ESSAYS ON SCHOOL FINANCE AND TEACHER PERFORMANCE
By
Paul N. Thompson

A DISSERTATION
Submitted
to Michigan State University
in partial fulfillment of the requirements
for the degree of
Economics - Doctor of Philosophy
2014

ABSTRACT
ESSAYS ON SCHOOL FINANCE AND TEACHER PERFORMANCE
By
Paul N. Thompson
Chapter 1 analyzes the Ohio fiscal stress labeling system, a statewide financial intervention system that labels school districts with projected deficits in the general fund. Labeled school districts
are required by the state to implement a financial recovery plan that balances budgets, with recovery operated by the district or the state depending on the level of projected deficits. This chapter
examines the effect of these labels on school district financial behavior and housing prices from
2000-2012. In response to these labels school districts decrease capital and operating expenditures,
with larger percentage reductions in capital, and increase local property tax revenue funding operating expenditures. These labeled school districts are in much better financial positions following
successful recovery and maintain financial viability well after recovery is complete. House prices
fall following a state takeover of the district’s financial decision-making, suggesting that the state
takeover sends a stronger signal to residents than district-led recoveries. In addition to responding
to labels, school districts and homebuyers are responsive to earlier state interventions that alleviate
financial problems before labels become necessary.
Chapter 2 consider issues of equality and efficiency in two different school funding systems - a
state-level system in Michigan and a foundation system in Ohio. Unlike Ohio, the Michigan system
restricts districts from generating property or income tax revenue to fund operating expenditures.
In both states, districts fund capital expenditures with local tax revenue. The results indicate that
although average revenue and expenditures per pupil in Michigan and Ohio are almost identical,
the distributions of the various revenue sources are quite different. Ohio?s funding system has
greater equality in terms of total revenue, largely due to Ohio redistributing state funds to the least
wealthy districts while Michigan does not. This chapter finds that relatively wealthy Michigan

districts spend more on capital expenditures while relatively wealthy Ohio districts spend more
on labor and materials. This suggests that constraints on raising local revenue to fund operating
expenditures in Michigan could create efficiency issues.
Chapter 3 analyzes Empirical Bayes’ (EB) estimation, a popular procedure used to calculate
teacher value-added. This estimation strategy is often motivated as a way to make imprecise estimates more reliable. In this paper we review the theory of EB estimation and use simulated and
real student achievement data to study its ability to properly rank teachers. This chapter compares
the performance of EB estimators with that of other widely used value-added estimators under
different teacher assignment scenarios. This chapter finds that, although EB estimators generally
perform well under random assignment of teachers to classrooms, their performance generally
suffers under nonrandom teacher assignment. Under nonrandom assignment, estimators that explicitly (if imperfectly) control for the teacher assignment mechanism perform the best out of all
the estimators we examine. This chapter also finds that shrinking the estimates, as in EB estimation, does not itself substantially boost performance.

This thesis is dedicated to my wife Katie, who was there to lean on during all the ups and downs
of the PhD process. I also dedicate this thesis to my best friend, Shiloh, who spent so many days
by my side and always there for a walk or a game of fetch when I needed it. I love you both and
couldn’t have done it with out you.
I also want to thank my parents who inspired me to pursue my PhD and a career in academia.

iv

ACKNOWLEDGEMENTS

I wish to thank my committee members who were more than generous with their expertise and
precious time. A special thanks to Dr. Michael Conlin, my committee chairman, for his countless
hours of reflecting, reading, encouraging, and most of all patience throughout the entire process.
Thank you Dr. Leslie Papke, Dr. Jeff Wooldridge, and Dr. Mark Skidmore for agreeing to serve
on my committee and providing helpful comments.
I want to thank the Institute of Education Sciences, whose Pre-Doctoral Training Grant (Award
#R305B090011) to Michigan State University helped fund much of this work. The Economics of
Education training program helped me find my passion in education research and allowed me the
opportunity to meet many in the field through trips to conferences, on campus speakers, etc.

v

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CHAPTER 1
1.1
1.2

1.3
1.4

1.5

1.6

SCHOOL DISTRICTS AND HOUSING PRICE RESPONSES
TO FISCAL STRESS LABELS: EVIDENCE FROM OHIO . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fiscal Stress Labels in Ohio . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Overview of Fiscal Stress Labels . . . . . . . . . . . . . . . . . . . . .
1.2.2 Fiscal Oversight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.3 Fiscal Emergency . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.4 Trends in Label Receipt . . . . . . . . . . . . . . . . . . . . . . . . . .
Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 School District Expenditures and Revenues . . . . . . . . . . . . . . .
1.4.2 Residential Home Sales . . . . . . . . . . . . . . . . . . . . . . . . . .
Empirical Specification and Results . . . . . . . . . . . . . . . . . . . . . . .
1.5.1 Difference-in-Differences Results . . . . . . . . . . . . . . . . . . . .
1.5.2 Event Study Results . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.3 Regression Discontinuity Results . . . . . . . . . . . . . . . . . . . . .
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

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CHAPTER 2
2.1
2.2

2.3

2.4

MICHIGAN AND OHIO K-12 EDUCATIONAL FINANCING
SYSTEMS: EQUALITY AND EFFICIENCY . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Institutional Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Michigan K-12 Finance . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Ohio K-12 Finance . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Similarities Between Ohio and Michigan Financing Systems . . . . . .
Data and Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Descriptive Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2.1 School District Revenue . . . . . . . . . . . . . . . . . . . .
2.3.2.2 School District Expenditures . . . . . . . . . . . . . . . . . .
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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CHAPTER 3
3.1
3.2

AN EVALUATION OF EMPIRICAL BAYES’ ESTIMATION OF
VALUE-ADDED TEACHER PERFORMANCE . . . . . . . . . . . 51
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Empirical Bayes’ Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

vi

3.3
3.4

3.5

3.6

3.7

Summary of Estimation Methods . . . . . . . . . . . . . . . . . . . . .
Comparing VAM Methods Using Simulated Data . . . . . . . . . . . .
3.4.1 Simulation Design . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Evaluation Measures . . . . . . . . . . . . . . . . . . . . . . .
Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Fixed Teacher Effects versus Random Teacher Effects . . . . . .
3.5.1.1 Random Assignment . . . . . . . . . . . . . . . . . .
3.5.1.2 Dynamic Grouping and Nonrandom Assignment . . .
3.5.1.3 Heterogeneity Grouping and Nonrandom Assignment
3.5.2 Shrinkage versus Non-Shrinkage Estimation . . . . . . . . . . .
3.5.3 Sensitivity Analyses . . . . . . . . . . . . . . . . . . . . . . .
Comparing VAM Methods Using Real Data . . . . . . . . . . . . . . .
3.6.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

APPENDICES . . . . . . . . . . . . . . . . . . . . . . .
APPENDIX A CHAPTER 1 TABLES AND FIGURES
APPENDIX B CHAPTER 2 TABLES AND FIGURES
APPENDIX C CHAPTER 3 TABLES AND FIGURES

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99
110

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

vii

LIST OF TABLES

Table A.1 Fiscal Stress Label Transitions from 2000-2012 . . . . . . . . . . . . . . . . . . 84
Table A.2 Table of Means - School District Demographic Characteristics . . . . . . . . . . 85
Table A.3 Table of Means - School District Financial Characteristics . . . . . . . . . . . . 86
Table A.4 Table of Means - Housing and Parcel Characteristics . . . . . . . . . . . . . . . 88
Table A.5 Effect of Fiscal Stress Receipt on Expenditures per pupil, by severity level . . . . 89
Table A.6 Effect of Fiscal Stress Receipt on Revenues per pupil, by severity level . . . . . . 89
Table A.7 Effect of School District Fiscal Stress Label Receipt on Housing Prices . . . . . 90
Table A.8 Estimated Discontinuity at Year 3 Ratio Cutoff . . . . . . . . . . . . . . . . . . 93
Table A.9 Regression Discontinuity Results . . . . . . . . . . . . . . . . . . . . . . . . . 96
Table A.10 Variable Names and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Table A.11 Comparison of Full and Analytic Samples . . . . . . . . . . . . . . . . . . . . . 98
Table B.12 Property Tax Rates and Taxable Values 2002-2010 . . . . . . . . . . . . . . . . 99
Table B.13 Revenue and Demographic Characteristics . . . . . . . . . . . . . . . . . . . . . 100
Table B.14 Revenue Regression Results Without District Fixed Effects . . . . . . . . . . . . 106
Table B.15 Revenue Regression Results With District Fixed Effects . . . . . . . . . . . . . 108
Table C.16 Simulation Results: Comparing Fixed and Random Teacher Effects Estimators . 110
Table C.17 Simulation Results: Comparing Shrunken and Unshrunken Estimators . . . . . . 111
Table C.18 Fraction of Teachers Ranked in Same Quintile by Estimator Pairs . . . . . . . . 112
Table C.19 Description of Value-Added Estimators . . . . . . . . . . . . . . . . . . . . . . 113
Table C.20 Definitions of Grouping-Assignment Mechanisms . . . . . . . . . . . . . . . . . 113
Table C.21 Description of Evaluation Measures of Value-Added Estimator Performance . . . 113

viii

LIST OF FIGURES

Figure A.1 Geographic Distribution of Labeled School Districts Across Ohio . . . . . . . . 84
Figure A.2 Yearly Number of Labels, by Label Severity . . . . . . . . . . . . . . . . . . . 85
Figure A.3 Operating and Capital Per Pupil Expenditures and Revenues (2010 $)

. . . . . 87

Figure A.4 Event Study Results - District Enrollment . . . . . . . . . . . . . . . . . . . . 90
Figure A.5 Event Study Results - Total Operating Expenditures PP . . . . . . . . . . . . . 91
Figure A.6 Event Study Results - Total Capital Expenditures PP . . . . . . . . . . . . . . . 91
Figure A.7 Event Study Results - Local Property Tax Revenue and Millage Rates

. . . . . 92

Figure A.8 Event Study Results: Housing Prices . . . . . . . . . . . . . . . . . . . . . . . 93
Figure A.9 Distribution of Projected General Fund Balance to Revenue Ratios . . . . . . . 94
Figure A.10 Change in District Finances and Housing Prices, by Year 3 Projected Ratio

. . 95

Figure B.11 Total Enrollment of Quintiles . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Figure B.12 Total Revenue Per Pupil

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Figure B.13 State Revenue Per Pupil

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Figure B.14 Local Revenue Per Pupil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Figure B.15 Local Operating Tax Revenue Per Pupil . . . . . . . . . . . . . . . . . . . . . 105
Figure B.16 Local Capital Property Tax Revenue Per Pupil . . . . . . . . . . . . . . . . . . 107
Figure B.17 Total Expenditures Per Pupil . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Figure C.18 Spearman Rank Correlations Across Different VAM Estimators . . . . . . . . . 112

ix

CHAPTER 1
SCHOOL DISTRICTS AND HOUSING PRICE RESPONSES TO FISCAL STRESS
LABELS: EVIDENCE FROM OHIO

1.1

Introduction

In the current financial climate, rising budget deficits have burdened many school districts and
local governments, leading some to the brink of bankruptcy. To help address these growing deficits,
many states have developed financial intervention systems that identify financially troubled school
districts or local governments and provide varying levels of state intervention.1 On one end of
the spectrum, some states heavily intervene and overhaul financial practices. One example is the
state of Michigan, where an emergency manager took over the financial decision-making for the
city of Detroit after bankruptcy and building nearly $20 billion of debt. In contrast, other states
monitor financial behavior of districts, but provide little, if any, intervention into financial practices.
The California financial monitoring system is an example of this approach, where one-fifth of all
school districts in the state had FY2013 deficits, but beyond short-term loans there is not much
state intervention.
I analyze one of these systems, the Ohio fiscal stress labeling system, which labels school
districts with projected deficits in their general fund and requires these districts to implement a
financial recovery plan that balances budgets. Districts with less severe deficits receive a fiscal
oversight label, under which districts are placed in charge of developing and implementing these
recovery plans. Districts in more severe financial trouble receive a fiscal emergency label, under
which the state takes over the financial decision making of the district. As part on this financial
takeover, the state assumes the responsibility of developing and implementing the recovery plan.
1 A 2013 Pew Charitable Trusts report found that 19 states currently have a financial intervention system in place.
Earlier work by, Honadle (2003) and Kloha, et al. (2005) found that 15 states had some fiscal health evaluation system
in place and nearly a third more states are considering using these indicators.

1

Despite the growing use of these financial intervention systems, little is known about the effects
of these programs. My paper fills this gap in the literature and provides the first evidence on the
effect of these fiscal stress labels on school district financial behavior and housing prices. Given
the distinction between whether financial recovery is operated by the district or by the state, the
Ohio system allows me to identify separate effects depending on the type of label received. I
compile a balanced panel of all 613 Ohio school districts from 2000-2012; collecting data on dates
of label receipt and removal, school district expenditures and revenues, projected deficits, tax rates,
taxable values, local tax election outcomes, and housing transactions. To estimate the effects of
these labels, I use three different identification strategies: difference-in-differences, an event study,
and a regression discontinuity design. Using these three approaches, I find that these recovery
plans do change financial behavior. I find that districts decrease capital and operating expenditures
following receipt of fiscal oversight, with larger percentage reductions in capital. Districts increase
local property tax revenue funding operating expenditures during both fiscal oversight and fiscal
emergency, while shifting their tax mix away from new capital projects. In addition to these effects
of label receipt, I also analyze the response of districts and residents to earlier state interventions
that try to alleviate financial problems before fiscal stress labels are necessary. I find that districts
with projected deficits are decreasing both capital and operating expenditures in response to these
early interventions. Residential home sale prices fall following receipt of fiscal emergency, but find
no statistically significant effects following fiscal oversight. But the regression discontinuity and
event study results suggest that this lack of an effect during fiscal oversight may be due to housing
prices falling in response to the financial changes made during these early interventions.
In addition to being the first paper to analyze the effects of this policy, this study also contributes
to the literature on the capitalization of school quality into housing prices. While much of this
literature has focused on the effect academic quality has on housing prices,2 my results suggest
2 Previous literature has focused on the effect of more transitory changes in school inputs and outputs on housing
prices. Most notably, Black (1999) finds that a $500 increase in per-pupil expenditures increases house prices by 2.2
percent. Cellini, et al. (2010) examine the effect of bond referenda passage on housing prices. They find that marginal

2

that residents also care about what these financial recoveries may mean for future academic quality
or expected tax rates. This paper also contributes to the literature on school district responses to
budgetary issues. Although previous literature3 has examined how districts react to budgetary
problems, these studies primarily focus on voluntary changes to finances as a result of budget
deficits. These voluntary changes are likely to be smaller and less expansive than those made
under the scrutiny of the mandated recovery plans examined here.
For states considering these types of policies, the structure of the state school funding system
is likely to play a role in how districts respond. In Ohio, school districts are able to supplement
state aid through local tax revenue funding operating expenditures. This setup allows fiscal stress
districts to increase taxes along with expenditure cuts to offset deficits. Given that fourteen states
have a similar funding structures to Ohio and eleven states place no restrictions on local tax revenue, districts in these other states may respond similarly to these types of labels. Districts in states
where local operating tax revenue is restricted, such as Michigan and California, would likely focus
more heavily on reductions in expenditures in response to these labels and recovery plans.

homebuyers are willing to pay $1.50 for an additional dollar of capital expenditure, largely due to increases in safety
and aesthetics of new and renovated buildings. Numerous studies of United States and international school districts
(Bayer et al., 2007; Black, 1999; Clapp et al., 2008; Dougherty et al., 2009; Gibbons and Machin, 2003, 2006;
Gibbons, Machin, and Silva, 2009; Fack and Grenet, 2010; Davidoff and Leigh, 2008) find around a three percent
increase in home prices resulting from a one standard deviation increase in test score levels. There is little evidence,
however, of capitalization of test score gains (Brasingtion and Haurin, 2006; Downes and Zabel, 2002; Kane et al.,
2006). Another set of papers has examined the effect of school report card grades, which combine multiple sources
of test score and district characteristics into a single rating for each school district. Figlio and Lucas (2004) examine
the capitalization effects of school district report card grades in Florida and find that report card grades do provide
valuable information about school quality to homebuyers. Studies examining these ratings in other settings find more
mixed results (Kane, Staiger, and Samms, 2003; Fiva and Kirkebøen, 2009; Zahirovic-Herbert and Turnbull, 2009).
The fiscal stress labels may capture aspects of school quality that these school district academic quality rankings fail to
signal, aspects that the housing market may value differently than achievement levels. For a more expansive review of
this literature, see the Black and Machin chapter in the “Handbook of the Economics of Education" or Nguyen-Hoang
and Yinger (2011).
3 Previous literature examining the responses of school districts to budgetary issues has analyzed how districts
exhibiting characteristics of fiscal distress behave. This literature largely finds, as expected, that districts in fiscal
distress respond by increasing revenue and/or decreasing expenditures. For a thorough review of this literature, see
Trussel and Patrick (2012).

3

1.2

Fiscal Stress Labels in Ohio

1.2.1

Overview of Fiscal Stress Labels

Ohio school districts with projected deficits in the general fund receive either a fiscal oversight
label or fiscal emergency label depending on the level of the deficit.4 Labeled districts are required
to develop financial recovery plans that outline changes to financial behavior that achieve balanced
budgets. These proposed changes include reductions in expenditures and/or increases in local tax
revenues. Under fiscal oversight, district school boards are required to develop and implement
recovery plans, incorporating recommendations made by the Auditor and the Ohio Department of
Education (ODE). Successful implementation of these recovery plans will result in removal of the
label, but failure to adopt or adhere to these recovery plans results in districts being placed into
fiscal emergency. Under this most severe label, a state commission assumes the role of financial
decision maker for the district, including handling the development and implementation of the
financial recovery plan.
After a district is notified of label receipt, a press release is issued on the Auditor’s website
that details to the public why the district received the label.5 This press release is often reported
in local newspapers in the days following its issuance. Similarly, a press release is posted to
inform residents when a label is changed or removed. Given the lack of local media coverage
prior to the publication of the press release, the initial label receipt is likely unanticipated.6 This
4 Given that the main variation of interest is between district-led recovery and state-led recovery, I choose to
combine fiscal caution and fiscal watch into one indicator for fiscal oversight. Differentiating between fiscal caution
and fiscal watch does not change the overall results. The fiscal emergency and fiscal watch labels were introduced in
1996, while the fiscal caution label was not instituted until 2001. For more detailed information regarding the history
of these labels, the various criteria used to select these districts, and the requirements associated with these labels
see the Ohio Auditor of the State website (http://www.auditor.state.oh.us/services/lgs/fiscalwatch/schools.htm) or the
Ohio Department of Education Website (http://www.ode.state.oh.us/gd/gd.aspx?page=2TopicRelationID=1012).
5 www.auditor.state.oh.us/newscenter/press/releases/category/Fiscal Caution, Watch, and Emergency
6 Examinations of newspaper reports gives no indication that residents are aware that the Auditor is examining
school district financial records or that a fiscal stress determination was made prior to the publication of the press
release. News reports covering districts that have been further downgraded to fiscal watch due to the failure to create
a recovery plan speculate about whether the district will fall into fiscal emergency, but no official word is given until
the press release is posted. The speculation is also likely due to the information these downgrades provide regarding

4

unanticipated change in the fiscal stress rating of the district serves as an exogenous informational
shock regarding the fiscal health of the district and is the main source of identification in this
analysis.
Data on the school districts labeled in these fiscal stress categories are obtained from the Ohio
Auditor and the ODE. Information collected includes the date the school district initially received
a fiscal stress label and, if no longer labeled, the date the label was removed. The data also include
information on whether a fiscal oversight or fiscal emergency label was received and dates of
transition from one label to another. Since 2000, 99 of the 613 school districts in Ohio have
received at least one of these labels. Including districts that are still currently labeled, districts are
labeled for 3.58 years on average. The average duration is 3.23 years for the subset of districts
where label removal is observed within the panel.
1.2.2

Fiscal Oversight

The process of receiving a fiscal oversight label starts with the yearly five-year forecast. Each
October, school districts must submit a five-year financial forecast to the Ohio Department of
Education. This forecast projects the expenditures and revenues of the district for the current fiscal
year and the next four fiscal years based on predicted changes in taxable property values, tax rates,
state aid, teaching and healthcare contracts, and other operating costs.7 Districts with projected
current year deficits that exceed two percent of general fund revenue receive a fiscal oversight
label, while districts with projected deficits in the second or third projected years receive other, less

the ability of school officials to handle these financial problems.
7 Districts are flagged if a forecast predicts a deficit (i.e. negative balance in the general fund) for the current fiscal
year or projects positive general fund balances that are less than two percent of projected revenue for that year. In
addition to current year deficits or low fund balances, district forecasts are flagged if deficits that exceed two percent
of projected revenue are present in the second or third projected years. Districts with projected deficits are given
an opportunity to make reductions in expenditure and/or increases in revenue in order to alleviate the deficit and
avoid receiving the fiscal caution label. Districts with current year projected deficits may avoid fiscal caution if they
immediately eliminate the deficit by reducing expenditures or through a tax advance from the county auditor to cover
the amount of the deficit, but otherwise do not have sufficient time to levy new taxation to cover the amount of the
deficit. Districts with deficits in the second or third projected year may eliminate the deficit through passage of new
tax referenda and/or reductions in expenditure.

5

invasive state interventions. Districts with year 2 projected deficits must submit a letter explaining
how they will eliminate the projected deficit, while districts with year 3 projected deficits are only
notified of the deficit with no formal requirement to submit any proposed financial changes to the
state. The main goal of these early interventions is to help districts with deficits to solve their
financial problems before fiscal stress labels become necessary.
After receiving a fiscal oversight label, the districts must develop a financial recovery plan. To
help districts in the development of these plans, the Auditor may conduct a performance audit of
the district that provides recommendations to help guide the district’s recovery plan.8 In addition,
the Department of Education may visit and inspect the district’s monthly financial situation and
provide technical assistance and training to school officials. After implementing a recovery plan,
a district is removed from fiscal oversight when the district projects positive fund balances for
the next two projected years. However, a district cannot be removed from fiscal oversight in the
same fiscal year in which the fiscal oversight label was received. On average, districts complete
successful financial recovery under fiscal oversight in 2.72 years.9
1.2.3

Fiscal Emergency

Districts that are unable to develop recovery plans on their own or fail to adhere to the recovery plan while under fiscal oversight are placed in fiscal emergency. A school district may also
receive fiscal emergency if the projected current year general fund deficit exceeds fifteen percent
of the general fund revenue and the school district has failed to gain voter approval on a levy that
would provide sufficient revenue to eliminate the deficit. School districts in fiscal emergency are
placed under the control of a financial planning and supervision commission, which assumes the
8 This performance audit identifies areas, in which the district can cut costs and raise additional revenue. These
identified areas serve as a guide for districts or the state commission in the development of financial recovery plans.
Recommendations often cited in these audits include freezing step increases for teacher salaries, reducing staff, increasing employee health insurance contributions, implement fee-based extracurricular activities or reduce extracurricular expenditures, and eliminating unnecessary busing, among others.
9 The average duration rises to 3.42 years if districts that have not been observed completing financial recovery
under fiscal oversight (i.e. those with a fiscal oversight label at the end of the panel) are included in the calculation.

6

responsibility of developing and implementing a financial recovery plan for the school district.10
The commission reviews and assumes responsibility for all projected revenues and expenditures
and has final approval on any tax levies and debt issuances the school district wishes to propose to
voters. The commission also has the authority to reduce the number of employees irrespective of
current employment contracts and collective bargaining agreements in order to achieve balanced
budgets.11
The Auditor is required to conduct a performance audit for districts in fiscal emergency and
these districts are eligible to receive two-year loans from the state. These loans, which are up to
the amount of a two year advance on the district’s state foundation aid, are intended to keep the
district solvent during its recovery.12 Once the district meets the objectives of the recovery plan
and eliminates the deficits that led to fiscal emergency, the district is removed from the label. In rare
cases where the district still has outstanding debt at the time of release from fiscal emergency, the
district is placed into fiscal watch until the debt is paid. On average, districts that are downgraded
to fiscal emergency spend 0.81 years in fiscal oversight. Once in fiscal emergency, successful
recovery takes an average of 3.62 years to complete, but in some cases has taken upwards of nine

10 This commission consists of five voting members including the Director of the Office of Budget and Management
and the State Superintendent. The other three members of the commission include a business person appointed by the
Governor, a business person appointed by the mayor or county auditor, and a parent with a child in the district appointed
by the State Superintendent. The business people must have at least five years experience in the public or private
sector in business management, public accounting, or another related field. The commission must include at least one
female member and one minority member if minorities constitute at least twenty percent of district enrollment. If the
commission fails to come to a consensus on a financial recovery plan within 120 days, the commission is dissolved and
a fiscal arbitrator is put in charge of recovery. The fiscal arbitrator assumes all powers and duties of the commission,
including creation and implementation of a financial recovery plan.
11 These reductions first eliminate administrative and non-teaching employees, giving preference to employees with
continuing contracts and those with greater seniority. If the budget is still not balanced following this first round of
layoffs, the commission may layoff teachers in order to achieve a balanced budget. The commission also may remove
the district superintendent and/or treasurer if they fail to comply with the commission’s recovery plan.
12 These loans are paid out of the School District Solvency Assistance Fund, which consists of two accounts,
the Shared Resource Account and the Catastrophic Expenditure Account. The Shared Resource Account provides
districts with a two year, interest free advance on the district’s state foundation payment in order to help the district
to remain solvent while it implements its recovery plan, but loans must be repaid within two years. The Catastrophic
Expenditures Account is used to issue grants to districts that suffer a catastrophic event that depletes the district’s
finances, but can also be used for solvency assistance if all of the Shared Resource Account funds have been allocated.

7

years.13
1.2.4

Trends in Label Receipt

Table A.1 provides the number of transitions from one fiscal stress state to another that occurred
between 2000 and 2012. At the start of 2000, six districts were in fiscal oversight and nine were
in fiscal emergency. Between 2000 and 2010, 80 districts transitioned from no label to fiscal
oversight and four transitioned from no label to fiscal emergency. Of the 86 districts labeled in
fiscal oversight, 19 transitioned to fiscal emergency because of the failure to adopt a financial
recovery plan during fiscal oversight. There were also 71 successful financial recoveries completed
during this time period, with 46 completed under fiscal oversight and the other 25 completed under
fiscal emergency.
Figure A.1 graphically depicts where these labeled districts are located across the state. The
map indicates that many of these labeled districts are clustered around the state’s various urban
centers. This pattern in the location labeled districts suggests that regional economic changes or
spillover effects among adjacent districts may play a role in the deteriorating finances in these
districts. Figure A.2 depicts the yearly number of districts labeled as fiscal oversight or fiscal
emergency from 2000-2012. The number of school districts in fiscal stress began increasing in
2002, primarily due to the sharp increase in the number of fiscal oversight labels. In 2001, six
districts were in fiscal oversight, but by 2005 there were 42 districts holding a fiscal oversight
label. While the number of fiscal emergency labels has remained relatively constant since 2005,
there has been a noticeable reduction in the number of fiscal oversight labels. Largely due to this
decline in the number of fiscal oversight labels, the total number of labels has fallen from 54 in
2005 to 37 in 2012.

