A number of empirical studies have tested the spatial mismatch hypothesis by examining the commuting times of blacks and whites. This note points out that the link between spatial mismatch and commuting times may be weak when employment probabilities decline as the distance from job site to residence increases. A simple spatial model of urban employment is developed in which a fixed number of agents live in the central city. Two examples are presented in which increased spatial mismatch may either increase or decrease the average commuting time of central city minorities, depending on the rate at which employment probabilities decline with distance.unemployment, insurance, compensation, older, workers, O'Leary, Wandner

Kelly DeRango

English

Research Papers in Economics

Upjohn Institute Working Papers Upjohn Research home page
2000
A Note on Commutes and the Spatial Mismatch
Hypothesis
Kelly DeRango
W.E. Upjohn Institute
Upjohn Institute Working Paper No. 00-59
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Citation
DeRango, Kelly. 2000. "A Note on Commutes and the Spatial Mismatch Hypothesis." Upjohn Institute Working Paper No. 00-59.
Kalamazoo, MI: W.E. Upjohn Institute for Employment Research.
http://research.upjohn.org/up_workingpapers/59A Note on Commutes and the Spatial Mismatch Hypothesis
Kelly DeRango
Research Fellow
W.E. Upjohn Institute for Employment Research
300 South Westnedge Avenue
Kalamazoo, Michigan 49007-4686
January 2000
ABSTRACT
A number of empirical studies have tested the spatial mismatch hypothesis by examining
the commuting times of blacks and whites. This note points out that the link between spatial
mismatch and commuting times may be weak when employment probabilities decline as the
distance from job site to residence increases. A simple spatial model of urban employment is
developed in which a fixed number of agents live in the central city. Two examples are presented
in which increased spatial mismatch may either increase or decrease the average commuting time
of central city minorities, depending on the rate at which employment probabilities decline with
distance.INTRODUCTION
The spatial mismatch hypothesis (SMH) claims that a spatial mismatch between central
city residential location and suburban job growth may result in poor labor market outcomes for
central city residents, and in particular for central city minorities. The most common argument for
this view is the observation that unemployed workers find jobs through a costly search process
(Kain 1968). Continuing this line of argument, it is assumed that search costs increase with
distance as transportation costs increase and as informal job networks (such as word of mouth)
convey less information about the availability of openings. Therefore, as spatial mismatch
increases, job market outcomes for central city minorities will get worse, holding constant other
relevant characteristics.
A common method of testing the SMH is to examine whether minorities have, on average,
longer commutes to work than whites after controlling for all other relevant characteristics.
Ihlanfeldt and Sjoquist (1998) recently reviewed a number of studies testing the spatial mismatch
hypothesis, including five that use a commuting-based test of the SMH. As can be seen in Table 1,
the results of these studies are mixed. Two studies (Wyly (1996) and Taylor and Ong (1995)) did
not find evidence of racial commuting differences, but three studies (Sabriel and Rosenthal (1996,
McLafferty and Preston (1992) and McLafferty and Preston (1996)) did find differences.
Ihlanfeldt and Sjoquist (1998) make two objections to commuting-based tests of the
SMH. The first is that in the standard monocentric economic model of an urban area, higher levels
of economic resources are associated with longer commuting times. Interpreting inter-racial
differences in commuting distances may be difficult if the researcher is not able to control for all
forms of income and wealth that lead some people to choose relatively long commutes. Second,2
they note that spatial mismatch may not produce longer commuting times for central city
minorities if there is not adequate public transportation from central cities to suburban areas.
The purpose of this note is to point out that the problems with commuting-based tests of
the SMH may be deeper than the above criticisms suggest; increased spatial mismatch may either
increase or decrease the average commuting time of central city minorities, depending on the rate
at which employment probabilities decline with distance. If employment probabilities decay with
distance at a sufficiently slow rate, increases in spatial mismatch may increase the average
commuting distance of central city residents. However, if employment probabilities decay with
distance at a sufficiently fast rate, decreases in spatial mismatch may increase the average
commuting distance of central city residents. The threshold rate is defined as the intermediate
case–the rate of decay in employment probabilities for which an increase in spatial mismatch
neither increases nor decreases the average commuting distance of employed central city
residents. By presenting examples of a model in which spatial mismatch decreases average black
commuting times, I establish that spatial mismatch does not necessarily imply an increase in black
commuting times, even when all economic resources relevant to location decisions are observable
and poor residents have adequate access to public transportation.
This result suggests that there are two alternative interpretations for the findings in Table
