consolidating rural school districts: potential savings...

Journal of Agricultural and Applied Economics, 32,3(December 2000):573–583@ 2000 Southern Agricultural Economics Association

Consolidating Rural School Districts:Potential Savings and Effects onStudent Achievement

Charles Jacques, B. Wade Brorsen, andFrancisca G. C. Richter

ABSTRACT

One frequently proposed policy is to consolidate rural school districts in order to savemoney by obtaining economies of size. The effects of school district size on both expen-ditures and standardized test scores are estimated for Oklahoma. Results indicate thateconomies of scale with respect to expenditures per student exist up to an average dailymembership (ADM) of 965 students,but thatas school districtsbecome larger,testsscoresdecline. Even if savings in school district administrationfrom consolidation are spent oninstruction, state average test scores would decrease slightly. Thus, school district consol-idation can reduce costs, but it will also reduce studentlearning.

Key Words: economies of size, education, plateau jimction, school district consolidation.

The efficient use of educational funds has beena topic of research since the late 1950s. Vari-ous studies have shown that economies ofscale exist in public schools, and that by con-solidating small school districts a more effi-cient use of school resources can be achieved.Most of these studies focus on economies ofscale in the average cost function of schooldistricts, but ignore the effect of school districtconsolidation on school quality.

Researchers such as Riew (1966, 1986),Cohn, White and Tweeten, and Lewis andChakraborty have found that economies ofscale exist in public schools with respect toaverage cost per student. Their research wasdone on school districts in Wisconsin, Iowa,

Charles Jacquesis an economist with American Ex-press, B. Wade Brorsen is a regents professor, andFranciscaG.C. Richter is a researchassistantin theDepartmentof AgriculturalEconomics at OklahomaStateUniversity.

Oklahoma, and Utah, respectively. Riew(1986) and Cohn found that economies ofscale exist up to between 1,500 and 1,700 av-erage daily attendance (ADA), while Whiteand Tweeten found economies of scale up to800 ADA. Increasing returns to scale are alsoknown to exist in other areas of rural publicfinance such as rural transportation costs(Deller and Nelson). Most of these studies findthat administrative or management cost is themain cause of decreasing per-unit cost.

In spite of these apparent economies, con-solidation usually faces strong opposition inthe districts being consolidated. One reasonthat those in small school districts resist con-solidation is that they perceive receiving fewereducational and non-educational benefits ifthey are forced to attend a large school. Fowl-er and Walberg, Eberts, Kenhoe and Stone,and Wendling and Cohen found school size tobe negatively related to student performance,even after controlling for demographics. But-

5’74 Journal of Agricultural and Applied Economics, December 2000

7.

6

5so

totalog#

8Ea)31

instructionalQ3z 1=5Qz administrative

1’

transportation

1o. —._ ——. —— —--———— 7—.—,-—— -––,-— ——.o 2 4 6 8 10 12 14 16 18 20

ADM (100)

Figure 1. Estimated average variable cost functions for Oklahoma school districts

ler and Monk argue that smaller rural schoolsare more efficient than larger suburban and ur-ban schools. They give three reasons for theefficiency of rural schools: a) rural districts areusually more homogeneous than urban com-munities, making teaching more productiveand requiring fewer administrative personnel,b) rural communities may be more stable thanurban communities, and c) there are usuallyfewer outside activities that compete withschooling in rural communities.

The objective of this research is to deter-mine the economies of scale with respect toaverage cost per student for Oklahoma publicschool districts. An additional objective is todetermine whether increasing school districtsize affects the quality of education as mea-sured by achievement test scores. This re-search differs from previous studies on schooldistrict economies of scale in both methodsand type of data used. A plateau function isused to estimate economies of scale in the av-erage variable cost function. This functionalform indicates that above a certain school dis-trict size constant economies of scale existwith respect to costs. This approach to the costfunction is similar to the von Liebig approach

to production used by Paris and Frank, Beattie,and Embelton. Also, a production function isestimated with school district test scores as theoutput (a measure of school quality) and var-ious student, parental, and school variables asinputs (Hanushek, 1986, 1996, 1997). Hierar-chical modeling is used. A correction is madefor heteroscedasticity to improve the precisionof the tests in both the cost and school-qualityfunctions. Previous research has either con-centrated on cost savings from school districtconsolidation without regard to school qualityor used variables such as graduation rate as aquality variable when conducting the analysisjointly. This research goes beyond past studiesin that we use achievement test scores byschool district as a proxy for educational qual-ity. This paper is also the first to look atwhether test scores could be increased in aconsolidation by reallocating the administra-tive cost savings to instruction.

