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will be less able to finance their own educational and other services, all other things remaining equal. Somewhat differently this might be considered in terms of the extent to which the benefit theory of taxation should be abandoned in the matter of educating the Nation's children.

CLASSES OF FORMULAS

Broadly there are two large classes of formulas. Those which "match" some part of State and local funds expended for a specific function, and those which are independent of the amount spent from State and local sources.

GRANT IN AID FORMULAS

Formulas which provide for "matching" of some share or percentage of State and local expenditures are used quite generally in other aids to education, in public assistance, and in highway aids. While not proposed in recent Senate bills for aid to elementary and secondary schools, matching a variable part of State-local expenditures for education has been proposed by some writers on the subject. Recently, for example, Mr. Erick L. Lindman, of the Washington State Department of Public Instruction has proposed a method of "Federal Aid for Education on an Equalized Matching Basis." He has also prepared and mimeographed other statements of his proposal, copies of which have been made available to the committee staff.

Basically, his proposal is to measure need for aid by the number of children of school age and to measure ability to finance education by income payments to individuals within each State, as reported by the Department of Commerce. He would then determine the "grant ratio" which Federal aid shall bear to State and local expenditures for education in each State; this ratio varies directly with need and inversely with ability to support education. The following are two different ways of expressing his formula, chosen so as to give a small amount of aid to every State. The formula can be adjusted, however, to give aid to a smaller number of States.

Each State's Federal grant would be based upon the average current school expenditures (excluding expenditures from Federal funds) in that State for, say, the two most recent years for which satisfactory financial data are available and upon a supplementary grant ratio for that State.

The grants might be computed as follows:

1. Each fiscal year the Commissioner of Education would determine the income per child for each State and for the continental United States from State and national total income payments figures certified by the Secretary of Commerce, which figures have been averaged for the three most recent years for which satisfactory data are available and from State and national figures certified by the Director of the Census as to the number of persons aged 5 to 17 years, inclusive, for the most recent date for which satisfactory data are available.

2. The Commissioner of Education would determine a preliminary grant ratio for each State by dividing the difference between twice the national average income per child and the income per child in that State by the income per child in that State.

3. The Commissioner would multiply the preliminary grant ratio for each State as computed above by the average current school expenditures in that State to obtain preliminary grant figures. If the sum of the preliminary grant figures for the State exceeds the total appropriation for aid to the States for the fiscal year, they would need to be reduced pro rata so that the grants actually made would not exceed the funds available. The plan might also provide that as a minimum no State is to have a grant ratio less than, say, 1 percent. The word “State" here means the several States and the District of Columbia.

From any appropriations for territories, dependencies, and possessions the Commissioner might make the allotments on the basis of the number of persons aged 5 to 17, inclusive, as certified by the Director of the Census, perhaps giving double weight to such population in Puerto Rico, Virgin Islands, Guam, and Samoa.

4 The College of Education Record, November 1943, and the Journal of Educational Research, April 1945.

To illustrate how this formula works, suppose that the national average income per school-age child was $4,000. Then, for a State with an income per school-age child of $2,000, the preliminary grant ratio would be ((2x$4,000) – $2,000) = $2,000, or $6,000-$2,000, which is 3. For a wealthier State, with an income per school-age child of $5,000 per school-age child, the preliminary grant ratio would be ((2x $4,000-$5,000) =$5,000, or $3,000:-$5,000, which 1s 0.6. Assuming that Federal appropriations were only sufficient to make onetenth of the preliminary grant allocations, the poor State would have an adJusted ratio of three-tenths, or 30 percent, and would receive Federal aid equivalent to 30 percent of the amount it spent from its own sources. The wealthier State would get 0.06 as a supplementary grant ratio or Federal aid equal to 6 percent of the amount it spent from its own sources.

Table I illustrates how this formula might operate, assuming that Federal appropriations for the purpose totaled $300,000,000, of which 98 percent was spent on the continent and 2 percent off the continent (table below).

The same results could be obtained in a slightly different way by substituting for steps (1) and (2) above, the following:

1. The Commissioner of Education would develop an index of need for each State based upon the percentage that the number of inhabitants 5 to 17 years of age in that State is of the total such population in continental United States; and for each State the Commissioner would also develop an index of ability, based upon the percentage in that State of total income payments in the continental United States during the three most recent years for which satisfactory data are available. Data on population and income payments would be furnished by the Department of Commerce.

TABLE I.Potential allocation of $300,000,000 Federal aid to education under a

variable matching formula for determining supplementary grants ?

