The Effect of Education Spending on Student

Achievement: Evidence from Property Values and

School Finance Rules

Corbin L. Miller∗

Cornell University

October 29, 2017

Find the latest draft at https://corbinmiller.website/research/

Abstract

Property values are a key factor in education finance and affect local property taxrevenue as well as the level of state aid provided to school districts. However, little isknown about the effect of property values on student achievement through their impacton revenue. In this paper, I estimate the effect of education spending on district-levelstudent outcomes in 24 states by leveraging changes in revenue driven by property valuevariation. I interact fixed school finance formulas that measure how local revenue andstate aid respond to changes in property wealth with state-level variation in propertyvalues to create a simulated instrument for school revenue. To construct this measure,I collected state administrative data on property values at the school district level. Theinstrument is strong and highly predictive of changes in revenue. I find that increasedspending improves graduation rates and student test scores. These results suggestthat large school finance reforms are not prerequisites for spending to improve studentoutcomes.

JEL Classification: H75; I22

Keywords: School Finance; High School Completion; Test Scores; Property Values

∗Email: clm297@cornell.edu. This work was funded in part by the C. Lowell Harris Dissertation Fellow-ship from the Lincoln Institute for Land Policy. I am thankful to Michael Lovenheim, Maria Fitzpatrick,Donald Kenkel, Doug Miller, and many seminar participants at Cornell University for helpful comments andsuggestions.

1 Introduction

The United States spends roughly 3.7 percent of its GDP on public K-12 education.1 De-

spite this large government investment, researchers are just beginning to understand the

relationship between school spending and student outcomes. As shown in Figure 1, public

schools were historically funded primarily through local property taxes with over 80 percent

of funds coming from local sources. This reliance on property taxes led to large disparities

in school spending across districts. Starting in the 1970s and 1980s, courts determined that

local funding of school districts is unconstitutional and states responded by enacting funding

formulas to reduce the relationship between local property values and school spending. In

many cases, formulas explicitly take into account property values by providing more fund-

ing for low-property wealth districts. Recent research that leverages exogenous variation

in expenditures from these school finance reforms provide the best evidence for the effect

of increased spending on student outcomes (Jackson et al., 2016; Lafortune et al., 2017).

Despite the increased importance of state funds, property values are still a major component

of education funding. While much effort has been devoted to estimating the effect of school

spending and quality on property values (Oates, 1969; Black, 1999; Bayer et al., 2007; Ries

and Somerville, 2010), little is known about the effect of market changes in property values

on student achievement through their impact on revenue.

In this paper, I estimate the effect of education spending on district-level student out-

comes in 24 states by leveraging changes in revenue driven by property value variation. I

interact fixed school finance formulas that measure how local revenue and state aid respond

to changes in property wealth with state-level variation in property values to create a sim-

ulated instrument for school revenue. From my first stage, I estimate that a 10 percent

increase in simulated revenue increases spending by 1 to 2 percent. This result suggests

that administrators do not perfectly offset the revenue from changes in property values by

1In FY2014, GDP was $17.43 trillion (U.S. Bureau of Economic Analysis, 2017) and total spending onpublic K-12 was $634 billion (National Center for Education Statistics, 2016).

1

adjusting tax rates and other school finance parameters. Identifying variation comes from

the interaction of property values and ex ante differences in district taxing behavior and

state finance formulas.

The student outcomes I examine are graduation rates and test scores. Graduation rates

are based on information from the National Center for Education Statistics Common Core

of Data (CCD). I use nationally-comparable math and reading test scores for 4th and 8th

graders, aggregated to the district level, from the Stanford Education Data Archive (SEDA).

Using my measure of simulated revenue as an instrument for spending in a two-stage least

squares framework, I find that a 10 percent increase in spending increases graduation rates

by 2.5 to 5 percentage points. For test scores, I find that a 10 percent increase in average

spending 5 to 8 years prior to the test increases 4th grade math and reading scores by about

0.09 standard deviations and 8th grade reading scores by 0.07 standard deviations. I find

some evidence that cuts to spending have a larger magnitude effect on graduation rates

than equivalent increases in spending. The relationship between spending and graduation

rates is concentrated in high-income districts, but evenly split across high and low property

wealth districts. Even though the effects are largest in high income districts, I am unable to

determine which types of students benefit in these districts.

My estimates for the effect of school spending on graduation rates are larger in mag-

nitude than those found in recent papers using variation from school finance reforms. The

main findings in Jackson et al. (2016) are based on individual-level data from the PSID, but

in alternative analyses they use the same CCD graduation rate measures I do and find that

a 10 percent increase in spending across 12 years of school increases graduation rates by 3.55

percentage points. Candelaria and Shores (2017) replicate this result and also find an effect

size of 5 percentage points in the highest poverty districts. Each of these papers uses the

number of graduates per 8th grader (four years prior) as a proxy for graduation rates. When

use this same measure, I find that increasing spending by 10 percent in the final two years of

high school increases graduation by 5.1 percentage points. When considering spending over

2

the last 4 years of high school this effect drops to 3.21 percentage points. When I estimate

the effect of each lagged year of spending, only spending in the year of and prior to grad-

uation have a significant effect, so averaging over additional years attenuates the estimate.

Another interesting difference in our results is they find larger effects for higher poverty

areas, while my estimates suggest that effects are concentrated in high income areas. The

identifying variation from school finance reforms comes predominantly through low income

areas spending much more, while high income areas do not see any effect on spending. My

instrument is strong for both low and high income districts so I am able to reliably estimate

the effect of spending in high income districts.

Whether or not increased spending improves student test scores is not a new question

in the literature. Since Coleman (1966) there have been dozens of studies attempting to

estimate the education production function (Todd and Wolpin, 2003). This debate has been

contentious and has not yet lead to a consensus (Hanushek, 2003; Krueger, 2003). The

most recent, well-identified estimates suggest that increasing total school resources does

indeed improve test scores. In particular, Lafortune et al. (2017) find that after 10 years of

increased spending by $1,000 per pupil, test scores increased between 0.12 and 0.24 standard

deviations. Others find that $1,000 per pupil increases test scores by 0.5 standard deviations

(Guryan, 2001) and a 10 percent increase in spending increases pass rates by between 1 and 2

percentage points (Papke, 2005). My test score estimates, in thousands of dollars per pupil,

are between 0.051 and 0.066 standard deviations.2 The parameter I estimate is the effect

of increased spending from 5 to 8 years before the test is taken, but Lafortune et al. (2017)

report the effect of increased spending for 10 years prior. If there is a cumulative effect of

being in a district with more resources, then scaling my estimates to 10 years rather than 4

years would give magnitudes in their range.

I make several contributions to the literature on the funding and productivity of pub-

2In my sample, average spending per pupil is $13,719.24, so $1,000 is a 7.29 percent increase. Scaling myestimates by 0.729 gives 0.09×0.729 = 0.066 for 4th grade test scores and 0.07×0.729 = 0.051 for 8th gradereading scores.

3

lic education. My main contribution is new empirical evidence for the effect of spending

on student achievement at the relevant margin for policy. The variation that identifies my

estimates is based on regular year-to-year variation in funding within existing policy struc-

ture rather than large, targeted overhauls of those structures as in school finance reforms.

My findings are thus evidence that replacing funding formulas are not a prerequisite for

increased spending to improve student outcomes. My new approach to estimating the effect

of local government spending also provides a number of contributions. One of the primary

innovations of this paper is a new compilation of data on school district property values

and school finance formulas. I collected administrative data from individual states regard-

ing property values at the school district level. I extracted much of this information from

various hard-copy records and non-searchable computer files. I also code up the key features

of school finance formulas and state-imposed property tax restrictions to simulate expected

changes in revenue based solely on changes in property values. I am able to take advantage

of new district-level test score data from the SEDA because my identification strategy does

not rely on policy variation during the time frame their measures are available. The second

contribution of my approach is that the first-stage and reduced form estimates of the effect of

property values on revenues and subsequent student outcomes are policy relevant. Property

values have a significant effect on both local revenue and state aid that are not undone by

responses in policy. Finally, my paper provides evidence of a causal relationship between

market fluctuations in property values and student outcomes due to the reliance on property

tax revenue. While school finance reforms decreased the cross-sectional relationship between

local property values and school spending, there remains a significant time-series relationship

that influences student outcomes.

My findings have implications for policy. I find that changes in property values affect

student outcomes through their effect on school spending. This link is not well known, but

is crucial for policymakers who are concerned with maintaining student outcomes through

volatile markets. Another policy-relevant result is that the effect of cuts in resources are

4

larger in magnitude than the effect of increased spending. This suggests that maintaining

consistent spending levels is better for students than expanding and contracting resources by

the same amount. Finally, increased spending improves test scores even when the spending

occurs prior to when students enter school. This relationship suggests that there are durable

or delayed effects of investments in school inputs on test scores.

The next section provides background information about the prior literature, property

taxes, and school finance programs in the United States. The data is discussed in Section 3.

Section 4 explains my simulated instrument and empirical strategy. I present my results in

Section 5, and Section 6 concludes.

2 Background

2.1 Prior Literature

A large literature attempts to apply the framework of production technologies to the ed-

ucation process. These studies estimate the relative importance of primary inputs, which

include an individual endowment of ability and the influence of families, peers, and schools

(Todd and Wolpin, 2003). The output of the education process is cognitive and noncognitive

skills that culminate in persistence in education and eventual labor market earnings.

The first study to examine the relative importance of school inputs and family inputs on

student achievement was Coleman (1966). Coleman finds that family characteristics explain

the majority of variation in test scores and spending explains little. At the time, people took

these results to mean that schools did not matter and the variation in student outcomes is

a result of family and peer effects. These counterintuitive results ignited decades of hotly-

debated research into the relationship between spending and student achievement, which

find contrasting evidence (see Hanushek, 2003; Krueger, 2003).

Recently, more well-identified studies leverage experimental or quasi-experimental varia-

tion in school inputs to examine their effect on student outcomes. These inputs include class

5

size (Krueger, 1999; Angrist and Lavy, 1999; Hoxby, 2000), teacher quality (Chetty et al.,

2011), and capital spending (Cellini et al., 2010; Martorell et al., 2016; Hong and Zimmer,

2016). Others exploit large changes in spending due to school finance reforms (SFRs). Card

and Payne (2002) find that increased spending from SFRs decreased the gap in SAT scores

across family background groups, but only observe the select sample that took the SAT.

Jackson et al. (2016) find that increased per pupil spending increased educational attain-

ment and adult earnings. Hyman (2017) finds that SFR in Michigan improved college-going

and completion.

Most relevant to the present study are those that use variation in spending from SFRs to

studying the impact of spending on graduation rates and test scores. Jackson et al. (2016)

study graduation using individual-level data from the PSID that leverages variation that

mostly occured during the 1970’s and 1980’s. They find that a 10% increase in spending in-

creased graduation rates by 9.8 percentage points for low income children, which corresponds

to an effect size of 14.7 percentage points given a $1,000 per pupil increase in spending.3

Candelaria and Shores (2017) use the same district-level graduation data from the CCD as

I do and find that a 10% increase in spending increased graduation rates by 5 percentage

points in the quartile with the highest fraction of free-lunch eligible students, which corre-

sponds to an effect size of 4.54 percentage points given a $1,000 increase in spending per

student.4

Most SFR studies that look at test scores do so in individual states. These include

Clark (2003) who finds no test score gains in Kentucky, Guryan (2001) who finds increased

4th grade test scores in Massachusetts, and Papke (2005) who finds increased proficiency

scores in Michigan. The exception that looks at test score measures nationwide is Lafortune

3Average revenue in their sample was $4,800 per pupil, so a 10% increase is $480 per pupil. Adjustingfor inflation to real 2013 dollars (this was in 2000 dollars) this is $665.05. This means a $1,000 increase inspending increased graduation rates by 9.8*1.504=14.736 percentage points (17.1 percent off a base of 79percent) for low-income children.

4Average total revenue was $7,950.2 per pupil, so 10% increase is $795. Adjusting for inflation to real2013 dollars (this was in 2000 dollars) this is $1,101.49. Thus need to adjust down by 1000/1,101.49=.908.So $1,000 increase in spending increases graduation rates by 4.54 percentage points (5.9 percent).

6

et al. (2017). They use restricted-access individual-level information from the state NAEP

to create measures of test score disparities between low and high income school districts.

They find that after reforms, low-income districts close the gap between their test scores and

those in high-income districts by 0.1 standard deviations, which gives an effect size of 0.12

to 0.24 standard deviations per $1,000 in annual spending per pupil.

My paper provides several contributions to these estimates of graduation rates and test

scores. First, I exploit a new source of exogenous variation that provides an opportunity

to see if previous results generalize to another context. Specifically, SFRs increase funding

disproportionately for low-income districts, which is also where previous studies tend to see

the strongest effects. My variation, on the other hand, provides similar variation to low and

high income districts. My variation is also more recent and corresponds to changes in funding

from a higher base level. Since education production likely exhibits diminishing returns, my

estimates provide some evidence on whether we have reached the flat of the curve. The

flexibility of my approach also allows me to take advantage of newly available data that

measures test scores at the district level on a scale that is comparable across states. Finally,

the effect of large, one-time changes in state funding structures may not generalize to other

sources of funding variation that are, or seem to be, more transitory changes in resources.

2.2 Simulated Instruments

My paper builds on previous work using simulated instruments. This method was pioneered

by Currie and Gruber (1996) in their work evaluating the affect of health insurance coverage

on health care utilization and outcomes. They face a reverse causality problem because

health status also affect insurance coverage and the consumption of health care. Their

solution leverages exogenous increases in health insurance coverage through expansion of

Medicaid to low-income children, and they use only the change in insurance coverage due

to these expansions to identify the effect of interest. Hoxby (2001) applies this strategy to

school finance by leveraging school finance reforms as the exogenous shift in policies. While

7

her primary focus is on features of the finance structures themselves, she is also able to assess

the effect of spending on student achievement.

In general, simulated instruments seek to help explain the relationship between some

output y and an intermediate outcome x. We take advantage of the fact that x is determined

by x = f(z) where f(·) is a mechanism that assigns a level of x given the characteristics in

z. Since z is not a valid instrument for x, the method fixes z and lets f vary due to policy

changes which gives x̃t = ft(z̄) or the portion of the change in x due to the change in ft. In

Currie and Gruber (1996), y is health outcomes, x is health care, f is health insurance, and z

are demographics. In Hoxby (2001), y is student outcomes, x is school spending, f is school

finance structure, and z are district characteristics that determine state funding. Instead

of relying on exogenous changes in f and fixed characteristics, I fix f and use exogenous

changes in one of the characteristics that effect state and local funding: property wealth.

