Socioeconomic Segregation in Large Cities in France and the United States

Abstract

Past cross-national comparisons of socioeconomic segregation have been undercut by lack of comparability in measures, data, and concepts. Using IRIS data from the French Census of 2008 and the French Ministry of Finance as well as tract data from the American Community Survey (2006–2010) and the U.S. Department of Housing and Urban Development Picture of Subsidized Households, and constructing measures to be as similar as possible, we compare socioeconomic segregation in metropolitan areas with a population of more than 1 million in France and the United States. We find much higher socioeconomic segregation in large metropolitan areas in the United States than in France. We also find (1) a strong pattern of low-income neighborhoods in central cities and high-income neighborhoods in suburbs in the United States, but varying patterns across metropolitan areas in France; (2) that high-income persons are the most segregated group in both countries; (3) that the shares of neighborhood income differences that can be explained by neighborhood racial/ethnic composition are similar in France and the United States; and (4) that government-assisted housing is disproportionately located in the poorest neighborhoods in the United States but is spread across many neighborhood income levels in France. We conclude that differences in government provision of housing assistance and levels of income inequality are likely important contributing factors to the Franco-U.S. difference in socioeconomic segregation.

Appendix: Measures and Methods for Income Segregation Statistics

NSI Calculation

NSI for a metropolitan area is defined as follows:

$$ NSI=\frac{\upsigma_N}{\upsigma_H}=\frac{\sqrt{\frac{{\displaystyle {\sum}_{n=1}^N{h}_n{\left({\overline{y}}_n-\overline{y}\right)}^2}}{H}}}{\sqrt{\frac{{\displaystyle {\sum}_{i=1}^H{\left({y}_i-\overline{y}\right)}^2}}{H}}}, $$

where H is the number of households in the metropolitan area, h _n represents the number of households in the nth neighborhood, y represents income for the ith household, ${\overline{y}}_n$ represents the average income for the nth neighborhood, and $\overline{y}$ indicates metropolitan average income. The numerator may be calculated for both France and the United States directly from the French Ministry of Finance IRIS data and the ACS data, respectively. The denominator—the standard deviation of metropolitan household income—may be directly calculated from the IRIS data for France from summing within-IRIS deviation (provided in the data) and between-IRIS deviation (calculated from IRIS means). For the United States, we estimate the denominator from counts of numbers of households in 16 income ranges in each metropolitan area. We do this by assuming a lognormal distribution of income and then using a maximum likelihood estimation to estimate the variability of tract income for each metropolitan income from the data. In practice, this is done using Stata’s intreg command, estimating an intercept-only model of metropolitan income from tract income counts in categories, which also generates an estimate of the variability of income. We then calculate the mean and standard deviation of household income unlogged from the logged mean and standard deviation estimates produced by intreg using formulas from Johnson et al. (1994).

Theil’s Segregation Index, Income Percentile Segregation Calculations, and Reardon’s Rank-Ordered H

If p denotes income percentile ranks for an income distribution, for any value of p, we dichotomize the income distribution at p and compute the segregation between those with income ranks less than p and those with income ranks greater than or equal to p. If H(p) is Theil’s information theory index of segregation (see James and Taeuber 1985), and E(p) is the entropy statistic for p (used in the calculation of H(p)), then the rank-order information theory index (H ^R) is defined as follows:

$$ {H}^R=2 ln(2){\displaystyle {\int}_0^1E(p)}H(p)dp. $$

We calculate H(p) and H ^R using methods described in Reardon and Bischoff (2011:1110–1111, and appendix A).We also apply their method for making income percentile graphs developed with H(p) to the standard index of dissimilarity, which is a straightforward extension.

We initially perform standard computations of Theil’s entropy index of segregation (H(p)) and the index of dissimilarity (D(p)) for everyone below p and at or above p for each of the income cut points available in the two data sets.

In the U.S. data, counts of households are reported in 16 categories. For the French data, we have reports of income deciles, from which we calculated counts of households in 10 income categories. We also compute the percentile corresponding to each of these cut points on the income distribution from the data (p).

We then regress these calculated segregation indexes (H(p)) on the corresponding percentiles (p). Our specification uses a fourth-order quadratic for p to allow for nonlinearity. (We found very little predictive change from adding a fifth order term.) We use the resulting curve to predict the segregation scores for all percentiles of the income distribution from the 10th to the 90th percentile in the two countries. These are shown in the Figs. 1 and 2 for both entropy and the index of dissimilarity.

To compute the rank-ordered H ^R statistic, we apply Reardon and Bischoff’s (2011: appendix A) integral evaluation formula to the fourth-order quadratic coefficients. The formula evaluates the integral and also applies a set of weights, which weight percentiles of the income distribution toward the center of the income distribution more heavily and give little weight to percentiles at the extremes.

Table 9 Comparison of tract and block group segregation, United States