About the Author
The cost of educational inputs varies significantly by geographic area and across time. For example, costs are typically higher in large urban areas than in suburbs and towns, and educational costs tend to rise with inflation. If an urban and a suburban district spend the same amount per student, given the differences in the cost of educational inputs, it is likely that the suburban district is able to procure more or higher quality educational resources and, as a result, provide a higher quality of education. Likewise, the purchasing power of a given educational expenditure tends to fall over time due to inflation.
In the absence of information on the variations in cost of educational inputs, policymakers have a difficult time deciding on resource allocations. Furthermore, researchers cannot adequately adjust educational expenditures for differences in resource costs when conducting educational productivity analyses. Thus, an educational cost index is useful to gain a comprehensive understanding of what monies spent on education actually purchase given differences in educational resource costs across time and geographic areas.
Educational cost indexes can be used by policymakers and researchers to adjust nominal expenditures for inflation and geographical differences in prices. In doing so, it is possible to investigate the magnitude of differences in real educational expenditures at a point in time and across time. This permits policymakers and researchers to determine how educational resources are actually distributed across geographic areas as well as the productivity effects of educational spending. For instance, educational production function studies often examine the relationship between educational spending per pupil and student outcomes (test scores, graduation rates, etc.).1 If there is significant variation (over time or across regions) in educational resource costs, using nominal spending per pupil would bias the resulting estimates.
Teachers' salaries typically constitute over 50 percent of school district budgets (U.S. Department of Education 1997a). As a result, a Teacher Cost Index (TCI) is the most significant component of an educational cost index. However, some of the standard approaches to adjusting for differences in teachers' salaries across school districts have potential problems. First, the labor market for teachers tends to be uncompetitive in certain respects. As a result, wages may not reflect productivity, which can lead to statistical problems that result in poor estimates of real differences in educational resource costs. Second, microlevel data on teachers' salaries and other educational resources are collected periodically. An educational cost index should be updated annually in order to be a more useful tool.
The purpose of this research is to develop a cost index using data drawn from an annual survey of individuals from the broader labor market. Because this index uses annual data, it can be updated annually, allowing researchers to track more closely how a major component of educational costs (teachers' salaries) is changing over time. Furthermore, because this index is estimated using data from a broader segment of the labor market, it may be less subject to potential statistical problems arising from calculating an index estimated from a sample of only teachers.
This paper begins with a review of the various price adjustment mechanisms that have been suggested and a discussion of an alternate approach that may be used to calculate a TCI using the Current Population Survey (CPS), a dataset that is collected monthly with annual reports on demographics, education, and income. Then there is a comparison of the results found in this report with results of previous work. The conclusion provides a summary and offers suggestions for further exploration in future work.
Various price adjustment mechanisms have been suggested in the literature. Hanushek and Rivkin (1997) propose deflating educational spending by the gross domestic product (GDP) deflator, which provides a measure of the goods and services given up as a result of investment in education. The drawback to using the GDP deflator is that it is not necessarily a good measure to use if one wishes to calculate how the quality of teachers that can be purchased with a given salary has changed over time because the GDP includes numerous goods and services unrelated to education. Productivity growth in service industries, such as education, typically is slower than in other sectors of the economy. Thus, salaries may rise (with productivity growth) in some sectors of the economy without causing commensurate increases in output prices (inflation). Because salaries may increase relative to productivity to a greater extent in education than in other sectors of the economy, inflation may be higher in education than in the economy as a whole. In other words, inflation in the prices of educational inputs may exceed that calculated by an economy-wide measure, such as the Consumer Price Index (CPI). For example, it is well known that the cost of college tuition has increased considerably faster than the CPI over the last generation. However, school districts have to keep salaries competitive with other sectors of the economy to retain the same quality teachers. As a result, the use of a general GDP deflator would tend to overstate the investment in education in terms of the quality of labor purchased.
Mishel and Rothstein (1997) and Rothstein and Miles (1995) advocate a different price deflator. They suggest deflating education expenditures by a price index geared to be more specific to education prices. This index, termed the Net Services Index (NSI), is calculated by eliminating the housing and medical care components of the service component of the CPI. The authors note that inflation as measured by the net services index is higher than the inflation rate in the economy as a whole. As a result, when educational expenditures are deflated using this index, the growth rate in real educational spending appears to be smaller than when nominal educational spending is deflated by a more general GDP deflator. This methodology has several potential problems. Perhaps the most important is that it is difficult to hold quality constant, and, hence, the index may be subject to measurement error.
