Has Income Segregation Really Increased? Bias and Bias Correction in Sample-Based Segregation Estimates

Abstract

Several recent studies have concluded that residential segregation by income in the United States has increased in the decades since 1970, including a significant increase after 2000. Income segregation measures, however, are biased upward when based on sample data. This is a potential concern because the sampling rate of the American Community Survey (ACS)—from which post-2000 income segregation estimates are constructed—was lower than that of the earlier decennial censuses. Thus, the apparent increase in income segregation post-2000 may simply reflect larger upward bias in the estimates from the ACS, and the estimated trend may therefore be inaccurate. In this study, we first derive formulas describing the approximate sampling bias in two measures of segregation. Next, using Monte Carlo simulations, we show that the bias-corrected estimators eliminate virtually all of the bias in segregation estimates in most cases of practical interest, although the correction fails to eliminate bias in some cases when the population is unevenly distributed among geographic units and the average within-unit samples are very small. We then use the bias-corrected estimators to produce unbiased estimates of the trends in income segregation over the last four decades in large U.S. metropolitan areas. Using these corrected estimates, we replicate the central analyses in four prior studies on income segregation. We find that the primary conclusions from these studies remain unchanged, although the true increase in income segregation among families after 2000 was only half as large as that reported in earlier work. Despite this revision, our replications confirm that income segregation has increased sharply in recent decades among families with children and that income inequality is a strong and consistent predictor of income segregation.

The Decline in Intergenerational Mobility After 1980

“…During the early 1980s there was a pronounced increase in the 90-10 income gap and a sharp rise in the income share of the top 1 percent (see Figure 1). At the same time, consumption inequality (Meyer and Sullivan, 2013), the returns to education (Goldin and Katz, 1999), and income segregation (Reardon et al, 2018) all grew markedly. With the advent of a more unequal society, concerns about a possible decline in equality of opportunity have risen to the forefront of policy discussion in the U.S.…”

Income Segregation: Up or Down, and for Whom?

“…The (unweighted) mean bias correction only for counts is .0068 while the mean total bias is .0114. Thus, estimates of the change in segregation by Logan et al (2018) and Reardon et al (2018) that corrected only for sample counts still overstated the growth in income segregation over this interval. Second, the three groups of points are roughly parallel.…”

“…This latter approach, however, complicates the resulting mathematical expressions and does not lead to a measurable improvement in performance in our simulated data. 2 A somewhat similar correction was subsequently advanced by Reardon et al (2018). Their correction applies to H and R, but not NSI.…”

“…If the full curve of values of estimated H at every percentile matches the estimated values form the unit-level household data, the overall value of H can be accurately estimated from it. Reardon et al (2018Reardon et al ( , p. 2138 argue that because 'there is no theoretical reason to expect systematic bias related to the binning of income data," this procedure is unlikely to bias results.…”

“…We find that social scientists cannot rely on published tract-level data to discover the real levels and trends in income segregation. After recognizing and seeking to take into account the upward bias associated with smaller samples after 2000, two research teams (Logan et al 2018 andReardon et al 2018) estimated that the post-2000 increase was about half of what had previously been reported. We take advantage of confidential census data files at the individual family level, obviating the need to interpolate income distributions within the categories that are used in public tract data and allowing us to account for variance in sampling probabilities.…”