The design of per student funding formula for allocating

school budgets

Jan HerczyńskiBaku, April 21, 2014

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Structure of the presentation

• Formulation of main problems of designing a per student formula

• Outlines of general methodological approach• Examples of different formulas with some

analysis and lessons learned (transition countries)

• Conclusions

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What is a per student formula

• Allocation formula for education tasks based primarily on student numbers

• May include many factors which characterize students

• Often leading to „weighted number of students”, not the physical number of students

• Sometimes includes elements not related to students

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Formulation of the problem

• Students are not carriers of education costs– Except for special cases, no specific expenditures are

associated with individual students• Main carriers of education costs are teachers

– Teacher salaries often represent more than 70% of school budgets

• Additional costs are related to school administration and to school facilities

BUT: number of students is the best measure of education tasks

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Formulation of the problem 2

• Education expenditure is not really proportional to number of students

• Main categories of school expenditures are proportional to number of classes: – Teacher salaries (according to curriculum norms), – Some ICT equipment (projectors, interactive

blackboards)

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Formulation of the problem 3

• Some expenditures are proportional to student numbers, but they are relatively small:– Water consumption, – Meals– Textbooks (if included in the formula).

• Some are proportional to school facility area, for example heating– School area is more in line with number of classes

than with number of students

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Formulation of the problem 4

• However, we cannot allocate funds on the basis of the number of classes– This would lead to division of students into smaller

classes to increase alllocation– Perverse incentive to reduce efficiency

• Similarly, we cannot base formulas on the number of teachers– This would lead to excessive employment of

teachers

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Methodological approach

Generally, one should use in the formula only factors which: • CAN predict class size or number of students

per full time equivalent teacher• CANNOT be influenced by local actors

We call these objective factors

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Methodological approach 2

Per class costs may also vary depending on additional factors: • Grades (different curriculum norms)• Instruction language• Integrated teaching for student with special

needs

These are usually related to teaching load

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Methodological approach 3

• A potential formula therefore should use factors which taken together: – Are objective, – Reflect teaching load.

• The criteria adopted should be reviewed to see how well they predict class sizes

• The formula must be verified by checking the variation of per class allocation

Jan Herczyński

Methodological approach 4

Factors which may be used in the formula: • School location (rural, mountain), • Population density,• School level (primary/secondary) or profile • Categories of students who need extra care

(special needs, minority, poor) if an objective identifying procedure exists

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Methodological approach 5

Factors which should not be used in the formula• Number of students in a class or a school (if

may be affected by local actions), • Teaching load, number of teachers (if they are

hired locally)• Area of school buildings (in the long run), • Teacher qualifications

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Main problem: rural schools

Smaller classes due to small number of students in small villages (difficult to transport students)

May be adressed through categorization of school location: • Urban / Rural (Poland)• Urban / Rural / Mountain (Georgia)• By population density (Macedonia)• Other criteria (Bulgaria)

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Rural schools 1

Macedonia, primary education: • Categorization of municipalities using

population density• 4 groups of municipalities• Coefficient based on also on grades• Additional coefficient for special needs

studentsData for 2011

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Formula for municipalities

• The formula for municipalities includes two elements: – Number of weighted students multiplied by a per

student amount (31 thousand MKD in 2011)– Lump sum for municipality (5 million MKD in 2011)

• The lump sum supports small rural municipalities with few small schools, and becomes irrelevant for large municipalities

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Coefficents for primary schools

Categories of population density

Grades1 – 4 5 – 8

Under 40 inhabitants per km2 1,6 1,8Between 40 and 50 inhabitants per km2

1,4 1,6

Between 50 and 70 inhabitants per km2

1,2 1,4

Above 70 inhabitants per km2 1 1,2

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Population density and class sizes

0 50 100 150 200 250 3005.00

10.00

15.00

20.00

25.00

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Class size and per student allocation

9 11 13 15 17 19 21 23 25 27 290

20,000

40,000

60,000

80,000

100,000

120,000

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Class size and per class allocation

9 11 13 15 17 19 21 23 25 27 29400,000

600,000

800,000

1,000,000

1,200,000

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What Macedonian example teaches us

• Good prior analysis of factors taken into account in the formula is necessary

• But sometimes non-perfect formula is better than no formula!

