Density, Market Share, Market Concentration, and Proximity: Comparing Measures of Competition in the Public School Sector

ABSTRACT

School choice researchers have used a range of measures to capture competition between schools, but few have assessed the relative utility of these different measures. Using district-level transactional data, we analyzed the relationship between nine measures of school competition and inflows and outflows of students to and from Arizona school districts: a) two measures of market density, and measures of market share and market concentration, and b) five measures that combine density, market share, or market concentration with proximity. Our analysis suggests that the number of charter schools within 10 miles of a district’s boundaries has the most statistical and practical significance as an indicator of competition.

KEYWORDS:

• School choice
• competition
• charter schools
• interdistrict choice

Acknowledgments

An earlier version of this article was presented at the University Council of Educational Administration (UCEA) annual meeting in 2013. We would like to thank Haiying Dong and David R. Garcia for their help in getting this project started and Margarita Pivovarova and the editor and reviewers for their feedback and comments, which helped us improve this article.

Disclosure statement

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Notes

1. For example, in the 2016 Household Education Survey, 84% of all public school students reported attending a district-assigned school. Of these, 22% moved to attend their schools. If this latter group was counted as choosers, the percentage of active choosers would be 34% (Descriptive statistics for the 2016 Household Survey are reported in U.S. Department of Education, 2018.  See also  Garcia, 2010; Garcia, Dong, McIllroy, & Ackman, 2010 and Grady, Bielick, & Aud, 2010, as cited in Egalite & Wolf, 2016).

2. The other states are: Colorado, Delaware, Florida, Idaho, Iowa, Minnesota, Nebraska, South Dakota, Texas, and Utah. Alaska and Arkansas require interdistrict open enrollment for students attending schools in facilities distress, while Vermont limits interdistrict open enrollment to high school students (Wixom, 2017).

3. An additional 5% of students enrolled in an Arizona public school for the first time (“late entry”) and 2% of students re-enrolled in their original schools after a short enrollment break.

4. Before public school choice policies were widely implemented, families’ school choice options were largely limited to residential choice, where families would decide to buy or rent a house because it provided access to a specific school by residential assignment (Hanushek & Rivkin, 2003; Hoxby, 2000).

5. Initially school districts were allowed to authorize charter schools. However, when school districts used charter schools to generate revenue, the state legislature curtailed districts’ chartering authority (Hartley, 1999; Powers & Potterton, 2019).

6. While our focus in this analysis is on competition within the public school sector, Arizona also has a private school tax credit for donations to a school tuition organization which was approved by the state legislature in 1997 (Powers & Potterton, 2019). School tuition organizations are nonprofit organizations that award scholarships to private school students. The state does not fund private schools directly. It is not likely that the private school tax credit introduced much competitive pressure for public schools. Private school enrollment in elementary-serving private schools was lower in 2007–2008 than in 1997–1998 (Authors’ calculations using data from the Private School Universe, results available on request).

7. Similar measures of density and proximity are also used in studies of the competition stemming from private school voucher programs (see Egalite, 2013 for a review).

8. Nonpromotional movement is student mobility between districts or charter schools that is not due to regular grade level progression.

9. There are 27 high school districts that span multiple elementary school districts and cross municipal boundaries. The larger number of small elementary districts provide greater options for interdistrict mobility for elementary grade students than for high school students. For example, in Phoenix’s city center, 11 elementary districts feed into one high school district. In addition, many charter high schools target at-risk students, so they are not competing for the general school population in the way that most elementary-serving charter schools and districts are (Maranto et al., 2010).

10. The counts of students attending the public schools (traditional and charter) within a district’s borders (the denominator for these calculations) can be understood as the number of students who remain within or travel to the district to attend school.

11. Our enrollment variable is the log of the total number of students eligible to re-enroll rather than total district enrollment since our focus here is on elementary students, and our sample included elementary and unified school districts. The latter have higher total enrollment because our counts are a subset of the students who were enrolled in these districts, which also included high school students. The total number of students eligible to re-enroll is highly correlated with total district enrollment, and total enrollment in kindergarten through 8th grade (.98 or higher).

12.  

13. Arizona school districts vary considerably in size and type from small rural elementary school districts serving a handful of students to a large urban unified school district that serves more than 50,000 kindergarten through 12th grade students. We dropped 43 districts that were largely small rural districts with few charter schools within or near their district boundaries from the sample because of missing information on multiple variables, which left us an initial sample of 159 districts that served 99% of the public school students in the state. An additional 16 districts were missing information on one variable, the percentage of ELL students. This latter group of districts was located in towns or rural areas and enrolled 1% of the public school students in the initial sample of 159 schools. None of the differences between our initial sample of 159 schools and the final sample of 143 schools were statistically significant. Descriptive statistics for the initial sample are provided in Appendix Table A1.

14. The counts in the total movers and total incoming variables also include the small number of students that move to or from destinations other than traditional school districts and charter schools (e.g., regional education services agencies, state operated institutions, and special education settings). The most common destination for most students are school districts and charter schools.

15. Towns are within urban clusters or areas with populations between 2,500 and 50,000 people but outside the urban center.

16. We calculated heteroskedasticity-consistent standard errors using the method described in Hayes and Cai (2007), an alternative method of estimating standard errors that does not assume constant variance of the error term.

17. Milliman and Maranto (2009) found that districts with higher test scores had larger charter market shares, which they suggested may be attributable to parent and teacher demand. In our sample, charter school market share was weakly correlated with district achievement (.16) and the relationship was marginally significant at p < .10.

18. The data used in the Hanuskek and Rivkin (2003) analysis predated Texas’ charter school and interdistrict open enrollment policies.

Additional information

Funding

The authors did not receive any outside financial support for the research reported here.