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Statistical Issues in Allocating Funds by Formula Appendix B A Review of Twelve Large Formula Allocation Programs To further our understanding of the statistical aspects of formula allocation procedures, the panel gave special attention to some of the largest federal programs and some others with special features. Federal agency officials responsible for several of these programs were invited to make presentations at panel meetings. In addition, the staff prepared program descriptions, using a standard format, for 12 programs, including the 10 largest in fiscal year 1999 and two others with features of particular interest. Box B-1 shows, as an example, the description that was prepared for the special education program. Each program agency was given an opportunity to review the description of its program, and several changes were made as a result of these reviews. This appendix, which presents findings from an analysis of features of these 12 programs, has two sections. The first section describes several features of each of the 12 programs, focusing particularly on aspects of their formulas and allocation processes that are unusual in some way or that may be less than optimum for producing equitable distributions and efficient outcomes, or for which the rationale is not obvious. The second section provides some general observations about features that were common to some or all of the programs. Table B-1 lists the 12 programs included in the analysis and shows their total obligations in FY 1999. Together, they account for FY 1999 obligations of $190.5 billion or 79.3 percent of total obligations for the 169 formula allocation programs listed in Category A of the Catalog of Federal Domestic Assistance in 2000. The
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Statistical Issues in Allocating Funds by Formula Box B-1 Formula Allocation Program Description CFDA number and name: 84.027 Special Education Grants to States Subprogram (if applicable): Basis for allocation: [ ] Amounts or shares in legislation [ x ] Formula in legislation [ ] Formula in regulations Source of funds: [ x ] General revenues [ ] Special (describe) Recipients: [ x ] States [ ] Other (describe) Matching provisions: [ x ] No [ ] Yes (describe) Type of formula: [ ] Closed [ x ] Other (describe) The basic formula is closed, but because of a variety of caps and hold-harmless provisions, an iterative process is required to determine the final allocations. Formula: The “permanent formula,” which first took effect in FY 2000, with FY 1999 as the base year, is: Ai t = Ai 99 + (At - SiAi99) (0.85 P1 i / Si P1 i + 0.15 P2 i / Si P2 i) Prior to FY 2000, allocations were based on state counts of children served in their programs. Definition of left-hand element: Ai t = amount allocated to state i in fiscal year t.
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Statistical Issues in Allocating Funds by Formula Definition of right-hand elements: Symbol Definition Source Remarks 1. Ai 99 Amount allocated to it h state in base year. 2. At Total amount available for allocation to states in fiscal year t. 3. P1 i Total population in age range mandated by the state’s program. Most recent data satisfactory to Sec. of Education Age ranges vary by state, max. range is 3 to 21. 4. P2 i No. of poor children in age range mandated by state’s program. Most recent data satisfactory to Sec. of Education See item 3. Analysis of formula elements: Need: P1 i and P2 i are indirect estimators of need. Capacity: None. Effort: Ai 99 is a measure of effort because it was based on state counts of the number of children served. Other: None.
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Statistical Issues in Allocating Funds by Formula Other formula features: Upper and lower limits: [ ] No [ x ] Yes (describe) Upper limit. (1) No state may receive more than an amount equal to the number of its children receiving special education services multiplied by 40 percent of the average per-pupil expenditure in U.S. public elementary and secondary schools. So far, appropriations have not been sufficient for this limit to take effect. (2) No state may receive more than its allocation for the previous year increased by the percentage increase in the total amount appropriated plus 1.5 percent. Lower limit. See Hold-harmless. Thresholds: [ x ] No [ ] Yes (describe) Hold-harmless: [ ] No [ x ] Yes (describe) As long as there is an increase in funds compared to the preceding fiscal year, no state may receive less than its allocation for that year. Additional provisions ensure that states will receive some minimum proportion of the increase in the amount appropriated for the current fiscal year. State minimum: [ ] No [ x ] Yes (describe) See Hold-harmless. Remarks: If there is a decrease in funds compared to the preceding year, but the amount is greater than the base year, the amount each state will receive is given by: Ai t = Ai 99 + (At - A99) × (Ai (t - 1) – Ai 99) / Si(Ai (t – 1) – Ai 99) If the amount is less than the base year, base year allocations are ratably reduced. Source: 20 U.S.C. 1411.