1. The “standard” interpretation might be that the evidence for spatial mismatch is weak. This
interpretation assumes that all of the MSAs studied have conditions in which spatial mismatch
increases the commuting times of minorities and decreases the commuting times of whites. The
“alternative” interpretation, suggested by the findings presented here, might be that spatial
mismatch is present in all of the cities studied; however, the conditions which map spatial3
mismatch into commuting times vary from city to city or over time. The key condition being
considered here is the rate at which employment probabilities decline with distance. Under this
interpretation, the results from the studies in Table 1 test whether employment probabilities
decline at a rate above or below the threshold rate. A finding that blacks have shorter commuting
times than whites would indicate that employment probabilities decline faster than the threshold
value. A finding that blacks have longer commuting times than whites would indicate that
employment probabilities decline slower than the threshold value.
Why might an increase in spatial mismatch decrease the average commuting time of
employed central city minorities? There are two countervailing effects when jobs move farther
from the central city. First, moving jobs from the central city to the suburbs means, for central city
residents, a larger proportion of available jobs now have longer commutes. Second, because
employment probabilities decline with distance, moving jobs farther from the central city means
that central city residents will find fewer jobs overall. Thus, jobs near the central city will now
have a larger share of central city residents’ employment. While the first effect tends to lengthen
the average commuting times of employed central city residents, the second effect tends to
shorten the average commuting times. Whether the first effect dominates the second is an
empirical question.
A HEURISTIC EXAMPLE
To clarify matters, consider a simple heuristic example (outlined in Tables 2a and 2b) of an
urban area on a line. The central city, where only blacks live, is located at the point farthest to the
left (A), and the suburb, where only whites live, is located at the point farthest to the right (C). All4
points are one mile apart. The probability of a central city resident finding a job at points A, B,
and C are 1, 0.5, and 0 respectively. In the baseline case (Table 2A), there is one vacant job at
point A and one at point B. Thus, the expected commuting time for central city residents is given
by the distance of each point from the central city weighted by the expected employment share for
each point. In the baseline case, the expected commute is [(1)1(0) + (1)0.5(1) + 0(0)(2)]/ [1(1) +
(1)0.5 + 0(0)] = 0.33 miles. Table 2B computes expected commuting times for blacks after a
redistribution of all the jobs at point B to point C. The new expected commuting time for central
city residents is now [(1)1(0) + (0)0.5(1) + 1(0)(2)]/ [1(1) + (0)0.5 + 1(0)] = 0 miles. Thus, an
increase in spatial mismatch results in decreased commuting time for central city minorities.
Given the specified employment probabilities at points A, B, and C in this example, any
redistribution of jobs from point A to point C will weakly increase expected commuting distance,
while any redistribution of jobs from point B to point C will weakly decrease expected commuting
distance. To understand the intuition behind this result, consider the distribution of distances from
the central city to particular job centers in a hypothetical urban area that has many job centers.
Further, consider a redistribution of jobs from the job center that has the minimum commuting
distance to any other job center. Such a move will increase average commutes unless the new
point has an employment probability of zero, in which case the commuting distance may stay the
same or increase depending on the prior distribution of jobs.
Now consider a redistribution from a job center that is relatively close to the central city
(call it point O) but is not the job center closest to the central city, to a point relatively far away.
This type of redistribution could either increase or decrease average commuting distance
depending on the distribution of employment probabilities. In fact, it is easy to see that any set of5
(0)100P % (1)100P" % (2)100P"2
100P % 100P" % 100P"
2 ’ " % 2"2
1 % " % "
2 (1)
employment probabilities in which there is a positive probability at O and zero probability at job
sites farther from the central city than O, will always decrease expected commutes. 
This example relies on a highly stylized and specific distribution of employment
probabilities. The next section explores a model in which employment probabilities are perhaps
more realistic. In that model, employment probabilities decline with distance at a constant rate and
do not ever reach zero. Nevertheless, the result of the current section remains intact: increases in
spatial mismatch may increase or decrease the commutes of central city residents depending on
how employment probabilities change with distance.
A SIMPLE MODEL
As before, consider three points on a line -A, B, and C- all 1 mile apart, with all blacks in
the labor force living at A. There are 300 jobs, 100 at each point. Let P be the employment
probability of central city residents in the central city and let " be the rate at which employment
probabilities decline with distance between job centers, with P0[0,1] and "0[0,1]. Thus, the
employment probabilities for black job seekers are P, P", and P"