Data

Data for this research were obtained from theOklahoma Department of Education (1996)for the 1994–1995 school year. There were

Jacques, Brorsen, and Richter: Consolidating Rural School Districts 575

557 school districts in Oklahoma in 1994–1995. Because of confidentiality, only 547 areused in this analysis (scores for school districtswith fewer than six students taking a test werenot reported).

Test scores by subject and grade wereavailable for each school district for the schoolyear 1994–1995. Subjects covered by the testswere reading, science, and math. Achievementtest results were from a Criterion ReferencedTest (CRT), which is unique to Oklahoma, andthe Iowa Test of Basic Skills (ITBS). TheITBS is a norm-referenced test. Our approachdoes not consider whether the tests are normreferenced or criterion referenced since we useraw scores. The CRTs are much easier testsand so scores on it are higher. The CRT isgiven to grades 5, 8, and 11. The ITBS is giv-en to grades 3 and 7. All types of tests wereequally weighted.

Problems arise when test scores are used asa measure of school performance. These prob-lems are a) tests scores are a one-shot measureof learning, imperfect measures of knowledge,and fail to measure all areas of knowledge; b)schools and teachers may adapt their proce-dures to “teach to the test”; and c) test scoresare due in part to schools, but also includestudent aptitude, social class, and other causes(Chubb and Moe, p. 198; Deaton and McNa-mara). In addition to all this, using averagetest scores loses information about the vari-ance within a school and, thus, a school’s abil-ity to produce equitable outcomes cannot bemeasured. Schools also teach social skills anda variety of other skills such as music and ath-letics which are not reflected in achievementtest scores. Since special education studentsusually do not take the tests, test scores do notmeasure how well schools are teaching thesestudents. Also, CRTs do a poor job of mea-suring how well schools are teaching theirmost gifted students. It is important to recog-nize the limitations of using test scores as a

proxy for school performance, such as theirinability to measure student aptitude (Borlandand Howsen). In spite of their limitations, testscores are an accurate measure of studentknowledge and imparting knowledge is cer-tainly the primary goal of schools.

Cultural and socioeconomic backgrounddetermine the ability of pupils to use educa-tional inputs (Deaton and McNamara). Studentdata included were the number of students foreach gender and each race by grade for eachschool district. Race data include Black, His-panic, Native American, and White. Parentaldata were derived from the 1990 census (Unit-ed States Department of Education) and referto parents with school-age children. The pa-rental data include proportion with at least abachelor’s degree, proportion with some col-lege, proportion with a high-school education,and proportion without a high school educa-tion. Other demographic data by school dis-trict were proportion of students obtaining afree or reduced-price lunch. The free lunchvariable is important because it reflects bothfamily income and family size.

Proportion of special education students byschool district was used because special edu-cation students are expected to require moreindividual attention and thus be more costly toteach. Some schools are more restrictive thanothers about whom they allow to take the tests.Schools can increase average tests scores bynot letting their weaker students take the tests.We use the percentage of students enrolled ineach grade who actually took the test to cor-rect for differences due to this practice.

ADM indicates school districts’ average

daily enrollment. ADM for the Oklahomaschool districts used in this research rangedfrom 20 students to 40,160 students. ADMwas used to calculate per-student expenditures.Expenditures per student were divided intothree categories: instructional, administrative,and transportation. Fixed costs, such as sink-ing fund and bond payments, were not includ-ed.

