FISCAL DECENTRALIZATION IN EDUCATION

A Three Part Hands-on Training Module

By Taryn Rounds ParryDepartment of Political Science

University of Georgia

October 1996

CONTENTS

Introduction: Why Use Intergovernmental Grants?

Part A: Types of Grants and their ImpactsA.1 Matching Rate and Local and Central Government Share of SpendingA.2 Local Government Response to a Change in IncomeA.3 Local Government Response to a Change in Central Government TransfersA.4 Local Government Response to a Change in Price A.5 Estimating Elasticities (optional exercise)

Part B: Lump Sum Grants Simulation 1: Foundation Grant

B1.1 Foundation SimulationsB1.2 Simulating Alternatives (optional exercise)B1.3 Evaluating Alternatives: EfficiencyB1.4 Evaluating Alternatives: EquityB1.5 Lorenz Curve (optional exercise)

Simulation 2: Poverty FormulaB2.1 Increase Capitation Transfer (same amount for all municipalities)B2.2 Increase Distributed According to Relative Poverty LevelB2.3 Comparing Alternatives

Part C: Matching Grants C.1 Simulation 1: Simple Matching Grant

and Compare to Lump-sum Grant (of same amount)

C.2 Simulation 2: Variable Matching Grant

FISCAL DECENTRALIZATION IN EDUCATION

INTRODUCTION

Suppose you are assigned to a country that is considering decentralization of education. What strategy should you recommend? What data need to be collected in order to evaluate various approaches to decentralization? This training module presents some important considerations in the decision to decentralize education (or other social services) and provides some simulation exercises to show the impact of various intergovernmental grant designs on the distribution of benefits and on stimulating local education expenditures.

This session begins by explaining why intergovernmental transfers are usually an essential part of decentralization in developing countries. Part A reviews the different types of grants and how their impacts may differ. In particular, the concepts of income and price elasticity are important for simulating the response of local governments to different grant formulae. Short exercises in this section teach techniques and concepts that participants will later apply in simulations using actual data in Parts B and C. Part B gives some examples of simulations of lump-sum type grants. The simulations reveal that providing resources may not be sufficient to stimulate higher education expenditures so that minimum required expenditures may be necessary. Part C gives some examples of simulations of matching grants. These grants are more successful in stimulating education expenditures than lump-sum grants.

This training package contains this written guide and a diskette with the following Excel files:

Part A edndec.xlsestelast.xls (optional exercise)

Part B foundatn.xls lorenz.xls (optional exercise)poverty.xls

Part C matching.xls

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INTRODUCTION

The Logic of Decentralization

Should education be decentralized?

1 To review briefly, some of the benefits of decentralization include the following:

greater diversity and increased responsiveness to the needs of the people (greater social efficiency)

more efficient administration as decisions can be made more quickly and with better information (technical efficiency)

additional cost savings if lower cost areas can pay lower wages and prices than when the system is centrally administered

Decentralization can have other benefits such as promoting greater participation, and generating more local support. It may generate greater local funding for services which can relieve fiscal stress experienced by central governments.

2 On the other hand, decentralization clearly has some problems:

The localities often lack the expertise and technical resources to perform the newly decentralized tasks. However, this is only a short-term problem, and a reason to implement decentralization slowly rather than abandoning it completely. The central government must support decentralization by providing support and helping the local governments develop the expertise required to perform the decentralized tasks.

Some services have economies of scale as well as diseconomies of scale. Standardization has some advantages, and centralized administration of education my require fewer resources than decentralized administration. For example, decentralized administration of education in Chile requires more personnel (per student) than when education was centrally provided.

One main concern with decentralization is inequity and inadequacy of resources. Centrally provided services often (not always) redistribute revenue to resource poor areas. If decentralization requires local communities to rely much more on their own resources, significant disparities will result. Especially in developing countries, many communities may not have adequate resources to provide even a minimally acceptable standard of education.

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Another concern that is particular to education is spillovers across local jurisdictions that may lead to less than optimal investment in education. Literacy and basic skills produce better informed citizens who have better health and who tend to have smaller families. Education has a positive impact on economic growth and a negative impact on crime. For these reasons a good education system benefits the entire nation. Education is a national public good, not a local public good, and pure local finance of education would lead to under-investment in education.

3 Intergovernmental transfers address some of the concerns with decentralized provision of education. They permit the central government to continue to be a major source of funds for education while at the same time, local officials can make expenditure decisions and see to the day to day operation of schools. This can help to reduce inequity by providing adequate resources, and it permits some national funding for a national public good.

4 However, intergovernmental grants are not without their own set of problems:

Rent-seeking Powerful local government officials will attempt to influence central government finance decisions in order to accrue more resources for their community. This will interfere with the development of grant distribution formula as they will want the formula to favor their characteristics. More than likely, their influence will have a detrimental impact of any equity improving aspects of the transfer mechanism.

Poor Decision Making The recipients of intergovernmental transfers tend to look upon grants as "free money" since they do not bear the costs of raising the funds. When local governments do not have to finance their own expenditures, they tend to spend inefficiently since spending brings local benefits while the costs are borne by others. Therefore, some incentives may be necessary to achieve greater efficiency.

Transfers Do Not Guarantee Higher Expenditures If demand for education is usually income inelastic and price inelastic, transfers may not overcome equity or spillover problems. Grants also tend to reduce local effort so that grants merely supplant local expenditures: If you spend $100 on education and I offer to give $100 that must be spent on education, you may continue to spend $100 on education, but now the $100 you used to spend on education can now be used for other things. The $100 can also be used to give local citizens a tax break.

5 POINT: The first question to address is whether decentralization is worthwhile. This means identifying how the present system is working (collection of baseline data) and determining what can be gained through decentralization. Another important consideration is what decisions are being decentralized? This module assumes finance and expenditure decisions are the decisions that are being decentralized, but decentralization may be more narrowly or more broadly defined. Box 1 shows list of questions and types of data that need to be collected in order to answer these questions.

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1.PART A: TYPES OF INTERGOVERNMENTAL GRANTS AND THEIR IMPACTS

6 Usually intergovernmental transfers are divided into the following three categories:

Box 1: Assessing the Situation

1. How does the current system work and what changes are proposed with decentralization?School Organization How is the schooling system organized? (pre-school-primary-secondary-vocational etc.)The structure of a school system is almost always set by the central government. Will this situation change with decentralization?Curriculum and Teaching Methods Is the curriculum a national curriculum (centrally deter mined)? Are there any adjustments for regional or cultural differences? Will decentralization permit localities to determine their own curriculum and teaching methods?Examinations and Supervision How are students and teachers evaluated? Are there national examinations? Which level of government performs the evaluations and sets examinations? Will this be changed under proposed decentralization plans?Teacher Recruitment and Compensation Which level of government sets accreditation standards? hires teachers? sets promotion rules and rules for dismissals? How are teachers' salaries determined? Which of these things are expected to change under proposed decentralization plans?Finance of Operating Expenditures How is school operation financed and in particular who pays teachers' salaries? Do intergovernmental transfers exist at present? How are they distributed? Are new transfer mechanisms proposed with the decentralization plans? What percent of this finance comes from local sources? Is this share expected to increase under decentralization? What are local government sources of revenue? How are localities expected to raise additional funds for education? What legal restrictions exist on their ability to raise local revenues? School Construction and Finance Who determines where schools are built? Who sets construction standards and are they uniform nationwide? How is school construction financed? Do any intergovernmental transfers exist specifically for financing school construction? How are these transfers distributed? How much of school construction costs are financed by localities at present? Is this share expected to change with decentralization?