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Statistical Issues in Allocating Funds by Formula TABLE B-1 Twelve Large Formula Allocation Programs Catalog Numbera Program Total Obligations FY 1999 ($billions) 93.778 Medical Assistance Program (Medicaid) 111.1 20.205 Federal-Aid Highway Program 26.2 93.558 Temporary Assistance for Needy Families (TANF) 18.8 84.010 Title I Education 7.7 10.555 National School Lunch Program (Food portion) 5.5 84.027 Special Education Grants to States 4.3 93.767 State Children’s Health Insurance Program (SCHIP) 4.2 93.658 Foster Care, Title IV-E 4.0 14.218 Community Development Block Grants Entitlement Grants 3.0 10.557 WIC (food portion) 2.9 93.959 Substance Abuse Prevention and Treatment Block Grants 1.5 66.458 EPA State Capitalization Grants 1.3 Total 190.5 aCatalog of Federal Domestic Assistance classification. first 10 programs are those with the largest obligations in FY 1999. In addition, the substance abuse block grants program is discussed for its unique approach to equalizing fiscal capacity between states, as is EPA’s state capitalization grants program, one of the few with numerical values of shares specified in legislation. FEATURES OF INTEREST BY PROGRAM Medical Assistance Program (Medicaid) Medicaid is by far the largest federal formula allocation program, accounting for 45 percent of total obligations for such programs in FY 1999. The key element of the formula is the federal medical assistance percentage (FMAP), which determines the proportions of state expenditures that will be reimbursed by the federal government. FMAP is also used,
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Statistical Issues in Allocating Funds by Formula either directly or indirectly, in several other formula allocation programs, including three covered by this report: Temporary Assistance for Needy Families, the State Children’s Health Insurance Program, and foster care. Therefore it is important to pay close attention to the structure and role of FMAP. The value of FMAP for each state is [1.00 – 0.45 (State PCI/ National PCI)2], where PCI stands for per capita income. FMAP is subject to the restriction that it cannot be less than 0.50 or greater than 0.83. A possible rationale for this formula is that the federal government should pay 55 percent of state Medicaid expenditures to a state whose per capita income is equal to the national per capita income. For states with per capita income below the national average, the federal government would pay a higher proportion, and vice versa. The lower limit of 50 percent was retained from a predecessor program that provided a flat matching rate of 50 percent to all states (U.S. General Accounting Office, 1983). At present, no states have per capita income so low that they are affected by the 0.83 upper limit on FMAP. However, several states with high per capita incomes are receiving 50 percent matching funds, more than they would receive if there were no lower limit. The FMAP formula uses the squared ratio of state to national per capita income. Within the 0.50 to 0.83 range, squaring enhances the effect of state variations from the national per capita income. Any state whose per capita income exceeds the national average by 5.4 percent or more receives a 50 percent match, whereas, if the ratio were not squared, this would occur only when the difference was 11.1 percent. The use of variable matching rates presumably represents an attempt to use federal funds to equalize (at least partially) the fiscal capacities of states to pay for the program. The formula uses per capita income as a proxy measure of fiscal capacity. Another option would be to use the Treasury Department’s indicator, total taxable resources, which is used for this purpose in the substance abuse and mental health block grant programs. In recent years, the values of FMAP for Alaska and the District of Columbia have been set by statute at levels higher than those dictated by the formula. Federal-Aid Highway Program The federal-aid highway program consists of several distinct subprograms, the largest of which use legislated formulas to apportion funds to the states. An unusual feature of the program is that all of the funding
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Statistical Issues in Allocating Funds by Formula comes from the highway trust fund, which is a financing mechanism established by law to account for receipts collected by the federal government from motor fuel taxes; sales taxes on heavy vehicles, trailers, and tires; and use taxes on heavy vehicles. The portion of the funds from these taxes that goes into the highway trust fund is specified by law; currently, small portions go to the U.S. Treasury for deficit reduction and for cleanup of leaking underground storage tanks. The highway trust fund is divided into two separate accounts: the highway account, which supports the federal aid highway program, and the mass transit account, which supports the federal transit formula grants program. Most of the distinct subprograms that make up the federal aid highway program have similar formulas,1 which take the general form: Ai = A S j wj Mi j / Mj where A = amount available for the subprogram Ai = amount apportioned to state i. Mi j is a measure of need (such as vehicle miles, lane miles, or population), for state i, with Mj = Si Mi j wj is the weight for the jth measure of need, with S j wj = 1. There are several questions that could be asked about the apportionment formulas for the subprograms. For example, how are the weights (wj) associated with the measures of need chosen, and how well does each of the measures of need reflect the needs that are intended to be met by the program? For several of the measures used, such as vehicle miles and lane miles, the data used in the apportionments are provided by the state agencies that receive the apportioned funds, so procedures have been established to ensure that states do not manipulate the figures in an effort to increase their shares. 1 For one of the larger programs, the high-priority projects program, there is no apportionment formula. The amount available for allocation each fiscal year is based on a percentage of the total authorized funding level for all high-priority projects over the life of TEA-21, pursuant to 23 U.S.C. § 117(b). Section 1602 of the authorizing legislation, P.L. 105-178, lists 1,850 specific projects, along with the dollar amounts authorized for them under this subprogram. Section 1603, P.L. 105-178, excludes several of these projects from the minimum guarantee calculation.
