The effect of increased funding on student achievement: Evidence from Texas's small district adjustment
Introduction
The extent to which financial resources lead to improvements in educational outcomes is a long-standing area of debate among education policy scholars as well as an issue of pressing importance in the current economic environment of limited state and local support for public schooling. While in general one would expect that increasing educational expenditures should yield improvements in student outcomes, disentangling the close relationship between school spending and district wealth, among other factors, is a difficult task.1 In the following we bring new evidence to bear on the issue of (i) how school districts spend additional discretionary funding, and (ii) whether the provision of additional funding through state formulae impacts academic achievement and attainment.
To do so we leverage a long-standing rule in the state funding formula for Texas's public schools that grants additional per-pupil allotments to geographically large districts with few students. We exploit the fact that the formula is discontinuous in size, at 300 square miles, and is kinked with respect the number of students, at 1373. Since the true relationship between size and sparsity and the cost of educating students is in all likelihood smooth, we can exploit the difference between the true smooth relationship and the kinked and discontinuous formula as a source of variation in per-pupil funding. Because this element of the formula determines in large part base per-pupil funding for districts, this variation is meaningful in determining per-pupil revenue and expenditures. Our data allow us to observe districts receiving more than $1600, or 13%, in additional per-pupil revenue that is arguably unrelated to the true cost of educating students. This is integral to understanding the relationship between funding and achievement.
The 10th Amendment to the U.S. Constitution places plenary authority for education with state governments. However, states have delegated significant responsibility for finance and operations to their local school districts. As a consequence, much of the within-state variation in local education spending reflects the tastes and preferences local communities have for education, as well as a community's resource endowments which reflect, among other things, local property tax wealth and labor market conditions. For the purposes of identifying the causal effect of discretionary funds on educational outcomes, concerns exist that the level of (and changes over time in) school resources are likely correlated with these and other factors at the district level that also affect student achievement. One approach to overcome the endogeneity of district resources is to exploit changes in state funding policies over time, often in response to court orders, or discontinuities in state spending formulas, which attempt to equalize funding across districts that vary in their ability to raise local resources for educational spending. While we refer readers to Jackson (2018) for a full accounting of the literature, a few specific examples are relevant here.
Guryan (2001), for example, exploits one such discontinuity in Massachusetts' education finance equalization scheme, which provided additional resources to low property wealth districts. His findings suggest that a one standard deviation increase inper-pupil spending increases test scores in math, reading, science and social studies from about one-third to about one-half of a standard deviation in 4th grade, although he finds no effects on 8th grade scores. Papke (2005) estimates effects from a discontinuity in Michigan's school finance equalization program designed to increase spending in the least funded districts. She finds that a 10% increase in spending increases the share of students passing a state exam in mathematics by roughly one to three percentage points. Another set of papers estimates effects of school finance reforms across the country on attainment and earnings, finding robust gains in both with effects driven by poorer districts (see Card and Payne, 2002; Jackson et al., 2016; Lafortune et al., 2018).2 Hyman (2017) bridges these by exploiting changes in Michigan's funding formula and estimating effects on long run outcomes, concluding that a 10% increase in funding led to a 7% increase in college enrollment and 11% increase in college completion, though in this case gains were concentrated among higher achieving and less-poor districts at baseline.
While these previous studies offer a wealth of insight, they are largely limited to evaluating effects of increases in funding in response to inadequate or unequal conditions. Moreover, we are in a unique context of sparse and rural schools, which are overlooked in much of the literature. Hence, while our study is similar to prior work in spirit, it differs in context, allowing us to provide new insights. We highlight four here.
First, we uniquely observe districts that receive additional funding not due to low wealth, but rather due to size and sparsity, irrespective of wealth. Thus we observe both poor and wealthy districts receiving additional funding that is plausibly exogenous, allowing us to ask whether the effect of an additional dollar is the same across these margins. Second, we add evidence from a new state. Prior work has either used survey data from nationwide reforms (e.g. Jackson et al., 2016; Lafortune et al., 2018), or state level data in large part focusing on reforms in Michigan (Chakrabarti and Roy, 2015, Chakrabarti and Roy, 2017; Chaudhary, 2009; Hyman, 2017; Papke, 2005; Roy, 2011), though examples exist in other states as well.3 Thus, evidence from a new state diversifies our knowledge base in a meaningful way. Third, our study is in the context of small and rural districts, a topic that has received very little attention in the literature (one might see Monk, 1990, or Andrews et al., 2002 for example). In fact, more than half of all school districts in the U.S. are classified as either “distant” or “remote”. As populations in the U.S. and elsewhere migrate toward urban centers, policy concerns for rural and sparse school districts become more salient. The literature has not provided much guidance. Fourth, our study observes the long run equilibrium effects of additional funding on district performance and characteristics driven by a policy change many years ago. Given that policy levers can affect funding but not responses, observing how districts fare in the long run across not only outcomes but also composition provides valuable insight.