Chambers (U.S. Department of Education 1997a, 1998b) tries to address the problem of measuring the quality of educational inputs by using a statistical technique known as a Hedonic Wage Model. This model examines "the overall patterns of variation in the salaries and wages of certificated and non-certificated personnel" (U.S. Department of Education 1998b). He estimates this model at the school district level using three waves (1987-88, 1990-91, 1993-94) of the Schools and Staffing Survey. The most significant component of the index is the TCI because teachers' salaries make up a large fraction of overall educational spending.
The regression methodology employed assigns dollar weights to the underlying characteristics, both teacher specific and location specific, that determine teachers' salaries. Using the results, one can calculate how much it costs to hire a teacher with a given set of characteristics in one region relative to another and how these costs change over time.
This technique accounts for school districts having control over the types of teachers they hire and choosing to pay for differing sets of credentials. In other words, Chambers's work allows for an apples-to-apples comparison between districts even if they employ teachers with different observable characteristics, such as degree level and experience. His methodology also reflects the general labor market factors that influence salaries. For instance, it might be expected that, all things being equal, school districts in temperate climates could offer lower salaries than school districts with inclement weather and still attract teachers of equal quality.
The potential problem with Chambers's work is that teachers with similar observable characteristics (experience, degree level, etc.) may have very different unobservable qualities. In the labor market outside of education, differences in workers' wages are thought to reflect differences in their productivity. But, teacher wages are set institutionally and, thus, may not reflect teacher quality (Hanushek 1997). Local administrators may be able to observe the subtle differences in quality; however, these differences are not observable in the data. As a result, we might expect that school districts paying higher wages can attract more energetic and more intelligent teachers, even though on average they have the same experience and degree level as schools in other districts. In the technical literature, this inability to adequately capture quality is known as an omitted variable problem. If unobservable teacher quality is correlated with observable characteristics, such as region or degree level, the estimated coefficients, and hence the TCI, are biased. Relatively little research has been conducted to determine the extent to which this issue arises in the context of teacher labor markets.2
Hanushek (1997) suggests two alternatives to deal with this problem. The first is to adjust teacher salaries with a general price deflator, such as the CPI or the GDP deflator. Education spending deflated in this manner would provide a measure of the goods and services society gives up to purchase education. The problem with this approach is that price indexes are not available on the state or school district level. Consequently, this method would allow for a comparison of educational spending in one year versus another, but not in one school district versus another. Furthermore, this approach may not allow researchers to gain much insight into how the true quality of educational inputs changes over time, given that productivity may grow more slowly in education than in other sectors of the economy. If this is the case, over time, a general price deflator would tend to overstate the quality of educational inputs purchased.
The second alternative is to use information from the broader labor market to calculate a cost index rather than limit the analysis to teachers and teacher salaries. The underlying assumption in this approach is that school districts must pay wages that are competitive with the wages of college graduates in their area. If they do not, new college graduates and some top-quality teachers will be attracted to other occupations in which the economic rewards are greater.
Following Hanushek's suggestion, it was possible to estimate general hedonic wage models for all college graduates in 1987-88, 1990-91, and 1993-94.3 This methodology allows us to decompose wages into the part attributable to individual characteristics (e.g., education, experience, and occupation) and the part attributable to community characteristics (e.g., crime rates, housing values, and climate conditions). In competitive labor markets, differences in community factors will influence wages. For instance, holding all else constant, communities with high crime rates would have to pay higher wages to compensate individuals for the monetary and psychological costs associated with living in high crime areas.
To perform this analysis, data drawn from several sources were used: the CPS, the U.S. Geological Survey, the National Weather Service, and the County and City Data Book.4 The CPS is a nationally representative survey that includes individual wage information as well as detailed background characteristics, such as age, occupation, marital status, and education level. In addition, this dataset has state identifiers that provide a link with state-level community factors, such as crime rates, climate, and urbanicity.
