525 Rouse and Barrow School Expenditure

8/7/2019 525 Rouse and Barrow School Expenditure

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Using market valuation to assess public

school spending

Lisa Barrowa, Cecilia Elena Rouseb,*

a

Economic Research Federal Reserve Bank of Chicago, Chicago, IL 60404, USAbFirestone Library, Industrial Relations Section, Princeton University, Princeton, NJ 08544, USA

Received 19 June 2002; received in revised form 5 December 2002; accepted 15 December 2002

Abstract

We examine whether school expenditures are valued by potential residents and whether the

current level of public school provision is inefficient by estimating the effect of state education aid on

residential property values. We find evidence that, overall, state aid is valued by potential residents

and that school districts do not overspend on education. However, we find that districts mayoverspend in areas where residents have fewer schooling options but find no difference in efficiency

by the degree of district unionization. One interpretation of these results is that increased competition

may reduce overspending on public schools in some areas.

D 2003 Elsevier B.V. All rights reserved.

JEL classification: I2; H4

Keywords: School choice; Education spending; Efficiency; Competition; Tiebout

1. Introduction

An enduring question in education policy is whether spending additional resources

on schools improves student outcomes. Some researchers point to evidence that

schooling inputs, such as lower pupil teacher ratios, longer school terms, and more

qualified teachers, improve test scores and wages (e.g., Card and Krueger, 1992;

Angrist and Lavy, 1999; Finn and Achilles, 1990; Krueger, 1999). Others point to

research that suggests improvements in school inputs, and expenditures in particular,

do not result in higher student achievement (e.g., Betts, 1995; Hanushek, 1986;

0047-2727/$ - see front matterD 2003 Elsevier B.V. All rights reserved.

doi:10.1016/S0047-2727(03)00024-0

* Corresponding author. Tel.: +1-609-258-4042; fax: +1-609-258-2907.E-mail address: [email protected] (C.E. Rouse).

www.elsevier.com/locate/econbase

Journal of Public Economics 88 (2004) 17471769


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Hanushek et al., 1996). Many of these researchers also argue that teachers unions and

bloated bureaucracies inhibit improved schooling inputs from generating better outputs,

resulting in inefficiency in public school provision (Chubb and Moe, 1990; Hoxby,

1996). Thus, it is the inefficiency in public school provision that interferes withadditional spending improving student outcomes. The typical approach in the existing

literature is to estimate directly the relationship between schooling expenditures and

student outputs, such as test scores or eventual wages. However, the importance of test

scores to adult outcomes is unclear, and it is rare to be able to link schooling inputs

to later outcomes because of the cost and difficulty in implementing long longitudinal

surveys and the unreliability of asking retrospective information on schooling inputs in

labor market surveys.

An alternative approach to analyzing whether schools effectively use additional expen-

ditures is to consider whether the market appears to value the spending, such as by

examining the relationship between school spending and property values. In the U.S. the

provision of elementary and secondary education is largely determined at the local level.

Therefore, if individuals make residential choices based on their preferences for schooling,

property values should reflect how schooling in an area is valued by potential residents (see,

e.g., Barrow, 2002; Black, 1999).

An advantage of considering the market valuation of spending is that it permits an

assessment of the value of school spending using a more contemporaneous measure of

(the perception of) the provision of schooling. In addition, one can assess whether

schools receiving additional revenue are inefficient in their provision of education by

testing whether a $1 increase in outside funding generates a (properly discounted) $1increase in housing values. On the one hand, as argued by Tiebout (1956), if

individuals choose their residence based on the provision of public goods, then the

optimal level of such public goods should be provided. By this argument, the

provision of schooling in the U.S. may well be efficient because schools compete

with one another through the residential housing market. This form of competition

insures both allocative and productive efficiency as parents who would like a different

kind or bundle of schooling can choose a different neighborhood, as can those who do

not believe that the quality of schooling merits their tax dollars.

On the other hand, there are several obstacles that may prevent the majority of school

districts from achieving the optimal level of schooling. First, because it is costly tomove, parents may not be perfectly mobile or have perfect information about localities

and the provision of education. In particular, low-income families may not be able to

choose to move out of the inner-city in order to reside in a district providing their

preferred level of education. In addition, a Tiebout equilibrium requires that parents have

a choice of different kinds of communities. Over the past 20 years many states have

centralized education finance to improve equity in the provision of schooling (Kenny

and Schmidt, 1994), housing discrimination limits the choices of some individuals (e.g.,

Yinger, 1998), and choices are more limited in communities with only a few school

districts. Each of these factors may limit the ability of parents to choose their preferred

provision of schooling.In this paper we adopt a market-based approach to examine both whether additional

spending on schools appears to increase school outputs, as perceived by the housing

L. Barrow, C.E. Rouse / Journal of Public Economics 88 (2004) 174717691748


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market, and whether public schools are inefficient. Because most of the debate surround-

ing school finance in the U.S. is implicitly about whether current spending is too high,1 we

focus on testing whether the current level of public school provision is inefficiently high.

We consider efficiency for the situation in which local school spending continues to befinanced (primarily) by a property tax as occurs in the majority of school districts in the

U.S. In this case, housing choices may be distorted by the property tax. Nevertheless, if

families have the option of choosing to send their children to the school of their choice,

communities may still achieve the second-best schooling optimum. Therefore, we test for

whether the current level of school spending is efficient conditional on the inefficiency

induced by the property tax.

In order to evaluate effectively the question of the efficiency of school spending, we

have assembled a rich and unique set of data on school districts. Our data sources

consist of both original data collected from state tax and education agencies as well as

various Census data. We find evidence that, on net, additional school spending leads to

increased property values, suggesting that additional expenditures may improve student

outcomes. In addition, we find that, on net, the current level of funding of public school

districts is not inefficiently high. That said, we find evidence of differences in the

valuation of spending across school districts. Particularly, we find that school districts

may overspend in large school districts, in those facing less competition, in primarily

rental property districts, and in areas in which residents are poor or less educated. In

contrast, we find no evidence that unionized districts spend beyond the optimal level,

thereby spending education dollars inefficiently. One interpretation of these results is that

increased competition has the potential to reduce overspending on public schools insome areas.

The rest of the paper is organized as follows. Section 2 outlines the theoretical model

upon which we base our statistical tests for the efficiency of school spending, Section 3

explains our empirical strategy, Section 4 describes our data, Section 5 contains results and

Section 6 concludes.