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Statistical Issues in Allocating Funds by Formula In most of the programs, the apportioned funds are used by the states for specific projects for which they are required to provide matching funds. In most instances the federal share is 80 percent. Unlike the Medicaid program, the highway program has no provisions that attempt to equalize fiscal capacity among states. The legislation that reauthorized the program for FY 1998 to 2003 contains a table of state percentages adding to 100 percent, with a provision that for FY 1998 each state’s apportionments over a specified set of subprograms, as a percent of such apportionments to all states, should equal the value shown in the table. Each fiscal year thereafter, these percents are modified to ensure that each state will receive a minimum of at least 90.5 percent of its percentage share of contributions to the highway trust fund account, based on the latest data available at the time of apportionment. The shares of states falling below that minimum return are increased and the shares of the remaining states are proportionately decreased so that the shares continue to total 100 percent (P.L. 105-178, Section 1104 or 23 U.S.C. § 105). The legislation authorizes as much funding as necessary, designated as minimum guarantee funds, to achieve the modified target state percentages. A portion of each state’s share of these funds is added to the amounts apportioned to it under five other subprograms, all of which use formulas to apportion funds to the states. The remainder is made available to the states under the surface transportation program. The net result is that all of the apportionments are formula-driven, but the overall share of these apportionments received by each state is the numeric value specified in the law, as modified by the minimum guarantee provision. Temporary Assistance for Needy Families (TANF) The TANF program was created by 1996 legislation designed to change the nation’s welfare system into one requiring work in exchange for time-limited assistance. It replaced the Aid to Families with Dependent Children (AFDC) and Job Opportunities and Basic Skills Training (JOBS) programs. The goals of TANF are to promote work, responsibility, and self-sufficiency and to strengthen families. States operate their own programs, subject to certain statutory requirements. TANF block grants to the states are based on their expenditures for AFDC benefits and administration, emergency assistance, and the JOBS program during the period just prior to passage of the 1996 welfare reform
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Statistical Issues in Allocating Funds by Formula legislation. There are three different options for measuring these historical expenditures; we are not aware of the rationale for making these choices available. The AFDC program, which matched state expenditures at a rate determined by the FMAP formula, was by far the largest of the three programs replaced, thus the amounts of TANF block grants depended indirectly on the FMAP formula. Therefore, to the extent that the use of FMAP reduced differences in fiscal capacity between states, it can be said that the TANF block grants also did this. Under the heading of maintenance of effort, states are required to maintain their own spending at 80 percent of FY 1994 levels. For states that meet certain work requirements, the mandatory state effort is reduced to 75 percent. The program includes several performance-related incentive and penalty provisions, many of which require the states to maintain detailed data collection and reporting systems. The 1996 legislation provided for appropriation of $16.8 billion each year for the federal block grants through FY 2002. The deadline for reauthorization is September 2002, with the likelihood that new allocation formulas will be considered. Title I Education Throughout the United States and especially in the South, there was considerable resistance to compliance with the Supreme Court’s 1954 decision in Brown v. Board of Education, requiring desegregation of public schools. In the mid-1960s, the Johnson administration and Congress developed a carrot and stick approach to encourage compliance, with civil rights legislation providing the stick and the provision of federal funds for education, under Title I of the Elementary and Secondary Education Act, as the carrot. Title I funds were available only to jurisdictions complying with desegregation requirements. For most formula allocation programs, federal funds are allocated to the state agencies, which are then responsible for further distribution to subordinate jurisdictions. In this program, however, since school year 1999-2000, funds have been distributed by the U.S. Department of Education directly to school districts.2 2 There are some exceptions for school districts with less than 20,000 population.