The results from the hedonic wage models were used to calculate a General Wage Index (GWI) that illustrates how wages for individuals with a given set of characteristics vary across states and over time. In effect, we are predicting how much an individual in a given state would be expected to be paid relative to how much that same individual (or an individual with exactly the same observable characteristics) would make if he or she lived in a different state (or in a different year) that had a different set of characteristics.5
Although this methodology allows us to make adjustments for geographical variations in aggregate measures, such as crime, given the constraints of the data, it does not allow adjustments at the school district level as Chambers has done. However, to the extent possible, we replicate model specifications employed by Chambers' specification to compare state TCIs using each methodology.6 In the analysis below, the correlation between the two indexes is examined to determine the extent to which the two measures differ in measuring educational inflation and variation in educational costs across states.
The effects of the explanatory variables on the wage rate in 1987-88, 1990-91, and 1993-94 are listed in appendix table A-2.7 To facilitate comparison of the results with U.S. Department of Education (1997a and 1998b), the specification of the wage models are similar to his. However, a test of the hypothesis that the explanatory variables have the same effect on the wages of men and women was rejected.8 This indicates that wage models should be estimated separately for men and women. Despite this result, we chose, for two reasons, to present only the model results that have men and women pooled in the sample. First, the calculated average state wage rankings did not change significantly when we estimated the wage models separately. Second, we wanted to compare our results with Chambers, who only estimates pooled models.
Following U.S. Department of Education (1998b), the discussion of the variables is then broken into a discussion of discretionary factors and cost factors. The discretionary factors represent those characteristics over which employers have some degree of choice. For instance, employers in a particular labor market have a choice about whether to hire employees with advanced degrees. Cost factors represent characteristics of communities, such as crime rates, that are expected to influence local wage rates but are outside the control of employers.
In general, the effects of individual characteristics on wages are consistent with most labor market findings. For instance:
Several cost factors have a significant affect on wages. For instance, as might be expected, wages vary significantly with changes in the median value of housing. Roughly speaking, a 10 percent increase in housing values was associated with an increase in the wage rate of 1 percent. Likewise, wages tend to be lower in areas with more temperate climates, with a 10 degree difference in climate worth between 2 and 6 percent in wages. However, few other cost factors were statistically significant. Despite this, as a whole, they play an important in explaining patterns of variation in individual wages.9
Using the results from the hedonic wage models, we calculate the predicted wage in each state in each year. This illustrates how wages for individuals with a given set of characteristics vary across states and over time, holding constant all discretionary factors.10 In other words, this is the wage rate that is required to hire individuals of comparable skill in different states (that have different cost factors).
Table 1 shows the predicted state wage and ranking (1 = highest wage; 51 = lowest wage) in a particular year. The top five high-wage states in the 1987-88 school year were Alaska, Connecticut, California, New Jersey, and the District of Columbia. In school years 1990-91 and 1993-94, Alaska, California, Connecticut, and New Jersey remain in the top five for all 3 years. The five states with the lowest wage costs in 1987-88 were South Dakota, Mississippi, North Dakota, Arkansas, and Montana. There is slightly less consistency in the low-wage ranking, with only North Dakota, Montana, and South Dakota remaining in the bottom five in all 3 years.
There are significant differences in wages between states. In the most extreme case, the estimated wage in Alaska is roughly 1.6 times the estimated wage in South Dakota. To put this in perspective, if the 1987 average starting salary for a teacher in Michigan was $25,000, it would only cost about $19,300 to hire a teacher with comparable skills in South Dakota but would cost about $31,200 to hire an equivalent teacher in Alaska.
The predicted state wages listed in table 1 are used to create GWI for each state in each year. These indexes compare each state wage with the estimated 1987-88 national wage. Table 2 reports the GWI along with the percentage change, for individual states and the entire nation in wages from 1987-88, 1990-91, and 1993-94.
The calculated GWI shows the inflation rate in wages from 1987-88 to 1990-91 to be 15.7 percent and from 1990-91 to 1993-94 to be 8.8 percent. Over the entire period, 1987-88 to 1993-94, wages are calculated to have risen 25.9 percent. To gain some perspective of how this measure differs from other indexes used to adjust education expenditures, a comparison between various inflation adjustment indexes is presented in table 3. The comparison indexes are the CPI, the GDP deflator, the NSI, proposed by Mishel and Rothstein (1997) and Rothstein and Miles (1995), and two indexes calculated by Chambers (U.S. Department of Education 1997a): the Inflationary Cost of Education Index (ICEI), which includes teachers' salary costs as well as other educational costs (e.g. supplies and materials), and the teacher salary component of the ICEI. All indexes are scaled so that 1987-88 equals 100.
