Journal of Geographic Information System, 2011, 3, 306-311
doi:10.4236/jgis.2011.34027 Published Online October 2011 (http://www.SciRP.org/journal/jgis)
Measuring Public School Competition from Private
Schools: A Gravity-Based Index
Kaustav Misra1, Guangqing Chi2
1Department of Economics , Saginaw Valley State University, University Center, USA
2Department of Sociology and Social Science Research Center, Mississippi State University, Starkville, USA
Received April 26, 2011; revised April 25, 2011; accepted May 16, 2011
Abstract
This research develops a gravity-based index of public school competition from private schools within local
markets. Proponents of educational reform often call for policies to increase competition between schools. A
major hurdle for researchers examining this issue is to determine a workable definition of “competition” by
which they can measure the degree of competition within local markets. This study addresses this challenge
by developing a school competition index for public schools in the Jackson metropolitan area of Mississippi,
USA that considers the enrollments in public schools and the enrollments in their neighboring private
schools, as well as the distances between them. The school competition index reveals the degree of competi-
tion for each public school based on its spatial location relative to peer private schools operating within its
service area. This methodology can be useful for evaluating competition in other markets and redefining the
traditional market structure.
Keywords: Public School, Gravity-Based Index, Market, Competition, Education
1. Introduction
A sense that educational outcomes need improvement is
essentially universal, particularly in the United States,
where public schools lag behind other countries in
standardized student achievement scores [1]. There has
been a call for improved educational outcomes, yet such
outcomes have been rare because of the inefficiency of
public schools [2]. A public school, which is supported
by public funds, provides free education for children of a
district. Although a major percent of U.S. children go to
public schools for their education and funding to public
schools has been increased substantially, the performance
of public schools has not improved much over time [3].
Between 1996 and 2006, the national average American
College Testing (ACT) score has increased negligibly
from 20.8 to 21.0 (http://www.act.org/news/data.html).
This has come to the attention of parents as well as local
and state legislators.
In response to the underperformance of public schools,
two types of educational reforms have been proposed by
researchers: high-stake tests and market-type reforms [4].
Policy makers propose to increase th e achievement levels
of standardized test scores in the former, while in the
latter reformers propose to increase the number of school
choices available to students, primarily by introducing
voucher programs and tuition tax credits. The market-
type reforms free students from being restricted to at-
tending only public schools in the districts where they
reside and thus provide them the option to instead attend
private schools of their choice, regardless of their location.
In districts where such reforms have been implemented,
government-supplied vouchers and tuition tax credit pro-
grams have been put in place to offset the costs of private
school attendance. Policy reformers believe such promo-
tion of private school attendance generates market-based
competition for l ocal publ i c scho ol s.
Some researchers, such as Hoxby [5] and Couch,
Shughart and Williams [6], argue that the presence of
private schools increases public school qualities; however,
other researchers dispute that claim [7,8]. It is unclear
how private schools affect public schools because it is
difficult to measure the degree of competition across
educational markets. Previo us resear c h er s hav e e mpl o ye d
different proxies to capture the degree of inter-school
competition, but these techn iques do not reveal all of the
relevant information. For example, the most frequently
used competition computational techniques include the

K. MISRA ET AL.307
Herfindahl-Hirschman Index [9], the percentage of all
students in private schools [10,11], grade-specific com-
petition [12], and market share held by private schools
[13]. Each of these techniques is somewhat different from
the others. It is important to note that these techniques
rely on only the number of schools and student enroll-
ments. These techniques cannot provide accurate esti-
mates for competitiveness, as they ignore the distance
between the competitors. Previous literature (e.g., [8,9])
assumes that public school markets are geographically
bounded by law and follow the traditional market struc-
ture theory [14], where distance between the competitors
in the market does not have any place. Hence, a more
accurate measure of school competition is to consider not
only the number of schools and student enrollments, but
also the distance between the competitors.
The primary goal of this manuscript is to propose a
measure of school competition by considering not only
the number of schools and student enrollments, but also
distances between competitors. Specifically, this study
develops the school competition index to measure com-
petition for each public school from neighboring private
schools in the Jackson metropolitan area, Mississippi,
USA. To our best knowledge, this is the first research to
accommodate three major components of market compe-
tition: the number of competitors, the sizes of the com-
petitors, and the geographical distances among the com-
petitors. Most of the previous research used competition
variables by employing either one or two of the three
components, but not al l t hree t oget her [ 8-10,12].
2. Developing a School Competition Index
To isolate the school-specific competition effect, we
develop a gravity-based school competition index (SCI)
that employs three types of market attributes—the
number of competitors, the sizes of the competitors, and
the geographical distances among the competitors—in a
distance-decay function:
2
1
i
ij
ijij
A
Ed
E