13 The average duration is 3.93 years, 0.82 in fiscal oversight and 3.11 in fiscal emergency, if districts that have not
been observed completing financial recovery under fiscal emergency (i.e. those with a fiscal emergency label at the
end of the panel) are included in the calculation.

8

1.3

Data

The fiscal stress data described in Section 2 are augmented with data on school district finances,
tax rates, taxable values, election outcomes, test scores, and residential home sales. Data on school
district general fund revenues and expenditures from 2000-201214 come from the Ohio Auditor and
include the current balance in the general fund, an observable measure of district financial health.
Data on projected deficits, the main criteria used to select these districts, come from the ODE and
are discussed in more detail in Section 5.3. Detailed information on expenditures and revenues
is obtained from the NCES Common Core of Data. This information contains total revenues and
expenditures per year and disaggregated data for the specific components that make up these totals.
This allows me to analyze exactly which types of revenues and expenditures districts are targeting
in these recovery plans. In addition, student test score proficiency levels, school report card grades,
and district accountability status are collected from the Ohio Department of Education. Finally,
residential home sales data are collected for 63 of the 88 counties in Ohio.15
In Ohio, districts fund much of their operating and capital expenditures through local property
and income taxation. Tax revenue for operating expenditures is used for general school expenses
(e.g. teachers, supplies, etc.), while tax revenue for capital expenditures is largely restricted for
use only in funding the specific capital project. Given the flexibility of operating revenue, districts
with budget deficits may find it advantageous to adjust their tax mix away from capital projects
and towards greater operating taxation in order to offset these deficits. To examine this, I collect
data from the Ohio Department of Taxation on all tax rates levied by school districts. These data
include the specific purpose of each tax and the yearly tax rate. These tax data are supplemented
with yearly taxable values for real property, tangible personal property, and tangible public utility
property for each school district. Combining these two data sets allows me to separately calculate
14 The year used in this paper refers to the school year, so this data spans the 1999-2000 school year to the 20112012 school year.
15 As shown in Table A.11 in the Appendix, the 63 counties included in the analytic sample are quite representative
of the entire state. The districts in the analytic sample have slightly larger enrollments and spend slightly more per
student, but are nearly identical on all of the other covariates of interest.

9

the yearly tax revenue collected for operating and capital expenditures.
Renewal of existing taxation and implementation of new taxation is subject to voter approval.
Thus, I obtain data from the Ohio Secretary of State on school tax election outcomes for all property and income tax referenda from 2004-2012. The information collected includes the proposed
tax rate, the proposed dollar amount of the debt issuance (if a bond referenda), the number of yes
and no votes, the duration of the proposed tax, and the purpose of the tax.
Finally, housing sales data are collected from individual Ohio county auditors. These data
include the location of the property, the date of sale, the sale price, numerous characteristics of the
home, and the tax district in which the property resides.16 The data from these various sources
are linked to each parcel using the associated tax district. To ease the constraints in collecting
the housing transaction data, the sample is restricted to include only single-family homes with
sale prices that exceed $10,000. The analytic sample contains 1,011,726 parcel sales with all the
relevant parcel characteristics. For a full description of the data sets used in this analysis and an
explanation of the relevant variables see Appendix Table A.10.

1.4
1.4.1

Descriptive Statistics
School District Expenditures and Revenues

Tables A.2 and A.3 provide means and standard deviations for the school district financial and
demographic characteristics, broken down by the various stages of fiscal stress. Panel A provides
descriptive statistics for the 509 districts that never receive a fiscal stress label during the time
period examined in this study. Panel B provides descriptive statistics for the 80 labeled districts
that are observed both prior to receiving the label (Pre-Fiscal Stress) and during the time the label
is applied to the district (Fiscal Stress). Panel C provides the descriptive statistics for the 72 labeled
districts that are observed both during the time period the label is applied to the district and after
16 A tax district corresponds to a unique county-township-city-school combination. Within a school district there
may be a number of different tax districts. This means that the taxes faced by residents within a given school district
may vary depending on which tax district the resident resides.

10

the label is removed (Post-Fiscal Stress). While Panel A is mutually exclusive from panels B and
C, districts for which the whole fiscal stress duration is observed are found in both panels B and C.
Districts that never receive a label are smaller, less likely to reside in urban areas, have better
school report card grades, and have better financial situations than districts that are labeled. In the
pre-fiscal stress period, 35 percent of labeled districts have general fund deficits that are greater
than two percent of revenue, compared with only six percent of districts that never receive a label.
Districts that are never labeled also collect nearly $1,000 more per pupil in local revenue than
districts that are eventually labeled. In addition, as observed in Table A.2, enrollment is falling in
these labeled districts following receipt of the label.
Figure A.3 depicts yearly average expenditures and revenues per pupil for operating and capital
for each year relative to label receipt.17 In panel (a), operating expenditures per pupil in labeled
districts are rising more quickly than non-labeled districts18 prior to label receipt. Immediately
following label receipt, operating expenditures per pupil for labeled districts fall from about $9,250
to $9,075, after which labeled and non-labeled districts have nearly the same levels of operating
expenditures. The difference in trend between labeled and non-labeled districts is more noticeable
when examining capital expenditures. As observed in panel (b) of Figure A.3, capital expenditures
per pupil for districts that are never labeled is relatively constant over time, around an average of
$1,500. Conversely, capital expenditures for labeled districts fall from an average of $2,000 per
pupil two years prior to label receipt to around $900 per pupil during the year of label receipt
and fluctuates around that level in subsequent years. Districts also appear to alleviate these deficits
through increases in local operating property tax revenue. As observed in panel (c), labeled districts

17 Since the composition of districts may change (i.e. not observing years prior for districts receiving label prior to
2000 and not observing years post for districts receiving labels later in the time span of interest), I also generate these
figures using the same districts observed over the entire duration that I calculate these means. The results obtained
from these figures are largely unchanged when the composition of districts is kept constant.
18 Yearly means are calculated for non-labeled districts so that each labeled district observation is compared to the
non-labeled districts in the same year. I then calculate means for the variables of interest in each year relative to label
receipt for both the labeled districts observed in that time period and the yearly mean for the non-labeled districts
associated with those labeled district observations.

11

receive around $3,400 per pupil in operating revenue prior to label receipt, which is nearly $700
to $800 per pupil less than is received by districts that are never labeled. Following label receipt,
operating tax revenue per pupil received by labeled districts increases substantially, before leveling
off at around $4,000 per pupil three years after label receipt. Districts also are shifting away from
taxes for capital projects, as evidenced in panel (d) although this seems to be more of a steady
decline than a sharp change after the label is received.
Following successful financial recovery, as shown in Panel C of Table A.3, the general fund
balances, total expenditures, and total revenues of labeled districts are very similar to those of
districts that never receive a label. The only substantial difference between recovered districts and
those that are never labeled is in capital expenditures, where successfully recovered districts spend
$845 per pupil on capital compared with $1,482 for districts that never receive a label.19
1.4.2

Residential Home Sales

Table A.4 provides means and standard deviations for the characteristics of residential home
sales, again broken down by the various stages of fiscal stress. Examining Panels A and B of
Table A.4, homes in districts that never receive a label sell for an average of $147,171 while
homes sold in the pre-fiscal stress period in labeled districts sell for an average of $139,979. The
homes sold in districts that never receive a label also tend to be slightly larger, with living areas
averaging 1,704 square feet compared with 1,587 square feet in homes sold in pre-fiscal stress
labeled districts. The sale price of housing in labeled districts falls from an average of $139,979
to $133,267 following the receipt of the label. Given that the average characteristics of the homes
sold are nearly identical between the pre-fiscal stress and fiscal stress periods, this reduction in sale
prices is likely not attributable to changes in the composition of sold homes. Following the removal
19 Although much of this difference in capital expenditures can be attributed to the sharp drop in capital expenditures
following label receipt in panel (b) of Figure A.4, some may be attributed to funding received from the Ohio School
Facilities Commission (OSFC). Created in 1997, the OSFC has funded capital projects in over 300 school districts,
starting with the lowest wealth districts. Since 2000, 43 fiscal stress districts have been eligible to receive funding
through the program, while 217 non-labeled districts have become eligible.

12

of the label, the average sale price in labeled districts falls from $140,687 to $130,080, but again
the average characteristics of the homes sold during these two periods are very similar. In many
districts, however, a majority of the post-fiscal stress period occurs during the Great Recession, so
some aspects of the post-housing bubble may be causing these much lower sale prices during the
post-fiscal stress period.

1.5
1.5.1

Empirical Specification and Results
Difference-in-Differences Results

Districts receiving a fiscal stress label are required by the state to implement financial recovery
plans that achieve balanced budgets. The descriptive analysis provided in Table A.3 and Figure A.3
suggests that these recovery plans eliminate expenditures on capital projects and increase local tax
revenue for operating expenditures. However, the conclusions of this descriptive analysis may be
driven by other factors (e.g. size of general fund deficits, enrollment, regional economic trends,
etc.). Thus, to analyze the impact of transitioning from one fiscal stress state to another, I estimate
the following specification:

ln(ydt ) = α +β1 postFOdt +β2 postFE dt +β3 endFOdt +β4 endFE dt +γXdt +φ Ddt +λd +θt +εst
(1.1)
where ln(ydt ) is the natural log of a per-pupil expenditure or revenue variable for school district
d in year t; Xdt is a vector including the general fund balance to revenue ratio and indicators for
whether a district falls within one of the ratio cutoff values; Ddt is a vector of other time-varying
district characteristics; λd is a vector of school district fixed effects and θt is a vector of year fixed
effects; and εdt is an idiosyncratic error.
The main variables of interest are the four fiscal stress indicators for the various transitions into
and out of these labels. The postFOdt variable is an indicator for the time period following the
receipt of a fiscal oversight label, which identifies the effect of initial label receipt on school district

13

financial behavior. The postFE dt variable is an indicator for the time period following the receipt
of a fiscal emergency label, which identifies the differential effect of transitioning from district-led
recovery to state-led recovery.20 Given that changes to finances are likely to be different during
district-led recovery than changes resulting from state-developed recovery plans, we might expect
β2 = 0. For districts that complete financial recovery under fiscal oversight, the endFOdt variable
is an indicator for the time period following removal of the fiscal oversight label and identifies
the differential effect of transitioning from fiscal oversight to no label. Similarly, for districts that
complete financial recovery under fiscal emergency, the endFE dt variable is an indicator for the
time period following removal of the fiscal emergency label, identifying the differential effect of
transitioning from fiscal emergency to no label.
Table A.5 provides results of equation (1) when the specification considers per-pupil expenditure variables. Across each of the expenditure types, I find statistically significant reductions in the
period following initial label receipt (i.e. no label to fiscal oversight). As observed in column 1,
total expenditures per-pupil are 9.6 percent lower in districts following receipt of fiscal oversight
than non-labeled districts with the same general fund balance to revenue ratio. Total operating
expenditures per-pupil (column 2) are 3.7 percent lower in fiscal oversight districts than operating
expenditures in similar non-labeled districts. Expenditures on salaries (column 3) are 5.4 percent
lower following fiscal oversight and continue to decline by 2.9 after receipt of fiscal emergency.
Expenditures on employee benefits (column 4) are 2.6 percent lower in fiscal oversight districts
than in non-labeled districts with the same general fund balance to revenue ratio. In addition,
employee benefits fall by an additional 5.5 percent following the removal of the fiscal emergency
label, suggesting that employee contracts renegotiated during the commission’s recovery plan may
have large effects on employee benefits even after the financial recovery has been completed. These

20 Since nearly all of the fiscal emergency districts in the 2000-2010 time period were initially placed in fiscal
oversight, this indicator identifies the differential effect of being downgraded into fiscal emergency. As observed in
Table A.1, four districts transition immediately from no label to fiscal emergency. The choice of whether to include
these districts in the postFE variable makes little difference to the overall results and therefore are included.

14

long run effects on benefits may suggest that these districts may be able to renegotiate contracts at
lower rates during financial recovery, with these contracts remaining in effect well after recovery
is complete.
Fiscal oversight districts also make substantial reductions to capital expenditures. As observed
in columns 5 and 6 of Table A.5, total capital expenditures per pupil are 55.8 percent lower and per
pupil expenditures on new construction are 73.3 percent lower following receipt of fiscal oversight
compared to non-labeled districts with the same general fund balance to revenue ratio. I do not find,
however, any significant differential effects on capital expenditures following fiscal emergency
receipt or after removal of these labels. The larger percentage changes in capital expenditures
may suggest that capital projects are relatively easier for districts to eliminate or districts may
be eliminating capital projects at higher rates in order to minimize the reductions in operating
expenditures.
Table A.6 provides results of equation (1) when the specification considers revenue variables.
Although I find no statistically significant increases or reductions in total revenue (column 1) following label receipt, I find a 8.9 percent reduction in total revenue following the removal of the
fiscal emergency label, largely due to reductions of 7.5 to 8.1 percent in local, state, and federal
revenue. This drop in revenue following removal of fiscal emergency may suggest that districts do
not require as much revenue after successful completion of financial recovery. In addition, federal
revenue per pupil is 5.3 percent lower in fiscal oversight districts.21
Changes in local revenue in these districts are driven primarily by changes local property tax
revenue, as districts shift their tax mix away from taxes funding capital projects and towards taxes
that generate operating revenue that can be used to offset deficits. Local property tax revenue per
pupil increases by 4.9 percent following receipt of fiscal oversight compared to non-labeled districts with the same general fund balance to revenue ratio. While I find no statistically significant
21 These reductions in federal revenue come from reductions in Title I revenue, IDEA revenue, and non-specified
federal aid. Results of various federal sources are available upon request. These results suggest transitory changes in
federal aid, especially for districts in urban and low-income communities may have a large impact on district budgets.

15

differential change in local revenue per pupil following fiscal emergency receipt, the point estimate
suggests about a 6.7 percent increase in total local property tax revenue per pupil following fiscal
emergency. This increase in local property tax revenue, the sum of revenue collected for operating
and capital, is largely driven by additional property taxation to fund operating expenditures.22 As
observed in column 6, local property tax revenue for operating expenditures increases by 6.5 percent following fiscal oversight and an additional 9.2 percent following receipt of fiscal emergency.
While I find no statistically significant changes in property tax revenue for capital expenditures,
the point estimates suggest that capital property tax revenue is falling substantially in these districts. Given that operating revenue can be used to offset deficits while capital revenue is largely
earmarked for the specific capital project, it is not surprising that districts in fiscal stress would
shift their tax mix towards operating revenue and away from revenue for capital projects.
These changes to revenues and expenditures may positively or negatively impact housing prices
depending on the trade off between the reductions in the tax-services bundle these districts offer
residents and the increases in the financial viability of these fiscally stressed districts following
successful recovery. These labels may also provide a signal that the district is of lower quality,
which would likely be reflected in lower sale prices. Although Table A.4 suggested that home
prices fall following label receipt, these descriptive statistics do not account for changes in prices
due to the Great Recession and the collapse of the housing market, which severely impacted home
prices in Ohio. While the average characteristics of homes do not appear to change across different
fiscal stress time periods, controlling for the characteristics of individual homes will lead to more
reliable estimates of the effect of these labels on housing prices. Therefore, to better understand
how these labels may be impacting the housing market, consider a stylized hedonic model of the

22 Districts in Ohio can also use income taxes to fund operating expenditures. I find no statistically significant
effects on income tax revenue, a result that is not all that surprising given that many of the districts generating income
tax revenue are in rural areas of Ohio. As shown in Figure A.1, a majority of the labeled districts come from the areas
surrounding urban areas. In fact, of the 111 districts that have received at least one of these labels only 28 districts
implement an income tax.

16

differential effect of these labels on house prices:

ln(Pid jt ) = α +β1 FOdt +β2 FE dt +β3 endFOdt +β4 endFE dt +γZid jt +ωXdt +λd +φ j +θt +εid jt
(1.2)
where ln(Pid jt ) represents the natural log of the sale price of parcel i in school district d and
municipality/township23 j at month-year t; Zid jt is a vector of observable housing and parcel characteristics (e.g. number of rooms, number of bedrooms, number of bathrooms, indicators for the
amount of acreage24 , and the square footage of the home’s living area); Xdt is a vector of observable district-level financial characteristics (e.g. the general fund balance to revenue ratio, which is
one of the primary selection variables used by the Auditor when deciding to apply a fiscal stress
label, and the various eligibility cutoff points); λd is a vector of school district fixed effects; φ j is
a set of county fixed effects; θt is a set of month-by-year fixed effects; and εid jt is an idiosyncratic
error.
Table A.7 presents the results of the various specifications of equation (2). When I include
district and month-by-year fixed effects (column 1), I find that home prices fall by 5.6 percent
following the receipt of fiscal emergency,25 but find no statistically significant effects following
receipt of fiscal oversight. I also find that housing prices rise by 7.1 percent following the removal
of the fiscal emergency label, suggesting that the end of the state takeover may be sending a positive
signal about the quality of the district. This is in contrast to the statistically insignificant 6.5 percent
drop in home prices following successful recovery during fiscal oversight. The point estimates
of these removal variables suggest that districts may end up in a better financial position when
23 Parcels that lie within incorporated areas are linked to a given city or village j. Parcels in unincorporated areas
are linked to a given township j.
24 Intervals of acreage are used instead of total acreage due to the fact that actual acreage is missing for a large
percentage of the sample. In sensitivity checks, total acreage was used in place of these intervals and the general
results remained the same, although the power was reduced greatly due to the reduction in the sample size.
25 The magnitude of this effect is slightly below that of the 6.1 percent reduction in sale prices resulting from a
below average school report card grade, a traditional measure of overall academic quality. These school report card
grades are a rating that is based on student performance on standardized tests and other state accountability measures.
See Figlio and Lucas (2004) for more information on these report card grades.

17

recovery is undertaken by the state instead of the district. This may also suggest that the large cuts
in expenditures undertaken during fiscal oversight may have long-lasting effects on educational
services and academic quality in these districts, which would likely be capitalized into lowered
housing valuations after recovery is complete.
As suggested in Figure A.1, regional factors may influence district financial troubles, so controlling for county-level effects may account for region-specific factors that are influencing district
revenues and costs. Including county fixed effects (column 2) to the analysis yields nearly identical
results to those without the inclusion of these fixed effects. Including a county-by-year fixed effect
(column 3) to capture yearly economic changes across different parts of the state, yields similar
results although the point estimate is no longer statistically significant for the transition from fiscal
oversight to fiscal emergency. Even when including the county-by-year fixed effects, I continue to
find a 6.6 percent increase in the sale price following the removal of fiscal emergency.
1.5.2

Event Study Results

To account for the possibility that districts may be changing their behavior prior to receiving
the label, which would bias the above results, I also use a flexible event study framework. This
model also allows me to examine how soon after label receipt these recovery plans take effect
and for how long the effects of these recovery plans persist. If financially recovered districts are
maintaining balanced budgets in the future, at least some of these changes are expected to persist
over many years. To perform this analysis, I estimate the following model:
9

ln(ydt ) = α +

∑

βk FSdtk + γXdt + φ Ddt + λ d + θt + εdt

(1.3)

k=−6

where FSdtk is an indicator for k years before or after initial label receipt, with k = 0 signifying
the year of label receipt. Note that since I only observe outcomes starting in 2000, the FSdtk
indicators with k < 0 will be identified primarily off of districts that receive labels later in the

18

panel.26 Figures 4-8 depict the estimates of βk from equation (3) for enrollment, total expenditures
per pupil for capital and operating, an total local property tax revenue per pupil collected for capital
and operating. In each figure the black line represents the point estimates of the β coefficients for
each year relative to label receipt dummy variable and the grey shaded region represents the 95%
confidence interval from the standard errors clustered at the school district level.27
Since I examine per-pupil revenues and expenditures, changes in enrollment in these labeled
districts as a response to these labels will influence the changes observed in per-pupil revenues and
expenditures. Therefore, I first estimate equation (3) using district enrollment as the dependent
variable, with the results presented graphically in Figure A.4. Although I find no statistically
significant changes in district enrollments prior to initial label receipt, I find around a seven percent
reduction in enrollment within the first two years after label receipt, with enrollment continuing
to decline upwards of seven years after label receipt. These results suggest that parents may be
responding negatively to these labels and may be moving out of the district or sending their kids via
open enrollment to nearby, non-fiscally stressed districts. In addition, fewer people may be moving
into these financially troubled districts and/or fewer open enrollment children may choose districts
in fiscal stress. Given this large drop in district enrollment following label receipt, the increases in
local property tax revenue per pupil found estimating equation (1) are likely to overstated, while
the reductions in per-pupil expenditures are likely to be understated.
Reductions in per-pupil operating and capital expenditures occur immediately after label receipt, with reductions in per-pupil operating expenditures persisting much longer than reductions
26 Given that not all districts receive these labels at the same time, the β are identified off of a potentially different
k
set of labeled school districts, which may cause the estimates to be biased if there are unobserved heterogenous
treatment effects. To test for this bias, I first estimate equation (3) separately for only those districts for which I
observe outcomes for the year of label receipt. As the year of label receipt is observed for 87 districts out of the 102
that received a label between 2000-2010, restricting the estimation to this subset of the data yields results that are
qualitatively and quantitatively similar to those using all of the data. I also estimate equation (3) using a balanced
panel of school districts that I observe in all years. Although the results are similar to those using the unbalanced
panel, the standard errors become much larger due to the reductions in the sample size.
27 To ease interpretation of the coefficients, I drop the fiscal stress indicator for k = −1 (i.e. year prior to label
receipt). Thus the βk coefficients identify treatment effects relative to the effect for the year prior to label receipt. The
figures signify that this zero is imposed, by including a zero point estimate without an associated confidence interval.

19

in per-pupil capital expenditures. Figures 5 and 6 graphically depict results from equation (3) using
total operating or total capital expenditures per-pupil variables as dependent variables. Transitory
spikes are observed in both capital and operating expenditures per-pupil two or three years prior
to label receipt. These spikes could lead to label receipt if these rises in expenditures increase the
five-year forecast projections. In addition, there appear to be some marginally statistically significant reductions in per-pupil expenditures occurring the year prior to label receipt. These reductions
likely result from districts responding to earlier state interventions (see Sections 2.2 and 5.3 for a
greater discussion of these interventions). I find that total operating expenditures per-pupil (Figure
A.5) fall by 0.8 percent in the year before label receipt, while total capital expenditures per-pupil
(Figure A.6) fall by nearly 10 percent.
Even after the reductions made in the year prior, labeled districts continue to reduce per-pupil
expenditures in the years following label receipt. Total operating expenditures per-pupil fall by 5.4
percent in the year following label receipt, with reductions of between 3 and 5 percent persisting
upwards of nine years after label receipt. Reductions in per-pupil capital expenditures are much
more transitory, with statistically significant reductions occurring only in the first few years after
label receipt. Total capital expenditures per pupil fall by 75 percent in the first couple years after
label receipt compared to non-labeled districts with the same general fund balance to revenue ratio.
Despite the lack of statistical significance in later years, the point estimates suggest that about a
30 percent reduction in capital expenditures per-pupil remains as far out as eight years after initial
label receipt. This large reduction in capital expenditures in the first few years of fiscal stress
suggests that capital expenditures may be relatively easier to adjust and/or districts may eliminate
large capital projects at higher rates in an attempt to minimize cuts to operating expenditures. These
results are consistent with the results found in the earlier difference-in-differences analysis, where
reductions in capital expenditures were much larger than those made to operating expenditures.
Using local property tax revenue and millage rates as dependent variables in equation (2), the
results of which are depicted in Figure A.7, I find that districts are increasing local property tax

20

revenue funding greater operating expenditures immediately after label receipt. Labeled districts
experience a reduction in property tax rates for both capital and operating in the years leading up
to label receipt, suggesting that reductions in tax rates may lead to budget deficits in these districts.
Unsurprisingly, there are no statistically significant changes to local tax revenue in the year prior
to label receipt, as districts that pass new property or income taxes likely avoid receiving the label
all together. In addition, many districts do not have adequate time to raise new taxes in order to
avoid a label after being flagged by the ODE for deficits in the five-year forecast.
Following label receipt, per-pupil property tax revenue collected for operating expenses increases, while tax revenue funding capital expenditures falls. Operating property tax revenue perpupil, shown in Panel (a), rises by 9.8 percent in the first two years after label receipt. Although
operating property tax revenue per pupil begins to decline in the third year after label receipt, I still
observe a 5.7 to 8.6 percent increase relative to the year prior to label receipt that persists upwards
of nine years after initial label receipt. Property tax revenue for capital expenditures, depicted in
Panel (c), falls by 6 percent in the year of label receipt, but this reduction becomes statistically insignificant between the year after label receipt and five years after label receipt. These changes in
property tax revenues are largely driven by changes in the millage rates levied in these districts.28
Examining Panel (b), the millage rate for operating taxes increases by nearly 1.75 mills in the first
few years after label receipt. The millage rate begins to fall two or more years after initial label
receipt, but significant effects persist as far as six years after label receipt. There are no statistically
significant changes in the millage rate for capital projects, as shown in Panel (d), following label
receipt.

28 Millage rates increase primarily due to the frequency at which tax referenda are placed on the ballot and the
frequency at which these referenda are approved by voters. Districts propose and pass more tax referenda funding
operating expenditures after receiving one of these labels, with the largest increase in the number of referenda approved
occurring under fiscal emergency. In order to focus more heavily on increasing taxes for operating expenditures,
districts appear to shift away from new proposals for capital projects. Following label receipt, districts propose fewer
capital projects to voters, an effect that persists as far as five years after label receipt. While omitted here, results of
this analysis are available upon request.