District property wealth is not necessarily exogenous to school quality at the district level

so I use a shift-share measure of property wealth that captures the leave-one-out trend in

property wealth at the state level.

2.3 Property Taxes

Most school districts are governed by a school board with authority to levy property taxes

for school funding. This taxing authority is limited by statute and the approval of local

voters. Property taxes are ad valorem taxes on the value of property.5 Property tax revenue

is determined by the aggregate taxable value of property in the district and the property tax

rate as follows:

Property Tax Revenue = Property Wealth× Property Tax Rate. (1)

5Ad valorem taxes are a type of excise tax. The other kind of excise tax is a specific tax, which appliesto a quantity, such as excise taxes on a pack of cigarettes.

8

The tax rate is often reported in “mills,” or thousandths of a dollar. That is, a property tax

rate of 1 mills corresponds to a fraction of 11000

= 0.001. Nearly all property tax imposing

jurisdictions tax real estate such as residential and commercial properties. Other common

types of taxable property include motor vehicles, agricultural land, mineral wealth, and

certain types of property used in business such as machinery.

States impose a number of restrictions, known as tax and expenditure limits (TELs),

on the property taxing behavior of local governments. These restrictions determine the

taxable value of property and restrict the allowable level and growth of property tax revenue.

TELs were mostly enacted in reaction to the property tax revolt of the 1970s and 1980s.

As property assessors moved to more rigorous mathematical practices, many de facto tax

breaks from fractional or infrequent assessments were removed. TELs were largely a way

of codifying the tax breaks that homeowners were already receiving. States determine the

fraction of property that is subject to taxation – called the assessment rate – for each type

of property. Some types of real property such as historical or religious buildings are exempt

from taxation and their assessment rate is zero. Some properties are partially exempt and

are given a lower assessment rate such as homesteads and homes owned by low-income

seniors or veterans. Other TELs restrict taxing behavior to reduce the tax burden and

limit volatility in property tax payments. To reduce the tax burden, state impose fixed tax

limits, such as maximum or minimum millage rate requirements. States also limit the annual

change in assessed value, revenue, or tax payments. These dynamic limits are reflected in

my simulated instrument since they are predetermined responses to large fluctuations in

property values. This is an important difference between states in how and when increased

property values translate into revenue. The fixed limits are not part of my instrument since

they are accounted for in the base year characteristics and absorbed by district fixed effects.

As of 1999, 19 states had some sort of dynamic limit on the growth of property tax revenue.6

Previous studies find that introducing TELs decreased school inputs and weakened

6Appendix Table A4 lists each of the dynamic TELs as of 1999.

9

student outcomes. Student-teacher ratios increased significantly as a result of Oregon’s tax

limitation (Figlio, 1998). Figlio and Rueben (2001) also finds that TELs reduce the test

scores of education majors, and presumably their effectiveness as teachers. Downes et al.

(1998) finds that the introduction of TELs in Illinois caused small reduction in 3rd grade

math scores, but no effect on reading scores. I take TELs into account to improve my

instrument by considering these predetermined responses.

2.4 School Finance

School districts receive about 45 percent of their funding from local sources, 46 percent from

state sources, and the remaining 9 percent from federal sources. 80 percent of local revenue

is generated through property taxes. The majority of state revenue for education comes

from income and sales taxes.7 State funds are distributed to local school districts based on a

formula set by the state legislature, usually on a per pupil basis. In addition to the student

counts, state finance formulas depend on the ability of school districts to raise local revenue,

usually measured by property wealth. Other supplementary funds are distributed based on

program offerings through categorical grants or special circumstances like large geographic

districts that need addition funding for transportation.

Funds are available to school districts based on the following relationship:

Rdt = Lt(τ

dt ×W d

t ) + St(τdt ,W

dt ,X

dt ) + Ft(Z

dt ) (2)

where Rdt is the sum of revenue from all sources for district d and year t. Local revenue,

Lt(·), is a function of the revenue generated by applying the school property tax rate to

the property wealth within a district along with any tax and expenditure limits.8 Thus,

W dt is the market value of property, τ dt is the millage rate, and Lt(·) is everything else that

7In some states property tax revenue for schools is treated more like a state revenue source because stateseither directly collect the property tax, or receive funds from local districts that they then redistribute.

8Although TELs are imposed by the state, they directly affect the collection of local revenue.

10

converts the millage rate into the effective tax rate. The effective tax rate is the fraction

of market value of property that is received as property tax revenue. In some cases it is

useful to differentiate between the scaling factors involved in Ldt (·) and other non-linearities

introduced by TELs, and for this I will use `dt as a district-specific fraction to account for

this.9 The state revenue function, S(·), depends on local tax effort – measured by τ dt – and

tax capacity – measured by W dt – as well as characteristics of the district, Xd

t , such as student

counts and participation in certain educational programs. Transfers between state and local

revenues are captured in St and therefore, in cases where states redistribute revenue from

high-wealth to low-wealth areas, St can be negative. Federal revenue is a function of other

district characteristics, Zdt , such as the fraction of students eligible for free or reduced price

lunch.

Changes in total revenue come from multiple sources. States make minor legislative

adjustments of the state funding formulas and or districts adjust the tax rate. School finance

reforms constitute a fundamental change in the form of St that is above and beyond small

adjustments to the parameters of the existing system. For local revenue, Hoxby (2001) uses

the term inverted tax price to denote “the dollars that a district gets to spend if it raises

one dollar in local revenue” regardless of whether that dollar is generated by a change in the

tax rate or the tax base. Here I separate these two factors that determine revenue and use

the term tax price to refer specifically to∂Rd

t

∂τdt, or the change in revenue given an increase in

the tax rate, and I define the wealth price as∂Rd

t

∂W dt

, or the marginal change in revenue given a

unit increase in property wealth. The wealth price depends on how W dt interacts with each

revenue source. By differentiating both sides of Equation 2, the wealth price is

∂Rdt

∂W dt

=∂Ldt∂W d

t

+∂Sdt∂W d

t

. (3)

9That is, if the values of τdt and W dt do not put us near the non-linear parts of Ld

t (·), then Ldt (τdt ×W d

t ) =`dt × τdt ×W d

t .

11

and the tax price is

∂Rdt

∂τ dt=∂Ldt∂τ dt

+∂Sdt∂τ dt

. (4)

Thus, the wealth price and the tax price are not only the change in revenue from local

property taxes, but responses in state aid given that change in revenue. When districts

choose their tax rate they respond to the tax price in order to raise the necessary revenue.

While districts might also consider the wealth price when setting tax rate, it is likely a

second-order priority.

Nearly all states use one, or a combination, of two types of funding formulae: (1)

foundation programs and (2) district power equalization.10 The most common school finance

policy is the foundation program, which applies to 40 states (45 counting states that also

use a district power equalization in a tiered system).11 The goal of a foundation plan is to

provide adequate funding by guaranteeing an amount of funding per pupil. The guaranteed

amount of spending per pupil is called the foundation level. To qualify for state aid, districts

are responsible for contributing a local share defined by applying the foundation tax rate, τ f ,

to their taxable property value. Foundation programs do not preclude districts from raising

additional funds by taxing above the foundation tax rate. Generally, foundation programs

can be described by

Sdt = Foundationt × ADMdt − Ldt (τ

ft ×W d

t )

where Foundationt is the foundation level, ADMdt stands for average daily membership,

which is a measure of the number of students in the district. The wealth price in this general

case is

∂Rdt

∂W dt

= `dt ×max{0, τ dt − τft }

10Hawaii’s single school district is entirely funded by the state and does not receive property tax revenue.North Carolina provides flat grants to districts which can be supplemented by local property tax revenue.

11Table A1 summarizes the type of school finance programs used in the United States.

12

and the tax price is

∂Rdt

∂τ dt= `dt ×W

ft .

The second most common set of school finance policies are district power equalization pro-

grams. To help subsidize funding for low-wealth districts, equalization programs guarantee

an amount of revenue for each percentage of tax rate regardless of district property wealth.

Many states with a guaranteed amount of spending per pupil through a foundation program

will also do some redistribution to help support districts with low levels of property wealth.

Generally a equalization plan distributes funds based on

Sdt = Ldt(τ dt ×

(max{W d

t ,W∗t } −W d

t

)),

where W ∗t is the guaranteed wealth level. Thus, the state tops up local revenue based on

what a district with the guaranteed wealth level would take in by levying the same tax rate.

The wealth price for this plan is

∂Rdt

∂W dt

=

`dt × τ dt , W d

t < W ∗t

0, W dt ≥ W ∗

t ,

and the tax price is

∂Rdt

∂τ dt=

`dt ×W ∗

t , W dt < W ∗

t

`dt ×W dt , W d

t ≥ W ∗t .

I use the finance rules of New Mexico and Georgia as an example of how I calculate

the wealth and tax price.12 I use the term wADMdt to refer to weighted average daily

membership or the weighted number of students.13 Figure 2 shows the distribution of wealth

price within states and across states. The within state variation comes from differences in

12Other states in my sample with a foundation program are summarized in Appendix Table A2 and stateswith a combination or tiered plan are summarized in Appendix Table A3.

13I use the same notation for districts across states, but in constructing the state finance formula I takeinto account the substantial differences in how states weight students in different grades or programs.

13

district characteristics, primarily the tax rate and wealth level relative to other districts

in the state. Across state variation also depends on these factors, but is also driven by

differences in the state’s funding formulas.

2.4.1 Foundation Example: New Mexico

New Mexico has a simple foundation program established by the New Mexico Public School

Finance Act in 1974. The foundation tax rate is 0.5 mills so local revenue is Ldt (τdt ×W d

t )

and state revenue is

Sdt = Foundationt × wADMdt − Ldt (0.0005×W d

t ).

Although there is no limitation in the law that requires Sdt to be positive, the finance rules

and characteristics of districts are such that this is not negative in practice. Total revenue

is then given by

Rdt = Foundationt × wADMd

t + Ldt ((τdt − 0.0005)×W d

t ) + F dt .

This gives a wealth price of

∂Rdt

∂W dt

= `dt × (τ dt − 0.0005).

Thus, without any action by the school district, revenue increases by a set fraction of any

increase in property wealth that depends directly on the local tax rate and the foundation

tax rate. Similarly, the tax price is

∂Rdt

∂τ dt= `dt ×W d

t

which depends on property wealth.

14

2.4.2 Foundation + Equalization Example: Georgia

Georgia’s Quality Basic Education Act provides funds per weighted pupil based on a founda-

tion program with an optional equalization component. The foundation tax rate is 5 mills.

The equalization component provides the difference between the revenue generated from 5

to 8.25 mills and what would have been generated by a district with that same millage rate

and property wealth as a district at the 90th percentile of wealth in the state. Local revenue

is still Ldt (τdt ×W d

t ) and state revenue is

Sdt = Foundationt×wADMdt −Ldt (0.005×W d

t )+min{0.00325, τ dt −0.005}×Ldt (max{W dt ,W

90t }−W d

t )

where W 90t is the 90th percentile of wealth across districts. There is no statutory limitation

on Sdt that keeps this value from being negative, but the state-level aggregate Sst is restricted

by not allowing the aggregate local share to be more than 25 percent of the state-level

foundation guarantee. Total revenue is then given by

Rdt = Foundationt×wADMd

t +Ldt ((τdt −0.005)×W d

t )+min{0.00325, τ dt −0.005}×Ldt (max{W dt ,W

90t }−W d

t ).

Thus, the wealth price is

∂Rdt

∂W dt

=

`dt ×

(τ dt − 0.00825

), if τ dt ≥ 0.00825 and W d

t ≤ W 90t

0, if τ dt ≤ 0.00825 and W dt ≤ W 90

t

`dt ×(τ dt − 0.005

), if W d

t > W 90t

and the tax price is

∂Rdt

∂τ dt=

`dt ×W d

t if W dt ≥ W 90

t

`dt ×W 90t if W d

t < W 90t

.

15

So, if districts have wealth below the 90th percentile, they gain state revenue and lose local

revenue from each dollar of increased property wealth. For districts with a tax rate between

5 and 8.25 mills the increase in local revenue and decrease in state revenue cancel each other

out and total revenue is unchanged. Districts at or above the 90th percentile of wealth are

not effected by the equalization component and only experience the foundation portion of

the plan.

3 Data

3.1 Data Sources

The data for this project are combined from several sources. My primary source of data is

the National Center for Education Statistics’ Common Core of Data (CCD). I supplement

the CCD with additional district-level information including a database of district property

values collected from individual states, test scores, and median household income.

3.1.1 NCES Common Core of Data

The CCD is a comprehensive, national database of all public schools and school districts

in the United States. Fiscal information is available annually back to 1995 and non-fiscal

characteristics are available back to 1987. The variables I use from the CCD include ex-

penditures, revenues, and the number of students in several race categories and in certain

educational programs. Expenditures are reported in a number of categories including in-

structional spending, capital outlays, and administrative spending. Revenues are reported

in several fine categories and aggregated to local, state, and federal sources. One subcategory

necessary for my identification strategy is property tax revenue, which I divide by district

property wealth to calculate the effective tax rate. The endogenous variable of interest that I

instrument for in my identification strategy is total expenditures, which I report in thousands

of dollars per pupil. I use student count data to create controls for total student enrollment,

16

the fraction of students who are black or Hispanic, have an individualized education plan

(IEP)/are in special education, or are eligible for free or reduced price lunch.

3.1.2 School District Property Wealth Database

The CCD does not include a measure of district property wealth, which is crucial for my

estimation strategy. Most states have an agency (usually a Department of Revenue or

Department of Taxation) that oversees local auditors who assess values for property tax

purposes. Due to this responsibility, summaries of property values at each geographic level

of taxation (e.g. county, municipality, school district) are often available from these state

agencies. I collected this information individually from states and created the first school

district-level database of property values covering years 1999-2014.14 This database includes

information for 24 states.15 These measures of property wealth are predominantly made up

of residential and commercial real property but may also include other types of property.

I input the raw data based on state records and convert the property wealth measures to

total market value of property within the district, wherever possible.16 These state records

are then merged to the CCD information at the school district level. This is mostly done by

matching on district name, but in some cases there are other unique identifiers consistent

between the state and CCD records that were used. See Online Appendix B for a full

description of data sources and steps taken to create the database.

