Jay G. Chambers
American Institutes for Research
About the Author
During the late 1970s and early 1980s, Dr. Jay G. Chambers served as the Associate Director of the Institute for Research on Educational Finance and Governance (IFG) at Stanford University, a national R&D center funded by the National Institute of Education. He is a nationally recognized expert in the analysis of patterns of resource allocation and cost variations in educational organizations and in recent years has played a major role in cost analyses of special education programs. He also was the principal investigator for A Study of Chapter 1 Resources in the Context of State and Local Resources for Education, conducted for the U.S. Department of Education, Office of Policy and Planning.
Dr. Chambers has directed two major school finance reform studies in Illinois and Alaska; he has directed a large-scale cost analysis of early intervention services in California; and, he has completed a cost analysis of migrant summer school programs.
Dr. Chambers served as an expert witness in the Levittown school finance reform case in New York State. He has also directed a major comparative study funded by the National Institute of Education on differences in the patterns of resource allocation and decision-making in public and private schools.
Currently, Dr. Chambers is Co-Director of the Center for Special Education
Finance (CSEF) at the American Institutes for Research (AIR).
Public School Teacher Cost
Differences Across the United States:
Introduction
to a Teacher Cost Index (TCI)
Jay G. Chambers
American Institutes for Research
Since the mid-1970s, a number of studies have focused on the development of methodologies and empirical estimation of a cost-of-education index (CEI).1 A CEI is designed to adjust for differences in the purchasing power of the educational dollar in different locations. Because personnel expenditures account for about 80 percent of local school budgets, most of the previous studies of education cost differences have focused attention on the analysis of personnel costs.2 Thus, the development of an adequate methodology for addressing the differences in the costs of personnel would aid in the development of a CEI. But how are teacher cost differences defined?
Most educators readily acknowledge that school districts in different geographic locations encounter different costs in acquiring and retaining teachers with similar qualifications. That is, teacher salaries reflect not only the cost-of-living and desirability of a given geographic location, but also a school district's preference for teacher qualifications (e.g., educational preparation or experience levels). The studies of personnel cost differences address the following question:
How much more or less does it cost in different jurisdictions to recruit and employ school personnel with similar characteristics into similar jobs and job assignments?
Accurately measuring geographic cost differences has been one of the pre-eminent measurement challenges in education. The challenge of this task lies in identifying and measuring the factors that define similar characteristics and similar jobs, as well as those factors that reflect differences in the cost-of-living and desirability across geographic locations.
Until recently, no national data have been available to support a comprehensive analysis of the variations in teacher salaries. With the advent of the Schools and Staffing Survey (SASS), which was first conducted during the 1987-88 school year by the (NCES), a data source emerged that supports the empirical analysis required to develop a national, geographical teacher cost index (TCI).
The study described in this paper draws on a sample of over 40,000 public
school teachers, derived from the SASS database for school year 1990-91, to
conduct the statistical analysis of teacher salaries and cost. In conjunction
with the SASS data, the analysis also uses data from the Census Bureau (e.g.,
population and population density), the Bureau of Labor Statistics (BLS) (e.g.,
unemployment rates), the Federal Bureau of Investigation (FBI) (e.g., crime
rates), and the National Climatic Data Center (NCDC) (e.g., climatic
conditions).
The importance of developing a CEI is that it may be used in two significant ways. First, it may be used to adjust educational expenditure or teacher salary data for differences in the purchasing power of the educational dollar in different communities. For the most part, published information on educational expenditures and salaries of school personnel across states and other local jurisdictions is based on actual reported values.3 However, because of the existing variations in the costs of comparable educational resources across these jurisdictions, it is difficult to make comparisons of the level of educational services being provided in different locations. In order to make such comparisons, it is necessary to adjust reported data on average educational expenditures and teacher salaries for differences in the purchasing power of the educational dollar across jurisdictions.