2. What are the country's attributes?What is the distribution of income? Is there a large degree of variation in income and resources across the country? Do climate and natural resources vary greatly? What are the different cultures in this country and where are their cultural centers? Is there one common language or are many languages spoken? What is the political system and in particular, how are local government officials chosen? Who are the minorities and are they represented by the political system? Do any channels exist for citizen participation in national or local decision making?

3. What are the potential gains from decentralization?Social EfficiencyThe greater the uniformity of the education system and the greater the disparities in cultures, climate, and resources, the greater the potential for decentralization to improve "social efficiency" or improving the match between citizen preferences and the quality, type, curriculum, methods, and quantity of education provided. However, if minorities or low-income groups are shut out of the local decision making process or if local officials are chosen by the central government, these gains are minimized. Technical EfficiencyIn theory decentralization is expected to improve technical efficiency and lower costs. In practice it is difficult to assess. First some data are needed regarding costs under the current system and how these costs compare to local costs. Are centrally determined teacher salaries much higher than other local salaries? Will decentralization permit localities to determine teacher and staff salaries? Will decentralization permit localities to use cheaper local resources? Is central administration slow and encumbered by red tape? EquityMany expect decentralization to worsen inequities. However, if the present centralized system is already inequitable in the way resources are distributed through intergovernmental transfers, legal restrictions or other policies, decentralization may not be any worse.

General Revenue Sharing--the central or state government shares revenue (from a sales tax for example) with lower levels of government. Usually the distribution is on a per-capita basis, but the distribution formula can be more complicated.

Block Grants--are specified for a specific type of expenditure, but have few or no other restrictions attached. Their benefit is lower administrative costs, and few compliance costs for recipients.

Categorical Grants--are not only for a specific type of expenditures, but have many strings attached. They are expensive to administer for both the grantor and the recipient of the grant.

7 The first two types of transfers are mainly to equalize or redistribute resources. Categorical grants are given in order to induce local governments to spend more on education. Despite all their restrictions, they may not be very successful. This occurs if the grant funds are used to substitute for locally funded education expenditures, and the money the locality used to spend on education is used for other purposes. The net effect is the same as if no requirements were given. For this reason, categorical grants often have revenue effort or minimum expenditure requirements.

Distribution of Grants

8 Both block and categorical grants can be distributed as project grants (by application) or by formula (by specified criteria). The simplest type of formula grant is a capitation grant which is based solely on population or number of clients (students in the case of education). Both types of distribution methods are used for education. Usually capital investment in new schools or extensions of schools are funded by project grants, while operating expenditures are funded by capitation grants.

9 This training module will focus on two main types of formula grants: lump-sum and matching grants. Both project and formula grants can be lump-sum or matching grants. Matching grants require the local government to spend money (on education) in order to receive any money. Lump-sum grants do not have this requirement and hence, are unrelated to local expenditures on education.

10 With a matching grant, the central government will match each local dollar spent on education with a specific amount of centrally-raised funds for local education expenditures. For example, if the central government matches every local dollar spent on education with a dollar from the central government, half of total education expenditures would be funded by the central government and half would be financed by local revenues.

11 Matching grants lower the "price" of education from the local government's point of view--one dollar increase in expenditures costs less than one dollar of local revenue. Lump-sum grants work by increasing the local government's total income by giving them more income to spend. Because of this difference in design, matching grants stimulate spending more than lump-sum grants--assuming no expenditures requirements. This principle will be illustrated in the simulation in part C.1 below.

12 Since the matching amount in the example above is one dollar for one dollar of local expenditures, the matching rate (R) is equal to one. However, the matching rate can be any amount. If the matching rate is less than one, the central government will fund less than half of total education expenditures, and if the matching rate is greater than one, the central government will fund more than half of total education expenditures. Since local governments in developing countries often do not have access to major sources of revenue, the matching rate should typically be higher than one; otherwise the transfer payment will not be very large. Matching grants can be open-ended (no limit of grant received) or closed-ended (grant amount is limited so that after a certain level of local expenditures, the grant received will not increase).

13 The purpose of the following exercise is to show how to calculate the share of education spending financed by the central government (C) and the share of spending financed by the local government (L) when the matching rate (R) is known. Alternatively, sometimes the central and local government shares are known, and then the matching rate (R) must be calculated. These calculations will be used in the matching grant simulations in part C below.

Exercise A.1: Determining the Matching Rate, Central Government Share, and Local Government Share of Spending

14 Open the file edndec.xls and go to the worksheet entitled "Matching Rates." Table 1 gives you the opportunity to calculate the central government share of education spending (C), the local government share (L), and the matching rate (R). The variables have the following relationships:

C = R / (1+R)

C = 1 - L

R = (1/L) -1

Use the above equations to complete the colored blanks in table 1.

15 To interpret your results you can think about the central government share as the percentage decrease in the localities price of education. For example, if R=1, then each local dollar generates one grant dollar so the grant finances 1/2 of total education expenditures. For the locality the price of education decreases by 50%. If R=.5, then each local dollar generate fifty cents in grant funds, and the grant finances 1/3 of total expenditures. For the locality the price of education decreases by 33%.

A.2 LOCAL GOVERNMENT RESPONSE TO A CHANGE IN INCOME

16 Since education is a normal good (rather than an inferior good), higher income should increase expenditures on education as well as on other normal local goods. How much expenditures on education increase depends on the income elasticity of demand. A lump-sum grant will increase a community's resources so we need to estimate whether the community will increase education spending by a little or by a lot after receiving the lump-sum grant. In the following exercise, income elasticity of demand is referring to the locality's income elasticity of demand for education.

17 The purpose of this exercise is to learn how to calculate income elasticity and how to use it to determine the change in education expenditures due to a lump-sum grant. This formula will be used in the simulation exercises in part B.

EXERCISE A.2: Calculating Income Elasticity of Demand

18 In the same file (edndec.xls) go to the worksheet entitled "Income Elasticity" and follow the steps below. NOTE: the level of observation in this exercise is the local government and it's demand for education (not the individual's demand for education).

19 Table 2 provides an opportunity to calculate income elasticity using different types of data. The formula for calculating income elasticity of demand (EY) is:

EY = %DQ = DQ/Q = DQ * Y %DY DY/Y DY * Q

where %DQ = percentage change in education expenditures due to the lump-sum grant%DY = percentage change in local government income Q = original education expendituresDQ = change in education expenditures due to the lump-sum grant Y = original local government income DY = change in local government income or the amount of the lump-sum grant (or the

change in the lump-sum grant amount)

Step 1 For the first eight localities, calculate the change in education expenditures

Step 2 Next calculate the percentage change in education expenditures

Step 3 Calculate the percentage change in income. Remember that the new grant (or the change in grant amount) is the change in income.