3.1.3 School Finance Formulas

I compile information about school finance formulas from multiple sources. U.S. Department

of Education National Center for Education Statistics (2001) provides an overview of each

14Property wealth data is not available in each state and year. See Online Appendix B for a descriptionof data sources and availability for each state.

15The states in the database are Arkansas, Connecticut, Florida, Georgia, Idaho, Illinois, Iowa, Kansas,Kentucky, Massachusetts, Minnesota, Mississippi, Nevada, New Hampshire, New Jersey, New Mexico, NewYork, North Carolina, North Dakota, Ohio, Oklahoma, Oregon, Texas, and Washington.

16For some states there are different assessment rates for different types of property and values disaggre-gated enough to calculate market values.

17

state’s funding formula as of the 1998-1999 school year, which provides a useful starting

point. I supplement these descriptions with additional information from laws and statutes

as well as documentation from state Departments of Education.

I do not attempt to capture every factor that influences state funding. Instead I focus

on the bulk of funding that comes from foundation entitlements and parts of state funding

that depend on property wealth. The main feature that needs to be reflected in the school

finance formulas is the wealth price. This means that the response to a change in property

wealth will be correct in terms of direction and relative magnitude, but the scaling will be off

to the extent that I have not accounted for all other categorical grants or other components

that are unrelated to property wealth.

3.1.4 Student Achievement Data

Graduation rate data come from the CCD and test score measures come from the Stanford

Education Data Archive (SEDA). Each data source has its own strength and limitations.

Graduation data comes from the CCD completion information at the district level for

most years from 1992 to 2010. I calculate graduation rates by taking the number of diplomas

awarded in a given year and dividing by the number of students in the cohort expected to

graduate that year based on lagged student counts. Thus, the completion rate can be

calculated using a number of cohorts such as the number of students in 11th grade the

previous year, number of students in 10th grade two years ago, and so on. Specifically,

Gradgt =Diplomast

Studentsgt−(12−g)

where Gradgt is the gth grade cohort graduation rate in year t, Diplomast is the number

of diplomas awarded, and Studentsgt−(12−g) is the number of students in gth grade 12 − g

years prior to t. There is some year-to-year variation in district coverage. One important

example is years 2003 to 2005, when completion information was only recorded for school

18

districts serving more than 1000 students.17 My preferred estimates only include districts

with data from 2003 to 2005, but results are not sensitive to this restriction. It is important

to note that this measure is only a proxy for the graduation rate. This measure will also

pick up changes in student composition that occur between the year the cohort is measured

and when the number of diplomas is measured. It also does not account for students who

receive a GED or complete high school in a different school district.

The SEDA is a collection of academic achievement, achievement gaps, and school and

neighborhood economic and racial composition at various levels of aggregation. The SEDA

includes a comprehensive database of district-level test scores for school years 2009 to 2013.

The basis for these measures are state standardized tests, which are then adjusted based on

comparing the distributions of those tests with the NAEP.18 For a subset of large, diverse

districts, there are also measures of the average gap between white students and black stu-

dents. These test score measures are reported on the scale of NAEP scores, but I standardize

these at the grade-subject level based on the mean and standard deviation in 2009. After

2009 I allow the mean and standard deviation to evolve as the distribution of achievement

shifts over time. One of the strengths of the SEDA test score measure is that it covers over

80 percent of districts in the United States. The second key strength is that the measures are

comparable across time and geography, which allows me to do this district-level, nationwide

analysis. The primary limitation of these data is that they are currently only available for a

limited number of years.

3.1.5 Other State and District Controls

Other data used in my analysis includes median household income and additional measures

used in school finance formulas. The median household income for each school district comes

from the 2000 Census and the American Community Survey (ACS) 5-year estimates. These

17I convert the dropout rates reported from 2003 to 2005 into number of diplomas awarded using theirdropout rate and the base number of students reported in order to calculate graduation rates the same wayfor all years of the CCD.

18See Reardon and Kalogrides (2017) for a full discussion of how these measures are constructed.

19

sources provide an estimate of district income for 1999 and then 2009 onward. To account

for district-level changes in income, particularly during the great recession, I impute values

linearly between the district value in 1999 and the value in 2009. This captures the potential

drop in incomes in areas most deeply affected by the recession. Some school finance formulas

include a measure of the cost of living to adjust for within state differences in the cost of

teacher salaries.19

3.2 Creating a Balanced Panel of School Districts

Over time, new school districts are formed, old districts are absorbed into existing districts,

and some local districts are consolidated into regional districts that serve a larger geographic

area. This regional consolidation is especially apparent in the Midwest, where small, rural

districts have been combining more and more (Gordon and Knight, 2009). To create a

balanced panel of school districts, I combine all districts that are ever associated with each

other. For example, Appendix Figure A1 shows the boundaries of two school districts in

Minnesota, Brewster and Round Lake. These two districts consolidated into Brewster-Round

Lake Public Schools in 2014. Therefore, I treat these two school districts as a single district

across the entire analysis period. I sum the property values and student counts in these two

districts and average the median income and test scores.

I aggregate school districts for two additional reasons: regional district overlap and

availability of property value data. Some states have municipality-level elementary districts

and regional high school districts that serve multiple municipalities. Even if I have the

property values for each municipality it is not possible to distinguish how the change in

property values for a municipality affects each district separately. Appendix Figure A2

illustrates this issue with three municipalities in New Jersey. Bellmawr, Runnemede, and

Gloucester municipalities each provide for their own elementary services, and Black Horse

Regional High provides secondary services for all three. In both situations, I combine school

19These additional variables are outlined in Online Appendix B.

20

districts to the lowest level for which I have data and use the aggregated school district in

my analysis. Another issue is most property value data is reported at the school district

level, but for some states, the data is at the municipality or county level. In some cases, it

is not possible to perfectly map property values to school districts.

The number of school districts in my sample of 24 states starts at 8,061 in 1999 and

falls to 7,649 by 2014 due to actual consolidations. After making my additional district

consolidations due to data limitations, my balanced panel consists of 6,500 districts.20 I also

drop districts with fewer than 100 students in order to insulate against large fluctuations

in per pupil measures due to the large percentage change implied by a small change in the

number of students. This accounts for about eight percent of districts and results are robust

to including these districts.

I make several exclusions to reduce noise and volatility in my per-pupil measures, which

are similar to the exclusions in Lafortune et al. (2017). Specifically, I remove districts with

fewer than 100 students at any time and district-year observations with enrollment: more

than double the district’s mean enrollment, more than 15 percent different from enrollment

in either adjacent year, or more 10 percentage points above or below the district’s average

growth in enrollment. I also remove district-year observations with per pupil expenditure

or simulated revenue more than 5 times larger or smaller than the state average. Together,

these restrictions affect roughly 19.5% of district-year observations. My main conclusions

are not sensitive to these restrictions.

3.3 Summary Statistics

Summary statistics for my main estimation samples with graduation rates or SEDA test

scores are presented in Table 1. This underscores the fact that each outcome is available for

distinct subset of data. The first two columns present means and standard deviations for

the graduation rate sample where spending information is available for at least 1 year prior

20I perform additional analyses to show my results are robust to dropping all consolidated districts. Theseresults are available in Online Appendix A.

21

and for at least 4 years prior. The last column reports statistics for the sample with SEDA

test scores. The graduation rate samples cover about 3,000 school districts, while the test

score sample has over 6,000 school districts. The average graduation rate is just over 0.8.

My sample consists of districts from 24 states. To speak to the external validity of my

estimates, Table 2 compares the characteristics of districts in states including in my sample

and those that are not included. These differences are calculated as of 2009. The first column

shows statistics for the districts in states in my sample, column (2) provides statistics for

districts in states not in my sample, column (3) displays the p-value of the difference between

column (1) and (2), and the final column is statistics for all districts. The 24 states in my

sample account for 55 percent of all students and 56 percent of districts. Districts are similar

in their average number of students and teachers, and in income. There are some differences

in property tax revenue per student and fractions of students eligible for free or reduced price

lunch, in special education or who are a racial minority. However, these differences are small

and provide evidence that my results would generalize to other states not in my samples.

4 Method

The central challenge in estimating the causal effect of total spending on student achievement

is endogeneity in the relationship between expenditures and student outcomes. For example,

districts with a higher number or percentage of children who come from low-income families

receive addition funding through programs such as Title I. This negatively biases cross-

sectional estimates. On the other hand, districts with a higher fraction of parents that

are high income or are more engaged in education also get additional resources through a

higher willingness to pay taxes for education and potentially donations to the district. This

situation instead causes a positive bias in a cross-section. These are just two examples of the

bias that comes from factors related to both educational outcomes and levels of spending. It

is unclear which type of bias dominants in any given sample, so cross-sectional OLS estimates

22

using feasible data are difficult to interpret in a causal way. Controlling for fixed differences

between districts accounts for many of these cross-sectional biases, but changes in student

or family characteristics will bias time-series estimates.

4.1 Simulated Instrument

To address these endogeneity concerns, I construct an instrument that captures the me-

chanical response in revenue to changes in property values through fixed school funding

formulas. States regularly change the funding level per student to adjust for student needs

and changing costs of education. Districts also frequently change their tax rates based on

their budgetary needs and the current level of property wealth. Both of these policy decisions

are likely to be correlated with changes in student performance. To address this problem,

my instrument fixes both state funding formulae and district property tax rates in a base

year. The only determinant of funding left to vary is property wealth. With fixed tax rules,

increased property wealth leads to increased property tax revenue and, often, decreased state

transfers.

Specifically, I start with a district’s base year effective tax rate, which is given by

ETRd0 =

Property Tax Revenued0W d

0

,

where Property Tax Revenued0 is the total revenue from property taxes in the base year and

W d0 is the total market value of property in the base year.21 Previous research finds that

property values are determined, in part, by the quality of schools in the area (Oates, 1969;

Black, 1999; Bayer et al., 2007; Ries and Somerville, 2010). Thus, student achievement may

directly affect property values in the district. To avoid this simultaneity issue, I calculate

21For some districts I am unable to recover market values from the assessed values. These districts willhave values that vary properly for identification but the first stage coefficient will be scaled incorrectly.

23

simulated property wealth in year t as

W̃ dt =

W st −W s

0

W s0

×W d0

where W st and W s

0 are state-level property wealth in year t and the base year, respectively. I

use state-level changes that omit the focal district to remove any potential impact of district-

level changes on the aggregate. This can also be done at other levels of aggregation (e.g.

CBSA or national). The higher the level of aggregation, the less concern about characteristics

of the district impacting property values.22 My measure of simulated property wealth is a

Bartik-style shift-share where the share is the baseline level of property wealth and the shift

is changes in the state-level (Bartik, 1994).

Simulated local revenue, L̃dt is then the base year effective tax rate times simulated

wealth, or

L̃dt = ETRd0 × W̃ d

t .

Here the effective tax rate absorbs most of the Ldt function by accounting for assessment

rates, delinquency rates, and exemptions. Simulated state revenue, S̃dt , is calculated by

substituting a combination of the base year statutory tax rate, τ d0 , base year effective tax

rate, ETRd0, base year student counts, and current year simulated property wealth into the

base year state funding formula. That is,

S̃dt = S0(τd0 , W̃

dt , wADM

d0 , L̃

dt ).

Here, S0 captures important characteristics of funding formulas in the base year that de-

termine the response in state revenue to changes in property values. The set of variables

included in simulated state revenue depend on the particular state funding formula. To

explain how I construct simulated state revenue, consider the examples of New Mexico and

22I perform additional analyses with simulated wealth generated by national changes in wealth and alter-native state-level changes. These analyses are available in Online Appendix A.

24

Georgia. In New Mexico, the foundation amount was $2,344.09 per weighted pupil in 1999

and the only other variables state funding depends on are student counts and property

wealth. Thus, simulated state revenue for New Mexico is calculated as

S̃dt = $2, 344.09× wADMd0 − `dt × 0.0005× W̃ d

t ,

and it follows that simulated revenue is:

R̃dt = $2, 344.09× wADMd

0 + (ETRd0 − `dt × 0.0005)× W̃ d

t .

For Georgia, the foundation amount in 1999 was $2,038.74 per weighted pupil, so simulated

state revenue is

S̃dt = $2, 039×wADMd0 −`dt×0.005×W̃ d

t +`dt×min

{3.25

1000, τ d0 − 0.005

}×max{0, W̃ 90

t −W̃ dt }

and simulated revenue is

R̃dt = $2, 039×wADMd

0 +(ETRd0−`dt×0.005)×W̃ d

t +`dt×min

{3.25

1000, τ d0 − 0.005

}×max{0, W̃ 90

t −W̃ dt }.

This same procedure is carried out for each district in my sample.

4.2 Empirical Strategy

I estimate two-stage least squares (2SLS) models relating student achievement to per pupil

spending, using simulated revenue per pupil as an instrument for actual per pupil spending.

The first stage equation for per-pupil spending is:

Spendingdt = α0 + α1R̃dt + α2W

dt +Xd

tα3 + γd + γs(d)t + ηdt (5)

25

where Spendingdt is endogenous spending in district d year t, W dt is the market value of

property, Xdt is a vector of district characteristics including log number of students, median

household income, fraction of students with an IEP, fraction of student eligible for free or

reduced price lunch, fraction of black student, and fraction of Hispanic students. District

fixed effects are given by γd and state-by-year fixed effects are given by γs(d)t where s(d)

indicates the state in which district d is located.

The second stage is:

Adt = β0 + β1̂Spendingdt + β2W

dt +Xd

tβ3 + δd + δs(d)t + εdt , (6)

where Adt is student achievement for grade T and ̂Spendingdt is predicted spending from the

first stage and other measures are as described in the first stage. In both stages, standard

errors are clustered at the district level.

Education is a cumulative process, so even if student achievement responds directly

to education spending, it is unlikely to do so in the same year. Instead of measuring the

immediate effect of spending on contemporaneous test scores, I consider current and lagged

district spending individually and on average. Ideally, I would examine the effect of spending

over the past four years on fourth grade test scores and spending over the past eight years

on eighth grade test scores. In practice, my instrument performs better near the base year,

so I restrict my attention to the lags with a strong first stage.

