Selected Papers in School Finance 1994
Walter W. McMahon
Professor
University of Illinois at Urbana-Champaign
About the Author
Walter W. McMahon is Professor of Economics and Professor of Education at the University of Illinois at Urbana-Champaign. He specializes in the economics of education, focusing on internal and external efficiency, equity, and financing of education systems, as well as human resource development policies and economic growth.
McMahon has published five books including: Financing Education; Overcoming Inefficiency and Inequity; Education, Economic and Social Development; Investing in Higher Education; An Efficiency-Based Management Information System, and 72 articles in established economics and education journals. His current work involves econometric analyses and computer simulations of the impact of education on economic growth and on other nonmonetary aspects of development, with applications to the developing countries of South America, East Asia, Sub-Saharan Africa, and Eastern Europe.
In recent years, McMahon has completed education sector assessments for the governments of Kuwait, Pakistan, Nepal, and Indonesia; and has served as a consultant to the World Bank, USAID, ILO, OECD, and NSF; and has designed projects in Malawi and Pakistan. He has had resident appointments at the Brookings Institution, London School of Economics, INSEE Research Development (Paris), IUI Economics Institute (Stockholm) Erasmus University (Rotterdam), and the Institute of Development Studies at the University of Sussex.
McMahon has presented various papers at the American Economics Association and Educational Finance Association meetings and is on the editorial board of the Economics of Education Review. He is currently Chair of the Faculty Advisory Committee to the Illinois Board of Higher Education. He obtained his doctorate at the University of Iowa, with pre and post doctoral fellowships at the University of Chicago and London School of Economics.
Intrastate Cost Adjustments
Walter W. McMahon
Professor
University of Illinois at Urbana-Champaign
Within states, geographic differences in the cost of education (COE), the cost of living (COL), and the unit costs of government services (COGs) are known to be considerable. Recipients of public services, including school children and welfare recipients in what often are high-price inner-city areas, receive proportionally less aid than do those with equal need in low-price areas.
The rationale for trying to convert nominal values to real terms by removing the effect of price differences is clear. On efficiency grounds, comparison in real terms is more meaningful and permits the removal of disguised subsidies. On horizontal equity grounds, equal needs warrant responses with equal resources. Yet, there are formidable conceptual and empirical problems. A conceptually clean identification and measurement of regional cost differences is needed. Different issues are raised when deciding how these measures are to be used in making regional cost adjustments.
With respect to empirical measures, several studies have produced interstate indices of COL (McMahon 1991; Nelson 1991), COE (Barro 1994), COGs, and prevailing wages (Barro 1994; Halstead 1992). The COGs are determined primarily by prevailing wages, so the latter two are essentially the same thing. Within states, indices have been produced, for each of the above, but these tend to be limited to a few specific localities in each state, as in work by the American Chamber of Commerce Research Association (ACCRA) (1994), Halstead (1992, pp. 140-179), and McMahon and Chang (1991, pp. 16-23). Intrastate COL, prevailing wage, or COE indices covering all localities within a state are available only for a few states, mostly those states where a large investment has been made, and include indices formulated by Simmons et al. (1973) for Florida; Chambers, Odden, and Vincent (1976) for Missouri; Chambers (1980a) for California; Augenblick and Adams (1979) for Texas; Wendling (1979) for New York; Rosenthal, Moskowitz, and Barro (1981) for Maryland; and Nelson (1994) for Michigan. Chambers and Fowler (1995) have recently produced a teachers' cost index (TCI) at state-wide and district levels. Texas has attempted to provide a COE adjustment. Only a few other states, including Florida, Alaska, and Ohio, have introduced regional cost adjustment factors into their school aid formulas, usually by adjusting for differences in consumer prices or the COL.
Measures of unit-cost differences covering all small local areas within states do not exist because of the enormous cost associated with collecting price data in each locality and repeating the correlation process periodically to keep this data updated. Also, budget studies must be made periodically of the school district or household expenditures to which the index is to apply to determine appropriate weights.
The first section of this paper considers the conceptual issues that affect both a COL index and a COE index (or cost-of-direct-services index), including consideration of what each index covers. This section offers new insights that relate to endogenous prices and costs, the treatment of nonmonetary amenities, and a conceptually clean measure of unit costs. This section also considers the potential use of these indices to study equity, as well as the kinds of adjustments that need to be made when considering their potential use for making regional cost adjustments in financial transfer mechanisms.
The second section of this paper presents the theoretical model and methods of measuring cost differences among school districts. The third section presents the empirical results, reporting cost differences among school districts, counties, and states. New information in this section includes the use of local data at the school-district level, nationwide, that are available for the first time. The (NCES) has mapped the decennial census data to school districts in a way that has made this study possible (U.S. Department of Education 1994). School-district-level COL indices are missing for a small number of districts in New York, New Jersey, and California, but cost indices are computed for all other school districts in the United states. They also are reported after normalization within each state, with the statewide index at 100 in order to isolate intrastate differences. Indices more relevant to the cost of education are computed for all counties within each state, and then for statewide cost indices for each state, based on these school district-level data. The fourth section of this paper summarizes the conclusions and considers major implications.
It is important to begin this discussion by distinguishing between a COE index and a COL index. A COE index is normally based directly on the prices paid by local schools for teachers' and administrators' salaries and for other items, such as heating or books; these prices are weighted by the relative importance of each item in school district budgets. It generically is a COGs index, although the latter is known to change very closely with locally prevailing wages (R2 = 0.98, as computed by Halstead 1992, pp. 125-79). Details of construction of these indices were developed by Barro (1994) and Halstead (1992, pp. 125-79), respectively.
There are several variants of COE indices. One is to augment the COGs-type index with costs unique to the education process itself (as distinguished from area-wide production costs facing all kinds of producers), such as the high cost of educating large numbers of low-achieving children. A second variant is to estimate structural demand and supply using equations specific to education in each locality (McMahon 1970; Brazer and Anderson 1983) in order to obtain structural estimates of the cost functions of school districts.
A COL, on the other hand, seeks to measure the cost of living faced by teachers, administrators, and other local employees. If teachers' job markets work, teachers will move at the margin, and school district budgets will reflect these local costs. In any event, these are the costs, or potential costs, faced by school districts, since about 80 percent of the operating costs of school districts are salaries for teachers, administrators, and maintenance personnel. Their cost of living entails weights that reflect the climate (for example, heating costs); these also affect school district costs. This second approach does not use local teachers' salaries or other endogenous costs that are subject to manipulation by local school districts. All of the states that have made or recommended the use of regional cost adjustments have used a modified COL index, except for Ohio's use of prevailing wages (which essentially is a COGs index) and Texas, which uses a COE adjustment.