Second, in addition to their importance for reporting expenditure and
salary data, such cost-of-education adjustments play a significant role in
analyses of the demand for educational services and inputs across communities.4 Studies of educational resource allocation have commonly had
to use measures such as average teacher salaries or other proxy variables (e.g.,
opportunity wages in other occupations) to reflect relative costs of school
resources. Unfortunately, variations in average teacher salaries reflect both
variations in costs, as well as the qualifications of the teaching staff.
Analysis of demand for school inputs requires an index of the relative cost of
comparable inputs. The importance of accurately controlling for costs in
these analyses is that ultimately such studies are often focused on addressing
the impact of changes in state or federal policies or funding formulas. Without
the ability to control for the impact of input costs on choices of local school
district officials, it is not possible to isolate the effects of state and
federal policies on patterns of resource allocation in local schools.
Barro (1992) developed a model that adjusts the variations in average teacher salaries for variations in the levels of education and experience. Other researchers (e.g., McMahon and Chang 1991) have suggested using a cost-of-living adjustment to account for variations in the purchasing power of the education dollar. Unfortunately, neither of these alternatives is adequate. To capture such variations in teacher costs requires a comprehensive analysis of the patterns of teacher compensation. It requires a model that portrays the complexities of the employment transaction between an individual teacher and the school district: that is, one that accounts for school district preferences for teacher qualifications and individual teacher preferences for working and living conditions in local communities.
The model used for the development of the TCI--referred to by economists as the hedonic wage model--provides a comprehensive conceptual framework for understanding and sorting the various factors that underlie variations in the patterns of teacher salaries. This model is well suited to isolate the impact of regional amenities and costs of living on teacher salaries while controlling for various teacher and job characteristics.
In an earlier paper, Chambers (1981a) described the hedonic wage model as follows:
The intuitive notion underlying this theoretical structure is that individuals care both about the quality of their work environment as well as the monetary rewards associated with particular employment alternatives, and that they will seek to attain the greatest possible personal satisfaction by selecting a job with the appropriate combination of monetary and non-monetary rewards. Similarly, employers are not indifferent as to the characteristics of the individual to whom they offer particular jobs. The result of these simultaneous choices is the matching of individual employees with employers. It is the result of this matching process itself that reveals implicitly the differential rates of pay associated with the attributes of individual employees and the working conditions offered by employers. More formally, it is the supply of, and demand for, individuals with certain personal attributes to any particular kind of job assignment that determines the equilibrium wages of labor as well as the implicit market prices attached to the personal and job characteristics.
The implicit relationship observed between wages and the personal and job characteristics of individuals is referred to as a hedonic wage index. The word hedonic literally refers to the physical and psychic pleasures that one can derive from engaging in certain activities. In the context of labor markets, the word hedonic refers to the satisfactions or utility derived by employees from the characteristics of the work place and the profits or the perceived productive value derived by employers from the characteristics of employees they assign to certain jobs. The hedonic wage index permits one to decompose the observed variation in the wages paid to labor into the dollar values attached to each unit of the personal and workplace characteristics (p.51).
Ordinary least squares regression is used to estimate the parameters of the model. The estimated coefficients provide a foundation for determining the wage premiums (positive or negative) associated with particular personal, job, or location characteristics.
This analysis reveals wage premiums for attributes of the workplace and the employee that are not commonly included in regular salary schedules. For this reason, the coefficients are said to provide estimates of the implicit prices of particular attributes. The patterns of implicit prices for worker attributes result from the process of matching the combination of teacher characteristics embodied in a given individual teacher to the job characteristics embodied in a given job assignment. The employment of teachers in particular schools represents a process of choice for the teachers (on the supply side) and for the school district decision-makers (on the demand side) that reveals the trade-offs among the teacher attributes and job characteristics. These trade-offs provide the basis for the set of implicit prices.
The TCI analysis presented here accomplishes two primary objectives. First, the TCI component extends the analysis of teacher salaries to include specific variables that reflect the costs of living and the amenities of the jurisdictions in which public school systems are located. Second, the empirical analysis of teacher salaries is used to estimate a TCI for each school district in the United States.