Step 4 Last, calculate the income elasticity of demand for each community

20 For the last eight localities the income elasticity of demand is known, and instead you are required to determine the size of the local governments' response (change in education expenditures).

Step 5 First calculate the percentage change in income due to a new (or increase in) lump-sum grant.

Step 6 Using the information from step 5, the income elasticity (given in the last column) and the formula for calculating income elasticity, calculate the change in education spending. (HINT: first you must solve the income elasticity formula for the change in education expenditures)

Step 7 Using the information from step 6, calculate the new local education expenditures (original spending plus the change in spending)

21 In the simulation exercises in part B the income elasticity will be given, and the change in income due to the change in formula will be calculated. Then using this information in the above formula will determine how communities will respond: How much more education will they provide when they are given a lump-sum grant?

22 One key problem with determining income elasticity is determining how to measure community income, and then finding these data. At the local level, "income" could be aggregate household income or it could reflect the size of the available tax bases. Especially in developing countries, however, local governments may have very limited ability to tax. An alternative is to use local government income (revenue), but this measure is not a perfect measure of income since revenue depends on both the rate and the tax base size.

23 Another problem with respect to using income elasticity in determining the local governments' response to a lump-sum grant in centralized countries is that many localities may have a limited ability to determine local expenditures--there are no data on the expenditure choices these governments would make once they are given more discretion. It is also true that oftentimes higher level government staff choose local government leaders--thus, local government decisions may be strongly influenced by higher levels of government. Therefore, it is preferable to perform simulations using data from a country that is already decentralized with some fraction of education spending financed by local revenues, and some financed by the central government. Otherwise, the elasticities can only be guessed at so the results of the simulation are less accurate.

A.3 LOCAL GOVERNMENT RESPONSE A CHANGE IN LUMPSUM CENTRAL GOVERNMENT TRANSFERS

24 The purpose of this exercise is to provide an alternative way to estimate the local governments' response to a lump-sum grant for education. The advantage of this method is that data on local and central government education expenditures are more readily available while exercise A.2 above requires data on local income which are often not available. This method of determining the local government's response will be used in part B2 below.

25 This approach assumes a different view of the situation. Rather than view the central government grant as increased income to the locality, it is viewed as central government expenditures for education. In this case, when the central government spends more on education in the community (it receives a larger transfer), the local government is expected to cut back on its own education expenditures. Therefore, this elasticity will be negative.

26 The elasticity estimated is the elasticity in local expenditures with respect to central government transfers (ECGT). The formula for estimating the local government's response is as follows:

ECGT = %DLE = DLE/LE = DLE * CGT %DCGT DCGT/CGT DCGT * LE

where %DLE = percentage change in local education expenditures due a change in central government expenditure (in the form of a lump-sum grant) on education

%DCGT = percentage change in central government education transfers LE = original local education expendituresDLE = change in local education expenditures due to change in central government education

expenditures CGT = original central government education transfers DCGT = change in central government education transfers which is the amount of the lump-

sum grant (or the change in the lump-sum grant amount)

EXERCISE A.3: Local Government Response to Central Government Transfers

27 Open the file edndec.xls and go to the worksheet labeled "Expenditure Elasticity" . This worksheet contains Table 3 which looks very similar to Table 2 except in this case the local government response to central government spending will be estimating using the above formula. The difference in this case is that data are required on central government transfers rather than on local government income. It will not yield the same solutions as for table 2.

Repeat the same steps as in exercise A.2, only applying the new elasticity formula.

A.4 LOCAL GOVERNMENT RESPONSE TO MATCHING GRANTS

28 A matching grant lowers the "price" of education from the local government's point of view. Therefore, the responsiveness of the local government to the matching grant can be interpreted as a price elasticity. The locality's price elasticity of demand will determine how much expenditures on education increase as a result of a matching grant. The price elasticity should be negative since as price goes down the quantity demanded goes up.

29 The purpose of the following exercise is to practice calculating price elasticity. These calculations will be used in the simulations in part C of this training module. The formula for calculating the price elasticity of demand (EP) is:

EP = %DQ = DQ/Q = DQ * P %DP DP/P DP * Q

where %DQ = percentage change in education expenditures due to the matching grant%DP =percentage change in price. With a matching grant the percent decrease in price is equal to

the central government's share of education expenditures Q = original education expendituresDQ = change in education expenditures due to the matching grant P = original price DP = change in price

EXERCISE A.4 Calculating Price Elasticity of Demand

30 In the file edndec.xls go to the worksheet entitled "Price Elasticity". Table 4 provides an opportunity to calculate the price elasticity of demand, and to calculate the change in education expenditures, given the price elasticity.

31 The percentage decrease in price is equal to the central government's share of education expenditures. For example, if the central government's share is 25%, the local government pays 75%. The percentage decrease in price for the local government is 25%. In this case the central government's share is known, but if only the matching rate was known, then you would have to calculate the central government's share.

32 For the first eight localities calculate the percent increase in local government expenditures and then calculate the price elasticity.

For the next eight localities you must determine the new local government expenditures given the price elasticity and the percentage change in price. This can be done all in one calculation. However, there are

several ways to make this calculation--you may want to calculate the percentage increase in expenditures before calculating new expenditures.

Closing points:

33 NOTE: The above exercises were based on just one method of calculation. However, there are many ways to set up and solve the same arithmetic. In doing your own simulations, you may choose to set up your equations in a different form than those used in these exercises.

34 POINT: The price elasticity of demand is used to determine how local governments will respond to a matching grant. Two methods are suggested to evaluate the local governments' response to a lump-sum grant: income elasticity, and elasticity with respect to central government transfers. These two methods will not necessarily give the same solution. Choice of method is in part determined by data availability, but also by the situation.

35 POINT: The most important part of the simulations is determining the income and/or price elasticity with as much accuracy as possible. The exercises above are overly simplistic because they assume no other factors affect the change in local expenditures. Normally, estimation of income and price elasticities requires the collection of data and the use of multiple regression analysis to control for all influences on expenditures. The following optional exercise provides an opportunity to estimate elasticities using multiple regression.

36 In the U.S., both estimates of income elasticity and price elasticity are expected to be a fraction (between 0 and 1), but for developing countries where education finance has always been a central government responsibility, it is not clear what the local government response will be to education financed by intergovernmental transfers.

37 SUGGESTION: Since estimates of elasticities are imprecise, do more than one simulation using a high and low estimate when simulating the impact of a transfer. This will show how sensitive the outcome is to the income or price elasticity of demand for education.

The remainder of this training module will demonstrate how to use these elasticities to simulate the impact of intergovernmental transfers on total education expenditures.

A.5 ESTIMATING ELASTICITIES (OPTIONAL EXERCISE)

38 The exercises above were not a realistic means of determining a community's actual income or price elasticity because they implicitly assumed there were no other influences on the demand for education. The most common way to control for these other influences would be to employ multiple regression analysis to estimate the localities' demand for education. The purpose of this exercise is to provide an opportunity to estimate elasticity using multiple regression analysis. In this case you will estimate the local government response to a change in the central government transfer for education.