[graphic]

Prelimi-
nary
grant

Prelimi-
Twice the

nary Fed-
ratio=
twice the
Average eral

Supple-
national
national
State and
grants=

mentary State average

local cur- prelimiaverage

Supple- Federal income income

rent exStates ranked by 1941-43

income

nary grant mentary grants penditures ratios mulper child

grant column 5) average per capita income per child a per child

($7,736) aged 5 to

minus

for educa- tiplied by ratios n.ulti. minus 17

State

tion, average (ad- plied by State income 1941-42,

current income

justed) column 7 1942-43 3 school per child

(thouper child divided (thousands) expendi

sands) by State

tures income

(thousands)

per child
(1)
(3) (4) (5)

(6)

(8)

Continental total
(average).
$3,868
$2,097, 708 $2,197, 776

$294, 000 Mississippi...

1, 395 $6, 341 4. 54552 15, 916 Arkansas.

72, 346 0.60438 9, 619 1, 565 6, 171 3. 94313 14, 101 55, 602 52429 South Carolina.

7, 393 1, 651 6,085 3. 68565

18, 133 66,832 . 49005 Alabama 1, 749 5, 987

8, 886

3. 42310 Kentucky.

24, 192 82, 812

. 45514

11, 011 1, 767 5, 969

3. 27804 North Carolina.

24, 706 83, 458 44915 11,097 1, 799 5,937 3. 30017 37, 027 122, 195 . 43880 Georgia.

16, 247 1, 971 5, 765

2.92491 27, 311 79 882 Tennessee

38890

10, 621 2,044 5, 692 2.78474 27, 465 New Mexico.

76, 483 37026

10, 169 1, 877 5, 859 3. 12147

8, 628 Louisiana

26, 932 41504 3, 581 2, 322 5, 414 2. 33161 Oklahoma

26, 774 62, 427

31002

8,300 2,092 5,644 2. 69790 31, 344 West Virginia

84, 563
. 35872

11, 244 2, 030 5, 706

2.81084
28, 951

81, 377 . 37374 10, 820 1 Each State's allotment or supplementary grant is the product of the amount which it has been spending for education and its supplementary grant ratio, which ratio for each State varies directly with the number of children 5 to 17 years of age, inclusive, and inversely with the fiscal ability of the State, as shown by income payments to individuals in that State. a State income per child

was computed by dividing the average of 1941-43 income payments in each State by the 1940 Census figure for persons aged 5 to 17 in each State.

3 Computed from U. S. Office of Education releases. The figures shown do include a minor amount of Federal funds (less than 2 percent) which were not shown separately in the published reports.

Supplementary grant ratios were adjusted from the preliminary ratios by the following process: (a) The grants for the 3 states affected by the 1 percent floor provision-see footnote 5—were subtracted from the supplementary grant total, $294,000,000; (6) the amount remaining for grants to other States was divided by the total of preliminary grants; (c) the quotient (0.13296214) was multiplied by each of the preliminary grant ratios to yield the adjusted ratios of col. 7.

TABLE I.-Potential allocation of $300,000,000 Federal aid to education under a

[graphic]

$20, 176

3,068 3, 433 6, 367 1, 702

1. 167

4, 045 2, 713 1,014 8,750 7, 720 1,841 4,711 6,546 2, 908 1,886 7,725 1,906

837
1, 770
6, 418
21, 814
7, 999
9, 303

905
8, 632
1.732
5, 437
5, 634
680

854
12,599

164

117 1, 637

25 797

$70, 820 64, 671

522, 278 5, 247, 146

39, 508

variable matching formula for determining supplementary grants—Con.

States ranked by 1941-43 average per capita income

Prelimi

nary

grant Twice the

ratio= national

twice the

national
State

average
income

average
income

income
per child
per child

per child
aged 5 to
($7,736)

minus
minus
17

State
State
income

income
per child

per child
divided
by State

income

per child (2) (3) (4)

(1)

Texas.
South Dakota..
Florida.
Virginia.
Arizona
New Hampshire.
Nebraska.
North Dakota
Vermont.
Minnesota
Missouri
Idaho
Kansas.
Iowa.
Colorado.
Maine.
Wisconsin
Utah
Wyoming
Montana
Indiana
Pennsylvania.
Michigan
Ohio.
Oregon.
Illinois.
Maryland..
Massachusetts.
New Jersey
Rhode Island
Washington.
New York
Delaware
District of Columbia.
California...
Nevada
Connecticut.

