Article summary
Relationship between types of school
district expenditures and student
performance
C H A R L E S J A C Q U E S and B . W A D E B R O R S E N * {
6532 W. Saddlehorn Rd., Glendale, AZ 85310 and {Department of Agricultural Economics, Oklahoma State University, Stillwater, OK 74078-6026
An educational production function is estimated using achievement test scores to proxy school output, with socio-economic characteristics and expenditures in var- ious categories as inputs. The data are school district level expenditures. Unlike most past research, a correction is made for the heteroscedasticit y created by di� erences in school district size. Correcting for heteroscedasticit y leads to statistical tests with greater power.
Test scores were positively related to expenditures on instruction and instructional support, and are negatively related to expenditures on student support, such as counselling and school administration . The negative e� ect of counselling and admin- istration could be due to counsellors taking up classroom time or administrator s using classroom time with announcement s or assemblies. Alternatively, the causality could go the other way. It could be that schools with problems hire more adminis- trators and counsellors. The socioeconomic variables included may not fully capture the problems that a school faces.
The results show that spending is useful when targeted towards instruction. The e� ect, although statistically signi®cant, is not large. But, the research still ®nds that money matters if it is spent on instruction.
I . I N T R O D U C T I O N
The central issue in all policy discussions is usually
not whether to spend more or less on school
resources but how to get the most out of marginal
expenditures. Nobody would advocate zero spend-
ing on schooling, as nobody would argue for in®nite
spending on schooling. The issue is getting produc- tive uses from current and added spending.
(Hanushek, 1996).
Hanushek (1996) ®nds school expenditure s are not related to student performance . Borland and Howsen (1996) , how-
ever, ®nd that expenditures are at least marginally related
to school performanc e and marginally signi®cant. A meta-
analysis performed by Hedges et al. (1994) ®nds that
increasing per student expenditure s improves test scores. However, Hanushek (1994) points out that their meta-ana- lysis is ¯awed because they omitted many studies that show increasing expenditures has no e� ect. These studies used
aggregate expenditures as the explanatory variable. But di� erent categories of expenditures may have di� er-
ent in¯uences on test scores. For example, Brewer (1996) suggests that increased expenditures on administration might even reduce test scores. Ferguson and Ladd (1996),
using a high-quality dataset from Alabama (which has low spending levels) found instructional spending had a large e� ect on test scores, but did not report e� ects of nonin- structional spending. The interest in this study is whether speci®c types of expenditures result in test score improvement.
The objective of this research is to determine the in¯u- ence on student achievement of various types of school
Applied Economics Letters ISSN 1350±4851 print/ISSN 1466±4291 online # 2002 Taylor & Francis Ltd http://www.tandf.co.uk/journals
DOI: 10.1080 /1350485021014816 1
Applied Economics Letters, 2002, 9, 997 ± 1002
997
* Corresponding author. E-mail: brorsen@okstate.edu
expenditures in order to ®nd areas where additional invest- ment in education would give the greatest results. The goal is to ®nd the combination of educational investment , which under the constraint of limited resources, produces the most learning.
The study goes beyond previous research by estimating a production function with achievement test scores as output and various types of school expenditures as inputs. Results show how various categories of expenditures, such as instruction and administration a� ect achievement test scores. Various demographi c and school related variables are also included in the production function. The model isolates expenditure e� ects by including demographic and other school related variables as explanatory variables.
I I . M E T H O D S
The model uses school district averages of achievement scores on standardized tests as the dependent variable and eleven expense categories by school district as indepen- dent variables. Disaggregat e data were not available. Various socio-economic and school factors are also included to correct for other factors that in¯uence test scores. The data are cross-sectional . Because school district averages are computed across di� ering number of students, heteroscedastic disturbances are expected. Therefore, max- imum likelihood estimation (MLE) is used instead of ordinary least squares. MLE is needed to gain asymptoti- cally e� cient parameter estimates and valid hypothesis tests (Greene, 1993).