Each basic approach and each variant has both strengths and weaknesses, thus, it is not a matter of a search for the perfect index. Instead, the purpose for which the index is to be used must be considered. Also, the net gain in accuracy to be achieved is an important consideration if the choice is to collect the local price data and determine the appropriate weights in relation to the costs of this type of data collection.
Conceptually, what is needed for determining regional cost differences, either within states or among states, is a measure of price differences that determine the unit costs of purchasing a standardized market basket of inputs of fixed quality. The inputs purchased are specific to those needed to produce education by the district (the COE indices) or those needed to produce a given living standard for its teachers, administrators, and other school personnel (a COL index). These prices should not be subject to the control of the school district or the state, if the index is to be used not just for studying efficiency and equity but also potentially for purposes of reimbursing districts for differences in costs. Instead, the prices should be determined by the local markets in which schools and others purchase inputs. This is the first major conceptual issue to be discussed.
Issue 1: Avoiding Cost-Based Reimbursement and Cost Endogeneity
In economic theory, each school district (or local governmental unit) has an average cost curve showing the unit cost at each level of output of a given quality. This cost curve shifts vertically with any increase in salary rates or the price of other inputs.
Cost-Based Reimbursements
To reimburse in full for cost differences when those costs are under the control of the local unit, as are teacher and administrator salaries, encourages inefficiency and invites disaster. This practice is known to provide incentives to pad costs, including not only higher prices but also overutilization. Examples abound from studies of reimbursement of local health care providers by health insurance and other third-party payers. Both prices and utilization therefore must be regulated. Cost-based reimbursement is also common in the setting of public utility electricity rates. In these areas, the lack of true price competition leads to an escalation of unit costs and to considerable internal inefficiency. It also leads to the need for price or rate regulation, as in the case of the state judicial proceedings that set utility rates. These proceedings are characterized by state-level bureaucratic regulatory bodies that frequently are captured by the producers whose prices are being regulated.
In the case of school districts, cost-based reimbursement by states frequently is practiced for transportation, some special education programs, and other categorical programs. There needs to be a degree of regulation of prices, limits on eligibility and the services to be financed, and budget caps. It s obvious that expanding this practice any further is quite undesirable, even though it may be attractive to the providers, for the sake of preserving decentralized decision-making and internal cost efficiency.
The negative effects of endogenous prices and costs can be avoided if the prices on which the cost adjustments are based are kept outside the control of the school district and the state Government. This is true for prevailing wages throughout the community or for geographic differences in the COL. A COE index specific to the school district based on local teachers' and administrators' wages does not meet this test, although it is sometimes stressed that the portion of the budgets beyond school district control needs to be isolated for use in the COE (Chambers 1981, p. 61). Nor does a regional cost adjustment index based directly on teachers' wages meet the test. However, a COL index for the entire community or a COGs index based on prevailing wages would reflect conditions that are outside the school district's control. Where a county-wide price index is used, as is suggested later, the school district's maximum impact on county-wide prices for any or all items in the index can reasonably be assumed to be negligible because it is such a small part of the county-wide economy.
A similar cost-endogeneity problem arises when reimbursement is based on costs related to scale. Studies of school district costs frequently confirm the earlier finding by John Riew (1966) that the long-run average cost (LRAC) curve slopes downward to the point where the district reaches optimum scale, usually where it is large enough to have a high school with 800 to 1,000 pupils. This is followed by a long, flat section ("L-shaped" LRAC), then a rise showing unit costs in the gigantic megalopolis districts, such as Los Angeles, Detroit, and Chicago. Exceptions to this, of course (including some in studies without appropriate controls), are documented in the literature. This characterization is useful for making the basic point clear, that is, should the district be reimbursed for any possible differences in unit costs associated with scale?
The answer, based on the economic principles involved and not on the political clout of large and rural districts, is no. Major steps have been taken in most states to consolidate small rural districts to achieve lower unit costs and the economies of scale that accompany movement down the steep portion of the LRAC curve. At given levels of educational effectiveness, reimbursing districts for their higher costs due to inefficient scales or other inefficiencies would provide a short-run improvement for the children involved. In the long run, however, this would provide a clear disincentive to achieving greater efficiency.
The point is, regardless of economies of scale, inefficiencies (high unit cost at given levels of effectiveness, or learning per pupil), are included in school district cost functions. When these cost functions are estimated econometrically, using district enrollment as in the Chambers-Fowler teachers' cost index (TCI, 1995, p. 97), or when cost data are collected in other ways directly from school districts, such inefficiencies are included in the costs. If these costs or salaries are reimbursed, local school districts have no incentive to merge to reduce the cost involved and hence can manipulate the policy to avoid achieving greater efficiencies.
At the other end of the LRAC curve, if it does eventually reveal rising unit costs (at given educational effectiveness levels), this would help to explain why some large districts, such as Chicago, are experimenting with breaking up their large size in an effort to achieve greater efficiency by reducing the diseconomies of scale, as well as to secure greater parental involvement. Cost-based reimbursement for the diseconomies of large scale again endogenizes these costs in the long run and provides a disincentive to efforts to achieve greater cost effectiveness in these larger districts. (e.g., see Chambers and Fowler, 1995, p. 97, coefficient for DIST. ENROLLMENT > 100,000).
Avoiding Cost Endogeneity
As suggested above, cost endogeneity is one of the problems inherent in the approach that seeks to use either structural or reduced form (e.g., a TCI) estimates of school district demand and cost functions for making cost adjustments in funding formulas. This procedure may be justified, however, for analyses of cost differences, efficiency, and equity. It is quite consistent with the theory and is useful for empirical analysis of the behavior of school districts and what determines funding levels (Chambers 1980, p. 48; McMahon 1970), and subsequent articles that sought to estimate the cost and demand functions by simultaneous equation methods). It is the use of these econometric structural equation estimates of what are really the LRAC curves of the school district (Brazer and Anderson 1983) or of COE or TCI for making regional cost adjustments by states that entails the risk of endogenizing cost inefficiencies. Even though these econometric parameter estimates constitute statewide averages, they reflect teacher salaries and diseconomies of small scale that may imbed cost inefficiencies or be manipulated by state-level interest groups.
There is the possibility of using a broader COGs index largely based on prevailing wages, which now is being done in Ohio. In government, however, prevailing wages are of necessity, primarily wages that must be paid to maintenance personnel, since universal occupations such as retail trade and service positions must be used to maintain comparability across localities. One cannot include the salaries of microchip specialists or Wall Street brokers in the index. Since education is more human-capital intensive than most trade and service occupations, a COL index is more likely to approximate the true cost of living faced by teachers and administrators with comparable skills in different localities, and hence school district costs, than a COGs index.