21

To assess how quickly housing prices respond to these labels, I estimate the following model:
9

ln(Pid jt ) = α +

∑

βk FSdtk + γZid jt + ωXdt + λd + φ j + θt + εid jt

(1.4)

k=−6

The results of this analysis are presented in Figure A.8. In the year prior to label receipt housing
prices fall by 3.4 percent in labeled districts relative to non-labeled districts. This drop in housing
prices may be a response to residents observing the district’s five year forecast and capitalizing
the label receipt into valuations before it is received or residents may be capitalizing some of the
reductions we see in expenditures occurring in the year before label receipt. The point estimates,
although statistically insignificant, suggest housing prices continue to fall following label receipt,
declining by a total of 4.7 percent in the six years following label receipt.
There are two main explanations for the drop in housing prices. First, these labels may signal
negative information to residents and potential homebuyers about the financial health of the district,
lowering the perceived quality of the district. This helps explain the difference-in-differences
finding that residents respond more strongly to fiscal emergency labels. This suggested that a
stronger signal may be sent by the fiscal emergency label compared to the fiscal oversight label
due to the uncertainty surrounding the state takeover. The second explanation for the drop in
housing prices is that prices may capitalize the changes in district expenditures and revenues made
in response to the recovery plans associated with these labels. This helps explain the drop observed
in housing prices in the year before the label, as districts are making reductions to expenditures but
residents have not yet been informed about the district receiving a label.
1.5.3

Regression Discontinuity Results

While these changes to district finances and housing prices in the year before label receipt
may suggest that districts and homebuyers are anticipating label receipt, it is likely that these
changes are a result of the state intervention districts receive prior to label receipt. Recall from
Section 2.2 that districts with projected deficits exceeding two percent of general fund revenue in
22

the second or third projected years are subject to state intervention. Although these interventions
are not as stringent as those associated with the label, districts with deficits in the second or third
projected years do have the opportunity to work with state financial consultants to help solve
their financial problems before fiscal labels become necessary. To assess the effect of these early
interventions, I collect five-year financial forecasts of projected deficits from 2001-2012. Given
that all districts with projected deficits exceeding two percent of revenue in any of the first three
projected years receive some level of state intervention, I use a regression discontinuity design
comparing districts just above and below this two percent deficit to revenue ratio cutoff to estimate
the effect of receiving the state intervention on district finances and housing prices.
As with any regression discontinuity design, manipulation of the cutoff is a primary concern
regarding the validity of the design. Figure A.9 depicts the density of the projected general fund
balance to revenue ratio for each of the first three projected years. Of the 7,872 district years in
the sample, only 74 and 489 district-years are observed falling below the two percent cutoff in
projected year 1 (Panel a) and projected year 2 (Panel b), respectively. While these large discontinuities exist in the density at the two percent cutoff in the first two projected years, there does
not appear to be a noticeable discontinuity in the density at the cutoff in the projected year 3 ratio
(Panel c). The differences in these densities is likely due to differences in the incentive to manipulate the cutoff, which is based on the relative benefits and costs of manipulation. The benefit of
manipulation is the avoidance of the sanction associated with failing to meet the given two percent
deficit cutoff, while the main costs are the costs of reducing expenditures and/or increasing taxes
or the probability of detection if districts manipulate the assumptions of the forecast to avoid the
sanction.29 While the costs are likely to be the same regardless of the projected year used, the
benefit grows as the the deficit gets closer to being realized. The benefit of avoidance is higher in

29 As discussed previously in section 2.2, districts submit these five year forecasts and may manipulate the projections of revenues and/or expenditures in order to show a positive fund balance. While districts have much more
discretion over the projections for expenditures (e.g. projecting smaller increase in salary and/or other operating costs),
they may also exaggerate projected property value growth to increase projected property tax revenue.

23

projected year 1 than projected year 3 because the severity of the projected year 1 intervention (i.e.
label receipt) is more severe than the projected year 3 sanction (i.e. notified of deficit and given
assistance from fiscal consultant). In addition, some districts may want to fall below the cutoff in
projected year 3, in order to qualify for the assistance from the state.
While the endogenous sorting around the cutoff makes use of the year 1 and year 2 projected
ratio problematic in an RD design, the year 3 ratio provides a viable option for use in this type of
design. Although the density of year 3 projected ratio is continuous,30 the validity of the design
can also be called into question if districts on either side of the cutoff differ across other covariates.
To test this, I create bins of size 0.02 and run a regression of yearly changes in school district
characteristics to observe whether there are statistically significant differences in these covariates
on either side of the cutoff. The estimated discontinuities at the cutoff are reported in Table A.8,
but I find little evidence of endogenous sorting around the cutoff along these dimensions.
To get a better sense of how school districts are reacting to these early interventions, I examine
expenditures and tax revenues for districts just above and below the two percent general fund
deficit to revenue ratio from the year 3 projection. It is important to note that because I am using
the year 3 projection, I am examining how current expenditures and revenues are influenced by
deficits that are two years away from being realized. However, districts that fall below this cutoff
in year t need to make any changes in expenditures or revenues in year t or t+1 to avoid the year 2
sanction in year t+1 and the fiscal stress label in year t+2. Thus, it is expected that districts below
the cutoff will have yearly changes in expenditures and revenues that are different than the changes
of districts above this cutoff.
Figure A.10, which fits a local polynomial to the data on either side of the cutoff, suggests that
districts below this cutoff do behave differently between year t and year t+1 than districts above
the cutoff. In panel (a), we observe a change in operating expenditures per pupil for districts just

30 When applying the McCrary test to this data (McCrary 2008), I find a log difference in the density at the two
percent cutoff of -0.002, which suggests that there is no noticeable discontinuity in the density at the cutoff.

24

below the cutoff that is nearly $130 per pupil less than the change in operating expenditures for
districts just above the cutoff. There is a smaller, $50 discontinuity at the cutoff in terms of capital
expenditures per pupil (panel b). In addition to drops in expenditures, we observe a change in
operating tax revenue for districts just below the cutoff that is nearly $75 per pupil more than the
change in operating expenditures for districts just above the cutoff (panel c). Districts with larger
deficits (i.e. moving father left away from the cutoff), make much larger reductions in both capital
and operating expenditures than those at the cutoff.
I also examine whether homebuyers are capitalizing these financial changes into housing prices.
As depicted in panel (d), the change in the average district housing price between year t and year
t+1 is nearly $200 lower in districts just below the cutoff than those just above. But as the deficit
grows (i.e. as the ratio gets more negative), the reduction in the average district sale price falls
substantially, This may indicate that homebuyers are responding more strongly to observing large
drops in per-pupil capital and operating expenditures than to the small financial changes made by
districts near the cutoff.
To estimate the effect of these early interventions on school district expenditures, local property tax revenues, and housing prices, I estimate the following equation for districts that did not
currently have a label in year t:

∆Yid,t+τ = α + 1[ratio3t < −0.02]t β + f (ratio3t , γ) + ∆Xd,t+τ δ + εid,t+τ

(1.5)

where ∆Yid,t+τ represents yearly changes in expenditures per pupil, operating property tax revenue
per pupil, or the average sale price31 in school district d in year t + τ (τ = 0, 1); ∆Xd,t+τ is a
vector of changes in district and/or parcel controls; and εid,t+τ is an idiosyncratic error. The main
parameter of interest, β identifies the discontinuity in the outcomes around the two percent cutoff
31 To create this variable, I aggregate the parcel level housing transaction data to the school district level. This gives
the average price of all sold homes in the district in year t. I also create yearly averages of the parcel characteristics of
these sold homes to use as controls.

25

in the third projected year general fund balance to revenue ratio (ratio3). Districts that have year 3
projected deficits in year t are likely to make changes to expenditures and revenues during either
year t or t+1 in order to avoid additional sanctions in year t+1 and t+2.
Table A.9 reports estimates obtained from the above specification. Districts that are just below
the two percent deficit to revenue cutoff in year t do not differentially decrease operating expenditures per pupil (Panel A) compared to districts just above the cutoff between year t-1 and year t.
However, the change in operating expenditures per pupil between year t and year t+1 is $195 lower
for districts just below the cutoff, possibly as districts make a more concerted effort to avoid label
receipt in year t+2. I find no statistically significant differences in the yearly changes in capital
expenditures (Panel B) or operating property tax revenues (Panel C) for districts just below the
cutoff. As these deficits grow (i.e. as the projected year 3 ratio becomes more negative), however,
districts make much larger reductions to operating expenditures, reduce capital expenditures, and
increase local property taxes to fund operating expenditures, as evidenced by the coefficients on
the projected year 3 ratio variable. These results are very similar to what was observed in the
year before label receipt in the event study results. Recall from Section 3.2, where districts that
received a label were found to slightly reduce operating and capital expenditures in the year prior
to label receipt. Given that a majority of labeled districts have projected year 3 deficits that are
much larger than two percent of revenue,32 taking the event study and regression discontinuity
results together suggests that the changes in the year prior to label receipt are likely a response to
the early intervention program. The lack of a significant increase in local property taxes for labeled
districts in the year before label receipt (see Figure A.7), suggests that these labeled districts are
likely districts that tried to offset deficits through increasing local taxes, but failed to secure voter
approval.
Although districts just below the cutoff are making small cuts to per-pupil expenditures, hous-

32 Of the 99 labeled districts during the panel, 89 districts had projected deficits greater than eight percent of revenue
and 63 had projected deficits greater than fifteen percent of revenue.

26

ing prices in these districts appear to increase by about $2,000 between year t and t+1. This
may suggest that these small cuts in expenditures are more than offset by the positive benefits of
maintaining financial viability and avoiding further financial intervention. While homebuyers are
responding positively to expenditure changes in districts near the cutoff, they appear to react negatively to the larger financial changes observed for districts farther away from the cutoff. Although
housing prices are not very responsive to the projected ratio in general, as evidenced by the lack
of statistical significance on the year three projected ratio variable, they are responsive to large
deficits. When interacting the ratio with the indicator for whether the ratio is below the cutoff, we
see as the ratio gets more negative the housing price falls substantially. Again since a majority of
the districts receiving these labels have ratios that are well away from the cutoff, these results are
similar to the nearly three percent reduction in housing prices in the year before label receipt found
in the event study results. The similarity of the event study and regression discontinuity results
suggests that much of the drop in housing prices in labeled districts, at least in the year before the
label is received, is attributable to the changes in district finances and not likely due to foresight
into label receipt.

1.6

Conclusion

This paper examines the effects of Ohio fiscal stress labeling system on school district financial behavior and housing prices from 2000-2012. I find statistically significant changes in school
district finances in response to the mandated recovery plans associated with these labels. Districts
increase taxes for operating in conjunction with cuts in expenditures. Labeled districts reduce both
operating and capital expenditures, with the largest percentage cuts undertaken in capital expenditures. I also find that home prices fall following the receipt of a fiscal emergency label, but find
no statistically significant effects following fiscal oversight. This suggests that homebuyers are responding more strongly to the uncertainty surrounding the state takeover or what the state takeover
means for future academic quality. In addition to these labels, districts appear responsive to earlier

27

state interventions that help districts alleviate financial issues before labels become necessary.
To further inform states considering these types of policies, additional evidence is needed on
the effect these policies have on students and teachers in these districts. Given the housing price
results, these state financial takeovers may be sending a negative signal to residents. If parents
think the district is of lower quality, they may use open enrollment policies to switch their children
into more financially stable districts or move out of the district catchment area. The enrollment
results suggest that these districts are losing students following the receipt of these labels. If these
students are high-achieving, their exodus from the district could have negative effects on their
former peers (i.e. loss of a positive peer effect) and losses of many high-achieving students could
severely impact whether districts meet certain NCLB targets.
In addition, the number of full-time equivalent teachers is falling in districts following the receipt of these labels. While some of this reduction may be attributable to layoffs made in conjunction with these recovery plans, likely some of this reduction is due to teachers fleeing financiallytroubled school districts. If a majority of these are high-quality teachers, overall teacher quality in
these districts may be falling after label receipt and given the wide teacher value-added literature
we would expect a decline in teacher quality to negatively impact student test scores. In addition
to changes to student and teacher compositions, expansive cuts to programs in order to meet the
requirements of financial recovery may lower the quality of educational services offered by these
labeled districts, in turn lowering student achievement. Although the housing price results hint that
educational quality may have been reduced, future work will need to more carefully assess how
these financial recoveries are impacting students and educational quality in these districts.
While this policy has changed the financial behavior of financially troubled school districts in
Ohio, how districts respond to these policies in other states is likely to depend on the structure
of the state funding system. Given the institutional structures in place in Ohio, primarily that
districts can raise local operating tax revenue, districts appear to respond as one would expect –
increasing local taxes and making expenditure reductions to solve these budgetary issues. Districts

28

in other institutional settings, especially those in which local operating tax revenue is restricted,
may respond differently and focus more heavily on the expenditure cuts. As these intervention
systems also apply to local governments in many states, the effects of these systems on local
government financial behavior is also of interest. One might expect that residents may respond
more strongly to interventions into local governments than school districts, as the average resident
is more likely to use public services offered by local governments than school districts. Thus,
this study pushes future work to analyze the effects of financial intervention systems in other
institutional settings.

29

CHAPTER 2
MICHIGAN AND OHIO K-12 EDUCATIONAL FINANCING SYSTEMS: EQUALITY
AND EFFICIENCY

2.1

Introduction

In the current financial climate, reductions in property values and poor state fiscal conditions
have led to budgetary issues for local school districts. How districts choose to respond to these
financial pressures depends on the level of state funding and the different types of local taxes available to school districts. Districts that receive greater state aid will likely be sensitive to reductions
in state budgets, while districts with greater ability to raise revenue locally may respond to declining state and local economic conditions through the use of voter approved tax referenda.1 In
addition, districts with the ability to tax income may be better able to respond to declines in property values by switching their tax mix away from property taxation and towards greater income
taxation. Districts that are restricted from collecting local tax revenue for operating expenditures
may use other avenues, such as expenditure cuts and alternative revenue sources, to alleviate these
financial pressures.2 The feasibility of these other avenues will clearly depend on the wealth of
the districts. Preventing districts from generating local tax revenue for operating expenditures, but
not imposing these restrictions on capital expenditures, may also affect how districts allocate resources across capital and operating (i.e., labor and materials) expenditures. Therefore, in addition
to equality considerations, these restrictions may also have efficiency implications.
Much of the previous literature on equality in school funding has focused on law changes, usu1 Dye and Reschovsky (2008) find that local school districts increased property taxes by 37 cents for every dollar
lost in state aid.
2 Reschovsky (2004) argues that funding constraints limit the ability of districts to respond to reductions in state
aid and reductions in taxable values, exacerbating the financial problems facing these districts. Evidence from California suggests that these types of restrictions are often circumvented by increases in non-restricted revenue and
non-traditional funding sources, such as private donations (Brunner and Sonstalie, 2003; Brunner and Imazeki, 2005;
Hoane, 2004).

30

ally as a result of court rulings. As expected, these studies largely find that inequality in revenues
and expenditures is reduced as a result of these court-mandated reforms.3 Instead of focusing on
law changes, we consider how different funding systems impact inequality.4 We assess the degree of inequality in per pupil revenue and expenditures across districts under two distinct funding
systems – a state-level system (i.e. minimal local control) in Michigan and a foundation system
(i.e. greater local control) in Ohio.5 Both states use different mechanisms to adjust for inequality resulting from differences in tax base size. Michigan keeps state aid roughly the same for all
districts regardless of tax base size, but attempts to minimize inequality in revenue by restricting
the collection of local revenue to fund operating expenditures for general education students. The
Michigan system does allow residents to vote for property tax millages that finance capital projects
and expenditures on special and vocational education. Ohio allows districts to raise unrestricted
funds for operating expenditures through local property and income taxes, but accounts for the
large inequality this creates by giving a disproportionately large amount of state aid to districts
with the smallest tax bases. This paper assesses whether the degree of inequality in revenues and
expenditures varies across these two states. We also examine whether the allocation of resources
between capital and operating expenditures varies across the different funding systems.
Section II provides an overview of the Michigan and Ohio K-12 education financing systems.
Section III first describes the data and contains descriptive statistics on tax rates, taxable values
and district demographics. It then contains a comparison across different revenue sources and
whether this varies across districts based on property values per pupil. Finally, Section III compares
expenditures across districts and discusses whether the composition of these expenditures varies
3 Murray, Evans, and Schwab (1998) and Corcoran et al. (2004) find that inequality was reduced by 19 to 34
percent follow these reforms, relative to non-reform states. Also, see Springer, Liu, and Guthrie (2009), Roy (2011),
and Berry (2007). For a larger review of the state role on equity and adequacy, see Corcoran and Evans chapter in the
Handbook of Research in Education Finance and Policy (2008).
4 For an overview of different state aid formulas, see Loeb (2001), Hoxby (2001), Fernandez and Rogerson (2003),
and Yinger (2004).
5 Theoretical work by Fernandez and Rogerson (2003) suggests that the foundation system dominates the statelevel system in terms of total welfare.

31

across the states. Section IV concludes.

2.2

Institutional Details

The Michigan and Ohio K-12 education financing systems are quite complicated and differ
along several significant dimensions. Perhaps the most important difference is the restriction on
local tax revenue collection for operating expenditures in Michigan. This section provides an
overview of the Michigan and Ohio funding systems and discusses the differences and similarities
of the two systems.
2.2.1

Michigan K-12 Finance

In response to high property taxes and an unequal distribution of school funding across districts,
the Michigan K-12 finance system changed dramatically with the implementation of Proposal A
in 1996. Proposal A changed the power equalization finance system to a state level system and
reduced the funding obtained from local property taxes while increasing the funding from state
income and sales taxes. School districts with a millage rate over 18 in fiscal year 1993 had their
millage rate reduced to 18 and the new law stipulated that districts only impose this millage on
non-homestead properties.6,7 In addition to this non-homestead millage, the state allowed 32 of
the highest-spending school districts to levy a “hold harmless” millage. The state also imposed
a state level property tax of six mills along with increases in the sales, tobacco product, and real
estate transfer taxes. Proceeds from these taxes are deposited in the Michigan School Aid Fund
and distributed to the school districts through a per-pupil grant. This grant varies depending on
which school district the student resides, but does not depend on the amount of local property
taxes collected. The amount of the per-pupil grant is the difference between the amount of local
revenue that would be collected if the non-homestead millage is at its cap, usually 18 mills, and
6 Homestead properties are primary resident homes while non-homestead properties are mainly businesses and
rental properties.
7 Only 13 of the 552 school districts imposed a millage of less than 18 in fiscal year 1993. For these districts, the
non-homestead millage is capped at the 1993 rate.

32

the amount required to achieve the school district’s per-pupil grant allocation. The funds from the
grant are deposited into the school district’s general fund to pay for labor, material, utilities and
maintenance costs. Along with property tax millages to finance capital projects, local school districts can propose a “sinking fund” property tax millage, the revenues of which fund certain capital
expenditures and repairs.8 Local school districts can also generate funds using voter-approved
referenda for a recreational millage, which provide revenue for the operation of public recreation
facilities and playgrounds.
Each of the 552 local school districts in Michigan belongs to one of 57 intermediate school
districts (ISDs) that provide special and vocational education. Funding of ISDs did not appreciably
change due to Proposal A and a significant portion of ISD funding comes from local property taxes.
The variation across ISDs in regards to property tax revenue results in vastly different services
being offered across the ISDs. Some of these services are offered directly by the ISD, while
others are provided by the local school districts using ISD funds. An ISD can levy three types of
property tax millage: operational, special education and vocational education. Voters must pass
a referendum to change any of these millage rates and there are caps associated with all three
tax millages.9 The amount of revenue that is passed on to the local school districts varies across
ISDs.10 Along with these property taxes, voters may approve referenda for enhancement millages,
the proceeds of which are distributed by the ISD to their local school districts on a per student
basis.11
There have been a few post-2002 changes to the Michigan K-12 education financing system.
One noteworthy change occurred in 2008, when industrial personal property was exempted from
8 The maximum sinking fund millage is five mills for twenty years.
9 The operating millage rate cannot exceed 1.5 times the number of mills allocated to the ISD in 1993. The special
education millage rate cannot exceed 1.75 times the number of mills allocated to the ISD in 1993. The vocational
education millage rate is capped at 1 mill for those ISDs that did not levy this tax in 1993 and is capped at 1.5 times
the number of mills allocated to the ISD in 1993 for all other ISDs.
10 The majority of ISDs base the distribution of the revenue from the special education millage on the difference
between the special education costs of the district and the amount received in state aid. Other ISDs base the distribution
on average cost measures and the number of special education students.
11 The maximum enhancement millage is three mills for twenty years.

33

both the non-homestead property tax millage (which is usually 18 mills) and the state level property tax of six mills. During the same time commercial personal property was exempted from 12 of
the 18 non-homestead property tax mills.12 Since 2002, the number of students attending charter
schools has increased substantially in Michigan. Charter schools are operated as nonprofit corporations that, like public schools, are provided with the state per pupil foundation allowance but are
prohibited from levying taxes which results in capital expenses being paid for by the foundation
allowance or independent contributions.
2.2.2

Ohio K-12 Finance

The 613 public school districts and 49 joint vocational school districts13 in Ohio are primarily
funded through state aid and local property or income taxation. The role of the state in financing
education is to ensure that each district receives the necessary funds to provide an “adequate”
level of educational services to the students of the district. To do this, the state first determines
the amount of per pupil expenditures that are necessary to achieve this adequate education level.14
School districts are required to raise at least 20 mills of property tax revenue in order to cover some
(or all) of this adequacy amount. Currently, the state calculates the local share of the adequacy
amount by assuming school districts levy 23 mills of property taxes.15 After netting out this local
“charge-off,” the state provides districts with the remaining revenue needed to achieve the adequacy
amount.
Ohio school districts also have the option to supplement state aid through additional property
12 Personal property is tangible assets of a business such as computers, machinery and equipment. Real property
refers to land and buildings.
13 These vocational schools span one or more counties within the state. They provide vocational training to students
from public school districts within the counties the vocational school operates. High school students from these public
school districts can opt to pursue this vocational training in place of a traditional public high school education, if
accepted into the vocational program.
14 For documentation on the adequacy formula, see the Ohio Legislative Service Commission “School Funding
Complete Resource.” (http://www.lsc.state.oh.us/schoolfunding/edufeb2011.pdf)
15 There are a few districts that impose less than 23 mills. The state supplements these districts with enough funds
to meet the revenue that would have been received had the district levied 23 mills. This additional state supplement is
called gap aid.

34

and income taxation, subject to voter approval. Districts are able to tax both real and tangible personal property.16 Similar to Michigan, districts can issue debt through bonds for capital projects
and improvements to classroom facilities. In addition to debt issuances, permanent improvement
property tax levies fund short-term, at most five year, capital improvements. In contrast to Michigan, Ohio districts also have the option to propose additional taxes financing operating expenditures. Revenue for operating expenditures is generated through either current expense millages
or emergency operating levies. These current expense taxes can either be property or income
taxes that raise revenue over a period of five or more years.17 Emergency operating taxes collect
a district-specified amount of revenue for a period of, at most, five years. In addition to taxes
approved by voters, each district is allocated a set amount of property tax millage that is levied
without voter approval. Districts primarily allocate the revenue from this “inside millage” towards
either current expenses or permanent improvements.
There have been a few significant policy changes since 2002 that have changed the way schools
are funded. In 2010, Ohio adopted an evidence-based funding formula that determined the adequacy amount based on the number and type of staff needed to provide a basic level of education. This funding formula also changed how the local share of funding is calculated. Prior to
2010, the local “charge-off” was calculated using recognized valuation.18 Starting in 2010, the
local “charge-off” for districts at the 20-mill floor was calculated using total valuation, while the
charge-off of all other districts continued to be calculated using recognized valuation. Beginning
16 There are two classes of real property in Ohio: class I includes all real residential and agricultural property and
class II includes all real commercial, industrial, mineral, and railroad property.
17 Prior to 2006, Ohio school districts could levy income taxes on the traditional income tax base (adjusted gross
income net personal and dependent exemptions). After 2006, districts were given the option of only taxing the earned
income of residents. This earned income is not subject to personal and dependent exemptions.
18 Recognized valuation spreads out the inflationary increase in real property from reappraisal over three years to
prevent the state share of funding to fluctuate greatly from one year to the next. Thus, the recognized valuation of a
district in the year of reappraisal is the total valuation - (2/3)*Inflationary Increase. A year after reappraisal, recognized
valuation becomes the total valuation - (1/3)*Inflationary Increase. Two years after reappraisal, recognized valuation
is equal to total valuation. Also, since the school fiscal year runs from July to June and the tax year runs from January
to December, valuation from two years prior is used in the calculation of the local charge-off. For example, valuation
from 2008 is used in the calculation for the 2009-2010 school year.

35

in 2006, Ohio gradually phased out taxation on business tangible personal property, with the state
providing districts with funds to offset the loss in revenue resulting from this phase out.
2.2.3

Similarities Between Ohio and Michigan Financing Systems

There are several similarities between the two school funding systems. Michigan and Ohio
both have school choice programs, which allow students to attend a school district even if they
do not reside in that district. The state provides the attending district with additional funds to
educate these students. For school districts that have capacity and elect to enroll students residing
outside the district boundaries, Michigan requires the district to hold a lottery to determine which
students are able to attend - with preference given to students with siblings who are already school
of choice students in the district. Unlike Michigan, school districts in Ohio do not hold lotteries to
determine which students are able to attend via open enrollment. Instead, the school superintendent
determines which students are allowed to enroll in the school district when the number of open
enrollment applications exceeds the number of slots available. School districts in Ohio also have
the option to limit what students are eligible to enroll in the district through open enrollment.19
Another similarity is that both states have legislation that restricts the growth of local property
taxes. The 1978 Headlee Amendment in Michigan requires that property tax rates be decreased
(i.e. “rolled back”) if the growth in assessed values, excluding new construction and improvements,
exceeds the growth in inflation. County, municipality, intermediate school district and school
district property tax rates are “rolled back” so that the same amount of property taxes, in real
terms, are collected from the old base.20 For parcels that do not transfer ownership, Proposal A
also restricts the growth of individual parcel property assessments to the lesser of the inflation
rate and five percent. For parcels that do transfer ownership, the taxable values are assessed at 50
percent of the true cash value. Ownership transfers usually result in a significant increase in the
19 Currently, 431 Ohio school districts allow any student from the state to apply for open enrollment. Of the
remaining districts, 62 only accept students from adjacent districts and 120 have no open enrollment policy in place.
20 Millage used to retire debt, along with the 6 mill state level property tax, are not subject to these Headlee roll
backs.

36

amount of property tax paid on these properties. Residents can “override” these Headlee rollbacks
by voting on referenda that returns the tax rate back to its prior level or by voting on renewal
specifying the prior tax rates.21
In Ohio, property taxes for current expenses (provided total current expense millage is greater
than 20 mills), classroom facilities and permanent improvements are subject to property tax rollbacks. Bonds, emergency operating levies, and all inside millage are exempt from these property
tax rollbacks. All real property (both class I and class II) is assessed at 35 percent of true value.
Tangible personal property is assessed at a rate between 23 percent and 100 percent of true value.
Similar to Michigan, these property tax rollbacks require that class I and class II property tax rates
be reduced in proportion to the increase in assessed values. Tangible personal property is exempt
from these rollbacks. Since changes in assessed valuation of class I and class II property differ,
the rollback factor is different for both classes of real property. Therefore, often class I and class
II real property are taxed at different rates, while tangible personal property is taxed at the voted
millage rate.