The following equation was estimated using maximum likelihood estimation:
Y ˆ S ‡ X¿ ‡ G¯ ‡ EC ‡ u ‡ " …1†
where Y is a vector of average test scores for each school district/grade/test combination, S is a matrix that contains student e� ects which vary by school district and grade. Student e� ects are proportions for each grade by race and gender, and the percentage of students taking the tests. Since the proportions by race and gender sum to one, this procedure required leaving one variable in the intercept, which was white males.
The socioeconomic e� ects matrix, X, varies only by school district. It includes the percentage of students in special education, the percentage of students receiving free or reduced-price lunches, and four levels of education attainment of the parents. The proportion without a high school education was left in the intercept, since the total summed to one. A matrix of dummy variables G includes the type of test (NRT or CRT), the kind of test (maths, reading, or science), and grade level of the test (third and seventh for the NRT, and ®fth, eighth, and eleventh for the CRT). The variable for CRT, grade 11, maths test was included as part of the intercept.
E is a matrix of eleven expense variables for each school district, each as a per student expenditure; u is a random school/grade e� ect, and " is a heteroscedastic error vector. The elements in u are ui ¹ N…0; ¼
2 u †, and the elements in "
are "ij ¹ N…0; ¼ 2 =ni†; i being the index for school/grade and
j for test. This error term structure is created by aggregat- ing test scores of students within each grade within each school district. Disaggregat e data would have been used had it been available. Richter and Brorsen (2002) ®nd that while disaggregat e data is superior, the gains from using aggregate data are small.
Family background is one of the major factors determin- ing performance on achievement tests (Chubb and Moe, 1990). By including these e� ects in the model, we are better able to measure the e� ects of various types of school expen- ditures on achievement test scores.
Brewer (1996) argues that test scores and expenditures are simultaneousl y related and uses a simultaneous equa- tions estimator. However, he ®nds little signi®cance with his simultaneous-equations-estimator , which may suggest that he was unable to ®nd adequate instruments to identify his parameters. See Staiger and Stock (1997) for a discus- sion of the problems created when instruments are weak. Ferguson and Ladd (1996) also argued for endogeneit y of expenditures in Alabama because poorer performing schools were given additional money. Oklahoma does not allocate expenditures based on test scores and thus there should be little or no simultaneity here. There can still be bias due to missing explanatory variables. The parental, student, and school variables may not adequatel y capture all the cultural di� erences between communities.
I I I . D A T A
Data for this research were obtained from the Oklahoma Departmen t of Education (1996). Test results were from the Criterion Referenced Test (CRT) and the Iowa Test of Basic Skills (ITBS), which is also known as the Norm Referenced Test (NRT). Test scores by school district and grade were available for each school district for the school year 1994-1995 . The CRT is given to grades 5, 8, and 11, and ascertains whether or not students are at grade level. The NRT is given to grades 3 and 7, and is a test of knowl- edge level, not a test of grade level. Both the CRT and NRT have three tests, reading, science, and math. No test scores were provided when less than six students took the tests due to concerns about con®dentiality.
Using parental in¯uences and student in¯uences as explanatory variables alleviates much of the e� ects of social class alluded to by Chubb and Moe (1990). Student data include number of students for each gender and each race by grade for each school district. Race data include Asian, Black, Hispanic, Native American and White.