Note that by including the actual property values in the district in the regression, I

make it clear that identification from my simulated instrument does not come from within-

district variation in property wealth. Instead the instrument is the interaction of changes

in property wealth with the fixed tax rules. The exclusion restriction will only be violated

if changes in unobserved factors related to changes in both student outcomes and spending

are also related to changes in property values differently by base-year policy. Districts would

have to set their tax rules in 1999 based on the money they would get from the change in

26

property values in the rest of the state which is not related to changes in their own property

values but is related to changes in their student outcomes, which is unlikely.

5 Results

I show the individual-lag first stage effect of log simulated revenue on log total expenditures

for the graduation rate samples and SEDA test score samples in figures, with corresponding

tables available in the appendix. The y-axis of the figures are the estimated first-stage

coefficient given a 10 percent increase in spending and the x-axis is number of years relative

to when the cohort is set to graduate. Coefficients are shown as dots, 95% confidence intervals

are shown as whiskers, and F statistics for each estimate are in brackets. Each column of

the table correspond to one of the relative years on the x-axis and each panel is one of the

samples.

First-stage estimates for the graduation rate samples are shown in Figure 3, with corre-

sponding results in Appendix Table A6. The coefficients are mostly between 0.01 and 0.02,

which means that a 10 percent increase in simulated revenue increases spending by 1 to 2

percent. This suggests that school districts and state governments respond to the mechanical

change in revenue from changes in property values, but not enough to fully counteract the

increase in revenue. The figures also show a pattern where estimates with a short lag (4 years

or less) have a strong first stage, while estimates with a longer lag have smaller coefficients

not statistically different from zero and F statistics less than 10.

Similar estimates for the SEDA test score samples are reported in Figure 4 and Appendix

Table A7. The coefficients are centered around 0.02 for the later lags and drop down to be

around 0.01 for the earlier lags. These effects are similar to the magnitude of those in the

graduation rate samples. These estimates show a pattern that is opposite of the graduation

rate samples, with stronger estimates for the longer lags and estimates that go to zero with

F statistics below 10 for lags less than 3 years.

27

Table 3 reports estimates with various averages of the prior years of simulated revenue

and spending. Column (1) is the average of the current year and the previous year, column(2)

is the average of the current year and the previous 4 years, estimates with the average of

this year and the past 8 years are shown in column(3), and the last column has estimates

averaged from 5 to 8 years prior to when the outcome is measured. Panels A through D

have estimates for the graduation rate samples and panel E has results for the SEDA test

score sample. The estimates using average lags are consistent with the individual lags in

the pattern of first-stage strength. The first stage is strong for averages of 1, 4, and 8 lags

for graduation sample, but not for the average of 5 to 8 years prior. The SEDA test score

sample has a strong first stage for the 8-year lag and the 5-8 year average, but not for the 1

and 4 year lags.

Simulated revenue is a strong instrument near the base year of 1999, but the farther

away from the base year the weaker it gets. Graduation rates are measured from the base

year until 2010, but test scores are first measured in 2009. Thus, the short lags in the

graduation sample and the long lags in the SEDA test score sample are strong because they

come from the years that the simulated instrument is strong. Since my 2SLS results are only

reliable when the first stage is strong I only focus on the 1 and 4 year lags for the graduation

rate results and the average from 5 to 8 years for the test score sample.

The results of my 2SLS analysis are reported in individual lags as both graphs and

tables and average lags in a table similar to the first stage results. Instead of showing

all the individual lags I only report the results for the lags that have a strong first stage.

Figure 5 shows the individual lag results for graduation rates, with corresponding estimates

in Appendix Table A6. The coefficients are positive and significant in the year of and before

graduation, but small and not statistically significant 2 to 4 year prior. The average lag

results in Table 4 suggest that a 10 percent increase in spending increases graduation rates

between 3 and 5 percent. These results suggest that increased spending is most effective at

improving graduation rates for those near graduation.

28

Figure 6 and Appendix Table A9 report the 2SLS results of spending on SEDA test

scores. The coefficients are generally positive, significant, and around 0.1 standard deviations

in magnitude. The exception is for 8th grade math scores, which are similar in magnitude for

4 and 5 lags, but less precisely estimated, and nearer to zero for the longer lags. The average

lag results in Table 5 suggest that increasing spending by 10 percent in the 5 to 8 years prior

to the test increase 4th grade math and reading scores by 0.09 standard deviations each, 8th

grade math scores by 0.03 standard deviations (not statistically significant), and 8th grade

reading scores by 0.07 standard deviations. It is important to note that increased spending

has a lasting impact on test scores and improvements made before students enter school have

a significant effect several years later.

5.1 Validity Checks

If my measure of spending is correlated with changes in the types of students in the district,

then estimates for graduation rates could be due to changes in student composition rather

than changing the outcomes of students. I explore whether this is the case in Table 6, which

shows the effect of spending in the current and previous year in the graduation rate sample

in the first 5 columns and average spending 5 to 8 years prior in the test score sample int

he last 5 columns. The first column shows estimates for the log number of students and

columns (2) through (5) show estimates for the fraction of students in different categories

including fraction black, fraction Hispanic, fraction with an IEP (special education), and

fraction eligible for free or reduced price lunch. A 10 percent increase in spending increases

the number of students by 246 to 270 or 5 to 6 percent. The fraction of students that are black

increased by 0.2 or 0.05 (not statistically significant) percentage points, fraction Hispanic

increased by 1.33 or 1.13 percentage points, fraction of students with an IEP increased by 0.28

or 0.02 (not statistically significant) percentage points, and fraction of students eligible for

free or reduced-price lunch decreased by 0.6 (not statistically significant) or 0.82 percentage

points. This rules out large changes in student composition driving my results. In fact, the

29

small changes are generally in the direction that would work against finding an effect if they

were true shifts in the district population. The changes are also consistent with retaining

the students most in danger of dropping out.

As a falsification test, I also estimate the effect of spending over several following years

on outcomes in the current year. Table 7 shows the effect of average spending over the

following four years on graduation rates. The first stage is strong, but the 2SLS estimate

is small, negative, and not statistically significant, suggesting that spending does indeed

need to occur previous to experiencing beneficial outcomes. I am unable to do a similar

falsification test for test scores because I do not have a strong first stage for spending in any

years following my measures of test scores.

5.2 Exploring Mechanisms

Although my instrument only allows me to estimate the causal effect of total resources, it is

instructive to examine the categories on which districts choose to spend their extra funds.

Table 8 shows 2SLS estimates of log expenditures on local, state, and federal revenue in

thousands of dollars per pupil for the graduation rate sample and test score sample separately.

The majority of increased revenue comes through local sources, but state aid also increases.

Table 9 and Table 10 report 2SLS estimates of total expenditures on mutually exclusive and

collectively exhaustive subcategories of spending for the graduate rate sample and test score

sample, respectively. These estimates suggest that the majority of increased spending was

devoted to current expenditures, capital outlay, and payments to state organizations. The

larger than average payments to the state, other schools, and private schools are consistent

with districts bearing a portion of the responsibility of students who would otherwise attend

but are attending other schools. Table 11 breaks up current expenditure into instructional,

support service, and other categories. This shows that the majority of current expenditures

are instructional expenditures, but support services also receive a significant portion of the

30

funds.23

I also explore heterogeneity in the effect of spending on graduation rates. In Table 12

I show results for the sample split by whether the change in simulated revenue is positive

or negative. The first two columns show estimates for increases in simulated revenue and

the last two columns show results when simulated revenue has decreased from the previous

year. The first stage is too weak for the average spending of the current and previous

year in the loss domain to make any useful comparison. The estimate from column (4)

suggests that a 10 percent decrease in spending over the past 4 years reduces graduation

rates by 8.3 percentage points. The corresponding estimate in column (2) suggests that a

10 percent increase in spending increases the graduation rate by 1 percentage point, but it

is not precisely estimated.

Table 13 splits the sample by districts with above or below the average income in their

state or average wealth in their state as of 1999. Comparing columns (1) and (2) suggests that

high income districts receive the benefits of increased spending when it comes to graduation

rates while low income districts receive little, if any, benefit. However, in columns (3) and

(4) the effect of spending on graduation is the same for high and low wealth districts.

6 Conclusion

This paper addresses the question of whether money spent on education affects graduation

rates and test scores using the interaction of market changes in property values with fixed

school finance rules as an instrument for spending. I find that a 10 percent increase in

spending increases graduation rates by 2.5 to 5 percentage points. A 10 percent increase in

spending also increases 4th grade math and reading scores by 0.09 standard deviations and

8th grade reading scores by 0.07 standard deviations. Increased spending primarily goes to

current expenditures, new construction, and payments to other organizations such as the

state government and local private schools. The harm of decreased spending on high school

23Additional tables with estimates for each subcategory of spending are available in Online Appendix A.

31

completion is larger than the benefit of an equivalent increase. Spending has lasting effects

on test scores, so that students benefit from investments made before they even begin school.

The relationship between property values and local revenue is not unique to school

finance. Thus, my approach can be applied directly to other locally-financed public programs.

This is especially useful in other cases where it is difficult to measure the effect of resources

on outcomes because of the relationship between the outcome and the level of investment,

such as the number of police officers and the level of crime. While other contexts do not have

the same type of equalization schemes as seen in school finance, other state-level limitations

on local taxing behavior provide between-state variation in wealth prices.

32

References

Angrist, J. and Pischke, J.-S. (2009). Mostly Harmless Econometrics: An Empiricist’s Com-panion. Princeton University Press, 1 edition.

Angrist, J. D. and Lavy, V. (1999). Using Maimonides’ Rule To Estimate The Effect OfClass Size On Scholastic Achievement. Quarterly Journal of Economics, 114(2):533–575.

Bartik, T. J. (1994). The Effects of Metropolitan Job Growth on the Size Distribution ofFamily Income. Journal of Regional Science, 34(4):483–501.

Bayer, P., Ferreira, F., and McMillan, R. (2007). A Unified Framework for MeasuringPreferences for Schools and Neighborhoods. Journal of Political Economy, 115(4):588–638.

Bazzi, S. and Clemens, M. A. (2013). Blunt Instruments: Avoiding Common Pitfalls in Iden-tifying the Causes of Economic Growth. American Economic Journal: Macroeconomics,5(52):152–186.

Black, S. E. (1999). Do Better Schools Matter? Parental Valuation Of Elementary Education.Quarterly Journal of Economics, 114(2):577–599.

Candelaria, C. A. and Shores, K. A. (2017). Court-Ordered Finance Reform on Spendingand Graduation Rates. Forthcoming, Education Finance and Policy.

Card, D. and Payne, A. A. (2002). School finance reform, the distribution of school spending,and the distribution of student test scores. Journal of Public Economics, 83(1):49–82.

Cellini, S. R., Ferreira, F., and Rothstein, J. (2010). The Value of School Facility Invest-ments: Evidence from a Dynamic Regression Discontinuity Design. Quarterly Journal ofEconomics, 125(1):215–261.

Chetty, R., Friedman, J. N., Hilger, N., Saez, E., Schanzenbach, D. W., and Yagan, D.(2011). How Does Your Kindergarten Classroom Affect Your Earnings? Evidence fromProject Star. Quarterly Journal of Economics, 126(4):1593–1660.

Clark, M. A. (2003). Education reform, redistribution, and student achievement: Evidencefrom the Kentucky Education Reform Act. Unpublished working paper, Mathematica Pol-icy Research, (October).

Coleman, J. S. (1966). Equality of Educational Opportunity (COLEMAN) Study (EEOS).Technical report.

Cragg, J. G. and Donald, S. G. (1993). Testing Identifiability and Specification in Instru-mental Variable Models. Econometric Theory, 9(2):222–240.

Currie, J. and Gruber, J. (1996). Health Insurance Eligibility, Utilization of Medical Care,and Child Health. The Quarterly Journal of Economics, 111(2):431–466.

33

Downes, T. A., Dye, R. F., and McGuire, T. J. (1998). Do Limits Matter? Evidence onthe Effects of Tax Limitations on Student Performance. Journal of Urban Economics,43(3):401–417.

Figlio, D. (1998). Short-Term Effects of a 1990s-Era Property Tax Limit: Panel Evidenceon Oregon’s Measure 5. National Tax Journal, 51(1):55–70.

Figlio, D. N. and Rueben, K. S. (2001). Tax limits and the qualifications of new teachers.Journal of Public Economics, 80(1):49–71.

Gordon, N. and Knight, B. (2009). A spatial merger estimator with an application to schooldistrict consolidation. Journal of Public Economics, 93(5-6):752–765.

Guryan, J. (2001). Does Money Matter? Regression-Discontinuity Estimates from EducationFinance Reform in Massachusetts.

Hanushek, E. A. (2003). The Failure of Input-Based Schooling Policies. The EconomicJournal, 113(485):F64–F98.

Hong, K. and Zimmer, R. (2016). Does Investing in School Capital Infrastructure ImproveStudent Achievement? Economics of Education Review, 53:143–158.

Hoxby, C. M. (2000). The Effects Of Class Size On Student Achievement: New EvidenceFrom Population Variation. Quarterly Journal of Economics, 115(4):1239–1285.

Hoxby, C. M. (2001). All School Finance Equalizations Are Not Created Equal. QuarterlyJournal of Economics, 116(4):1189–1231.

Hyman, J. (2017). Does Money Matter in the Long Run? Effects of School Spending onEducational Attainment. Forthcoming, American Economic Journal: Economic Policy.

Jackson, C. K., Johnson, R. C., and Persico, C. (2016). The Effects of School Spendingon Educational and Economic Outcomes: Evidence from School Finance Reforms. TheQuarterly Journal of Economics, 131(1):157–218.

Kleibergen, F. and Paap, R. (2006). Generalized reduced rank tests using the singular valuedecomposition. Journal of Econometrics, 133(1):97–126.

Krueger, A. B. (1999). Experimental Estimates Of Education Production Functions. Quar-terly Journal of Economics, 114(2):497–532.

Krueger, A. B. (2003). Economic Considerations and Class Size. The Economic Journal,113(485):F34–F63.

Lafortune, J., Rothstein, J., and Schanzenbach, D. W. (2017). School Finance Reform andthe Distribution of Student Achievement. Forthcoming, American Economic Journal:Applied Economics.

Martorell, P., Stange, K., and McFarlin, I. (2016). Investing in schools: capital spending,facility conditions, and student achievement. Journal of Public Economics, 140:13–29.

