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.

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 grants1

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.

2 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.

4 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; (b) 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 variable matching formula for determining supplementary grants-Con.

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.

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

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 (Por the index of need) divided by the percent of income payments in the State (Pa-or the index of ability) minus a fixed equalization factor (E). Mathematically, his formula is:

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 :

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

The first alternative was

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).

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.

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 formula1

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.

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.