998 C. Jacques and B. W. Brorsen
Parental data for parents with school age children were
derived from 1990 school district census data (US Department of Education, 1995). Educational attainment
of the parents was divided into four categories; proportion
with (i) at least a bachelor’s degree, (ii) with some college, (iii) with a high school diploma, and (iv) no high school
diploma. The disadvantag e of Census data is that it is from
®ve years before the tests were taken. Some schools do not allow special needs children to take
the test. Therefore, a percentage of students in the given
grade who took the test is included. School information used was proportion of special education students by dis-
trict and proportion of students obtaining a free or
reduced-price lunch by district (Oklahoma Department of
Education, 1996). The free-lunch variable is especially important because it is a function of family size as well
as family income. School size was measured by average daily membership
(ADM). The average expenditures per category are thus
costs per student enrolled. The State of Oklahoma requires
each district to use the same accounting procedure so the numbers should be comparable, but there are undoubtedly
some di� erences in the way expenses are allocated. Means
and standard errors for each of the eleven expenditure
categories are in Table 1. These categories are de®ned below:
(1) Instructional expenditures deal directly with tea-
cher±student interaction. Included here are salaries
and bene®ts for teachers, teacher’s aides, clerks,
tutors, translators, and interpreters. (2) Instructional sta� support services include activities
associated with assisting instructional sta� with
content and provide teachers with concepts and tools that enhance the learning process. This
includes `in service’ training such as workshops,
demonstrations , school visits, and courses for col- lege credit. Help in developing curriculum and instruction techniques are included here as well as media services such as library, audiovisual, educa- tional television, and computer assisted instruction services.
(3) Student support services include attendance and social work services, guidance services, health ser- vices, individual psychological services, speech pathology and audiological services. Include are individual counselling, identi®cation of problems arising from the home, school, or community, iden- ti®cation of attendance problems, identi®cation of health problems such as visual or auditory , and testing (SAT, etc.).
(4) School Administration includes activities of the school principals and their o� ce subordinates such as assistant principals, secretaries, clerks and other assistant s in general supervision of all opera- tions of a particular school or group of schools.
(5) General Administration and Business activities are those of the Superintendent’ s o� ce and school busi- ness including, the ®scal and budgeting process for schools at the district level.
(6) Student transportatio n services are those transpor- tation services mandated by state law such as trans- portation from home to school, and nonmandate d services, such as transportatio n to school activities.
(7) Operations, maintenance, child nutrition, and com- munity service operations are in this category.
(8) Facilities acquisition and construction includes acquisition of buildings, remodelling, construction of buildings, additions to buildings, installing built- in equipment, and site improvement.
(9) Classi®ed by the state’s accounting system as `other outlays’, this includes debt service, a clearing account, and funds transfer.
(10) Included in this category are scholarships given to students, student aid, and sta� awards, all sup- ported by outside revenue sources. In addition, workers’ compensation claims, tort claims, and medical care claims and reimbursements are included here.
(11) The accounting system classi®es this activity as `repayment’.
Using MLE, these expenditure categories are tested for economic and statistical signi®cance in regard to their e� ect on achievement test scores.
I V . R E S U L T S
Instructional expenditures, student support, and student transportatio n were signi®cant at the 0.10 level (Table 2). The other expense variables in the model were insigni®cant.
School district expenditures and student performance 999
Table 1. Oklahoma school district average achievement test scores
Variable Min. Mean Std. dev. Max.
Grade 3 math a
15.2 25.7 2.461 32.2 Grade 3 reading
a 11.3 17.7 1.856 25.2
Grade 3 science a
11.7 18.2 1.727 25.1 Grade 5 math
b 52.0 72.3 5.557 89.0
Grade 5 reading b
55.0 80.9 4.903 94.0 Grade 7 math
a 16.9 25.9 3.314 36.9
Grade 7 reading a
16.8 22.6 2.351 30.7 Grade 7 science
a 17.7 25.5 2.391 37.1
Grade 8 math b
55.0 74.5 6.092 91.0 Grade 8 reading
b 52.0 76.1 5.257 91.0
Grade 8 science b
52.0 73.0 4.731 84.0 Grade 11 reading
b 36.0 67.1 7.495 92.0
Grade 11 math b
44.0 75.2 5.169 87.0
a Norm referenced test scores.
b Criterion referenced test scores.
Note: The means are unweighted averages of each district’s proportion and therefore they will not match state averages.
Instruction
The instructional expenditures coe� cient was 0.82, indicat- ing that for another $1000 per student in instructional expenditures, there should be almost a point increase in test scores. Thus teachers, textbooks, and supplies are a productive place to spend money.