2.3
2.3.1

Data and Descriptive Statistics
Data

We obtained school district specific variables from the National Center for Education Statistics
(Local Education Agency Finance Survey and Common Core of Data), the Michigan Department
of Education, the Ohio Department of Education, the Michigan Department of Treasury, and the
Ohio Department of Taxation. Detailed information on school district revenues and expenditures
is obtained from the Local Education Agency Finance Survey. These data consist of annual school
district information from 2002 through 2010.22 These data include information on total revenues,
21 Many districts pass referenda stipulating a “maximum” non-homestead property tax millage of over 18. While
the districts are restricted to only levy 18 mills, passing this type of referenda allows a district facing a Headlee rollback
to maintain an 18 millage rate without voting on another referendum.
22 Year corresponds to the school fiscal year from July 1st to June 30th. Thus, we analyze data from the 2001-2002
school year to the 2009-2010 school year.

37

total federal revenues, total state revenues, total local revenues, and total expenditures. These data
also include a measure of total enrollment in the district, which we supplement with data on the
number of general education and special education students from the Ohio and Michigan Departments of Education. School district demographic data are obtained from the NCES Common Core
of Data and the Small Area Income and Poverty Estimates. These data include the number of free
and reduced priced lunch students, enrollments broken down by race, number of schools in the
district, and the number of school-aged children in poverty.
We also collect annual tax rates and taxable property valuations from the Michigan Department
of Treasury and the Ohio Department of Taxation. The tax information provides all the taxes levied
in each year from 2002 through 2010 and includes information for whether the tax funds operating
or capital expenditures. We then aggregate these tax rates at the district level, which provides
us with a total district tax rate to fund operating expenditures and a total tax rate to fund capital
expenditures. We then multiply these two aggregate tax rates by the total taxable value in the
district for each year, which gives an estimate of the total local property tax revenue collected to
fund operating and capital expenditures. We also obtain a measure of the level of income taxes
collected by Ohio districts for operating expenditures from the Local Education Agency Finance
Survey.
2.3.2

Descriptive Statistics

Table B.1 contains the average school district property tax rates for Michigan and Ohio along
with taxable value information. There are interesting differences to note across the states. While
both the local school districts and the intermediate school districts in Michigan collect property
taxes, the local school districts in Ohio have a much higher overall millage rate from which to
generate unrestricted operating revenue. This is due to the fact that Michigan imposes a dollar
for dollar “tax” on revenue generated from the non-homestead millage and, therefore, this nonhomestead revenue should be and is considered state revenue in our analysis. For Ohio, the local

38

revenue generated to cover the adequacy amount defined by the state is considered local revenue.
While we do not have district level information on these adequacy amounts, for most Ohio districts,
especially the relatively wealthy districts, we expect that the current tax rates more than cover the
adequacy amount and a nominal change in the tax rates will not change the revenue obtained from
the state. Table B.1 also indicates that the taxable values, on which these local property taxes
are imposed, are greater for Michigan. Since the average number of students in a school district is
2,774 for Michigan and 2,870 for Ohio (Table B.2), the taxable value difference between Michigan
and Ohio is not the result of Ohio having larger school districts. Taxable values differ across the
two states because Ohio properties are assessed at only 35 percent of true value compared with a
50 percent assessment rate in Michigan; resulting in the taxable value per pupil being over twice
as large in Michigan.
Table B.2 indicates that, along with slightly larger enrollments, Ohio school districts have
slightly greater total expenditures and total revenue on average than Michigan.23 This results in
almost identical total expenditures per student and total revenue per student, on average, for the
two states. Total revenue is slightly greater in Ohio than Michigan because while Ohio districts
average $8.3 million (23.1-14.8) less in state revenue, they average $10.6 million (16.8-6.22) more
in local revenue than Michigan. Local revenue is comprised primarily of local property and income
taxes but there are other sources of local revenue including school lunch receipts, student activity
receipts, student fees and transfers from other school districts.24 Greater local tax revenue by Ohio
districts is expected because the larger overall millage rates more than offset the lower taxable val-

23 Using the Consumer Price Index, dollar figures in all tables and figures have been converted into 2010 dollars.
24 Excluding local property and income tax revenue, Ohio districts average $2.7 million annually from other local
revenue sources while Michigan districts average $3.0 million annually. This includes revenue from other school
districts (primarily payments associated with school choice programs and transfers from the ISDs), which average
$1.4 million and $0.4 million annually for Michigan and Ohio districts, respectively. While we include these transfers
from other school districts as local revenue, it may be more appropriate to classify some as state revenue.

39

ues.25,26 This greater local tax revenue collection in Ohio is mainly attributable to Ohio’s current
expense millage and is not appreciably affected by local income tax revenue, which averages only
$400,000 annually for Ohio school districts.
While Ohio generates more local revenue for operating expenses, Michigan generates significantly more for capital expenditures. The reason the taxation for capital expenditures differ so
dramatically is in part due to the Ohio School Facilities Commission (OSFC). The OSFC is a state
agency that provided funds for capital expenditures (e.g. school building construction and renovations) to the school districts. Besides the number of special education students and number of Title
I schools, the averages of the other school district demographic characteristics are similar across
the states.27 While the difference in the number of Title I schools is surprising, the fewer number
of special education students in Michigan local school districts is partly attributable to the fact
that many Michigan special education students attend schools operated by the intermediate school
districts.28
2.3.2.1

School District Revenue

Figures B.1 through B.6 present yearly student enrollment and per pupil revenue from different
sources across different quintiles based on average annual taxable property values per pupil. To
compare the inequality in these various revenue sources, separate graphs are provided for Michigan
25 The local taxes collected as reported by the districts in the Local Education Agency Finance Survey are less than
the amounts calculated using the millage rates and taxable value information. Part of this difference is attributable to
the fact that when we use the millage rates and taxable value information from the Michigan Department of Treasury
and the Ohio Department of Taxation, we do not take into account the various tax exemptions received by some
property owners nor delinquent payments.
26 It is important to note that the difference in local revenue per pupil would be less if the non-homestead millage
in Michigan was considered local revenue or if the local revenue generated by Ohio districts to achieve the adequacy
amount was considered state revenue.
27 It should be noted that the number of free and reduced lunch students is not available for Ohio in 2008, but
removing this variable from our regressions does very little to change the main conclusions. In addition, the median
income by school district is available in the 2000 U.S. Census and 5-year estimates are available from the Census for
all Ohio, and almost all Michigan school districts from 2005-2009, 2006-2010 and 2007-2011. We construct annual
median income by district by interpolating this information.
28 In addition, the structure of special education financing in Ohio provides districts more incentive to classify a
student as special education relative to Michigan.

40

and Ohio.29,30 Figure B.1 depicts how total enrollment in the different quintiles changes across
years. It is interesting to note that the poorer and poorest quintiles are the smaller, more rural,
school districts. While all Michigan quintiles saw an enrollment decrease between five and ten
percent, enrollment of the wealthier and wealthiest quintiles in Ohio remained stable across the
years while the others, especially the median quintile, experienced a significant decline.31 Figure
B.2 presents total revenue per pupil obtained from the Local Education Agency Finance Survey.
While the more wealthy quintiles in Michigan have greater total revenue per pupil than the other
quintiles, this relationship does not hold for Ohio. The Ohio quintile with the highest average total
revenue per pupil in 2010 is the median quintile. The dramatic increase in this quintile across years
is in part attributable to its 14 percent drop in enrollment, as depicted in Figure B.1. Also note that
in 2002, all Michigan quintiles, besides the poorest, had greater total revenue per pupil than their
corresponding Ohio quintiles. By 2010, Ohio districts in all quintiles had total revenue per pupil
that exceeded their corresponding Michigan quintiles. This is the result of total revenue per pupil
declining for all Michigan quintiles from 2002 to 2010, while total revenue per pupil for Ohio
quintiles has increased over the period. For several Michigan quintiles, the largest decrease in total
revenue per pupil occurred in the last year or last several years of our data when the United States
experienced a significant recession. Interestingly, total revenue per pupil for most Ohio quintiles
increased during this Great Recession, suggesting that perhaps Ohio districts are better able to
respond to economic downturns because of their ability to generate local revenue for operating
expenditures. Thus, the structure of the state school financing system may greatly influence how
economic downturns impact school districts.
29 The wealthiest quintile are the 20 percent of school districts with the largest taxable values per pupil, wealthier
quintile are the districts from 20 percent to 40 percent, median quintile are the districts from 40 percent to 60 percent,
poorer quintile are the districts from 60 percent to 80 percent, and poorest quintile are the 20 percent of school districts
with the smallest taxable values per pupil.
30 The quintiles are based on the average annual taxable property values per pupil so that a district remains in a
given quintile across all years. To ensure that the composition of each quintile does not change across years, the seven
districts with at least one year of missing information are dropped (48 district-year observations).
31 Because Detroit and other districts around Detroit are dropped due to missing at least one year of data, the actual
decline in enrollment for the poorest Michigan quintile is likely larger than depicted in Figure B.1.

41

As demonstrated in panel (a) of Figure B.3, Michigan’s slight decrease in total revenue per
pupil is primarily attributable to a decrease in state revenue. Given that Michigan restricts how
much revenue can be raised locally to fund operating expenditures, it is not unexpected that Michigan districts usually receive more in state revenue per pupil than comparable Ohio districts. Interestingly, Michigan distributes state revenue relatively evenly across school districts, but districts
in the wealthiest quintile receive nearly $600 more in state revenue per pupil than districts in the
other quintiles. This distribution of state aid, which is provided irrespective of district wealth, is
consistent with what would be expected given the framework of the Michigan funding laws, which
targets inequality by restricting collection of local property taxes. In contrast, Ohio attempts to
address inequality by allocating significantly more state revenue to less wealthy districts. Districts
in the wealthiest quintile in Ohio receive between $3,000 and $5,800 less state revenue per pupil
than districts in the poorest quintile, but this difference has decreased across years.
Unlike Ohio, which addresses inequality through disproportionate state aid to the poorest districts, Michigan addresses inequality by placing restrictions on the use of local property taxes for
operating expenditures. These restrictions explain the large differences in local revenue we observe in Figure B.4 between Ohio and Michigan districts in all taxable value quintiles. Michigan
districts obtain approximately two and a half times less local revenue than similar districts in Ohio.
Due to unrestricted property and income taxation at the local level in Ohio, the gap in local revenue between the richest and poorest districts is much larger in Ohio than in Michigan. While the
wealthiest Michigan school districts raise approximately $2,000 per pupil more in local revenue
than the poorest districts, the wealthiest districts in Ohio raise $5,000 more per pupil than the poorest districts. This disparity between the top and bottom is so large in Ohio that even though the
state gives disproportionately more state revenue to the relatively poor districts it is not enough to
offset this $5,000 per pupil gap.
In addition to the disparity in total local revenue, the restrictions placed on taxes for operating
expenditures in Michigan may result in different mixes of taxes for capital and operating expen-

42

ditures across the two states. Figure B.5 focuses strictly on local operating tax revenue, which
is generated exclusively through property taxes in Michigan, while Ohio districts generate local
operating revenue through property and income taxes. The minimal local property tax revenue
collected by Michigan districts for operating expenditures is obtained primarily from the hold
harmless millage of wealthy districts and the special education millage of the intermediate school
districts. In contrast to Michigan, a significant portion of local revenue in Ohio is generated from
local taxes and almost all is unrestricted, as state revenue is often used towards funding special
education. As expected based on Figure B.4, the amount of local operating tax revenue generated
is greater in the relatively wealthy districts and significantly greater in the wealthiest districts. In
Ohio, a relatively small fraction of local operating revenue is from income taxes but use of these
taxes has increased since 2006 – especially in poorer, agricultural districts that have low taxable
value bases, but relatively higher taxable income bases.32
As state revenue has decreased and local revenue for operating expenditures has largely remained constant from 2002 to 2010, property tax revenue for capital expenditures has increased
in Michigan. As depicted in Figure B.6, the Michigan quintiles increased property tax revenue for
capital expenditures by between $200 and $300 per pupil, with the largest increase occurring in the
wealthiest quintile. Ohio districts in all quintiles collect less tax revenue for capital expenditures
than districts in the corresponding Michigan quintiles. For the median, poorer, and poorest quintiles, this difference is partly attributable to the Ohio School Facilities Commission (OSFC), which
designated $7 billion for capital expenditures to, primarily, the relatively poor school districts between 2002 and 2010.33 The OSFC made these capital funds available to the least wealthy districts
32 As found in Spry (2005) and Hall and Ross (2010), a majority of districts using these income taxes are districts in
rural areas. Ross and Nguyen-Hoang (2013) show that Ohio districts use the income tax as a supplement to property
taxation.
33 The decision to use a significant portion of the tobacco settlement funds to subsidize school capital investments
was, in part, a response to a General Accounting Office report entitled “School Facilities: Profiles of School Condition
by State.” The 1996 report summarized results from a national survey of school buildings and concluded that the
physical condition of school buildings in Ohio was worse than the school building condition in, if not all, almost all
other states. For example, the report indicates that 61 percent of the 3,600 Ohio schools surveyed indicate at least one
on-site building in inadequate condition compared to only 34 percent for the 3,325 Michigan schools surveyed.

43

first by ranking the districts based on a weighted average of taxable value per pupil and median
income.34 This capital expenditure subsidy from the OSFC is likely to have crowded out some
capital expenditures by the school districts. Interestingly, the wealthier and wealthiest quintiles
in Ohio, mainly comprised of school districts that did not have access to these OSFC funds, also
obtain significantly less tax revenue for capital expenditures than comparably wealthy Michigan
school districts. Perhaps these wealthy Ohio districts preferred to have local tax revenue fund operating expenditures rather than capital expenditures. Because of the constraints Proposal A places
on raising local operating revenue, the wealthy Michigan districts do not have this choice.
Although the above figures give some sense of the inequality of revenue in both states, these
figures do not account for differences in district size and demographics that may contribute to
differences in revenue across the two states. To better account for these other factors we estimate
the following regression equation:

ln(yst ) = β0 ln(TaxableValuest ) + Xst β + λs + θt + εst

(2.1)

where ln(yst ) is the natural log of either total revenue, state revenue, or local revenue of district s
in year t; ln(TaxableValuest ) is the total taxable value for the district in year t; Xst is a vector of
school district demographics that includes median income, total and special education enrollment
counts, the number of white students, the number of students eligible for free/reduced priced lunch,
the total number of schools and Title I schools, total district population and total school-aged
population in poverty; λs is a vector of school district fixed effects; θt is a vector of year fixed
34 The OSFC began offering funds to the most needy school districts in 1997 and by 2010 funds had worked up to
the 450th spot in the rankings. The state has contributed a certain percentage of the capital funds and this percentage
depends on the district rankings with poorer districts having lower rankings receiving a greater percentage. For most
districts, the state’s percent contribution is one minus the ranking list percentile. For example, a district ranked 61
out of the 613 school districts would be at the tenth percentile and the state contribution would be 90 percent of the
total project cost. Most districts raise their share by passing a referendum that generates property taxes so that the
district can sell bonds. A few districts use existing property taxes, cash on hand and voluntary contributions to raise
the local share. In recent years especially, many districts chose not to pursue the available funding or were unable to
pass referenda to fund the district’s portion of the costs.

44

effects; and εst is an idiosyncratic error term. Tables B.3 and B.4 contain estimates when school
district fixed effects are not and are included in the specification, respectively.
The estimates from the specification without fixed effects uses primarily across school district
variation to identify the relationship between taxable value and revenue. These estimates in Table
B.3 suggest that a ten percent increase in total taxable value is associated with approximately a
1.3 percent increase in total revenue for both states, while a ten percent increase in median income
is associated with a 2.12 percent increase in total revenue for Michigan and a negligible change
for Ohio. When median income is not included as a covariate, the coefficient on taxable value
when total revenue is the dependent variable increases to 0.146 for Michigan and to 0.139 for
Ohio. As expected based on the graphs in Figure B.3, the coefficient estimates associated with
taxable value indicate that state revenue is larger in Michigan districts with greater taxable values.
In Ohio, however, state revenue is significantly less in high taxable value school districts compared
to low taxable value districts, since the state funding laws give these low taxable value districts
disproportionately more state aid. In terms of local revenue, the coefficient estimates indicate that
low taxable value districts obtain less in local revenue than high taxable value districts and this
difference is greater in Ohio. The results in Table B.3, along with the greater variance in taxable
value and median income for Michigan (see Tables B.1 and B.2), suggest that there is greater
inequality in Michigan than in Ohio.
The estimates from the fixed effects specifications in Table B.4 use within-school district,
across-year variation to identify the relationship between changes in taxable value and changes
in revenue. These estimates indicate that an increase in taxable value is associated with a significant increase in state, local and total revenues for Michigan school districts. For Ohio school
districts, an increase in taxable value is associated with an increase in local revenue, a decrease in
state revenue, and a slight increase in total revenue. Table B.4 also suggests that changes in median
income are associated with relatively small increases in revenue for Michigan school districts and

45

a negligible change in revenue for Ohio districts.35
The graphs in Figures B.2 and B.3 suggest that total and state revenues decreased for Michigan
and increased for Ohio school districts during the Great Recession. It is also interesting to consider
how this recession affected taxable values, inequality and the relationship between taxable value
and revenue. Due in part to differences in assessment procedures, Ohio’s assessed values started
to decrease in 2007 (affecting school district’s 2007-8 taxable values) while Michigan did not
experience this decline in taxable values until the 2009-10 school year (denoted as year 2010). The
taxable value per pupil decreased less than taxable values in both states because of the decline in the
number of students. However, the variance of the taxable value per pupil in both states was much
larger after 2007 compared to the prior years. In addition, based on the estimates in Table B.5, the
relationship between total taxable value and revenue does appear to change slightly as the result
of the Great Recession. Table B.5 estimates similar specifications as in Tables B.3 and B.4 except
an interaction term, ln(Total Taxable Value) * Great Recession indicator, is included as a covariate
to allow for the relationship between taxable value and revenue from 2002 to 2007 to differ from
this relationship from 2008 to 2010. The coefficient estimates associated with this interaction
term indicate that the positive relationships between taxable value and total/state revenues are
stronger during the Great Recession for Michigan school districts but not for Ohio school districts.
While these positive coefficient estimates are statistically significant in the Michigan regressions,
the magnitudes suggest a relatively small increase in these positive relationships during the Great
Recession.
The results in Tables B.3 and B.4 suggest that the Ohio funding system leads to more equitable
funding than the Michigan system. Targeting equality through disproportionate state aid to the
poorest districts appears to be more effective at promoting equality than imposing constraints on
what local revenue can be used to fund. A problem with the Michigan system is that even with
35 Because median income is not available annually by district (requiring us to interpolate when constructing these
annual measures - see footnote 27), the coefficient estimates pertaining to median income should be viewed with
caution when using within-district, across-year variation for identification.

46

constraints that limit how much local revenue can be used for operating expenditures, local revenue
is greater in high taxable value districts and does not offset the fact that state aid is not targeted to
relatively poor districts. These constraints may also hinder the ability of Michigan school districts
to react to economic downturns, exacerbating this inequality. While wealthy districts in Michigan
may be able to counteract these downturns with funding from other local sources, the relatively
poor districts in Michigan do not get much funding from other sources, making them the least able
to respond to these downturns. The Table B.5 results suggest that the inequality in Michigan may
be growing during the Great Recession. Another problem is that these constraints could lead to
inefficiencies in terms of how local school districts allocate resources between capital, labor and
materials.
2.3.2.2

School District Expenditures

Figure B.7 demonstrates that the pattern in total expenditures per pupil is quite similar to total
revenue per pupil both in terms of level and across quintiles. As with total revenue per pupil,
total expenditures per pupil on average are similar across the states with expenditures in Michigan
decreasing slightly across years while increasing in Ohio. Also similar to total revenue per pupil,
Michigan’s decrease in total expenditure per pupil was more prevalent during the Great Recession
while Ohio districts experienced an increase during this time period. The main difference in per
pupil revenue and expenditures is that there are a number of quintile-years where total expenditures
per pupil are slightly greater than total revenue per pupil. This is most often the case for the more
wealthy quintiles in the earlier years of our data. Perhaps more wealthy Ohio and Michigan districts
were able to draw on reserve funds to supplement expenditure beyond what they raise in yearly
revenue and that these reserve funds were less available in later years.
Figure B.7 does not provide details on the composition of these expenditures – specifically
capital versus operating. How capital expenditures of Ohio school districts compare to those in
Michigan school districts depends on whether the comparison is between relatively poor or rela-

47

tively wealthy districts. Defining relatively poor districts in Ohio as those below the median OSFC
ranking and in Michigan as below the median taxable value per pupil, the average annual capital
expenditure per pupil is $1,922 in the relatively poor Ohio districts and $999 in the relatively poor
Michigan districts. Interestingly, over half of these Ohio expenditures are state funds distributed
by the OSFC. In terms of the relatively wealthy districts (i.e. districts above the medians), annual
capital expenditures per pupil are $1,027 for Ohio and $1,321 for Michigan.36 Not only do Michigan’s relatively wealthy districts spend 29 percent more in capital expenditures per pupil, over ten
percent of the capital expenditures made by Ohio’s relatively wealthy districts are state funds from
the OSFC.37
In terms of operating expenditures, there are difficulties in making a comparison because the
structure of special and vocational education, along with input prices, differs across Ohio and
Michigan. However, it is interesting to note that the student-teacher ratio in Ohio averaged 16.88
from 2002 to 2010 while averaging 18.64 in Michigan.38 In summary, these descriptive statistics
suggest that while Michigan districts spend more per pupil on capital expenditures than Ohio districts not eligible for state capital funds, Ohio districts spend a larger fraction on teachers. The
constraints on Michigan districts that limit how much local revenue can be raised to pay for operating expenditures may result in an inefficient resource allocation between capital, labor and
materials.
36 A possible explanation for these greater apparent capital expenditures is that wealthy Michigan districts may
be able to circumvent the Proposal A restrictions on supplementing operating expenditures by classifying some ambiguous expenditures as capital. While wealthy Michigan districts do attempt to circumvent these restrictions, this
is unlikely the reason for the significant difference in capital expenditures as well as capital taxation. As for capital
expenditures, over 72 percent is accounted for by new construction in both Ohio and Michigan. It is likely difficult
to supplement operating expenditures with expenditures on new construction. Expenditures on new construction is 28
percent more per pupil in relatively wealthy Michigan districts than in relatively wealthy Ohio districts. As for capital
taxation, we include classroom facility millages in Ohio as capital taxation while it is clear that much of this revenue
would be classified as operating expenditures in Michigan districts. If Michigan districts are circumventing Proposal
A, including Ohio tax revenue from classroom facility millages as capital revenue in Figures B.5 and B.6 should make
the comparison across states more comparable.
37 Stone (2014) documents the dramatic increase in capital spending by Michigan school districts immediately after
the implementation of Proposal A and how this increase was larger for wealthier school districts.
38 Even after adjusting for possible differences in special education expenditures by local school districts, the
student-teacher ratio is significantly higher in Michigan than in Ohio.

48

2.4

Conclusion

This paper considers equality and efficiency issues of two different school funding systems
- a state-level system and a foundation system. The state-level system in Michigan provides all
districts with nearly the same amount of state revenue for general operating expenditures and places
restrictions on the ability of districts to raise operating revenue through local property taxes. Most
notably, Michigan districts have restrictions on raising additional property tax revenue to fund
operating expenditure for general education students but do not have these restrictions on capital
expenditures. In contrast, Ohio districts are able to raise unrestricted property and income taxes to
fund operating and capital expenditures. To account for the large differences in local tax revenue
generated by poor versus wealthy districts, Ohio allocates state aid based on the district tax base
size.
Our results indicate that, while the average revenue per pupil and expenditure per pupil of
Michigan and Ohio school districts are almost identical between 2002 and 2010, they have slightly
decreased over this period for Michigan and increased for Ohio. We also find that Michigan districts receive a significantly larger proportion of total revenue from the state while Ohio districts
receive a larger proportion from local property and income taxes. In terms of degree of equality,
measured by how revenue and expenditures vary across districts based on taxable value per pupil,
there is less variation across Ohio districts. This suggests that the Ohio funding system leads to
greater equality than the Michigan funding system. In terms of the distribution of expenditures, we
find that wealthy Michigan districts spend more per pupil on capital expenditures while wealthy
Ohio districts spend more per pupil on labor and materials. This suggests that the constraints on
raising local revenue to fund operating expenditures in Michigan could create efficiency issues.
Despite Ohio and Michigan spending similar amounts per pupil on average from 2002 to 2010,
there are noticeable differences in student achievement on the National Assessment of Educational
Progress (NAEP) 2003, 2005, 2007 and 2009 math and reading exams (Source: http://nces.ed.gov/
nationsreportcard/states/). Ohio performs better on these exams than Michigan irrespective of
49

grade and year.39 Across all states, Ohio most often ranks between 12 and 18 in exam performance
while Michigan most often ranks between 30 and 37. Perhaps the efficiency issues associated with
the Michigan school funding system are contributing to the difference in student performance
across the states. Ohio not only outperforms Michigan on these NAEP exams, but the difference
in performance has increased across years. While Ohio’s ranking has slightly improved from
2003 and 2009 for almost all grades and subjects, Michigan’s ranking has steadily declined across
years. Perhaps the reductions in revenue and expenditures have contributed to the decline in student
performance in Michigan.