34

National Center for Education Statistics (2016). Table 236.10. Summary of expendituresfor public elementary and secondary education and other related programs, by purpose:Selected years, 1919-20 through 2013-14.

Oates, W. E. (1969). The Effects of Property Taxes and Local Public Spending on PropertyValues: An Empirical Study of Tax Capitalization and the Tiebout Hypothesis. Journalof Political Economy, 77(6):957–971.

Papke, L. E. (2005). The effects of spending on test pass rates: Evidence from Michigan.Journal of Public Economics, 89(5-6):821–839.

Reardon, S. F. and Kalogrides, D. (2017). Linking U. S. School District Test Score Distri-butions to a Common Scale. CEPA Working Paper No. 16-09, pages 1–50.

Ries, J. and Somerville, T. (2010). School Quality and Residential Property Values: Evidencefrom Vancouver Rezoning. Review of Economics and Statistics, 92(4):928–944.

Stock, J. H. and Yogo, M. (2005). Testing for Weak Instruments in Linear IV Regression.The National Bureau of Economic Research, (Identification and Inference for EconometricModels: Essays in Honor of Thomas Rothenberg):1–73.

Todd, P. E. and Wolpin, K. I. (2003). On The Specification and Estimation of The ProductionFunction for Cognitive Achievement. Economic Journal, 113(485):F3–F33.

U.S. Bureau of Economic Analysis (2017). Table 1.1.5. Gross Domestic Product.

U.S. Department of Education National Center for Education Statistics (2001). Public SchoolFinance Programs of the United States and Canada: 199899. Technical report, WashingtonD.C.

Verstegen, D. A. and Jordan, T. S. (2009). A Fifty-State Survey of School Finance PoliciesAnd Programs: An Overview. Journal of Education Finance, 34(3):213–230.

35

7 Figures & Tables

Figure 1: Historical Sources of School District Revenue

Notes: Data from U.S. Department of Education, National Center for Education Statis-tics, Biennial Survey of Education in the United States, 1919-20 through 1949-50; Statisticsof State School Systems, 1959-60 and 1969-70; Revenues and Expenditures for Public Ele-mentary and Secondary Education, 1979-80; and Common Core of Data (CCD), “NationalPublic Education Financial Survey,” 1989-90 through 2013-14.

36

Figure 2: Distribution of estimated wealth price in 1999

Notes: The wealth price is the fraction of each additional dollar of property wealth thatdistricts take in as revenue. Calculations of the wealth price based on policies in 1999 canbe found in Online Appendix B.

37

Table 1: Summary statistics for main estimation samples

(1) (2) (3)10th Grade Cohort SEDA Test1-year 4-year Lag Score Sample

Graduation Rate 0.81 0.82(0.17) (0.18)

Average Lagged Spending 12.57 12.38 12.58(4.21) (3.87) (4.20)

Average Lagged Simulated Revenue 7.08 6.97 6.93(4.02) (3.80) (3.93)

Fraction Special Education 0.13 0.13 0.14(0.05) (0.05) (0.04)

Fraction Black 0.10 0.10 0.08(0.18) (0.17) (0.15)

Fraction Hispanic 0.11 0.12 0.13(0.18) (0.19) (0.20)

Fraction Free-Reduced Price Lunch 0.37 0.39 0.43(0.23) (0.22) (0.22)

Number of Students 5,198 5,261 4,414(23,628) (22,377) (24,028)

Median Household Income 56,755 56,093 57,016(21,649) (21,209) (22,547)

Property Wealth ($100,000s) 23,040 25,072 20,800(124,240) (130,256) (110,586)

Districts 2,987 2,986 6,111N 24,530 19,077 28,376

Notes: Means are reported with standard deviations in parentheses. Statistics are calculatedfor three estimation samples. The 10th grade cohort graduation rates with 1 lag are availablefrom 2000-2010 and with 4 lags are available from 2003-2010. SEDA test scores are availablefor 2009-2013 so the spending variables lagged 5 to 8 years cover years 2001-2008. Allmonetary variables are in real 2013 dollars.

38

Table 2: Summary statistics for characteristics of districts in and out of the sample

(1) (2) (3) (4)Not P-value of (2)-(1)

In Sample In Sample or Fraction All

I. District-level AveragesNumber of Students 3,703 3,754 0.848 3,725Number of Teachers 255 220 0.042 239Student-Teacher Ratio 13.5 14.8 0.000 14.1Spending Per Student 15,169 14,719 0.481 14,970Property Tax Revenue Per Student 5,742 4,925 0.002 5,381Median Household Income 56,328 53,546 0.000 55,111Fraction with an IEP 0.131 0.136 0.000 0.133Fraction FRPL Eligible 0.405 0.407 0.632 0.406Fraction Black 0.077 0.063 0.000 0.071Fraction Hispanic 0.116 0.105 0.001 0.111Fraction White 0.743 0.751 0.092 0.747

II. Observation CountsStudents 26,592,100 21,418,996 0.55 48,011,096Districts 7,182 5,706 0.56 12,888States 24 26 0.48 50

Notes: Panel I displays averages for the variables indicated and panel II displays counts.Columns (1), (2), and (4) report averages of the indicated variables. Column (3) reports thep-value of the difference between column (2) and column (1) for panel I and the fraction inthe sample for panel II. Values are based on 2009.

39

Figure 3: First-stage effect of a 10% increase in simulated revenue on total expenditure forgraduate rate samples – individual year lags

8th Grade Cohort Sample 9th Grade Cohort Sample

10th Grade Cohort Sample 11th Grade Cohort Sample

Notes: Figure 3 presents point estimates (divided by 10), 95 percent confidence intervals, andF statistics in brackets, from individual regressions of lagged total expenditures on simulatedrevenue with the same lag for samples with non-missing graduation rates. Models also includecontrols for district property wealth, median household income, fraction of students who areblack, fraction Hispanic, fraction special education, fraction eligible for free or reduced pricelunch, district fixed effects, and state-by-year fixed effects. Standard errors are clustered atthe district level.

40

Figure 4: First-stage effect of a 10% increase in simulated revenue on log expenditure forSEDA test score samples – individual year lags

4th Grade Math Sample 4th Grade Reading Sample

8th Grade Math Sample 8th Grade Reading Sample

Notes: Figure 4 presents point estimates (divided by 10) and 95 percent confidence intervals,and F statistics in brackets, from individual regressions of lagged total expenditures onsimulated revenue with the same lag for samples with non-missing test scores. Models alsoinclude controls for district property wealth, median household income, fraction of studentswho are black, fraction Hispanic, fraction special education, fraction eligible for free orreduced price lunch, district fixed effects, and state-by-year fixed effects. Standard errorsare clustered at the district level.

41

Table 3: First stage estimates of log simulated revenue on log spending – average lags

(1) (2) (3) (4)1-year lag 4-year lag 8-year lag 5-8 years lag

A. 8th Grade Graduation Cohort SampleLog Sim. Rev. 0.153∗∗ 0.169∗∗ 0.191∗∗ 0.042

(0.028) (0.026) (0.029) (0.045)F 29.34 41.30 42.91 0.85Districts 2,884 2,880 2,819 2,820N 18,602 16,564 9,550 9,551

B. 9th Grade Graduation Cohort SampleLog Sim. Rev. 0.136∗∗ 0.181∗∗ 0.216∗∗ 0.107∗∗

(0.024) (0.024) (0.026) (0.041)F 32.60 58.04 69.54 6.72Districts 2,987 2,987 2,976 2,977N 23,558 19,649 10,466 10,468

C. 10th Grade Graduation Cohort SampleLog Sim. Rev. 0.138∗∗ 0.173∗∗ 0.208∗∗ 0.106∗∗

(0.022) (0.024) (0.026) (0.041)F 40.81 51.12 63.78 6.56Districts 2,987 2,986 2,978 2,979N 24,530 19,077 10,438 10,440

D. 11th Grade Graduation Cohort SampleLog Sim. Rev. 0.140∗∗ 0.173∗∗ 0.217∗∗ 0.119∗∗

(0.022) (0.027) (0.026) (0.041)F 40.58 40.84 69.98 8.28Districts 2,985 2,977 2,959 2,960N 21,995 16,331 10,002 10,004

E. SEDA Test Score SampleLog Sim. Rev. 0.058 0.049 0.243∗∗ 0.264∗∗

(0.033) (0.027) (0.019) (0.021)F 3.13 3.22 159.08 151.30Districts 5,905 5,904 5,900 5,906N 26,863 26,854 26,841 26,860

Notes: This table reports the results of first stage regressions of total expenditures on sim-ulated revenue with average lags for samples with non-missing graduation rates. Column(1) is the average of the current and previous year, column (2) is the average of the currentand the past 4 years, column (3) is the average over the past 8 years, and column (4) isthe average from 5 to 8 years prior to the measured outcome. Models also include controlsfor district property wealth, median household income, fraction of students who are black,fraction Hispanic, fraction special education, fraction eligible for free or reduced price lunch,district fixed effects, and state-by-year fixed effects. Standard errors are clustered at thedistrict level: * p < 0.05, ** p < 0.01.

42

Figure 5: Two-stage least squares estimates of log spending on graduation rates

8th Grade Cohort 9th Grade Cohort

10th Grade Cohort 11th Grade Cohort

Notes: Figure 5 presents point estimates (divided by 10), 95 percent confidence intervals,and F statistics in brackets, from individual 2SLS regressions of graduation rates on laggedlog total expenditures instrumented by lagged log simulated revenue. Models also includecontrols for district property wealth, median household income, fraction of students who areblack, fraction Hispanic, fraction special education, fraction eligible for free or reduced pricelunch, district fixed effects, and state-by-year fixed effects. Standard errors are clustered atthe district level.

43

Table 4: Two-stage least squares estimates of log spending on graduation rates

(1) (2) (3) (4) (5) (6) (7) (8)8th Grade Cohort 9th Grade Cohort 10th Grade Cohort 11th Grade Cohort

1-year lag 4-year lag 1-year lag 4-year lag 1-year lag 4-year lag 1-year lag 4-year lagLog Spending 0.508∗∗ 0.321∗∗ 0.376∗∗ 0.351∗∗ 0.274∗∗ 0.423∗∗ 0.243∗∗ 0.419∗∗

(0.127) (0.116) (0.104) (0.107) (0.084) (0.109) (0.079) (0.122)Dep. Var. Mean 0.79 0.79 0.76 0.76 0.81 0.82 0.85 0.85F 72.23 97.87 77.79 110.38 78.74 102.03 85.64 91.26Districts 2,832 2,814 2,985 2,979 2,986 2,983 2,981 2,964N 18,550 16,498 23,556 19,641 24,529 19,074 21,991 16,318

Notes: This table reports results from two-stage least squares regressions of graduation rateson average lagged log total expenditures instrumented with average lagged log simulatedrevenue. Models also include controls for district property wealth, median household income,fraction of students who are black, fraction Hispanic, fraction special education, fractioneligible for free or reduced price lunch, district fixed effects, and state-by-year fixed effects.Standard errors are clustered at the district level: * p < 0.05, ** p < 0.01.

44

Figure 6: Two-stage least squares estimates of log spending on SEDA test scores

4th Grade Math 4th Grade Reading

8th Grade Math 8th Grade Reading

Notes: Figure 6 presents point estimates (divided by 10), 95 percent confidence intervals, andF statistics in brackets, from individual 2SLS regressions of test scores on lagged log totalexpenditures instrumented by lagged log simulated revenue. Models also include controlsfor district property wealth, median household income, fraction of students who are black,fraction Hispanic, fraction special education, fraction eligible for free or reduced price lunch,district fixed effects, and state-by-year fixed effects. Standard errors are clustered at thedistrict level.

45

Table 5: Two-stage least squares estimates of log spending on test scores

(1) (2) (3) (4)4th Grade 8th Grade

Math Reading Math ReadingLog Spending, 4-8 years prior 0.896∗∗ 0.941∗∗ 0.290 0.677∗

(0.353) (0.317) (0.330) (0.303)F 170.07 170.02 159.39 167.86Districts 5,905 5,902 5,914 5,908N 27,536 27,530 27,602 27,606

Notes: This table reports results from two-stage least squares regressions of test scoreson average lagged log total expenditures instrumented with average lagged log simulatedrevenue. Models also include controls for district property wealth, median household income,fraction of students who are black, fraction Hispanic, fraction special education, fractioneligible for free or reduced price lunch, district fixed effects, and state-by-year fixed effects.Standard errors are clustered at the district level: * p < 0.05, ** p < 0.01.

46

Table 6: Two-stage least squares estimates of log spending on student composition

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)Graduate Rates SEDA Test Scores

Total Black Hispanic IEP FRPL Total Black Hispanic IEP FRPLLog Spending 2455.523∗∗ 0.024∗ 0.133∗∗ 0.028∗∗ -0.059 2693.944∗∗ 0.005 0.113∗∗ 0.002 -0.082∗

(440.566) (0.011) (0.016) (0.009) (0.042) (439.817) (0.006) (0.014) (0.010) (0.038)Dep. Var. Mean 5198.42 0.10 0.11 0.13 0.37 4629.82 0.08 0.13 0.14 0.43First-stage F 172.73 172.73 172.73 172.73 172.73 172.73 191.11 191.11 191.11 191.11Districts 2,986 2,986 2,986 2,986 2,986 2,986 5,779 5,779 5,779 5,779N 24,529 24,529 24,529 24,529 24,529 26,733 26,733 26,733 26,733 26,733

Notes: This table reports results from two-stage least squares regressions of student compo-sition outcomes on average lagged log total expenditures instrumented with average laggedlog simulated revenue. The outcome for the first column is total number of students, whilethe outcome for columns (2) through (5) are the fraction of students in the given category.Models also include controls for district property wealth, median household income, fractionof students who are black, fraction Hispanic, fraction special education, fraction eligible forfree or reduced price lunch, district fixed effects, and state-by-year fixed effects. Standarderrors are clustered at the district level: * p < 0.05, ** p < 0.01.

47

Table 7: Two-stage least squares estimates of future log spending on graduation rates

Average Spending, Next 4 YearsLog Spending -0.012

(0.072)F 80.08Districts 2,986N 25,038

Notes: This table reports results from two-stage least squares regressions of graduation rateson average log total expenditures over the next four years instrumented with log simulatedrevenue averaged over the same years. Models also include controls for district propertywealth, median household income, fraction of students who are black, fraction Hispanic,fraction special education, fraction eligible for free or reduced price lunch, district fixedeffects, and state-by-year fixed effects. Standard errors are clustered at the district level: *p < 0.05, ** p < 0.01.

