It is Surprisingly Hard to Measure Income Segregation

• In Event: Measuring Socioeconomic Status to Contextualize Educational Achievement: A Discussion on Methods, Applications, and Challenges

Abstract

A growing scholarship finds increasing residential segregation by income in the US (Reardon & Bischoff 2011; Bischoff & Reardon 2014; Massey, Rothwell, & Domina 2009; Owens 2016; Jargowsky 1996; Reardon, Bischoff, Owens, & Townsend 2018) such that class appears to be catching up to race as a primary source of both residential and school segregation (Massey, Rothwell, & Domina 2009; Owens, Reardon, & Jencks 2016). However, scholars have recently shown that the increase in residential income segregation is exaggerated due to asymmetric bias from sampling variation from 2000 to 2007, when the Census Bureau switched from measuring income in the Census to measuring it in the ACS (Logan, Foster, Ke, & Li 2018; Reardon, Bischoff, Owens, & Townsend 2018).

We consider two different, more powerful sources of bias that countervail finite sampling bias. One is downward bias due to response error in the measurement of income. Measurement error adds noise to income distributions such that it increases the spread of tracts’ income distributions and exaggerates the extent to which they overlap, making them appear less segregated. This is particularly concerning because income measures are error-prone such that segregation estimates are typically underestimated by 20 to 30 percent. This bias is even greater when reported annual income is used to proxy for long-run economic status, which leads to biases on the order of 50 percent.
The other downward bias we consider is pooling bias. In pooled samples like those used by the ACS, tract- and metro-level income variation over time appears as within-tract variation such that between-tract differences are underestimated and within-tract variation is overestimated. Because the ACS uses pooled sampling and the Census does not, the transition from Census to ACS income data downwardly biases the income segregation trend.

We propose a correction that deconvolves coarsened income by estimating tract means and standard deviations in log-dollars using constrained heteroskedastic ordered probit models (Reardon, Shear, Castellano, & Ho 2017), then adjusting the means and standard deviations to remove noise (Reardon, Kalogrides, & Ho 2017) and correct for pooling bias. We assess this method via simulation.

We use this approach to replicate key findings from Reardon, Bischoff, Owens, and Townsend (2018) and Massey, Rothwell, and Domina (2009). We find that the magnitude of income segregation and its increase from 2000 to 2007 have been severely understated such that the segregation of long-run income (e.g. a 7-year average) has already surpassed white/black segregation.

Authors

• Josh Gagné, Stanford University

• Sean F. Reardon, Stanford University