Key Takeaways

ºÚÁϳԹÏÍø

• Optimal district enrollment at which cost per pupil at a minimum is 1,709 students with the cost of $11,192.99 per student.
• 95% confidence interval of optimal district enrollment is 1,157 to 2,254 students.
• 80 Indiana school districts are below 1,157 Average Daily Membership (ADM).
• 118 school districts are above the optimal enrollment.
• 99 school districts are within the optimal enrollment range.

ºÚÁϳԹÏÍø

As the Indiana Legislature is focusing on possible school consolidation, it’s important to understand what the data suggest about optimal student enrollments, especially when one considers the multiple factors — learning, finance, student programming and opportunities — that are part of the equation.  An earlier study out of Purdue in 2009^[1] sought to address these issues by determining an optimal level of student enrollment. Now, the Center for Evaluation and ºÚÁϳԹÏÍø Policy (CEEP) at Indiana University is examining this issue with new data and methods to determine an optimal student enrollment that supports economies of scale.

The 2009 study determined that the optimal enrollment was 1,942 students, within a range of 1,300 to 2,903 students at a 95% confidence interval. The optimal cost per pupil was $9,413.93. Student enrollment within 5% of the optimal costs came in at 547 to 6,889 students.

As the legislature convenes for 2026, there has been substantial discussion on the role of school consolidation and what is the optimal funding structure that promotes the best use of taxpayer support in Indiana. The assumption is that school consolidation will increase enrollment, but reduce marginal costs. However, as found in ’s (2009) study, economies of scale do not lead to perpetual lower per pupil costs. Twenty years later, we revisit Zimmer et al.’s study using the most recent school year expenditure data. We imitate the analysis done in the 2009 study, within certain data limitations- explained below, to observe changes in optimal enrollment and per pupil cost at which economies of scale are achieved. 

Updating the 2009 Study provides an initial review in order to answer that question- what is the optimal enrollment for economies of scale in Indiana.

Data

ºÚÁϳԹÏÍø

There have been substantial changes to the Indiana public school finance, particularly in the funds used. Currently, the school districts operate using a fund accounting system of ºÚÁϳԹÏÍø, Operations, and Referendum funds that previously were broken out into General, Capital Projects, Transportation, and Bus Replacement. 

This change in fund accounting has made studying the issue in 2026 more difficult as the expenses have been reported differently. Specific costs like transportation, which were previously available as a separate fund, have to be pulled out of the operations fund and totaled for each school district. Further, the enmeshing of transportation costs within operations funds was not always consistent across the school districts. For instance, Beech Grove school district paid for all of its transportation funds from the operating referendum. This additional calculation of costs required a significant amount of time and effort and limited how many different data points we could analyze.

For this report, Form 9 data submitted by all public-school districts in Indiana were utilized for the 2024-2025 school year (December 2024 and June 2025 Form 9 Data Reports). This information included 290 school districts. The data were in raw form by fund, account, and object numbers. The first task was to determine total fund expenses for education, operations, and operating referendum funds. These expenditure funds were the best way to capture operating costs for school districts based on how data is reported by school districts biannually to the Indiana Department of ºÚÁϳԹÏÍø. While other funds, including federal and state grants and the rainy-day fund, could be used for operating expenditures, the best and most consistent funding sources were the three funds utilized. Over time, they provide the majority of the funding for school district operational expenses. These three funds capture property tax revenues (operations and operating referendum funds) and state tuition support (education fund) to provide the overall operating costs for a school district.

Subsequently, the total fund expenditures were calculated as the sum of the account expenditures for each fund (ºÚÁϳԹÏÍø 101, Operations 300, Operating Referendum 160) for each school district. This process was used for the December 2024 and June 2025 Form 9 data. The totals for each Form 9 were then added together to get the total school-year expenditures for the district.

After determining the total expenses for these funds, an amount per student was calculated using the latest Average Daily Membership (ADM) reported to the Indiana Department of ºÚÁϳԹÏÍø for Fall 2024. That data set may be found at and is the Corporation Enrollment by Grade Level under Attendance and Enrollment. The ADM used was the K-12 enrollment. Enrollment in Pre-K was excluded since this is not a source of funding for school operations or education funds.

Methodology

ºÚÁϳԹÏÍø

Our study methodology closely follows Zimmer, DeBoer and Hirth (2009), with several significant modifications necessitated by data limitations. While Zimmer et al. (2009) use cross-sectional data collected from 292 Indiana school districts over a period of three years (2004 to 2006), our analysis focuses on one school year (2024-2025). The analysis follows the Logarithmic Ordinary Least Squares estimation (OLS) instead of the Two-Stage Least Squares (2SLS) approach used in the 2009 study. Thus, the fixed and random effects are not applicable, and there is no endogeneity correction. Our analysis, therefore, does not capture the changes to teacher salaries due to enrollment, attendance, etc. and cannot make causal claims on changes in enrollment due to per pupil costs. Consequently, the estimated relations should be understood as conditional association and not as causal effects. However, the analysis can still estimate the quadratic (non-linear) relation between enrollment and per-pupil costs and derive an enrollment level that minimizes predicted costs conditional on observed characteristics. 

Similarly, Zimmer et al. (2009) use a wide array of socioeconomic, demographic, and performance variables, which we did not have access to. Therefore, the present study estimates a reduced-form cost function, retaining core variables necessary to identify economies of scales. Below is the model equation for this study:

Eq. 1

Where, X_i = enroll, enroll², attend, schsize, tesala, sec;
Y_j = school type

The above model preserves the quadratic enrollment structure that is key to measuring the economies and diseconomies of scale.