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Statistical Issues in Allocating Funds by Formula One element of the formula, the state per pupil expenditure, is restricted to a range extending from 32 to 48 percent of the national average. The role of this element in the formula is ambiguous. It could be regarded as a relative measure of either need or effort. In either case, however, the fact that a statewide average is used means that within-state variations are not taken into account. The program has eligibility thresholds, with the result that a difference of one in the estimate of the number of eligible children or total school-age children for a school district can determine whether or not the district receives any funds. For example, to be eligible for a concentration grant, the estimated number of eligible children for a school district must be at least 6,500, or it must exceed 15 percent of the total estimated school-age population. In recent years, current estimates of number of eligible children by school district have been developed and updated biennially by the Census Bureau, with a model-based estimation procedure using data from the decennial census, the Current Population Survey, and administrative sources. This system replaced the earlier use of decennial census-based estimates, which were updated only every 10 years. However, for the past four fiscal years, Congress has enacted a 100 percent hold-harmless provision, so that lacking any significant increase in annual appropriations, the revised estimates have had little effect in shifting funds to areas where needs have increased more rapidly. The nature of the small-state minimum allocation is such that some states receive considerably more per eligible child than they would receive in the absence of this provision. Although this is the fourth largest federal formula allocation program, it accounts for only about 2 percent of total expenditures for public schools. Another 5 percent comes from other federal programs. Much larger amounts of state funds are distributed to school districts. The distribution of New York state funds for public elementary and secondary education equals about twice the total amount distributed to all states under the federal Title I program. National School Lunch Program In simplest terms, this program pays the states a specified amount per lunch served to schoolchildren under the program. The amount paid per lunch (the national average price) varies according to whether the lunch
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Statistical Issues in Allocating Funds by Formula is a paid, reduced price, or free meal. These national average prices are updated annually, based on the food away from home series of the consumer price index. Special prices have been established for Alaska and Hawaii because of the high costs of food and labor in those states. Schools are also entitled to receive a fixed value of commodities from the U.S. Department of Agriculture for each meal served; in some cases, schools can elect to receive cash instead of the donated commodities. The amounts paid to the states depend on eligibility determinations by the schools and on their reports of the numbers of lunches served in each category. The program regulations include a system of reports and audits in an attempt to ensure accuracy. One goal of the program is to promote high nutritional standards for lunches served to schoolchildren. There is an elaborate set of regulations covering this aspect. The special prices for Alaska and Hawaii established by legislation call attention to the fact that the Bureau of Labor Statistics does not produce state-level consumer price indices, so that price variations between states cannot be routinely included in allocation formulas. Special Education Grants to States When this program was initiated by the Education for All Handicapped Children Act in 1975, annual allocations to the states were based on their certified counts of individuals being served under their programs, that is, a measure of effort. The current allocation procedure, based on the 1997 amendments to the act, is quite different. Each state receives its base year (FY 1999) allocation plus a proportion of the additional funds available, as determined by the state’s share of two weighted quantities: total number of children in the age ranges mandated by the state’s program and number of children in poverty in these age ranges. The weights are 0.85 and 0.15, respectively. The age ranges mandated by the individual state programs vary, with the maximum range for allocation purposes being from 3 to 21 years.3 The quantities used in the current formula to allocate additional funds have elements of both need and effort. They are indirect measures of 3 For some state programs, coverage extends to 22 or 23 years of age, but only ages 3 through 21 are considered for allocation purposes.
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Statistical Issues in Allocating Funds by Formula Equalizing Fiscal Capacity Among States One goal that is either stated or implicit for several formula allocation programs, whether general or highly focused, is to equalize the capacities of the recipient jurisdictions to provide services to their citizens. To meet this goal, allocations must vary inversely with the recipients’ fiscal capacities. When equalization is a goal, per capita income is normally used as a measure of fiscal capacity, the only alternative in U.S. federal programs being the Treasury Department’s measure of total taxable resources by state, which is used in the substance abuse block grants program.6 Of the 12 programs reviewed, 4 had equalization provisions; for 3 of these 4 programs, the provisions operate by providing for varying “match rates,” that is, the proportions of states’ expenditures that are reimbursed by the federal government. In the Medicaid and foster care programs, match rates are determined by the FMAP formula, varying from 83 percent for states with the lowest per capita income to 50 percent for those with the highest per capita income.7 As noted earlier, several states with high per capita incomes are receiving 50 percent matching funds, more than they would receive if there were no lower limit. In the SCHIP program, an “enhanced FMAP” formula leads to match rates that vary from 65 to 85 percent. The same states that receive 50 percent matching funds under FMAP receive 65 percent under SCHIP’s enhanced FMAP. For the substance abuse block grant program, there are no matching provisions, but total taxable resources, used as a measure of fiscal capacity, is a component of the formula for allocating appropriated funds to the states. Measures of need and geographic cost differentials enter directly into the allocation formula, and the measure of total taxable resources operates inversely, so that states with lower taxable resources receive higher shares. The TANF program could be said to provide for some movement toward smaller disparities in fiscal capacity between states in a less direct way. The TANF block grants were based primarily on states’ historical expenditures under the AFDC program, which used the FMAP formula to determine federal match rates. 6 Some states, for example, New York, use measures of wealth based on assessed values of real estate in formulas for allocating state funds to school districts. 7 At this time, no states are at the 83 percent level.