2. A (highly) stylized model of public good valuation

2.1. Basic model

Our market-based approach for assessing public school spending is based on

Brueckners bid-rent model of property value determination (Brueckner, 1979;

Brueckner, 1982; Brueckner, 1983). The result derived from this model is that

efficient public good provision occurs at the level that maximizes aggregate property

value. In the bid-rent model of the housing market, consumers are assumed to have

1 For example, many who argue that the public provision of schooling in the U.S. is likely inefficient note

that during the 1963 64 school year the government spent $2609 per pupil (in 1995 dollars), compared to $6459

per pupil spent during 199596, an increase of over 147 percent (Digest of Education Statistics, 1996), without

comparable increases in student achievement.

L. Barrow, C.E. Rouse / Journal of Public Economics 88 (2004) 17471769 1749


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identical preferences, and their utility depends on the level of schooling provided, E;

other local public goods, G; housing units, H; and the numeraire good, B. All residents

in a community consume the same level of the public goods, Eand G. Costless

mobility is assumed such that consumers with the same level of income must achievethe same utility level.2 As a result, house prices (rents) adjust to insure that residents

are indifferent between different houses. Formally, a resident with income Iachieves

utility hI and her consumption bundle must satisfy

UE; G; H; B hI: 1

This equality is guaranteed since if a consumer could achieve higher utility elsewhere,

she would move. A residents budget constraint can be written as B R I, where Rrepresents the rent paid for housing and the price ofB is normalized to 1. Then, R

must satisfy UE; G; H; I R hI. This equation determines the bid-rent function

R RE; G; H; I: 2

The bid-rent function specifies the rent necessary to equalize an individuals utility

across differing residences. Differentiating Eq. (2) with respect to Egives

REE; G; H; I UEE; G; H; I R

UBE; G; H; I R; 3

where subscripts denote partial derivatives. Eq. (3) shows that the required change in

the rent resulting from a change in Eis equal to the marginal rate of substitutionbetween education and the numeraire good, B. Similarly, the required change in the

rent resulting from a change in Gis equal to the marginal rate of substitution between

the other public goods and B.

Next, assume that local revenues for schooling are financed exclusively by a residential

property tax rate, tE, and the other public goods by a residential property tax, tG. The

property tax rates are applied to both land and improvements to ensure that the choice of

housing-factor inputs is not distorted. Letting d be the discount rate, the value of an

individual house i is

Pi R tE tG Pi

d

RE; G; Hi; Iid tE tG

: 4

The aggregate value of housing property is defined as the sum of the individual property

values within a community:

PXNi1

Pi XNi1

RE; G; Hi; Ii

d tE tG; 5

where Nis the number of houses in the community.

2 We could also allow for heterogenous preferences, in which case residents with the same preferences and

income would have to achieve the same level of utility.



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Assuming that the state contributes amountSto local school districts (the local

community fully finances the other public goods, G, for simplicity), the community budget

constraint is

tE tG P CEE; N S CGG; N; 6

where CEand CGare (convex) cost functions forEand G. The fact that cost is a

function of the community size, N, reflects potential congestion costs. Combining Eqs.

(5) and (6) gives

P1

d XN

i1

RE; G; Hi; Ii CEE; N S CGG; N

" #: 7

Aggregate property values are a function of the aggregate rents, state aid, the discount

rate, and the production costs of education and the other public goods. Differentiating

Eq. (7) with respect to the state aid and assuming that changes in state money for

education have no effect on the provision of other public goods, i.e. AG=AS 0,yields

AP

AS

1

d XN

i1

REE; G; Hi; Ii CEEE; N

" #AE

AS

1

d; 8

where, as shown in Eq. (3), REis equal to the marginal rate of substitution between

education and the numeraire good, B. As a result, Eq. (8) establishes thatAP=AS1=d when the Samuelson condition for the optimal provision of education issatisfied, i.e., the sum of the marginal rates of substitution between education and

the numeraire equals the marginal cost of providing education. (A similar condition

holds for all other public goods as well.) Assuming thatR is a strictly concave

function ofEand Gand thatCEis convex in Eand G, it follows thatPin Eq. (7) is

strictly concave in Eand G. As a result, aggregate property value reaches a global

maximum at values ofEand Gwhere the Samuelson condition holds, ceteris paribus.Thus, one can determine whether education is under-provided or over-provided relative

to the property value maximizing level as AP=AST1=d. Note that under- or over-provision of education may result either from productive or allocative inefficiencies.

One might conclude that education is over-provided in a district in which the right

level of education is being provided but the district is not cost minimizing.

Alternatively, the district may be productively efficient but not provide the property

value-maximizing level of education.

Because the null hypothesis on the coefficient of interest, that on state school

aid, depends on the discount rate, we use two rates in constructing our hypothesis

tests regarding school efficiency: 7.33 percent, which is the average real 30-yearconventional mortgage rate from 1980 to 1990, and the lower risk return of 5.24

percent, which is the average real 30-year Treasury bond yield from 1980 to



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1990.3 In addition, we adjust these discount rates for the average marginal U.S.

income tax rates between 1979 and 1989.4

2.2. Discussion of assumptions and omissions

The result above derives from a number of rather strong assumptions and omissions

that may not hold in reality. In this section we include a brief discussion of two of these

issues. We refer the interested reader to Barrow and Rouse (2002) for a more complete

discussion of these and other assumptions.

2.2.1. AG=AS 0First, we assume that state spending on education does not affect the provision of other

public goods. From the standpoint of basic economic theory this assumption seems

unrealistic since funding is fungible, and if a district receives aid from the state, the

equivalent to an increase in income, then the share devoted to education should be equal to

the marginal propensity to spend out of income (which would be about 510 cents on the

dollar; Hines and Thaler, 1995).

