. This property means that after intersecting a game with a symmetric or anonymous game the difference between the values of two comparable players does not increase. We prove that the Shapley–Shubik index, the absolute Banzhaf index, and the Johnston score satisfy this property. We also give counterexamples for Holler, Deegan–Packel, normalized Banzhaf and Johnston indices. We prove that the Egalitarian property is a stronger condition for efficient power indices than the Lorentz domination.     

What’s so special about Euclidean distance?

In this paper, we provide an application-oriented characterization of a class of distance functions monotonically related to the Euclidean distance in terms of some general properties of distance functions between real-valued vectors. Our analysis hinges upon two fundamental properties of distance functions that we call “value-sensitivity” and “order-sensitivity”. We show how these two general properties, combined with natural monotonicity considerations, lead to characterization results that single out several versions of Euclidean distance from the wide class of separable distance functions. We then discuss and motivate our results in two different and apparently unrelated application areas—mobility measurement and spatial voting theory—and propose our characterization as a test for deciding whether Euclidean distance (or some suitable variant) should be used in your favourite application context. We would like to thank an editor and especially two anonymous referees for very useful comments which helped us to improve the paper substantially.     

The replacement principle for the provision of multiple public goods on tree networks

This article considers the provision of two public goods on tree networks where each agent has a single-peaked preference. We show that if there are at least four agents, then no social choice rule exists that satisfies efficiency and replacement-domination. In fact, these properties are incompatible, even if agents’ preferences are restricted to a smaller domain of symmetric single-peaked preferences. However, for rules on an interval, we prove that Miyagawa’s (Soc Choice Welf 18:527–541, 2001) characterization that only the left-peaks rule and the right-peaks rule satisfy both of these properties also holds on the domain of symmetric single-peaked preferences. Moreover, if agents’ peak locations are restricted to either the nodes or the endpoints of trees, rules exist on a subclass of trees. We provide a characterization of a family of such rules for this tree subclass.     

No externalities: a characterization of efficiency and incentive compatibility with public goods

We show that efficient anonymous incentive compatible (dominant strategy) mechanisms for public goods eliminate externalities, i.e., each individual is unable to change the welfare of anyone else. The characterization is used to derive existence and non-existence results for models with a finite number of individuals and to explain existence results in the continuum. A similar characterization and conclusions are demonstrated for private goods in (J Econ Theory 85:169–225, 1999). However, unlike private goods, elimination of externalities with public goods implies that individuals cannot change the outcome. Hence, such mechanisms provide only weak incentives for truth-telling.     

On randomized rationality

In contrast to the traditional notion of rationalizability of stochastic choice which requires the preference relations to be strict, we propose a notion of rationalizability without requiring the preference relations to be strict. Our definition is based on the simple hypothesis of a two-stage choice process: stage (i) a preference relation R is drawn according to a probability assignment; stage (ii) an alternative is picked from each feasible set according to a uniform lottery over the R-greatest set in it. We provide a necessary and sufficient condition for rationalizability of stochastic choice. Since our framework is general enough to subsume the traditional case, our result also provides an alternative characterization of the traditional notion of rationalizability. We also show the equivalence between the two notions of rationalizability in a specific case.     

One-mode projection analysis and design of covert affiliation networks

Within the field of national security and counterterrorism a great need exists to understand covert organizations. To better understand these cellular structures we model and analyze these cells as a collection of subsets of all participants in the covert organization, i.e., as hypergraphs or affiliation networks. Such a covert affiliation network structure is analyzed by evaluating the one-mode projection of the corresponding hypergraph. First we provide a characterization of the total distance in the one-mode projection using its corresponding cell-shrunken version. Secondly we evaluate the one-mode projection with respect to the secrecy versus information tradeoff dilemma every covert organization has to solve. We present and analyze affiliation networks representing common covert organizational forms: star, path and semi-complete hypergraphs. In addition we evaluate an example of a covert organization wishing to conduct an attack and compare its performance to that of the common covert organizational forms. Finally we investigate affiliation networks that are optimal in the sense of balancing secrecy and information. We show how any affiliation tree can be improved by altering its structure. Finally we prove that among covert organizational forms in the class of hypertrees with the same number of cells uniform star affiliation networks are optimal.     

Responses of the ichthyofauna to urbanization in two urban areas in Southeast Brazil

In this study, we evaluated the trophic structure and composition of the ichthyofauna in streams from non-urbanized and urbanized areas in two municipalities with approximately 30,000 inhabitants. We sampled fish fauna in nine pool-run stretches, four located in urban and five in non-urban areas. We adapted a physical habitat index (PHI) that summarized the physical attributes of the habitat, and a fish-based biotic integrity index (IBI) for the trophic structure of fish assemblage. Higher median scores of habitat parameters characterized non-urban stretches owing to better riparian vegetation and shading, bank stability and larger substrates. Diversity, richness and evenness indexes, as well as the abundance and biomass comparison (ABC), did not differ between urban and non-urban areas. The PHI was significantly correlated with the IBI and a non-metric multidimensional scaling (NMDS) analysis showed differences in the composition of the ichthyofauna. These results illustrated a common process in fish assemblages subjected to environmental impact, in which the generalist species replaced more specialist species, altering the species composition but maintaining a similar community structure. In general, the species responses were dependent on their trophic plasticity and foraging habitats. We showed that in a gradient of habitat alteration, species composition and thophic structure are better indicators of degradation than simple diversity indexes. We also discuss the implications of the urbanization in small towns toward changes in the species composition of freshwater fish, and the utilization of biotic and abiotic characteristics to document these changes.     

Sophisticated voting rules: the case of two tournaments

A voting rule maps voter preferences into outcomes, and is called sophisticated if there exists a voting tree whose sophisticated outcomes coincide with the voting rule for every voter preference. As yet, no complete characterization of such rules is available. In this paper, we provide an important step toward this characterization by completely solving the problem when there are two possible sets of voter preferences.The second author was supported by the Office of Naval Research, Grant N00014-92-J-1387.