Beyond the Census Tract: Methods for Studying the Geographical Scale of

Metropolitan Racial Segregation

Sean F. Reardon, Stanford UniversityBarrett A. Lee, Penn State University

Glenn Firebaugh, Penn State UniversityStephen A. Matthews, Penn State University

Kendra Bischoff, Stanford UniversityChad R. Farrell, University of Alaska

David O’Sullivan, University of Auckland

RC-28 meeting in Brno, Czech Republic, Friday, May 25, 2007

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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

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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

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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

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Definitions, continued

Geographical scale of segregation refers to the size or ‘radius’ of the local environments whose compositions are being compared

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Region A

0%

50%

100%

Region B

0%

50%

100%

Region C

0%

50%

100%

Region D

0%

50%

100%

Pe

rce

nta

ge B

lack

0 8 16 24 32 40

Distance (km)

Figure 1: Stylized Racial Distribution in Four Hypothetical Regions

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“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)

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Bounded-Region Problem: Individual and Tract Proximity

1 6

543

2

Tract A

Tract DTract C

Tract B

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From tract-based to local environment-based 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

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Local Environments

1 6

543

2

Tract A

Tract DTract C

Tract B

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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

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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)

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Example: Segregation Profiles for Selected Metropolitan Areas and Racial Group Combinations

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

500 1000 2000 4000

Scale (m)

Seg

rega

tion

(H).

Richmond, VA Black-WhiteDallas-Plano-Irving, TX White-Black-Hispanic-AsianOakland-Fremont, CA Hispanic-WhiteCincinnati-Middletown, OH Asian-White

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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

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Does size of ‘catchment area’ matter? Part 2: Black-White Segregation Profiles for Selected

Metropolitan Areas

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

500 1000 2000 4000

Scale (m)

Seg

rega

tion

(H).

Philadelphia, PASt. Louis, MO-IL

Nassau-Suffolk, NYJacksonville, FL

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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

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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 macro-

segregation

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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

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Resources

• Working papers available at:– http://www.pop.psu.edu/mss/– click on “publications”

• Plans for software/data dissemination

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Appendix material

If there is time in the presentation, some of the appended material might be discussed as well.

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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

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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)

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Checkerboard Problem

City A City B

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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)

Mean Segregation Levels by Local Environment Size and Racial Group Combination

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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* --- -.358***

Hispanic home ownership -.225** --- ---

% manufacturing .466** .348* ---

% college -1.004* --- ---

Intercept .166 -.318 -.288

Adjusted R2 .424 .332 .417

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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***

% Asian --- .374*** .339* ---

Hispanic home ownership --- .294* --- ---

Minority/white income --- --- --- .642**

% Retirement --- --- -1.130*** ---

Intercept -.056 -.237 -.332 -.471

Adjusted R2 .437 .362 .606 .501