We opt, therefore, for an index based on county-wide prices, even though a COE index has the distinct advantage of being specific to school purchases. Although this is the COE index's greatest strength, it is also its greatest weakness for purposes of making cost adjustments in school aid formulas. School district expenditures and state policies for reimbursing schools would not affect a geographic COL index or a cost-of-government-services index based on area-wide prevailing wages, since school district expenditures constitute less than 5 percent of local expenditures. It is these area-wide price factors that determine local input prices that in turn shift the long-run (and short-run) average cost curves of school districts vertically, consistent with the logic of unit costs in economic theory.
In particular, salaries, wages, and benefits, as indicated above, constitute about 80 percent of the total operating costs of schools, with salaries at about 64 percent and employee benefits comprising another 16 percent. They largely are determined by, and rise and fall with, the local prices of housing, heating, food, and health care. This occurs because school district personnel being hired for the first time or who are otherwise at the margin will move to districts offering more in real terms for comparable skills. The other 20 percent of school inputs are largely purchased locally at prices comparable to the purchases of teachers, administrators, and other school personnel. The same is true for the cost of competitive health care or other public services, which also tend to be service intensive. The purchasing power of payments under non-education-related entitlements, such as welfare or social security, would depend, in principle, even more heavily on the local cost of living.
The use of prices times quantities differentiates a geographic COL index from a geographic price index. Both indices give greater weight to those prices of items that appear large in the household budget (for example, annual housing costs) and less weight to the price differences for items that are a small part of household budgets (for example, salt). This gives greater weight to the costs of living (or producing) in the locality, such as the higher costs of heating or cooling, which also applies to the higher costs of heating or cooling school buildings. The objective of COL indices is to determine the price or cost of the same real living standard at different locations. If net savings are approximately zero, as they are over a typical life cycle, it is these living costs that will determine teacher salaries and benefits.
Issue 2: The Treatment of Nonmonetary Amenities
When using a geographic COL index, prevailing wages, or an education cost index to make regional cost adjustments, an important point to remember is that these indices do not remove the value of the differences in local amenities that are both relevant to the quality of life and production costs. Amenities include: access to forests, lakes, ocean beaches, and sunny climate; proximity to major cities and access to job opportunities; access to good schools and colleges; access to cultural opportunities; pleasant neighborhoods; and a lower local crime rate. The cost of living in a particular neighborhood may be higher, but the amenities may also be higher, thereby justifying the higher living costs. If local price levels are higher because of these nonmarket amenities, this will affect the cost of living and the prices of goods and services for school districts.
The need to consider adjustments for amenities is not unique to a COL index but is common to all market-based regional cost adjustments. A correction for some negative amenities is already included in both a COL index and a COE index for high heating, air conditioning, and transportation costs. On the other side of the coin, a further correction for positive amenities is included when using a COL index by choosing to use the county-wide rather than the local school district cost of living, since teachers are likely to choose to live outside of the highest-cost, highest-amenity districts, but nevertheless nearby. The TCI index based primarily on teachers' salaries at the school district level also makes this additional correction for amenities in that teachers and other employees are likely to be willing to accept somewhat lower salaries (that is, not pass on the higher living costs entirely to their employers) and to live nearby or absorb some of the monetary costs themselves, since they are receiving the nonmonetary benefits of the better environment.
Before using a COL index, even where it is county-wide, or a COE index to deflate living costs or school district costs, a qualitative judgment needs to be made about the presence or absence of extraordinary community-wide or on-the-job amenities for the locality in question. If these amenities are substantial, an additional adjustment based on this judgment needs to be made. The Illinois Task Force on School Finance (1993) recommended downward adjustment of geographic differences in the cost of living by about 30 percent to reduce any monetary distortions attributable primarily to extraordinary nonmonetary amenities. This may be too high when done across the board in this fashion, but there is no doubt that, in specific locations, nonmonetary amenity benefits exist that partially justify somewhat higher living costs.
Widely accepted, precise valuation of amenities for all areas is likely never to be practical.1 It is dependent to some extent on advances in the broader research in economics or nonmarket economics and shadow pricing (Bloomquist, Berger, and Hoehn 1988). In the last analysis, the amount of the higher living costs in those specific areas where significant amenities exist that are absorbed by the employees versus the employers will depend on the elasticity of demand for school district employees in those locations (Nelson 1993). If there are a large number of substitute employees available at a salary that covers the differential cost of living, then demand is elastic, and employees may have to absorb some of these higher costs and accept some of their total compensation in the form of nonmonetary amenities.
Issue 3: A Theoretically Clean Concept of Cost
Cost indices do not reflect pure differences in cost if they contain elements that really measure higher quality or that meas-ure other partly demand-related factors.
Quality or Effectiveness
For example, training adjustments, which reimburse districts that hire teachers with more or better training, may be justified on the grounds of providing incentives to districts to improve the education of their teachers. But as pointed out by Chambers (1981a p. 42), these are not true unit-cost-based COE indices. Such incentive payments also do not encounter the prior objection of encouraging increases in the price without also requiring improvements in the quality of these inputs.
Equity
Beyond this, COE and TCI indices have sought to include reimbursement for higher costs where there are larger numbers of less able or disadvantaged pupils in the pupil mix. Although the objectives for doing this may be worthy, and although some compensation for these local conditions does need to be provided, such reimbursement can be and usually is provided through the provision of statewide foundation levels, special pupil weightings, or separate categorical programs for poor, disabled, or other special-needs students. This paper takes the position that including these elements in a cost index obscures the meaning of a pure cost adjustment. "Costs" normally refers exclusively to the supply side, whereas the equation used to predict TCI is a reduced form that includes demand factors. The rationale for responding to special local educational needs comes from the demand side, that is, the statewide demand for public goods, including merit goods. The latter, seeking to equalize outcomes among pupils, is philosophically a Rawlsian positivist or humanitarian level of vertical equity that reflects public demand (Rawls 1977).
The Politics and Equity of Regional Cost Adjustments
Since prices and unit costs tend to be highest in high-income areas, both among states and within states (except for some higher-cost urban ghettoes), the net effect of any regional cost adjustment of federal or state grants will tend to redistribute state aid toward the higher-income suburban districts. Poverty and a higher incidence of need often will be found together, especially in the lower-income and rural areas. Therefore, legislators from the highest-income districts, with some exceptions, will tend to favor regional cost adjustments, and those from low-income and rural districts will tend to oppose such adjustments.
Some ways to compensate for the inequities that accompany sudden introduction of regional cost adjustments are needed. These are discussed in the conclusions section later.
To measure intrastate cost-of-living differences, one first must find the intrastate COL determinants for which data exist in the 1990 U.S. census and then obtain school district data on related differences in the costs of producing education or other public services. The following focuses on COL differences, since, as indicated above, if the results are ever to be used for regional cost adjustments, COL differences do not entail the problem of endogenizing costs.
This theory focuses on the structural demand, supply, and price of goods and services purchased by teachers and other public employees, which in turn largely determine the nominal salaries of those individuals with given skill levels, hence cost of education and other public services. The input prices shift the average and marginal cost curve for the production of public goods, and hence the market supply curves, vertically.