48

Table 8: Two-stage least squares estimates of log simulated revenue on source of revenue

(1) (2) (3) (4) (5) (6)Graduation Rate SEDA Test Score

Local State Federal Local State FederalLog Simulated Revenue 11.892∗∗ 1.506∗ -0.146 8.234∗∗ 0.227 -0.568∗∗

(1.437) (0.761 (0.221) (0.894) (0.433 (0.111)Dependent Variable Mean ($1,000s) 5.42 6.07 0.92 5.71 5.95 0.87Baseline Fraction 0.41 0.51 0.08 0.44 0.48 0.09F 78.74 78.74 78.74 155.52 155.52 155.52Districts 2,986 2,986 2,986 5,779 5,779 5,779N 24,529 24,529 24,529 26,733 26,733 26,733

Notes: This table reports results from two-stage least squares regressions of various sourcesof revenue on average lagged log total expenditures instrumented with log simulated revenueaveraged over the same years. Models also include controls for district property wealth,median household income, fraction of students who are black, fraction Hispanic, fractionspecial education, fraction eligible for free or reduced price lunch, district fixed effects, andstate-by-year fixed effects. Standard errors are clustered at the district level: * p < 0.05, **p < 0.01.

49

Table 9: Two-stage least squares estimates of log spending on total expenditure sub-categories – Graduation Rate sample, one-year lag

(1) (2) (3) (4) (5) (6) (7) (8)Current Non-Elmentary Capital Payments to: Interest

Expenditure or Secondary Outlay State Other Schools Private Charter PaymentsSpending ($1,000s) 8.080∗∗ 0.836∗∗ 3.881∗∗ 2.157∗∗ 0.244∗ 0.184∗ -0.011 0.555∗∗

(0.909) (0.155) (1.177) (0.495) (0.113) (0.090) (0.108) (0.155)Dep. Var. Mean 10.62 0.09 1.25 0.06 0.13 0.060 0.019 0.25Baseline Fraction 0.86 0.01 0.09 0.00 0.01 0.004 0.001 0.02First-stage F 78.74 78.74 78.74 78.74 78.74 78.74 78.74 78.74Districts 2,986 2,986 2,986 2,986 2,986 2,986 2,986 2,986N 24,529 24,529 24,529 24,529 24,529 24,529 24,529 24,529

Notes: This table reports results from two-stage least squares regressions of various expen-diture categories on average lagged log total expenditures instrumented with log simulatedrevenue averaged over the same years. Models also include controls for district propertywealth, median household income, fraction of students who are black, fraction Hispanic,fraction special education, fraction eligible for free or reduced price lunch, district fixed ef-fects, and state-by-year fixed effects. Standard errors are clustered at the district level: *p < 0.05, ** p < 0.01.

Table 10: Two-stage least squares estimates of log spending on total expenditure sub-categories – SEDA sample, five to eight year lag

(1) (2) (3) (4) (5) (6) (7) (8)Current Non-Elmentary Capital Payments to: Interest

Expenditure or Secondary Outlay State Other Schools Private Charter PaymentsSpending ($1,000s) 2.926∗∗ -0.027 2.172∗∗ 1.836∗∗ 0.512∗∗ 0.100∗∗ -0.055∗ 0.408∗∗

(0.511) (0.032) (0.879) (0.371) (0.144) (0.039) (0.027) (0.076)Dep. Var. Mean 10.57 0.07 1.27 0.07 0.23 0.059 0.016 0.25Baseline Fraction 0.86 0.01 0.08 0.00 0.02 0.005 0.003 0.02First-stage F 155.52 155.52 155.52 155.52 155.52 155.52 155.52 155.52Districts 5,779 5,779 5,779 5,779 5,779 5,779 5,779 5,779N 26,733 26,733 26,733 26,733 26,733 26,733 26,733 26,733

Notes: This table reports results from two-stage least squares regressions of various expen-diture categories on average lagged log total expenditures instrumented with log simulatedrevenue averaged over the same years. Models also include controls for district propertywealth, median household income, fraction of students who are black, fraction Hispanic,fraction special education, fraction eligible for free or reduced price lunch, district fixed ef-fects, and state-by-year fixed effects. Standard errors are clustered at the district level: *p < 0.05, ** p < 0.01.

50

Table 11: Two-stage least squares estimates of log spending on current expenditure sub-categories

(1) (2) (3) (4) (5) (6)Graduate Rates SEDA Test Score

Instructional Support Services Other Instructional Support Services OtherLog Spending 4.825∗∗ 3.111∗∗ 0.143∗∗ 2.235∗∗ 0.740∗∗ -0.048

(0.591) (0.425) (0.048 (0.333) (0.233) (0.026Dep. Var. Mean 6.53 3.65 0.44 6.47 3.66 0.44Baseline Fraction 0.53 0.29 0.04 0.52 0.30 0.04First-stage F 78.74 78.74 78.74 155.52 155.52 155.52Districts 2,986 2,986 2,986 5,779 5,779 5,779N 24,529 24,529 24,529 26,733 26,733 26,733

Notes: This table reports results from two-stage least squares regressions of various cur-rent expenditure categories on average lagged log total expenditures instrumented with logsimulated revenue averaged over the same years. Models also include controls for districtproperty wealth, median household income, fraction of students who are black, fraction His-panic, fraction special education, fraction eligible for free or reduced price lunch, districtfixed effects, and state-by-year fixed effects. Standard errors are clustered at the districtlevel: * p < 0.05, ** p < 0.01.

Table 12: Two-stage least squares estimates of log spending on graduation rates – gainsversus losses

(1) (2) (3) (4)Gain Loss

1-year Lag 4-year Lag 1-year Lag 4-year LagLog Spending 0.225∗∗ 0.099 0.142 0.831∗∗

(0.049) (0.098) (0.487) (0.259)Dep. Var. Mean 0.82 0.82 0.81 0.81First-stage F 154.81 117.42 3.49 35.50Districts 2,376 2,173 2,655 2,491N 10,735 7,974 13,073 10,101

Notes: This table reports results from two-stage least squares regressions of graduation rateson average lagged log total expenditures instrumented with log simulated revenue averagedover the same years separately for years when simulated revenue increased in the first twocolumns and when simulated revenue decreased in the last two columns. Models also includecontrols for district property wealth, median household income, fraction of students who areblack, fraction Hispanic, fraction special education, fraction eligible for free or reduced pricelunch, district fixed effects, and state-by-year fixed effects. Standard errors are clustered atthe district level: * p < 0.05, ** p < 0.01.

51

Table 13: Two-stage least squares estimates of log spending on cohort graduation rates –high and low income districts

(1) (2) (3) (4)Low Income High Income Low Wealth High Wealth

Log Spending 0.017 0.702∗∗ 0.339∗∗ 0.313∗

(0.072) (0.295) (0.108) (0.133)Dep. Var. Mean 0.80 0.83 0.81 0.82First-stage F 42.28 15.34 43.78 36.24Districts 1,715 1,271 1,995 991N 14,386 10,143 16,322 8,207

Notes: This table reports results from two-stage least squares regressions of 10th grade cohortgraduation rates on average lagged log total expenditures instrumented with log simulatedrevenue averaged over the same years. Column (1) is the sample of districts whose medianincome is below the state-level median income, column (2) is districts above the state-levelmedian income, columns (3) and (4) are districts below and above the state-level median ofproperty wealth. Models also include controls for district property wealth, median householdincome, fraction of students who are black, fraction Hispanic, fraction special education,fraction eligible for free or reduced price lunch, district fixed effects, and state-by-year fixedeffects. Standard errors are clustered at the district level: * p < 0.05, ** p < 0.01.

52

A Online Appendix - Additional Figures and Tables

Figure A1: Example of District Consolidation - Minnesota

Notes: Boundaries shown for 2 school districts (Brewster and Round Lake) in Minnesota,which consolidated into a single school district (Brewster-Round Lake) in 2014.

53

Figure A2: Example of Overlapping/Nested Districts - New Jersey

Notes: Boundaries for 4 school districts in New Jersey are shown. Bellmawr, Runnemede,and Gloucester are K-8 districts and Black Horse is a regional 9-12 district.

54

Table A1: School Finance Formula Type for Each State

District Power Combination/State Foundation Equalization Tiered

Alabama XAlaska XArizona XArkansas XCalifornia XColorado XConnecticut XDelaware XFlorida XGeorgia XIdaho XIllinois XIndiana XIowa XKansas XKentucky XLouisiana XMaine XMaryland XMassachusetts XMichigan XMinnesota XMississippi XMissouri XMontana XNebraska XNevada XNew Hampshire XNew Jersey XNew Mexico XNew York XNorth Dakota XOhio XOklahoma XOregon XPennsylvania XRhode Island XSouth Carolina XSouth Dakota XTennessee XTexas XUtah XVermont XVirginia XWashington XWest Virginia XWisconsin XWyoming XTotal 40 3 5

Notes: Adapted from Verstegen and Jordan (2009). Not included: Hawaii and North Car-olina. Hawaii’s single school district is fully funded by the state. North Carolina uses a flatgrant system.

55

Table A2: School Finance Overview - Foundation Programs

State Foundation Tax Rate ∂R∂W d

t

Arkansas 25 mills (0.025) τ dt /2 + 0.0125Idaho 3 mills (0.003) τ dt − 0.003Iowa 5.4 mills (0.0054) 1.25× τ dt − 0.0068

Kansas 20 mills (0.02) τ dt − 0.02 +[1− AV PP d

t−1

AV PP 75t−1

]×min

{0, τ dt − 0.02

}Massachusetts 9.4 mills (0.0094) τ dt − 0.0094Minnesota None τ dt − 3530

9039

Mississippi 28 mills (0.028) τ dt − 0.028Nevada 7.5 mills 0New Hampshire 6.6 mills (0.0066) τ dt − 0.0066New Jersey None 0New Mexico 0.5 mills (0.0005) τ dt − 0.0005North Dakota 32 mills (0.032) τ dt − 0.032Ohio 20 mills (0.02) τ dt − 0.023

Oklahoma 18 mills (0.018) τ dt − 0.018− min{τdt ,0.02}wADMd

t

Oregon 5 mills (0.005) τ dt − 0.005Washington 10 mills (0.01) τ dt − 0.01

Notes: τ dt represents the property tax rate in district d and year t, AV PP dt is average

property value per pupil, AV PP 75t is 75th percentile of AV PP d

t , and wADMdt is weighted

average daily membership. See the Online Appendix B for more information about eachstate’s finance program and full calculations of these values.

Table A3: School Finance Overview - Combination/Tiered Programs

State Foundation Tax Rate ∂R∂W d

t

Florida 6.509 mills (weighted) τ dt − .0009009Georgia 5 mills (0.005) min

{τ dt − 0.0825, 0

}Illinois (Low Wealth) None τ dt − ∂LocalShare

∂W dt

× ADMdt

Illinois (Medium Wealth) τ dt − (∂Local%∂W d

t− 0.93)× 0.02

0.82× Ft × ADMd

t

Illinois (High Wealth) τ dt

Kentucky 3 mills (0.003) (τ dt − 0.003)×(

1 + 1.5ADMs

t− 1

ADMdt

)Texas 8.6 mills (0.0086) τ dt − 0.0086− min{0.0064,τdt −0.0086}

wADMdt

Notes: See Online Appendix B for more information about each state’s finance program andfull calculations of these values.

56

Table A4: States with Tax and Expenditure Limits

State Limit On Level Description

Arkansas Value Individual Income limited to 5% for homesteads and 10%for non-homesteads

California Value Individual Increase in assessed value limited tomin{0.02, CPI}

Illinois Revenue Aggregate 29 of 102 counties opted into the PTELL pro-gram by 1999. This limits the increase in prop-erty tax revenue to min{0.05, CPI}

Indiana Revenue Aggregate The maximum levy is the maximum levy fromthe previous year adjusted by the assessedvalue growth quotient (AVGQ)

Iowa Value Individual Increase limited to 3%

Maryland Value Individual 10% limit in annual increase with a 3-yearphase in for all increases

Massachusetts Revenue Individual Increase limited to 2.5% annually

Michigan Value Aggregate Increase limited to min{0.05, CPI}Nebraska Spending Aggregate Increase limited by an amount that changes

annually

Nevada Revenue Aggregate Increase limited to 6%

New Jersey Spending Aggregate Increase limited to min{0.03, CPI}New Mexico Value Individual Increase limited to 3%

Ohio Revenue Aggregate Tax rates automatically adjust as assessmentsincrease to keep revenue generated from a taxlevy fixed. 3-year phase in of value increases

Oklahoma Value Individual Increase limited to 5%

Oregon Value Individual Increase limited to 3%

Texas Value Individual Increase limited to 10%

Washington Revenue Aggregate Increase limited to 6% above the highest levelin the last three years

West Virginia Revenue Aggregate Increase limited to 1% per year (tax rates de-creased if assessments raise more than 1%)

Wisconsin Revenue Aggregate Increase in revenue per pupil cannot exceed$208.88 in 1998-1999, which will be adjustedfor inflation in future years

Notes: States with no dynamic limits (as of FY1999): Alabama, Alaska, Arizona, Colorado.Connecticut, Delaware, Florida, Georgia, Hawaii, Idaho, Kansas, Kentucky, Louisiana,Maine, Minnesota, Mississippi, Missouri, Montana, New Hampshire, New York, North Car-olina, North Dakota, Pennsylvania, Rhode Island, South Carolina, South Dakota, Tennessee,Utah, Vermont, Virginia, and Wyoming. 57

Table A5: State Summary Statistics

(1) (2) (3) (4) (5)Balanced Panel School Districts

Raw SEDA Test SEDA Test CCD CohortStates Districts All Scores Score Gaps Graduation Rate

Arkansas 245 238 236 49 234Connecticut 166 137 135 27 106Florida 67 67 67 0 67Georgia 180 180 178 124 177Idaho 106 103 84 2 95Illinois 835 812 657 62 423Iowa 358 313 283 12 272Kansas 287 274 207 16 231Kentucky 174 173 164 25 165Massachusetts 402 230 225 29 210Minnesota 330 322 289 32 288Mississippi 149 79 79 58 79Nevada 16 16 15 2 16New Hampshire 144 102 89 0 67New Jersey 567 333 311 52 211New Mexico 80 80 66 6 73New York 715 658 571 59 588North Carolina 115 115 115 83 115North Dakota 145 129 53 2 93Ohio 609 605 602 75 571Oklahoma 493 469 321 21 346Oregon 165 164 136 10 157Texas 979 973 768 152 855Washington 247 247 211 34 222Total 7,574 6,819 5,862 932 5,661

Notes: The number of districts per state in my sample are shown. The first column reportsthe raw number of traditional public school districts reported in the CCD and column (2) isthe number of districts in my balanced panel. Columns (3) through (5) are the number ofdistricts with nonmissing values in the balanced panel for the variables indicated.