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Statistical Issues in Allocating Funds by Formula Measures of Need For some programs that allocate a fixed total appropriation, a direct estimate of the number of people in each jurisdiction who are eligible for program benefits or services is a major element of the allocation formula. Examples include WIC (children under age 5 with family incomes less than 185 percent of poverty) and Title I education (children ages 5 to 17 in families with incomes below the poverty line). Both programs rely on model-based estimates of eligibles, using the latest data available from several sources. For WIC, estimates by state are updated annually, and for Title I education, estimates by school district are updated every other year.8 In other programs, estimates of population for various categories are used, along with other elements, as indirect indicators of need. The community development block grant program uses total population as an element in one of its two alternative formulas and population in poverty in both of them. Population also appears indirectly in two other indicators of need: overcrowded housing units and population growth lag. The substance abuse block grants program, in the absence of reliable state estimates of the number of substance abusers, uses weighted estimates of population for groups believed to be at highest risk. The special education program uses the mean of two population estimates: the number of persons in the age range served by each state’s program and the number of poor children in those age ranges. The federal-aid highway program, in its national highway system subprogram, uses lane miles on principal arterial highways divided by population as one of four indicators of need. The SCHIP program faces a difficult problem in trying to measure need. Initially, allocations were based on estimates of the low-income (below 200 percent of the poverty level) uninsured children by state. However, continuing this method of allocation would have penalized states that had been more successful in enrolling children in their health insurance programs, so the basis for the allocation was changed to the mean of estimates, by state, of the total number of low-income children and the number of low-income uninsured children. Further adjustments may be necessary in order to reflect future changes in the distribution of eligible and enrolled children by state. 8 Note, however, that in both of these programs, efforts to improve targeting to current needs by obtaining the best estimates feasible of eligible populations have been undermined by the inclusion of 100 percent hold-harmless provisions in the allocation procedures (see discussion below).
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Statistical Issues in Allocating Funds by Formula Some programs use indicators of need other than population. One of the elements used in the community development block grant allocation formulas is an estimate of the number of housing units built before 1940. The highway program uses a variety of need indicators, including, for example, vehicle miles traveled on principal arterial routes (excluding the interstate system) and diesel fuel used on highways, in allocation formulas for its subprograms. Prior to the introduction of legislated shares in FY 1988, the allocation formula for the EPA state capitalization grants program was based in part on estimates of states’ needs for wastewater treatment and water pollution control facilities, as identified in periodic surveys conducted by the EPA. Geographic Cost Differentials If the needs of states and other jurisdictions are to be established in dollar terms, it seems reasonable that geographic cost differentials should be taken into account in establishing the level of need in each area. In programs like Medicaid, in which varying proportions of state program expenditures are reimbursed by the federal government, such differentials are, at least to some degree, taken into account automatically. Of the programs that allocate fixed total appropriations each year, two include cost factors in their formulas. The SCHIP allocation formula includes a cost factor based on mean annual wages in the health services industry by state. The formula for the substance abuse block grants program has a more complex cost factor, with elements representing the costs of rents, services, and supplies. In each of these programs, there are restrictions that prevent the cost factor from having its full potential effect on the allocations. The formula for the SCHIP cost factor is: SCFi = 0.15 + 0.85Wi /W where Wi and W are average wages in the health sector for the state and the country, respectively. The constant factor attenuates the effect of this element on the allocation. In the substance abuse block grants program, the cost of services index for a state cannot be less than 0.9 or more than 1.1. In the school lunch program, presumably in recognition of higher food costs in Alaska and Hawaii, the Department of Agriculture has set higher average lunch prices for those two states. One might ask whether data on food costs for all states should be used to set prices that vary by state. One
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Statistical Issues in Allocating Funds by Formula obstacle to doing this is that the Bureau of Labor Statistics does not routinely provide data on retail and wholesale prices by state. Ostensibly because of the higher cost of health services, the value of FMAP for Alaska has been legislatively increased over what it would be if the standard formula were used. The value of FMAP for the District of Columbia has also been increased by legislation. Combining Multiple Elements in Formulas It will be evident by now that many programs use allocation formulas that combine several different elements of need, fiscal capacity, and effort. As noted earlier, the allocation formulas for subprograms of the highway program determine each state’s share of the amount available for the subprogram by taking a weighted average of the state’s share of each of several elements of need: Ai /A = Sj wj Mi j / Mj where A = amount available for the subprogram Ai = amount allocated to state i Mi j is a measure of need (such as vehicle miles, lane miles, or population) for state i, with Mj = Si Mi j wj is the weight for the jth measure of need, with Sj w j = 1 A similar approach, which could be called “weighted average of shares,” is used to combine elements of need in the alternative allocation formulas for the community development block grant program. However, other programs, including special education and SCHIP, use a “share of weighted averages” approach to accomplish the same purpose: Ai /A = Sj wj Mi j/ SiSj wj Mi j The substance abuse block grants program uses a complex two-stage process for combining elements. In the first stage, elements of need are combined using the weighted average of shares approach. Separate elements of cost are combined in similar fashion. In the second stage of the process, indices representing population (need), cost, and fiscal capacity for
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Statistical Issues in Allocating Funds by Formula each state are multiplied and the products summed over all states to determine the shares, i.e.: Ai /A = Ni Ci Fi / Si Ni Ci Fi This brief look at methods of combining multiple elements in allocation formulas suggests two questions that deserve further study: What is an appropriate basis for determining the relative weights that should be given to different elements of need? What are the relative merits of the three alternative methods of combining elements that we have described: the multiplicative approach, the weighted average of shares, and the share of weighted averages? Stability Versus Targeting Current Need A matter of great concern, for both legislators and recipients of formula grant funds, is how the allocations to each jurisdiction change from year to year, especially in absolute terms. Legislators for areas whose amounts or shares decline are likely to face hard questions from their constituents. Unexpected or unpredictable declines in federal program funding can cause difficulties for state and local program administrators, for example, school officials planning their budgets for the coming school year. Still, most fund allocation programs are designed to meet fairly specific needs and to equalize, at least in part, the fiscal capacity of states to meet those needs. As needs and fiscal capacities change, one would expect allocations to be responsive to those changes. Except for open-ended programs like Medicaid and foster care, there is clearly a trade-off between stability and improved targeting of current needs, especially if annual program funding remains level or declines. One approach to better targeting of funds is to improve the formula inputs, primarily by updating the data used to estimate needs and fiscal capacity. Sometimes improved estimators, such as the model-based estimates that have been developed for the Title I education and WIC programs, can be developed and introduced into the formula allocation process. However, these estimates, although on the average they may reflect needs more accurately than the inputs previously used, are still subject to error, which can be relatively large in some instances, such as the Title I education program, which requires estimates by school district, and the
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Statistical Issues in Allocating Funds by Formula SCHIP program, which requires state estimates for a narrowly defined subset of the total population. In order to maintain some degree of stability, the allocation procedures for several programs have (or have had at various times in the past) hold-harmless provisions that guarantee that each recipient will receive, at a minimum, a specified proportion of the prior year’s amount.9 The specified proportion may be 100 percent or it may be less or more than 100 percent. In some programs, hold-harmless provisions remain the same from year to year; in others they have been established for a limited period, especially at times when revised formulas were being introduced. In some programs, if there has been an increase in appropriations from the prior year, only the increase has been used to bring recipients closer to their fair shares based on updated estimates. In 2 of the 12 programs reviewed, hold-harmless provisions have clearly undermined efforts to improve the targeting of allocations to current needs. In the Title I education program, a model-based estimation procedure, with estimates updated biennially, has replaced the earlier use of decennial census-based estimates, which were updated only every 10 years. However, for the past four fiscal years, Congress has enacted a 100 percent hold-harmless provision, so that lacking any significant increase in annual appropriations, the revised estimates have had little effect in shifting funds to areas where needs have increased most rapidly. In the WIC program, in which similar steps have been taken to improve estimates of need, there is a 100 percent hold-harmless provision, called a “stability grant.” Of the balance (if any) available for food grants after allowing for stability grants, 80 percent is used for grants to cover increases in food costs due to inflation, and only the remaining 20 percent is allocated to states that are not receiving their fair shares as determined from current estimates of need. Prior to the introduction of a 100 percent hold-harmless provision in the Title I education program, the legislation covering basic grants included a partial hold-harmless provision based on a step function, with higher rates for jurisdictions with higher poverty. Areas with 30 percent or more poor school-age children were guaranteed at least 95 percent of the prior year’s grant; areas with 15-30 percent poor school-age children were guaranteed 90 percent; and those with fewer than 15 percent poor school-age 9 In some instances, the total amount available may be insufficient to meet the hold-harmless guarantee; in such cases allocations to all participants are “ratably reduced” to add to the total available funds.