Instructiona l support
Instructional support is positive but insigni®cant with a parameter value of 0.63. Instructional support such as workshops, seminars, and computers, may increase teacher productivity, and therefore achievement test scores may increase.
Student support
Student support had a coe� cient of 7 1.64, suggesting that spending in this category is unproductive. Expenditures in this area tend to take students out of the classroom, so a negative e� ect is reasonable. This could be a causality pro- blem. Schools with serious problems may have more need
to spend money in this category. Our socio-economic vari- ables may not fully capture factors causing schools to have more needs in this area
School administration
The parameter value for school administration (Principal’s o� ce) was 7 1.06. Brewer (1996) hypothesized two possible e� ects of administration expenditures on student perfor- mance. One is that more administration actually lowers output by reducing teacher productivity, and has a negative marginal product at current expenditure levels. The other hypothesi s is a less severe indictment of administration . It states that increased administration does not actually lower educational output, but displaces funds that could be used in a more productive manner. Our results support his ®rst hypothesi s for the Principal’s o� ce and the second for the Superintendent’ s o� ce.
Transportation
The coe� cient of transportatio n expenses was positive and signi®cant. This is likely a missing variable problem. Those
1000 C. Jacques and B. W. Brorsen
Table 2. School district per student averages for Oklahoma school district variables
Variable Min. Mean Std.dev Max.
Parents without hs education 0.00 0.20 0.091 0.68 Parents with hs education 0.00 0.39 0.098 0.69 Parents with some college 0.00 0.28 0.087 1.00 Parents with Bachelor’s degree 0.00 0.14 0.084 0.58 Proportion Black males 0.00 0.02 0.056 0.80 Proportion Black females 0.00 0.02 0.055 0.92 Proportion Indian males 0.00 0.11 0.119 0.78 Proportion Indian females 0.00 0.11 0.113 0.73 Proportion Spanish males 0.00 0.01 0.033 0.35 Proportion Spanish females 0.00 0.01 0.035 0.47 Proportion Asian males 0.00 0.002 0.008 0.17 Proportion Asian females 0.00 0.002 0.007 0.08 Proportion White males 0.00 0.38 0.141 1.00 Proportion White females 0.00 0.35 0.132 0.86 Proportion free or reduced lunch 0.00 0.54 0.185 1.00 Proportion special education 0.00 0.12 0.040 0.52 Proportion taking tests 0.28 0.89 0.097 1.00 Instructional expenditures
a 1582.00 2740.00 558.137 9870.00
Instructional support a
0.00 120.00 97.520 1360.00 Student support
a 0.00 160.00 113.233 690.00
Principal’s o� ce a
0.00 220.00 112.694 720.00 Superintendent’s o� ce
a 130.00 400.00 220.155 2640.00
Student transportation a
5.00 240.00 136.757 1700.00 Operations, child nutrition
a 420.00 880.00 283.420 3990.00
Facilities, construction a
0.00 157.00 372.940 4207.00 Other: debt service
a 0.00 10.00 152.998 1050.00
Other expenses a
0.00 2.00 11.561 151.00 Repayment
a 0.00 1.00 10.003 220.00
a These are per student expenditures.
Note: The means are unweighted averages of each district’s proportion and therefore they will not match state averages.
school districts that have large land areas and few students
require larger expenditures per student on transportation .
Most such schools are located in western Oklahoma.
Eastern Oklahoma has historically been behind Western Oklahoma in terms of education level and job salaries
(Warner, 1995; Jacques and Brorsen, 1998). Thus this vari-
able may capture regional di� erences that the other vari-
ables failed to measure.
Insigni®cant expense variables
Superintendent’ s o� ce and business expenses were insignif- icant both statistically and economically, as were operating expenses and lunch programmes. Construction and acqui- sition shows little relationship to test scores; however, the data were for a single year, and it is not surprising that construction in a particular year would not a� ect achieve- ment test scores in that year. The other three categories, classi®ed as `other’ by the accounting system were also insigni®cant.
