Measuring Public School Competition from Private Schools: A Gravity-Based Index

doi:10.4236/jgis.2011.34027

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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

E-mail: [email protected], [email protected] state.ed u

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:

ijij





 (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

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.

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

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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