School District Average Variable Cost

Plots of the residuals from the regression ofexpenditures against ADM and proportion ofspecial education indicated that a plateau func-tion would be appropriate. The following av-erage cost equation was estimated using non-linear optimization in SAS:

576 Journal of Agricultural and Applied Economics, December 2000

(1) C = d + AHZ(A.M<M)+ BZ(A.M>M)+ SD + E.

C is a 547 X 1 vector of the average variablecost per student, S is a 547 X 1 vector ofproportion of special education students, andIf is a 547 X 2 matrix with average dailymembership (ADM) in the first column andADM squared in the second one. D is a 547X 1 vector of population density for the 1995–1996 school year since data from the previousyear were not available. l(.l is an indicatorfunction and M is a constant denoting the levelof ADM corresponding to the corner of thespline function. If ADM is greater than orequal to M, then C is equal to r& + B + W,but if ADM is less than M, C equals aS + Ml+ 8D. Continuity at the point ADM = M was

imposed, and e is a heteroskedastic errorterm. 1 Multiplicative heteroscedasticity is as-sumed, so variance is modeled as:

(2) u? = exp(y ’z,)

where Zj = [1ADA4,AZM@] and y = [ln cr2mla2]are the parameters to estimate. The index i des-ignates school district. Correction for multipli-cative heteroscedasticity was performed using-maximum likelihood as described in Greene(p. 567). This correction provided asymptoti-cally efficient parameter estimates. Estimationof (1) was performed using separate equationswith a) average variable costs (administrativeplus instructional plus transportation expendi-tures), b) average administrative costs, c) av-erage instructional costs, and d) average trans-portation costs as the dependent variable. Allcosts were calculated on a per-student basis.The proportion of special education studentswas not significant in the administrative costs

1ButlerandMonk (1985) suggestincludlngamea-sure of qualityin the cost function. Following Butlerand Monk’s ideas, the cost function was reestimatedby two-stageleastsquareswithqualityincludedas anexplanatoryvariable.The reducedform was obtainedfor quality.Then an instrumentalvariableestimateforschool qualitywas obtainedby averagingtheestimatesover gradesand kinds of tests.This estimatewas in-troduced in the instructionaland total cost functionsbut was not significantin eithercase. Thus the recur-sive system used for the cost and quality equationscould not be rejected.

equation as expected, and was therefore re-moved from it. Also, density was eliminatedfrom the administrative and instructional costequations, once the non-significance of its pa-rameter estimate supported the lack of theo-retical reasons for density to serve as an ex-planatory variable.

School Quality

The regression for school quality has schooldistrict average achievement scores on stan-dardized tests as the dependent variable andinverted average daily membership by schooldistrict as an independent variable. Various so-cio-economic and school factors are also in-cluded to correct for other factors that influ-ence test scores. The data can be viewed as apanel with cross-sections of school districtsobserved fifteen times each, at most. 2 A hier-archical linear model, which is a random ef-fects model with adapted degrees of freedom,is used (Arminger et al., 531). This model al-lows introducing a common correlation amongobservations from a single school district andis estimated using PROC MIXED in SAS. Be-cause school district averages are from differ-ing number of students, heteroscedasticity isexpected. The model used for variance is theone presented in equation (2) where z is nowa vector whose first element is one and theothers are values for all the explanatory vari-ables used in the quality function and the num-ber of students taking the test. The index Znow represents each particular kind of testigrade/school district combination. Maximumlikelihood estimation (MLE) is used to gainasymptotically efficient parameter estimatesand valid hypothesis tests (Greene, 567). TheMLE is performed by iterating around the hi-erarchical linear model.

The following equation was estimated us-ing maximum likelihood estimation:

(3) Y=pG+&l+cDX+qA+E

2Recall that five grades have been used for theanalysisandwithineachgradethreekindsof testsmaybe takenby the students.This gives 15 observationsat most for each school district.