2 for points A, B, and C,
respectively. Expected black employment at points A, B, and C is 100P, 100P", and 100P"
2,
respectively. Thus, the average commute for an employed black worker is given by
Now consider the effect of shifting one job from B to C so that the number of jobs at
points A, B, and C is 100, 99, and 101 respectively. Expected black employment at points A, B,6
(0)100P % (1)99P" % (2)101P"2
100P % 99P" % 101P"
2 ’ 99" % 202"2
100 % 99" % 101"
2 (2)
and C is 100P, 99P", and 101P"
2, respectively. The new mean commuting time for blacks is
given by
This example of spatial mismatch will result in longer commuting times when equation (2) is
greater than equation (1). This occurs when employment probabilities decay slowly as the distance
from a job center to a central city residence increases, specifically when " is larger than its
threshold value, (in this case, approximately 0.37). However, the new mean commuting time for
blacks will decrease with spatial mismatch when " is less than 0.37.
CONCLUSION
This note develops a simple spatial model of urban employment in which the employment
probabilities of central city residents depend negatively on the distance from a job site to a
person’s home. The main result is that the relationship between spatial mismatch and commuting
distance is indeterminate. Spatial mismatch may either increase or decrease the average
commuting distance of central city minorities, depending on the rate at which employment
probabilities decline with distance. When no restrictions are placed on employment probabilities,
spatial mismatch is consistent with minority commutes that are longer, shorter or the same as
those of whites. Absent knowledge of how employment probabilities change with distance, it may
be difficult to test the SMH using comparisons of minority and white commuting times or
distance.7
REFERENCES
S. Gabriel and S. Rosenthal.  1996. “Commutes, Neighborhood Effects and Earnings: An Analysis
of Racial Discrimination and Compensating Differentials,” Journal of Urban Economics,
40, pp. 61-83.
K. Ihlanfeldt and D. Sjoquist.  1998.  “The Spatial Mismatch Hypothesis: A Review of Recent
Studies and Their Implications for Welfare Reform,” Housing Policy Debate, 9, pp. 849-
892.
J. Kain.  1968.  “Housing Segregation, Negro Employment, and Metropolitan Decentralization,”
The Quarterly Journal of Economics, 82, pp. 175-183.
S. McLafferty and V. Preston.  1992.  “Spatial Mismatch and Labor Market Segmentation for
African American and Latina Women,” Economic Geography 68, pp. 406-431.
S. McLafferty and V. Preston.  1996.  “Spatial Mismatch and Employment in a Decade of
Restructuring,” Professional Geographer, 48, pp. 417-467.
D. B. Taylor and P. Ong.  1995.  “Spatial Mismatch or Automobile Mismatch? An Examination
of Race, Residence and Commuting in U.S. Metropolitan Areas,” Urban Studies, 32, pp. 
1453-1473.
E. Wyly.  1996.  “Race, Gender and Spatial Segmentation in the Twin Cities,” Professional
Geographer, 48, pp. 431-444.8
Table 1. Recent Commuting-Based Studies of the Spatial Mismatch Hypothesis
Study Data Finding
Wyly (1996) 1980 and 1990 PUMS for
Minneapolis/St. Paul
Increase in mismatch over time
did not increase black
commuting times
McLafferty and Preston (1992) 1980 PUMS for Northern 
New Jersey
Black and Hispanic women
have longer commutes (time)
than white women
McLafferty and Preston (1996) 1980 and 1990 PUMS for 
New York
Large difference in commuting
times for central city blacks and
whites, small difference for
suburban blacks and whites
Gabriel and Rosenthal (1996) 1985 and 1989 American
Housing Survey
Blacks have commutes 14%
longer than those of Asian or
white counterparts
Taylor and Ong (1995) 1977/78 and 1985 AHS 
for 10 MSAs
No evidence of difference in
commuting times
Source:  Ihlanfeldt and Sjoquist (1998).9
Table 2A. Baseline Case, Heuristic Example
Central City Suburb
Job Centers A B C
Distance from central city (miles) 0 1 2
Probability that a central city resident finds a vacant job 1 0.5 0
Number of vacant jobs 1 1 0
Average commute for employed central city residents = 0.33
Table 2B. Increase Spatial Mismatch, Heuristic Example
Central City Suburb
Job Centers A B C
Distance from central city (miles) 0 1 2
Probability that an central city resident finds a vacant job 1 0.5 0
Number of vacant jobs 1 0 1
Average commute for employed central city resident = 010
Table 3A. Baseline Case, Simple Model
Central City Suburb
A B C
Number of vacant jobs 100 100 100
Distance from central city 0 1 2
Probability that a central city resident finds a vacant job P "P "
2P
Expected employment of central city residents P100 "P100 "
2P100
Table 3B. An Increase in Spatial Mismatch, Simple Model
Central City Suburb
A B C
Number of vacant jobs 100 99 101
Distance from central city 0 1 2
Probability that a central city resident finds a vacant job P "P "
2P
Expected employment of central city residents P100 "P99 "
2P101

Commutes, Neighborhood Effects and Earnings: An Analysis of Racial Discrimination and Compensating Differentials,”

Housing Segregation, Negro Employment, and Metropolitan Decentralization,”

Spatial Mismatch and Employment in a

Spatial Mismatch or Automobile Mismatch? An Examination of Race,

The Spatial Mismatch Hypothesis: A Review of Recent Studies and Their Implications for Welfare Reform,” Housing Policy Debate, 9,

A Note on Commutes and the Spatial Mismatch Hypothesis

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A Note on Commutes and the Spatial Mismatch Hypothesis

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