Differences in community-wide demands for all goods and services are determined largely by business demands for personnel and real estate, personal demands for products that depend on per capita personal income, and local tastes. Business demands and personal income reflect the production advantages or disadvantages in the locality, much as prevailing wages do. But personal income also reflects human capital and income from the financial assets of the wage and salary earners.
As demand rises, the prices of transportable goods such as clothing rise, but supplies then respond. Geographic differences in these prices do not remain large, although some do persist, reflecting local monopoly and different retailer costs. But supplies of other items, such as housing and land, and hence, housing costs are not perfectly elastic, and their prices rise.
The structural demand function in equation (1) below expresses the quantity of goods and services demanded in any particular locality (q) as a negative function of price, p (a1 < 0), a positive function of per capita income, Y (a2 > 0), and a positive function of population change, P, reflecting tastes for the locality (a3 > 0):
The supply price is a positive function of quantity, q (a4 > 0), an ambiguous function of population growth and/or density (a5 > or < 0), and a positive function of housing costs, H (a6 > 0), or other costs that are price inelastic.
When these demand and supply equations are solved simultaneously, eliminating q, and then multiplied through by the appropriate quantity weight, q, representing the standardized market basket of goods and services designed to maintain the same level of well-being in each area, the result is a reduced-form equation for the cost of living:
In equation (3), housing costs (H) and income (Y) logically can be expected to have a positive effect, and population change (P) and density have net effects that are indeterminate, since both operate in two directions (McMahon 1991, pp. 403-413; Nelson 1991, pp. 103-104).
It is not practical to estimate the underlying structural demand and supply equations by simultaneous equation methods, because many goods and services are included in each budget, and there are no separate measures for p and q. There are also many localities involved for which detailed price data are needed.
It is possible, however, to aggregate across commodities and to estimate using the reduced-form equation. The U.S. Bureau of Labor Statistics (BLS) took the lead in collecting price data and developing budget studies to determine weights for regional COLs based on these budget studies. Although this was discontinued in 1981 (U.S. Bureau of Labor Statistics 1982), it still provides a benchmark for a cross-check on work herein, which is based on more recent ACCRA data.
The concept behind the model is one of living costs of a middle-income family of four, which is probably reasonably typical of teachers' or school administrators' salaries. The BLS concept also includes larger weights for heating costs in the North, for example, or air conditioning costs in the South, not unlike heating and cooling costs or other supply-side costs faced by school districts, as mentioned above.
The model given by equation (3) first was estimated using the BLS data from 1981, the last year in which such data were collected, with the results as shown in equation (4) (Table 1). The results were as expected. The equation was tested over several years, with the conclusion that there was no evidence of significant change in the structure over time. The addition of climate, population levels, and other variables were tried separately but did not improve upon the explanation (McMahon 1991, pp. 434-38).
F. Howard Nelson estimated this model for states using 1988 ACCRA data for 178 localities (Nelson 1991), providing independent verification of the earlier results. However, Nelson's estimate also established significant differences among regions similar to those found earlier by McMahon and Melton (1978) using seemingly unrelated regression methods. New home value (NV), when added by Nelson, either is not significant or, in the West only, appears to be highly colinear with H (the median home value) and to cause its t-value to become highly insignificant. Population density, D, is not significant except in the East, where again it appears to be colinear with H, lowering the t-statistic for H (Nelson 1991, p. 106).
Therefore, equation (4) was re-estimated and is shown as equation (5) in Table 1, using the 1990 ACCRA data and values of H, Y, and P specific to each school district. There are no data on square miles and on population density by school district, so this equation cannot be used for a district-level index. The effect of this variable in Nelson's (1991) study appeared to be highly colinear with H, disturbing the result, so density was not included.
Tests were performed for hetero- oscedasticity, with all the Chi-squares indicating that the hypothesis that there is significant heteroscedasticity cannot be rejected. A correction for heteroscedasticity was made, with the results as shown in both equations (5) and (6) in Table 1. The dependent-variable heteroscedasticity method was used, estimating alpha by regressing the dependent variable times b times alphagainst the squared deviation. For equation (6), "= 0.0611 and its SE = 0.0025.2.2
------------------------------------------------------------------------------------------------ (4) COL 1981 = 0.182 H + 0.002 Y - 0.56 DP + 67.6 R2 = 0.552 (2.61) (1.63) (-2.22) (5) COL = 0.217 H + 0.025 Y - 0.0037 DP + 85.83 R2 = 0.532 & = 0.0658 (13.58) (0.25) (-0.006) n = 293 t = 24.10 (6) COL = 0.182 H + 0.015 Y + 0.078 DP + 89.14 (11.43) (0.16) (1.28) 1.59 NC - 3.91 S + 4.77 NE R2 = 0.591 & = 0.0611 (-1.34) (-3.46) (3.29) n = 293 t = 24.12
Partial correlation coefficients for equation (6):
0.56 (H); 0.01 (Y);
0.08 (DP); -0.08 (NC); -0.20 (S); 0.19 (NE); 0.95 (Constant)
Standardized coefficients (betas):
0.64 (H); 0.006 (Y); 0.06 (DP);
0.08 (NC); 0.18 (S); 0.15 (NE); 0 (Constant)
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Definitions
COL 1981 = the cost of living as measured by the Bureau of Labor Statistics
(1982) for 1981, the last year in which it was computed by the
Bureau.
COL = Cost of living in 1990, as measured using ACCRA (1993) data.
H = is the value of housing (the median value of an existing house).
Y = is the per capita personal income, in thousands of dollars.
DP = is the percent change in population for the preceding decade divided by 2 (or for 5 years, in the case of equation [4]).
NC, S, and NE = regional dummy variables, where 1 = North Central, 1 = South, and 1 = Northeast, respectively. 1 = West is omitted to allow for a numeraire.
With this much-larger ACCRA sample and recent data specific to school districts, the results in equations (4) and (5) are similar. The coefficient for H is about the same, as is the R2. The effect of income is slightly larger and less significant, but its effect is picked up by the median value of housing (value of a standardized house is not available by district) and in equation (6) by the Northeast dummy variable, so its true significance to geographic price differences should not be underestimated. The effects of change in population are smaller for 1990 than they were for 1981 following the large oil price shock, which resulted in a northern states recession and movement toward the oil-producing states. This suggests a modest structural change, but not one that is totally unexpected.