From 1987-88 to 1990-91, the GWI compares most closely with the CPI; however, there is little difference in any of the inflation measures. For 1990-91 to 1993-94, the GWI closely parallels the CPI. Over this period, there is considerably more variation in the various inflation measures, with the Teacher ICEA measure exceeding the GWI by about 15 percent and the NSI exceeding the GWI by almost 50 percent.
These differences have dramatic implications for the adjustment made to compare educational spending in one time period with another. For instance, the average expenditure per pupil in 1990-91 was $5,258 (in 1992 dollars) and in 1993-94 was $5,767 (in 1994 dollars; U.S. Department of Education 1998a). Inflating the 1990-91 spending to 1993-94 using the GWI suggests that the $5,258 was worth $5,721 in 1993-94, slightly less than the actual expenditures in that year. This suggests that actual educational expenditure was more than keeping pace with inflation in salaries. In contrast, the Teacher ICEA suggests the 1990-91 expenditure level was worth $5,789 in 1993-94, and the NSI suggests it was worth $5,942. Both of these adjustments indicate that actual expenditure was failing to keep pace with inflation in teachers' salaries. The differences between the GWI and Chambers' TCI are explored in more detail below.11
The GWI is compared with Chambers' TCI in several different ways. First, we report the correlation between the two indexes in each school year. Second, we report the correlation between the indexes in the state rank in wages (in each school year and in the average state rank over the 3 years). Finally, we detail the correlation in the inflation calculation generated by each of the indexes.12 Table 4 lists these results.
In each school year, the correlations between the two indexes and the state rankings are relatively high (over 0.8) and are statistically significant. This indicates that both measures of geographic cost differences tend to be consistent in the sense that both indexes show similar relative state rankings. In contrast, we find the correlation between the two inflation measures is not statistically significant (at the 5 percent level). Thus, there is not a high degree of similarity in the measures of inflation in individual states.
Given that there are some slight differences in model specification and that Chambers is using cost factors aggregated to the school district level, whereas in our model cost factors are aggregated to the state level, it is not surprising that there are some differences in magnitude between the two indexes and in state wage ranking. However, the differences in the inflation measures are more pronounced and it seems unlikely that these factors fully account for the discrepancies in the results.
One explanation for the divergence in findings is that the uncompetitive nature of teacher labor markets biases the estimates of the coefficients, which, in turn, leads to a biased TCI. Although it is difficult to determine empirically whether this is true, one might hypothesize that the degree of bargaining power of teachers in a state would be an important determinant of whether the effect of the cost factors affecting teacher salaries differs markedly from the effect of the cost factors on the labor market as a whole. All things equal, one might expect the two wage indexes to be of similar magnitude and show similar rates of inflation in states in which the teacher labor market is similar to the labor market as a whole and to diverge in states in which teachers have greater bargaining power. One check of this hypothesis is to examine the patterns to difference between Chambers' TCI and the calculated GWI to see if teacher costs tend to be higher in states with significant teacher bargaining power (e.g., strong teachers' unions) and if the wage increase in those states tends to outpace increases in wages in the broader labor market.
Table 5 shows, for each state, the magnitude of difference between Chambers' TCI and the calculated GWI.13 There are some significant differences in state TCIs. Based on the hypothesis above, one might expect Chambers' TCI to be larger than the GWI in northeastern states where a high percentage of school districts have collective bargaining (98.1 percent), and similar in south central and southwestern states where fewer school districts have collective bargaining arrangements (about 10 percent) (U.S. Department of Education 1996). There is some evidence that this pattern exists. The average differential (across all years) between Chambers' TCI and the GWI in the northeastern states is 24.6, and the average differential in the south central and southwestern states is -0.8.14 Clearly, the value of the two indexes are more similar in states that have a lower percentage of school districts with collective bargaining. Although this is only cursory evidence, it does suggest a link between unionization and the estimate of the TCI. However, there are a multitude of possible explanations for the observed differences, given the extent to which the labor markets in these regions differ.15 In addition, the sample sizes in some states are relatively small, which can lead to unstable estimates of state-level wages.