Nevertheless, we believe the assumption is not unrealistic in our case because we

limit our analysis to independent school districts, about 92 percent of all elementary

and secondary school districts in the U.S. (1992 Census of Governments, Government

Finances). Independent school districts, as defined by the Census of Governments, are

fiscally and administratively independent of other government entities, such as town-

ships and counties, and thus are considered governments themselves. Dependent schooldistricts, on the other hand, are dependent on a parent government. The parent

government of a dependent school district has the ability to shift public expenditure

among various public goods, whereas independent districts provide education and are

unable to spend revenues on public goods other than education. As a result, any state

aid received by an independent district either must be spent on the provision of

education or rebated to residents in the form of a tax rate reduction. Thus, only

indirectly may increased state aid lead to an increase in the provision of other public

goods in the county or township in which the school district is situated (because the

reduction in school taxes can be off-set by an increase in taxes to fund other public

goods).5

3 The nominal mortgage rate is from the Federal Home Mortgage Corporation (obtained from the Federal

Reserve Board of Governorshttp://www.bog.frb.fed.us/releases/h15/data/a/cm.txt). The nominal 30-year

Treasury bond yield (constantmaturity) is from the U.S. Treasury Department (obtained from the Federal

Reserve Board of Governorshttp://www.bog.frb.fed.us/releases/H15/data/a/tcm30y.txt). We use the personal

consumption expenditure price index to calculate the real rates.4 We calculate the marginal tax rate for 1979 to 1989 using the average income in the our sample for 1980

and inflating to current dollars for the subsequent years. The marginal tax rate we use is the average of these tax

rates over the 11 years. This average marginal tax rate is 26.7%.5 We examined this issue empirically by considering the relationship between county-level expenditures on

other public goods and state aid for education. We found thatAG=AS 0 seems to hold for the independentschool districts examined in this paper while AG=AS> 0 seems to apply to dependent districts that can moreeasily shift expenditures between budget categories.

http://%20http//www.bog.frb.fed.us/releases/h15/data/a/cm.txthttp://%20http//www.bog.frb.fed.us/releases/h15/data/a/cm.txthttp://%20http//www.bog.frb.fed.us/releases/h15/data/a/cm.txthttp://%20http//www.bog.frb.fed.us/releases/h15/data/a/tcm30y.txthttp://%20http//www.bog.frb.fed.us/releases/h15/data/a/tcm30y.txthttp://%20http//www.bog.frb.fed.us/releases/h15/data/a/tcm30y.txthttp://%20http//www.bog.frb.fed.us/releases/h15/data/a/tcm30y.txthttp://%20http//www.bog.frb.fed.us/releases/h15/data/a/cm.txt


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2.2.2. Business property

The model specified above also omits business property from consideration.6 Empir-

ically, we do not include business property in our estimation because data are not available

for most states. However, when we include it (along with other types of property, such aspersonal property) for the (few) states for which we have the data, it has not changed the

estimated coefficients substantially. As a result, we conclude that our treatment of

commercial property is unlikely to have a large effect on our conclusions about education

spending.

3. Empirical framework

Based on the theoretical framework, we estimate the following reduced-form equation:

Pjcst a0 Xjcsta1 Hjcsta2 Wcsta3 bSjcst nj ejcst; 9

where Pjcstis the aggregate house value per pupil in school districtj, in county c, in state s,

and yeart, Xjcstare a set of demographic characteristics about the districts population, Hjcstare characteristics of the housing stock of the district, Wcstare county characteristics, and

Sjcstis state revenue per pupil for education spending. njis a district fixed-effect and ejcstis

a normally distributed random error term.

b is a coefficient that represents the efficiency of school district spending on education.

In response to receiving an additional dollar of state aid, local school districts may take

several actions. A district facing expenditure constraints might increase educationspending by the entire dollar; an unconstrained district might reduce local property taxes

while simultaneously increasing education spending by less than $1. The estimate ofb

captures school district efficiency by summarizing the total effect on property values of

allowing school districts to adjust on both the tax and spending margins. One implication

is that we do not control for tax rates in this equation.

By far the most difficult empirical challenge to overcome is to control for all

characteristics that are correlated with state schooling revenue and housing values as

omitted factors may bias the results. In the 1970s many states relied on categorical aid to

fund education. During this time, state revenue was primarily determined by a flat grant

per pupil or by a flat grant in which the pupil count was weighted by the characteristics of

the students in each school district (such as grade level, special education needs, and

transportation). Between the 1970s and the 1990s many states changed their formulas in

order to equalize education funding across rich and poor districts. Many of the formulas

now incorporate the wealth of the district measured as property value per pupil, such that

property-rich districts receive less state aid while property-poor districts receive more.7 As

a result, while the relationship between district state funding per pupil and district assessed

valuation per pupil was relatively flat in 1980, the relationship has become more

7 This is a very broad generalization. See Card and Payne (1997), Evans et al. (1997), Murray et al. (1998)

for more details on state financing plans.

6 In 1986, approximately 61 percent of gross assessed valuation was due to residential (nonfarm) property

(1987 Census of Governments, Taxable Property Values).



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negatively sloped in 1990 for states that have made equalizing changes to their state

financing formulas.8

Fig. 1 depicts predicted total state aid per pupil in 1980 and 1990 versus aggregate

house values per pupil in 1980 for Colorado and West Virginia. Each graph also includes

regression fitted values from regressing predicted total state aid per pupil in each year on

aggregate house values per pupil in 1980. Colorado is an example of a state in which state

Fig. 1. Predicted state aid per pupil in 1990 and 1980 versus aggregate residential property value per pupil in

1980. Note: both 1980 and 1990 state aid are predicted from the state school financing formulas using thecharacteristics of the districts in 1980. All values are in 1994 dollars per pupil.

8 We have modeled which states change their financing formulas and which states adopt more or less

equalizing formulas by aggregating our data to the state level and estimating binary and multinominal logit

models. While we found some evidence that the average state household income and/or property values may

partially determine state behavior, the evidence was neither overwhelming nor systematic.



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school aid was made more equalizing. In 1980, the slope of the regression fitted line is

relatively flat while in 1990 the slope of the regression fitted line is more negative,

indicating that property-poor districts are getting more aid per pupil than wealthier

districts. While West Virginia adopted a more generous school financing formula in1990, as evidenced by the upward shift in the regression fitted line in 1990, the state did

not adopt a formula that increased the degree of equalization between 1980 and 1990. This

is evidenced by the slopes of the regression fitted lines remaining relatively similar. West

Virginias school financing formula generates some equalization, however, as can be seen

by the negative relationship between predicted state aid per pupil and aggregate house

values per pupil.

Because moving toward greater equalization is likely to result in districts with declining

property values receiving greater increases in state aid per pupil, we expect that the

coefficient estimate on changes in state aid will be negatively biased. We attempt to address

this potential problem in three ways. First, we control for a variety of district and county

characteristics that may be correlated with education provision and district property values.

For example, we include demographic characteristics of the district as well as the county

crime rates. These measures vary over time as well. Second, we focus on estimates that

contain school district fixed-effects (which we implement through first-differenced equa-

tions). This allows us to parcel out any time-invariant features of districts that may be

correlated with state education revenues and house values (such as distance to employment

centers, climate, and relatively stable characteristics about the student and local populations).