 (1)
where Ei is the public school’s enrollment, Ej is its
neighboring private schools’ enrollments,1 and d
represents the distances between the public school and
each neighboring private school (i and j denote the public
school and neighboring private schools, respectively).
This gravity-based index considers the number of
competitors, the sizes of competitors, and the distances
between local competitors. It is important to include the
three attributes because each plays a role in affecting
competition. First, the number of competitors influences
market concentration, and a higher market concentration
increases market outcomes more than a lower market
concentration [8]. Second, a competitor can compete for
market share based on size (a small firm may not be able
to compete with a big firm because the small firm will
always face resource constraints).
Third, the distance between local competitors is an
important factor of competition. According to Tobler’s
First Law of Geography [15], everything relates to
everything else, but the near ones do more than the
distant ones. The effect of competition from a closer
competitor is higher than the effect from a distant
competitor in the same market. Market and human spatial
behavior are closely related to each other specifically in
the assessment of accessibility and mobility [16]. In the
market place, decisions related to the space are often
related to distance and time, because increasing travel
distance or cost can have an inverse effect on the possible
usage [17]. When selecting a potential school, people
prefer nearer ones given everything else the same because
longer distances mean higher cost and investment.
Therefore, travel distance or cost should be included as
part of the school choi ce deci si on as wel l .
While developing this index, it is necessary to
consider at what distances private schools are competi-
tive to public schools as the law of diminishing returns
assume that the degree of competition will start
decreasing after an optimal distance [18]. To do this, we
refer to the accessibility literature and seek to identify
the maximum distance to identify the neighboring
private schools of a public school. Garreau [19] argues
that 45 minutes is the desirable commuting time
regardless of mode of transportation. Dong et al. [20]
suggest 27.1 minutes and 31.1 minutes based on
activity-based accessibility and trip-based accessibility,
respectively. Wheeler [21] finds that the spillover effect
of economic growth and activity of a county in the
United States starts to decline roughly after 40 miles. In
this study, we use 40 miles as the maximum distance at
which a private school can compete with a public
school.2 We define and identify a public school market
and measure its competition by drawing a circle with a
40-mile radius around each public school. All private
schools within the circle are considered competitors of
hat public school.
1It is legitimate to consider including measures of school qualities such
as average GPA, but such data are not publicly available for private
schools. Enrollment, then, is the only publicly available choice for
p
roximately representing school qualities. This imposes a limitation to
this study. Quality data, for example test scores or student cognitive
abilities for private schools should be incorporated into the development
of the competition index in future research when such data become
available.
t
2In future research, sensitivity analysis could be conducted by using
other distance radiuses.

K. MISRA ET AL. 308
3. Data metropolitan area of Mississippi (Figure 1). The primary
reason for selecting this area for the research is that the
Jackson metropolitan area is the single largest populated
are a in the state of Mississippi. The number of public and
private schools in the Jackson area is significantly higher
than the numbers in other areas of Mississippi, and the
larger number provides a good number of samples for the
analysis. Moreover, the per capita income in the Jackson
metropolitan area is much higher than the Mississippi av-
erage (Bureau of Economic Analysis, 2005), which allows
residents in the Jackson area to afford private schools
more than residents outside of the Jackson area. Again,
this increases the samples of competitors for the analysis.
In this study, public school annual enrollment data for the
academic year 2005-2006 are obtained from the Missi-
ssippi Assessment and Accountability Reporting System
of the Mississippi Department of Education. We collect
private school enrollment data for the academic year 2005-
2006 from the National Center for Education Statistics.
The collected data are at the school level. Most previous
studies are conducted with enrollment data at the school
district, county, or state levels; because the data used in this
research are at the school level, this study provides finer
estimates of school competition than previous studies. The schools considered in this study include both high We consider the public schools located in the Jackson
Figure 1. High School Enrollments in the Jackson Metropolitan Area, Mississippi, USA, 2005–2006.