In this study, we have calculated a cost index derived from an annual labor market survey, the CPS, that contains individuals both within and outside the teaching profession. This extension of Chambers's work on TCIs along the lines suggested by Hanushek (1997) can be considered a preliminary attempt to deal with a potential statistical problem associated with using observed teacher salaries as the dependent variable in a hedonic wage regression. The potential problem is that teacher labor markets are not fully competitive; therefore, an index calculated using a sample of only teachers may misrepresent the true cost of hiring a teacher, of given attributes, in one labor market versus another (and the changes in cost over time).
A comparison between our results with Chambers' TCI shows that both samples yield similar state wage rankings; however, the GWI measure of wage inflation in the United States as a whole is more similar to the CPI than to Chambers' TCI. There are also some significant differences between the two indexes in state-level inflation measures. We offer cursory evidence that these observed differences are a result of significant differences in the bargaining power of teachers and the bargaining power of those in the labor market as a whole. There are plausible alternative explanations for the observed differences, so it would be premature to jump to the conclusion that the differences are due to uncompetitive teacher labor markets. Given the magnitude of the differences between the two indexes in measuring inflation in individual states, additional study to reconcile the findings reported here with those of Chambers is warranted.
A second benefit of using the CPS is that it permits annual updates of the index, which allows researchers to more closely track how a major component of educational costs (teachers' salaries) is changing over time. The drawback to using this survey has been that, although it allows us to make adjustments for geographical variation in aggregate measures, such as crime, given the constraints of the data we cannot make adjustments at the school district level as Chambers has done. However, starting in 1996, the CPS included county-level identifiers. These identifiers allow researchers to link community cost factor information at the county level (rather than the state level). In turn, this permits researchers to calculate county-level TCIs and to study in greater detail the factors contributing to the differences between Chambers' TCI and the calculated GWI.
Details on Data and Methodology
Model Specification
The specific model we estimate takes the following form:
where t is the year, Wij is the wage for individual i in state j, Di is a vector of individual specific characteristics (age, experience, degree level, occupation), Cj is a vector of community cost factors (crime rate, unemployment rate, urbanicity), and St is a vector of state dummy variables. The estimated coefficients from this model
The sample used was restricted in a number of ways. First, we eliminated anyone from the sample who did not have at least a bachelor's degree. We did this because we wanted to construct a sample of individuals who would be eligible to teach in public schools and this excludes those who have less than a bachelor's. We also eliminated individuals who reported only working part time, those with hourly wage rates below the national minimum wage, and those whose wage appeared to be an outlier (based on the frequency distribution of wages within the occupational classification code).17 Table A-1 lists sample statistics and data sources for all variables.
To calculate a GWI for a particular state for a particular year, we hold constant the discretionary factors that influence salaries (they are set at the mean of the sample), set the cost factors equal to the mean value in the state for which we are calculating the cost index, and set the state dummy variable for the state in question equal to one. More formally, the wage for state j in year t is:
where Wijt represents the wage for state j in year t, Dit represents the overall sample mean of the discretionary factors, Cjt represents the mean values in state j of the cost factors, and Sjt equals 1 for state j in year t. The estimated national wage is calculated, using the above formula, and setting all variables (including those in C and S) to the sample mean for a particular year.
Using the 1987-88 estimated national wage as a base, the GWI for state j in year t is:
1 For a review of such educational production function studies, see Hanushek (1986).
2 See Goldhaber and Brewer (1997) for a detailed discussion of this issue. 3 For more information on the Hedonic Wage Model methodology, see Chambers 1981.
4 Data used in this analysis were provided by Jay G. Chambers. Variable definitions and sample statistics for selected variables are listed in the appendix.
5 The specific model is described more formally in the appendix. 6 Details on how the state-level wage index is calculated are reported in the appendix. 7 Appendix table A-2 lists the estimated coefficients and gives their statistical significance.
8 F-tests of the null hypothesis that the pooled (men and women) wage models (for 1987-88, 1990-91, and 1993-94) are not statistically different from the models estimated separately were rejected at the 1 percent level.