The coefficients of Y do not always reach the 0.05 level since its effect is picked up by H. Equation (6) was recalculated, dropping Y, with the result that the predictions were unaffected, as is suggested by its very small standardized regression coefficient (beta) in the bottom line of Table 1. Specifically, the regression on the ACCRA sample was recalculated, all the predicted COLs were recomputed, and the result was compared with both the prediction using Y and with ACCRA's direct measure of the cost of living. In more than 90 percent of the cases, the net difference to the prediction was less than three one-hundredths (0.03) of one percentage point, with and without Y in the regression. In all other cases, the difference was extremely small (less than 0.15 of one percentage point), except for Charleston, SC, and Greenville, SC. In these cases, the prediction with Y for Charleston was about 0.4 of a percentage point better than with the ACCRA actual measure and 0.5 of a percentage point worse for Greenville. 3 Estimates of the partial correlation and standardized regression (beta) coefficients shown in Table 1 indicate that Y is contributing almost nothing (less than 1 percent) to the total explanation. Its multicolinearity with H raises its standard error but does not bias the coefficient. For equation (6) without Y, NE and NC become a proxy for Y and take on slightly larger coefficients (4.79 and -1.48). The other coefficients are essentially unaffected (H = 0.183 and P = 0.080). Y is retained in equation (6) to gain the advantage of comparability with other results, equations (4) and (5) and earlier studies, since it is a logical part of the explanation and does not affect the outcome.
In further analysis of the regional dummy variables, since Nelson (1991) and McMahon and Melton (1978) found these regional differences to be significant earlier, this regression was then recalculated separately for each of the four regions by seemingly unrelated regression methods (not shown). The coefficients in the separate regional equations and the t-statistics are remarkably similar to those in equation (6). In fact, they are nearly identical, so equation (6) is chosen, with the regional dummy variables acting like shift factors. It has been corrected for heteroscedasticity, as mentioned above.
The 293 school districts in the ACCRA sample were then separated into 31 primary metropolitan statistical areas (PMSAs), 176 metropolitan statistical areas (MSAs), and 184 nonmetropolitan areas, and separate regressions were run for each group. However, this led to an inferior result, presumably because there is more homogeneity and less variation left to explain within each category.
The result shown in equation (6) is still the preferred result. It is used for prediction of the regional cost of living among all of the more than 14,000 school districts in the United States for which ACCRA cost-of-living data do not exist. Where the direct ACCRA measures do exist, they were used for these 293 localities. Equation (6) has the highest R2 (0.591, which is good for cross-sectional data) and the best t-statistics (except for Y).
It is the introduction of the regional dummy variables that causes the population change variable to become positive and more significant, as can be seen by comparing equations (5) and (6). Presumably, the movement out of the more heavily populated Northeast and North Central areas to the lower-cost South and higher-cost West areas allows the effect of population increases to be revealed in a more consistent fashion. The t-statistic for P still is below the 0.05 level. But the coefficient for P does reach the 90 percent confidence level (that is, the 0.10 level) and therefore contributes to the predictive accuracy of the result with a high degree of probability.
SOURCE: Actual: ACCRA (1994), 1990. Predicted: Eq.(6), using McMahon (1995).
Figure 1 compares the actual ACCRA COL values with the model-predicted cost of living values for the 293 sample districts. This is for the purpose of testing the predictive accuracy of the equation that will be used to predict the cost of living in the many thousands of school districts in the Nation for which ACCRA values do not exist. The school districts are ranged along the horizontal axis, from the lowest actual COL on the left to the highest on the right. Figure 1 reveals that the model does a reasonably good job of predicting the cost of living, with some underprediction in the lowest-COL districts and the largest errors tending to occur in the highest property value largest PMSAs, which are generally to the right on the graph. The largest prediction errors are for Philadelphia, for Kodiak Island in the Aleutian chain in Alaska, and for Fairbanks. In each of these cases, the ACCRA COL value is considerably above the predicted value, which is based primarily on the somewhat lower-than-average cost of housing in these places. The theory presented earlier would suggest that the cost of transportation to the distant parts of Alaska could help to explain the high prices and price inelasticity of all items (for resupply) and hence higher living costs in these (and similar) locations. Philadelphia has higher urban living costs but some relatively less highly valued housing. The prediction error for this city could reflect the high cost of urban living for low-income people with modest housing assessments.
Model-predicted values for differences in the cost of living among school districts within a state are illustrated in Table 2, and differences in the costs of education based on a variant of these are shown in Table 3. Differences among states in these costs are shown in Table 4.
Differences in the cost of living for the 15 highest-COL, 15 medium-COL, and 15 lowest-COL school districts in Illinois in 1990 are shown in Table 2, some in PMSAs, some in MSAs, and some in nonmetropolitan areas. First, the predicted cost of living is shown, and then, in the last column, it is normalized to a statewide mean of 100 within the state.
-------------------------------------------------------------------------------------------------------------------
Census Average value Per capita
School classification Population of county of housing income Predicted Normalized
County District of area 1990 1980 (in thousands) (in thousands) COL percent COL percent
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Highest cost of living
Du Page H-1 MSA* 781,666 658,858 $496.43 $72.05 179.86 178.09
Cook H-2 MSA 5,105,067 5,253,628 483.78 61.68 176.54 174.81