39 The NAEP math and reading exams in Michigan and Ohio are taken by fourth and eighth graders.

50

CHAPTER 3
AN EVALUATION OF EMPIRICAL BAYES’ ESTIMATION OF VALUE-ADDED
TEACHER PERFORMANCE

3.1

Introduction

Empirical Bayes’ (EB) estimation of teacher effects has gained recent popularity in the valueadded research community (see, for example, McCaffrey et al. 2004; Kane & Staiger 2008; Chetty,
Friedman, & Rockoff 2011; Corcoran, Jennings, & Beveridge 2011; and Jacob & Lefgren 2005,
2008). Researchers motivate the use of EB estimation as a way to decrease classification error
of teachers, especially when limited data is available to compute value-added estimates. When
there are only a small number of students per teacher, teacher value-added estimates can be very
noisy. EB estimates of teacher value-added reduce the variability of the estimates by shrinking
them toward the average estimated teacher effect in the sample and, therefore, are often referred to
as “shrinkage estimators.” As the degree of shrinkage depends on class size, estimates for teachers
with smaller class sizes are more affected, potentially helping with the misclassification of these
teachers. EB estimation may also be less computationally demanding than methods that view the
teacher effects as fixed parameters to estimate. Finally, EB estimation has been motivated as a way
to estimate teacher value added when including controls for peer effects and other classroom-level
covariates.
This paper analyzes the performance of EB estimation using both simulated and real student
achievement data. We first provide a detailed theoretical derivation of the EB estimator, which
has not previously been explicitly derived in the teacher value-added literature. This theoretical
discussion also provides the basis for our hypotheses for how EB and other value-added estimators are expected to perform under the different simulation scenarios we examine. We test our
theoretical predictions by comparing the performance of EB estimators to estimators that treat the

51

teacher effect as fixed. We first use a simulation, where the true teacher effect is known, comparing
performance under random teacher assignment and various nonrandom assignment simulation scenarios. In addition to the random vs. fixed teacher effects comparison, we also examine whether
shrinking the estimates improves performance. Finally, we apply these estimators to real student
achievement data to see how the rankings of teachers vary across these estimators in practice.
Despite the potential benefits of EB estimation, we find that the estimated teacher effects can
suffer from severe bias under nonrandom teacher assignment. By treating the teacher effects as
random, EB estimation assumes that teacher assignment is uncorrelated with factors that predict
student achievement – including observed factors such as past test scores. While the bias (technically, the inconsistency) disappears as the number of students per teacher increases – because
the EB estimates converges to the so-called fixed effects estimates – the bias still can be important
for the kinds of data used to estimate teacher VAMs. This is because the EB estimators of the
coefficients on the covariates in the model are inconsistent for fixed class sizes as the number of
classrooms grows. By contrast, estimators that include the teacher assignment indicators along
with the covariates in a multiple regression analysis are consistent (as the number of classrooms
grows) for the coefficients on the covariates. This generally leads to less bias in the estimated
teacher VAMs under nonrandom assignment without many students per teacher.
The paper begins in Section 2 with a detailed theoretical derivation of the EB estimator and
is followed in Section 3 by a description of the five estimators we examine. Section 4 describes
our simulation design and the different student grouping and teacher assignment scenarios we
examine, with Section 5 providing the results of this analysis. Section 6 provides an analysis of
these estimators using real student achievement data and Section 7 concludes.

3.2

Empirical Bayes’ Estimation

There are several ways to derive Empirical Bayes’ estimators of teacher value added. We adopt
a so-called “mixed estimation” approach, as in Ballou, Sanders, and Wright (2004), because it is

52

fairly straightforward and does not require delving into Bayesian estimation methods. Our focus
is on estimating teacher effects grade by grade. Therefore, we assume either that we have a single
cross section or multiple cohorts of students for each teacher. We do not include cohort effects;
multiple cohorts are allowed by pooling students across cohorts for each teacher.
Let yi denote a measure of achievement for student i, randomly drawn from the population.
This measure could be a test score or a gain score (i.e. current score minus lagged score). Suppose
there are G teachers and the teacher effects are bg , g = 1, ..., G. In the mixed effects setting, these
are treated as random variables as opposed to fixed population parameters. Viewing the bg as
random variables independent of other observable factors affecting test scores has consequences
for the properties of EB estimators.
Typically VAMs are estimated controlling for other factors, which we denote by a row vector
xi . These factors include prior test scores (with the exception of when a gain score used as dependent variable) and, in some cases, student-level and/or classroom-level covariates. We assume the
coefficients on these covariates are fixed parameters. We can write a mixed effects linear model as

yi = xi γ + zi b + ui ,

(1)

where zi is a 1 × G row vector of teacher assignment dummies, b is the G × 1 vector of teacher
effects, and ui contains the unobserved student-specific effects. Because a student is assigned to
one and only one teacher, zi1 + zi2 + · · · + ziG = 1. Equation (1) is an example of a “mixed model”
because it includes the usual fixed population parameters γ and the random coefficients b. Even if
there are no covariates, xi typically includes an intercept. If xi γ is only a constant, so xi γ = γ, then
γ is the average teacher effect and we can then take E(b) = 0. This means that bg is the effect of
teacher g net of the overall mean teacher effect.
Equation (1) is written for a particular student i so that teacher assignment is determined by the

53

vector zi . A standard assumption is that, conditional on b, (1) represents a linear conditional mean:

E(yi |xi , zi , b) = xi γ + zi b

(2)

E(ui |xi , zi , b) = 0.

(3)

which follows from

An important implication of (3) is that ui is uncorrelated with zi , so that teacher assignment is
not systematically related to unobserved student characteristics once we have controlled for the
observed factors in xi .
If we assume a sample of N students assigned to one of G teachers we can write (1) in matrix
notation as
y = Xγ + Zb + u,

(4)

where y and u are N × 1, X is N × K, and Z is N × G. In order to obtain the best linear unbiased
estimator (BLUE) of γ and the best linear unbiased predictor (BLUP) of b, we assume that the
covariates and teacher assignments satisfy a strict exogeneity assumption:

E(ui |X, Z, b) = 0, i = 1, ..., N.

(5)

An implication of assumption (5) is that inputs and teacher assignment of other students does not
affect the outcome of student i.
Given assumption (5) we can write the conditional expectation of y as

E(y|X, Z, b) = Xγ + Zb

54

(6)

In the EB literature a standard assumption is

b is independent of (X, Z),

(7)

E(y|X, Z) = Xγ + ZE(b|X, Z) = Xγ = E(y|X)

(8)

in which case

because E(b|X, Z) = E(b) = 0. Assumption (7) has the implication that teacher assignment for
student i does not depend on the quality of the teacher (as measured by the bg ).
From an econometric perspective, equation (8) means that γ can be estimated in an unbiased
way by OLS regression of
yi on xi , i = 1, ..., N.

(9)

Consequently, we can estimate the effects of the covariates xi by omitting the teacher assignment
dummies. Practically, this means we are assuming teacher assignment is uncorrelated with the
covariates xi .
Under (5) and (7), the OLS estimator of γ is unbiased and consistent, but it is inefficient if we
impose the standard classical linear model assumptions on u. In particular, if
Var(u|X, Z, b) = Var(u) = σu2 IN

then

Var(y|X, Z) = E[(Zb + u)(Zb + u) |X, Z]
= ZVar(b)Z +Var(u) = σb2 ZZ + σu2 IN ,

55

(10)

where we also add the standard assumption that the elements of b are uncorrelated
Var(b) = σb2 IG ,

(11)

and σb2 is the variance of the teacher effects, bg .
Under the assumption that σb2 and σu2 are known – actually, it suffices to know their ratio – the
BLUE of γ under the preceding assumptions is the generalized least squares (GLS) estimator,
γ ∗ = [X (σb2 ZZ + σu2 IN )−1 X]−1 X (σb2 ZZ + σu2 IN )−1 y.

(12)

The N × N matrix ZZ is a block diagonal matrix with G blocks, where block g is an Ng × Ng
matrix of ones and Ng is the number of students taught by teacher g. The GLS estimator γ ∗ is the
well-known “random effects” (RE) estimator popular from panel data and cluster sample analysis.
Note that the “random effects” in this case are teacher effects, not student-specific effects.
Before we discuss γ ∗ further, as well as estimation of b, it is helpful to write down the mixed
effects model in perhaps a more common form. After students have been designated to classrooms,
we can write ygi as the outcome for student i in class g, and similarly for xgi and ugi . Then, for
classroom g, we have

ygi = xgi γ + bg + ugi ≡ xgi γ + rgi , i = 1, ..., Ng ,

(13)

where rgi ≡ bg + ugi is the composite error term. Equation (13) makes it easy to see that the BLUE
of γ is the random effects estimator. It also highlights the assumption that bg is independent of the
covariates xgi . Further, the assumption E(ugi |Xg , bg ) = 0 implies that covariates from student h do
not affect the outcome of student i. We can also see that OLS pooled across i and g is unbiased for
γ because we are assuming E(bg |Xg ) = 0.
As shown in, say, Ballou, Sanders, and Wright (2004), the BLUP of b under assumptions (5),

56

(7), and (10) is
b∗ = (Z Z + ρIG )−1 Z (y − Xγ ∗ ) ≡ (Z Z + ρIG )−1 Z r∗ ,

(14)

where ρ = σu2 /σb2 and r∗ = y − Xγ ∗ is the vector of residuals. Straightforward matrix algebra
shows each b∗g can be expressed as

b∗g

= (Ng
=

+ ρ)−1

Ng

∑ rgi∗ =

i=1
2
σb
2
σb + (σu2 /Ng )

= Ng−1

r¯g∗
σb2

r¯g∗ =

where
r¯g∗

Ng
Ng + ρ

σb2 + (σu2 /Ng )

(y¯g − x¯ g γ ∗ ),

(15)

Ng

∑ rgi∗ = y¯g − x¯ gγ ∗

(16)

i=1

∗ = y − x γ ∗ within classroom g.
is the average of the residuals rgi
gi
gi

To operationalize γ ∗ and b∗g we must replace σb2 and σu2 with estimates. There are different
ways to obtain estimates depending on whether one uses OLS residuals after an initial estimation
or a joint estimation method. With the composite error defined as rgi = bg + ugi we can write
σr2 = σb2 + σu2 . An estimator of σr2 can be obtained from the usual sum of squared residuals from
the OLS regression
ygi on xgi , i = 1, ..., Ng , g = 1, ..., G.

(17)

Call the residuals r˜gi . Then a consistent estimator is
N

σ˜ r2

G g
1
=
∑ ∑ r˜gi2 ,
(N − K) g=1
i=1

which is just the usual degrees-of-freedom (df) adjusted error variance estimator from OLS.
To estimate σu2 , write
rgi − r¯g = ugi − u¯g ,

57

(18)

where r¯g is the within-teacher average, and similarly for u¯g . A standard result on demeaning a set
of uncorrelated random variables with the same variance gives Var(ugi − u¯g ) = σu2 (1 − Ng−1 ) and
Ng

so, for each g, E ∑i=1 (rgi − r¯g )2 = σu2 (Ng − 1).When we sum across teachers it follows that
N

G g
1
∑ ∑ (rgi − r¯g)2
(N − G) g=1
i=1

(19)

has expected value σu2 . To turn (19) into an estimator we can replace the rgi with the OLS residuals,
as before, r˜gi , from the regression in (17). The estimator based on the OLS residuals is
N

σ˜ u2 =

G g
1
∑ ∑ (˜rgi − r˜g)2.
(N − G) g=1
i=1

(20)

With fixed class sizes and G getting large, the estimator that uses N in place of N − G is not
consistent. Therefore, we prefer the estimator in equation (20), as it should have less bias in
applications where G/N is not small. With many students per teacher the difference should be
minor. We could also use N − G − K as a further df adjustment, but subtracting off K does not
affect the consistency.
Given σ˜ r2 and σ˜ u2 we can estimate σb2 as
σ˜ b2 = σ˜ r2 − σ˜ u2 .

(21)

In any particular data set – especially if the data have been generated to violate the standard assumptions listed above – there is no guarantee that expression (21) is nonnegative. A simple
solution to this problem (and one used in software packages, such as Stata) is to set σ˜ b2 = 0 whenever σ˜ r2 < σ˜ u2 . In order to ensure this happens infrequently with multiple cohorts, we compute σ˜ u2
by replacing r˜g with the average obtained for the particular cohort. This ensures that, for a given
Ng

cohort, the terms ∑i=1 (˜rgi − r˜g )2 are as small as possible. In theory, if there are no cohort effects

58

we could use an overall cohort mean for r˜g . But using cohort-specific means reduces the problem
of negative σ˜ b2 when the model is misspecified.
An appealing alternative is to estimate σb2 and σu2 jointly along with γ, using software that
ensures nonnegativity of the variance estimates. The most common approach to doing so is to
assume joint normality of the teacher effects, bg , and the student effects, ugi , across all g and i
– along with the previous assumptions. One important point is that the resulting estimators are
consistent even without the normality assumption; so, technically, we can think of them as “quasi” maximum likelihood estimators. The maximum likelihood estimator of σu2 has the same form as
in equation (20), except the residuals are based on the MLE of γ rather than the OLS estimator. A
similar comment holds for the MLE of σb2 (if we do not constrain it to be nonnegative). See, for
example, Hsiao (2003, Section 3.3.3).
Unlike the GLS estimator of γ, the feasible GLS (FGLS) estimator is no longer unbiased (even
under assumptions (5) and (7)), and so we must rely on asymptotic theory. In the current context,
the estimator is consistent and asymptotically normal provided G → ∞ with Ng fixed. In simulations, Hansen (2007) shows that the asymptotic properties work well when G and Ng are roughly
around 40. In practice, this means that the number of teachers, G, should be substantially larger
than the number of students per teacher, Ng . Typically this is the case in VAM studies, which are
applied to large school districts or entire states and therefore include many teachers. Often the
number of students per teacher is fewer than 100 with several hundred or even several thousand
teachers.
When γ ∗ is replaced with the FGLS estimator and the variances σb2 and σu2 are replaced with
estimators, the EB estimator of b is no longer a BLUP. Nevertheless, we use the same formula
as in (15) for operationalizing the BLUPs. Conveniently, certain statistical packages – such as
Stata 12 with its “xtmixed” command – allow one to recover the operationalized BLUPs after
maximum likelihood estimation. When we use the (quasi-) MLEs to obtain the b∗g we obtain what
are typically called the Empirical Bayes’ estimates.

59

One way to understand the shrinkage nature of b∗g is to compare it with the estimator obtained
by treating the teacher effects as fixed parameters. Let γˆ and βˆ be the OLS estimators from the
regression
yi on xi , zi , i = 1, ..., N.

(22)

Then γˆ is the so-called “fixed effects” (FE) estimator obtained by a regression of yi on the controls
in xi and the teacher assignment dummies in zi . In the context of the model

y = Xγ + Zβ + u

(23)

E(u|X, Z) = 0, Var(u|X, Z) = σu2 IN ,
γˆ is the BLUE of γ and βˆ is the BLUE of β . As is well-known, γˆ can be obtained by an OLS
regression where ygi and xgi have been deviated from within-teacher averages (see, for example,
Wooldridge 2010, Chapter 10). Further, the estimated teacher fixed effects can be obtained as
ˆ
βˆg = y¯g − x¯ g γ.

(24)

Equation (24) makes computation of the teacher VAMs fairly efficient if one does not want to run
the long regression in (22).
By comparing equations (15) and (24) we see that the EB estimator b∗g differs from the fixed
effects estimator βˆg in two ways. First, and most importantly, the RE estimator γ ∗ is used in
ˆ Second, b∗g shrinks the average of the residuals
computing b∗g while βˆg uses the FE estimator γ.
toward zero by the factor
σb2
σb2 + (σu2 /Ng )

=

1
1 + (ρ/Ng )

(25)

where
ρ = σu2 /σb2 .

60

(26)

Equation (25) illustrates the well-known result that the smaller is the number of students for teacher
g, Ng , the more the average residual is shrunk toward zero.
A well-known algebraic result – for example, Wooldridge (2010, Chapter 10) – that holds for
any given number of teachers G is that
γ ∗ → γˆ as ρ → 0 or Ng → ∞.1

(27)

Equation (27) can be verified by noting that the RE estimator of γ can be obtained from the pooled
OLS regression
ygi − θg y¯g on xgi − θg x¯ g
where
θg = 1 −

σu2
σu2 + Ng σb2

1/2

= 1−

1/2
1
.
1 + (Ng /ρ)

(28)

(29)

It is easily seen that θg → 1 as ρ → 0 or Ng → ∞. In other words, with many students per teacher
or large teacher effects relative to student effects, the RE and FE estimates can be very close. But
they are never identical. Not coincidentally, the shrinkage factor in equation (25) tends to unity
if ρ → 0 or Ng → ∞. The bottom line is that with a “large” number of students per teacher the
shrinkage estimates of the teacher effects can be close to the fixed effects estimates. The RE and
FE estimates also tend to be similar when σu2 (the student effect) is “small” relative to σb2 (the
teacher effect), but this scenario seems unlikely.
An important point that appears to go unnoticed in applying the shrinkage approach is that in
situations where γ ∗ and γˆ substantively differ, γ ∗ suffers from systematic bias because it assumes
teacher assignment is uncorrelated with xi . Because γ ∗ is used in constructing the b∗g in equation
(15), the bias in γ ∗ generally results in biased teacher effects, and the teacher effects would be biased even if (15) did not employ a shrinkage factor. The shrinkage likely exacerbates the problem:

61

the estimates are being shrunk toward values that are systematically biased for the teacher effects.2
The expression in equation (15) motivates a common two-step alternative to the EB approach.
In the first step of the procedure, one obtains γ˜ using the OLS regression in equation (17), and
obtains the residuals, r˜gi . In the second step, one averages the residuals r˜gi within each teacher to
obtain the teacher effect for teacher g. We call this approach the “average residual” (AR) method.
After obtaining the averages of the residuals one can, in a third step, shrink the averages using the
empirical Bayes’ shrinkage factors in equation (15). Typically the estimates in equations (18) and
(20), based on the OLS residuals, are used in obtaining the shrinkage factors. We call the resulting
estimator the “shrunken average residual” (SAR) method.
With or without shrinking, the AR approach suffers from systematic bias if teacher assignment,
zi , is correlated with the covariates, xi . In effect, the AR approach partials xi out of yi but does not
partial xi out of zi , the latter of which is crucial if xi and zi are correlated. The so-called “fixed
effects” regression in (22) partials xi out of zi , which makes it a more reliable estimator under
nonrandom teacher assignment – perhaps much more reliable with strong forms of nonrandom
assignment.
It is also important to know that the SAR approach is inferior to the EB approach under nonrandom assignment. The logic is simple. First, the algebraic relationship between RE and FE means
ˆ than the OLS estimator, γ.
˜ Consequently, under
that γ ∗ tends to be closer to the FE estimator, γ,
nonrandom teacher assignment, the estimated teacher effects using the RE estimator of γ will have
less bias than the estimates that begin with OLS estimation of γ. Second, if teacher assignment is
2 Without covariates, the difference between the EB and fixed effects estimates of the b is much less important:
g
they differ only due to the shrinkage factor. In practice, the fixed effects estimates, βˆg , are obtained without removing
an overall teacher average, which means βˆg = y¯g . To obtain a comparable expression for b∗g we must account for the
GLS estimator of the mean teacher effect, which would be obtained as the intercept in the RE estimation. Call this
estimator µb∗ , which in the case of no covariates is γ ∗ . Then the teacher effects are
∗
∗
∗
∗
b∗
g = µb + ηg (y¯g − µb ) = ηg y¯g + (1 − ηg )µb = y¯g − (1 − ηg )(y¯g − µb ),
where ηg is the shrinkage factor in equation (25). Compared with the FE estimate of bg , b∗g is shrunk toward the
overall mean µb∗ . When the teacher effects are treated as parameters to estimate, the b∗g are biased because of the
shrinkage factor, even when they are BLUP.

62

uncorrelated with the covariates, the OLS estimator of γ is inefficient relative to the RE estimator under the standard random effects assumptions (because the RE estimator is FGLS). Thus, the
only possible justification for SAR is computational simplicity. But the saving is likely to be minor
unless the number of controls in xi is very large. For the kinds of data sets widely available, the
computational saving from using SAR rather than EB is likely to be minor.
Finally, we must emphasize that fixed effects estimation of the teacher VAMs allows any correlation between zi and xi , and thus expect it to outperform EB estimation and strongly outperform
SAR under nonrandom assignment. The bias due to nonrandom allocation of students to teachers
is also discussed in Rothstein (2009, 2010).

3.3

Summary of Estimation Methods

In this paper we examine five different value-added estimators used to recover the teacher
effects and apply them to both real and simulated data. Some of the estimators use EB or shrinkage
techniques, while others do not. They can all be cast as a special case of the estimators described
in the previous section. For clarity, we briefly describe each one, with additional reference to each
of these specifications provided in Table C.4.
The estimators can be obtained from a dynamic equation of the form

Ait = λ Ai,t−1 + Xit δ + Zit β + vit ,

(30)

in which Ait is achievement (measured by a test score) for student i in grade t, Xit is a vector
of student characteristics, and Zit is the vector of teacher assignment dummies. This is similar
to equation (1) but with the lagged test score written separately from Xit for clarity. Also, Xit
is omitted from the estimation of the teacher effects in the simulation analysis below, as student
characteristics are not included in the data generating process. The EB estimator we analyzed in
Section 2 was for the case of a single cross-section of students. Thus, we use only one grade – fifth

63

grade – for the analysis.
We first analyze EB LAG, a dynamic MLE version of the EB estimator that treats the teacher
effects as random. This technique obtains the estimates of the teacher effects using the normal
maximum likelihood in the first stage, regressing Ait on its lag, Ai,t−1 , and Xit . In the second stage,
the shrinkage factor is applied to these teacher effects. As described in Rabe-Hesketh and Skrondal
(2012), this two step procedure can be performed in one-step using the “xtmixed” command in
Stata 12 with teacher random effects. The predicted random effects of this regression are identical
to shrinking the MLE estimates by the shrinkage factor. This procedure is generally justified even
if the unobservables do not have normal distributions, in which case we are applying quasi-MLE.
A second estimator we consider is the average residual (AR) method described in Section 2. This
technique mainly differs from EB LAG in that it uses OLS in the first stage. The residuals of this
OLS regression are obtained, and then we average these residuals by classroom to calculate the
estimated teacher effects. We expect the EB LAG estimator to outperform the AR estimator in
most scenarios, given that MLE is being used in the first-stage instead of OLS.
We compare the estimators that treat the teacher effect as random with an estimator that explicitly controls for the teacher effect through the inclusion of teacher assignment dummy variables.
This third estimator applies OLS to (30) by pooling across students and classrooms. This “dynamic
OLS,” or DOLS estimator treats the teacher effects as fixed parameters to estimate. The inclusion
of the lagged test score accounts for the possibility that teacher assignment is related to students’
most recent test score. Guarino, Reckase, and Wooldridge (forthcoming) discuss the assumptions
under which DOLS consistently estimates β when (30) is obtained from a structural cumulative
effects model, and the assumptions are quite restrictive. Nevertheless, their simulations show the
DOLS estimator often estimates β well even when the assumptions underlying the consistency of
DOLS fails.
Given that EB estimation is often motivated as a way to increase precision and decrease misclassification, we also analyze whether shrinking AR and DOLS estimates enhances performance.

64

Thus, the fourth estimator we analyze is our shrunken average residual (SAR) estimator. This
estimator takes the AR estimates and shrinks them by the shrinkage factor described in Section 2
(see Equation (25)). Shrinking the AR estimates does not result in a true EB estimator since AR
uses OLS in the first stage, but it is commonly used as a simpler way of operationalizing the EB
approach (see, for example, Kane & Staiger, 2008). As discussed in Section 2, with a sufficiently
large number of students per teacher, the EB LAG estimator converges to the DOLS estimator but
SAR does not. Thus, as the number of students per teacher grows, we would expect EB LAG
to perform more similarly to DOLS than SAR. Finally, we consider a shrunken DOLS (SDOLS)
estimator, which takes the DOLS estimated teacher fixed effects and shrinks them by the shrinkage
factor derived in Section 2. Although SDOLS is rarely done in practice and is not a true EB estimator, we include it as an exploratory exercise in order to better determine the effects of shrinking
itself when the number of students per teacher differs. When the class sizes are all the same, the
shrunken estimates (SDOLS and SAR) will only differ from the unshrunken estimates by a constant positive multiple. Thus, shrinking the DOLS or AR estimates will have no effect in terms of
ranking teachers. It is important to keep in mind that, unlike DOLS and SDOLS, the AR and SAR
estimators do not allow for general correlation between the teacher assignment and past test scores
(or other covariates).

3.4

Comparing VAM Methods Using Simulated Data

The question of which VAM estimators perform the best can only be addressed in simulations in
which the true teacher effects are known. Therefore, to evaluate the performance of EB estimators
relative to other common value-added estimators, we apply these methods to simulated data. This
approach allows us to examine how well various estimators recover the true teacher effect under a
variety of student grouping and teacher assignment scenarios. Using data generated as described
in Section 4.1, we apply the set of value-added estimators discussed in Section 3 and compare the
resulting estimates with the true underlying teacher effects.

65

3.4.1

Simulation Design

Much of our main analysis focuses on a base case that restricts the data generating process to a
relatively narrow set of idealized conditions. These ideal conditions do not allow for measurement
error or peer effects and assume that teacher effects are constant over time, but include these as
sensitivity tests of the main results. The data are constructed to represent grades three through
five (the tested grades) in a hypothetical school. For simplicity and comparison with the theoretical predictions, we assume that the learning process has been going on for a few years but only
calculate estimates of teacher effects for fifth grade teachers – a single cross section.3 We create
data sets that contain students nested within teachers, with students followed longitudinally over
time in order to reflect the institutional structure of an elementary school. Our simple baseline data
generating process is as follows:

Ai3 = λ Ai2 + βi3 + ci + ei3
Ai4 = λ Ai3 + βi4 + ci + ei4

(31)

Ai5 = λ Ai4 + βi5 + ci + ei5

in which Ai2 is a baseline score reflecting the subject-specific knowledge of child i entering third
grade; Ait is the grade-t test score (t = 3, 4, 5); λ is a time constant decay parameter, where lambda
is set equal to zero in the simulations for lag scores greater than one year prior; βit is the teacherspecific contribution to growth (the true teacher value-added effect); ci is a time-invariant studentspecific effect (may be thought of as “ability” or “motivation”); and eit is a random deviation for
each student. We assume independence of eit over time, a restriction implying that past shocks
to student learning decay at the same rate as all inputs (see Guarino, Reckase, & Wooldridge,
3 Despite only estimating value-added for grade 5 teachers, we keep the three grade structure when generating the
student test scores since the fifth grade achievement is based on more than just the current teacher and prior test score
of the student; it is a function of all prior teacher, unobservable student, and random influences. Thus, to ignore that
process and generate fifth grade test scores based on a “baseline” fourth grade test score seems inappropriate given
this context.