$2,771
2, 535
3, 606
2, 880
3, 287
3, 289
3, 041
2, 523
3,082
3, 262
3, 557
2,983
3, 486
3, 470
3,633
3,374
3,612
3, 294
3, 613
3, 566
4, 151
3,868
4, 654
4, 805
5, 586
5, 230
4, 940
5,049
5,360
5, 388
6, 532
5, 870
6,011
11, 918
7, 710
8, 146
6, 490

$4, 965
5, 201
4, 130
4,856
4, 449
4, 447
4, 695
5, 213
4,654
4, 474
4, 179
4,753
4, 250
4, 266
4, 103
4, 362
4, 124
4, 442
4, 123
4,170
3,585
3, 868
3,082
2,931
2, 150
2, 506
2, 796
2,687
2, 376
2, 348
1, 204
1, 866
1, 725
(5)

26
(5)
1, 246

1. 79177
2. 05168
1, 14531
1. 68611
1, 35351
1.35208
1. 54390
2. 06619
1. 51006
1. 37155
1. 17487
1. 59336
1. 21916
1. 22939
1. 12937
1. 29283
1. 14175
1. 34851
1. 14116
1, 16938

.86365
1.00000
.66223
.60999
. 38489
47916
56599
53218
. 44328
. 43578
. 18432
.31789
. 28697
(5)

(5)
. 19199

Territories and possessions

Children 5-17 years

of age

Alaska.
Guam
Hawaii.
Puerto Rico
Samoa
Virgin Islands

Total, off continent.

55, 577 6,000,000

756, 970

1, 377, 750

The income per child in the District of Columbia and Nevada was, for the period studied, greater than twice the national average, so that the subtraction in col. 3 would yield a negative quantity; therefore, these States were assigned the floor percentage. Similarly, the division in col. 4 would yield a preliminary grant ratio of 0.00337 for California, so this state was also assigned the floor percentage. Preliminary grants are not computed for these States since the adjusted grant ratios do not depend on preliminary ratios.

1

2. The Commissioner would determine a preliminary grant ratio for each State by dividing the difference between twice its index of need and its index of ability by its index of ability.”

This expression of the formula could be termed a “full equalization” formula if Federal appropriations were sufficient to make all the grants called for by the grant ratios.

OTHER ALLOCATION FORMULAS

There are a wide variety of bases which have been used in allocating other Federal grants in aid. These include population, area, road mileage, uniform sum per State, costs, financial need, etc. Two bases have been most generally proposed for use in educational formulas: (1) population of school age—the potential group to be served by this aid—and (2) ability to finance education, in view of the apparent interest in providing for the equalization of educational opportunities.

One way in which these two factors could be combined would be to weight the population of school age in each State by a factor expressing the differential in the abilities of the State to support education; that is, by an index of financial need.

The amount of Federal aid apportioned to each State would be an amount which bears the same ratio to the total amount of Federal funds appropriated as that State's population of school age weighted by its financial need bears to the sum for all States of such weighted population figures. The index of financial need of the respective States could be computed as follows:

1. The Secretary of Commerce would certify to the Commissioner an estimate of the average of per capita income payments in each State for the three most recent calendar years for which satisfactory data are available.

2. The Commissioner would then compute the index of financial need for each State by dividing the difference between the average of per capita income payments in, say, the three richest States and the per capita income of that State by the per capita income of that State. If it is desired to give some aid to the

M=

Pa

5 Both expressions are derived from the Lindman formula. He proposed that a matching ratio for each State (M) should equal a fixed Federal support level (R) multiplied by the percent of school age population in the state (P1-or the index of need) divided by the percent of income payments in the State (Po-or the index of ability) minus a fixed equalization factor (E). Mathematically, his formula is :

RXP

E

Pa For the formulas in the text, E has been given a value of 1, which will permit full equalization, and R has been given a value of 2. to make a possible a positive value of M (1. e., a Federal grant) to almost every State. The formula then becomes :

2 P

2 P Pa the preliminary grant ratio (M)= -1=

Pa

Pa 2 P, --Pa

which is the

Pa second alternative expression of the formula in the text. The first alternative was derived from this same base, as follows:

2 Pi

2 P
Since M= -1, then M+1=
Pa

Pa
Multiplying both sides by United States total school age population over United States
total income payments (in other words, by the reciprocal of national average income per
school age child).

total school pop. Pix total school pop.
total inc. pay'ts.

(M+1) (tote

=2X

Pa X total inc. pay'ts. but the numerator of the latter fraction is school age population in a State, and the denominator is income payments in a State, so that the two become the reciprocal of State income per school-age child. Therefore M +1

2 National inc. per school child State inc. per school child And

2 x Nat. inc. per child
M=

State income per child
2 x Nat. inc. per ch. - St. inc. per ch.
M=

State income per school child.