Lake H-3 MSA 516,418 440,397 453.85 31.77 171.47 169.79
Cook H-4 MSA 5,105,067 5,253,628 423.36 59.50 165.51 163.88
Lake H-5 MSA 516,418 440,397 397.29 41.67 161.31 159.72
Cook H-6 MSA 5,105,067 5,253,628 362.45 51.60 154.30 152.78
Cook H-7 MSA 5,105,067 5,253,628 339.93 49.07 150.16 148.68
Cook H-8 MSA 5,105,067 5,253,628 332.30 37.45 148.60 147.14
Lake H-9 MSA 516,418 440,397 316.97 36.07 146.60 145.15
Cook H-10 MSA 5,105,067 5,253,628 302.44 39.20 143.19 141.78
Cook H-11 MSA 5,105,067 5,253,628 283.68 38.39 139.76 138.38
Lake H-12 MSA 516,418 440,397 273.86 38.85 138.78 137.42
Lake H-13 MSA 516,418 440,397 270.49 51.23 138.34 136.98
Cook H-14 MSA 5,105,067 5,253,628 275.62 37.93 138.28 136.92
Du Page H-15 MSA 781,666 658,858 267.62 25.17 137.51 136.15
Middle cost of living
Tazewell M-1 MSA 123,692 132,078 54.40 13.12 97.49 96.53
Cook M-2 MSA 5,105,067 5,253,628 53.79 9.61 97.47 96.51
La Salle M-3 Nonmetropolitan 106,913 112,033 53.72 13.43 97.44 96.48
Sangamon M-4 MSA 178,386 176,070 52.24 13.11 97.40 96.44
Grundy M-5 Nonmetropolitan 32,337 30,582 51.20 12.38 97.38 96.42
La Salle M-6 Nonmetropolitan 106,913 112,033 53.49 11.88 97.38 96.42
Clinton M-7 MSA 33,944 32,617 51.67 10.54 97.37 96.41
Macon M-8 MSA 117,206 131,375 54.59 14.84 97.37 96.41
Menard M-9 MSA 11,164 11,700 53.27 13.29 97.36 96.40
St. Clair M-10 MSA 262,852 267,531 52.77 11.71 97.35 96.40
Washington M-11 Nonmetropolitan 14,965 15,472 53.07 12.07 97.35 96.40
McLean M-12 MSA 129,180 119,149 50.06 13.81 97.30 96.34
Peoria M-13 MSA 182,827 200,466 53.89 13.17 97.30 96.34
Cook M-14 MSA 5,105,067 5,253,628 52.55 13.02 97.29 96.33
Champaign M-15 MSA 173,025 168,392 51.18 10.45 97.23 96.27
Lowest cost of living
Mercer L-1 Nonmetropolitan 17,290 19,286 22.84 10.51 91.54 90.64
Pike L-2 Nonmetropolitan 17,577 18,896 21.84 10.70 91.50 90.60
Fulton L-3 Nonmetropolitan 38,080 43,687 23.02 10.64 91.48 90.58
Johnson L-4 Nonmetropolitan 11,347 9,624 15.98 8.91 91.40 90.50
St. Clair L-5 MSA 262,852 267,531 20.42 5.37 91.37 90.47
Pike L-6 Nonmetropolitan 17,577 18,896 20.40 9.80 91.22 90.32
Pike L-6 Nonmetropolitan 17,577 18,896 20.40 9.80 91.22 90.32
Pulaski L-8 Nonmetropolitan 7,523 8,840 22.23 7.37 91.20 90.31
Bureau L-9 Nonmetropolitan 35,688 39,114 20.56 7.64 91.15 90.25
White L-10 Nonmetropolitan 16,522 17,864 19.64 10.05 91.07 90.17
Alexander L-11 Nonmetropolitan 10,626 12,264 20.38 8.09 90.94 90.04
Jefferson L-12 Nonmetropolitan 37,020 36,558 17.08 9.10 90.94 90.04
Hancock L-13 Nonmetropolitan 21,373 23,877 19.38 9.78 90.89 90.00
Hancock L-14 Nonmetropolitan 21,373 23,877 18.05 9.36 90.65 89.75
Fulton L-15 Nonmetropolitan 38,080 43,687 17.59 10.17 90.48 89.59
* Metropolitan statistical area SOURCE: McMahon (1995).
--------------------------------------------------------------------------------------------- Average value Per capita Population of housing income Cost of Normalized County 1990 1980 (in thousands) (in thousands) education cost of education --------------------------------------------------------------------------------------------- Lake 516,418 440,397 $160.99 $22.55 $116.93 $121.17 Du Page 781,666 658,858 151.47 21.83 114.64 118.79 McHenry 183,241 147,897 110.04 17.03 109.08 113.03 Kane 317,471 278,405 124.36 17.74 108.44 112.37 Cook 5,105,067 5,253,628 125.21 19.07 107.36 111.24 Kendall 39,413 37,202 86.44 14.88 105.88 109.71 Will 357,313 324,460 90.51 15.04 104.28 108.05 Champaign 173,025 168,392 60.78 12.61 104.08 107.85 De Kalb 77,932 74,624 81.73 13.77 103.17 106.90 Grundy 32,337 30,582 74.46 14.30 102.48 106.19 Winnebago 252,913 250,884 67.43 15.10 101.73 105.41 Monroe 22,422 20,117 64.45 13.38 100.98 104.63 Boone 30,806 28,630 66.81 14.43 100.45 104.08 McLean 129,180 119,149 56.45 14.15 100.11 103.73 Rock Island 148,723 165,759 48.58 12.75 99.58 103.18 Sangamon 178,386 176,070 63.57 14.73 98.94 102.52 Woodford 32,653 33,320 56.55 13.57 98.66 102.24 St. Clair 262,852 267,531 64.02 13.61 98.57 102.14 Adams 66,090 71,622 38.30 10.45 98.40 101.96 Ogle 45,957 46,338 57.10 12.89 98.17 101.73 Clinton 33,944 32,617 55.01 10.99 98.11 101.66 Stephenson 48,052 49,536 50.02 13.32 97.73 101.27 Effingham 31,704 30,944 49.18 11.01 97.71 101.25 Menard 11,164 11,700 53.07 13.12 97.62 101.15 Kankakee 96,255 102,926 55.36 11.69 97.59 101.12 Madison 249,238 247,661 46.57 12.16 97.29 100.81 Jackson 61,067 61,649 46.51 10.68 97.15 100.67 Coles 51,644 52,260 41.36 11.22 97.13 100.65 Logan 30,798 31,802 52.18 11.24 96.93 100.44 La Salle 106,913 112,033 54.92 12.68 96.83 100.33 Piatt 15,548 16,581 44.73 12.95 96.79 100.30 Peoria 182,827 200,466 52.01 13.99 96.42 99.91 Jo Daviess 21,821 23,520 47.77 12.64 96.41 99.90 Morgan 36,397 37,502 38.42 11.99 96.39 99.88 Livingston 39,301 41,381 48.37 12.23 96.38 99.87 Tazewell 123,692 132,078 50.52 14.03 96.35 99.84 Lee 34,392 36,328 45.25 12.39 96.20 99.69 Washington 14,965 15,472 44.74 11.35 96.09 99.57 Putnam 5,730 6,085 46.28 13.10 96.03 99.50 Randolph 34,583 35,652 44.52 11.34 96.02 99.50 Douglas 19,464 19,774 43.68 11.19 95.98 99.46 Jersey 20,539 20,538 44.49 10.68 95.91 99.38 De Witt 16,516 18,108 46.07 12.66 95.75 99.22 Marshall 12,846 14,479 44.95 12.63 95.71 99.18 Bureau 35,688 39,114 37.86 11.18 95.57 99.03 Whiteside 60,186 65,970 44.51 11.83 95.48 98.94 Jefferson 37,020 36,558 41.35 11.09 95.44 98.89 Wabash 13,111 13,713 41.55 10.97 95.39 98.84 Perry 21,412 21,714 40.27 11.24 95.31 98.76 Macon 117,206 131,375 49.19 14.41 95.31 98.76 Williamson 57,733 56,538 38.75 10.85 95.19 98.64 Moultrie 13,930 14,546 39.72 11.77 95.07 98.51 Ford 14,275 15,265 38.24 12.84 95.02 98.46 Henry 51,159 57,968 38.41 11.89 95.01 98.45 Macoupin 47,679 49,384 38.92 11.31 94.98 98.42 Johnson 11,347 9,624 32.75 9.21 94.92 98.36