39 To estimate elasticities in general, the model should be a "log transformation" model--where all variables are logged. In a log transformation model the coefficients on community income can be interpreted as an estimate of income elasticity of demand, and if the grant is a matching grant, the coefficient on price reduction (central government share) can be interpreted as an estimate of price elasticity of demand. These models can be either pooled time-series or cross-sectional models.

40 How accurate the estimate for elasticity is depends upon the completeness of the regression model. If the model is poorly specified, the estimate can suffer from omitted variable bias. A well-specified model for explaining education expenditures should include both demand-side and supply-side influences such as a measure of the size of the market (number of pupils--or specify quantity on a per pupil basis), prices of other local public goods in addition to the tax price of education, measures of the economic base and income, costs of inputs, amount and quality of inputs (e.g. student-teacher ratios), and any indicator of the "taste" for education such as the average level of education. The model must also be free of autocorrelation and heteroskedasticity. Specifying the model on a per-pupil basis can reduce heteroskedasticity problems. Also, the larger the number of observations, the better the model estimates.

EXERCISE 5 Estimating Elasticities (optional)

41 The dependent variable in this model should be local education expenditures per pupil.

Step 1 Before going on, consider what factors will influence local education expenditures. Write down your ideal model. (See above paragraph for suggestions.)

Step 2 Open the file, estelast.xls. This file contains real data on 68 urban localities in Chile. Normally the next step is to convert all variables into natural logs (using the natural log function (Ln)). To save time, however, this step has been done for you.

Step 3 Estimate your model using the natural log of local government education expenditures as your dependent variable. You may have to use a model that is very different from your "ideal" model given data limitations. This model should include central government transfers on education.

Step 4 After determining your estimate of central government transfer elasticity (that is local response to the central government education transfer), evaluate the estimate based on your knowledge of econometrics and regression modeling. Consider what additional data you would need, and how the model might be specified differently.

You may want to try estimating several alternative models. You may wish to refer to Annex A, Table A.3 in The Design and Administration of Intergovernmental Transfers (Winkler, 1993) for a sample model. This is a different sample so results will not be the same as in this table.

Using this data and the variables used in Table A.3 referred to above, gives the following results where the dependent variable is municipal education expenditures.

Variable Estimated Coefficient T statistic

SES 1.7 1.88

CGT_S -2.49 1.74

NERPOP 0.53 2.20

DENSITY 0.02 0.27

EDWAGES 0.78 1.72

ST_TCHR -2.21 3.24

PERPUB -0.56 0.98

Intercept 30.4 2.11

Variable Definitions*

SES Socioeconomic levelCGT_S Central government transfer per studentNERPOP Non-earmarked local revenue per capitaDENSITY Population density in 1990EDWAGES Education wages ST_TCHR Student-teacher ratioPERPUB Percent of students attending public schools

*This is a log transfromation model so all variables including the dependent variable have been logged using the natural log function.

PART B

SIMULATIONS OF LUMP-SUM GRANTS

B1 FOUNDATION GRANT SIMULATION

42 One common type of lump-sum grant for education in the U.S. is the foundation grant. The purpose of the foundation grant is to provide a basic level or foundation level of education expenditures in resource-poor localities while leaving wealthier localities to fund their own education expenditures. Thus, the foundation grant is inversely related to the community's own-source revenue. NOTE: Municipal own-source revenue is labeled “non-earmarked revenue” in the files for the simulation exercises.

43 The purpose of the following exercise is to demonstrate a simulation of the foundation grant using data from a developing country. This country already has a capitation grant for education which covers 90% (on average) of total education expenditures. One problem, however, is that resource poor, mainly rural communities rely almost exclusively on the grant to fund education. Wealthy communities, on the other hand, make considerable expenditures for education in addition to the capitation grant. The foundation grant has been suggested as an alternative that would give resource-poor communities the option to spend more on education. With this new formula, the wealthiest municipalities will not qualify for a grant and they will have to cover all education expenditures with their own revenues. However, resource-poor municipalities will receive a larger grant with the foundation grant formula than they would with the capitation grant.

EXERCISE B1.1: Foundation Grant

44 The foundation grant is simply a lump-sum grant that depends on the amount of per-pupil tax base in the community. The standard formula for a foundation grant is as follows:

Gi=B-(R**Vi)

where Gi= the foundation grant amount per pupil to locality iB= the basic per pupil grant or foundation levelR*= the basic tax rate (a standard rate set in the formula); this rate may be a minimum rate, or the

average tax rateVi= per pupil tax base in locality i

NOTE: If the formula produces a negative number, the locality does not receive any grant

In the following exercise local non-earmarked revenue per pupil is used as a substitute for per pupil tax base. The basic tax rate (R*) should then be interpretted as the amount of local non-earmarked revenue the locality is expected to spend on education.

45 Open the file foundatn.xls and go to the first worksheet: Foundation Grant. In this example, we have collected information on local revenue (labeled as non-earmarked revenue), local education expenditures, the capitation grant, local government income, and total education expenditures. All of these figures are given on a per-pupil basis. In this example, local income is measured by local revenue plus the capitation grant from the central government. Second, since data on the local tax base per pupil are not available, local non-earmarked revenue per pupil is used as an alternative for Vi in the formula above. These data are found in columns A through F.

46 Follow the directions below to complete this simulation:

step 1 Assume that the foundation level (B in the above equation) is 65 (thousand) per student and that the basic tax rate (R*) is .28 (28% of local revenues are expected to be spent on education). Using this information develop a formula to calculate the foundation grant each locality will receive--in Column H.

NOTE: If the formula generates a negative value, the foundation grant amount will be zero. You can do this using an if statement or by simply replacing negative values with a zero.

step 2 In column I calculate the change in income (DY) which is the difference between the central government capitation grant and the foundation grant.

step 3 Next, determine how the locality will respond to the change in income. Recall the formula for determining the change in education expenditures from part A above (para. 19), and in column J calculate the change in education expenditures (DQ) given the change in income (DY). Assume previous research has determined the income elasticity of demand equals .96.

(Hint: using the formula for calculating income elasticity, you must solve for the change in quantity (of education spending). Then plug in the change in income, the original income and original expenditures, and the income elasticity.)

step 4 Calculate total education expenditures with the foundation grant in column K. (Hint: add the change in spending to original spending.)

47 Compare the change in education expenditures (Col. J) with the change in grant amount (Col. I). The outcome of this simulation shows that the additional expenditures on education are much lower than the additional grant amount received by the communities. This simulation reveals an important drawback with the use of grants. Communities can choose to use the revenue from the grant for education, but the money they used to spend on education they now have available for other purposes. They might choose to reduce their revenue effort or they might spend on it on other local functions.1

48 Note, however, that this problem is more relevant to situations where the grant recipient (state or locality) funds a fairly large portion of education expenditures. In developing countries most local governments spend so little on education that even if they reduce their education expenditures, they cannot make a large change in total education expenditures. If local governments in a developing country are given a grant that is earmarked for education, and this grant is well-monitored, the grant will go toward increasing education expenditures.

1    ? A word of caution: The elasticity used in the simulation represents the municipalities' response on average. Some localities might be more responsive and others less responsive. Be careful in your own simulations that you do not get unrealistic results.