Third, we instrument for changes in state education revenue with changes in the state

school financing formulas. To construct our instrument, we first programmed each statesfinancing formulas in effect in 197879 and 199091. We then calculated the amount of

both the basic state aid and the total state aid that each district should have received

according to our computer programs in 1980 and 1990.9 Total state aid includes basic

state aid (usually the foundation amount) plus some additional components such as aid for

special and vocational education. In order to minimize the effect of changing district

characteristics on our calculations of the 1990 state aid, we estimate the amount of state aid

in 1990 using the formulas from 1990 and the district characteristics in 1980. (The

estimated amount of state aid in 1980 is constructed using the 1980 formulas and the

district characteristics in 1980.) We refer to this instrument as the predicted state aid.10

The disadvantage of the predicted state aid instrumental variables strategy is that it relieson the assumption that changes in district housing values are not correlated with district

characteristics in 1980 (which we use to construct the instrumental variable). To the extent

10 Unlike instrumental variables used in many recent works (see Card, 1995, for some examples), we do not

have an a priori reason to think that our instrument will affect certain districts more than others. Our instrumental

variable is designed to recover changes in state school finance formulas which affect all districts. An empirical

investigation of this issue is available from the authors on request.

9 We predict the amount of state aid that each district receives according to the formulas as described in the

Public School Finance Programs (1978, 1990). In some states we also supplemented these descriptions of the

formulas with additional information from the states or from the state statute when necessary. We used total

assessed valuations by district nationwide in 1980 and 1990 (which we collected) to determine the amount of state

aid. The correlation between our prediction of total state aid and the actual level of state aid is 0.39 in 1980, and

0.53 in 1990 if the 1990 district characteristics are used and 0.33 if the 1980 district characteristics are used.



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that 1980 to 1990 changes in residential housing values are correlated with district

characteristics in 1980, the instrumental variables results may be inconsistent.11

We also note that our strategy is to include an array of district and county characteristics

to proxy for the districts underlying cost function for education, rather than to controldirectly for education costs. We do so for two reasons. First, education costs (as opposed to

expenditures) are inherently more difficult to observe, and second, if we use education

expenditure as a proxy for local education cost, we do not have a strategy for addressing the

endogeneity of local education expenditure in addition to state aid. Many state school

financing formulas calculate a total amount of school financing need for each district

based on pupil counts in the district. One common feature of this portion of the formulas is

to assign different weights to different types of pupils in generating a total pupil count. More

specifically, the formulas give more weight to pupils that are more costly to educate, such as

students with special education needs. As a consequence, this feature of the formulas will

induce some positive correlation between local education costs and state aid. Given that

state aid is negatively correlated with property values, our IV estimates may be downward

biased to the extent to which we have not properly proxied for local education costs.12

4. Data

For most of our empirical analysis we use data from the 1980 and 1990 decennial census

school district data files, the 1977 and 1987 Census of Governments, and the USA Counties

1996CD-ROM. In order to generate our instrumental variables, we have also merged these

data with data we collected on tax rates and the total assessed valuation (adjusted to marketvalue both by the statutory assessment ratio and assessment-to-sales ratios where possible)

by school district from 1980 and 1990.13 The unit of observation is an independent school

district. As a result, we drop all school districts from the following statesAlaska, District

of Columbia, Hawaii, Maryland, North Carolina, and Virginiain which there are no

independent districts. We also lose most districts in Connecticut, Massachusetts, Rhode

Island, and Tennessee in which the majority of school districts are dependent on a parent

government.

In addition, we limit the sample to unified school districts that did not change between

1980 and 1990 (that is, they did not merge or split apart). We exclude districts in California

because we could not obtain property value data with which to model the school financingformulas. We also exclude school districts with zero enrollment in either 1980 or 1990,

11 To assess these results, we have also constructed instrumental variables by predicting state aid using

synthetically constructed districts. In general, the results generated using the synthetically predicted state aid are

similar to those using the predicted state aid, suggesting that any potential bias in our preferred instrument may

not significantly change the results. See Barrow and Rouse (2002) for more information.12 If we additionally control for total or local expenditure per pupil our results are very similar.13 Note that the dependent variable in our regressionsaggregate residential property values per pupilis

from the 1980 and 1990 decennial censuses. This measure of aggregate property value for a school district equals

the sum of aggregate owner-occupied house values and an estimate of the asset value of the rental property

derived from aggregate gross rent. Further, we use the pupil measure from the Census of Governments rather than

the pupil measure from the Census of Population for our dependent variable to avoid measurement error induced

bias in our coefficient estimate.



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and those for whom we are missing data on our instruments and aggregate property values.

The final analysis sample includes 9076 observations, about 92 percent of all independent,

unified school districts, 95 percent of all students in independent, unified school districts,

and 61 percent of all elementary and/or secondary districts in existence in 1991 based on

the 1992 datafile from the Census of Government Finances. A more detailed description of

the data is available from the authors upon request.Means of selected school district characteristics in 1980 and 1990 are presented in

Table 1. On average, aggregate house values per pupil increased by 40 percent between

1980 and 1990. State aid per pupil also increased from 1980 to 1990 (63 percent) arising

from both increases in total state aid as well as declining enrollment over the time period.

5. Empirical analysis

5.1. Ordinary least squares estimation (OLS)

In Table 2 we present ordinary least squares (OLS) estimates of the cross-sectional

relationship between aggregate residential property value per pupil and state aid for

Table 1

Means and standard deviations

Mean S.D.

School district characteristicsChange in aggregate residential property

value per pupil ($1000s) 51.274 104.653

Change in actual state aid per pupil 1053.516 817.188

Change in predicted basic aid per pupil 1120.730 1661.020

Change in predicted total aid per pupil 1147.038 1719.297

Change in average household income ($1000s) 2.377 6.411

Change in % population with at least

16 years of education 3.835 2.975

Change in % housing units owner occupied 1.307 3.821Change in % children enrolled in private school 2.603 3.176

Change in total housing units (1000s) 6.424 24.280

Change in enrollment (1000s) 3.768 16.212Change in % households in urban areas 1.296 7.514

County characteristics

Change in crime index 348.994 1352.677

% Missing change in crime index 0.766 8.718

Change in % voting Republican 13.432 6.854Change in % voting Democratic 0.639 6.741

Change in % county employees organized 1.558 20.905

% Missing change in county employees organized 3.122 17.394

Change in % employed in manufacturing 4.324 24.713

Notes: there are 9076 observations. All dollar values are in 1994 dollars. All means are weighted by studentenrollment in 1980. Changes in predicted state aid are calculated using the state school financing formulas and

the 1980 characteristics of school districts.