The TCI is designed to reflect variations in teacher salaries associated with factors that are outside the control of local school decisionmakers. Thus, calculation of the TCI requires controlling for (i.e., holding statistically constant) the differences in teacher qualifications and job assignments, while simulating the effects of the factors that reflect differences in costs of living and attractiveness of local jurisdictions. The analysis of teacher costs presented in this paper controls for two major categories of teacher and job attributes:5
How do teacher salaries vary with factors outside local control? These cost factors encompass variations in the costs of living, competitiveness of the labor markets, levels of crime, quality of the weather, availability of alternative job opportunities, and other attributes of the regions and districts that affect their attractiveness as places to live and work. It is anticipated that less attractive jurisdictions will have to pay relatively higher salaries to attract comparable teachers.
Highlights of the variations in teacher salaries in relation to each of the cost factors are presented below.
The differences in teacher salaries associated with these variables are cost differences. They reflect the variations in salaries paid to comparable teachers working in similar job assignments across local school systems. That is, all else equal, districts in more urbanized settings tend to pay higher relative salaries for comparable teachers. In addition, districts located in faster growing regions, regions with climates characterized by colder temperatures and greater quantities of snowfall, and regions with higher rates of crime pay higher relative salaries to teachers, holding all else constant. At the same time, districts in more remote regions pay somewhat higher-than-average salaries to compensate for reduced access to some of the amenities of living in more urbanized areas.6
Table 1 presents state-by-state and overall patterns of variation in the TCI. It designates the number of districts for which data are included, along with the weighted mean, standard deviation, and minimum and maximum values of the index within each state. The overall mean value of the TCI for the United States is scaled to a value of 100. This means that the index is scaled so that the average student attends a district with a TCI value of 100. The variation in the TCI across the United States ranges from a low of 53 to a high of 137. This means that teacher costs for a district located in the lowest cost region of the United States are 53 percent of those faced by the district serving the average student. The highest cost district pays 37 percent higher teacher costs than the district serving the average student. The lowest cost region of the United States is located in South Dakota, while the highest cost region is located in Alaska. Another way of looking at these numbers suggests that districts in the highest cost regions of the country pay 2.6 times (= 137/53) as much to place comparable teachers in comparable classrooms and schools as districts in the lowest cost regions of the country. The standard deviation of the TCI is 11.7 percent; that is, most of the districts are within plus or minus 11.7 percent of the average.
Table 1. State-by-state estimates of the teacher cost index (TCI)
