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Centralized or decentralized control of school resources? A network model

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Abstract

The typical school district in the US consists of a central office overseeing primary, middle and high schools. The school district budget is allocated between the central administration and the constituent schools, who can spend these funds on personnel and non-personnel. We model this allocation problem as a network data envelopment analysis problem which solves for the technically efficient allocation of the budget within the district. The goal is to identify the allocation which yields the best aggregate performance for each school district in our sample. In our examination of 70 school districts in the Dallas, Texas area we find that test scores could be increased by approximately five normal curve equivalent (NCE) points by campuses reducing technical inefficiency and by an additional four NCE points by optimally reallocating the school district budget. Our illustrative model suggests that school districts could increase achievement test scores if more of their budgets were spent on campus personnel like teachers and less on non-personnel items like supplies, and if personnel resources were reallocated from the secondary to the elementary level. Furthermore, while the average school district in our sample allocates 21 % of their budget to the central office, our network model indicates that if resources were optimally allocated, the average school district would allocate only 16 % of their budget to the central office.

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Notes

  1. For surveys, see Worthington (2001) or Johnes (2004).

  2. Davis and Kortanek (1971) provided a dynamic, general equilibrium mathematical programming model to simulate decentralization; however, this was a theoretical exercise.

  3. We allow for multiple inputs, \(x \in \Re_{+}^{N},\) and multiple outputs \(y \in \Re_{+}^{M},\) where N is the number of different inputs and M is the number of different outputs.

  4. Another possibility is that these are public goods which would mean that each school effectively shares the total overhead. Of course there is a middle case, with mixed public/private good status.

  5. In constructing all our spending-based input measures, we follow Gronberg et al. (2011, 2012) and Imazeki and Reschovsky (2004) and exclude spending on food service and student transportation.

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Authors and Affiliations

  1. Department of Economics, Oregon State University, Corvallis, OR, 97331, USA

    Shawna Grosskopf

  2. Department of Economics, Southern Methodist University, Dallas, TX, 75275, USA

    Kathy Hayes

  3. Bush School of Government and Public Service, Texas A&M University, College Station, TX, 77843, USA

    Lori L. Taylor

  4. Department of Economics, Texas A&M University, College Station, TX, 77843, USA

    Lori L. Taylor

  5. Economics and Finance, Southeast Missouri State University, Cape Girardeau, MO, 63701, USA

    William Weber

Authors
  1. Shawna Grosskopf
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  2. Kathy Hayes
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  3. Lori L. Taylor
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  4. William Weber
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Corresponding author

Correspondence to Shawna Grosskopf.

Appendix: the labor cost index

Appendix: the labor cost index

The hedonic model is a very simple one, wherein wages are a function of labor market characteristics, job characteristics, observable teacher characteristics, and unobservable teacher characteristics. Formally, the specification can be expressed as:

$$\ln (W_{idjt}) = \alpha_i + D_{dt}\delta + T_{it}\gamma + \mu_j + \epsilon_{idjt}$$
(3)

where the subscripts i,d,j and t stand for individuals, districts, labor markets and time, respectively, W idjt is the teacher’s full-time-equivalent monthly salary, D dt is a vector of job and labor market characteristics that could give rise to compensating differentials, T it is a vector of individual characteristics that vary over time, the μ j are labor market fixed effects and the α i are individual teacher fixed effects. Any time-invariant differences in teacher quality will be captured by the fixed effects.

The data on teacher salaries and individual teacher characteristics come from the TEA and Texas’ State Board for Educator Certification (SBEC). The measure of teacher salaries that is used in this analysis is the total full-time equivalent monthly salary, excluding supplements for athletics coaching. The hedonic model includes controls for teacher experience (the log of years of experience, and the square of log experience) and indicators for the teacher’s gender, race (black, Hispanic or Asian/Indian), educational attainment (no degree, master’s degree or doctorate), teaching assignment (math, science, special education, health and physical education or language arts) and certification status (certified in any subject, and specifically certified in mathematics, science, special education or bilingual education). Only teachers with complete data who worked at least half time for a charter school or traditional Texas school district during the analysis period are included in the analysis. The hedonic wage analysis covers the 5 year period from 2004–2005 to 2008–2009.

The job characteristics used in this analysis allow for teachers to expect a compensating differential based on student demographics, school size, school type or district size. The student demographics used in this analysis are the percentage of students in the district who are economically disadvantaged, limited English proficient, black and Hispanic. We measure school size as the log of average campus enrollment in the district. There are three indicators for school type (elementary schools, middle schools, high schools). The analysis also includes four indicators for school district size: one indicator variable for very small districts (those with less than 800 students in average daily attendance), one for small districts (those with at least 800, but less than 1,600 students), one for midsized school districts (those with at least 1,600 but less than 5,000 students) and one for very large school districts (those with more than 50,000 students in average daily attendance).

In addition to the metropolitan area fixed effects, we include three indicators for local labor market conditions outside of education. We updated the National Center for Education Statistics’ Comparable Wage Index to measure the prevailing wage for college graduates in each school district (Taylor 2006, Taylor and Fowler 2006). We include the Department of Housing and Urban Development’s estimate of Fair Market Rents (in logs) and the Bureau of Labor Statistics measure of the metropolitan area unemployment rate.

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Grosskopf, S., Hayes, K., Taylor, L.L. et al. Centralized or decentralized control of school resources? A network model. J Prod Anal 43, 139–150 (2015). https://doi.org/10.1007/s11123-013-0379-2

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