lecture notes7

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ECO 4554 Economics of State and Local Government

Lecture Notes

INTERGOVERNMENTAL GRANTS

Key Points 1. Dollars are fungible. Even if the use of grant funds is restricted to a particular program, the grant

funds can be used to replace local funds that would have been spent on the program. The local funds can then be spent on other programs or returned to the taxpayers through a reduction in local taxes.

2. Because of fungibility, (a) a community may spend less of its own local funds on a public service

when it receives a grant than it would spend without the grant, and (b) the effect of categorical grants on public service expenditure is often no different than the effect of general grants.

3. A matching grant has a more stimulative effect on expenditure than a lump-sum grant because a

matching grant has both an income effect and a substitution effect while a lump-sum grant has only an income effect.

4. Economic theory suggests that a lump-sum grant should have the same effect on expenditure on

public services as an increase in the community’s aggregate income. The empirical evidence indicates, however, that a lump-sum grant increases public service expenditure five times more than an equal increase in community income.

Synopsis

Intergovernmental grants are a major source of revenue for state and local governments. State governments receive grants from the national government and local governments receive grants from both national and state governments. A grant may be either general or categorical, it may be either lump sum or matching, and it may be either open-ended or closed-ended. We begin by defining each of these pairs of terms. Next, we show the effect of a lump-sum grant on a community’s total expenditure on a public service. Using this lump-sum grant as a benchmark, we then demonstrate four propositions about grants: (1) a categorical grant often has the same effect as a general grant so that the restrictions placed on use of the categorical grant are not effective; (2) a matching grant increases a community’s expenditure on a public service more than a lump-sum grant of the same amount; (3) a matching grant may reduce the amount of local funds that the community spends on the public service even though total spending increases; (4) an open-ended grant increases spending on a public service by at least as much as, and sometimes more than, a closed-ended grant. The most efficient structure for a grant (whether it is matching or lump sum, for example, or whether it is general or categorical) depends on the objective of the grant. We look at several examples of designing a grant to achieve specific objectives. We then note that, in fact, few grants from the national government to state and local governments in the U.S. seem to be efficiently structured. Finally, we look at an anomaly in the economics of intergovernmental grants, the flypaper effect. The flypaper effect reflects an inconsistency between economic theory and empirical evidence. We first describe the inconsistency and then offer four explanations. Two of the explanations claim that there

ECO 4554: Economics of State and Local Government Intergovernmental Grants

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is really no flypaper effect. The theory is correct but the empirical evidence is misinterpreted. The other two explanations claim that the flypaper effect is real. The empirical evidence is correct but the theory incorrectly omits some important considerations.

Lecture Notes

I. Types of grants (see Fisher, Figure 9-4)

A. General vs. categorical

1. General grant: A general grant is unrestricted as to use; it may be used for any public expenditure program. (Examples: federal revenue sharing grants, sales tax revenues collected by the state and returned as grants to the community in which they were collected.)

2. Categorical grant: A categorical grant is designated for a specific public

expenditure program. (Examples: federal grants to the states for Medicaid, unemployment compensation, education, and mass transit.)

B. Lump sum vs. matching

1. Lump-sum grant: A lump-sum grant does not require the government receiving the grant to spend any of its own funds on the good or service for which the grant is provided.

2. Matching grant: A matching grant requires the receiving government to

spend some of its own funds on the good or service for which the grant is provided. The grant provides an additional amount of funding for the good or service to match the amount provided by the receiving government.

a. The match is not necessarily dollar-for-dollar. If R is the matching

rate and M is the share of funding provided by the grant, then M=R/(1+R).

b. Examples

(1) Suppose R=1.0. This means the grant matches local funding dollar-for-dollar so that the grant provides $1.00 for each $1.00 of local funds spent. If R=1.0, then M=1/2 and the grant provides exactly one-half of the total expenditure on the good or service.

(2) If R=0.5, the grant provides $0.50 for each $1.00 of local

funds spent. When R=0.5, M=1/3 so the grant provides one-third of the total expenditure on the good or service.

C. Closed-ended vs. open-ended

1. Closed-ended: The maximum amount of grant funding that a community can receive from a closed-ended grant is limited.


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2. Open-ended: There is no maximum amount of grant funding that a community can receive from an open-ended grant.

II. Effects of grants on expenditure by the recipient government

A. The effect of a grant on a community’s expenditure on public services depends on the type of grant. We use a lump-sum grant as a benchmark with which to compare other types of grants.

1. A lump-sum grant is equivalent to an increase in the community’s income. It

increases the total resources available to the community. It is equivalent to an increase in the median voter’s real income, but does not change the median voter’s tax-price for the public service. The median voter’s demand increases because of this income effect. As a result of the increase in demand, the median voter’s preferred expenditure on the public service increases from E0 to E1. See PowerPoint Slides Figure 7-1.