66

2012 for a more detailed discussion of this “common factor restriction” assumption). In all of
the simulations reported in this paper, the random variables Ai2 , βit , ci , and eit are drawn from
normal distributions with means of zero. The standard deviation of the teacher effect is .25, the
standard deviation of the student fixed effect is .5, and the standard deviation of the random noise
component is 1. These give relative shares of 5, 19, and 76 percent of the total variance in gain
scores (when λ = 1), respectively. Given that the student and noise components are larger than
the teacher effects, we call these “small” teacher effects. We also conduct a sensitivity analysis
using “large” teacher effects, where the true teacher effects are drawn from a distribution with a
standard deviation of 1. The baseline score is drawn from a distribution with a standard deviation
of 1. We also allow for correlation between the time-invariant child-specific heterogeneity, ci , and
the baseline test score, Ai2 , which we set to 0.5. This correlation reflects that students with better
unobserved “ability" likely have higher test scores as well.
Our data are simulated using 36 teachers that teach 720 students per cohort. In order to create
a situation in which there is a substantial variation in class size – to showcase the potential disparities between EB/shrinkage and other estimators – we vary the number of students per classroom.
Teachers receive classes of varying sizes, but receive the same number of students in each cohort.
Of the 36 teachers we simulate, twelve teachers have classes of 10 students, twelve teachers have a
class size of 20, and twelve teachers have class sizes of 30. The mean and standard deviation of the
true teacher effects of the 36 teachers we estimate are 0.501 and 0.244, respectively. We simulate
the data using both one and four cohorts of students to provide further variation in the amount of
data from which the teacher effects are calculated. In the case of four cohorts, data are pooled
across the cohorts so that value-added estimates are based off of sample sizes of 40, 80, and 120,
instead of 10, 20, and 30 as in the one cohort case. Therefore, we would expect that estimates in
the four cohort case to be less noisy than those from the one cohort case, possibly mitigating the
potential gains from EB estimation.
To create different scenarios, we vary certain key features: the grouping of students into classes

67

and the assignment of classes of students to teachers within schools. We generate data using each
of the seven different mechanisms for the assignment of students outlined in Table C.5. Students
are grouped into classrooms either randomly, based on their prior year achievement level (dynamic
grouping or DG), or based on their unobserved heterogeneity (heterogeneity grouping or HG).
In the random case, students are assigned a random number and then grouped into classrooms
of various sizes based on that random number. In the grouping cases, students are ranked by
either the prior test score or the student fixed effect and grouped into classrooms of various sizes
based on that ranking. Teachers are assigned to these classrooms either randomly (denoted RA) or
nonrandomly. Teachers assigned nonrandomly can be assigned positively (denoted PA), meaning
the best teachers are assigned to classrooms with the best students, or negatively (denoted NA),
meaning the best teachers are assigned to classrooms with the worst students.
These grouping and assignment procedures are not purely deterministic, as we allow for a
random component with standard deviation of 1 in the assignment mechanism. As a sensitivity
analysis, we also run simulations setting this standard deviation to 0.1, meaning the grouping of
students into classrooms is more nonrandom. We use the estimators discussed in Section 3, but with
only a constant, teacher dummies (if applicable), and the lagged test score included as covariates.
We use 100 Monte Carlo replications per scenario in evaluating each estimator.
3.4.2

Evaluation Measures

For each estimator across each iteration, we save the individual estimated teacher effects and
also retain the true teacher effects, which are fixed across the iterations for each teacher. To study
how well the methods recover the true teacher effects, we adopt five simple summary measures
using the teacher level data. The first is a measure of how well the estimates preserve the rankings
ˆ between the estimated
of the true teacher effects. We compute the Spearman rank correlation, ρ,
teacher effects and the true effects and report the average ρˆ across the 100 iterations. Second,
we compute a measure of misclassification. These misclassification rates are obtained as the per-

68

centage of above average teachers in the true quality distribution (i.e. teachers with true βg > 0)
who are misclassified as below average in the distribution of estimated teacher effects for the given
estimator. Given that this is just an arbitrary cutoff point, we also obtain the fraction of teachers
that are misclassified in the tails of the distribution (e.g fraction of above average teachers that are
misclassified in the bottom quintile).
In addition to examining rank correlations and misclassification rates, it is also helpful to have a
measure that quantifies some notion of the magnitude of the bias in the estimates. Given that some
teacher effects are biased upwards and others downwards, it is difficult to capture the overall bias
in the estimates in a simple way. We create a statistic, θˆ , that captures how closely the magnitude
of the deviation of the estimates from their mean tracks the size of the deviation of the true effects
from the true mean. To calculate this measure, we regress the deviation of the estimated teacher
effects from their overall estimated means on the analogous deviation of the true effects generated
from the simulation for each estimator. We can represent this simple regression as
¯
βˆg − βˆ = θˆ (βg − β¯ ) + residualg ,

(32)

in which βˆg is the estimated teacher effect and βg is the true effect of teacher g. From this simple regression, we report the average coefficient, θˆ¯ , across the 100 replications of the simulation
for each estimator. This regression tells us whether the estimated teacher effects are correctly distributed around the average teacher. If θˆ = 1, then a movement of βg away from its mean is tracked
by the same movement of βˆg from its mean.
When θˆ ≈ 1, the magnitudes of the estimated teacher effects can be compared across teachers.
If θˆ > 1, the estimated teacher effects amplify the true teacher effects. In other words, teachers
above average will be estimated to be even more above average and vice versa for below average
teachers. An estimation method that produces θˆ substantially above one generally does a good job
of ranking teachers, but the magnitudes of the differences in estimated teacher effects cannot be

69

trusted. The magnitudes also cannot be trusted if θˆ < 1; in this case, ranking the teachers becomes
more difficult because the estimated effects are compressed relative to the true teacher effects.
In addition to ranking teachers correctly, the magnitude of the estimated teacher effects is
also important in policy applications. It is helpful to examine the extent to which shrinking the
estimates, as in the EB methods, increases bias in these noisy estimates. Thus, we report the
average value of θˆ across the simulations because it provides evidence of which methods, under
which scenarios, produce estimated teacher effects whose magnitudes have meaning. This measure
also provides insight into why some methods rank teachers relatively well even when the estimated
effects are systematically biased.
The precision of these methods is also a key consideration when evaluating the overall performance. As described in Section 2, EB methods are not unbiased when thinking about the teacher
effects as fixed parameters we are trying to estimate. However, if the identifying assumptions
hold, these methods should provide more precise estimates. This is one motivation for using such
methods, as estimates should be more stable over time, leading to a smaller variance in the teacher
effects. As the teacher effect is fixed for each teacher across the 100 iterations, we have 100 estimates of each teacher effect. As a summary measure for the precision of the estimators, we
calculate the standard deviation of the 100 teacher effect estimates for each teacher and then take
a simple average across all teachers.
To further analyze the variance-bias tradeoff for each of these estimators, we also include
average mean squared error (MSE). This measure averages the following across all g teachers and
across simulation runs:
MSEg = (βg − βˆg )2

(33)

This provides a simple statistic to determine whether the bias induced by shrinking is justifiable
due to gains in precision.

70

3.5

Simulation Results

Tables C.1 and C,2 report the five evaluation measures described in Section 4.2 for each particular estimator-assignment scenario combination. For ease in interpreting the tables, a quick guide
to descriptions of each of these estimators, grouping-assignment mechanisms, and evaluation measures can be found in Appendix tables C.4 through C.6. As these shrinkage and EB estimators are
often motivated as a way to reduce noise, one might expect these approaches to be most beneficial
with very limited student data per teacher. Thus, we estimate teacher effects using both four cohorts and one cohort of data. The tables show results for the case λ = .5. Though not reported,
we also conducted a full set of simulations for λ = 0.75 and λ = 1, and the main conclusions are
unchanged. The full set of simulation results is available upon request from the authors.
3.5.1

Fixed Teacher Effects versus Random Teacher Effects

We first compare the performance of the DOLS estimator, which treats teacher effects as fixed
parameters to estimate, to the AR and EB LAG estimators that treat teacher effects as random in
Table C.1. Under nonrandom assignment of teachers, we expect DOLS, which explicitly controls
for teacher assignment through the inclusion of teacher assignment indicators, to perform better
than those estimators treating the teacher effects as random. When teacher assignment is based on
the lagged test score, DOLS directly controls for the assignment mechanism by including both the
lagged score and teacher assignment indicators and should perform particularly well in this case.
The simulation results presented here largely support this hypothesis.
3.5.1.1

Random Assignment

We begin with the pure random assignment (RA) case, where EB-type estimation methods are
theoretically justified. The results of the random assignment case are given in the top panel of Table
C.1 and they suggest very little substantial difference between the performance of the fixed and
random effects estimators under this scenario. As the theory suggests, EB LAG performs well in

71

the four cohort case, with rank correlations between the estimated and the true teacher effects near
0.86, which is nearly the same as the 0.85 rank correlation for DOLS and AR. In addition to very
similar rank correlations, the misclassification rates are very similar across the three estimators,
with about 15 percent of above average teachers misclassified as below average. The similarities
between the three estimators in terms of rank correlation and misclassification rates remains when
using only one cohort. Reducing the amount of data used to estimate the teacher effects lowers the
performance of all estimators, decreasing the rank correlations and increasing the misclassification
rates. With one cohort, rank correlations between the estimated and true teacher effects are about
0.65 to 0.67, and between 25 and 26 percent of above average teachers are misclassified as below
average.
In addition to rank correlations and misclassification rates, we also examine the bias and precision of the estimators. While DOLS and AR appear to be unbiased with average θˆ values close to
1, EB LAG substantially underestimates the magnitudes of the true teacher effects with an average
θˆ value of 0.78 using four cohorts and 0.49 using one cohort. This bias is likely the result of the
shrinkage technique that is applied, but this shrinkage does cause EB LAG to be slightly more
precise than AR or DOLS. While DOLS and AR both have similar average standard deviations
of the estimated teacher effects near 0.13 and 0.27 in the four and one cohort cases, respectively,
EB LAG has lower average standard deviations of 0.12 and 0.18, respectively. Given the precision
gain in EB LAG, the MSE measure suggests that EB LAG may be preferred to DOLS or AR under
random assignment.
We now move to the cases where the students are nonrandomly grouped together, but teachers
are still randomly assigned to classrooms. We allow for nonrandom grouping based on either
the prior year test score (dynamic grouping, DG) or student-level heterogeneity (heterogeneity
grouping, HG). Under these DG-RA and HG-RA scenarios in Table C.1, we see a fairly similar
pattern as in the RA scenario, although the overall performance of all estimators is somewhat
diminished, especially in the HG-RA scenario.

72

3.5.1.2

Dynamic Grouping and Nonrandom Assignment

The performance of thes various estimators diverges noticeably under nonrandom teacher assignment. We continue to nonrandomly group teachers as described above, but now allow for nonrandom assignment of students to teachers. Classes with high test scores or high unobserved ability
can be assigned to either the best (positive assignment) or worst (negative assignment) teachers. A
key finding of this analysis is the disparity in performance of estimators that treat teacher effects
as random (e.g. AR and EB LAG) compared with the DOLS estimator. These results suggest that
when there is nonrandom teacher assignment based on the prior test score estimators explicitly
controlling for the teacher assignment should be preferred to those that treat the teacher effects as
random.
DOLS substantially outperforms AR and EB LAG under the DG-PA scenario. When using
four cohorts, DOLS has a rank correlation of 0.86 under DG-PA, while AR and EB LAG have rank
correlations of 0.60 and 0.76, respectively. AR and EB LAG also have large misclassification rates,
with 28 to 32 percent of above average teachers being misclassified as below average compared
with only 23 percent for DOLS.
In addition to misclassifying and poorly ranking teachers, the AR and EB LAG methods also
underestimate the magnitudes of the true teacher effects. While DOLS has an average θˆ value
of 0.99, the AR and EB LAG estimators have average θˆ values of 0.53 and 0.49, respectively.
While some of the bias of the EB LAG estimates can be attributed to shrinkage, the larger issue
is the bias caused by the failure of the AR and EB LAG approaches to net out the correlation
between the lagged test score (i.e. the assignment mechanism in these DG scenarios) and the
teacher assignment, a correlation that DOLS explicitly allows for with the inclusion of teacher
dummies in the regression. Just as in the random assignment case, DOLS and EB LAG have
similar MSE measures, while the MSE for AR is slightly larger. In the four cohort case, DOLS,
EB LAG and AR have MSE values of 0.02, 0.02, and 0.04, respectively. Similar results are found
if we instead examine the DG-NA case.
73

These simulation results also verify an important result of the theoretical discussion: the performance of EB LAG approaches the performance of DOLS as the number of students per teacher
grows. We see less of a disparity in the performance of DOLS and EB LAG when computing
VAMs using four cohorts compared to one, but the relative performance of AR does not improve
with more students per teacher. For example, under DG-PA with one cohort of students, AR and
EB LAG have rank correlations of 0.38 and 0.45, respectively, compared to 0.63 for DOLS. With
four cohorts of students, the rank correlation for EB LAG is much closer to that for DOLS (0.76
and 0.86, respectively) than is the rank correlation for AR (0.60). This theoretical result is also applicable to the SAR estimator we examine below, which is used as a simpler way to operationalize
the EB approach. In summary, EB LAG, which uses random effects estimation in the first stage,
is preferred to those using OLS (AR and SAR) under nonrandom teacher assignment, as these
estimates approach the preferred DOLS estimates that treat teacher effects as fixed.
3.5.1.3

Heterogeneity Grouping and Nonrandom Assignment

As a final scenario we examine the case of nonrandom teacher assignment to students grouped
on the basis of student-level heterogeneity. The results for these HG scenarios are especially unstable: all estimators do an excellent job ranking teachers under positive teacher assignment, and
all estimators do a very poor job under negative teacher assignment. In the HG-PA case with four
cohorts of students, the magnitudes of the estimated VAMs are amplified as seen by the large average values for θˆ between 1.43 and 1.61. This improves the ability of the various estimators to rank
teachers as evidenced by the high rank correlations of about 0.94 for all estimators. The EB LAG
estimator performs the best in this scenario, as it performs as well as the other estimators in terms
of ranking and misclassification of teachers but has the smallest MSE measure. Under HG-NA
with four cohorts, the performance of all estimators falls substantially, largely caused by severely
underestimated teacher effects (θˆ values between 0.15 and 0.33). These compressed teacher effect
estimates make it difficult to rank teachers in this scenario, resulting in low rank correlations for

74

all estimators between 0.38 and 0.41. Just as in the HG-PA scenario, the performance of the three
estimators under HG-NA is very similar across the evaluation measures we examine.
Why is the performance of DOLS, AR, and EB LAG so similar under HG-PA and HG-NA,
while differing so greatly under DG-PA and DG-NA? Despite correlation between the baseline
test score and the student fixed effect, the lagged test score appears to be a weak proxy for the
assignment mechanism in the HG scenarios. Since none of the three estimators do well at allowing
for the correlation between the assignment mechanism and the teacher assignment in these cases,
the distinction between estimators that include teacher fixed effects and those that treat teacher
effects as random is less stark. As found in Guarino, Reckase, and Wooldridge (forthcoming), a
gain score estimator with student fixed effects included is the most robust in these HG scenarios,
as it does allow for the correlation between the assignment mechanism (i.e. student fixed effect)
and the teacher assignment (i.e teacher dummy variables). Their results lend further support for
our conclusions here that allowing for this correlation is extremely important in the performance
of these value added estimators when there is nonrandom assignment.
3.5.2

Shrinkage versus Non-Shrinkage Estimation

Use of EB and other shrinkage estimators is often motivated as a way to reduce the noise in
the estimation of teacher effects, particularly for teachers with a small number of students. Greater
stability in the estimated effects is thought to reduce misclassification of teachers. We observed
in section 3.1 that EB LAG was generally outperformed by the fixed effects estimator, DOLS.
However, under nonrandom teacher assignment, we are unable to tell how much of the bias in the
EB LAG estimator is due to treating the teacher effects as random and how much is due to the
shrinkage procedure. To examine the effects of shrinkage itself, we compare the performance of
unshrunken estimators, DOLS and AR, with their shrunken versions, SDOLS and SAR, in Table
C.2. Although SDOLS is not a commonly used or theoretically justified estimator, we explore it
here to identify whether shrinking teacher fixed effect estimates could be useful in practice.

75

Our simulation results show that there is no substantial improvement in the performance of the
DOLS or AR estimators after applying the shrinkage factor to the estimates. Using four cohorts
of students, the performance measures for DOLS and AR compared to their shrunken counterparts
are nearly identical to two decimal places across all grouping and assignment scenarios. Even with
very limited data per teacher in the one cohort case, when we would expect shrinkage to have a
greater effect on the estimates, we find very little change in the performance of the estimators after
the shrinkage factor is applied.
In the one cohort case, shrinking either the DOLS or AR estimates slightly decreases (in the
second decimal place) both the average θˆ values and average standard deviation of the estimated
teacher effects. This increased bias in the estimates is expected when applying the shrinkage factor
and, depending on the scenario and estimator we examine, the effect of this precision-bias tradeoff
may increase or decrease the MSE measure when comparing the shrunken and unshrunken estimates. Shrinking the DOLS and AR estimates generally reduces the MSE but makes no substantial
difference on the misclassification rate of teachers.
The effect of shrinkage itself does not appear to be practically important for properly ranking
teachers or ameliorate the performance of the biased AR estimator found in the DG-PA and DGNA scenarios. Given that shrinking the AR estimates does little to mitigate the performance drop of
AR under DG-PA and DG-NA, our evidence suggests that shrinking teacher fixed effects estimates
is preferred over shrinking teacher random effects if such techniques are desired.
3.5.3

Sensitivity Analyses

As mentioned in Section 4.1, we also test the sensitivity of these results by changing some
of the parameters of the model. First, we increase the standard deviation of the distribution from
which the true teacher effects are drawn. Using these “large” teacher effects, all estimators increase
in performance and EB LAG performs similarly to DOLS in the DG-PA and DG-NA cases. The
AR method, however, continues to suffer in performance under DG-PA and DG-NA compared

76

to DOLS. Second, we allow for more non-randomness (i.e. decrease the amount of noise) in the
assignment of teachers into classrooms. As the assignment of teachers becomes more nonrandom,
the performance of AR and EB LAG suffers even more greatly in terms of lower rank correlations
and higher misclassification rates than what is observed in the results in Table C.1 and C.2. Given
that some models use multiple prior test scores (e.g. EVAAS, VARC) and we also estimate DOLS,
AR, and EB LAG with multiple lagged test scores as a sensitivity analysis. Although adding
multiple lags improves the performance of AR and EB LAG in the random assignment case, the
performance of these estimators still suffers greatly compared to DOLS in the DG-PA and DG-NA
scenarios. As a final sensitivity test we include a peer effect (e.g. avg. ci of student’s classmates)
in the underlying DGP. Even when peer effects are included, EB LAG and AR continue to suffer
in performance under the DG-PA and DG-NA cases.

3.6

Comparing VAM Methods Using Real Data

We also apply these estimation methods to actual student-level test score data and examine the
rank correlations between the estimated teacher effects of the various estimators for each school
district. In addition to rank correlations, we also examine whether teachers are being classified in
the extremes uniformly across all of the estimators we examine. Although the real data does not
allow comparison between the estimated effects and the true teacher effects, we are able to make
comparisons between the estimated effects of different estimators. This comparison provides a
measure of the sensitivity of the estimated teacher effects to specifications that shrink the estimates
and/or treat the teacher effects as random or fixed. The results of this analysis provide some
perspective on the impact of shrinking and Empirical Bayes’ methods in a real-world setting.
3.6.1

Data

We apply the five methods described in Section 3 to data from an anonymous southern U.S.
state. The data span 2001 through 2007 and grades four through six, but test scores are collected

77

for each student from grades three through six. The data set includes 1,488,253 total students from
which we have at least one current year score and one lagged score. Only 482,031 students have
test scores for all grades. The data set also contains 43,868 unique teachers that we observe for a
varying number of cohorts of students. We observe 39 percent of teachers for only one year, but
we do see 20 percent of teachers for four or more years. These teachers, on average, teach about
26 students per year, with only a small percentage (less than two percent) teaching more than 30
students per year. The high percentage of teachers that we observe for only one year could motivate
researchers to employ shrinkage and EB estimators as a way to reduce precision problems due to
minimal data.
We estimate teacher effects district-by-district using equation (30) with controls for various
student characteristics and include dummies for the year. Student characteristics include race,
gender, disability status, free/reduced price lunch eligibility, limited English proficiency status,
and the number of student absences from school. As discussed above, the teacher effects are
estimated using data on multiple cohorts (between one and seven) of students. For simplicity and
comparison with the simulation results, we estimate the value-added measures for those teachers
with fifth grade students in the 67 districts, but again teachers receive multiple cohorts of students.
Overall, we estimate 20,749 teacher effects using test score data from the annual assessment exam
administered by the state.
3.6.2

Results

Figure C.1 presents box plots that depict the distributions of the within-district rank correlations
between the various lagged score estimators, DOLS, SDOLS, AR, SAR, and EB LAG. The results
presented here are from using math scores, but the results are similar when reading scores are used.
As in the discussion of the simulation results, we first compare the DOLS estimator, which treats
the teacher effects as fixed, with the estimators that treat the teacher effects as random. Comparing
DOLS and AR, we find that the median rank correlation is around 0.99, but there are nine districts

78

with rank correlations below 0.90 and 2 districts with correlations below 0.50. We also observe
a slightly lower median rank correlation between DOLS and EB LAG, at around 0.97, with five
districts with rank correlations below 0.90 and three below 0.50. These results are not inconsistent
with our simulation results: the performance of DOLS, AR, and EB LAG is very similar under
cases of random assignment of teachers to classrooms, but the performance of AR and EB LAG is
substantially different from DOLS under non-random assignment based on prior test scores. Thus,
it could be the case that these outlier districts observed in the left tails of the top two box plots
may be composed of schools that engage more heavily in nonrandom assignment of teachers to
classrooms.
Comparing the two estimators that treat teacher effects as random, AR and EB LAG, we find
that while the median rank correlation is 0.96, nine districts have rank correlations of between
0.82 and 0.92. These results suggest that the estimates are somewhat sensitive to how the teacher
effects are calculated in the first stage. This was also the case in the simulated results, where the
performance of the AR estimator suffered more than the performance of the EB LAG estimator in
cases of non-random assignment based on the prior test score.
For a thorough comparison with the simulation results, we also compare the shrunken and
unshrunken estimates of DOLS and AR using the real data. We find median rank correlations
of around 0.97 for both the DOLS and SDOLS comparison and the AR and SAR comparison,
suggesting that shrinkage has a small impact on the estimates. It appears that in certain cases,
shrinkage may have a larger impact on the DOLS estimates, as two districts have rank correlations
of 0.50 and 0.72. Our simulation results suggested that shrinking the estimates had very little
impact on estimator performance.
In addition to rank correlation comparisons, we also examine the extent to which teachers
are classified in the tails of the distribution by the different estimators. If shrinkage is having
some effect, we would expect to see some teachers classified in the extremes to be pushed toward
the middle of the distribution after applying the shrinkage factor. Table C.3 lists the fraction of

79

teachers ranked in the same quintile, either the top or bottom, by different pairs of estimators.
Comparing across estimators that assume fixed teacher effects to those that assume random teacher
effects, we do not see much movement across quintiles. For example, comparing DOLS to EB
LAG, we find that about 91 percent of the teachers that are classified in the top quintile using
DOLS are also in this quintile using EB LAG. This suggests that teacher assignment may not
be largely based on prior student achievement or that the prior test score is a poor proxy for the
true assignment mechanism. If the prior test score or other covariates insufficiently proxy for the
underlying assignment mechanism, then the choice to include teacher assignment variables will
matter little in how teachers are ranked.
Comparing the rankings of unshrunken and corresponding shrunken estimators, we see that
about 90 percent of teachers are ranked in the same quintile by both the unshrunken estimators
(DOLS and AR) and their shrunken counterparts (SDOLS and SAR). This suggests that shrinking
the estimates results in some reclassification of teachers in the tails to quintiles in the middle of
the distribution. Using real data, however, we are unable to tell whether this reclassification is
appropriate. Our simulated analysis suggested that shrinking the estimates had little impact if any
on misclassification rates.

3.7

Conclusion

Using simulation experiments where the true teacher effects are known, we have explored the
properties of two commonly used Empirical Bayes’ estimators as well as the effects of shrinking
estimates of teacher effects in general. Overall, EB methods do not appear to have much advantage, if any, over simple methods such as DOLS that treat the teacher effects as fixed, even in
the case of random teacher assignment where EB estimation is theoretically justified. Under random assignment, all estimators perform well in terms of their ability of ranking teachers, properly
classifying teachers, and providing unbiased estimates. EB methods have a very slight gain in
precision compared to the other methods in this case.

80

We generally find that EB estimation is not appropriate under nonrandom teacher assignment.
The hallmark of EB estimation of teacher effects is to treat the teacher effects as random variables that are independent (or at least uncorrelated) with any other covariates. This assumption
is tantamount to assuming that teacher assignment does not depend on other covariates such as
past test scores (this is also true for the AR methods). When teacher assignment is not random,
estimators that either explicitly control for the assignment mechanism or proxy for it in some way
typically provide more reliable estimates of the teacher effects. Among the estimators and assignment scenarios we study, DOLS and SDOLS are the only estimators that control for the assignment
mechanism (again, either explicitly or by proxy) through the inclusion of both the lagged test score
and teacher assignment dummies. As expected, DOLS and SDOLS outperform the other estimators in the nonrandom teacher assignment scenarios. In the analysis of the real data, we found
that the rank correlations between, say, DOLS and EB LAG or DOLS and SAR are quite low for
some districts, suggesting that the decision among these estimators is important. Thus, if there is a
possibility of nonrandom assignment, DOLS should be the preferred estimator.
As predicted by theory and seen in the simulation results, the random effects estimator, EB
LAG, converges to the fixed effects estimator, DOLS, as the number of students per teacher gets
large. Therefore, it could be that EB LAG is performing well in large samples simply because the
estimates are approaching the DOLS estimates. However, the average residual methods, AR and
SAR, do not have this property. Thus, despite the recent popularity, we strongly caution using SAR
as a simpler way to operationalize the EB LAG estimator. If EB-type methods are being used, it is
important to estimate the coefficients in the first stage using random effects estimation (as in our
EB LAG estimator) rather than OLS.
Lastly, we find that shrinking the estimates of the teacher effects does not seem to improve the
performance of the estimators, even in the case where estimates are based on one cohort of students.
The performance measures are extremely close in our simulations for those estimators that differ
only due to the shrinkage factor – DOLS and SDOLS or AR and SAR. The rank correlations

81

for these two pairs of estimators are also very close to one in almost all districts. Also, we find
in the simulations that shrinking the AR estimates, which is a popular way to operationalize the
EB approach, does not reduce misclassification of teachers. Thus, our evidence suggests that the
rationale for using shrinkage estimators to reduce the misclassification of teachers due to noisy
estimates of teacher effects should not be given much weight. Accounting for nonrandom teacher
assignment when choosing among estimators is more imperative.
Given the robust nature of the DOLS estimator to a wide variety of grouping and assignment
scenarios, it should be preferred to AR and EB methods when there is uncertainty about the true
underlying assignment mechanism. If the assignment mechanism is known to be random, applying
these AR and EB estimators can be appropriate, especially when the amount of data per teacher
is minimal. However, given that the assignment mechanism is not likely known, blindly applying
these AR and EB methods can be extremely problematic, especially if teachers are truly assigned
nonrandomly to classrooms. Therefore, we stress caution in applying theses AR and EB methods and urge researchers to be mindful of the underlying assignment mechanism when choosing
between the various value-added methods.