Other variables in the model
Regarding the parents’ education variables, only `Parents with a Bachelor’s degree’ was signi®cant. But as educa- tional level increased, so did both the level of statistical signi®cance and the parameter level. Increasing the percen- tage of parents with at least a bachelor’s degree by 11%, has about the same e� ect as increasing per student expen- ditures on instruction by $1000 per student.
The race and gender variables were insigni®cant with the exception of black and white females, and Indian males. Proportion of students receiving a free or reduced-price lunch was signi®cant and negative. Increasing the number of students receiving free or reduced-price lunches by 10% decreases test scores by about one half of a point. The special education variable was also signi®cant and nega- tive, as was the percentage of students per class allowed to take tests.
V . C O N C L U S I O N
Schools that spend more on instruction have higher test scores than those that spend less in those areas. However, schools that spend more on school administration (princi- pal’s o� ce) and student support have lower test scores than schools that spend less. Since school districts have limited funds, increased spending on any category whose para- meter estimate is statistically insigni®cant results in a mis- allocation of resources away from more productive areas such as instruction.
On a national level using statewide data, spending per student ranged from over $9000 in New Jersey to just over $3000 in Utah in 1993±1994. Oklahoma ranked 46th in spending per student, in 1993±1994 (Hanushek, 1996). Because of Oklahoma’s low expenditures, the marginal return to education expenditures may be positive in Oklahoma, but not in other states.
The methods here may yield more powerful tests than previous research due to the larger variations in expendi- tures, larger number of observations , and the correction for heteroscedasticit y when using aggregate data. Also, Hanushek (1986, 1996) used aggregate expenditures while
School district expenditures and student performance 1001
Table 3. Parameter estimates of the e� ects of various factors on Oklahoma public school achievement test scores
Variable Parameter est.
Std. error p-value
Intercept 78.41 1.306 0.0001 Grade 3 math
a 7 49.40 0.224 0.0001 Grade 3 reading
a 7 57.45 0.224 0.0001 Grade 3 science
a 7 56.87 0.224 0.0001
Grade 5 math a
7 2.68 0.223 0.0001 Grade 5 reading
a 5.94 0.223 0.0001
Grade 7 math a 7 49.50 0.222 0.0001
Grade 7 reading a
7 52.65 0.222 0.0001 Grade 7 science
a 7 49.77 0.222 0.0001 Grade 8 math
a 7 0.67 0.224 0.0029
Grade 8 reading a
1.07 0.224 0.0001 Grade 8 science
a 7 1.99 0.224 0.0001
Grade 11 reading a 7 7.97 0.230 0.0001
Parents w/Bachelor’s degree 7.35 1.355 0.0001 Parents w/some college 1.94 1.299 0.1366 Parents w/ high school education 1.00 1.297 0.4390 Proportion White female 1.26 0.612 0.0390 Proportion Black female 7 13.16 1.692 0.0001 Proportion Indian female 7 0.97 0.771 0.2065 Proportion Hispanic female 7 0.32 2.023 0.8759 Proportion Asian female 8.11 7.393 0.2728 Proportion Black male 7 0.15 1.720 0.9304 Proportion Indian male 7 2.28 0.733 0.0019 Proportion Spanish male 7 3.56 1.945 0.0671 Proportion Asian male 7 4.69 6.156 0.4458 Percent subsidized lunch 7 5.23 0.697 0.0001 Percent special education 7 4.20 2.380 0.0780 Percent taking test 7 4.43 0.583 0.0001 Instructional exp
b 0.82 0.239 0.0006
Instructional support exp b
0.63 1.034 0.5404 Student support exp
b 7 1.64 0.811 0.0439
Principal’s o� ce b
7 1.06 0.887 0.2312 Superintendent’s o� ce
b 7 0.61 0.594 0.3080 Student transportation
b 1.45 0.791 0.0669
Operations, nutrition, etc. b
0.22 0.495 0.6551 Facilities construction
b 0.18 0.223 0.4182
Other: debt payment, etc. b
0.60 0.554 0.2797 Other
b 0.97 6.567 0.8826
Repayments b
7 2.41 7.512 0.7488
a These are intercept-shifting dummy variables.
b These are average per student expenditures in thousands of
dollars. Note: A random e� ects model was estimated with MLE correcting for heteroscedasticity due to aggregation. There were 6602 observations.
our results show that expenditures in some categories have negative e� ects.
The results show that money spent on instruction leads to a small increase in student performance. If spending is to be increased and the goal is to increase the average test score, then money appears to be best spent on teachers, teacher supplies, and teacher training.
A C K N O W L E D G E M E N T S
Charles Jacques is a senior econometrician with American Express and B. Wade Brorsen is a regents pro- fessor and Jean & Patsy Neustadt Chair in the Department of Agricultural Economics at Oklahoma State University. The authors wish to thank Francisca G.-C. Richter for technical assistance.
R E F E R E N C E S
Borland, M. V. and Howsen, R. M. (1996) Competition, expen-
ditures and student performance in mathematics: A comment
on Couch et al., Public Choice, 87, 395±400. Brewer, D. J. (1996) Does more school district administration
lower educational productivity? Some evidence on the
`administrative blob’ in New York public schools, Economics of Education Review, 15(2), 111±24.
Chubb, J. E. and Moe, T. M. (1990) Politics, Markets and
America’s Schools, Washington, DC: The Brookings Institution.
Ferguson, R. F. and Ladd, H. F. (1996) How and why money matters: An analysis of Alabama schools, in Holding Schools
Accountable. Washington, DC: The Brookings Institution,
pp. 265±298. Greene, W. H. (1993) Econometrica Analysis. Second Edition,
Englewood Cli� s, NJ: Prentice-Hall.
Hanushek, E. A. (1996) School Resources and Student
Performance, in Does Money Matter? (ed.) G. Burtless,
Washington, DC: The Brookings Institution, pp. 43±70.
Hanushek, E. A. (1994) Money might matter somewhere: A
response to Hedges, Lane, and Greenwald, Educational
Researcher, 23(4): 5±8.
Hanushek, E. A. (1986) The economics of schooling: Production
and e� ciency in public schools, Journal of Economic
Literature, 24, 1141±77.
Hedges, L. V. and Greenwald, R. (1996) Have times changed?
The relation between school resources and student perfor-
mance, in Does Money Matter? (ed.) G. Burtless,
Washington, DC: The Brookings Institution, pp. 74±90.
Hedges, L. V., Laine, R. D. and Greenwald, R. (1994) Does
money matter? A metaanalysis of the e� ects of di� erential
school inputs on student outcomes, Educational Researcher,
23(3), 5±14.
Jacques, C. and Brorsen, B. W. (1998) Can money diminish stu-
dent performance disparities across regions? Journal of
Regional Analysis & Policy, 28, 35±45.
Oklahoma Department of Education (1996) Unpublished electro-
nic data (Oklahoma Department of Education, Oklahoma
City, OK).
Richter, F. G. C. and Brorsen, B. W. (2002) Aggregate vs. disag-
gregate data in the measurement of school quality.
Unpublished working paper, Oklahoma State University.
Staiger, D. and Stock, J. H. (1997) Instrumental variables regres-
sion with weak instruments. Econopmetrica, 65, 557±86.
United States Department of Education (1995) School District
Data Book, 1990 Census School District Special Tabulation,
Oklahoma, National Center for Education Statistics, United
States Department of Education, Washington DC (CD
Rom).
Warner, L. A. (1995) An over view of Oklahoma’s economic
history, Oklahoma Business Bulletin, 63, 5±21.
1002 C. Jacques and B. W. Brorsen