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Statistical Issues in Allocating Funds by Formula children were guaranteed 85 percent. A difference of one person in the estimate of poor school-age children or total school-age children for a jurisdiction could therefore make a substantial difference in the size of the grant for that jurisdiction. The special education program allocation rules ensure that as long as there is an increase in funds compared with the preceding fiscal year, no state may receive less than its allocation for that year. Additional provisions ensure that states will receive some minimum proportion of any increase in the amount appropriated for the current fiscal year. The SCHIP program has a hold-harmless provision that applies to shares rather than amounts. Recent legislation provided that, starting with FY 2000, no state’s share could be less than 90 percent of its share for the preceding fiscal year, or less than 70 percent of its FY 1999 share. Upper and Lower Limits Several formula allocation programs place upper and lower limits on one or more formula components, so that these components are allowed to vary only within restricted ranges, with the result that some jurisdictions receive either more or less than they would have received if these limits did not apply. A notable example of these kinds of limits is the restriction of FMAP to a range between 50 and 83 percent. As noted earlier, no states are currently affected by the upper limit, but several of the states with the highest per capita incomes benefit substantially from the 50 percent lower limit, both in the Medicaid program and in other programs that rely on FMAP (or its enhanced version) to determine matching percentages. Other examples of limits, by program, are: Federal highway program. No state can receive less than 90.5 percent of its estimated contributions to the highway trust fund. Title I education. State per pupil expenditure, which is multiplied by the estimated number of eligible children to provide an estimate of need, is restricted to a range between 80 and 120 percent of the national average per pupil expenditure. Special education. No state may receive more than an amount equal to the number of its children receiving special education services multiplied by 40 percent of the average per-pupil expenditure in U.S. public elementary and secondary schools. So far, appropriations have not been sufficient for this limit to take effect. In addition, no state may receive more than its
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Statistical Issues in Allocating Funds by Formula allocation for the previous year increased by the percentage increase in the total amount appropriated plus 1.5 percent. SCHIP. From FY 2000 on, no state’s share can exceed 145 percent of its FY 1999 share. Substance abuse block grants. The cost of services index for a state cannot be less than 0.9 or more than 1.1, and the fiscal capacity index for a state cannot exceed 0.4. The rationales for some of these limits appear fairly obvious. The 40 percent limitation for special education is based on a long-range target, set for the program when it was first enacted, that the federal government should eventually pay that proportion of the costs of special education. The federal highway program distributes funds collected from user taxes, and it seems reasonable that each state should receive at least some minimum proportion of the taxes attributable to it. The reasons for other limit provisions, including those placed on the values of FMAP, are less obvious. The general impression conveyed is that formula developers did their best to develop equitable and effective allocation formulas and processes, taking into account needs, fiscal capacities, and levels of effort, but may have then been led, either because of concerns about data quality or by political considerations, to depart from their initial formulations. Small-State Minimums Of the 12 programs reviewed, 5 have provisions that guarantee a minimum amount or share to every state. The SCHIP program guarantees a minimum of $2 million, about 0.047 percent of the total appropriation for FY 2000, to every state. The highway and EPA state capitalization grants programs each guarantee a minimum share of 0.5 percent to every state, and the substance abuse block grants program guarantees a minimum of 0.375 percent. The specification of the state minimum for basic grants in the Title I education program is not quite so simple. Each state must receive a minimum of the smaller of (a) 0.25 percent of the total grants to states, or (b) the average of (1) 0.25 percent of total state grants, and (2) 150 percent of the national average grant per eligible child, multiplied by the estimated number of eligible children in the state. What this works out to is that if the state’s proportion of U.S. eligible children is equal to or greater
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Statistical Issues in Allocating Funds by Formula than .00167, it will receive a share of at least 0.25 percent. If the proportion is less than .00167, the state’s share will be somewhat smaller.10 Although none of these programs uses total population as an indicator of need, it may still be of interest to observe that according to the 2000 census there are seven states that had less than 0.25 percent of the total U.S. population, with Wyoming, the smallest, having 0.16 percent. There are seven additional states that have more than 0.25 but less than 0.50 percent of the total. At least in some of the programs, provisions for small-state minimums ensure that grant amounts per person exceed the national average. One can see two kinds of justifications for these provisions, one practical and one political. Most programs require states to incur expenses to set up programs to administer the receipt and use of federal grant funds, and some of the costs may be more or less fixed regardless of a state’s population. The other, political consideration is that small states have disproportionate representation in the Senate and their votes are needed to pass authorization and appropriation legislation for the programs. Target Allocation Units Of the 12 federal funds allocation programs reviewed, 10 allocate funds to states, often with special provisions for allocations to territories and American Indian tribes. The exceptions are the Title I education and community development block grants programs. For the Title I education program, which initially allocated funds to state education agencies and later to counties, the U.S. Department of Education now allocates funds directly to school districts. Clearly, it is much more difficult to develop precise estimates of the number of eligible children, which is the key component of the allocation formula, for school districts rather than for counties or states. But this is not a new requirement; previously it was up to the states to allocate the funds they received to school districts, and they used a variety of estimation procedures to do this. Shifting the burden to the federal government appears to have reflected the view of Congress that the federal program agency, the U.S. Department of Education, could do a better job.11 10 For a detailed analysis of the effects of the small-state minimum, in conjunction with other formula features, on the Title I education allocations, see Brown (2002). 11 As noted earlier, Congress may have had some reservations about this change, because states were given the option to make the allocations themselves for all school districts with populations under 20,000.
