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The design of per student funding formula for allocating
school budgets
Jan HerczyńskiBaku, April 21, 2014
2
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
Jan Herczyński
3
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
Jan Herczyński
4
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
Jan Herczyński
5
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)
Jan Herczyński
6
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
Jan Herczyński
7
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
Jan Herczyński
8
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
Jan Herczyński
9
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
Jan Herczyński
10
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
Jan Herczyński 11
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
Jan Herczyński 12
13
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)
Jan Herczyński
14
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
Jan Herczyński
15
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
Jan Herczyński
16
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
Jan Herczyński
17
Population density and class sizes
0 50 100 150 200 250 3005.00
10.00
15.00
20.00
25.00
Jan Herczyński
18
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
Jan Herczyński
19
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
Jan Herczyński
20
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
Jan Herczyński
21
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
Jan Herczyński
22
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
Jan Herczyński
23
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
Jan Herczyński
24
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%
Jan Herczyński
25
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
Jan Herczyński
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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
Jan Herczyński
27
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
Jan Herczyński
28
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
Jan Herczyński
29
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
Jan Herczyński
30
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
Jan Herczyński
31
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
Jan Herczyński
32
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
Jan Herczyński
33
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
34
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
Jan Herczyński
35
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
Jan Herczyński
36
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
Jan Herczyński
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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%
Jan Herczyński
38
Budget of initial school as function of student numbers
Jan Herczyński
39
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
Jan Herczyński
40
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.
Jan Herczyński
41
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
Jan Herczyński
42
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
Jan Herczyński
43
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
Jan Herczyński
44
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