-------------------------------------------------------------------------------------------- Average value Per capita Population of housing income Cost of Normalized County 1990 1980 (in thousands) (in thousands) education cost of education -------------------------------------------------------------------------------------------- Jasper 10,609 11,318 $40.34 $10.24 $94.89 $98.32 Bond 14,991 16,224 34.67 10.40 94.84 98.28 Iroquois 30,787 32,976 38.93 11.29 94.74 98.17 Cumberland 10,670 11,062 38.88 10.52 94.68 98.10 McDonough 35,244 37,467 32.06 10.25 94.63 98.06 Vermilion 88,257 95,222 39.63 11.54 94.60 98.02 Union 17,619 17,765 37.08 10.30 94.57 97.99 Carroll 16,805 18,779 40.11 12.12 94.56 97.98 Knox 56,393 61,607 38.37 11.99 94.35 97.76 Christian 34,448 36,446 36.14 11.38 94.33 97.74 Shelby 22,261 23,923 34.70 11.06 94.25 97.66 Montgomery 30,728 31,686 33.82 10.58 94.21 97.62 Mercer 17,290 19,286 34.10 12.06 94.19 97.60 Marion 41,561 43,523 33.26 10.79 94.14 97.54 Massac 14,752 14,990 30.88 10.10 94.13 97.54 Schuyler 7,498 8,365 36.62 10.07 94.04 97.45 Crawford 19,464 20,818 33.03 11.17 94.01 97.41 Richland 16,545 17,587 33.23 11.84 94.01 97.41 Wayne 17,241 18,059 36.52 10.44 93.99 97.39 Calhoun 5,322 5,867 36.68 9.51 93.92 97.32 Clark 15,921 16,913 32.81 11.16 93.89 97.29 Fayette 30,893 22,167 31.57 10.13 93.79 97.19 Edgar 19,595 21,725 33.14 11.42 93.74 97.13 Mason 16,269 19,492 34.44 11.12 93.68 97.07 Edwards 7,440 7,961 33.70 10.95 93.68 97.07 White 16,522 17,864 28.84 10.67 93.53 96.92 Gallatin 6,909 7,590 33.42 10.44 93.52 96.91 Brown 5,836 5,411 29.79 8.89 93.51 96.90 Saline 26,551 28,448 32.01 9.73 93.50 96.89 Scott 5,644 6,142 32.07 10.46 93.44 96.83 Hancock 21,373 23,877 30.47 10.98 93.42 96.80 Warren 19,181 21,943 33.28 10.80 93.39 96.77 Henderson 8,096 9,114 32.94 10.43 93.35 96.73 Cass 13,437 15,084 33.27 10.99 93.32 96.70 Lawrence 15,972 17,807 32.17 10.29 93.28 96.66 Clay 14,460 17,807 30.20 9.18 93.18 96.55 Fulton 38,080 43,687 28.71 10.33 93.11 96.48 Pope 4,373 4,440 29.39 8.98 93.10 96.47 Stark 6,534 7,389 31.65 10.87 93.05 96.42 Franklin 40,319 43,201 30.45 10.10 93.01 96.38 Greene 15,317 16,661 30.87 10.19 92.78 96.14 Hamilton 8,499 9,172 28.37 10.00 92.66 96.02 Pike 17,577 18,986 24.81 10.22 92.60 95.95 Hardin 5,189 5,383 25.26 8.36 92.22 95.56 Pulaski 7,523 8,840 23.73 9.14 91.41 94.72 Alexander 10,626 12,264 22.58 8.53 91.27 94.57 ------------------------------------------------------------------------------------------------
unweighted mean,statewide 100
SOURCE: McMahon (1995).
It is not possible to show all estimated values, even for one state, because there are about 900 school districts in Illinois alone and 14,300 in the nation. However, the patterns that can be observed in Table 2 are typical for other states. The complete data set reporting the cost of living and per capital personal income for school districts nationwide, as well as county and state cost indices, is available on diskette from NCES' National Data Resource Center (NDRC).4
For Illinois, (see Figure 1), the highest living costs are predicted for Du Page and Lake counties, which are high-income suburbs of Chicago, with values ranging from about 40 to 30 percent (or in the most extreme case, 78 percent) above the statewide norm. All of the predicted values of the cost of living substitute the ACCRA COL values, where they exist, since the latter are based on direct measures of actual price data in those localities. However, the ACCRA sample in a particular county is sometimes not representative, however. In these cases, the predicted values based on the census data for all school districts within the county can serve as a cross-check.
It will be noted in some school districts in Du Page County and Lake County, the average value of houses ranges from $268,000 to $496,000. It is doubtful in these ases that the district's teachers, school administrators, or maintenance personnel live within the district, even though in some districts this is a requirement for employment. In this event, although the cost of living may be high, the costs associated with the provision of education in those districts is not as high. Similarly, the true costs in some of the lowest-COL districts may be understated, since teachers who agree to teach there also live outside the district.
When considering intrastate differences in the cost of education based on inputs purchased by school districts, it will be assumed that school personnel normally live not only within the district but also in nearby districts within the same county, and that school districts also purchase some of their other inputs within the county, but outside of the district. Table 3 presents a measure of the cost of living within the county that also can be considered to be an estimate of the cost of education for the school districts in that county. The predicted values are based on the housing values in all school districts within each county, the county-wide per capita personal income, and population change.
The county-wide predicted cost of living (or educational cost), however, is computed by obtaining a population-weighted mean of the COL measures for each school district within that county. Based on this, the normalization procedure then computes an unweighted mean, which is more meaningful in this case than a weighted mean, for reasons that are discussed below. Because of the effect of this county-wide population-weighted averaging, the normalized educational cost differences among school districts are not as extreme, ranging from 121.17 in the districts in the highest-cost counties to 94.57 in the school district facing the lowest costs.
Note that in Column 1, in both Tables 2 and 3, the highest COLs and school district costs are not in PMSAs, but instead in suburban MSAs, and the lowest costs are generally found in the nonmetropolitan areas.
Differences in costs among states based on the local COL for all school districts within each state, with the averages weighted by the population of each school district, are shown in Table 4. These then are normalized to relate to a nationwide base of 100 in the last column.
The normalization procedure for school districts (Table 2), for counties (Table 3), and for states (Table 4) takes the simple unweighted mean of all units within each larger jurisdiction as a base to get the normalized index, each index number relating to a base of 100 for the jurisdiction. This is because it is more meaningful to express the index for all persons living within a given county (or other unit) in relation to the costs faced by persons living within other counties, and not in relation to all persons in the state, many of whom may live within the same (larger) county. This is in sharp contrast to the county-wide COL index, which is a population-weighted mean of the school districts within that county, and to the statewide index, which in effect weights the index for each county by its population.
Considering the results for the cost of living by states, the variation among states using these new census data is not identical but similar to estimates made previously (McMahon 1991). It is not precisely identical, because this new estimate is based on the weighted means of very specific school-district-level data, whereas earlier estimates started with county-wide data.
SOURCE: McMahon (1995).