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education per pupil in 1980 and 1990. The results from simple bivariate regressions

are presented in columns (1) and (4); the remaining columns sequentially add district

and then county characteristics and Census division indicators. We estimate a negative

and statistically significant relationship between property values and state aid per pupil

in columns (1) and (4) reflecting the redistributive intent of state education aid. The

estimates in columns (2) and (5) include the levels for the relevant year of a quadratic

in average household income, the percentage of the population with at least 16 years

of education, the percentage of the population that is unemployed, the percentage ofhousing units that are owner occupied, the percentage of housing units that are vacant,

the percentage of occupied housing units that were built more than 10 years ago, the

Table 2

Cross-sectional OLS estimates from 1980 and 1990 of the effect of state aid on aggregate house values per pupil

1980 1990

(1) (2) (3) (4) (5) (6)

State aid per pupil 23.142 14.221 19.300 22.296 3.541 4.894(1.194) (0.911) (0.997) (1.271) (0.687) (0.718)

Average household income 5.166 2.973 9.330 8.507

(0.254) (0.292) (0.208) (0.222)

Average household income 0.308 0.161 0.214 0.183squared divided by 10,000 (0.022) (0.023) (0.012) (0.012)

% Population with at least 3378.585 3070.073 1505.819 1120.390

16 years of education (143.937) (148.190) (148.548) (145.142)

% Housing units owner 1460.617 1070.326 3155.466 2748.225occupied (81.191) (82.311) (119.514) (118.884)

% Children enrolled in private 709.688 1050.040 3577.272 3535.423school (124.889) (127.135) (150.339) (144.972)

Total housing units (1000s) 0.313 0.284 0.425 0.424

(0.025) (0.026) (0.024) (0.025)

Enrollment (1000s) 0.785 0.697 1.478 1.449(0.062) (0.064) (0.075) (0.075)

% Households in urban areas 251.551 192.573 110.452 209.398

(23.248) (25.010) (29.205) (29.324)

P-value: state aid = 18.61

(d 0:0733*1 mtra 0.000 0.000 0.000 0.000 0.000 0.000P-value: state aid= 26.03

(d 0:0524*1 mtra 0.000 0.000 0.000 0.000 0.000 0.000

R2 0.040 0.524 0.548 0.033 0.770 0.805

Notes: the dependent variable is the aggregate residential property value per pupil in 1980 or 1990. Standard

errors are in parentheses. There are 9076 observations. All equations include a constant. Columns (2) and (5) also

include the percent unemployed, the percent of housing units that are vacant, the percent of occupied housing

units built more than 10 years ago, the percent of households that moved into their house less than 10 years ago,

and the percent of the population over 55 years of age; columns (3) and (6) include the variables included in the

column (2) or (4) specification in addition to the variables listed under county characteristics in Table 1,

indicators for the Census division of the school district and dummy variables indicating if the crime index or the

percent of county employees that are unionized are missing. Columns (2), (3), (5), and (6) all include a dummy

variable indicating whether the percent of the population that moved in 10 years ago is missing. The equations are

weighted by student enrollment in 1980. All dollar values are in 1994 dollars.a

d is the discount rate; mtr is the marginal tax rate. See text.



13/23

percentage of the population that moved into their house less than 10 years ago, the

percentage of the population over 55 years of age, the percentage of children enrolled

in private schools, total housing units in the district, public school district enrollment,

and the percentage of housing units that are in urban areas. In columns (3) and (6) wealso add indicators for the districts Census division and the levels of the FBIs serious

crime index, the percentage of voters that voted for the Republican candidate in the

most recent presidential election, the percentage of voters that voted for the

Democratic candidate in the most recent presidential election, the percentage of the

county employees that are union members, and the percentage of workers employed in

manufacturing.14 We expect that the coefficient estimates on changes in state aid per

pupil will increase when the additional covariates are included.

As expected, the coefficient estimates in columns (2) and (5) increase such that we

estimate a $1 increase in state aid will decrease property values by $14 in 1980 and will

increase property values by $3.5 in 1990, effects that are statistically significant. The

effects decrease somewhat in columns (3) and (6) when we add the county and Census

division variables. These estimates are significantly different from 18.61 (corresponding to

a discount rate of 0.0733 adjusted by the marginal tax rate) and 26.03 (corresponding to a

discount rate of 0.0524 adjusted by the marginal tax rate), the range of estimates we would

expect if districts were spending efficiently.

In Table 3 we control for school district fixed-effects by estimating (via OLS) the

change in aggregate residential property value per pupil associated with the change in state

aid for education per pupil. Again, the results from a simple bivariate regression are

presented in column (1); the remaining two columns sequentially add district and thencounty characteristics and Census division indicators. The regressors are similar to those in

Table 2 in that we control for the levels of the variables from 1980 and well as the change

from 1980 to 1990. Once again, we tend to estimate a negative relationship between

property values and state aid per pupil, although the estimates tend to be less negative than

those in Table 2, reflecting the importance of controlling for all time-invariant district

characteristics.

Based on the OLS results in Tables 2 and 3, one would conclude both that the increased

expenditures are not valued in the housing market and that school districts are not

generating increases in property values consistent with property value maximization since

a $1 increase in their state education aid does not generate a (properly discounted) $1increase in property values.

5.2. Instrumental variables (IV) estimation

5.2.1. Overall

Our OLS coefficient estimates on state aid per pupil are likely biased for two reasons.

As discussed above we expect the estimates to be negatively biased because most states

have moved to more equalizing state financing formulas. Additionally, the estimates may

14 We also include dummy variables indicating whether there are missing values for the percentage of

households that moved into their house less than 10 years ago, the FBI crime index, and the percentage of county

workers who are organized.