82

APPENDICES

83

APPENDIX A CHAPTER 1 TABLES AND FIGURES

Table A.1 Fiscal Stress Label Transitions from 2000-2012
Oversight
in 2000

Emergency
in 2000

No Label
to Oversight

No Label
to Emergency

Oversight
to Emergency

Oversight
to No Label

Emergency
to No Label

6

9

92

4

19

57

30

Figure A.1 Geographic Distribution of Labeled School Districts Across Ohio

84

Figure A.2 Yearly Number of Labels, by Label Severity
60	
  

Number	
  of	
  Labels	
  

50	
  

40	
  

30	
  

20	
  

10	
  

0	
  
2000	
  

2001	
  

2002	
  

2003	
  

2004	
  

2005	
  

2006	
  

2007	
  

2008	
  

2009	
  

2010	
  

2011	
  

2012	
  

Year	
  
Fiscal	
  Oversight	
  

Fiscal	
  Emergency	
  

Table A.2 Table of Means - School District Demographic Characteristics
Panel A
Never in
Fiscal Stress
Total Enrollment
Proportion Free/Reduce Lunch Students
Number of Schools in District
FTE Teachers
Poor School Report Card Grade
Urban District
School Districts

Panel B†
Pre-Fiscal Fiscal
Stress
Stress

Panel C‡
Fiscal Post-Fiscal
Stress
Stress

2,761
(4,192)
0.22
(0.13)
5.57
(8.31)
163
(254)
0.16
(0.20)
0.16
(0.36)

3,007
(2,620)
0.29
(0.17)
6.43
(4.73)
16.99
(1.81)
0.22
(0.22)
0.36
(0.48)

2,840
(2,383)
0.32
(0.16)
5.69
(4.24)
17.64
(2.00)
0.36
(0.39)
0.37
(0.49)

3,738
(7,689)
0.28
(0.16)
7.28
(13.60)
17.36
(2.05)
0.30
(0.36)
0.35
(0.48)

3,411
(6,043)
0.35
(0.18)
7.07
(12.49)
17.12
(1.73)
0.23
(0.32)
0.35
(0.48)

507

80

80

72

72

Note: Pre-Fiscal Stress corresponds to the time period prior to the declaration of fiscal stress for labeled districts. Fiscal Stress
corresponds to the time period a fiscal stress label is attached to the district. Post-Fiscal Stress corresponds to the time period
after the label has been removed. Non-Fiscal Stress corresponds to all non-labeled jurisdictions. Standard Deviations are given in
parentheses.
†Panel B includes districts that appear in both the pre-FS period and the FS period.
‡Panel C includes districts that appear in both the FS period and the post-FS period.

85

Table A.3 Table of Means - School District Financial Characteristics
Panel A
Never in
Fiscal Stress
Gen Fund Balance/Revenue Ratio
Ratio < -0.02

Total Expenditure PP
Operating Expenditures PP
Capital Expenditures PP
Total Salaries PP
Total Employee Benefits PP

Total Revenue PP
Total Federal Rev PP
Total State Rev PP
Total Local Rev PP
Local Prop Tax Rev PP
Local Oper Prop Tax Rev PP
Local Cap Prop Tax Rev PP
Local Income Tax Rev PP

School Districts

Panel B†
Pre-Fiscal Fiscal
Stress
Stress

Panel C‡
Fiscal Post-Fiscal
Stress
Stress

Overall District Finances
0.04
0.01
0.02
(0.10)
(0.09)
(0.09)
0.35
0.36
0.34
(0.37)
(0.33)
(0.33)
District Expenditures
10,906
10,572
10,250
(2,323)
(2,064)
(1,891)
8,691
9,227
8,917
(1,189)
(1,525)
(1,163)
1,775
748
822
(1,819)
(985)
(1,107)
5,397
5,398
5,321
(789)
(826)
(706)
1,752
2,060
1,941
(337)
(436)
(417)
District Revenues
10,436
11,295
11,028
(2,178)
(2,306)
(2,182)
654
1019
776
(394)
(673)
(557)
5,408
5,521
5,121
(2,537)
(2,197)
(2,549)
4,373
4,755
5,131
(1,467)
(1,684)
(1,762)
3,807
4,292
4,644
(1,626)
(2,005)
(1,982)
3,369
3,807
4,177
(1,509)
(1,880)
(1,932)
426
479
460
(320)
(373)
(368)
76
160
210
(215)
(333)
(403)

0.21
(0.16)
0.06
(0.14)
11,164
(4,413)
9,140
(3,524)
1,482
(1,034)
5,473
(1,693)
1,829
(552)
11,330
(4,665)
636
(331)
5,216
(3,851)
5,478
(3,122)
4,758
(3,540)
4,177
(3,205)
567
(432)
251
(450)
507

80

80

72

0.16
(0.12)
0.05
(0.15)
10,986
(1,718)
9,486
(1,130)
845
(902)
5,564
(754)
2,055
(367)
11,639
(1,809)
1,104
(708)
5,209
(1,777)
5,327
(1,751)
4,581
(1,891)
4,086
(1,810)
495
(368)
350
(572)
72

Note: Pre-Fiscal Stress corresponds to the time period prior to the declaration of fiscal stress for labeled districts. Fiscal
Stress corresponds to the time period a fiscal stress label is attached to the district. Post-Fiscal Stress corresponds to the time
period after the label has been removed. Never in Fiscal Stress corresponds to all non-labeled school districts. Standard
Deviations are given in parentheses. Per-pupil variables are given in 2010 $.
†Panel B includes districts that appear in both the pre-FS period and the FS period.
‡Panel C includes districts that appear in both the FS period and the post-FS period.

86

Figure A.3 Operating and Capital Per Pupil Expenditures and Revenues (2010 $)
2300	
  

9400	
  

Total	
  Capital	
  Expenditures	
  Per	
  Pupil	
  

Total	
  Opera+ng	
  Expenditures	
  per	
  Pupil	
  

9600	
  

9200	
  
9000	
  
8800	
  
8600	
  
8400	
  

2100	
  
1900	
  
1700	
  
1500	
  
1300	
  
1100	
  
900	
  
700	
  

8200	
  

500	
  
5	
  Before	
   4	
  Before	
   3	
  Before	
   2	
  Before	
   1	
  Before	
   Year	
  of	
   1	
  A6er	
   2	
  A6er	
   3	
  A6er	
   4	
  A6er	
   5	
  A6er	
  
Label	
  

5	
  Before	
   4	
  Before	
   3	
  Before	
   2	
  Before	
   1	
  Before	
   Year	
  of	
   1	
  A5er	
   2	
  A5er	
   3	
  A5er	
   4	
  A5er	
   5	
  A5er	
  
Label	
  

Years	
  Rela+ve	
  to	
  Label	
  Receipt	
  

Years	
  Rela5ve	
  to	
  Label	
  Receipt	
  

Labeled	
  Districts	
  

Districts	
  Never	
  Labeled	
  

Labeled	
  Districts	
  

(a) Operating Expenditures Per Pupil

(b) Capital Expenditures Per Pupil

4400	
  

650	
  

4200	
  

Capital	
  Tax	
  Revenue	
  Per	
  Pupil	
  

Opera&ng	
  Tax	
  Revenue	
  Per	
  Pupil	
  

Districts	
  Never	
  Labeled	
  

4000	
  

3800	
  

3600	
  

3400	
  

3200	
  

600	
  

550	
  

500	
  

450	
  

400	
  
5	
  Before	
   4	
  Before	
   3	
  Before	
   2	
  Before	
   1	
  Before	
   Year	
  of	
   1	
  A5er	
   2	
  A5er	
   3	
  A5er	
   4	
  A5er	
   5	
  A5er	
  
Label	
  

5	
  Before	
   4	
  Before	
   3	
  Before	
   2	
  Before	
   1	
  Before	
   Year	
  of	
   1	
  A4er	
   2	
  A4er	
   3	
  A4er	
   4	
  A4er	
   5	
  A4er	
  
Label	
  

Years	
  Rela&ve	
  to	
  Label	
  Receipt	
  

Years	
  Rela3ve	
  to	
  Label	
  Reciept	
  

Labeled	
  Districts	
  

Districts	
  Never	
  Labeled	
  

Labeled	
  Districts	
  

(c) Operating Tax Revenues Per Pupil

Districts	
  Never	
  Labeled	
  

(d) Capital Tax Revenues Per Pupil

87

Table A.4 Table of Means - Housing and Parcel Characteristics
Panel A
Never in
Fiscal Stress
Sale Price (2010 $)
Rooms
Bedrooms
Total Baths
Living Area (Sq. Ft.)
Year Home Built

School Districts

Panel B†
Pre-Fiscal
Fiscal
Stress
Stress

Panel C‡
Fiscal
Post-Fiscal
Stress
Stress

147,171
(64,913)
6.32
(0.62)
3.07
(0.25)
1.66
(0.39)
1,704
(330)
1961
(17)

139,979
(57,058)
6.18
(0.59)
3.01
(0.28)
1.63
(0.41)
1,587
(298)
1960
(18)

133,267
(58,147)
6.15
(0.52)
3.03
(0.21)
1.61
(0.33)
1,585
(335)
1959
(17)

140,687
(57,626)
6.18
(0.52)
3.02
(0.21)
1.62
(0.35)
1,584
(289)
1960
(18)

130,080
(56,211)
6.18
(0.50)
3.03
(0.21)
1.63
(0.36)
1,622
(295)
1960
(18)

409

73

73

60

60

Note: Pre-Fiscal Stress corresponds to period before label receipt. Fiscal Stress corresponds to the time a fiscal
stress label is attached to the district. Post-Fiscal Stress corresponds to the period after the label is removed.
Never in Fiscal Stress corresponds to all non-labeled jurisdictions. Standard Deviations are given in parentheses.
†Panel B includes districts that appear in both the pre-FS and FS periods.
‡Panel C includes districts that appear in both the FS and post-FS periods.

88

Table A.5 Effect of Fiscal Stress Receipt on Expenditures per pupil, by severity level
(1)

(2)

(3)

(4)

(5)

(6)

Total
Expend

Operating
Expend

Total
Salaries

Employee
Benefits

Capital
Expend

New
Construct

No Label to Fiscal Oversight

-0.096***
(0.023)
Fiscal Oversight to No Label
0.021
(0.017)
Fiscal Oversight to Fiscal Emergency
-0.020
(0.046)
Fiscal Emergency to No Label
-0.011
(0.025)
GF Balance/Rev Ratio
-0.004
(0.037)
Ratio ≤ -0.02
0.026*
(0.013)
Constant
8.877***
(0.010)

-0.037***
(0.009)
0.017*
(0.009)
-0.023
(0.018)
0.010
(0.013)
-0.019
(0.015)
0.020***
(0.005)
8.720***
(0.004)

-0.054*** -0.026**
(0.009)
(0.012)
0.022***
0.015
(0.008)
(0.014)
-0.029*
0.018
(0.017)
(0.025)
0.017
-0.055**
(0.012)
(0.025)
-0.035** -0.109***
(0.015)
(0.021)
0.017*** 0.027***
(0.006)
(0.008)
8.263*** 7.015***
(0.004)
(0.007)

-0.558*** -0.733***
(0.152)
(0.258)
0.191
0.010
(0.137)
(0.247)
-0.181
-0.042
(0.328)
(0.610)
0.078
0.204
(0.242)
(0.477)
0.575**
0.758**
(0.280)
(0.384)
0.035
0.255*
(0.089)
(0.139)
6.098*** 5.030***
(0.063)
(0.106)

Observations
7,337
7,337
7,337
7,337
7,337
7,337
R-squared
0.58
0.94
0.94
0.91
0.25
0.30
Dependent variables are natural logs of the listed per-pupil variables. Each specification contains controls for
school district time varying demographics, school district fixed effects, and year fixed effects. Robust standard
errors, clustered at the school district level given in parentheses.
*** p<0.01, ** p<0.05, * p<0.1

Table A.6 Effect of Fiscal Stress Receipt on Revenues per pupil, by severity level

No Label to Fiscal Oversight

(1)

(2)

(3)

(4)

Total
Revenue

Federal
Revenue

State
Revenue

Local
Revenue

0.001
(0.021)
Fiscal Oversight to No Label
0.010
(0.020)
Fiscal Oversight to Fiscal Emergency
-0.001
(0.041)
Fiscal Emergency to No Label
-0.089***
(0.029)
GF Balance/Rev Ratio
0.158***
(0.029)
Ratio ≤ -0.02
0.006
(0.010)
Constant
8.875***
(0.009)

-0.053**
-0.032
0.016
(0.022)
(0.031)
(0.015)
-0.050*
-0.006
0.023
(0.027)
(0.032)
(0.020)
0.013
-0.039
0.026
(0.046)
(0.063)
(0.028)
-0.081*** -0.077 -0.075***
(0.031)
(0.053)
(0.027)
0.104*** 0.138*** 0.187***
(0.039)
(0.044)
(0.032)
0.010
0.005
0.005
(0.013)
(0.015)
(0.010)
5.560*** 8.010*** 8.118***
(0.014)
(0.013)
(0.008)

(5)

(6)

(7)

Local Prop Oper Prop Cap Prop
Tax Rev
Tax Rev Tax Rev
0.049**
(0.019)
-0.013
(0.021)
0.067
(0.045)
-0.070***
(0.025)
0.049*
(0.028)
0.010
(0.009)
7.958***
(0.007)

0.065***
(0.020)
-0.003
(0.025)
0.092**
(0.047)
-0.054*
(0.028)
0.046*
(0.028)
0.011
(0.009)
7.834***
(0.007)

-0.049
(0.061)
-0.102
(0.066)
-0.043
(0.081)
-0.098
(0.085)
0.144*
(0.083)
0.016
(0.033)
5.690***
(0.027)

Observations
7,336
7,329
7,336
7,336
7,336
7,336
6,749
R-squared
0.70
0.91
0.74
0.93
0.96
0.97
0.77
Dependent variables are natural logs of the listed per-pupil variables. Each specification contains controls for school district
time varying demographics, school district fixed effects, and year fixed effects. Robust standard errors, clustered at the school
district level given in parentheses.
*** p<0.01, ** p<0.05, * p<0.1

89

Table A.7 Effect of School District Fiscal Stress Label Receipt on Housing Prices
(1)

(2)

(3)

ln(Parcel Sale Price)
0.012
0.013
-0.032
(0.035)
(0.035)
(0.031)
Fiscal Oversight to No Label
-0.065
-0.064
-0.029
(0.057)
(0.057)
(0.025)
Fiscal Oversight to Fiscal Emergency -0.056*
-0.056*
-0.012
(0.029)
(0.029)
(0.026)
Fiscal Emergency to No Label
0.071*** 0.071*** 0.066***
(0.015)
(0.015)
(0.013)
GF Balance/Rev Ratio
-0.019
-0.018
-0.003
(0.050)
(0.050)
(0.030)
No Label to Fiscal Oversight

District FE
Time (Month-Year) FE
County FE
County-Year FE

X
X

X
X
X

X
X
X

Observations
1,011,726 1,011,726 1,011,726
R-squared
0.54
0.54
0.55
Each specification contains controls for school district financial statistics and demographics, parcel characteristics, and set of fixed effects.
Robust standard errors, clustered at the school district level given in
parentheses. *** p<0.01, ** p<0.05, * p<0.1

Figure A.4 Event Study Results - District Enrollment
0.04	
  

0	
  

6+	
  
5	
  
4	
  
3	
  
2	
  
1	
   Year	
  of	
   1	
  A8er	
   2	
  A8er	
   3	
  A8er	
   4	
  A8er	
   5	
  A8er	
   6	
  A8er	
   7	
  A8er	
   8	
  A8er	
   9+	
  
Before	
   Before	
   Before	
   Before	
   Before	
   Before	
   Label	
  
A8er	
  

-­‐0.04	
  

-­‐0.08	
  

-­‐0.12	
  

-­‐0.16	
  

Grey shaded region depicts the 95% confidence interval for the estimated effect in each year relative to label receipt. Y-axis gives
point estimate from equation (3) using ln(enrollment) as dependent variable.

90

Figure A.5 Event Study Results - Total Operating Expenditures PP
0.02	
  

0	
  

6+	
  
5	
  
4	
  
3	
  
2	
  
1	
   Year	
  of	
   1	
  A8er	
   2	
  A8er	
   3	
  A8er	
   4	
  A8er	
   5	
  A8er	
   6	
  A8er	
   7	
  A8er	
   8	
  A8er	
   9+	
  
Before	
   Before	
   Before	
   Before	
   Before	
   Before	
   Label	
  
A8er	
  

-­‐0.02	
  

-­‐0.04	
  

-­‐0.06	
  

-­‐0.08	
  

-­‐0.1	
  

Grey shaded region depicts the 95% confidence interval for the estimated effect in each year relative to label receipt. Y-axis gives
point estimate from equation (3) using ln(operating expenditures PP) as dependent variable.

Figure A.6 Event Study Results - Total Capital Expenditures PP
0.5	
  

0.25	
  

0	
  

6+	
  
5	
  
4	
  
3	
  
2	
  
1	
   Year	
  of	
   1	
  A8er	
   2	
  A8er	
   3	
  A8er	
   4	
  A8er	
   5	
  A8er	
   6	
  A8er	
   7	
  A8er	
   8	
  A8er	
   9+	
  
Before	
   Before	
   Before	
   Before	
   Before	
   Before	
   Label	
  
A8er	
  

-­‐0.25	
  

-­‐0.5	
  

-­‐0.75	
  

-­‐1	
  

Grey shaded region depicts the 95% confidence interval for the estimated effect in each year relative to label receipt. Y-axis gives
point estimate from equation (3) using ln(capital expenditures PP) as dependent variable.

91

Figure A.7 Event Study Results - Local Property Tax Revenue and Millage Rates
0.15	
  

3	
  

0.13	
  

2.5	
  

0.11	
  
2	
  
0.09	
  
1.5	
  

0.07	
  
0.05	
  

1	
  

0.03	
  

0.5	
  

0.01	
  
-­‐0.01	
  

6+	
  
5	
  
4	
  
3	
  
2	
  
1	
   Year	
  of	
   1	
  A9er	
   2	
  A9er	
   3	
  A9er	
   4	
  A9er	
   5	
  A9er	
   6	
  A9er	
   7	
  A9er	
   8	
  A9er	
   9+	
  
Before	
   Before	
   Before	
   Before	
   Before	
   Before	
   Label	
  
A9er	
  

0	
  
-­‐0.5	
  

-­‐0.03	
  
-­‐0.05	
  

-­‐1	
  

(a) Total Local Operating Property Tax Revenue PP

(b) Total Local Operating Property Tax Millage Rate

0.2	
  

1	
  

0.1	
  

0	
  

6+	
  
5	
  
4	
  
3	
  
2	
  
1	
   Year	
  of	
   1	
  A7er	
   2	
  A7er	
   3	
  A7er	
   4	
  A7er	
   5	
  A7er	
   6	
  A7er	
   7	
  A7er	
   8	
  A7er	
   9+	
  
Before	
   Before	
   Before	
   Before	
   Before	
   Before	
   Label	
  
A7er	
  

0.5	
  

6+	
  
5	
  
4	
  
3	
  
2	
  
1	
   Year	
  of	
   1	
  A7er	
   2	
  A7er	
   3	
  A7er	
   4	
  A7er	
   5	
  A7er	
   6	
  A7er	
   7	
  A7er	
   8	
  A7er	
   9+	
  
Before	
   Before	
   Before	
   Before	
   Before	
   Before	
   Label	
  
A7er	
  

0	
  

-­‐0.1	
  

6+	
  
5	
  
4	
  
3	
  
2	
  
1	
   Year	
  of	
   1	
  A7er	
   2	
  A7er	
   3	
  A7er	
   4	
  A7er	
   5	
  A7er	
   6	
  A7er	
   7	
  A7er	
   8	
  A7er	
   9+	
  
Before	
   Before	
   Before	
   Before	
   Before	
   Before	
   Label	
  
A7er	
  

-­‐0.5	
  
-­‐0.2	
  
-­‐1	
  

-­‐0.3	
  

-­‐0.4	
  

-­‐1.5	
  

(c) Total Local Capital Property Tax Revenue PP

(d) Total Local Capital Property Tax Millage Rate

Grey shaded region depicts the 95% confidence interval for the estimated effect in each year relative to label receipt. Y-axis gives point estimate from equation (3) using
ln(local tax revenue) or millage rate as dependent variable.

92

Figure A.8 Event Study Results: Housing Prices
0.06	
  

0.04	
  

0.02	
  

0	
  

6+	
  
5	
  
4	
  
3	
  
2	
  
1	
   Year	
  of	
   1	
  A8er	
   2	
  A8er	
   3	
  A8er	
   4	
  A8er	
   5	
  A8er	
   6	
  A8er	
   7	
  A8er	
   8	
  A8er	
   9+	
  
Before	
   Before	
   Before	
   Before	
   Before	
   Before	
   Label	
  
A8er	
  

-­‐0.02	
  

-­‐0.04	
  

-­‐0.06	
  

-­‐0.08	
  

-­‐0.1	
  

Grey shaded region depicts the 95% confidence interval for the estimated effect in each year relative to label receipt. Y-axis gives
point estimate from equation (4) using ln(parcel sale price) as dependent variable.

Table A.8 Estimated Discontinuity at Year 3 Ratio Cutoff
Enrollment

Population

Poverty 5-17

-13.74
(31.85)

24.81
(90.16)

35.48
(30.06)

FRL Students Black Students
-284.39
(238.70)

-13.26
(19.30)

White Students
-0.61
(21.58)

Dependent variable is change from year t-1 to year t for
the listed variable. Estimated discontinuity from regression of the given variable on 0.02 width bins of the year
3 projected ratio around the -0.02 cutoff. Each cell gives
the estimate of the -0.02 to 0 bin relative to the -0.02 to
-0.04 bin. Robust standard errors given in parentheses.
*** p<0.01, ** p<0.05, * p<0.1

93

300
250
Frequency
150
200
100
50
0

0

50

100

Frequency
150
200

250

300

Figure A.9 Distribution of Projected General Fund Balance to Revenue Ratios

0
.5
Year 1 Projected General Fund Balance to Revenue Ratio

1

-.5

0
.5
Year 2 Projected General Fund Balance to Revenue Ratio

(b) Year 2 Projected Ratio

50

100

Frequency
150
200

250

300

(a) Year 1 Projected Ratio

0

-.5

-.5

0
.5
Year 3 General Fund Balance to Revenue Ratio

(c) Year 3 Projected Ratio

94

1

1

Change in Capital Expenditures PP from year t to t+1
-800
-600
-400
-200
0
200

Change in Operating Expenditures PP from year t to t+1
-200
-100
0
100
200

Figure A.10 Change in District Finances and Housing Prices, by Year 3 Projected Ratio

-.4

-.2
0
.2
Year 3 Projected General Fund Balance to Revenue Ratio

.4

-.4

-.2
0
.2
Year 3 Projected General Fund Balance to Revenue Ratio

.4

(c) Operating Property Tax Revenue per Pupil

Change in Yearly Avg. District Sale Price from year t to t+1
-10000
-8000
-6000
-4000
-2000

-.4

.4

(b) Capital Expenditures per Pupil

Change in Operating Tax Revenue PP from year t to t+1
-50
0
50
100
150

(a) Operating Expenditures per Pupil

-.2
0
.2
Year 3 Projected General Fund Balance to Revenue Ratio

-.4

-.2
0
.2
Year 3 Projected General Fund Balance to Revenue Ratio

(d) Avg. Yearly Housing Price

95

.4

Table A.9 Regression Discontinuity Results
Panel A: Operating Expenditures per Pupil

1[Projected Year 3 Ratio < -0.02]
Projected Year 3 Ratio

Year t-1 to Year t

Year t to Year t+1

42.01
(69.25)
275.56***
(70.38)

-195.15**
(50.42)
372.71***
(92.32)

5,814
0.07

5,315
0.14

Observations
R-squared

Panel B: Capital Expenditures per Pupil

1[Projected Year 3 Ratio < -0.02]
Projected Year 3 Ratio

Year t-1 to Year t

Year t to Year t+1

126.83
(119.29)
857.06***
(316.85)

-83.13
(116.44)
621.75**
(301.84)

5,814
0.01

5,315
0.01

Observations
R-squared

Panel C: Operating Property Tax Revenue per Pupil

1[Projected Year 3 Ratio < -0.02]
Projected Year 3 Ratio

Year t-1 to Year t

Year t to Year t+1

-9.61
(18.06)
-195.08***
(59.12)

34.94
(22.91)
-294.18***
(67.64)

5,813
0.07

5,314
0.07

Observations
R-squared

Panel D: Avg. Yearly District Sale Price

1[Projected Year 3 Ratio < -0.02]
Projected Year 3 Ratio
Projected Year 3 Ratio*
1[Projected Year 3 Ratio < -0.02]

Year t-1 to Year t

Year t to Year t+1

345.62
(1,220.84)
-1,627.81
(3,530.90)
7,910.29
(13,840.46)

2,002.13*
(1,206.59)
743.35
(3,941.61)
27,409.54*
(14,429.34)

Observations
4,286
3,929
R-squared
0.24
0.25
Dependent variable is yearly change in the listed variable. Each specification
contains controls for yearly changes in school district financial characteristics,
parcel characteristics, and a flexible polynomial of the projected year 3 ratio.
Robust standard errors, clustered at the school district level given in parentheses
*** p<0.01, ** p<0.05, * p<0.1

96

Table A.10 Variable Names and Definitions
Variable Name

Description

Fiscal Stress Indicators†
Fiscal Oversight
= 1 if school district is labeled in fiscal caution or fiscal watch at time t
Fiscal Emergency
= 1 if school district is labeled in fiscal emergency at time t
District Financials†
GF Balance/Rev Ratio
The end of year balance in the general fund divided by general fund revenue
Ratio < -0.02
=1 if the deficit in the gen fund exceeds 2% of gen fund revenue
Total Expend
Total expenditures divided by total enrollment
Operating Expend
Total operating expenditures divided by total enrollment
Total Salaries
Total expenditures on employee salaries divided by total enrollment
Employee Benefits
Total expenditures on employee benefits divided by total enrollment
Capital Expend
Total capital expenditures divided by total enrollment
New Construct
Total expenditures on new construction projects divided by total enrollment
Total Revenue
Total revenue divided by total enrollment
Federal Revenue
Total federal revenue divided by total enrollment
State Revenue
Total state revenue divided by total enrollment
Local Revenue
Total local revenue divided by total enrollment
Local Prop Tax Rev
Total local property tax revenue divided by total enrollment
Oper Prop Tax Rev
Total local property tax revenue for operating expenditure divided by total enrollment
Cap Prop Tax Rev
Total local property tax revenue for capital expenditure divided by total enrollment
Local Inc Tax Rev
Total local income tax revenue divided by total enrollment
District Demographics•
Total Enrollment
Total district enrollment
Proportion Free/Reduced Lunch Proportion of students that are eligible for free and reduced price lunch
Number of Schools in District
Total number of schools in the district
FTE Teachers
Total full-time equivalent teachers in the district
Poor School Report Card Grade School Report Card Grade is below average
Urban District
= 1 if school district is in an urban area
Parcel Characteristics
ln(Sale Price)
The natural log of the sale price
Rooms
The total number of rooms in the house
Bedrooms
The total number of bedrooms in the house
Total Baths
The total number of bathrooms in the house (half bath = 0.5)
Living Area
The total square footage of the living area in the house
Year Home Built
The year when house was originally constructed
† Sources: Data from Ohio Auditor website and Ohio Department of Education website’s list of fiscal caution, fiscal
watch, and fiscal emergency districts.
‡ Sources: Data from Ohio Auditor, Ohio Department of Taxation, and Common Core of Data
• Sources: Common Core of Data and Ohio Department of Education
Sources: Data from 62 of 88 counties in Ohio. Data was downloaded from individual county auditor websites
using parcel search tools or data set downloads.