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Statistical Issues in Allocating Funds by Formula The community development block grants program allocates funds to metropolitan cities (central cities of metropolitan areas and other large cities) and large urban counties, collectively known as entitlement areas, and to states for the remaining nonentitlement areas. As noted earlier, the definitions of the metropolitan cities and urban counties are revised by the Statistical Policy Office of the Office of Management and Budget after each decennial census. Close attention is given to this process by jurisdictions that are “on the bubble” for qualifying as entitlement areas. The nature of these allocation units is such that data for several of the measures of need included in the two alternative allocation formulas, including poverty population, number of overcrowded housing units, and number of housing units built prior to 1940, are only available from the most recent decennial census. It might be appropriate in this kind of situation to consider the trade-offs involved in basing the allocations on measures of need that may not be quite as directly connected to the program goals, but for which current data could be more readily obtained. Data Inputs Provided by Recipients Much of the data for states and other areas that are used in allocation formulas comes from the Bureau of the Census and other federal statistical agencies, for example, the Bureau of Economic Analysis and the Bureau of Labor Statistics, or program agencies, for example, the Internal Revenue Service. However, for several fund allocation programs, data for important formula elements are compiled and provided by the same state agencies that operate the programs that the federal grants are intended to support. In these programs, precautions are needed to ensure that the data are compiled by the states according to clearly defined definitions and procedures, and that audits and other quality control methods are used to monitor adherence to those definitions and procedures. For the Medicaid and foster care programs, the allocations (federal matching funds) are based on reports by the states of their eligible expenditures in state operated programs. Given the size of the Medicaid program especially, regulations (probably quite complex) for reporting and quality-control procedures to monitor accuracy undoubtedly exist, yet there have been reports of gaming by the states to increase their payments. The special education program initially based allocations on reports by states on the number of students served by their programs, but for FY 2000 this approach was replaced by a formula that depends on federal estimates of
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Statistical Issues in Allocating Funds by Formula total children and children in poverty in the age ranges served by their programs. This change in the allocation process may have been due in part to congressional concerns that some states may have been enrolling some students in special education programs when it was not appropriate. Several of the subprograms in the highway program use formulas with elements, such as lane miles and vehicle miles, for which data are provided by the states. In the Title I education program, the data on per pupil expenditures are reported by the states to the U.S. Department of Education. At the April 2000 Workshop on Formulas for Allocating Program Funds, it was reported that California had recently changed its method of counting school attendance (the denominator of per pupil expenditures) in an effort to increase its share. Unlike most states, it had previously defined attendance to include excused absences, thus putting itself at a disadvantage in relation to states that were not including them (National Research Council, 2001:22). REFERENCES Burnam, M.A., P. Reuter, J.L. Adams, A.R. Palmer, K.E. Model, J.E. Rolph, J.Z. Heilbrunn, G.N. Marshall, D. McCaffrey, S.L. Wenzel, and R.C. Kessler 1997 Review and Evaluation of the Substance Abuse and Mental Health Services Block Grant Allotment Formula. RAND Drug Policy Research Center, MR-533-HHS. Santa Monica, CA: RAND. National Research Council 2001 Choosing the Right Formula: Initial Report. Panel on Formula Allocations. T. Louis, T. Jabine, and A. Schirm, eds. Committee on National Statistics, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
Representative terms from entire chapter: