Beyond the Census Tract: Methods for
Studying the Geographical Scale of
Metropolitan Racial Segregation
Sean F. Reardon, Stanford University
Barrett A. Lee, Penn State University
Glenn Firebaugh, Penn State University
Stephen A. Matthews, Penn State University
Kendra Bischoff, Stanford University
Chad R. Farrell, University of Alaska
David O’Sullivan, University of Auckland
RC-28 meeting in Brno, Czech
Republic, Friday, May 25, 2007
Acknowledgments
• Technical support: Steve Graham and Yosef Bodovski,
Penn State Population Research Institute
• Funding: National Science Foundation (SES-0520400
and SES-052045), Penn State Children, Youth and
Families Consortium, Penn State Population Research
Institute
2
Part of a Larger Project – Three Objectives
1. Develop methods for studying the
geographical scale of segregation (the
talk today)
2. Design strategies for estimating the
determinants of segregation at different
geographical scales in U.S. cities
3. Specifying outcome-sensitive models of
the consequences of segregation in U.S.
cities
3
Defining Terms
Segregation – extent to which individuals’ local
environments differ in their composition on some
population characteristic, such as race (“racial
segregation”)
• Each individual’s local environment is relatively similar in
racial composition  little racial segregation/ great
variation in racial composition  high racial segregation
• Corresponds to Massey’s ‘evenness’ dimension
4
Definitions, continued
Geographical scale of segregation refers to
the size or ‘radius’ of the local
environments whose compositions are
being compared
5
Figure 1: Stylized Racial Distribution in Four Hypothetical Regions
100%
Region A
50%
0%
100%
Region B
50%
0%
100%
Region C
50%
0%
100%
Region D
50%
0%
0
8
16
24
32
40
Distance (km)
6
“Beyond the census tract” -But what’s wrong with census tracts?
1.
Bounded-region problem: Indifference to proximity
within and across tracts. Residents of:
–
–
different tracts have no proximity
same tract have equal proximity
2.
Fixed-boundaries problem: You cannot vary radius size
to study segregation at different geographic scales (the
issue of interest here)
3.
Arbitrary-size problem: Census tracts vary greatly in
size, so you aren’t comparing “like with like” in
comparing “local environments” (next slide)
7
8
Bounded-Region Problem: Individual and
Tract Proximity
1
6
Tract B
3 4
5
Tract A
Tract C
Tract D
2
9
From tract-based to local environmentbased methods
How to solve the three problems of using tracts to study
segregation (bounded-region, fixed-boundaries -- so you
cannot study segregation at different geographical
scales -- and arbitrary-size)?
• Focus on location of individuals, their residential
proximity
• Each person at center of local environment (LE)
• LE made up of distance-weighted average of populations
at each point within radius
• Compare LE racial mix to larger region
• Segregation = average degree to which individual LEs
differ from overall composition of city
10
Local Environments
1
6
Tract B
3 4
5
Tract A
Tract C
Tract D
2
11
Types of local environments
• Strength of LE approach: flexibility
• Three types of LEs of interest:
– Micro: pedestrian neighborhood
– Meso: elementary school, daycare, police substation
– Macro: shopping, church, high school
• Researcher can compare level of segregation
across different-sized LEs – “segregation profile”
is curve showing level of segregation across
different-sized LEs
12
Segregation measure: H
• Theil’s information theory index (H)
• Compares racial mix of LEs to metro as whole –
how much less diverse is former than latter?
• Maximum seg = 1 (LEs are monoracial)
• Minimum seg = 0 (LEs match metro)
• Can be extended to multi-group situation
• H computed for minority-W combinations
• H computed for LEs of varying radii (500m,
1000m, 2000m, 4000m)  segregation profiles
for cities (next slide)
13
Example: Segregation Profiles for Selected Metropolitan
Areas and Racial Group Combinations
0.7
0.6
Richmond, VA Black-White
Dallas-Plano-Irving, TX White-Black-Hispanic-Asian
Oakland-Fremont, CA Hispanic-White
Cincinnati-Middletown, OH Asian-White
Segregation (H).
0.5
0.4
0.3
0.2
0.1
0.0
500
1000
2000
4000
Scale (m)
14
Does size of LE or ‘catchment area’ matter? Top 10 Hispanic-White
Segregated Metro Areas by LE size
H500
Metro Area
H4000
Metro Area
.469
Essex Co., MA
.315
Los Angeles, CA
.464
Springfield, MA
.303
Newark, NJ
.434
Hartford, CT
.291
Camden, NJ
.433
New York, NY
.287
Chicago, IL
.428
Philadelphia, PA
.280
Hartford, CT
.423
Los Angeles, CA
.277
Philadelphia, PA
.422
Camden, NJ
.270
Detroit, MI
.420
Newark, NJ
.263
Bakersfield, CA
.411
Providence, RI
.259
Milwaukee, WI
.405
Boston, MA
.254
Oxnard, CA
15
Does size of ‘catchment area’ matter? Part 2:
Black-White Segregation Profiles for Selected
Metropolitan Areas
0.7
0.6
Segregation (H).