58

Table A6: First stage estimates of log simulated revenue on log spending for graduation ratesamples – individual year lags

No Lag 1 Lag 2 Lags 3 Lags 4 Lags 5 Lags 6 Lags 7 Lags 8 LagsA. 8th Grade Cohort Graduation Rate

Log Sim. Rev. 0.139∗∗ 0.138∗∗ 0.131∗∗ 0.110∗∗ 0.123∗∗ 0.079∗ 0.003 -0.006 0.041(0.027) (0.029) (0.030) (0.029) (0.032) (0.035) (0.044) (0.054) (0.058)

F 25.46 23.09 18.58 14.33 14.29 5.20 0.01 0.01 0.49Districts 2,884 2,884 2,882 2,881 2,880 2,874 2,866 2,844 2,820N 18,602 18,602 18,410 17,960 16,565 15,418 13,891 12,056 9,551

B. 9th Grade Cohort Graduation RateLog Sim. Rev. 0.126∗∗ 0.130∗∗ 0.124∗∗ 0.140∗∗ 0.143∗∗ 0.100∗∗ 0.077 0.056 0.081

(0.024) (0.024) (0.023) (0.024) (0.029) (0.032) (0.041) (0.049) (0.052)F 28.39 30.30 28.18 32.93 23.98 9.41 3.47 1.31 2.45Districts 2,987 2,987 2,987 2,987 2,987 2,987 2,987 2,983 2,977N 23,770 23,558 23,027 21,231 19,651 17,798 15,648 13,293 10,468

C. 10th Grade Cohort Graduation RateLog Sim. Rev. 0.135∗∗ 0.125∗∗ 0.122∗∗ 0.126∗∗ 0.094∗∗ 0.079∗∗ 0.066 0.059 0.093

(0.022) (0.022) (0.024) (0.025) (0.029) (0.032) (0.041) (0.050) (0.054)F 39.21 33.30 26.38 26.00 10.53 6.00 2.55 1.40 3.00Districts 2,987 2,987 2,987 2,987 2,987 2,987 2,987 2,984 2,979N 25,057 24,530 22,760 21,002 19,079 17,334 15,362 13,253 10,440

D. 11th Grade Cohort Graduation RateLog Sim. Rev. 0.124∗∗ 0.124∗∗ 0.126∗∗ 0.137∗∗ 0.083∗∗ 0.062 0.044 0.091 0.088

(0.020) (0.022) (0.024) (0.027) (0.032) (0.037) (0.047) (0.054) (0.058)F 37.56 31.11 27.53 26.43 6.62 2.84 0.87 2.80 2.29Districts 2,985 2,985 2,985 2,982 2,977 2,977 2,975 2,974 2,960N 23,766 21,995 20,281 18,275 16,333 15,299 14,096 12,710 10,004

Notes: This table reports the results of individual first stage regressions of total expenditureson simulated revenue with the same lag for samples with non-missing graduation rates.Models also include controls for district property wealth, median household income, fractionof students who are black, fraction Hispanic, fraction special education, fraction eligible forfree or reduced price lunch, district fixed effects, and state-by-year fixed effects. Standarderrors are clustered at the district level: * p < 0.05, ** p < 0.01.

59

Table A7: First stage estimates of log simulated revenue on log spending for test scoresamples – individual year lags

No Lag 1 Lag 2 Lags 3 Lags 4 Lags 5 Lags 6 Lags 7 Lags 8 LagsA. SEDA 4th Grade Math Scores

Log Sim. Rev. 0.065∗ 0.043 0.020 0.076∗∗ 0.143∗∗ 0.187∗∗ 0.213∗∗ 0.258∗∗ 0.198∗∗

(0.033) (0.029) (0.035) (0.031) (0.027) (0.025) (0.023) (0.028) (0.030)F 3.98 2.16 0.32 6.16 29.12 55.22 89.38 87.16 42.95Districts 6,031 6,031 6,032 6,032 6,032 6,032 6,032 6,032 6,032N 27,672 27,666 27,668 27,670 27,671 27,673 27,673 27,673 27,675

B. SEDA 4th Grade Reading ScoresLog Sim. Rev. 0.068∗ 0.041 0.018 0.075∗∗ 0.143∗∗ 0.184∗∗ 0.214∗∗ 0.259∗∗ 0.197∗∗

(0.033) (0.029) (0.035) (0.031) (0.026) (0.025) (0.023) (0.028) (0.030)F 4.29 1.99 0.27 6.02 29.49 54.14 90.36 88.60 42.52Districts 6,028 6,028 6,029 6,029 6,029 6,029 6,029 6,029 6,029N 27,666 27,660 27,662 27,664 27,665 27,667 27,667 27,667 27,669

C. SEDA 8th Grade Math ScoresLog Sim. Rev. 0.063∗ 0.044 0.036 0.071∗∗ 0.129∗∗ 0.173∗∗ 0.203∗∗ 0.254∗∗ 0.192∗∗

(0.032) (0.029) (0.035) (0.030) (0.025) (0.025) (0.022) (0.028) (0.030)F 3.86 2.27 1.06 5.68 25.87 48.66 84.69 84.37 40.65Districts 6,058 6,058 6,058 6,059 6,059 6,059 6,059 6,059 6,059N 27,756 27,750 27,751 27,754 27,755 27,757 27,757 27,757 27,759

D. SEDA 8th Grade Reading ScoresLog Sim. Rev. 0.061 0.042 0.026 0.058 0.136∗∗ 0.180∗∗ 0.212∗∗ 0.258∗∗ 0.199∗∗

(0.032) (0.029) (0.035) (0.030) (0.025) (0.024) (0.022) (0.028) (0.030)F 3.60 2.11 0.55 3.82 28.47 54.45 89.50 87.88 44.13Districts 6,054 6,054 6,054 6,055 6,055 6,055 6,055 6,055 6,055N 27,762 27,756 27,757 27,760 27,761 27,763 27,763 27,763 27,765

Notes: This table reports the results of individual first stage regressions of total expenditureson simulated revenue with the same lag for samples with non-missing test scores. Modelsalso include controls for district property wealth, median household income, fraction ofstudents who are black, fraction Hispanic, fraction special education, fraction eligible forfree or reduced price lunch, district fixed effects, and state-by-year fixed effects. Standarderrors are clustered at the district level: * p < 0.05, ** p < 0.01.

60

Table A8: Two-stage least squares estimates of log spending on graduation rates

No Lag 1 Lag 2 Lags 3 Lags 4 Lags 5 Lags 6 Lags 7 Lags 8 LagsA. 8th Grade Cohort Graduation Rate

Log Spending 0.473∗∗ 0.539∗∗ 0.193 0.006 -0.039 0.097 0.201 -0.380 -0.242(0.124) (0.139) (0.104) (0.109) (0.124) (0.168) (0.420) (0.499) (0.438)

Dep. Var. Mean 0.79 0.79 0.79 0.79 0.79 0.78 0.79 0.79 0.79F 65.38 57.18 48.90 46.85 47.43 24.83 4.73 1.62 2.54Districts 2,832 2,832 2,831 2,824 2,814 2,809 2,787 2,752 2,672N 18,550 18,550 18,359 17,903 16,499 15,353 13,812 11,964 9,403

B. 9th Grade Cohort Graduation RateLog Spending 0.333∗∗ 0.402∗∗ 0.032 0.006 0.035 0.039 -0.155 -0.412 -0.393

(0.101) (0.109) (0.090) (0.092) (0.107) (0.140) (0.192) (0.262) (0.275)Dep. Var. Mean 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.75 0.76F 75.26 64.70 52.07 67.55 53.65 28.13 12.65 5.16 5.46Districts 2,985 2,985 2,985 2,985 2,980 2,977 2,970 2,962 2,914N 23,768 23,556 23,025 21,229 19,644 17,788 15,631 13,272 10,405

C. 10th Grade Cohort Graduation RateLog Spending 0.251∗∗ 0.292∗∗ 0.088 0.098 0.145 0.264 0.051 -0.370 -0.228

(0.076) (0.095) (0.083) (0.096) (0.146) (0.179) (0.221) (0.266) (0.207)Dep. Var. Mean 0.81 0.81 0.82 0.82 0.82 0.81 0.81 0.81 0.81F 89.67 55.68 50.46 57.83 34.04 22.15 10.51 5.22 6.35Districts 2,986 2,986 2,986 2,986 2,984 2,984 2,980 2,964 2,932N 25,056 24,529 22,759 21,001 19,076 17,331 15,355 13,233 10,393

D. 11th Grade Cohort Graduation RateLog Spending 0.185∗∗ 0.265∗∗ 0.060 0.071 0.119 0.248 0.064 -0.332 -0.281

(0.074) (0.085) (0.065) (0.085) (0.155) (0.235) (0.287) (0.195) (0.265)Dep. Var. Mean 0.85 0.85 0.85 0.85 0.85 0.84 0.85 0.86 0.86F 82.22 62.60 59.52 59.06 27.74 13.68 6.08 7.55 5.29Districts 2,982 2,981 2,977 2,972 2,965 2,956 2,948 2,934 2,880N 23,763 21,991 20,273 18,265 16,321 15,278 14,069 12,670 9,924

Notes: This table reports results from individual two-stage least squares regressions of gradu-ation rates on lagged log total expenditures instrumented with lagged log simulated revenue.Models also include controls for district property wealth, median household income, fractionof students who are black, fraction Hispanic, fraction special education, fraction eligible forfree or reduced price lunch, district fixed effects, and state-by-year fixed effects. Standarderrors are clustered at the district level: * p < 0.05, ** p < 0.01.

61

Table A9: Two-stage least squares estimates of log spending on SEDA test scores

No Lag 1 Lag 2 Lags 3 Lags 4 Lags 5 Lags 6 Lags 7 Lags 8 LagsA. 4th Grade Math

Log Spending -3.132 -1.727 5.767 1.130 -3.132 1.062∗∗ 0.778∗ 0.788∗ 0.898(2.082) (2.127) (12.503) (1.341) (2.082) (0.438) (0.348) (0.341) (0.466)

F 6.16 4.20 0.31 6.48 6.16 56.85 91.08 88.42 44.02Districts 5,906 5,905 5,905 5,906 5,906 5,907 5,907 5,907 5,907N 27,547 27,540 27,541 27,544 27,547 27,548 27,548 27,548 27,550

B. 4th Grade ReadingLog Spending -1.815 -2.683 8.258 1.285 -1.815 0.989∗∗ 0.992∗∗ 0.881∗∗ 0.711

(1.593) (2.221) (17.512) (1.324) (1.593) (0.415) (0.315) (0.304) (0.411)F 6.54 3.96 0.26 6.33 6.54 55.76 92.07 89.87 43.58Districts 5,903 5,902 5,902 5,903 5,903 5,904 5,904 5,904 5,904N 27,541 27,534 27,535 27,538 27,541 27,542 27,542 27,542 27,544

C. 8th Grade MathLog Spending -1.922 -0.725 -1.115 1.016 -1.922 0.570 0.374 0.281 -0.266

(1.763) (1.711) (3.494) (1.340) (1.763) (0.431) (0.329) (0.305) (0.406)F 6.08 4.32 1.05 5.99 6.08 50.25 86.40 85.61 41.70Districts 5,916 5,915 5,915 5,916 5,916 5,917 5,917 5,917 5,917N 27,614 27,607 27,608 27,611 27,614 27,615 27,615 27,615 27,617

D. 8th Grade ReadingLog Spending 0.250 0.658 -3.384 0.058 0.250 0.627 0.699∗∗ 0.732∗∗ 0.491

(1.618) (1.811) (6.011) (1.426) (1.618) (0.389) (0.297) (0.298) (0.401)F 5.69 4.12 0.54 4.08 5.69 56.11 91.19 89.13 45.22Districts 5,910 5,909 5,909 5,910 5,910 5,911 5,911 5,911 5,911N 27,618 27,611 27,612 27,615 27,618 27,619 27,619 27,619 27,621

Notes: This table reports results from individual two-stage least squares regressions of testscores on lagged log total expenditures instrumented with lagged log simulated revenue.Models also include controls for district property wealth, median household income, fractionof students who are black, fraction Hispanic, fraction special education, fraction eligible forfree or reduced price lunch, district fixed effects, and state-by-year fixed effects. Standarderrors are clustered at the district level: * p < 0.05, ** p < 0.01.