14/23

be attenuated due to measurement error which is exacerbated in first-differenced

equations. As a result, we instrument for changes in state aid with changes in predicted

state aid, an instrument that holds the school districts characteristics constant at their

1980 levels. The first-stage relationship (not shown) is between observed changes in state

aid per pupil and the instrumental variables, predicted basic state aid and predicted total

state aid. These estimates suggest that both instruments are significantly correlated with

observed changes in state aid per pupil; a $1 increase in predicted aid is associated withapproximately a 9 cent increase in actual state aid, controlling for district and county

characteristics. The IV estimates are presented in Table 4. The estimates in column (1) use

Table 3

OLS estimates of the effect of change in state aid on change in aggregate house values per pupil

(1) (2) (3)

Change in state aid per pupil 18.823 3.232 6.522(1.330) (0.966) (0.980)

Change in average household income 7.967 7.239

(0.350) (0.365)

Change in average household income 0.021 0.026squared divided by 10,000 (0.023) (0.022)

Change in % population with at least 5657.455 4868.962

16 years of education (381.985) (370.410)

Change in % housing units owner occupied 4126.895 4400.536(233.916) (231.523)

Change in % children enrolled in private 3113.585 2973.682

school (275.595) (267.307)

Change in total housing units (1000s) 0.767 0.872

(0.062) (0.065)

Change in enrollment (1000s) 1.181 1.331

(0.148) (0.149)

Change in % households in urban areas 1155.674 1100.085

(99.653) (95.752)

P-value: state aid= 18.61

(d 0:0733*1 mtra 0.000 0.000 0.000P-value: state aid= 26.03

(d 0:0524*1 mtra 0.000 0.000 0.000R2 0.022 0.613 0.647

Notes: the dependent variable is the change (from 1980 to 1990) in the aggregate residential property valueper pupil. Standard errors are in parentheses. There are 9076 observations. All equations include a constant.

Column (2) also includes the change in the percent unemployed, change in the percent of housing units that

are vacant, change in the percent of occupied housing units built more than 10 years ago, change in the

percent of households that moved into their house less than 10 years ago, change in the percent of the

population over 55 years of age, and the 1980 levels of all included variables; column (3) includes the

variables included in the column (2) specification in addition to the variables listed under county

characteristics in Table 1, 1980 levels of the county characteristics, indicators for the Census division of the

school district and dummy variables indicating if the change in the crime index or the percent of county

employees that are unionized are missing. Both columns (2) and (3) include a dummy variable indicating

whether the 1980 percent of the population that moved in 10 years ago is missing. The equations are

weighted by student enrollment in 1980. All dollar values are in 1994 dollars.ad is the discount rate; mtr is the marginal tax rate. See text.



15/23

the change in predicted basic state aid and those in column (2) use the change in predicted

total state aid. We continue to control for the district and county characteristics as well as

Census divisions as described above. The magnitudes of the IV estimates are remarkably

similar across the two calculations of state aid. A $1 increase in state aid increases

aggregate housing values per pupil between $29 and $30. These results suggest that

increases in state aid increase property values, which reflects that potential residents valuethe education expenditure.

We also report the P-values for the test of the null hypothesis that districts are

spending education money efficiently, i.e., that the coefficient on state aid equals 18.61

or 26.03. In both cases we can reject that the coefficient equals the smaller of the two

values while we cannot reject equivalence at the larger value. Thus, we conclude that

there is no evidence of massive overspending by school districts on net. This

interpretation, however, depends heavily on the assumed discount rate. Another way

to evaluate the precision of the finding is to consider the range of discount rates over

which one would reject the null hypothesis that school districts spend inefficiently by

overspending. Given the point estimates in Table 4 of about 30, if the true discountrate is lower than 4.55 percent, school districts overspend and if the true discount rate

is more than 4.55 percent, school districts underspend. Thus, the finding that school

districts do not overspend would hold for a fairly wide range of discount rates (those

greater than 4.5 percent).

An important question is whether increases in state aid truly translate into increases

in education provision at the district level for our inferences about the efficiency of

school expenditures only hold ifyE=ySp0 (see Eq. (8)). To provide some evidence onhow the additional state aid is spent, we study the relationship between state aid and

district total expenditures on education, local school property tax rates, and local

revenues for education. We estimate instrumental variables models identical to those inTable 4 except for the dependent variable. The results, in Table 5, suggest that changes

in state aid for education increase education expenditure, decrease school district tax

Table 4

IV estimates of the effect of change in state aid per pupil on change in aggregate house values per pupil

Instrumental variable

Change in predicted Change in predictedbasic state aid total state aid

(1) (2)

Change in actual state aid 29.260 30.285

per pupil (5.074) (5.001)

P-value: state aid = 18.61

(d 0:0733*1 mtra 0.036 0.020P-value: state aid = 26.03

(d 0:0524*1 mtra 0.525 0.395

Notes: the dependent variable is the change (from 1980 to 1990) in aggregate residential property values per

pupil. The endogenous variable is the change in actual state aid per pupil. Standard errors are in parentheses. See

text or the notes to column (3) ofTable 2. There are 9076 observations.ad is the discount rate; mtr is the marginal tax rate. See text.



16/23

rates, and have no effect on total local revenue for public schools.15 The results from

estimating the effect of changes in state aid on total education expenditures are

presented in column (1).16 A $1 increase in state aid per pupil increases total

expenditures per pupil by approximately 83 cents. These results suggest that education

provision responds to changes in state aid, i.e. yE=ySp0, such that our estimate of theeffect of changes in state aid per pupil on changes in aggregate house values per pupil

leads to inferences about efficiency.

The results presented in columns (2) and (3) suggest that school districts may use some

of the increase in state aid per pupil to decrease their own tax burden. In column (2) we

show that a $1 increase in state aid per pupil is associated with a decrease in school district

property tax rates by 8 9 cents per $10,000 of aggregate property value. Increasing

property values over the decade may explain some of the decline in tax rates. Further, the

results in column (3) suggest that districts may have reduced their tax rates by enough to

decrease their local contribution to public schools; a $1 increase in state aid per pupil is

associated with a 56 cent decline in total local revenue per pupil, although the effect is

not statistically significant.

5.2.2. Differences by school district characteristics

The previous section tested for whether state aid translates into property value

increases, on net. This aggregate estimate, however, may mask important differences

Table 5

IV first-differenced estimates of the effect of change in state aid per pupil on school expenditures, property tax

rates, and property tax revenue

Dependent variableChange in total Change in school district Change in

expenditures per pupil property tax rates local revenue

(1) (2) (3)

Instrumental variable = change in predicted basic state aid per pupil

Change in actual state aid 0.831 0.089 0.062per pupil (0.076) (0.008) (0.049)

Instrumental variable = change in predicted total state aid per pupil

Change in actual state aid 0.833 0.080 0.048per pupil (0.074) (0.007) (0.048)

Number of observations 8460 8460 8460Notes: for each equation estimated, the endogenous variable is the change in actual state aid per pupil. Standard

errors are in parentheses. See text or column (3) ofTable 2 for other covariates. The equations are weighted by

district student enrollment in 1980. The mean of the dependent variable for column (1) estimates is 1353.92; the

mean for column (2) is 2.577; the mean for column (3) is 589.44. The school district property tax rate units aredollars raised per 10,000 dollars of property value. Changes in predicted state aid are calculated using the state

school financing formulas and the 1980 characteristics of school districts.

