Per Student Allocation Formulas:From Principles to Coefficients

Jan HerczyńskiBaku, April 21, 2014

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Structure of the presentation

• „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

„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 care of teachers

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„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 needs

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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, Nmount

i =number of mountain students in municipality i

• Municipality i will obtain funds proportional to: Ni + 0.5 * Nmount

i

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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 and 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) Jan Herczyński 16

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 implementationJan Herczyński 24

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: – 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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