# Projecting Educational Expenditures - Projections Using Average Annual Increases in Expenditures, Projections Using Average Annual Percentage Increases in Inflation

### regression data national statistics

Every responsible educational organization estimates the amount of expenditures necessary to provide services desired by its students, staff, and faculty. Utilizing historical financial data, an analyst can use a variety of statistical methods to project fairly accurately what expenditures will be needed to provide the same level of educational services in future years. Though there are a number of sophisticated and reliable statistical methods used to project expenditures, three methods are prevalent: (1) average annual increases in expenditures; (2) average annual percentage increases in inflation (i.e., the Consumer Price Index); and (3) regression analysis. These methods have been validated and refined by use in a wide variety of economic, political, and social contexts. Moreover, the accuracy of these expenditure projection methods has improved with advances in data definitions, data reporting, generally accepted accounting principles, and data collection methods.

## Projections Using Average Annual Increases in Expenditures

Although a variety of methods can be used to project educational expenditures, one of the simplest methods is to survey states and educational institutions (e.g., state departments of education or local district offices) to find out some details about their historical spending patterns for educational dollars (see Table 1). Then, based on this contextual information, one would use an average annual increase in educational expenditures–taken over some period of time–to project an incremental increase to the most recent year's actual data.

Table 2 provides sample state-level projections for educational expenditures over multiple time periods using the average annual increases in expenditures to determine projected expenditures for the 2003 academic year. The ten-year projection using the average annual increase methodology is $5,678; the seven-year projection using the average annual increase is $5,714, the five-year projection using the average annual increase is $5,797; and the three-year projection using the average annual increase is $5,786. Notice that the ten-year and seven-year expenditure projections are substantially lower than the remaining projections due to the inclusion of an unusually low increase in 1997.

**TABLE 1**

Usually, the longer the time period used when computing an average annual increase, the less likely the probability that an atypical yearly increase (i.e., an annual increase, or decrease, that does not fall within the trend over a period of time) will influence negatively the estimated level of expenditure. In the case of an atypical increase (or decrease) in expenditures, due caution should be noted when examining the results.

## Projections Using Average Annual Percentage Increases in Inflation

Another method used to project educational expenditures is to use an average annual percentage increase in inflation–taken over some period of time–to project an incremental increase to the most recent year's actual data. Again, the longer the time period used when computing an average annual increase, the less likely the probability that an atypical yearly increase will negatively influence the estimated level of expenditure. Table 2 also provides sample state-level projections for educational expenditures over multiple time periods using the average annual percentage increases in expenditures to estimate a projected expenditure for the 2003 academic year. The ten-year projection using the average annual percentage increase in inflation methodology is $5,525; the seven-year projection using the average annual increase is $5,520, the five-year projection using the average annual increase is $5,513; and the three-year projection using the average annual increase is $5,679. Notice that the five-year expenditure projection is substantially lower than the

**TABLE 2**

remaining projections due to the inclusion of an unusually low increase in 1999.

## Projections Using Regression Analysis

This statistical technique for predicting educational expenditures–specifically called Ordinary Least Squares (OLS) Regression Analysis–consists of constructing a line that "best fits the data" over a certain period of time (see Figure 1). The line of best fit (also known as the *regression line*) is the one line–and the only line–that falls as close as possible to every coordinate simultaneously and can be used to make fairly accurate expenditure projections (Because this discussion is limited to linear regression, and does not include non-linear regressions, the mathematical functions discussed will be equations for straight lines). Now the process of expenditure projections using regression analysis involves two steps: (1) determining the mathematical equation for the regression line; and (2) using the mathematical equation to predict scores.

The mathematical equation for the straight line in Figure 1 expresses a direct relationship between time (along the horizontal axis) and expenditures (along the vertical axis). The general form of the equation for a line is Y = bX + a, where Y is the predicted expenditure, b is the slope of the line, a is Y-intercept, and X is the year to be predicted. Theoretically, every line extends infinitely in both directions, but for the purposes of this discussion, the line extends along the horizontal axis from the year 1992 to 2003.

For each set of expenditure data analyzed, a specific regression line is fitted onto the graphed data using the mathematical methods of ordinary least squares. The formulas for the slope–referred to as

**FIGURE 1**

the *regression coefficient*–and the Y-intercept–referred to as the *regression constant*–are derived using calculus and can be found in any statistics book. Once the specific regression equation has been determined, the prediction of educational expenditures is straightforward: Substitute the values of X, a, and b into the equation and solve for Y. For example, the ten-year projection using OLS regression analysis is $5,541; the seven-year projection using regression analysis is $5,663; the five-year projection using regression analysis is $5,656; and the three-year projection using regression analysis is $5,580. Notice that the seven-year and five-year expenditure projections are substantially lower than the remaining projections due to the inclusion of an unusually high increases as a percentage of expenditure in 1998 and 1999.

## Summary

Despite the improvements in the precision of expenditure projections methods, it is important to remember that the usefulness of any economic or financial estimate rests upon the strength and validity of the assumptions used to define the context of the analysis. For example, local school districts are expected to provide a broad-based curriculum, fully-equipped classrooms, quality teaching materials, new technologies, qualified teachers, and a wide range of programs, services, and products. Simply investing more money into a school district's total available revenue is not enough to improve educational services or student attainment. However, targeting new expenditures to effective programs that improve the quality of the education system for students, staff, and faculty can improve educational services. And, accurately projecting distributions of revenues and expenditures is key for these types of school improvements.

Two major institutions provide primary resources in the determination of educational expenditures: the National Center for Education Statistics (NCES) and the National Education Association (NEA). The National Center for Educational Statistics is the primary federal institution for collecting, analyzing, and reporting educational data related to education in the United States. Annually, NCES sends surveys to state educational agencies and uses this data to publish reports and develop estimates for publications such as *The Condition of Education, The Digest of Education Statistics,* and *Early Estimates of Public Elementary and Secondary Education Statistics.* The National Education Association presents its expenditure projections in a combined annual report called *Rankings and Estimates.* The *Rankings* portion of the report presents expenditure data useful in determining how states differ from one another on selected demographic, economic, political, and social arenas. The *Estimates* portion of the report provides projections of information about educational expenditures in addition to data on student enrollment, school employment, personnel compensation, and other educational finances. The data elements presented by both of these organizations permit general assessments of trends and should be used with the understanding that specific contextual elements influence their interpretations.

## BIBLIOGRAPHY

McDOWELL, LENA M. 2001. *Early Estimates of Public Elementary and Secondary Education Statistics: School Year 2000–2001* (NCES 2001–331). U.S. Department of Education. Washington, DC: National Center for Education Statistics.

NATIONAL CENTER FOR EDUCATION STATISTICS. 2001. *The Digest of Education Statistics.* Washington, DC: U.S. Department of Education.

NATIONAL CENTER FOR EDUCATION STATISTICS. 2001. *Projections of Education Statistics to 2011.* Washington, DC: U.S. Department of Education.

NATIONAL EDUCATION ASSOCIATION. 1999. *Investing in Public Education: The Importance of Schooling in the New Global Economy.* Washington, DC: National Education Association.

NATIONAL EDUCATION ASSOCIATION. 2001. *Rankings and Estimates–Rankings of the States 2000 and Estimates of School Statistics 2001.* Washington, DC: National Education Association.

## INTERNET RESOURCES

NATIONAL CENTER FOR EDUCATION STATISTICS. 2002. <http://nces.ed.gov/edstats>.

NATIONAL EDUCATION ASSOCIATION. 2002. <www.nea.org>.

R. ANTHONY ROLLE

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