15 We have also explored the effect of changes in state aid on education inputs and outcomes, namely, district

pupilteacher ratios and high school dropout rates. We find small, statistically insignificant effects.16 We define district total expenditure on education as the sum of current expenditure (as defined by Murray

et al., 1998), intergovernmental expenditure, construction expenditure, expenditure on other capital, and interest

on debt.



17/23

across districts. A natural implication of the theoretical framework is that areas with

better performing markets should be more efficient. For example, because households

with greater income can afford to consider a wider range of school districts in which to

reside and can more easily afford private schools, we expect that school spending inwealthier areas should be more efficient. Similarly, school district characteristics may

affect the efficiency of school spending. In this last section we consider whether the

relationship between state aid and property values varies by household and district

characteristics.17

We begin by asking whether property values in wealthier and more educated public

school districts are more responsive (positively) to changes in state aid. To do so we

use 1980 characteristics to divide districts into quintiles based on the average

household income and the proportion of householders who do not have a high school

degree. We classify those in the lowest quintile as being low income or having low

education and those in the highest quintile as being high income or having high

education.18 The average income of districts classified as low income is $28,973; the

average for those classified as high income is $55,526. Fifty percent of householders

in less educated districts have less than a high school education, whereas only 17

percent of householders in highly educated districts have less than a high school

education.

In the upper panel ofTable 6, we estimate the results by income. The results in both

columns (1) and (2) suggest that low-income districts could increase aggregate property

values by decreasing spending on public schools since each additional dollar of state aid

raises property values by less than the properly discounted value of the additionalspending. We also find that the difference in the effect of state aid on property values

between low- and high-income communities is statistically significant. The estimates

reported in the middle panel allow for variation by the education level of the community.

Again we find that districts in less-educated communities more likely to overspend on

public schooling than those in high-education communities.

Finally in the bottom panel ofTable 6 we differentiate schools by whether housing

in the school district is primarily owner or renter occupied. Eighty-four percent of

housing units in owner-occupied districts are occupied by owners. Renter-occupied

districts have only 52 percent of housing units owner occupied. Assuming that owner

occupation of housing provides another proxy for resources, we expect that districtswith a low percentage of owner-occupied housing may be less efficient than those in

owner-occupied districts. The results suggest that school district efficiency indeed

varies by the percent of housing in a district that is owner occupied. Compared to

largely owner-occupied districts, districts with high rental rates appear to overspend on

public schooling.

17 In Tables 6 and 7 we restrict the effects of the other covariates to be the same across the districts and only

interact state education revenues with the demographic or district characteristic in question. We also interact the

instruments with these categories.18 In Tables 6 and 7 we adopted the rule of defining the categories based on the 20th and 80th percentiles

(when weighted). The exception is the categorization of districts into competitive or not competitive using the

HerfindahlHirschman Index. The results are not generally sensitive to small changes in these cut-off choices.



18/23

Overall, it appears that districts with poorer and less-educated residents overspend onschools relative to wealthier and more highly educated districts. Note that the difference in

coefficient estimates between the wealthier and poorer districts reflects differences in the

relative values of the marginal rates of substitution between education and other goods and

the marginal costs of providing education. One potential factor driving these differences

may be lack of mobility. The restricted mobility may arise because of a lack of income,

restricted access to credit markets, or discrimination. Alternatively, if one believes that

districts with poorer and wealthier (or more- and less-educated) residents have similar

marginal rates of substitution between education and other goods, then the difference may

reflect an inherently higher marginal cost of providing education in the poorer districts.

For example, the presence of peer effects may lower the cost of schooling production inwealthier or highly educated communities relative to less-advantaged communities

(Benabou, 1993).

Table 6

IV first-differenced estimates of the effect of change in state aid per pupil on aggregate house values per pupil by

selected characteristics of the school district residents

Type of state aid used as instrumentChange in predicted Change in predicted

basic state aid per pupil total state aid per pupil

Average household income

Low (bottom 20th percentile) 11.018 8.452

(10.071) (9.963)

Average (20 to 80th percentile) 9.816 11.465

(6.053) (5.959)

High (top 20th percentile) 90.661 91.767

(12.698) (12.328)

P-value: low = high 0.000 0.000

Education

Low (top 20th percentile in share 4.165 1.782

of persons without a HS diploma) (8.721) (8.433)

Average (20 to 80th percentile in share 35.373 37.106


High (bottom 20th percentile in share 36.889 39.928



Percent owner occupied

Renter-occupied districts 3.000 1.556

(bottom 20th percentile) (7.166) (7.027)Mixed 39.610 40.509

(20 to 80th percentile) (8.233) (5.809)

Owner-occupied districts 57.114 58.007

(top 20th percentile) (10.679) (10.642)

P-value: high renter = high owner 0.000 0.000

Notes: see notes to Table 4. The demographic groups are based on their values in 1980 weighted by pupils in

1980.



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In Table 7 we conduct a similar exercise for district characteristics. In the top panel

ofTable 7 we test for differential efficiency by the level of public school competition,

as measured by the Herfindahl Hirschman Index (HHI).19 Researchers argue that an

HHI based on the concentration of enrollment in a geographic area reflects the market

power of public schools in the area and therefore the degree of choice that parents

may have (Borland and Howsen, 1992; Hoxby, 1996). Thus, we would expect that

districts with less market power would be more efficient than those in less-competitive

areas. The HHI ranges from 0 to 1. Districts in areas with only a few large school

districts will have values close to 1 as the districts monopolize student enrollments;

Table 7

IV first-differenced estimates of the effect of change in predicted state aid per pupil on aggregate house values per

pupil by selected characteristics of the school district

Type of state aid used as instrumentPredicted basic Predicted total

state aid per pupil state aid per pupil

County Herfindahl Index (HHI)

Low 50.649 50.884

(HHI < 0.15/competitive) (7.901) (7.715)

Average 30.194 28.312

(0.15VHHIV 0.46) (7.718) (7.191)

High 0.644 3.296(HHI>0.46/not competitive) (10.261) (10.936)


District size in 1980

Small 51.828 51.142

(bottom 20th percentile) (11.927) (11.857)

Average 35.812 36.272

(20 to 80th percentile) (6.620) (6.452)

Large 20.703 15.889(top 20th percentile) (10.498) (9.603)

P-value: small = large 0.000 0.000

Unionization in 1980

Unionized 31.149 33.305

(5.729) (5.735)Non-unionized 40.730 42.375

(11.140) (11.232)

P-value: unionized = non-unionized 0.438 0.466

Notes: see notes to Table 4. The school district characteristic groups are based on their values in 1980 weighted by

pupils in 1980. Unionized districts have at least 50 percent of instructional employees unionized and at least one

contractual agreement in effect. Due to missing unionization information at the district level, the unionization

regression contains only 9015 observations.

