A Spatial Analysis of District Participation in Public School Choice

ABSTRACT

This study examines the supply-side decision to participate in interdistrict school choice by incorporating a district’s own characteristics, those of its neighbors and a strategic component based on neighboring districts’ decisions. A spatial Durbin probit model is applied to data from Massachusetts and estimates of direct, indirect, and total effects are found. Results indicate that local capacity and average test scores affect a district’s own decision to participate. Furthermore, local socioeconomic characteristics, test scores and a district’s own decision influences neighboring district participation. Policy implications include consideration of increases in interdistrict tuition and changes in state aid for economically disadvantaged choice students.

KEYWORDS:

• Educational economics
• interdistrict choice
• spatial Durbin probit
• school choice

Acknowledgments

I would like to thank Robert O’Donnell at the Massachusetts Department of Elementary and Secondary Education for help with data retrieval and clarification. I would also like to thank Brian White of Macalester College who assisted with the GIS calculations on mileage among nearest neighbors. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. The Massachusetts Department of Elementary and Secondary Education generally refers to the interdistrict choice program as “the school choice program”. In order to avoid confusing with other types of choice including intra-district and charter schools, the program will be referred to as interdistrict choice in this paper.

2. Changes to the law in 1993 allowed districts to limit the number of incoming students and required districts to hold a lottery if applications exceeded seats.

3. These figures do not include the two virtual choice districts.

4. Arsen and Ni (2012) argue that parental preferences are heterogeneous and some may prefer such things as updated facilities, strong athletics or safety over academics. Erickson (2017) finds that preference for high academic quality is strong but that in some circumstances, other factors, such as safety, play a role.

5. Arsen and Ni (2012) make the case that public schools are entrenched in an institutional environment that may make it difficult to adjust to competitive pressures. Evidence on responsiveness is mixed. Hoxby (2003), for example, finds productivity increases in Milwaukee after the introduction of a voucher system and improvements in Michigan and Arizona in response to charter schools. Ghosh (2010) finds evidence that the school choice program in Massachusetts positively affects per-pupil expenditures and pupil-teacher ratios. Arsen and Ni (2012), on the other hand, find no evidence of a sifting of resources in response to increased competition.

6. While the impact of this decision was recognized early on, then Senate president William Bulger believed the bill would not have passed if additional transportation spending had been included (Massachusetts Districts, 1991).

7. Zeehandelaar (2012) makes the case that the demographics of a community can affect the power balance of those who advocate for particular policies. It is possible that interdistrict choice could affect different stakeholders differently and that the demographics of a community might play a role in the bargaining power of each constituency. However, it seems reasonable to assume that the main drawback (larger class sizes) and the main benefit (marginal increase in revenues for the district) are interests that are aligned between groups (teachers and parents). In practice, it would be impossible to measure exactly where the marginal dollars are allocated and therefore difficult to model the effect of demographics on decision making beyond predicting general community sentiment.

8. Hatch (2018) explains the actual average tuition cost exceeds $6000 when special education expenses are added.

9. Class size reduction policies are popular with both teachers and parents alike (Howell, West, & Peterson, 2011). And while there is much debate about the connection between class size and student achievement (Hoxby, 2000; Schanzenbach, 2014), the assumption of increasing marginal disutility associated with class size is supported by the literature. Horng (2009) utilizes a conjoint analysis of teacher preferences and finds an interval estimate of utility for class sizes of 15, 20 and 33 students. She estimates the decrease in teacher utility per added student to be 1.68 between 15 and 20 students, and 8.23 between 20 and 33 students. In a separate study, parents were surveyed about optimal class size and a majority responses fell somewhere between 15 and 25 students with fewer than 2% choosing a number greater than 30 (Haimson, 2008). Finally, Ready and Lee (2007) examine achievement differences in small (<17), medium (17–25) and large (>25) classes finds that moving from medium to large is the most detrimental to students.

10. Target local contributions are capped at 82.5% by law.

11. The foundation budget, which theoretically provides adequacy, differs from the required budget in many communities due to the nature of the state aid formula. However, districts are free to spend more than required.

12. The derivations of Equations (1(1) $S_1={\alpha }_i/\left(2\beta \right)$(1) )–(7(7) $\gamma >\frac{{\propto }^2}{4\beta n^2}\left(2n^2-2n+1\right)$(7) ) are shown in Appendix C.

13. S_m is replaced by S₀ in Equations (3)(3) $N{B}_{idc}=n\left[\propto \left(S_1-S_m\right)-\beta \left(S_1^2-S_m^2\right)\right]$(3) and (5(5) $N{B}_c=\gamma -\left(n-1\right)\left(S_1^2-S_m^2\right)$(5) ) and S₁ is replaced with (n/(n−1)S₀ in Equation (5)(5) $N{B}_c=\gamma -\left(n-1\right)\left(S_1^2-S_m^2\right)$(5) . The derivatives of each net benefit with respect to S₀ are negative. Additionally, the derivative with respect to S₀ is more negative for consolidation than for interdistrict choice.

14. Golgher and Voss (2016) provide a straightforward explanation of the calculation and interpretation of direct and indirect effects.

15. Five districts were dropped due to missing data on state testing, two additional districts were dropped due to a lack of GIS data. Some vocational districts participate, however since the decision surrounding the participation of these districts are more complicated, they are not included in the analysis.

16. Three districts operating in 2019 were not operating in 2009 so enrollment from first year of operation is used in the calculation of long term enrollment change.

17. Individual schools that serve exclusively special-needs populations and those that serve as alternative schools were eliminated from this calculation.

18. Percentage owner occupied and percentage school age were taken from the American Community Survey for 2017. All other data was taken from the Massachusetts DESE website and is for FY2019 with exceptions made when more recent data was not available. This includes average class size (FY2017), Students per grade per school (FY2018) and percent student population that is white (FY2018).

19. The coefficient on the indirect effect of testing has a t-prob of.102 when K=2. While technically insignificant at the usual 10% benchmark, this result indicates a fairly high level of confidence in its effect.

20. When the estimations are run using more neighbors than 3, the Durbin probit results show significance but none of the direct, indirect or total effects are significant. For each district, the mean distance to the three nearest neighbors was found. Across all districts, the median for this value is 9.44 miles. The distance to the furthest of three neighbors was also found for all districts and the mean value is 12.19 miles.

21. Ghosh (2013), using different methodology, provides a separate estimation including average values of neighboring districts but finds none to be significant.

22. Author’s calculation using school choice data from Massachusetts DESE (2019).

23. Data shown in Table 4 shows that 170 districts were accepting new students through school choice in 2019. This is slightly less than the 186 districts with choice students enrolled as some had participated in earlier years and the students were still enrolled in the district.

24. See Bruhn (2019) for a discussion of the lottery system.