--------------------------------------------------------------------------------------------------- Descriptive statistics on TCI ---------------------------------------------- Number of Total Standard State districts enrollment Mean deviation Minimum Maximum --------------------------------------------------------------------------------------------------- United States 14,494 40,116,02 100 11.7 53 137 Alaska 36 94,330 114 8 96 137 Alabama 129 725,115 88 5.4 76 97 Arkansas 322 431,490 87 4.1 78 97 Arizona 205 630,816 97 6.9 84 106 California 991 4,813,64 109 7.6 77 119 Colorado 176 573,985 99 7.6 71 116 Connecticut 160 453,468 114 3.9 103 118 District of Columbia 1 80,694 107 0 107 107 Delaware 16 96,384 102 4.2 96 106 Florida 67 1,862,18 95 5.4 79 107 Georgia 184 1,150,17 92 8.8 71 106 Hawaii 1 159,285 92 0 92 92 Iowa 429 483,176 90 4.7 76 98 Idaho 110 217,555 94 4.7 72 102 Illinois 942 1,795,47 107 13.1 72 120 Indiana 295 937,324 98 6.3 80 106 Kansas 302 436,494 88 7.6 58 99 Kentucky 176 630,091 89 5.5 76 99 Louisiana 65 774,724 85 3.9 74 92 Massachusetts 269 730,024 114 3.8 88 120 Maryland 22 669,620 104 5.7 86 112 Maine 215 208,599 104 4.4 95 111 Michigan 552 1,560,80 105 7.5 86 115 Minnesota 429 751,268 99 8.9 73 111 Missouri 538 805,029 95 9 71 107 Mississippi 149 491,684 84 3.8 74 91 Montana 503 148,411 94 5.2 76 119 North Carolina 133 1,084,489 93 5.1 80 101 North Dakota 262 117,531 89 5.3 68 111 Nebraska 728 269,106 90 6.9 58 118 New Hampshire 148 163,778 109 3.9 101 113 New Jersey 534 1,007,16 113 4.5 96 119 New Mexico 86 296,471 90 5.2 74 97 Nevada 17 201,316 95 4.1 87 108 New York 627 2,361,04 115 12.7 89 129 Ohio 610 1,766,73 102 6.5 83 113 Oklahoma 586 568,711 87 4.3 68 95 Oregon 292 483,507 100 6.5 72 108 Pennsylvania 499 1,629,157 106 8 86 120 Rhode Island 36 136,086 111 1.7 108 112 South Carolina 80 451,308 90 5.9 79 102 South Dakota 172 125,316 87 4.4 53 92 Tennessee 132 819,229 90 4.8 77 98 Texas 1,042 3,380,80 93 8.3 70 106 Utah 40 444,832 97 4.4 73 110 Virginia 129 984,702 96 8.2 75 108 Vermont 236 90,215 101 2.7 95 108 Washington 294 810,011 106 9.1 75 116 Wisconsin 424 796,114 99 6.7 85 109 West Virginia 54 318,577 86 3 78 93 Wyoming 49 97,976 88 4.4 78 107 ----------------------------------------------------------------------------------------------------
SOURCE: U.S. Department of Education, , Schools and Staffing Survey, 1990-91.
The five states with the highest average teacher costs are, in order from highest to lowest, New York (115), Massachusetts (114), Connecticut (114), Alaska (114), and New Jersey (113). Four of these states are located in the northeastern portion of the United States. Calculations of standard errors indicate that the differences among the top five states are not statistically significant.7
The five states with the lowest average teacher costs are, in order from lowest to highest, Mississippi (84), Louisiana (85), West Virginia (86), Oklahoma (87), and South Dakota (87). Four of these states are located in the South (using the state classification scheme provided in SASS). Once again, based on the standard errors of these estimates, none of the differences among the lowest five states is statistically significant.
The five states with the largest within-state variation in TCI
values (based on the size of the standard deviations presented in the table) are
Illinois, New York, Washington, Missouri, and Minnesota. The states with the
lowest within-state variation8 are Rhode Island,
Vermont, West Virginia, Massachusetts, and Mississippi. In general, states with
larger numbers of school districts tend to have a larger variance. Among the
five states that exhibited the highest within-state variation, the average
number of districts per state is 566, while the average number of districts in
the five states with the lowest within-state variation is 149.
Table 2 presents the descriptive statistics for the TCI broken down by region of the United States, level of per-pupil revenue in the district, population of the metropolitan area or county of location, distance from the central city, district enrollment, type of city, and percentage of students living in poverty.