Table 1. Number of Oklahoma School Districts by Size, Percent of Total State Average DailyMembership, Percent of Special Education Students Enrolled and Expenditures per Student

Expendituresper Student ($Y

Adminis-Percent of Percent of tration

ADM N total ADM Spec. Ed. and Transp. Instruction Total

Fewer than 100 35 0.4 13.0 2,827 4,145 6,973100–200 89 2.3 14.3 2,271 3,777 6,048200-300 79 3.3 12.6 2,101 3,457 5,559300–400 65 3.7 13.1 2,027 3,288 5,315400–500 65 4.9 12.3 1,901 3,205 5,106500-1,000 91 11.1 12.0 1,679 2,905 4,584Greater than 1,000 123 74.4 10.9 1,583 2,780 4,363

‘ Expendhuresdo notincludelong-termcosts such as bond paymentsand sinking fund.Note: The meansareunweighed averagesof each district’sproportionand thereforetheywill not matchstateaverages.

where Y is a vector of test scores for schooldistricts, G is a matrix of dummy variablesthat includes the type of test (ITBS or CRT),the kind of test (math, reading, or science),and grade level of the test (third and seventhfor the ITBS, and fifth, eighth, and eleventhfor the CRT). The variable for CRT, grade 11,math test was included as part of the intercept.

The matrix S contains student effectswhich vary by school district and grade. Stu-dent effects are proportions for each grade byrace and gender, and the percent of studentstaking the tests. Since the proportions by raceand gender sum to 1, this procedure requiredleaving one variable in the intercept, whichwas white males.

The socioeconomic effects matrix X variesonly by school district. It includes the percentof students in special education, the percent ofstudents receiving free or reduced-price lunch-es, two expenditure-per-student variables (in-structional and administrative), and four levelsof educational attainment of the parents. Theproportion of parents without a high schooleducation was left in the intercept, since thetotal summed to 1. A is a vector of invertedaverage daily membership values and e is aheteroscedastic error term.3

3At a reviewer’srequest,two othervariablesweretestedfor inclusionin the model: densityandan inter-actiontermfor instructionalandadministrativeaveragecosts. These variableswere added independentlyand

Results

The number of school districts by ADM andtotal average variable costs are shown in Table1. There are 123 of the 547 school districtswith greater than 1000 ADM. School districtswith greater than 1000 ADM accounted for74.3 percent of the state’s total public schoolenrollment in 1995. Those with over 500ADM had more than 85 percent of the state’stotal enrollment. As ADM increases, the av-erage cost-per-student decreases. However the

decline in average cost is small, above 500ADM. The percentage of special educationstudents drops as district size increases. Table2 shows descriptive statistics of the variablesused in the estimation procedures.

Results show that economies of scale existin Oklahoma public school districts. As Table3 shows, the estimated spline function indi-cates that for school districts larger than 965average daily membership no significant econ-omies of scale exist. The plateau for averagevariable costs is $4430 per student. An in-crease in special education students increasesinstructional and transportation costs andtherefore proves to be an important variable inthe average total cost function.

The transportation cost function is almost

their p-values were calculated at 0.1442 and 0.1055respectively. Therefore, they were not included in thefinal model.


Table 2. Descriptive Statistics for Oklahoma School Districts

Variable Mean Std. Deviation

Average test score’Parents woihigh school educationParents w/high school educationParents with some collegeParents with Bachelor’s degreeParent’s median income ($)Proportion Black malesProportion Black femalesProportion Indian malesProportion Indian femalesProportion Spanish malesProportion Spanish femalesProportion White malesProportion White femalesProportion free or reduced lunchProportion special educationProportion taking testsAverage daily membershipTotal Expenditures per student’

49.590.200.390.280.13

26,438.000.020.020.110.110.010.010,380.340.540.120.89

1,163.005,121.00

26.480.090.100.090.08

7,015.000.060.060.120.110.030.030.140.130.180.040.10

3,190.001,127.00

Note: The meansareunweighed averagesof each district’sproportionand thereforetheywill not matchstateaverages.aThese are average per-student test scores, across all achievement tests.

h Average daily school district student membership.