Variables

ºÚÁϳԹÏÍø

In imitating the analysis done by Zimmer et al. (2009), we have tried as much to retain the same set of explanatory variables as in their study. Teacher salary and parent apathy- measured by attendance, are variables associated with diseconomies of scale in addition to school corporation enrollment and corporation average school size. This is because increased enrollment reduces teacher union costs and allows the unions to form and grow stronger (Tholkes, 1991)^[2]. Cotton (1996)^[3] argues that increased enrollment from school consolidation reduces inputs from parents and students and increases bureaucracy. Astone and McLanahan (1991)^[4] and Sewell and Shah (1967)^[5] state that attendance is a good measure of parent and student input or engagement. Below is a descriptive list of variables in our model.

Per-pupil cost: This (costpp) is the dependent variable in our model and was calculated as described above using Form 9 data for December 2024 and June 2025 and following the method of the Indiana ADM report for Fall 2024. This was then logarithmically transformed for our analysis.

Enrollment and scale variables: This is the total K-12 enrollment per district. For the analysis the log and the square of the log of district enrollment were calculated. The logarithmic transformation (​ln(enroll) and [ln(enroll)]²) captures the nonlinear (quadratic) relationship between enrollment and cost per pupil.

Average school size: This is the ratio of the district enrollment and the total schools per district (schsize). 

Attendance rate: This variable (attend) serves as the proxy for parent-student involvement, same as conceptualized by Zimmer et al. (2009). However, we used the  school-level attendance rate, while Zimmer et al. used the attendance rate at the district level obtained from the administrative records. To transform the school attendance rate to that for each district, we calculated the sum of the products of the school-level attendance rates and the school enrollment, divided by the total enrollment per district.

Secondary school enrollment rate within the District: This variable (sec) captures the higher cost intensity associated with secondary education. This was the ratio of district-level enrollment in grades 9 through 12 to the total district enrollment.

Teacher salary: This variable (tesala) is included as the cost driver in our model contrary to the instrumentalization of the variable across the three-year period in the study by Zimmer and colleagues. This is because we use the average teacher salary for one school year. This information was supplied by Indiana ºÚÁϳԹÏÍø Employment Relations Board using their Annual Collective Bargaining Report submitted by school districts in Indiana.

School type classification: School corporations are classified as- rural, town, metropolitan and suburban, which act as proxy for geographic and structural cost differences. This variable (school type) is included as a categorical control in our model.

Estimation strategy

ºÚÁϳԹÏÍø

The cost function is estimated using Ordinary Least Squares (OLS) regression with all variables in logarithmic form. This transformation of variables enables interpreting the variable coefficients (like β₁, β₂, etc.) as elasticities. The key parameters of interest are β₁- captures economies of scale and β₂- captures diseconomies of scale. When these coefficienst take a negative and a positive, respectively, they imply a U-shaped cost curve, indicating the value of district enrollment at which the cost per pupil is the lowest, such that to the left of that enrollment level, the curve shows continuous fall in per pupil cost. In other words, as enrollment increases up, to that point, costs fall indicating economies of scale. To the right of this enrollment, the curve indicates that a rise in enrollment will increase the cost per pupil, i.e., diseconomies of scale.

The optimal enrollment, then, is the enrollment at which the cost function is the lowest. The mathematical formula being:

All other explanatory variables (right side of Eq. 1) are held at their sample mean values, similar to the optimization procedure described by Zimmer et al.

Results

ºÚÁϳԹÏÍø

Our analysis shows that the optimal district enrollment at which cost per pupil at a minimum is 1,709 students, and the cost is $11,192.99 per student. The 95% confidence interval of the optimal district enrollment is 1,157 to 2,254 students. The enrollment range for which the predicted cost per pupil remains within the 5% range of the cost minimizing level is 447 to 6,752 students.

We concluded based on a small, one-year review of the 2009 study - almost 20 years later - that the current optimal district enrollment is about 12% less than the optimal enrollment from the previous study. Further, the current optimal range of 1,157 to 2,224 compared to the 2009 study of 1,300 to 2,903 represents about 12% less for the optimal lower end of the enrollment range and 23% less for the upper end of the enrollment range. 

The graph below shows the district size based on the Fall 2024 ADM counts.

Using the current optimal enrollment, this analysis finds that there are 80 school districts below 1,157 ADM or 27.5% of all Indiana school districts (290 total public-school districts).

Looking at the other end of the ADM count, there are 118 districts above the optimal enrollment or 41% of all Indiana school districts.

Ninety-nine school districts were found to be within the optimal enrollment range using the updated study. This is 34% of Indiana school districts.

Conclusions

ºÚÁϳԹÏÍø

Much discussion in Indiana has taken place around the minimal school district size with student enrollment counts of 1,000 being used arbitrarily as a baseline^[6]. This discussion has not looked at the other end of the enrollment range. This review determined that school district expenditures appear to increase per student once the enrollments exceed 2,224 students This is a natural evolution of schools as bigger school districts have more layers of administration and supervision as well as larger buildings which require more maintenance and upkeep to operate. A final thought on expenses of larger districts can be analyzed along lines of quality-of-life issues and that larger districts offering more programming and better facilities can offer greater quality of life for residents.^[7]

Appendix: ADM Counts by District

ºÚÁϳԹÏÍø

Districts with under the Optimal 1,157 students

School Districts with Optimal Enrollment

School Districts in Excess of 2,224 Optimal Enrollment