Some things to look for: Although the change in spending is generally less than the change in income, make sure that total education spending is not less than the total grant received for education. If this were true then this would imply that the grant is not well-monitored and grant money meant for education is leaked to other expenditures. Second, the original municipal education expenditures should always be larger than the difference between the change in grant and the change in spending. If not, the simulation has predicted an impossible response because spending cannot be reduced by more than the amount the locality was spending on education. The foundation simulation does produce some unrealistic results. In your own time, you may want to go back and see if you can find these problems.

49 When the locality or state spend at least as much of its own funds on education as it receives from the education grant, the grant may have a minimal effect on total education spending. If this is the situation, it may be necessary to mandate increased expenditures on education by the amount of the education grant. However, such a mandate can be difficult and costly to implement.

B1.2 Simulating Alternatives (Optional Exercises)

Alternative 1: Minimum Expenditures Mandate

50 The purpose of this exercise is to show how such a mandate will affect education expenditures in the above situation. What would happen if all municipalities were required to spend the average education expenditures per student (53.6)?

step 1 This simulation requires only one step. Go to the worksheet labeled “Minimum Expenditures.” In Column M determine the impact of this requirement on education expenditures. This requires using an IF statement. If education expenditures are less than the average (53.6), then they must spend 53.6. If the locality already spends more than the average, they are not affected by the new requirement.

If you have extra time, you may want to try varying the foundation formula by completing the optional exercises below.

51 Once one simulation has been calculated, it is relatively simple to simulate the impact of different circumstances. The next two worksheets contain the same data, but instead the simulations will use a different formula.

Alternative 2Step 1 Block the formulas you used for columns H-K and copy them (just copy the first line, not all lines).

Step 2 Go to the worksheet entitled "increased base" and copy the formulas to the same columns.

Step 3 In the foundation formula change the foundation level (B) to 70 instead of 65. Copy this change for the entire column. The rest of the columns will adjust automatically.

Alternative 3Step 1 Again block your original formulas in Columns H-K and copy

Step 2 Go to the worksheet entitle "lower rate" and copy the formulas in the same columns

Step 3 In the foundation formula change the rate (R*) from .28 to .15. Copy this change for the entire column.

52 Alternatively, you may want to redo the simulation using a different income elasticity.

POINT: Simulations enable comparisons of outcomes using different parameters in a formula, or using different elasticities or assumptions concerning the local government response. Especially in developing nations it is wise to consider a range of elasticities since neither the income or price elasticity is known with much certainty.

B1.3 Evaluating Alternatives: Efficiency

53 Once simulations have been performed, the next step is to compare and evaluate the results according to equity and efficiency criteria. The purpose of this exercise is to compare outcomes based on efficiency criteria. Efficiency in this exercise refers to additional local spending for each peso (or other currency unit) received from the central government transfer to the local government.

EXERCISE B1.3

Step 1 Go to the worksheet entitled "Compare Expenditures" which contains the central government transfer for four different situations and the corresponding expenditures with each. Next compute the averages for all columns.

Step 2 For each alternative divide the average amount of expenditures on education by the average transfer to calculate expenditures per transfer.

Step 3 Finally, the table below can be found below the data in the worksheet (go to rows 72-83). Complete this table in order to compare the results of each alternative. Comment on the findings. Do some alternatives appear similar in terms of efficiency, or is one clearly more efficient than the others? On your own time you might want to go back and find the expenditures per transfer for the original capitation grant.

AverageCentral AverageGovernment Education ExpendituresTransfer Expenditures per Transfer

Transfer Description (Per Pupil) (Per Pupil) (Per Pupil) Alt. A Base=65; rate=.28

Alt. B Base=65; rate=.15

Alt. C Base=70; rate=.28

Alt. D Base=65; rate=.28 w/ min. exp. reqmt.

B1.4 Evaluating Alternatives: Equity

54 Equity is another concern with intergovernmental grants. The purpose of this exercise is to demonstrate how to analyze the equity impact of a transfer. In this exercise equity refers to size of the difference in total education expenditures in high and low resource localities. (Note: other exercises below will present some alternative measures of equity.) With decentralization, some differences in spending are expected, but how large are they? Second, equity may be evaluated by noting whether the grant amount communities receive offset (at least partially) their differences in resources.

55 Several methods may be used to evaluate or illustrate the equity impacts of a grant. One method is to compare spending and amount of grant received by high and low resource localities. Since the foundation grant is highest for low resource localities and low or non-existent for wealthy localities, the impact on equity is expected to be positive. The method of analysis used below is to divide the municipalities into quintiles based on local resources, and to show for each quintile the components of education expenditures funded by the central government and the component funded by local governments.

EXERCISE B1.4

Step 1 Go to the worksheet labeled "Quintiles." This worksheet contains the same data as in the "compare expenditures" file. The first step is to sort these data by non-earmarked revenue per pupil. Note: Be sure to block the entire data set before sorting, or it will only sort the specified column.

Step 2 Determine the number of municipalities in each quintile and calculate the foundation grant received per pupil for each quintile. HINT: For these data, the quintiles are as follows:

low Rows 2-152 16-283 29-424 43-55high 56-69

Step 3 Calculate average education expenditures per pupil with the foundation grant (Column D) for each quintile

Step 4 Go to rows 72-79 where a table has been set up for you. The first column should list: quintile one, quintile two, etc. The second column should contain the corresponding foundation transfer per pupil and the third column should contain the corresponding municipal education expenditure. Assume that the difference between total expenditures and the central government transfer are made up by municipal expenditures.

Optional If time permits, create a bar-graph which shows total education expenditure per pupil with components showing education expenditures funded by the central government transfer and the municipal education expenditures. Completed charts are available as handouts during the class. If you wish to draw the chart yourself, follow the instructions below:

Block the table in step 4 and then click on Chart Wizard. Then click where you want to locate the graph--choose where cells are empty below the table. If you need help--follow these instructions:

1) Select "column" and click on <next>2) Select format #3 and click on <next>

3) Select data series in columns, use first 1 column for category x, use first 1 row for legend text. click on <next>4) At this point DO NOT HIT <ENTER> until you have entered the chart title, and Axis titles. When you finish with one title, click on the next title to continue. When you have finished click on <finish> or hit enter and Chart Wizard will draw your graph.

Alternatively, you may wish to develop a table that provides the same information.

Step 6 For each quintile calculate the average education expenditures per pupil with the mandated expenditures (Column O).

Step 7 Prepare a second table and bar-graph identical to the table and graph in steps 4 and 5, but using the data from the mandated expenditures alternative.

How do the alternatives compare in terms of equity?

56 If you finish and have more time, you may want to prepare bar graphs for the original capitation transfer and education expenditures. You will have to go back to the foundation grant worksheet for this information. Alternatively, you might try the optional exercise below and follow instructions for making a Lorenz curve.

B1.5 Lorenz Curve (Optional exercise)

57 An alternative method to illustrate the equity impacts of a grant is to develop a Lorenz curve and/or compute a Gini coefficient. Open the file entitled lorenz.xls. This file contains the municipal education expenditures for all 325 municipalities in Chile in 1990. These data are on a per-pupil basis. The distribution of education expenditures is thought to be quite inequitable since a few wealthy municipalities contribute significantly to education expenditures while resource poor municipalities spend little or nothing in addition to the central government transfer. The purpose of creating the lorenz curve is to illustrate this inequality in municipal expenditures.