LTotal expenditures per district divided by average daily membership.

linear and economies of scale barely exist forsmall and medium-sized school districts, Aschool district with 150 ADM will spend ap-proximately $255 per student for transporta-tion whereas another with 1500 or higherADM spends $119 per student. Density is ahighly significant explanatory variable. Trans-portation costs in Oklahoma are less than 5percent of average total variable cost, so anincrease in transportation costs due to consol-idation would have only a small effect on totalcosts. A few districts in Western Oklahoma areso large that transportation costs could becomean important factor, However, Oklahoma lawhas a provision allowing school districts cov-ering a large area to continue to receive statesupport even if they do not meet minimumADM requirements.

The minimum average cost for total, ad-ministrative, and instructional expenditureswas reached (the corner of the plateau) at 965ADM, 998 ADM, and 985 respectively, Thisindicates that school districts’ economies ofscale are about the same whether average ad-ministrative costs, average instructional costs,

or average total variable costs are used. Theslope of the average cost function for admin-istration is less steep than that for instruction,indicating that the effects of economies ofscale are greater for instruction expenditures(Figure 1).

Table 4 includes the parameters describingschool quality. As expected, an increase in theproportion of parents with either some collegeor at least a bachelor’s degree results in anincrease in achievement test scores. Resultsshowed that school districts with more minor-ity students have lower achievement testscores, similar to Hanushek’s (1986) andSander’s findings. The parameter describingstudents receiving subsidized lunches is neg-ative and significant, indicating that as the per-centage of a school’s students receiving sub-sidized lunches increases, achievement testscores decrease. The subsidized lunch variableis also an indication of a district’s median in-come of parents. As the percentage allowed totake tests increases, the average test scores de-crease. Instructional expenditures are positiveand statistically significant. Expenditures for


Table 3. Parameter Estimates for Oklahoma School District Average Cost Function

Variable Parameter Estimate Asymptotic Std. Error

Average Total Variable Costs

Constaut ($1000) 6.23 0.026

Proportion Special Education 2.94 1.022Density (ADM/area) –0.10 0.039ADM/100 –0.45 0.072(ADM/100)Squared 0.02 0.005Corner of Plateau—Costs ($1000) 4.43Corner of Plateau—ADM (100) 9.65

Average Instructional Variable Costs

Constant ($1000) 3.85 0.131

Proportion Special Education 1.49 0.626

ADMI1OO –0.25 0.040

(ADM/100)Squared 0.01 0.003

Corner of Plateau—Costs ($1000) 2.78

Corner of Plateau—ADM (100) 9.98

Average Administration Variable Costs

Constant ($1000) 2.27 0.074

ADM/100 –0.17 0.030

(ADM/lOO)Squared 0.01 0.002

Corner of Plateau—Costs ($1000) 1.43

Corner of Plateau—ADM (100) 9.85

Average Transportation Variable Costs

Constant ($1000) 0.26 0.020

Proportion Special Education 0.21 0.105

Density (ADM/area) –0.01 0.003

ADM/100 –0.02 0.004

(ADM/lOO)Squared 0.0006 0.0002

Comer of Plateau—Costs ($1000) 0.15

Comer of Plateau—ADM (100) 14.93

Note: The estimationmethodused was iterated generalized least squares. Multiplicative heteroscedasticity was assumed

and the above variables were used in the variance equation.

administration are negative and statisticallysignificant at the 10-percent level. This indi-cates that school districts which spend moreon instruction and less on administration havestudents that perform better on achievementtests. Brewer argued that money spent on ad-ministration could reduce quality of educationbecause administrators may use up students’or teachers’ time. Ferguson and Ladd foundthat increased spending on classroom instruc-tion has a positive effect on test scores, al-though Hanushek (1986, 1996, 1997) has longargued that spending has little effect. Our re-search confirms the arguments of Brewer andFerguson and Ladd and only mildly disagrees

with Hanushek as the effect of increasedspending is small.