9 An F-test of the null hypothesis that the coefficients of the cost factors are jointly equal to zero was rejected at the 1 percent level. 10 Details on the method used to calculate the predicted wage are in the appendix.
11 Chambers' TCI is the teachers' salary component of his Cost of Education Index.
12 State-level TCIs were obtained from Chambers.
13 The GWI is subtracted from Chambers' TCI.
14 The northeastern states are Connecticut, Maine, Massachusetts, New Hampshire, New Jersey, New York, Pennsylvania, Rhode Island, and Vermont. The south central and southwestern states are Alabama, Arkansas, Kentucky, Louisiana, Missouri, Oklahoma, Tennessee, and Texas.
15 Although it is outside the scope of this study, one way to determine what factors are driving the observed differences in cost indexes is to regress the difference between the two indexes on a vector of state-level variables, such as the demographic composition of the state and the degree of competitiveness of labor markets in the state.
16 All regressions and sample means are weighted by the variable earnwt, which represents the number of individuals in the population, and the standard errors of the coefficients are multiplied by a scalar adjustment (1.8940 for 1987, 1.9925 for 1990, and 1.8402 for 1993) for the survey design. Details on the weighting variable and the scalar adjustment are detailed in Chambers's work (U.S. Department of Education 1997b).
17 The elimination of outliers is consistent with the construction of the sample used by Chambers (U.S. Department of Education 1997b).
Chambers, Jay G. 1981. "The Hedonic Wage Technique as a Tool for Estimating the Costs of School Personnel: A Theoretical Exposition with Implications for Empirical Analysis." Journal of Education Finance. 6(3): 330-354.
Goldhaber, Dan D. and Dominic J. Brewer. 1997. "Why Don't Schools and Teachers Seem to Matter? Assessing the Impact of Unobservables on Educational Productivity." Journal of Human Resources. 32(3): 505-523.
Hanushek, Eric A. 1986. "The Economics of Schooling: Production and Efficiency in the Public Schools. " Journal of Economic Literature, XXIV (3): 1141-78.
Hanushek, Eric A. 1997. Adjusting for Differences in the Costs of Educational Inputs. Working paper.
Hanushek, Eric A. and Steven G. Rivkin. 1997. "Understanding the 20th Century Growth in U.S. School Spending." Journal of Human Resources, 32, 1: 35-67.
Mishel, Lawrence and Richard Rothstein. 1997. Measurement Issues in Adjusting School Spending Across Time and Place. Washington, DC: Economic Policy Institute.
Rothstein, Richard and Karen H. Miles. 1995. Where's the Money Gone? Changes in the Level and Composition of Education Spending. Washington, DC: Economic Policy Institute.
U.S. Bureau of the Census. County and City Data Book: 1994. Washington, DC: 1994.
U.S. Department of Education, National Center for Education Statistics. Schools and Staffing in the United States: A Statistical Profile 1993-94. NCES 96-124. Washington, DC: 1996.
U.S. Department of Education, National Center for Education Statistics. Measuring Inflation in Public School Costs. NCES Working Paper 97-43. Washington, DC: 1997a.
U.S. Department of Education, National Center for Education Statistics. A Technical Report on the Development of a Geographic and Inflationary Differences in Public School Costs. Washington, DC: 1997b.
U.S. Department of Education, National Center for Education Statistics. Digest of Education Statistics, 1997. NCES 98-015. Washington, DC: 1998a.
U.S. Department of Education, National Center for Education Statistics. Geographic Variations in Public Schools' Costs. NCES Working Paper 98-04. Washington, DC: 1998b.
This report was prepared while the author was an employee at the CNA Corporation.
The author would like to thank Jay Chambers and Ann Win of the American Institute for Research for supplying the data used in this analysis and Dave Reese of the CNA Corporation for his assistance on the project.
Background on Price Adjustment Mechanisms
Methodology and Data
Results
Discretionary Factors
Cost Factors
General Wage Index
Comparison Between the GWI and Chambers' TCI
Conclusion
Appendix 
will be used to calculate TCIs for each state in each of the 3 years.16
Construction of the Data and Sample Statistics
Calculation of Cost Indexes
Footnotes