Step 1 The first step is to sort the data from lowest to highest municipal expenditures. However, there may also be missing data for some municipalities.

Step 2 Next the data must be divided into deciles. Since there are 325 municipalities in this data set, there are approximately 32 municipalities in each decile.

Step 3 Next compute the sum of municipal expenditures per pupil for each decile and put this result in the table provided next to the data.

Step 4 In the column next to the sums, calculate the cumulative expenditures per pupil.

Step 5 Divide the cumulative sum for each decile by the total sum of municipal expenditures per pupil (for all municipalities) and multiply by 100 to get the cumulative percentage of spending per pupil going to each decile.

Step 6 Next we want to make a graph of the Lorenz curve. To do this you need to make a second table. Start the table in Column I and enter 10%, 20%...up to 100% in this column. Next, copy the contents (not formula) of the cumulative percentage of spending per pupil for each decile. For comparison to a perfectly equal distribution enter another column with the same contents as Column H (just copy it).

Step 5 From the table you created in step 6 you can now make a line graph showing the Lorenz curve. Column H is for the X axis and Columns I and J are for the Y axis. The graph should look like the one that will be given out during class.

B2 LUMP-SUM POVERTY-BASED GRANT

58 An alternative measure of equity is to include measures of actual needs rather than (or in addition to) measures of local tax base. The goal is to design a grant that provides more aid to areas with greater needs. Winkler (1993) presents several alternative measures of need in education including the percent of the population living in poverty (measured by a household survey) and the average performance of schools on a national achievement test. (Note that this last method may create perverse incentives since localities receive higher funds for lower test scores.) If equity is an explicit concern, grant formulas may also include measures of need in place of or in addition to measures of the communities' resource base per pupil.

Situational Context

59 In the simulation of the foundation grant, the entire capitation grant was replaced with the foundation grant. The situation for the following simulation is different from the situation assumed above. In this situation the central government in planning to increase the capitation grant by 15 (thousand pesos) per pupil. However, it is suggested that rather than distribute this grant on an equal basis (per capita) that it be weighted by the poverty level. The point of this simulation is to compare the equity impact of simply increasing the capitation grant in all localities versus the impact of weighting the increase by the inverse of the locality's poverty rate. Before simulating the poverty formula, we will simulate a simple increase in the capitation grant.

B2.1 Increase Capitation Grant (Equal Increase per Pupil for all Localities)

60 We will simulate the impact of simply raising the capitation grant by 15 (thousand pesos) for all localities. Note: In this simulation, however, the municipal response will be simulated using an alternative method to the one used with the foundation grant. In order to simulate the change in local education expenditures resulting from the increased grant, recall the following relationship from part A (para. 25):

E=DLE * CGTo

DCGT LEo

61 Winkler (1993: Annex A.3) estimated municipal spending on education using the log transformation model. The dependent variable was municipal spending per public school student. The coefficient on central government expenditures (transfers) per public student gives the municipal response to increasing the central government grant. In three different models this coefficient equaled -.27, -.28 and -.32. A 1% increase in the central government transfer led to a .3% decrease in municipal spending on average. In other words, E in the above equation is equal to -.3. This information can be used to determine the municipal response in local education expenditures to the increase in the central government transfer.

Step 1 Go to the file entitled poverty.xls. In the first simulation the current grant will be increased by 15 (thousand since figures are in thousands of pesos). In Column H add 15 to central government education transfer

Step 2 In Column I calculate the decrease in municipal expenditures, the decrease can be calculated as follows: E=-.3 and in all cases the change in the central government transfer (DCGT) is 15. Solving the equation above for the change in municipal expenditures (DLE) we get:

DLE=-.3*LEo*(15/CGTo)

Step 3 In Column J calculate municipal education expenditures after the transfer increase Step 4 In Column K calculate the total education expenditures with the flat increase in the grant.

62 This completes the simulation of the flat increase in the current central government transfer. This simulation of an addition to an existing grant is more realistic and more accurate than the previous foundation grant simulation for several reasons. First, elasticities are measured on the margin--for small changes--and the change in the transfer amount (15) is a small amount. It is more difficult to predict how municipalities will respond to large changes from the current situation. Second, the municipal response elasticity was consistently estimated while the income elasticity was not based on empirical information.

B2.2 Increase in Grant Weighted by Poverty Level

63 In the second simulation the distribution of the original grant remains the same, but the additional 15 per pupil transfer will be distributed using a poverty-based formula. This "poverty formula" is based on a formula illustrated in Winkler (1993):

Gi = 15.0[POVi/POV]

where Gi = grant per pupil to the ith municipalityPOVi= poverty rate in the ith municipalityPOV= the average poverty rate

64 This simulation will be done on the same template using Columns M through Q.You can try doing this simulation on your own or follow the instructions below.

Step 1 Column M should contain the ratio of the municipalities poverty rate to the average poverty rate. You will have to calculate the average poverty rate. At the bottom of column C a cell has been designated for this calculation.

Step 2 Column N is the new central government transfer including the poverty transfer

Step 3 Column O is the change in municipal expenditures using the same formula as above (See step 2 in B2.1 on previous page).

Step 4 Column P is the municipal response after the new central government transfer

Step 5 Column Q is the new education expenditures (Central government plus municipal expenditures)

B2.3 Comparing the Alternatives by Poverty Quintiles

65 The purpose of this exercise is to compare the equity impacts of the lump-sum transfer of 15 (thousand pesos) and the poverty based transfer simulations. In the file poverty.xls the worksheet labeled "quintiles" contains the outcomes of the above simulations. Total central government education transfers with the lump-sum grant equal to 15 are given in column H and the corresponding municipal expenditures are found in Column I. The total central government transfers with the poverty grant are given in Column L and the corresponding municipal education expenditures are given in Column M.

Step 1 To compare the two simulation outcomes on distributional impact, first sort the data from lowest to highest poverty rate. (Remember to block entire data set before sorting.)

Step 2 Determine the number of municipalities in each quintile --13 or 14 each.

Step 3 Calculate the average central government transfer per pupil and municipal expenditures per pupil for each quintile.

Step 4 Complete the tables in rows 76-83 in columns A-I. The goal is to create a table with one column containing the list of quintiles. For example:

Highest povertysecond quintilethird quintilefourth quintileLowest poverty

and next to this column place the central government transfers (with the flat lump-sum grant) and corresponding municipal expenditures per pupil for each quintile.

Step 5 Create an identical table for the poverty based grant as well as the unweighted lump-sum grant.

Optional Next use the tables created in steps 4 and 5 to create bar graphs showing total spending per pupil and the portions covered by the transfers and municipal expenditures with each transfer (poverty and lump-sum). These graphs can be used to illustrate the equity impact of the poverty formula. Does the poverty grant make much difference? Note that this comparison includes the original capitation transfer plus the increase in the transfer which is relatively small.

In the interest of saving time these graphs have been done for you and will be passed out during class.