Our parameter of interest is the inverse ofADIW1OO, which indicates whether disecon-omies of scale exist for schools’ quality of ed-ucation.4 When ADM equals 100, the param-

4Equations with linear a function of ADM and thesquare root function of ADM were estimated as alter-native functional forms. The results from these func-tional forms were similar to that of the inverse ADMfunction. They all indicate diseconomies of scale in testscores. The ADM coefficient of the linear function didnot have the statistical significance of the inverse ofADM parameter, and was deemed inappropriate be-cause it indicates that increasing school district size by


Table 4. Parameter Estimates for Quality of Schooling Using Average Achievement TestScores as the Dependent Variable

Variable Parameter Estimate Pr > Itl

InterceptGrade 3 mathGrade 3 readingGrade 3 scienceGrade 5 mathGrade 5 readingGrade 7 mathGrade 7 readingGrade 7 scienceGrade 8 mathGrade 8 readingGrade 8 scienceGrade 11 readingParents/Bachelor’s degreeParents wlsome collegeParents wihigh school educationProportion White femaleProportion Black femaleProportion Indian femaleProportion Spanish femaleProportion Black maleProportion Indian maleProportion Spanish malePercent subsidized lunchPercent special educationPercent taking testAdministrative Expenditures ($1000)Instruction Expenditures ($1000)Inverse of Average Daily Membership (100)

77.82–50.03–58.05–57.44

–2.865.73

–50.25–53.05–50.16

–0.980.83

–2.33–7.65

3.091.430.37

–0.14–2.75–0.65–0.22–2.66–0.53–2.51–1.01– 1.48–3.25–0.29

0.370.64

0.00010.00010.00010.00010.00010.00010.00010.00010.00010.00020.00040.00010.00010.00010.05300.62600.72910.06660.19550.84450.05030.27170.03080.00850.29000.00010.08960.00410.0062

Note: The grade/test variables are intercept-shifting dummy variables. The estimation method used was iterated gen-

eralized least squares. Multiplicative heteroscedasticity was assumed and number tested was used in the varianceequation along with the above variables.

eter adds 0.64 to achievement test scores. ForADM equal to 1,000, the parameter adds0.064 to achievement test scores. As ADM be-

one student decreases test scores by the same magni-tude whether the school district size is 20 or 40,000.The square root function had statistically significantparameter estimates when linear and square root pa-rameters were tested jointly (0.02 significance). Theminimum test scores were at 8,100 ADM. This func-tional form was considered inappropriate because fewschool districts are near 8,100 ADM, and there is noevidence to conclude test scores should increase above8,100 ADM. Also we were interested in rural schooldistricts, typically with less than 1,000 ADM, and thesquare root function did not fit the data well in thatrange.

comes bigger the effect decreases even more.This indicates the effect of increasing schooldistrict size results in lower achievement testscores.s

Ostrom (1998) argues that small publicagencies often operate more effectively thanlarge ones. Some of the reasons she gives forinefficiency in police departments in metro-

5 Plots of the residuals without ADM includedshowed that a few of the smallest school districts (mostwith ADM less than 50) did very poorly on theachievement tests. Test scores may have been hurtfrom having one teacher teach multiple grades. Thusstudents in schools that cannot afford one teacher pergrade may benefit from consolidation.


politan areas may well apply to rural schooldistricts. Education requires the active in-volvement of citizen consumers (students andparents) for input resources to have a benefi-cial effect. Parents are likely to participatemore in small schools. The head of the publicagency (superintendent) can monitor internalperformance based on more detailed and ac-curate information in a small unit rather thana large one.

Discussion

The first objective of this research was to de-termine the economies of scale with respect toaverage cost per student for Oklahoma schooldistricts. As Figure 1 shows, economies ofscale for school expenditures in Oklahoma ex-ist up to an average daily membership of 965.From ADM of 100 to 1000, total variablecosts decline by $1738 (28 percent) per stu-dent, instructional costs decline by $1007(26.6 percent) per student, administrative costsdecline by $679 (32.2 percent) per student,and transportation costs by $119 (44.8 per-cent) per student. At first glance it appears thatsavings from school district consolidationcould provide more funds for increasing thenumber of teachers or purchase of teachingtools such as computers. This makes economicsense if the consolidation does not require ad-ditional capital expenditures, such as build-ings.

An additional objective was to determinewhether increasing average school district sizeaffects the quality of education as measuredby achievement test scores. Achievement testscores were inversely related to ADM, and theeffects were stronger as school districts be-came smaller. Most of the effects of disecon-omies of scale are for school districts less than1000 ADM.