E0 E1

Median Voter’s Demandwith Lump-sum Grant

Public Service

Tax-priceMedian Voter’s Demandwithout Lump-sum Grant

MC

2. The increase in expenditure, ΔE=E1-E0, expressed as a percentage of the

original expenditure level, E0, depends on the median voter’s income elasticity of demand:

(ΔE/E0) = (G/I0) * ηI

using the point elasticity formula where G is the grant (equal to the change in income), I is the initial income, and ηI is the income elasticity of demand for the public service.

B. A categorical grant often has the same effect as a general grant.

1. Proposition: Restricting the use of a grant to a specific public service usually has no effect on a community’s total expenditure on the public service. The increase in total expenditure on the public service is the same whether the grant is categorical or general. See PowerPoint Slides Figure 7-2.


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2. Dollars are fungible. For example, a community can spend part of a general

grant on urban mass transit and part on fire protection. But if the community receives a categorical grant designated only for urban mass transit, it can use the entire grant for urban mass transit and reallocate some its own local funds from urban mass transit to fire protection. The increase in urban mass transit spending and the increase in fire protection expenditure are the same with either the general grant or the categorical grant.

3. Suppose a community receives a general lump-sum grant.

a. The general grant increases the median voter’s consumption possibilities from those shown by budget line ab to those shown by budget line cd. The median voter chooses to spend part of the grant on urban mass transit so total expenditure on urban transit increases from E1 to E2.

E1 E2

Budget line

with grant

Urban transit

All other services

Budget line

without grant

b d

a

c

b. The increase in total expenditure on urban transit is less than the

amount of the grant. The rest of the grant is either spent on other public services or used to reduce taxes so that the median voter can spend more on privately-provided goods and services.

4. Suppose the general grant is replaced by a categorical grant of the same

amount designated for urban transit only. The amount of the categorical grant is sufficient to finance the expenditure level E0 of urban mass transit.

a. The categorical grant increases the median voter’s consumption

possibilities from those shown by ab to those shown by the kinked budget line afd. With the categorical grant, the median voter’s preferred expenditure on urban mass transit is still E2, exactly the same as with the general grant.


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E1 E2

Budget line

with grant

Urban transit

All other services

Budget line

without grant

b d

f a

c

E0

b. Both the general grant and the categorical grant have the same effect

on urban mass transit spending. Restricting use of the grant to urban mass transit has no effect on total expenditure because the grant simply replaces other funds that the community would have spent on urban mass transit, allowing those funds to be reallocated to other publicly- or privately-provided services.

5. There is one situation in which a categorical grant increases a community’s expenditure on the public service more than a general grant. See PowerPoint Slides Figure 7-3.

a. Suppose the median voter’s preferred level of urban mass transit

expenditure even with the grant is less than E0. In this case, the community spends only a portion of a general grant on urban mass transit and uses the rest of the grant for other purposes.

b. Now suppose the general grant is replaced by a categorical grant that

can only be spent on urban mass transit. The grant is larger than the amount the median voter wishes to spend on urban mass transit, but because the grant cannot be used for other purposes, the community spends the entire grant on urban mass transit.

c. In this case, total expenditure on urban mass transit with a general

grant is less than E0 because some of the grant funds are used for other purposes. Total expenditure on urban mass transit with a categorical grant is E0, exactly equal to the grant. Only in this situation does the categorical grant increase urban mass transit expenditure more than a general grant of the same amount.

d. Note that in both cases the grant completely replaces local funds that

would be spent on urban mass transit without the grant. With the grant, the community spends none of its local funds on urban mass transit.


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C. A matching grant is more stimulative than a lump-sum grant of the same amount. See

PowerPoint Slides Figure 7-4.

1. Proposition: A community’s expenditure on a public service increases more with a matching grant than with a lump-sum grant of the same amount. Matching grants are more stimulative per dollar of grant than lump-sum grants.

2. A matching grant has two effects on local expenditures. Like a lump-sum

grant, it increases total resources available to the community (the income effect). But a matching grant also reduces the tax-price of the public service to the community (the substitution effect), providing an incentive for the community to substitute the public service, which is now cheaper, for other goods and services.

3. Let P be the price to local taxpayers for each $1.00 of expenditure on the

public service. Then,

P=1-M =1-[R/(1+R)] =1/(1+R).

a. If there is no grant, R=0, M=1, and P=$1.00. The local taxpayers pay the entire cost of the good or service. The price to them of each dollar of expenditure on the public service is exactly $1.00.

b. If R=1, then M=1/2, and P=$0.50. The price to the local taxpayers

for an additional $1.00 expenditure on the public service is $0.50. The grant reduces the tax-price to the community’s taxpayers by 50 percent.

c. If R=0.5, M=1/3, and P=$0.67. The price to the local taxpayers for

an additional $1.00 expenditure on the public service is $0.67. The grant reduces the tax-price to the community’s taxpayers by 33.3 percent.

