Per Student Allocation Formulas:
From Principles to Coefficients
Jan Herczyński
Baku, April 21, 2014
Structure of the presentation
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„Money follows the student”
Top down and bottom up formulas
Formulas for schools and for municipalities
Objective and non-objective factors
How to set the coefficients?
Buffers
Assessing the formula
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2
„Money follows students”
• In public finance, it is essential to focus
financing on functions, not on facilities
• However, usually supporting the
beneficiary requires supporting the service
provider
• In education, this is a distinction of
financing teaching process or teachers
• But good education requires taking good
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care of teachers
„Money follows students” 2
• The best although imperfect measure of
education tasks is the number of students
(or full time equivallent students)
• In theory, this gives the financing system
flexibility when student numbers change
• In practice, the flexibility requires good
education governance
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„Money follows students” 3
• Individual students usually do not have
specific costs, while individual teachers do
• This creates tension between allocation of
funds per student and spending of funds
per teacher
• The resolution of this tension is a difficult
and politically sensitive task
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„Money follows students” 4
• This tension is due to the fact that the main
driver of per student costs is class size
• Procedure based on „Money follows
students” must allocate more funds to
schools/municipalities with smaller class
sizes
• Inclusion of the impact of class size in per
student formula is a major challenge
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„Money follows students” 5
Different countries use different factors to
reflect class size in the formula:
• Rural/mountain location (Poland, Georgia)
• School size (Lithuania)
• Population density (Macedonia)
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„Money follows students” 6
• Money may follow the student to the
paying agency (eg. local government) or to
the school itself (depending on the form of
education decentralization)
• The principle „money follows students”
assumes that some procedure (formula)
will determine how much money follows
which type of student
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Top down – bottom up
Two basic types of formulas:
• Top down formula starts with the funds
allocated in the national (regional) budget
for education and attempts to distribute
those funds fairly and adequately
• Bottom up formula starts with
expenditures associated with teaching one
student and attempts to assess school
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needs
Top down – bottom up 2
Top down formula:
• The simplest top down formula allocates
the same amount of funds to each student,
• Student voucher is equal to total available
funds divided by the number of students
• In practice formulas always use some
coefficients to recognize different costs of
teaching different groups of students
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Top down – bottom up 3
Top down formula:
• For example, we may assess that mountain
schools need 50% more funding than others
• Ni = number of all students, Nmounti =number
of mountain students in municipality i
• Municipality i will obtain funds proportional
to: Ni + 0.5 * Nmounti
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Top down – bottom up 4
Top down formula:
• Top down formulas are in principle simple
but with many coefficients may become
confusing
• Polish national allocation formula is top
down, but number of coefficients grew from
21 in 2000 to over 40 now
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Top down – bottom up 5
Bottom up formula:
• Bottom up formulas are never simple
• Calculation of costs of educating one
student is based on current norms
(programs etc.) and input costs (teacher
salaries, energy prices)
• Calculation also always assumes some
conditions in the school, such as class sizes
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Top down – bottom up 6
Bottom up formula:
• CNFIPS in Romania has calculated 27
different per student norms for different
types and locations of schools (not
implemented)
• Lithuania has introduced many per student
norms based on school size (implemented)
• Those calculations are usually complicated
Janand
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prohibit understanding and dialogue
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To schools – to local governments
• We discussed in previous session two models
of education decentralization,
• The formula should allocate the funds to the
institution actually responsible for budgets
(principle of subsidiarity)
• So we have two types of formulas, to schools
and to local governments
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To schools – to local governments 2
Formula to schools:
• Need to reflect many specific factors and
conditions of individual schools
• Should cover: (a) basic teaching costs, (b)
support for students in need, (c) support for
strong students, (d) maintenance of buildings
• Some advanced countries use separate
formulas for each component (UK, Australia)
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To schools – to local governments 3
Formula to schools:
• Paradoxically, implemented formulas to
schools in post communist countries are
usually very simple,
• Georgia uses simple vouchers, Armenia uses
vouchers with lump sum
• This unavoidably leads to implementation
problems
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To schools – to local governments 4
Formula to local governments:
• As most local governments have at least a
few schools, their specific financial needs
may be averaged
• Formulas may use factors not applicable to
schools, but applicable to larger units, such
as population density or relative wealth of
the municipality
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To schools – to local governments 5
Formula to local governments:
• In practice, formulas typically use school
characteristics
– But Macedonia uses population density
• If local governments are very small
(Armenia), no difference between the two