PART CSIMULATION OF MATCHING GRANTS

66 As explained in part A, the matching grants we will simulate in this section differ from lump-sum grants in that they require local government expenditures on education in order to receive any funds from the central government. In effect, the matching grant reimburses the local governments for a fraction of their education expenditures and thus, lowers the price of education as perceived by the local governments (note: the total cost of education to the central government does not change).

67 Since matching grants reduce the price of education relative to other public goods, they increase local consumption of education more than an equivalent lump-sum grant. In economic terms, the matching grant lowers the "price" of education and therefore, it has both an income effect (when the price of education decreases, the locality has more real income to spend) and a substitution effect (the locality will substitute expenditures on education for other local expenditures since education is relatively cheaper with the matching grant). Both the substitution effect and the income effect work to increase education expenditures. Lump-sum grants, on the other hand, only have an income effect.

68 For the following simulations, the scenario given in part B2 above remains the same: The central government is planning to increase the transfer for education by 15 (thousand pesos) per pupil. The simulations in this section demonstrate the impact of using a matching formula as opposed to distributing the grant on a lump-sum basis. The purpose of the first simulation is to illustrate that the impact of the lump-sum increase by 15 (thousand pesos) per student on total education expenditures is smaller than the impact of a simple matching grant that costs the same amount (15 thousand pesos) for the central government. Hence, if the goal is to promote education spending, the matching grant is a better design.

C1.1 SIMULATION 1: SIMPLE MATCHING GRANT

69 For the simulation exercise in this section, open the file Matching.xls and go to the worksheet labeled "Simple Matching". In Cell N2 is the amount "1.7" which is the matching rate for this simulation. By using this rate, the central government spends approximately 15 thousand pesos.In Cell O2 is the amount "-0.6" which is the estimated price elasticity for this simulation. To complete this simulation, follow the steps below.

Step 1 In Cell P2 calculate the central government share. Recall the formula from part A above: M=R/(1+R). The central government's share represents the percentage decrease in price for the municipality. Since this represents a price decrease to the municipal government, make this amount negative by putting a negative in front of the formula.

Step 2 In Column Q determine the municipalities' response to the matching grant given the price elasticity in cell O2. Recall the formula from part A above: DQ=EP*%DP*Q.

Step 3 In Column R calculate total local education expenditures which is the municipal response (DQ) plus original local education expenditures (Q).

Step 4 In Column S calculate the matching transfer received from the central government (given total local education expenditures in Column R)

Step 5 In Column T determine new education expenditures per pupil (matching grant plus local education expenditures)

Step 6 In Column U calculate total education expenditures per pupil. This should equal the original central government transfer plus the new education expenditures calculated in step 5.

Step 7 In Column V calculate the total central government transfer per student (Original plus matching)

Step 8 Choose two cells and determine the Average for columns V and U. This shows the total expenditures on education per pupil, and the total cost to the central government per pupil.

Step 9 Make a small table in the worksheet or complete the table below. Calculate the average education expenditures per pupil and average transfer from the central government per pupil with the lump-sum grant equal to 15 (thousand pesos per student). The results of the lump-sum transfer have been placed in this file--see Columns In the same table put the average education expenditures per pupil and average transfer from the central government for the simple matching grant (from step 8 above) and the lump-sum transfer of 15. The average transfer should be about the same. As should always be true for a matching grant costing the same amount as a lump-sum grant, the education expenditures with a matching grant will be larger.

Lump-Sum Grant Simple Matching Grant Variable Matching Grant

Average EducationExpenditures perPupil

Average Central GovernmentTransfer perPupil

Expenditures perTransfer

C.2 SIMULATION 2: VARIABLE MATCHING GRANT

70 One problem with the simple matching grant is that it rewards communities that spend more on education, but the communities that spend more generally have more resources. As a result the distribution of the simple matching grant worsens rather than improves equity. The purpose of this exercise is to simulate a variable matching grant formula that addresses this inequity. In this simulation the matching rate will vary according to local circumstances by using a formula suggested by Winkler (1988:Annex D.1). With this formula, the matching grant varies inversely with relative fiscal capacity and directly with municipal education finance of the municipality. The distribution formula is as follows:

Gi = MEi [1-.25(NERi/NER)]

where Gi = matching grant per pupil to the ith municipalityMEi= education expenditures per pupil in the ith municipalityNERi= non-earmarked local revenues per pupil in the ith municipalityNER= average non-earmarked local revenues per pupil

NOTE: the .25 in the above equation is an abitrary weight placed on the relative wealth of the community. This weight can be increased to increase the equalizing effect of the grant.

71 Since municipal expenditures on education are relatively low, this matching grant alone would not lead to sufficient revenue to provide a basic level of education. Instead, this simulation assumes the same situation as above: this matching grant is in addition to the lump-sum capitation grant already in place. To perform this simulation tab over to the worksheet labeled "Variable Matching Grant" and follow the directions below.

Step 1 Calculate the average non-earmarked local revenue per student. (A cell is designated for this calculation at the bottom of the non-earmarked revenue column.)

Step 2 In Column M calculate the ratio of non-earmarked revenues in each municipality to the average non-earmarked revenue per student

Step 3 In Column N calculate the matching rate for each municipality. Hint: the matching rate for each municipality is determined by the formula in brackets above

[1-.25(NERi/NER)] This is the matching rate because it is the portion of municipal spending the central government will provide. NOTE: if this produces a negative number, replace it with a zero.

Step 4 In Column O determine the share of education spending paid by central government matching grant by recalling the formula used in part A.1 (para. 14): M=R/(1+R)This is the percent decrease in price for the municipality so put a negative in front of your formula to produce a negative number.

Step 5 In Column P determine the change in municipal education expenditures assuming the price elasticity equals -.6

Step 6 In Column Q determine municipal education expenditures after the matching grant is implemented. (Hint: original spending plus the change in spending)

Step 7 In Column R calculate the central government matching transfer (Hint: matching rate multiplied by new municipal education expenditures)

Step 8 In Column S calculate total education expenditures after the matching grant is implemented. (Hint: original central government transfer plus new municipal expenditures plus new matching grant)

Step 9 In Column T calculate the total central government transfer (Hint: add matching grant to original lump-sum per-capita grant)

Step 10 Find total and average education expenditures per pupil and total and average central government transfer by calculating the sum and the average for columns S and T. Again, cells are designated for these calculations at the bottom of these columns.

Step 11 Compare the results in step 10 with the total education expenditures per pupil and total central government transfer for the simple matching grant and for the lump-sum grant of 15,000 per pupil.

72 The variable matching grant should have a more positive impact on equity compared to the simple matching grant. Although there probably won't be time during the training session, you should have learned the tools to compare the impact of each matching grant (simple and variable). First, compute how much of the additional grant goes to each quintile (use non-earmarked revenue to determine quintiles). Then follow the steps done in earlier simulations to create a bar graph to illustrate total education spending, central government transfers and municipal education expenditures by quintile.

73 This concludes the simulation exercises in this training module. However, the attached appendix describes a grant formula (called a Guaranteed Tax Base) that combines both a lump sum and matching grant in one formula. Although the formula appears to be simple, evaluating its impact is not. This point is illustrated by performing a very simplified simulation of the formula.