Our empirical strategy leverages Texas's funding formula by controlling for smooth functions of size and sparsity in regression models, and observing differences across districts attributable to residual variation in funding resulting from kinks and discontinuities in the formula. To allow for cumulative effects of exposure, we measure the average additional funding students experienced by each grade. We find that districts receiving additional funding perform significantly better in both reading and math, and better in terms of high school graduation and dropout rates. We estimate that exposure to an additional $1000 per year in the base funding level over students' schooling years, or equivalently a 10% increase in expenditures, improves reading scores by almost 0.1 standard deviation and math scores by more than 0.07. Yet, these average gains mask heterogeneity.
When we break out gains by grade, we find that benefits are largely concentrated among later grades, after students have had longer exposure to increased funding. Likewise, when we observe effects by the share of students in a district who are poor or Hispanic, we find that gains are largely concentrated among the poorest and most minority districts (and likewise in later grades for them). We also show an annual $1000 increase in funding decreases high school dropout rates by almost 2 percentage points, off a base of 4%. Again, gains are concentrated in poorer districts. Still, these gains in achievement and attainment are not sufficient to close the level gap between poor districts and their wealthier counterparts. Hence, while increased funding can narrow gaps, it is unlikely that disparities can be entirely eliminated through additional school resources alone.
We also observe long-run student outcomes through access to National Student Clearinghouse records for students in our districts who interacted with the College Board, through the PSAT, SAT, or AP exams. We find little increase in the share of students taking the SAT, but among those who did we find that SAT score gains approximate our results for state standardized tests. An additional $1000 per year since 3rd grade leads to a 0.1 standard deviation increase in SAT scores, though estimates are noisy, again with larger and statistically meaningful effects in poorer districts. We also observe a 9 percentage point increase in college enrollment, though only a 4 percentage point increase in college graduation.
When we ask how districts spend additional discretionary funds we find that they keep original spending shares largely intact, with a marginal decrease in the share of funding dedicated to direct instruction in favor of a slight increase in the share of funds allocated toward administration. Thus increasing funding increases levels but does not dramatically change shares. We also find a small but meaningful decrease in the student-teacher ratio, between 5 and 10%, which likely contributes to gains among other potential factors. Using historical Census records, we find little evidence of selective migration to districts receiving additional funding, as measured by the share of students who are poor. We do find a slight decrease in the share of students who are Hispanic.
Taken together, while these findings suggest that increased discretionary funds yield meaningful academic gains, supporting the “money matters” camp (Greenwald et al., 1996; Guryan, 2001; Hyman, 2017; Jackson et al., 2016; Lafortune et al., 2018; Papke, 2005; Roy, 2011), they also suggest that additional funding does not generate gains uniformly to all schools, and that districts may be somewhat constrained in how they can shift resources across inputs, especially when faced with high fixed costs, lending some credence to the limited capacity argument (Hanushek, 1986, Hanushek, 2003).
Section snippets
Data
The majority of data for this project come from publicly available data from the Texas Education Agency (TEA). In few cases measures were unavailable and had to be requested via email correspondence with the TEA. District revenue and expenditure data come from Texas's Public Education Information Management System (PEIMS) which date back to 1997 with some exceptions. These provide annual district level measures of revenue, by source (Local, State and Federal), including the taxable value of
School funding in Texas
Texas funds education through what is commonly referred to as a foundation program. This model of education finance is meant to guarantee similar districts equal per-pupil revenue from equal effort (tax rates) regardless of property wealth. To do so the state first determines the cost of educating each student in a district, which is a function of both student “type”, for example regular or special education, and district characteristics, such as sparsity and the cost of living. Then the share
Estimation strategy
Our empirical strategy is based on the assumption that the formula providing additional funding to small and sparse districts does not perfectly capture the true relationship between size and sparsity and educational costs. If it is the case that the cost of educating students is kinked exactly at 1373 students and discontinuous precisely at 300 square miles, as described in Eq. 2, we cannot exploit any variation. If not, we can exploit the difference between the true and formulaic
Residual variation in funding
We begin by estimating our main model from Equation7 on various components of district revenue in Table 2. These specifications control for smooth functions of size and sparsity and proxies in commute and bus miles, g(·), the cost of education adjustment and whether the district is k-12 or consolidated, Xi(t), and for region-year fixed effects, τr∗t, to match outcome equations that follow.
Beginning with columns 1 through 5 we show the impact of an additional $1000 on total revenue, and then
Interpretation and policy
Our estimates suggest that a $1,000 increase in base funding yields a 0.1 s.d. increase in reading scores, and a near 0.08 increase in math. In addition, dropout rates decline, graduation rates marginally increase, as does college enrollment and to a smaller degree graduation. These gains are largely concentrated in later grades (for test scores) and among poorer districts. Here we situate these in the literature.
Conclusion
We address two questions: (i) how do school districts receiving additional discretionary funds allocate these resources; and (ii) does the provision of additional funding through state formulas impact academic achievement and attainment? We find that students in districts receiving additional discretionary funds due to a size and sparsity allotment perform better on a host of academic measures, net of our controls for the true costs of size and sparsity.
Results suggest that a $1,000 increase in
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