0.5
0.4
0.3
Philadelphia, PA
St. Louis, MO-IL
Nassau-Suffolk, NY
Jacksonville, FL
0.2
0.1
0.0
500
1000
2000
4000
Scale (m)
16
How did we construct the seg profiles?
Data and procedures (GIS)
• 2000 US census data for 100 largest metro areas –
provides block counts of racial groups
• Divide block map into 50x50m cells, and estimate racial
group counts for each cell (sensitivity analysis - this size
works well)
• Smooth grid, preserving block counts
• Apply proximity function (distance-decay function, so
nearby populations are weighted more heavily) to
compute racial composition of LEs
• Segregation = average degree to which individual LEs
differ from overall composition of city
17
H ratio
• Scale-specific Hs complemented with H ratio
• H4000/H500 operationalizes slope of
segregation profile
• High value = flatter slope
• Low value = steeper slope
• Share of micro-segregation due to macrosegregation
18
Contributions
• Conceptualizes segregation as variation in racial
composition of local environments – segregation is
average of the LE variations
• Solves problems of tract-based approaches:
– Bounded region (so proximity is 1 for all residents in a tract and
0 for all residents outside the tract)
– Fixed-boundaries (so you can’t compare segregation at different
geographical scales)
– Arbitrary size
• Segregation profile a useful tool:
– captures segregation at multiple scales
– introduces new dimension of segregation (slope)
• Results highlight scale-sensitive nature of segregation
patterns, determinants
19
Resources
• Working papers available at:
– http://www.pop.psu.edu/mss/
– click on “publications”
• Plans for software/data dissemination
20
Appendix material
If there is time in the presentation, some of
the appended material might be discussed
as well.
21
Next steps
• Technical improvements:
– fine-tuning LE size to granularity
– increasing realism of landscape (adding barriers)
• Need scale-specific theory of segregation
• What accounts for micro-seg, macro-seg,
relation between them (slope)?
• Factors differentiating intrametropolitan space
• More attention to consequences
• Implications of segregation scale for age groups
22
Average interquartile range in tract size
25 highest-density metro areas: 1.1 to 6.2 km2
25 lowest-density metro areas: 2.5 to 27.8 km2
Average min/max tract size for 100 largest metro areas
Minimum: .4 km2 (.16 mi2)
Maximum: 1,319.0 km2 (509.3 mi2)
Tract size for Riverside-San Bernardino-Ontario metro area
Median: 4.9 km2 (1.9 mi2)
Mean: 121.3 km2 (46.8 mi2)
Minimum: .5 km2 (.2 mi2)
Maximum: 20,700.4 km2 (7,992.5 mi2)
23
Checkerboard Problem
City A
City B
24
Mean Segregation Levels by Local Environment Size
and Racial Group Combination
Groups
H500
H1000
H2000
H4000
H ratio
B-W
.447
(.141)
.403
(.141)
.349
(.132)
.279
(.117)
.611
(.100)
H-W
.282
(.086)
.242
(.086)
.200
(.082)
.154
(.072)
.526
(.148)
A-W
.212
(.049)
.168
(.047)
.133
(.045)
.103
(.041)
.476
(.112)
W-B-H-A
.343
(.099)
.304
(.096)
.258
(.089)
.204
(.079)
.584
(.094)
25
Determinants of Hispanic-White Segregation by Local Environment Size
Predictor
H500
H4000
H (tract)
Northeast
.063**
.037
.064**
Midwest
.000
-.013
.011
South
.000
-.038
-.025
Metro population (log)
.021
.027**
.054***
% Hispanic
.265***
.242***
---
% Black
.247*
.231**
---
Hispanic/white income
-.174*
---
Hispanic home ownership
-.225**
---
---
% manufacturing
.466**
.348*
---
-.358***
% college
-1.004*
---
---
Intercept
.166
-.318
-.288
Adjusted R2
.424
.332
.417
26
Determinants of H Ratio (H4000/H500) by Racial Group Combination
Predictor
B-W
H-W
A-W
W-B-H-A
Northeast
-.091*
-.032
-.121***
-.079***
Midwest
.049
-.032
-.067*
.037
South
-.048
-.138***
-.060**
-.065**
Metro population (log)
.045***
.043*
.072***
.025*
% Black
.314**
---
---
.593***
% Hispanic
.120*
.388*
-.135**
.513***
.339*
-----
% Asian
---
.374***
Hispanic home ownership
---
.294*
---
Minority/white income
---
---
---
% Retirement
---
---
Intercept
-.056
-.237
-.332
-.471
Adjusted R2
.437
.362
.606
.501
-1.130***
.642**
---
27