-1 or,

three States with the highest per capita income, it could be provided that for no State should the population figure be multiplied by a weight (index of financial need) lower than (say) 1 percent (0.01).

Figures on population aged 5 to 17 years, inclusive, for each State, would be furnished by the Bureau of the Census.

As an illustration of this formula, suppose that the average per capita income in the three States with the largest per capita incomes was $1,400. Then, for a poor State with a per capita income of $400, the index of financial need-the weight to be applied to population of school age would be ($1,400 – $400) =$400 or $1,000-$400, which is 2.5. For one of the wealthier States, with a per capita income of $1,000, the weight would be ($1,400-$1,000) = $1,000 which is $400: $1,000, or 0.4. Thus population of school age in the poorer State would have considerably more weight than population in the richer State, and the amount of Federal aid per school-age child will be proportionately greater in the poorer States. TABLE II.Potential allocation of $300,000,000 Federal aid to education under a

weighted population formula?

[graphic]

Grand total....

30,502, 258 20,758, 169 $300,000,000 Total, continental United States...-- $861

29,745, 288

281, 774,895 Mississippi..

386

$850 2. 20207 615, 886 Arkansas.

1, 356, 224 19, 600, 342 429

807 1.88112 530, 264 South Carolina..

997, 490 14, 415, 868 468

768 1. 64103 Alabama

562, 097 922, 418 13, 330, 917 481

755 1.56965 Kentucky.

799, 238

1, 254, 524 18, 130, 560 482

754 1.56432 756, 229 North Carolina.

1, 182, 984 17, 096. 653 512

724 1. 41406 Georgia...

1,026, 826 1, 451, 994 20, 984, 423 513

723 1. 40936 Tennessee

837, 040 1, 179, 691 17,049, 061 523

713 1. 36329 755, 506 New Mexico

1, 029, 974 14, 885, 330 537

699 1. 30168 Louisiana

152, 346

198, 306 2,865, 946 565

671 1. 18761 Oklahoma

615, 384 730, 836 10, 562, 145 575

661 1. 14957 608, 627 West Virginia

699, 659 10, 111, 571 581

655 1. 12737 Texas..

521, 781

588, 240 8, 501, 328 654

582 .88991 South Dakota.

1, 601, 087

1, 424, 823 20, 591, 744 685

551

.80438 Florida..

159, 360 128, 186 1,852, 562 695

541

77842 424,068 Virginia.

330, 103 4,770, 695 709

527

.74330 688, 614 Arizona.

511, 847 7, 397, 285 713

523 .73352 New Hampshire..

129, 590 95, 057 1, 373, 777 724

512 .70718 Nebraska.

104, 903 74, 185

1,072, 132 738

498

67480 North Dakota

302, 544 204, 157 2,950, 506 740

496 .67027 Vermont.

168, 424 112, 890

1, 631, 502 745

491 .65906 Minnesota..

82, 099
54, 108

781,976 752

484 .64362 611, 907 393, 836 Missouri.

5, 691, 774 758

478 . 63061 Idaho.

806, 208 508, 403 7,347, 512 780

456
58462 129, 044

75, 442 Kansas.

1,090, 298 793

443

55864 Iowa.

402, 469 224, 835 3, 249, 347 801

435

54307 Colorado.

555, 068 301, 441 4, 356, 468 807

429

.53160 251, 845 Maine.

133, 881 1,934, 867 812

424

. 52217 Wisconsin

198, 867 103, 842 1, 500, 739 820

416
. 50732

699, 929 Utah.

355, 088 5, 131, 782 825

411
49818 149, 059

74, 258 Wyoming

1,073, 187 827

409

49456 57,848 Montana

28, 609 413, 461 863

373

43221 123, 386 Indiana

53, 329 770, 718 892

344

38565 740, 020 Pennsylvania.

285, 389 4, 124, 482 898

338

37639 2, 245, 015 Michigan..

845, 001 12, 212, 074 997

239 . 23972 1,167,804 Ohio ..

279, 946 4,045, 819 1,002

234 23353 1, 443, 268 337,046 4,871, 037 1 The formula allocates Federal aid according to population 5 to 17 years of age, inclusive, as weighted by the difference between the per capita income of the 3 richest States and of that State divided by the per capita income in that State.

Department of Commerce figures indicate that average per capita income for continental United States in 1941-43 was $861; for the 3 richest States, it was $1,236; and for the 3 poorest States it was $421.

3 To determine the apportionment, it is necessary to divide the amount of the appropriation by the total of the preceding column (total of indexes of financial need); the result is the amount per weighted population to be given; this amount must then be multiplied by the index of financial need for each State or Territory to determine the apportionment.

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