97

Table A.11 Comparison of Full and Analytic Samples
Full Sample Analytic Sample
Fiscal Oversight
Fiscal Emergency
Below Avg Report Card Grade
Urban
GF Balance/Rev Ratio
Ratio ≤ -0.02
Revenue per Pupil
Expenditures per Pupil
Total Class I Millage Rate
Proportion of Free/Reduced Lunch
Proportion Black
Total Enrollment
Number of Schools in District
Pupil Teacher Ratio
Proportion Above Math Proficiency
Proportion Above Reading Proficiency
Observations

98

0.05
(0.21)
0.02
(0.13)
0.19
(0.40)
0.19
(0.39)
0.18
(0.19)
0.10
(0.30)
11,129
(4,402)
10,973
(4,591)
29.60
(6.56)
0.24
(0.18)
0.05
(0.14)
2,888
(4,684)
5.86
(9.08)
17.28
(2.47)
75.24
(11.37)
0.82
(0.08)
6,749

0.05
(0.21)
0.02
(0.13)
0.19
(0.39)
0.19
(0.39)
0.18
(0.19)
0.09
(0.29)
11,313
(4,756)
11,159
(4,889)
30.04
(6.93)
0.23
(0.17)
0.06
(0.15)
3,075
(5,170)
6.22
(10.14)
17.27
(2.60)
75.34
(11.51)
0.82
(0.08)
5,209

APPENDIX B CHAPTER 2 TABLES AND FIGURES

Table B.12 Property Tax Rates and Taxable Values 2002-2010
Michigan
School District Millage

Ohio

Class I Class II

School District Millage

Debt

4.20
(2.85)

Debt

3.19
(2.61)

3.19
(2.61)

Hold-Harmless

0.33
(1.85)

Current Expenses

23.06
(5.96)

26.69
(9.42)

Sinking Fund

0.33
(0.75)

Emergency Operating

2.48
(3.97)

2.48
(3.97)

Recreational

0.02
(0.21)

0.88
Permanent Improvements (1.03)

1.00
(1.13)

Non-Homestead

17.62
(1.72)

Classroom Facilities

0.14
(0.21)

0.14
(0.22)

Intermediate SD Millage
Debt

0.003
(0.03)

Vocational Education

0.76
(0.86)

Special Education

2.67
(1.03)

Enhancement

0.03
(0.19)

Operating

0.21
(0.13)
School District Taxable Values (in Millions)

Homestead

349
(578)

Class I

269
(402)

Non-Homestead

218
(391)

Class II

79
(219)

Industrial Personal Property

16.2
(110)

Tangible Personal Property

28
(61)

Commercial Personal Property

2.00
(16.2)

Tangible Public Utility Property

15
(28)

99

Table B.13 Revenue and Demographic Characteristics

Students
Total Expenditures (in Millions)
Total Revenue (in Millions)
State Revenue (in Millions)
Local Revenue (in Millions)
Taxable Value per Student (in Thousands)
Total Local Operating Revenue (in Millions)
Total Local Capital Revenue (in Millions)

Michigan

Ohio

2774
(4714)
32.6
(63.40)
31.2
(59.80)
23.1
(41.50)
6.22
(12.20)
307
(908)
0.953
(3.61)
2.76
(5.57)

2870
(4552)
33.8
(67.90)
34
(67.40)
14.8
(32.30)
16.8
(30.60)
133
(159)
13.9
(27.70)
1.83
(3.78)
0.4
(1.07)
396
(714)
2251
(2112)
824
(2749)
18.7
(36.20)
3314
(6301)
489
(1851)
5.81
(8.98)
4.09
(8.20)
5523

Total Local Income Tax Revenue (in Millions)
Special Education Students
White Students
Free or Reduced Lunch Students
Population (in Thousands)
Population Ð Ages 5-17
Population in Poverty Ð Ages 5-17
Number of Schools
Number of Title I Schools
Number of Observations

100

117
(323)
2134
(2580)
939
(2930)
17.5
(36.20)
3165
(7423)
462
(2583)
6.11
(8.92)
2.97
(7.64)
4953

Figure B.11 Total Enrollment of Quintiles

Total	
  Enrollment	
  in	
  Quin5le	
  (1000s)	
  

450	
  

400	
  

Wealthier	
  

350	
  
Median	
  
300	
  
Wealthiest	
  
250	
  
Poorer	
  
Poorest	
  	
  

200	
  

150	
  
2002	
  

2003	
  

2004	
  

2005	
  

2006	
  

2007	
  

2008	
  

2009	
  

2010	
  

Year	
  

(a) Michigan

Total	
  Enrollment	
  in	
  Quin5le	
  (1000s)	
  

550	
  
500	
  

Wealthiest	
  

450	
  
Wealthier	
  

400	
  

Median	
  

350	
  
300	
  
250	
  

Poorer	
  
Poorest	
  	
  

200	
  
150	
  
100	
  
2002	
  

2003	
  

2004	
  

2005	
  

2006	
  

Year	
  

(b) Ohio

101

2007	
  

2008	
  

2009	
  

2010	
  

Figure B.12 Total Revenue Per Pupil
13500	
  
13000	
  
12500	
  
Wealthiest	
  

2010	
  Dollars	
  

12000	
  
11500	
  
11000	
  

Wealthier	
  
Median	
  
Poorest	
  	
  
Poorer	
  

10500	
  
10000	
  
9500	
  
9000	
  
2002	
  

2003	
  

2004	
  

2005	
  

2006	
  

2007	
  

2008	
  

2009	
  

2010	
  

Year	
  

(a) Michigan
15000	
  
Median	
  
14000	
  

Wealthiest	
  

2010	
  Dollars	
  

13000	
  

Poorer	
  
Poorest	
  	
  

12000	
  

Wealthier	
  

11000	
  

10000	
  

9000	
  
2002	
  

2003	
  

2004	
  

2005	
  

2006	
  

Year	
  

(b) Ohio

102

2007	
  

2008	
  

2009	
  

2010	
  

Figure B.13 State Revenue Per Pupil
9500	
  

2010	
  Dollars	
  

9000	
  

8500	
  
Wealthiest	
  
8000	
  
Wealthier	
  
Median	
  
Poorest	
  	
  

7500	
  

Poorer	
  
7000	
  
2002	
  

2003	
  

2004	
  

2005	
  

2006	
  

2007	
  

2008	
  

2009	
  

2010	
  

Year	
  

(a) Michigan
10000	
  
9000	
  

2010	
  Dollars	
  

8000	
  

Median	
  
Poorer	
  
Poorest	
  	
  

7000	
  
6000	
  
5000	
  

Wealthier	
  

4000	
  

Wealthiest	
  

3000	
  
2000	
  
2002	
  

2003	
  

2004	
  

2005	
  

2006	
  

Year	
  

(b) Ohio

103

2007	
  

2008	
  

2009	
  

2010	
  

Figure B.14 Local Revenue Per Pupil
4500	
  
4000	
  
Wealthiest	
  

2010	
  Dollars	
  

3500	
  
3000	
  
2500	
  

Wealthier	
  
Median	
  

2000	
  

Poorer	
  

1500	
  

Poorest	
  	
  

1000	
  
2002	
  

2003	
  

2004	
  

2005	
  

2006	
  

2007	
  

2008	
  

2009	
  

Year	
  

(a) Michigan
10000	
  
9000	
  
Wealthiest	
  

2010	
  Dollars	
  

8000	
  
7000	
  
Wealthier	
  

6000	
  

Median	
  

5000	
  
4000	
  

Poorer	
  
Poorest	
  	
  

3000	
  
2002	
  

2003	
  

2004	
  

2005	
  

2006	
  

Year	
  

(b) Ohio

104

2007	
  

2008	
  

2009	
  

2010	
  

Figure B.15 Local Operating Tax Revenue Per Pupil
1000	
  

9000	
  
Wealthiest	
  

900	
  

8000	
  

800	
  
700	
  

2010	
  Dollars	
  

6000	
  

600	
  
500	
  
400	
  

5000	
  

Wealthier	
  
Median	
  

4000	
  
3000	
  

300	
  

Wealthier	
  

200	
  
100	
  

Median	
  
Poorer	
  

2000	
  

Poorest	
  

1000	
  

Poorer	
  
Poorest	
  	
  

0	
  

0	
  
2002	
  

2003	
  

2004	
  

2005	
  

2006	
  

2007	
  

2008	
  

2009	
  

2002	
  

2010	
  

2003	
  

2004	
  

2005	
  

2006	
  

2007	
  

Year	
  

Year	
  

(a) Michigan Property Tax

(b) Ohio Property Tax

400	
  
350	
  

Poorer	
  

300	
  

2010	
  Dollars	
  

2010	
  Dollars	
  

Wealthiest	
  

7000	
  

250	
  

Median	
  

200	
  

Wealthier	
  
Poorest	
  	
  

150	
  
100	
  

Wealthiest	
  

50	
  
0	
  
2002	
  

2003	
  

2004	
  

2005	
  

2006	
  
Year	
  

2007	
  

(c) Ohio Income Tax

105

2008	
  

2009	
  

2010	
  

2008	
  

2009	
  

2010	
  

Table B.14 Revenue Regression Results Without District Fixed Effects
Total Revenue

State Revenue

Local Revenue

Michigan
Ohio
Michigan
Ohio
Michigan
0.146** 0.139** 0.103** -0.647** 0.386**
(0.017)
(0.029)
(0.015)
(0.047)
(0.050)

Ohio
0.849**
(0.025)

ln(Enrollment)

0.730**
(0.072)

0.751**
(0.055)

0.733**
(0.073)

1.151**
(0.081)

0.763**
(0.133)

0.353**
(0.060)

ln(Spec Ed Enrollment)

0.038**
(0.012)

0.153**
(0.025)

0.023*
(0.009)

0.143**
(0.036)

0.109**
(0.039)

0.081**
(0.026)

ln(White Enrollment)

-0.093** -0.123** -0.052** -0.070**
(0.018)
(0.026)
(0.009)
(0.018)

-0.130*
(0.051)

-0.148**
(0.033)

ln(Total Taxable Value)

ln(Free/Reduced Lunch Enroll)

-0.007
(0.013)

-0.036*
(0.016)

0.012
(0.007)

0.011
(0.021)

-0.106*
(0.043)

-0.023
(0.016)

Number of Schools

0.005**
(0.001)

0.002
(0.003)

0.004**
(0.001)

-0.009*
(0.004)

0.004
(0.005)

0.020**
(0.003)

Number of Title I Schools

-0.003*
(0.001)

0.001
(0.003)

-0.003**
(0.001)

0.013**
(0.004)

-0.003
(0.004)

-0.017**
(0.003)

ln(Population)

0.087*
(0.039)

-0.046
(0.053)

0.053
(0.028)

0.027
(0.079)

0.113
(0.161)

-0.063
(0.058)

ln(Population under age 18)

0.102
(0.070)

0.078
(0.055)

0.112
(0.071)

0.350**
(0.093)

0.166
(0.177)

-0.070
(0.064)

ln(Pop. under age 18 in poverty)

-0.029*
(0.013)

0.045**
(0.013)

-0.014
(0.011)

0.020
(0.018)

-0.260**
(0.042)

-0.058
(0.015)

Constant

7.57**
(0.169)

8.34**
(0.249)

7.98**
(0.148)

16.42**
(0.402)

1.70**
(0.598)

-0.846**
(0.247)

0.99
4726

0.95
4836

0.99
4726

0.9
4836

0.87
4723

0.97
4836

R-squared
Observations

Dependent variables are natural logs of the listed revenue variables. Each specification contains year fixed
effects. Robust standard errors, clustered at the school district level given in parentheses.
** p<0.01, * p<0.05

106

Figure B.16 Local Capital Property Tax Revenue Per Pupil
1500	
  
Wealthiest	
  
Wealthier	
  

1300	
  

2010	
  Dollars	
  

1100	
  
Median	
  
Poorer	
  

900	
  

Poorest	
  

700	
  

500	
  

300	
  
2002	
  

2003	
  

2004	
  

2005	
  

2006	
  

2007	
  

2008	
  

2009	
  

2010	
  

Year	
  

(a) Michigan
1000	
  
Wealthiest	
  

900	
  

2010	
  Dollars	
  

800	
  
Wealthier	
  

700	
  

Median	
  
Poorer	
  

600	
  
500	
  
400	
  

Poorest	
  	
  
300	
  
2002	
  

2003	
  

2004	
  

2005	
  

2006	
  

Year	
  

(b) Ohio

107

2007	
  

2008	
  

2009	
  

2010	
  

Table B.15 Revenue Regression Results With District Fixed Effects
Total Revenue

State Revenue

Local Revenue

Michigan
Ohio
Michigan
Ohio
Michigan
0.245** 0.097** 0.238** -0.574** 0.405**
(0.035)
(0.037)
(0.040)
(0.060)
(0.112)

Ohio
0.671**
(0.037)

ln(Enrollment)

0.335**
(0.120)

0.414**
(0.081)

0.381**
(0.136)

0.789**
(0.119)

0.103
(0.068)

0.165
(0.089)

ln(Spec Ed Enrollment)

0.027*
(0.012)

0.041
(0.023)

0.030*
(0.013)

0.048
(0.035)

0.021
(0.017)

0.037*
(0.017)

ln(White Enrollment)

-0.005
(0.007)

-0.169**
(0.056)

-0.002
(0.007)

-0.347**
(0.070)

-0.006
(0.015)

0.001
(0.072)

ln(Free/Reduced Lunch Enroll)

0.037**
(0.013)

0.018
(0.015)

0.037*
(0.015)

0.054*
(0.022)

0.041**
(0.014)

0.001
(0.012)

Number of Schools

0.003*
(0.002)

0.004
(0.003)

0.005*
(0.002)

0.006
(0.004)

-0.004
(0.002)

0.005*
(0.002)

Number of Title I Schools

-0.001**
(0.000)

0.000
(0.002)

-0.001
(0.000)

0.001
(0.003)

0.001
(0.001)

-0.003
0.002

ln(Population)

0.356**
(0.092)

-0.116
(0.202)

0.141
(0.106)

-0.063
(0.305)

1.505**
(0.343)

0.205
(0.164)

ln(Population under age 18)

0.015
(0.091)

0.515**
(0.161)

-0.070
(0.101)

0.551*
(0.240)

0.056
(0.241)

0.017
(0.119)

ln(Pop. under age 18 in poverty)

0.025**
(0.007)

0.002
(0.010)

0.036**
(0.007)

-0.002
(0.014)

-0.011
(0.021)

-0.006
(0.008)

Constant

5.63**
(0.690)

9.86**
(1.098)

7.73**
(0.747)

19.44**
(1.687)

-8.42**
(2.701)

-0.413
(0.931)

0.99
4726

0.97
4836

0.99
4726

0.94
4836

0.97
4723

0.99
4836

ln(Total Value)

R-squared
Observations

Dependent variables are natural logs of the listed revenue variables. Each specification contains school district fixed effects and year fixed effects. Robust standard errors, clustered at the school district level given in
parentheses.
** p<0.01, * p<0.05

108

Figure B.17 Total Expenditures Per Pupil
15000	
  

14000	
  

2010	
  Dollars	
  

13000	
  

Wealthiest	
  

12000	
  
Wealthier	
  
Median	
  
Poorest	
  

11000	
  

Poorer	
  
10000	
  

9000	
  
2002	
  

2003	
  

2004	
  

2005	
  

2006	
  

2007	
  

2008	
  

2009	
  

2010	
  

Year	
  

(a) Michigan
14000	
  

Median	
  

13500	
  

Wealthiest	
  
Poorer	
  

13000	
  

2010	
  Dollars	
  

12500	
  
12000	
  

Poorest	
  	
  

11500	
  
11000	
  
Wealthier	
  

10500	
  
10000	
  
9500	
  
9000	
  
2002	
  

2003	
  

2004	
  

2005	
  

2006	
  

Year	
  

(b) Ohio

109

2007	
  

2008	
  

2009	
  

2010	
  

APPENDIX C CHAPTER 3 TABLES AND FIGURES

Table C.16 Simulation Results: Comparing Fixed and Random Teacher Effects Estimators
λ = 0.5
Four Cohorts
One Cohort
G-A
Evaluation
DOLS AR EB LAG DOLS AR EB LAG
Mechanism
Type
Rank Correlation 0.85 0.85
0.86
0.65 0.65
0.67
Misclassification 0.15 0.15
0.15
0.25 0.25
0.26
Avg. Theta
1.01 1.01
0.78
1.03 1.03
0.49
RA
Avg. Std. Dev.
0.13 0.14
0.12
0.28 0.27
0.18
MSE
0.02 0.02
0.01
0.08 0.08
0.03
Rank Correlation 0.85 0.85
0.86
0.64 0.64
0.65
Misclassification 0.15 0.16
0.16
0.26 0.25
0.25
Avg. Theta
1.01 0.99
0.77
1.00 0.98
0.45
DG-RA
Avg. Std. Dev.
0.14 0.14
0.12
0.27 0.27
0.19
MSE
0.02 0.02
0.01
0.07 0.07
0.03
Rank Correlation 0.86 0.60
0.76
0.63 0.38
0.45
Misclassification 0.15 0.28
0.22
0.26 0.35
0.48
Avg. Theta
0.99 0.53
0.49
0.98 0.52
0.16
DG-PA
Avg. Std. Dev.
0.13 0.19
0.16
0.27 0.30
0.22
MSE
0.02 0.04
0.02
0.07 0.09
0.05
Rank Correlation 0.85 0.62
0.78
0.67 0.41
0.48
Misclassification 0.14 0.26
0.20
0.25 0.34
0.47
Avg. Theta
1.01 0.54
0.53
1.03 0.54
0.17
DG-NA
Avg. Std. Dev.
0.14 0.19
0.15
0.27 0.29
0.22
MSE
0.02 0.03
0.02
0.07 0.09
0.05
Rank Correlation 0.72 0.73
0.73
0.58 0.59
0.60
Misclassification 0.23 0.22
0.23
0.29 0.29
0.30
Avg. Theta
1.02 1.02
0.86
1.00 0.99
0.54
HG-RA
Avg. Std. Dev.
0.21 0.21
0.18
0.32 0.31
0.21
MSE
0.05 0.04
0.03
0.10 0.10
0.04
Rank Correlation 0.94 0.93
0.94
0.81 0.79
0.81
Misclassification 0.09 0.10
0.10
0.17 0.18
0.19
Avg. Theta
1.61 1.52
1.43
1.60 1.51
1.06
HG-PA
Avg. Std. Dev.
0.20 0.19
0.16
0.31 0.30
0.19
MSE
0.04 0.04
0.03
0.10 0.09
0.04
Rank Correlation 0.39 0.38
0.41
0.26 0.25
0.28
Misclassification 0.35 0.35
0.38
0.40 0.41
0.55
Avg. Theta
0.33 0.32
0.15
0.34 0.33
0.06
HG-NA
Avg. Std. Dev.
0.22 0.23
0.22
0.32 0.32
0.24
MSE
0.05 0.05
0.05
0.10 0.10
0.06
Note: Rows of each scenario represent the following:
First - Rank corr. of estimated effects and true effects
Second - Fraction of above average teachers misclassified as below average
Third - Average value of θˆ
Fourth - Average standard deviation of estimated teacher effects across 100
reps
Fifth - MSE measure

110

Table C.17 Simulation Results: Comparing Shrunken and Unshrunken Estimators
λ = 0.5
Four Cohorts
One Cohort
G-A
Evaluation
DOLS SDOLS AR SAR DOLS SDOLS AR
Mechanism
Type
Rank Correlation 0.85
0.85 0.85 0.85 0.65
0.66 0.65
Misclassification 0.15
0.15 0.15 0.15 0.25
0.25 0.25
RA
Avg. Theta
1.01
1.01 1.01 1.01 1.03
0.99 1.03
Avg. Std. Dev.
0.13
0.13 0.14 0.14 0.28
0.26 0.27
MSE
0.02
0.02 0.02 0.02 0.08
0.07 0.08
Rank Correlation 0.85
0.85 0.85 0.85 0.64
0.64 0.64
Misclassification 0.15
0.15 0.16 0.16 0.26
0.25 0.25
DG-RA
Avg. Theta
1.01
1.01 0.99 0.99 1.00
0.96 0.98
Avg. Std. Dev.
0.14
0.14 0.14 0.14 0.27
0.26 0.27
MSE
0.02
0.02 0.02 0.02 0.07
0.07 0.07
Rank Correlation 0.86
0.86 0.60 0.60 0.63
0.63 0.38
Misclassification 0.15
0.15 0.28 0.28 0.26
0.27 0.35
DG-PA
Avg. Theta
0.99
0.99 0.53 0.53 0.98
0.92 0.52
Avg. Std. Dev.
0.13
0.13 0.19 0.19 0.27
0.25 0.30
MSE
0.02
0.02 0.04 0.04 0.07
0.06 0.09
Rank Correlation 0.85
0.85 0.62 0.62 0.67
0.67 0.41
Misclassification 0.14
0.14 0.26 0.26 0.25
0.25 0.34
Avg. Theta
1.01
1.01 0.54 0.53 1.03
0.97 0.54
DG-NA
Avg. Std. Dev.
0.14
0.14 0.19 0.19 0.27
0.25 0.29
MSE
0.02
0.02 0.03 0.03 0.07
0.06 0.09
Rank Correlation 0.72
0.72 0.73 0.73 0.58
0.59 0.59
Misclassification 0.23
0.23 0.22 0.22 0.29
0.29 0.29
Avg. Theta
1.02
1.02 1.02 1.02 1.00
0.96 0.99
HG-RA
Avg. Std. Dev.
0.21
0.21 0.21 0.21 0.32
0.30 0.31
MSE
0.05
0.05 0.04 0.04 0.10
0.09 0.10
Rank Correlation 0.94
0.94 0.93 0.93 0.81
0.81 0.79
Misclassification 0.09
0.09 0.10 0.10 0.17
0.17 0.18
HG-PA
Avg. Theta
1.61
1.61 1.52 1.52 1.60
1.56 1.51
Avg. Std. Dev.
0.20
0.20 0.19 0.19 0.31
0.30 0.30
MSE
0.04
0.04 0.04 0.04 0.10
0.09 0.09
Rank Correlation 0.39
0.40 0.38 0.38 0.26
0.27 0.25
Misclassification 0.35
0.35 0.35 0.35 0.40
0.41 0.41
HG-NA
Avg. Theta
0.33
0.33 0.32 0.32 0.34
0.32 0.33
Avg. Std. Dev.
0.22
0.22 0.23 0.23 0.32
0.30 0.32
MSE
0.05
0.05 0.05 0.05 0.10
0.09 0.10
Note: Rows of each scenario represent the following:
First - Rank corr. of estimated effects and true effects
Second - Fraction of above average teachers misclassified as below average
Third - Average value of θˆ
Fourth - Average standard deviation of estimated teacher effects across 100 reps
Fifth - MSE measure

111

SAR
0.66
0.25
0.99
0.26
0.07
0.64
0.25
0.94
0.25
0.06
0.38
0.36
0.49
0.29
0.08
0.41
0.34
0.51
0.28
0.08
0.59
0.29
0.96
0.30
0.09
0.79
0.18
1.46
0.29
0.08
0.26
0.41
0.31
0.30
0.09

Figure C.18 Spearman Rank Correlations Across Different VAM Estimators

DOLS vs. AR

DOLS vs. EB LAG

AR vs. EB LAG

DOLS vs. SDOLS

AR vs. SAR

.4

.6

.8

1

Table C.18 Fraction of Teachers Ranked in Same Quintile by Estimator Pairs
DOLS SDOLS AR SAR
Top Quintile
SDOLS
AR
SAR
EB LAG

0.91
0.94
0.89
0.87

0.89
0.94
0.95

0.91
0.86 0.93

Bottom Quintile
SDOLS
AR
SAR
EB LAG

0.89
0.96
0.88
0.87

0.88
0.95
0.98

112

0.89
0.86 0.96

Table C.19 Description of Value-Added Estimators
Estimator

Acronym

Description

Teacher Effects

Two-step approach: Estimate teacher effects using MLE
EB LAG on dynamic equation and then shrink estimates by
shrinkage factor

Empirical Bayes’

Average Residual

AR

Estimate dynamic equation by OLS and compute residuals for each student. Then compute the average of these
residuals for each teacher to get estimated teacher effect

Random

Random

Shrunken Avg. Residual

SAR

Two-step approach: Compute average residual for each
teacher using residuals from OLS on dynamic equation.
Then shrink average residual for each teacher by shrinkage factor

Dynamic OLS

DOLS

Estimate teacher effects using ordinary least squares on
dynamic equation

Fixed

Shrunken DOLS

SDOLS

Two-step approach: Estimate teacher effects using dynamic equation and then shrink estimates by shrinkage
factor

Fixed

Random

Table C.20 Definitions of Grouping-Assignment Mechanisms
Name of G-A Mechanism

Acronym

Random Assignment
Dynamic Grouping - Random
Assignment
Dynamic Grouping - Positive
Assignment
Dynamic Grouping - Negative
Assignment
Heterogeneity Grouping Random Assignment
Heterogeneity Grouping Positive Assignment
Heterogeneity Grouping Negative Assignment

RA
DG-RA
DG-PA
DG-NA
HG-RA
HG-PA
HG-NA

Grouping students in
classrooms
Random
Dynamic (based on prior test
scores)
Dynamic (based on prior test
scores)
Dynamic (based on prior test
scores)
Static (based on student
heterogeneity)
Static (based on student
heterogeneity)
Static (based on student
heterogeneity)

Assigning students to teachers
Random
Random
Positive corr. between teacher effects and
prior student scores
Negative corr. between teacher effects and
prior student scores
Random
Positive corr. between teacher effects and
student fixed effects
Negative corr. between teacher effects and
student fixed effects

Table C.21 Description of Evaluation Measures of Value-Added Estimator Performance
Evaluation Measure
Rank Correlation
Misclassification
Average Theta
Avg. Std. Dev.
MSE

Description
Rank correlation between estimated teacher effect and true teacher effect
Fraction of above average teachers that are misclassified as below average
Average value of θˆ
Average standard deviation of estimated teacher effects across the 100 simulation reps
Average value of MSE = (β j − βˆj )2

113

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