19 The HHI is defined for each market as the sum of the squares of the market shares of all participants. In

this case, we define market share as the proportion of county public school enrollment in each district and sum the

squares of these proportions for each county.



20/23

districts with lower values face more competitive pressure. We base our HHI on the

concentration of public school enrollments in the county. The Federal Trade Commis-

sion (FTC) guidelines for horizontal mergers define markets with HHIs below 0.10 as

unconcentrated, HHIs from 0.10 to 0.18 as moderately concentrated, and HHIs above0.18 as highly concentrated. Using these guidelines, 74 percent of our school districts

are in highly concentrated markets. However, the FTC guidelines were not written for

school districts, which must exist in all counties, and will therefore generate markets

that are more concentrated than the typical product market. As a result, we use a more

moderate definition of concentration and divide the districts into those that are

somewhat competitive (HHI < 0.15, approximately 20 percent of our sample), those

that are monopolistic (HHI>0.46, approximately 34 percent of the sample), and those

in between.

The results in the top panel ofTable 7 suggest that property values in areas that face

little or no competition increase less in response to a change in state aid than districts

facing a relatively competitive market. Note that the property value response to changes in

the spending practices of school districts in not-competitive areas is significantly different

from the response to practices of those that face the most competition. We find some

evidence that those districts facing the least competition as measured by the HHI are

overspending.

Next we examine the effect of school district size. Undoubtedly there is an optimal

size for school districts as small districts may not be able to reach an efficient scale in

the production of education and large districts may be beyond the efficient scale. The

concern in education policy today is that large districts, such as those in New YorkCity and Chicago, are so large that administration and bureaucracy absorb resources

that efficiency would dictate should be directed towards instruction. Further, in these

areas residents have fewer choices among public school districts. Thus, in the middle

panel ofTable 7 we test for differences in efficiency by district size. Using both sets

of instruments, we find there is a significant difference between small and large

districts, suggesting that large districts are more likely to overspend than small districts.

The results are consistent with the idea that smaller districts perform better than large

districts; however, we cannot specifically identify the mechanism driving the efficiency

difference.

Finally, in the bottom panel ofTable 7, we examine the effect of teacherunionization on efficiency. The apriori effect of teachers unions on productivity is

unclear (Eberts, 1984; Eberts and Stone, 1987; Hoxby, 1996). On the one hand, unions

may increase schooling efficiency because they have a better understanding of the

educational production process or by giving their members voice to communicate

grievances with management (Freeman and Medoff, 1984). On the other hand, the

unions may predominantly exact rents from the school district and thereby decrease

efficiency. For this exercise we define those districts where at least 50 percent of the

teachers are organized and there is at least one collective bargaining agreement in

effect at the time as unionized. Approximately 45 percent of our sample school

districts were unionized in 1980. The results are in the bottom panel of the table. Wefind no evidence that unionized districts spend beyond the optimal level, thereby

spending education dollars inefficiently.



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6. Conclusion

In this paper we take a market-based approach to examine whether increased

school expenditures are valued by potential residents and whether the current level ofpublic school provision is inefficient (as perceived by potential residents). We find that,

on average, additional school spending is valued by potential residents. In addition, we

find that, on net, public school districts do not appear to spend increases in state aid

for education inefficiently. That said, we also find that large school districts, those

facing less competition, and those in areas with fewer homeowners and in areas in

which residents are poor or less educated, are more likely to overspend. In contrast, we

find no evidence that unionized districts spend beyond the optimal level, thereby

spending education dollars inefficiently. One interpretation of these results is that

increased competition has the potential to reduce overspending on public schools in

some areas.

Some care must be taken in interpreting these findings. First, the judgements about

school efficiency result from a model with potentially strong assumptions. While we

do not believe that violations of these assumptions would have a large impact on our

qualitative findings, they must be kept in mind. Second, based on our methodology, it

is unclear whether increased efficiency would generate higher or lower levels of

education spending. For example, while we find evidence that some districts overspend

on education, our analysis cannot reveal the source of the inefficiency and therefore we

cannot determine whether increased competition would lead to increases or decreases

in education spending. Competition may lead districts to decrease the amount ofeducation provided and thus decrease spending. Alternatively, competition may lead

districts to increase their productivity with little effect on the total spending. Finally,

we note that the competition we observe that improves efficiency may have the

consequence of increasing stratification which may decrease social welfare (Fernandez

and Rogerson, 1996, 1998; Benabou, 1993).

Acknowledgements

We thank Roland Benabou, Ben Bernanke, David Card, Anne Case, Jonas Fisher,Jonathan Gruber, Jeff Kling, Alan Krueger, Caroline Hoxby, Abigail Payne, Thomas

Romer, Lara Shore-Sheppard, and Daniel Sullivan for helpful conversations, and

seminar participants at the American Education Finance Association meetings, Cornell

University, the Federal Reserve Bank of Chicago, Hunter College, the John F. Kennedy

School of Government, the Joint Center for Poverty Research at the University of

Chicago, the meeting of the MacArthur Research Network on Inequality and Economic

Performance in Cambridge, MA, 1999, the Childrens Workshop of the National

Bureau of Economic Research, the National Center for Education Statistics Data

Conference, Princeton University, the World Congress of the Econometric Society, and

anonymous referees for insightful comments and suggestions. We also thank OlivierDeschenes, Jonathan Moore, Daniel Fernholz, Melissa Goodwin, Yvonne Peeples, Jeff

Wilder and particularly Kimberly Sked for outstanding research assistance. Barrow



22/23

thanks the National Science Foundation, and Rouse thanks the Mellon Foundation for

financial support. The views expressed in this paper are those of the authors and are

not necessarily those of the Federal Reserve Bank of Chicago or the Federal Reserve

System. All errors are ours.

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525 Rouse and Barrow School Expenditure

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