------------------------------------------------------- Predicted Normalized State cost of living cost of living ------------------------------------------------------- United States 105.12 100.00 Alabama 95.77 91.11 Alaska 115.66 110.03 Arizona 103.68 98.63 Arkansas 93.47 88.92 California 126.87 120.69 Colorado 103.21 98.19 Connecticut 127.77 121.55 Delaware 113.07 107.56 District of Columbia 116.17 110.51 Florida 103.25 98.22 Georgia 99.18 94.35 Hawaii 133.22 126.73 Idaho 99.16 94.33 Illinois 105.24 100.11 Indiana 97.78 93.02 Iowa 96.66 91.95 Kansas 97.23 92.49 Kentucky 96.74 92.03 Louisiana 95.46 90.81 Maine 110.32 104.95 Maryland 116.85 111.15 Massachusetts 125.25 119.15 Michigan 99.92 95.06 Minnesota 101.00 96.08 Mississippi 93.86 89.29 Missouri 98.45 93.65 Montana 99.50 94.65 Nebraska 94.54 89.93 Nevada 108.67 103.38 New Hampshire 118.98 113.18 New Jersey 124.48 118.41 New Mexico 100.40 95.51 New York 122.54 116.57 North Carolina 97.96 93.19 North Dakota 96.59 91.88 Ohio 101.11 96.18 Oklahoma 94.20 89.61 Oregon 102.61 97.61 Pennsylvania 111.38 105.95 Rhode Island 113.73 108.19 South Carolina 97.29 92.55 South Dakota 94.15 89.56 Tennessee 95.90 91.23 Texas 97.59 92.84 Utah 101.95 96.98 Vermont 107.31 102.08 Virginia 112.60 107.12 Washington 107.86 102.61 West Virginia 94.34 89.74 Wisconsin 99.81 94.95 Wyoming 100.29 95.41 -------------------------------------------------------
SOURCE: McMahon (1995).
Table 4 shows the variation in the cost of living, which on a statewide basis is also one estimate of the variation in the cost of education, to be from 126.73 in Hawaii to 89.29 in Mississippi. As one might expect, Connecticut, New Jersey, California, and Massachusetts are high-cost areas, and Mississippi, West Virginia, and South Dakota are low-cost areas.
----------------------------------------------------------------------------- School COL Predicted Normalized Location Type District ACCRA COL COL ----------------------------------------------------------------------------- Anchorage MSA A $110.62 $103.53 Bethel Non-Met B 110.86 94.40 Bethel Non-Met C 99.64 93.26 Bethel Non-Met D 97.94 91.67 Bristol Bay Non-Met E 108.92 101.94 Bristol Bay Non-Met F 96.71 90.52 Dillingham Non-Met G 108.77 101.80 Fairbanks North Non-Met H 105.21 98.47 Fairbanks North Non-Met I 129.0 129.00 120.74 Haines Non-Met J 105.86 99.07 Juneau Non-Met K 133.0 133.00 124.48 Ketchikan Gateway Non-Met L 146.4 146.40 137.02 Kodiak Island Non-Met M 145.0 145.00 135.71 Matanuska-Sustina Non-Met N 107.36 100.48 Nome Non-Met O 98.08 91.80 Nome Non-Met P 105.53 98.77 Sitka Non-Met Q 111.53 104.38 Skagway-Yakutat Non-Met R 101.89 95.36 Southeast Fairbanks Non-Met S 96.47 90.29 Wade Hampton Non-Met T 104.30 97.62 ----------------------------------------------------------------------------
Unweighted mean, statewide 106.84 100.00
NOTE: ACCRA = American Chamber of Commerce Research Association. COL = cost of living.
SOURCE: McMahon (1995).
Table 5 illustrates how, for a statewide index calculation (for Alaska), a population-weighted index is necessary. The higher cost indices for Anchorage, Fairbanks, Juneau, Ketchikan, and Kodiak are swamped by the lower-cost, largely rural areas, which are more numerous unless a population-weighted index is used for the state as a whole.
National estimates of intrastate geographic differences in the cost of living among school districts and of education cost differences among counties can be based on the 1990 census data that the NCES has mapped for each school district.5 Living costs range from about +78 percent in the highest school district MSAs to -11 percent in the lowest-cost nonmetropolitan school districts within each state. Education cost differences based on COL differences for the wider county-wide population-weighted average of the more localized school district areas are not as large (+21 percent to -6 percent in Illinois) as might be expected.
The rationale for using the COL of persons typical of teachers and school principals as an estimate of education costs is that salary costs plus benefits constitute about 80 percent of school budgets and are correlated with the rest. Also county-wide prices are not subject to manipulation by local districts or state-level interest groups where a cost index is being considered for use in making regional cost reimbursements. That is, a county-wide index avoids using costs such as teacher salaries that are endogenous to each district, which would likely encourage the school district to raise these costs when requested by employee groups, or not consolidated if a TCI were used, since they would be reimbursed. This is characteristic of cost-based reimbursement, which encourages not only higher prices, but also overutilization and other inefficiencies. A county-wide index also does not involve equity factors related to special local education needs. In economic theory, these needs and the degree of response to them are largely determined on the demand side and should be the focus of a separate policy decision concerning pupil weightings. A government-services index tends to be less relevant for schools, since it reflects prevailing wages of largely blue-collar service workers, whereas education is more human-capital intensive.
The use of any cost indices to make regional cost adjustments of state aid payments to local schools and welfare payments, for example, without making compensating changes in the financial transfer mechanisms, raises other kinds of problems. To preserve equity between low-income rural districts and the wealthier suburbs when regional cost reimbursements are introduced, it would be appropriate to move to a more economically sensible measure of effort in the school aid formula than the property tax mileage rate applied to equalized assessed property valuations. Property is a very narrow and inadequate measure of total family income or wealth in an industrialized society, so use of this measure, even though it is a "tax handle," leads to gross distortions (McMahon 1978). Per capita personal income is a much better measure of true ability to pay, since it reflects the earnings from human capital and interest and profits from financial assets, as well as real estate. Measures of personal income per capita from the 1990 census as in Table 2 are available in McMahon (1995) for every school district in the nation, based on the NCES mapping.
It is suggested, therefore, that the method presented here be used to explore equity in expenditure per pupil, further refinements to nonmonetary amenities, and efficiency together with school district budget data. At the same time, other features of the aid formula can be reviewed and corrected, particularly the measure of local fiscal effort. Eventually, consensus will be reached on the most appropriate method for measuring the cost of education for making regional cost reimbursements in aid formulas and, the author hopes, simultaneous changes in measures of local effort that more accurately reflect households' true ability to pay. Together, these can contribute to greater accuracy in measurement, incentives for efficiency, and greater pupil equity.
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[Estimating the Costs of an Educational Voucher System] 
[Cost of Measuring and Providing Opportunity to Learn]