Parameter estimates from Table 4 indicatethat consolidating small school districts intolarger ones would lower achievement testscores (The ADM inverse parameter). This de-crease in quality occurs even when controllingfor socio demographics and school expendi-tures. The net effect of consolidation onschool quality depends upon how losses from

the students in the small school district com-pare to the gains by the students in the large.Students from the large school district wouldhave increased test scores if all money savedwere spent on instruction exclusively. If aschool district with 100 ADM was mergedwith one having 1000 ADM, an extra $158 perstudent could be assigned for instruction. Butthe gains in achievement test scores for thestudents of the large school would be verysmall, only about 0.05 points. In the calcula-tion it has also been considered that studentswould experience a small loss in achievementtes~ scores because of the increased schoolsize.

For students from small schools, consoli-dation not only decreases expenditures per stu-dent on administration, but also on instruction(see Figure 1). Goetz and Debertin’s resultssuggest that most of the differences in instruc-tional expenditures are due to differences inpupil-teacher ratio. For instance, a reductionof $1007 on instruction expenditures per stu-dent would result if a school of 100 ADMwere merged with one of 1000 ADM (Figure1). Our estimates indicate that under this sce-nario a student from the small school wouldlose 0.7 points on achievement test scores. Asa result of the consolidation the students fromsmall schools are big losers. From the macrolevel the state’s average achievement testscores drop slightly due to consolidation evenif the money saved is reallocated to instruc-tion. Other costs of consolidating school dis-tricts can only be measured outside the mar-ketplace (Tholkes). In some rural communitiesthe school is an important place for social in-teraction. Loss of the local school may causethe community to lose an important part of itsidentity and could disintegrate social ties with-in the community. Politically, because the stu-dents from the small school district are biglosers from the merger, the parents of the stu-dents from the small school would likely fightthe consolidation.G

c Here the example from the Discussion section ispresented in more detail. Calculations were performedbefore rounding. Assume an average school district(called School District A) with 100 ADM was merged

582 Journal of Agricultural and Applied Econotnics, December 2000

Conclusion Behavioral Sciences, Chapter 10, Random Co-efficient Models. New York, NY Plenum Press,

If the objective of school district consolidationis simply to save money by establishing schooldistricts that operate on the minimum costcurve, the answer is to consolidate smallschool districts, if we assume that excess ca-pacity exists (no additional building andequipment costs). However, if school qualityis considered, school district consolidationmay result in decreasing the state’s averageachievement test scores.

Finally, not all small school districts exhib-it higher achievement test scores than largerdistricts. In addition to this, some small schooldistricts do not spend as much per student aslarger districts. If a policy of consolidation isimplemented it should be on a case-by-casebasis, with evaluation of the cost per studentand achievement test scores of the school dis-tricts in question. Oklahoma’s current policythat provides financial incentives to merge andonly imposes merging on very small districtsseems like a reasonable policy.

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with another average school district (School District B)with 1,000 ADM to create School District A–B. SinceA–B’s average variable cost is only $4,422 per student,district B would gain $1,738 per student from A (atotal of $173,800 or $173,800/1,100 = $158,02 perstudent). If A–B decides to spend all the extra moneyon instruction, the gain in test scores for a studentorig-inally from B would be $0.158 thousand times the pa-rameter for instruction (0.37) or 0.06 points. However,studentscoming from A face another scenario. The re-duction in instructional expenditures for the studentsfrom District A is $849.6 per student. (The instruc-tional expenditure difference from a 100 ADM schooldistrict and a 1000 ADM school district is $1007. Thisis subtracted from $158.02 to obtain the $849.6 reduc-tion.) Because of this, students lose 0.31 points each.But there is also a loss due to increased ADM of 0,58points (the inverse ADM parameter multiplied by (1/11) – 1), and a gain of 0.19 points per student due toreduced administrative costs. All these effects add to anet reduction of 0.7 points for each student originallyfrom A. This does not include the non-market costs ofconsolidation to the students in small schools, such ascosts of adjusting to a new environment.

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