Table 2. --The TCI, by region, per-pupil revenue, metropolitan population, distance from the nearest central city, district size, type of city, and percentage of children living in poverty
------------------------------------------------------------------------------------------------------------- Descriptive statistics on TCI -------------------------------------- Number of Total Standard Category districts enrollment Mean deviation Minimum Maximum ------------------------------------------------------------------------------------------------------------- Region Northeast 2,724 6,779,53 112 9.7 86 129 Midwest 5,683 9,844,37 100 10.4 53 120 South 3,287 14,519,98 92 7.8 68 112 West 2,800 8,972,13 104 9.7 71 137 Per-pupil revenue Less than $4,000 3,695 8,903,340 91 8.1 65 119 4,0006,000 7,122 22,072,043 99 10.0 53 120 6,0008,000 2,316 7,257,311 110 10.9 58 129 8,00010,000 797 1,382,471 111 7.6 62 123 More than 10,000 564 500,862 114 7.4 65 137 Metropolitan population Less than 5,000 686 166,555 84 9.2 53 119 5,000-20,000 3,341 2,521,938 85 6.3 66 137 20,000-50,000 2,999 4,170,191 88 5.8 72 123 50,000-100,000 1,519 3,201,822 92 5.9 78 112 100,000-500,000 2,458 8,348,309 95 7.2 73 119 500,000-1,000,00 1,188 5,578,574 100 7.8 85 118 More than 1,000, 2,303 16,128,638 110 8.7 84 129 Distance from the nearest central city Less than 10 miles 2,018 15,477,412 102 9.9 73 120 10-20 2,369 8,832,81 107 11.9 68 129 20-40 3,973 8,186,29 97 10.5 68 120 40-80 3,770 5,695,55 90 7.9 58 119 80-160 1,885 1,576,68 90 7.7 53 119 More than 160 479 347,281 100 11.2 65 137 District size Less than 500 students 5,154 1,103,979 91 10.3 53 137 5011,000 2,370 1,712,255 94 10.3 63 134 1,0015,000 5,374 12,270,304 98 11.3 71 137 5,00110,000 915 6,317,093 99 11.2 75 123 10,00125,000 480 7,135,233 100 10.4 72 119 25,00150,000 120 4,081,084 100 9.5 73 119 50,001100,000 44 2,960,552 100 7.8 85 120 More than 100,00 21 4,523,514 111 12.2 91 129 Type of city Large central city 811 8,579,610 108 10.9 83 129 Mid-size city 806 9,187,913 97 8.5 73 119 Urban fringe of large city 1,287 5,921,311 110 7.7 81 120 Urban fringe of mid-size city 810 2,861,090 99 10.0 71 118 Large town 418 1,154,387 92 8.5 58 119 Small town 4,158 8,812,909 93 9.9 70 137 Rural 6,174 3,596,914 92 8.7 53 137 Percentage of children living in poverty Less than 10% 4,808 11,733,121 105 8.5 62 134 10-20 4,834 13,299,197 97 9.0 53 137 20-40 3,656 12,941,309 99 14.5 58 137 More than 40 875 1,700,075 93 12.4 62 119 ---------------------------------------------------------------------------------------------------
SOURCE: U.S. Department of Education, , Schools and Staffing Survey, 1990-91.
Highlights of the pattern of variations in the TCI are presented below.
In addition to the TCI derived from the hedonic wage model, two alternative cost adjustments have been proposed: (1) a geographic cost-of-living (COL) index (McMahon and Chang 1991), and (2) an index of variations in average teacher salaries adjusted for differences in teacher education and experience (Barro 1994). As one would expect, the correlations between the TCI, the McMahon-Chang COL, and Barro's adjusted-average-teacher salary index are positive and relatively high (i.e., 0.76 and 0.72, respectively). However, there are significant differences in the values of these indices and what they represent. The COL accounts only for variations in the cost of living which, while an important part of teacher cost differences, does not capture all of the relevant factors (e.g., the effects of labor market competition, climate, crime, and urban amenities). The Barro index controls for teacher education and experience, but fails to control for variations in other teacher and school attributes that are within local control.
The potential for distortion between the TCI and COL is evident from a more detailed examination of the patterns of difference across the United States. For example, the COL values for the highest COL regions of the country--the metropolitan areas surrounding the cities of San Francisco and San Jose, California--exceed the average values of the TCIs for these same regions by more than 28 percentage points. These values represent significant differences in the perception of what constitutes high costs and provide a very different picture of the real purchasing power of the educational dollar. These results suggest that teachers are willing to trade salaries for the amenities of living in the San Francisco-San Jose areas. The state of Hawaii shows a similar pattern.
The TCI presented in this paper represents an attempt to account for most
of the factors that affect the ability of local school systems to recruit and
employ teachers with similar characteristics hired into similar jobs and job
assignments. It accounts systematically for the factors that underlie
differences in the cost of living, and for differences in regional amenities
that affect the attractiveness of places to live and work. Despite the high
correlations among these three models, there are some important differences in
the ordering of regions of the country according to these alternative indices,
as well as the magnitudes themselves. Using an inappropriate index for adjusting
salary or expenditure data can lead to significantly different conclusions about
the levels of educational services being provided in different regions of the
country.
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