62

Figure A3: First-stage effect of a 10% increase in simulated revenue on total expenditure forSEDA black-white test score gap samples – individual year lags

4th Grade Math Sample 4th Grade Reading Sample

8th Grade Math Sample 8th Grade Reading Sample

63

Table A10: First stage estimates of log simulated revenue on log spending for SEDA black-white test score gap samples – individual year lags

No Lag 1 Lag 2 Lags 3 Lags 4 Lags 5 Lags 6 Lags 7 Lags 8 LagsA. 4th Grade Math Gap

Log Sim. Rev. 0.025 0.095 0.162∗ 0.129∗ 0.201∗∗ 0.157∗∗ 0.145∗∗ 0.125∗ 0.132∗

(0.066) (0.063) (0.070) (0.056) (0.066) (0.055) (0.044) (0.058) (0.064)F 0.14 2.30 5.35 5.25 9.28 8.13 10.80 4.61 4.24Districts 1,325 1,325 1,325 1,325 1,325 1,325 1,325 1,325 1,325N 5,065 5,065 5,065 5,065 5,064 5,064 5,064 5,064 5,065

B. 4th Grade Reading GapLog Sim. Rev. -0.009 0.083 0.155 0.105 0.177∗∗ 0.154∗∗ 0.135∗∗ 0.166∗∗ 0.157∗

(0.074) (0.072) (0.079) (0.070) (0.072) (0.055) (0.047) (0.070) (0.073)F 0.02 1.33 3.80 2.29 6.04 7.86 8.11 5.69 4.62Districts 1,320 1,320 1,320 1,320 1,320 1,320 1,320 1,320 1,320N 5,017 5,017 5,017 5,017 5,016 5,016 5,016 5,016 5,017

C. 8th Grade Math GapLog Sim. Rev. 0.011 0.088 0.126 0.140∗∗ 0.145∗∗ 0.095∗ 0.097∗∗ 0.092 0.064

(0.065) (0.061) (0.065) (0.055) (0.058) (0.047) (0.038) (0.055) (0.063)F 0.03 2.06 3.72 6.61 6.19 4.05 6.38 2.78 1.01Districts 1,353 1,353 1,353 1,353 1,353 1,353 1,353 1,353 1,353N 5,067 5,067 5,067 5,067 5,067 5,067 5,067 5,067 5,067

D. 8th Grade Reading GapLog Sim. Rev. 0.013 0.072 0.086 0.080 0.140∗ 0.186∗∗ 0.162∗∗ 0.177∗∗ 0.080

(0.069) (0.067) (0.077) (0.073) (0.066) (0.056) (0.045) (0.064) (0.071)F 0.03 1.16 1.23 1.23 4.52 11.07 12.82 7.57 1.26Districts 1,330 1,330 1,330 1,330 1,330 1,330 1,330 1,330 1,330N 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909 4,909

Table A11: Two-stage least squares estimates of log spending on SEDA test score gaps

(1) (2) (3) (4)4th Grade 8th Grade

Math Reading Math ReadingLog Spending, 5-8 years prior -0.523 -0.518 0.862 0.860

(0.499) (0.503) (0.777) (0.588)F 22.97 22.25 12.74 22.78Districts 1,205 1,196 1,218 1,189N 4,942 4,890 4,932 4,768

64

Table A12: Two-stage least squares estimates of log spending on instructional expendituresub-categories – Graduation Rate sample, one-year lag

(1) (2) (3) (4) (5) (6)Instructional Teacher Salaries Instructional

Salaries Regular Special Vocational Other BenefitsSpending ($1,000s) 4.692∗∗ 9.770∗∗ 1.688∗∗ 0.410∗∗ 0.709∗∗ 1.942∗∗

(0.534) (1.142) (0.246) (0.060) (0.093) (0.246)Dep. Var. Mean 3.91 1.50 0.30 0.05 0.07 1.171Baseline Fraction 0.32 0.12 0.02 0.00 0.01 0.094First-stage F 78.74 78.74 78.74 78.74 78.74 78.74Districts 2,986 2,986 2,986 2,986 2,986 2,986N 24,529 24,529 24,529 24,529 24,529 24,529

Table A13: Two-stage least squares estimates of log spending on instructional expendituresub-categories – SEDA sample, five to eight year lag

(1) (2) (3) (4) (5) (6)Instructional Teacher Salaries Instructional

Salaries Regular Special Vocational Other BenefitsSpending ($1,000s) 2.197∗∗ 4.955∗∗ 1.073∗∗ -0.139∗∗ 0.230∗∗ 0.882∗∗

(0.261) (0.495) (0.134) (0.021) (0.035) (0.114)Dep. Var. Mean 3.84 1.61 0.31 0.05 0.07 1.113Baseline Fraction 0.34 0.17 0.03 0.01 0.01 0.113First-stage F 155.52 155.52 155.52 155.52 155.52 155.52Districts 5,779 5,779 5,779 5,779 5,779 5,779N 26,733 26,733 26,733 26,733 26,733 26,733

65

Table A14: Two-stage least squares estimates of log spending on support service expendituresub-categories – Graduation Rate sample, one-year lag

(1) (2) (3) (4) (5) (6) (7)Pupil Staff General School Operations &

Support Support Admin. Admin. Maintenance Transportation OtherPer-pupil Spending 0.908∗∗ 1.058∗∗ 0.151∗ 0.616∗∗ 1.324∗∗ 0.495∗∗ 0.470∗∗

(0.131) (0.142) (0.072) (0.098) (0.208) (0.097) (0.087)Dep. Var. Mean 0.47 0.38 0.24 0.48 0.86 0.429 0.244Baseline Fraction 0.04 0.03 0.02 0.04 0.07 0.034 0.020First-stage F 78.74 78.74 78.74 78.74 78.74 78.74 78.74Districts 2,986 2,986 2,986 2,986 2,986 2,986 2,986N 24,529 24,529 24,529 24,529 24,529 24,529 24,529

Table A15: Two-stage least squares estimates of log spending on suppport service expendi-ture sub-categories – SEDA sample, five to eight year lag

(1) (2) (3) (4) (5) (6) (7)Pupil Staff General School Operations &

Support Support Admin. Admin. Maintenance Transportation OtherPer-pupil Spending 0.378∗∗ 0.204∗∗ 0.159∗ 0.241∗∗ 0.341∗∗ 0.126∗∗ 0.129∗∗

(0.059) (0.060) (0.073) (0.042) (0.086) (0.052) (0.038)Dep. Var. Mean 0.44 0.35 0.29 0.47 0.86 0.433 0.234Baseline Fraction 0.04 0.03 0.03 0.04 0.08 0.040 0.024First-stage F 155.52 155.52 155.52 155.52 155.52 155.52 155.52Districts 5,779 5,779 5,779 5,779 5,779 5,779 5,779N 26,733 26,733 26,733 26,733 26,733 26,733 26,733

Table A16: Two-stage least squares estimates of log spending on capital expenditure sub-categories

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)Graduate Rates SEDA Test Scores

New Instructional Other Nonspecified New Instructional Other NonspecifiedConstruction Land Equipment Equipment Equipment Construction Land Equipment Equipment Equipment

Log Spending 3.564∗∗ 0.127 0.098∗ 0.120 0.0075 2.170∗∗ -0.043 0.102∗∗ -0.005 0.0022(0.953) (0.273) (0.048) (0.119) (0.018) (0.692) (0.157) (0.026) (0.064) (0.023)

Dep. Var. Mean 0.80 0.059 0.057 0.13 0.010 0.81 0.053 0.057 0.14 0.010Baseline Fraction 0.05 0.004 0.005 0.01 0.001 0.05 0.004 0.005 0.01 0.001First-stage F 78.74 78.74 78.74 78.74 78.74 155.52 155.52 155.52 155.52 155.52Districts 2,986 2,986 2,986 2,986 2,986 5,779 5,779 5,779 5,779 5,779N 24,529 24,529 24,529 24,529 24,529 26,733 26,733 26,733 26,733 26,733

66

Table A17: Two-stage least squares estimates of log spending on other expenditure sub-categories – Graduation Rate sample, one-year lag

(1) (2) (3) (4) (5) (6)Food Enterprise Other Community Adult Other Non-

Services Operations Elem/Sec Services Education Elem/SecPer-pupil Spending 0.206∗∗ 0.011 0.015 0.080 -0.034 0.760∗∗

(0.045) (0.011) (0.014) (0.055) (0.029) (0.130)Dep. Var. Mean 0.35 0.020 0.0024 0.048 0.018 0.010Baseline Fraction 0.03 0.002 0.0002 0.004 0.001 0.001First-stage F 78.74 78.74 78.74 78.74 78.74 78.74Districts 2,986 2,986 2,986 2,986 2,986 2,986N 24,529 24,529 24,529 24,529 24,529 24,529

Table A18: Two-stage least squares estimates of log spending on other expenditure sub-categories – SEDA sample, five to eight year lag

(1) (2) (3) (4) (5) (6)Food Enterprise Other Community Adult Other Non-

Services Operations Elem/Sec Services Education Elem/SecPer-pupil Spending -0.109∗∗ 0.003 0.008 -0.003 -0.014 0.010∗

(0.023) (0.007) (0.009) (0.023) (0.015) (0.005)Dep. Var. Mean 0.34 0.024 0.0026 0.043 0.014 0.005Baseline Fraction 0.04 0.002 0.0001 0.004 0.001 0.001First-stage F 155.52 155.52 155.52 155.52 155.52 155.52Districts 5,779 5,779 5,779 5,779 5,779 5,779N 26,733 26,733 26,733 26,733 26,733 26,733

Table A19: Two-stage least squares estimates of log spending on teacher counts – GraduationRate sample, one-year lag

(1) (2) (3) (4) (5) (6) (7)Total Teacher Total Library District School Student

Teachers Aides Counselors Specialists Admin. Admin. SupportLog Spending -277.164∗ -34.943 -24.022∗∗ -1.448 -2.935 -36.825∗∗ -39.986

(126.603) (27.846) (9.992) (1.844) (4.117) (14.608) (23.320)Dep. Var. Mean 332.33 70.205 11.3035 6.206 6.566 17.568 22.941Baseline Fraction 27.76 5.97 0.96 0.53 0.56 1.52 1.94First-stage F 78.74 78.74 78.74 78.74 78.74 78.74 78.74Districts 2,986 2,986 2,986 2,986 2,986 2,986 2,986N 24,529 24,529 24,529 24,529 24,529 24,529 24,529

67

Table A20: Two-stage least squares estimates of log spending on teacher counts – SEDAsample, five to eight year lag

(1) (2) (3) (4) (5) (6) (7)Total Teacher Total Library District School Student

Teachers Aides Counselors Specialists Admin. Admin. SupportLog Spending 290.151∗∗ -6.588 10.729∗∗ 5.019∗∗ 5.196 -0.556 68.891∗∗

(66.142) (46.941) (3.947) (1.658) (4.455) (8.482) (12.703)Dep. Var. Mean 283.61 59.353 9.3443 5.283 5.870 15.836 18.268Baseline Fraction 24.84 5.27 0.84 0.42 0.44 1.34 2.06First-stage F 155.52 155.52 155.52 155.52 155.52 155.52 155.52Districts 5,779 5,779 5,779 5,779 5,779 5,779 5,779N 26,733 26,733 26,733 26,733 26,733 26,733 26,733

68

Table A21: Two-stage least squares estimates of log spending on graduation rates and testscores (National Trends)

(1) (2) (3) (4) (5) (6)10th Grade Graduation Rate Test Scores: 5 to 8 Year Lag1-Year Lag 4-Year Lag G4 Math G4 Reading G8 Math G4 Reading

Log Spending 0.255∗∗ 3.038∗∗ 25.751 16.889 0.104 11.070(0.087) (1.137) (134.371) (91.366) (8.652) (87.661)

F 55.12 8.38 0.04 0.04 0.22 0.02Districts 5,753 5,547 5,905 5,902 5,914 5,908N 37,510 27,628 27,537 27,531 27,603 27,607

Notes: Standard errors clustered at the district level in parentheses: * p < 0.05, ** p <0.01. Coefficients are shown from 2SLS regressions with controls for log number of students,fraction with an IEP, fraction black, fraction Hispanic, fraction eligible for free or reducedprice lunch, median household income, and actual property values. Models also includedistrict and state-by-year fixed effects. Simulated revenue and total expenditure are inthousands of real 2013 dollars per pupil.

69

Table A22: Two-stage least squares estimates of log spending on graduation rates and testscores (No Combined Districts)

(1) (2) (3) (4) (5) (6)10th Grade Graduation Rate Test Scores: 5 to 8 Year Lag1-Year Lag 4-Year Lag G4 Math G4 Reading G8 Math G4 Reading

Log Spending 0.298∗∗ 0.422∗∗ 0.768∗ 0.796∗∗ 0.305 0.824∗∗

(0.095) (0.120) (0.355) (0.318) (0.330) (0.303)F 63.63 82.30 169.16 169.06 157.45 165.66Districts 2,781 2,778 5,469 5,466 5,473 5,469N 22,821 17,863 25,604 25,602 25,625 25,633

Notes: Standard errors clustered at the district level in parentheses: * p < 0.05, ** p <0.01. Coefficients are shown from 2SLS regressions with controls for log number of students,fraction with an IEP, fraction black, fraction Hispanic, fraction eligible for free or reducedprice lunch, median household income, and actual property values. Models also includedistrict and state-by-year fixed effects. Simulated revenue and total expenditure are inthousands of real 2013 dollars per pupil.

Table A23: Two-stage least squares estimates of log spending on SEDA test scores – gainsversus losses

Gains LossesG4 Math G4 Reading G8 Math G8 Reading G4 Math G4 Reading G8 Math G8 Reading

Log Spending 0.656 1.405 0.486 0.783 0.594 0.247 0.453 0.389(0.753) (0.720) (0.783) (0.747) (0.392) (0.357) (0.356) (0.321)

Dep. Var. Mean 0.20 0.14 0.13 0.22 0.19 0.14 0.15 0.26First-stage F 45.50 45.36 42.98 46.54 137.15 139.59 131.82 137.75Districts 3,689 3,693 3,710 3,723 4,565 4,562 4,578 4,564N 10,397 10,402 10,484 10,530 14,736 14,730 14,723 14,685

70

Table A24: Two-stage least squares estimates of log spending on SEDA test scores – highand low income districts

4th Grade Math

Low Income High Income Low Wealth High WealthLog Spending 1.049 -0.066 1.035∗ 2.262

(0.739) (0.597) (0.450) (1.704)Dep. Var. Mean -0.09 0.59 0.09 0.49First-stage F 48.87 39.16 98.97 9.08Districts 3,411 2,492 4,441 1,464N 15,743 11,783 20,482 7,054

4th Grade Reading

Low Income High Income Low Wealth High WealthLog Spending -0.235 0.930 0.742 3.313

(0.609) (0.595) (0.395) (1.712)Dep. Var. Mean -0.16 0.54 0.05 0.39First-stage F 48.33 39.58 99.29 9.05Districts 3,410 2,490 4,438 1,464N 15,723 11,797 20,477 7,053

8th Grade Math

Low Income High Income Low Wealth High WealthLog Spending -0.019 -0.771 0.299 1.345

(0.658) (0.644) (0.422) (1.387)Dep. Var. Mean -0.15 0.54 0.04 0.41First-stage F 43.60 36.19 88.50 8.64Districts 3,424 2,488 4,449 1,465N 15,830 11,762 20,551 7,051

8th Grade Reading

Low Income High Income Low Wealth High WealthLog Spending 0.939 -0.309 0.716 2.885

(0.637) (0.524) (0.399) (1.495)Dep. Var. Mean -0.06 0.67 0.16 0.50First-stage F 47.07 39.60 94.99 9.21Districts 3,419 2,487 4,443 1,465N 15,847 11,749 20,552 7,054

71