4. Suppose a community receives a matching grant of the same amount as the

lump-sum grant in II.A above.

a. The income effect of the matching grant is identical to the income effect of the lump-sum grant. But the matching grant also lowers the median voter’s marginal tax-price, making the public service cheaper and more attractive than alternative goods and services, public and private. This substitution effect reinforces the income effect so that public expenditure increases not just from E0 to E1, but from E0 to E2,


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E0E1

Public Service

Tax-priceMedian Voter’sDemand

MC=Tax-price

without grant

Tax-price

with grant

E2

P0

P1

b. The increase in expenditure, ΔE=E2-E0, expressed as a percentage of

the original expenditure level, E0, depends on the median voter’s price elasticity of demand:

(ΔE/E0) = (G/P0) * ηP

using the point elasticity formula where G is the grant (equal to the price reduction), P is the initial marginal tax-price of the public service, and ηP is the price elasticity of demand. (Note that the price elasticity of demand incorporates both the income effect and the substitution effect.)

D. A matching grant may reduce spending on the public service by the recipient government from its own local funds.

1. Proposition: Even though total expenditure on the public service increases

when the community receives a grant, the community may spend less of its own local funds on the public service.

2. Suppose the median voter’s demand for the public service is inelastic with

respect to the tax-price. (According to Fisher, Table 4-1, the demand for most public services is inelastic.) The matching grant reduces the price, but the percentage increase in the median voter’s desired expenditure on the public service is smaller than the percentage reduction in price. Therefore, the community actually spends less of its own local funds on the public service with the grant than it would spend without the grant.

3. Example

a. Before receiving a grant for urban mass transit, the community spends $1.00 of its own funds for each dollar of total expenditure on urban mass transit.

b. Suppose the grant reduces the tax-price to the median voter to $0.50.

Now, for each dollar of expenditure on urban mass transit, the


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community spends only $0.50 and the grant provides the other $0.50. The community has $0.50 to use for an increase in urban mass transit or for an increase in spending on other public services or to reduce local taxes, allowing taxpayers to spend more on privately-provided goods and services.

c. The grant reduces the tax-price by 50%. Suppose the median voter’s

elasticity of demand for urban mass transit is 0.40. Then, her/his desired mass transit expenditure increases by $0.20 (=0.40*$0.50), from $1.00 to $1.20. The grant provides $0.60 and the community provides the other $0.60. Total spending on urban mass transit increases from $1.00 to $1.20, but spending by the community from its own funds decreases from $1.00 to $0.60.

4. The community uses part of the grant to replace some of its own spending on

the public service, reallocating its funds to other purposes. To the extent that a matching grant simply replaces local spending, it is equivalent to a general lump-sum grant of the same amount.

E. An open-ended matching grant is at least as stimulative as, and sometimes more stimulative than, a closed-ended matching grant.

1. Proposition: A closed-ended matching grant is equivalent to an open-ended

matching grant below the maximum. Beyond the maximum, a closed-ended matching grant is equivalent to a lump-sum grant and is therefore less stimulative than an open-ended matching grant.

2. As long as the closed-ended grant is less than the maximum, it has the same

effect on expenditure as an open-ended grant.

a. Both grants increase the median voter’s income (income effect) and reduce the median voter’s marginal tax-price (substitution effect).

b. Example: Suppose the matching rate of the grant is 0.50. If the

community increases total expenditure on the public service by $1.00, the grant pays $0.33 and the community only has to pay $0.67 from its own funds. The price to the community of $1.00 worth of the public service is now $0.67.

3. Beyond the maximum, additional local spending is not matched by additional

grant dollars.

a. The grant has only an income effect and no substitution effect. It becomes equivalent to a lump-sum grant.

b. Example: Suppose the matching rate of the grant is 0.50 up to a total

grant amount of $100.

(1) The maximum is reached when total spending is $300 where the grant provides $100 and local funds provide the other


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$200. As above, the price to the community below the maximum is $0.67 per dollar of expenditure.

(2) Additional dollars of spending beyond $300 are not matched

by the grant. The community pays $1 from its own local funds for each additional dollar of expenditure beyond $300.

(2) Thus, when total expenditure reaches $300, the grant reaches

its maximum of $100. The grant increases the total resources available to the community by $100, but it no longer reduces the community’s tax-price for the public service. It becomes equivalent to a lump-sum grant of $100.

lecture notes7

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