74 Of course the variations of intergovernmental transfers formula are limitless. This module provides the foundations for performing your own analysis of education transfers by simulating and evaluating the impact of any education grant formula.

APPENDIX TO MATCHING GRANT SIMULATION

Guaranteed Tax Base2

75 The guaranteed tax base grant formula simulated in this exercise is a type of power equalizing grant. In a pure GTB formula B=0 and Ri is the local tax rate without any maximum. In that formula a locality only receives a grant if it's per pupil tax base is less than the guaranteed tax base. An alternative and simpler version of power equalizing is used by Winkler (1993) in his simulations. In another version the guaranteed tax base (V*) applies only to a maximum stat-specified tax rate so that if localities set a higher rate, it will only generate more local tax revenue and no additional grant funds. The GTB formula is as follows:

Gi=B+(V**Vi)*Ri

where Gi= the grant amount per pupil to locality iB= the basic per pupil grant or foundation level (in some cases, B is simply set to zero)V*= the guaranteed tax base per pupilVi= the per pupil tax base in locality iRi= the tax rate in locality i (in some cases a minimum rate allowed is used)

Again, if the formula produces a negative number, the locality does not receive any grant

76 This formula can be a matching grant or a lump-sum grant depending on the locality's situation. If the locality's tax base is less than the guaranteed base (Vi<V*), the locality receives both a lump-sum foundation grant and a matching grant. In this case, the local share (or tax price) is M=V i/V*. For this simulation, we will use a very simplistic example which you can later apply to authentic data.

77 Consider the following four localities. Determine the grant amount for each if B=100 and V*=50,000:

Locality Tax Base Rate Educ. Expd GTB Grantper pupil per pupil per pupil

-----------------------------------------------------------------------------------------------------------A 36,360 .055 2000 850.20B 50,000 .05 2500 100C 51,000 .05 2550 50D 60,000 .06 3600 0

78 Take a moment to consider how you would evaluate the impact of this grant in these four different communities. Which communities will receive a lump-sum grant and which will receive a matching grant or both? (Remember, a matching grant explicitly depends on the fiscal decisions of the locality.) This is an important question since income elasticity is needed to simulate a lump-sum grant while price elasticity is needed to simulate a matching grant.

79 Suppose the price elasticity of demand for education spending is estimated to be -.5 and that the income elasticity of demand for education is estimated to be 1.0.For simplicity assume that the average family income in each district is half as large as the per-pupil tax base. For example, average income in locality B would be 25,000Finally, suppose that the GTB formula is a follows:2    ? The following simulation is taken from Fischer, 1988: 380-4

GTB grant per pupil=$100+(50,000-V*)R (if negative, assume no grant is given)

80 Estimate new levels of spending and tax rates (for simplicity, assume there are no other local expenditures so this tax base is only used to provide education.) Evaluate those changes: Has education spending increased on average? has spending become more equal? To what degree? What happened to local tax effort? Has the grantor received a good return on the use of its funds? Would you recommend the adoption of the grant program?

ANSWERS:

Community D is easy--it receives no grant funds so there is no impact to simulate.Education expenditures and taxes will remain the same.

Community B receives a lump-sum grant of $100 per pupil. This district receives the foundation amount, but no matching aid. $100 is a .4% increase in income and since income elasticity of demand is exactly 1.0, the percent increase in spending should equal the percent increase in income--.4% Current spending is $2500 so a .4% increase is $10. The new level of spending should be $2510. To raise this amount of revenue requires a tax rate of .0482 (4.82%).

Community A receives both a lump-sum foundation grant and a matching grant. The impact is simulated as follows:

Community A will receive a lump-sum foundation grant =$100and under initial conditions community A would receive $750 in a matching grant ($13,640*.055). However, community A will alter its tax effort in response to the grant, and the grant amount will change as tax effort changes.

81 The tax price to community A for $1 of education expenditures with the matching grant is 36,360/50,000=.7272. In other words, community A must collect $.727 for each dollar of education expenditures. The remaining $.273 is supplied by the matching grant. From the community's point of view, price is lowered by .273 or 27.3%. Given the price elasticity of .5, per pupil spending should increase by 13.65%

If that were the only effect, per pupil spending in locality A would increase by $273 to $2,273.

82 However, community A also receives the lump-sum grant of $100 which is a .55% increase in income ($100/18,180). Again, since income elasticity equals one, there should be a .55% increase in per-pupil education expenditures. .0055*2000=$11

83 Thus total spending on education after the GTB grant will be $2284 (2273+11).The last step is to calculate the new tax rate needed to raise $2284 including the matching grant:

2284= (36,360*R) + 100 + (13,640*R)2184= 50,000*RR=.04368 or 4.37%

84 Community C also receives a type of matching grant, but the matching rate is negative. The impact of this grant is simulated as follows:

If community C increases its tax rate, the foundation grant will be reduced. On the other hand, if it lowers its tax rate, the foundation grant will increase.

The new "price" or share for locality C is VC/V* or 51,000/50,000=1.02. To spend an addition dollar per pupil, the district must raise $1.02 per pupil.

The increase in price is 2% and the since the price elasticity of demand is .5, education expenditures per pupil will decrease by 1% or by $25.50. Expenditures per pupil after the grant will only be $2524.50. The tax rate will fall as well since less revenue is needed. The new tax rate will be 4.849%

Analysis

85 Per-pupil spending increases only slightly by about 2.5% on average. Although spending increased in two localities, it fell in a third and remained constant in the fourth.

Only about 30% of the grant funds go to increased expenditures on education. The remaining 70% go to reducing tax effort.

Tax rates fell in all localities--a 7% decrease on average.

The variance in per-pupil spending is reduced only slightly. The ratio of the highest to lowest spending level is reduced to 1.58 from 1.8. But the dollar difference between the lowest and highest is greater than $1300.

Tax rates fell more in localities with lower per-pupil tax bases. The ratio of tax rate to per-pupil expenditures is more equal with the GTB grant. Before the grant the ratios were:

A=.025B=.02C=.0196D=.0167

86 Community A needed a tax rate of 2.5% to raise $1000 while communities B and C only needed a tax rate of about 2% and community D only needed a rate of 1.67 to raise the same amount of money. After the GTB grant, the required rates are only 1.91% for community A and 1.92% for community B.

REFERENCES

Fisher, Ronald, State and Local Public Finance, Glenview, IL: Scott, Foresman and Company, 1988.

Winkler, Donald. Decentralization in Education: An Economic Perspective. Paper prepared for Education and Employment Division, Population and Human Resources Department, The World Bank, Washington, DC. November, 1988.

Winkler, Donald. The Design and Administration of Intergovernmental Transfers. Latin American and the Caribbean Technical Department, Regional Studies Program Report No. 19, The World Bank, Washington, DC. July, 1993.

Wynne, Susan, Larry Schroeder, James Wunsch, and Taryn Rounds. Foundations for Decentralization Finance and Management Research: A Prologue to the Study of Institutions and Public Finance. (Sponsored by U.S.A.I.D.) Associates in Rural Development, Inc., Burlington, VT. June, 1990.