• After the formula is designed, its effects need to be thoroughly analyzed

• Public discussion is useful for preparing changes to the formula

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Rural schools 2

Bulgaria: • Categorization of municipalities using many

different criteria• 4 groups of municipalities• 4 values of unified cost standards – values of

per student allocation

Data from 2008

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Two levels of formulas

• A formula allocates funds to municipalities– Unified Cost Standard multiplied by number of

weighted students– No lump sum as in Macedonia

• Municipality must adopt a formula to allocate these funds to its schools– 80% on a simple per student basis– 20% based on locally selected criteria

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Groups of Bulgarian municipalities

1 Municipal center more than 70 thousand

15

2 Center between 10 and 70 thousand, density > 65

40

3 Center between 10 and 70 thousand, density <65, not mountains

139

4 Other 70

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Unified cost standards, 2008

Group UCS (Leva)

Relative to 1

1 980 100,0%2 1 051 107,2%3 1 105 112,8%4 1 184 120,8%

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Class sizes: groups are heterogenous

Mean Min.-Max 1 2 3 4

group

10

12

14

16

18

20

22

24

26

28

avera

ge c

lass s

ize

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UCS fit average class sizes

Mean Min.-Max 1 2 3 4

group

12000

14000

16000

18000

20000

22000

24000

26000

28000

30000

cla

ss a

llocatio

n

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Per class allocation and class size

10 12 14 16 18 20 22 24 26 28

average class size

12000

14000

16000

18000

20000

22000

24000

26000

28000

30000

cla

ss a

llocation

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What Bulgarian example teaches us

• It is difficult to capture real variation of class sizes using even multiple and rather complex criteria

• The average values mask significant variation• The variation may lead to unequitable

allocation of funds for education

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Rural schools 3

Georgia:• School receive funds directly from the Ministry

of Education• No other legal revenues of schools• Three values of vouchers: city, rural, mountain

Data from 2007

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Voucher and students per full time equivalent staff, by location

Students per FTE staff

Voucher (Lari)

Voucher per FTE staff

City 13,2 300 3 952

Rural 8,8 420 3 690

Mountain 6,1 510 3 117

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Students per FTE staff by school size and location

Students City Rural Mountain41 to 60 4,1 4,0 3,461 to 100 4,9 5,5 4,8101 to 200 7,0 7,7 6,9201 to 500 12,9 10,7 10,1Above 501 15,3 11,7 15,5

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What Georgian example teaches us

• School size is a better predictor of class size (or number of students per FTE staff) than school location

• There is huge variation of school sizes within each category of location

• Location is not a good criterion for allocation formula

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Rural schools 4

Lithuania: • Introduced a Student Basket (per student

amount) based on 4 categories of school• Schools are categorized by size (number of

students), leading to normative class sizes• Student Basket depends on size category (on

normative class size) and also on grade (teaching load)

Data from 2007Jan Herczyński

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What does the Student Basket cover

• All expenditures are divided into education process and education environment

• Education process includes teaching and related expenditures

• Education environment includes school maintenance and related costs

• Both include both salaries and material costs• Student basket covers only education process

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Local re-allocation

• Transfer to each municipality is defined as sum of school allocations for all schools located there

• Municipality must trasnfer these funds to schools

• Municipality has the right to re-allocate up to 5% of school budget to other schools

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Definition of school size categories Size

categoryInitial(1-4)

Basic(1-10)

Secondary(1-12)

Normativeclass size

XS up to 50 up to 130 10S 51 to 80 131 to

300up to 400 15

M 81 to 200 301 to 600

401 to 700

20

L over 200 over 600 over 700 25

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Relative values of per student amount

Size category

Grades

1 to 4 5 to 8 9 & 10 11 & 12XS 158% 188% 243% S 119% 141% 164% 181%M 90% 108% 125% 138%L 90% 100% 125% 132%

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Budget of initial school as function of student numbers

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What does Lithuania teach us

• Basing per student amount on school size may lead to problems of reporting of student numbers

• National per student formula plus local power of re-allocation works very well for education process

• In the sphere of education environment significant inequalities emerged

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Small schools – a different approach

Moldova (2012): • The formula for schools uses only one

differentiating factor, grade– Grade 1-3: 0,75, grade 4-7: 1, grade 8+: 1,32

• Per student normative A, per school normative B. – School budget: Weighted Students * A + B

• For large school first term dominates, for small school – the second.

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Another problem: minorities students

• Often attend smaller class sizes, due to number of students

• Often have additional curriculum requirements (teaching of the additional language)

A greater than 1 weight attached to minority students should take into account both of these factors

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Conclusions

• Designing a per student allocation formula is not a scientific activity, there are no strict rules and optimal models

• Every allocation system has its weaknesses and problems

• Understanding of these problems is necessary for taking appropriate mitigating measures, and hence for successfull implementation

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Conclusions 2

• Prior to implementation, detailed simulations are necessary

• Review of simulations should include:– Analysis of per class allocation– Vertical and horizontal equity– Cases of insufficient funding for specific schools

• Simulations often yield more useful information than pilots

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Conclusions 3

• Hard budget constraints should apply only to units with some budgetary independence, such as large schools or local governments

• Needs of every school are different, therefore a good system allows for some degree of flexibility

• The minimum form of such flexibility is to define reserve funds at the central or local level

Jan Herczyński