approaches outside of large cities
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Factors used in formulas
• A formula is usually a mathematical
expression defining the allocatin of funds
to a school or to a local government
• Formulas take into account some factors
which reflect different costs of providing
education
• Numbers defining the impact of different
factors are weights or coefficients
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Factors used in formulas 2
• Choice of factors to be used in the formula
is a key policy decision of the Ministry
• Factors which may be influenced or
changed by the local agent (school or
municipality) should not be used in the
allocation formula
• Factors which are independent of the local
agent are objective factors
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Factors used in formulas 3
• If there are few factors in the formula, their
strategic meaning is clear, but the formula
may be inadequately flexible
• If the number of factors is excessive, their
impact on the final allocation becomes
difficult to understand and analyze
• Typically, introduction of new coefficients
is the price paid for compromise
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Setting coefficients
• There are no objective scientific truths
which uniquely determine the values of
allocation coefficients
• Coefficients influence the allocation of
public funds to institutions or to levels of
local governments
• Coefficients express policy preferences and
are subject to debate and compromise
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Setting coefficients 2
• Nevertheless, coefficients need to
correspond to financial needs of schools or
municipalities
• Therefore setting the coefficients usually
proceeds in two steps:
– empirical averages or econometric regressions
provide initial values for discussions
– compromise with education stakeholders sets
the values for implementation
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Setting coefficients 3
• A rural factor in the formula reflects
relatively smaller classes in rural schools
• If it is very high, the motivation of rural
municipalities to rationalize school network
will decrease
• If it is too low, some rural municipalities
may find themselves unable to maintain
schools
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Setting coefficients 4
• Coefficients need to be universal, that is
should apply to all the schools or local
governments in the same way
• Correction coefficients for specific
institutions put favoritism in place of policy
• Correction coefficients for specific
institutions undermine budget discipline
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Buffers
• Buffers or hold harmless clauses limit the
impact of new formulas by keeping the
allocation close to historical allocation
• Buffers are almost always necessary when
a formula is being introduced for the first
time
• Buffers protect schools from sudden
decrease of budget allocation
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Buffers 2
• Narrow buffers limit the impact of new
formula but provide strong protection
against adjustment shock
• Wide buffers means the new formula has
stronger impact but schools may
experience greater shocks
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Buffers 3
• Poland had strong buffers from 1996 till
2000
• In 2000 the buffers were made weaker (per
student buffers)
• Since 2004 the buffers are no longer
applied
• Local education systems had time to adjust
to formula funding
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Assessing the formula
• Ministry need to be able to assess the
formula along several dimensions:
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Winners and losers,
Horizontal and vertical equity,
Efficiency,
Treatment of politically sensitive groups
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Assessing the formula 2
Winners and losers:
• It is extremely important to identify which
schools/local governments will win and
lose most under the formula,
• This could be individual schools, types of
schools, regions or municipalities,
• Especially important when the formula is
being introduced or seriously changed
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Assessing the formula 3
Dealing with winners and losers:
• If schools lose because they were historically
overfunded, buffers may be sufficient
• If schools lose because the formula does not
recognize their speficity, the Ministry may
consider revising the formula
• Ministry may want to adjust coefficients to
minimize the number of losers
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Assessing the formula 4
Horizontal equity:
• Horizontal equity means students in similar
conditions and schools should be funded
more or less at the same level,
• Systematic breaking of horizontal equity
indicates a weakness of the formula
• Example: Poland rural coefficient applies to
local governments close to large cities
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Assessing the formula 5
Vertical equity:
• Vertical equity means that different
treatment of schools of different level is
justified on policy grounds
• Ministry needs to monitor relative funding
of different education sub-sectors
• Excessive funding of a sub-sector indicates
a weakness of the formula
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Assessing the formula 6
Efficiency:
• Allocation formula is efficient if the funds
allocated to municipalities and schools are
adequate but not excessive
• Excessive allocation to specific schools or
municipalities means that others do not get
enough, leading to inefficient use of funds
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Assessing the formula 7
Sensitive groups:
• Ministry always needs to take into account
politically sensitive groups and ensure that
the formula does not discriminate against
them
• Those groups may include: national
minorities, special needs students,
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Assessing the formula 8
Simulations:
• Assessment of the formulas should always
include nationwide simulations of its effects
under various scenarios (coefficient values)
• Review of the simulation allows the ministry
to assess proposed allocation
• Simulations based on a sample of schools or
municipalities are not enough
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