K. MISRA ET AL. 309
schools (grades 9 - 12) and combined schools (schools
offering grades K-12). In total there are 48 public high
schools and combined schools in the Jackson metropoli-
tan area. We eliminated 16 schools from the final data set
because they typically serve special-education students
(schools for the disabled) or special groups of students
(schools for juvenile offenders), and such schools do not
face competition from the private schools. The final
sample data set includes, therefore, 32 public high
schools and combined schools as well as the 38 private
schools located within 40 miles of these public schools.
The locations and enrollments of these schools are
shown in Figure 1 and descriptive statistics for public
and private schools are shown in Table 1. In terms of
enrollment size, public schools are more evenly distrib-
uted, but most private schools are small.
4. Results
Table 2 provides the descriptive statistics for the gener-
ated gravity-based public scho ol competition index. This
table reveals how these public schools are distributed in
terms of school competition index in the study area.
Most of these schools are facing a low degree of compe-
tition from private schools.
The school competition index is further illustrated in
Figure 2. Smaller red dots represent public high or com-
bined schools with less competitio n fro m private schoo ls.
Bigger red dots represent public schools with higher
competition from pr ivate schools. The competition inde x
provides a more accurate estimate of public school com-
petition from private schools than previous studies be-
cause it includes three attributes of the market struc-
ture—the number of competitors, the sizes of the com-
petitors, and the geographical distances between the
competitors.
Two things are notable from Figure 2. One, the en-
rollment size of a public school is generally negatively
correlated with the competition that it faces from local
private schools. For example, a high school in the
northwest corner of the Jackson metropolitan area has
Table 1. Descriptive statistics of high school enrollments in
the Jackson Metropolitan Area, Mississippi, USA, 2005-2006.
Enrollment size Public high schools Private high schools
52 - 538 9 (28.13%) 29 (76.32%)
539 - 836 8 (25.00%) 5 (13.16%)
837 - 1133 8 (25.00%) 3 (7.89%)
1134 - 1431 6 (18.75%) 0 (0.00%)
1432 - 1728 1 (3.12%) 1 (2.63%)
Total 32 (100%) 38 (100%)
Table 2. Descriptive statistics of public school competition
index (SCI) in the Jackson Metropolitan Area, Mississippi,
USA, 2005-2006.
SCI range Frequency Percentage
0.01 - 0.05 10 31.25%
0.06 - 0.09 6 18.75%
0.10 - 0.18 7 21.87%
0.19 - 0.66 5 15.63%
0.67 - 13.70 4 12.50%
Total 32 100%
relatively higher enrollment th an the other public schoo ls
in the area (Figure 1), but this school faces less competi-
tion as compared to the other public schools (Figure 2).
In contrast, a school in the southeast corner of the area
(Figure 1) has a small enrollment size, but it faces much
more competition from private schools (Figure 2). Two,
the public schools that are located close to private
schools (especially those with high enrollments) face
more competition from these private schools. The public
schools that are located in the middle of the Jackson
metropolitan area h ave more neighboring private schools;
these public schools face higher competition from local
private schools.
5. Conclusions and Discussion
Proponents of educational reform often call for policies
to increase competition between schools. A major hurdle
for researchers examining this issue is to determine a
workable definition of “competition” by which they can
measure the degree of competition within local markets.
However, prior measures consider only the number of
schools and student enrollments in estimating competi-
tion between schools. Distance between potential
competitors is also an important factor of competition
because travel distance or cost affects school choice
decisions.
This research de velops a gravity-b ased index of pub lic
school competition from private schools within local
markets. We consider three factors—the number of
competitors, the sizes of competitors, and the distances
between local competitors—in order to comprehensively
measure the effect of competition. We demonstrate the
use of the method for developing a school competition
index for public schools in the Jackson metropolitan area
of Mississippi, USA that considers the enrollments in
public schools and the enrollments in their neighboring
private schools, as well as the distances between them.
The school competition index reveals the degree of
competition for each public school based on its spatial
location relative to peer private schools operating within
C
opyright © 2011 SciRes. JGIS

K. MISRA ET AL. 310
Figure 2. Public school competition index in the Jackson Metropolitan Area, Mississippi, USA, 2005-2006.
its service area. This methodology can be useful for
evaluating competition in other markets and redefining
the traditional market stru cture.
This study makes two contribu tions to the literature on
market structure and competition. First, this study adds
distance into the measure of school competition. The
distance between competitors is often ignored in the tra-
ditional market structure theory, but spatial proximity
plays an important role in the human decision-making
process [22]. Thus, it is important to consider distance
when determining market competition. Second, the grav-
ity-based competition index can be used to evaluate com-
petition-based educational reform programs. Prior compe-
tition measures may not be effective instruments for un-
derstanding school market strength since the distance
component is missing from the measures. This leads to
inappropriate policy recommendations and misallocation
of scarce resources because focusing on only one compo-
nent at a time without considering them together may un-
derestimate the true effect of competition. Because this
gravity-based index includes the three attributes of compe-
tition—the number of competitors, the sizes of the com-
petitors, and the geographical distances among the com-
petitors—it pr ovides a more a ccurate estima te of compet i-
tion and thus helps guide state and local public education
agencies in allocating their resources more effectively.
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opyright © 2011 SciRes. JGIS

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