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Projections of Education Statistics to 2014, published September 2005.

Appendix A. Projection Methodology: Expenditures of Public Degree-Granting Postsecondary Institutions

One current-fund expenditure model and one educational and general expenditure model were estimated for each of two types of degree-granting institutions—public 4-year and public 2-year. Projections are presented for public institutions only, because financial surveys of private institutions have been redesigned and there are not enough data to model with the new accounting method.

The degree-granting institution econometric models were selected on the basis of their statistical properties, such as the coefficients of determination (R2), the t-statistics of the variables, the Durbin-Watson statistic, and residual plots. These econometric models will yield good forecasting results only if the relationships that existed among the variables in the past continue throughout the projection period.

Degree-Granting Institutions Expenditure Models

Similar econometric models were developed for the two types of public institutions, 4-year and 2-year. Each of the models presented here contains variables measuring at least two of the following three factors historically associated with the level of expenditures: (1) the state of the economy; (2) the inflation rate; and (3) enrollments. Revenues of state and local governments per capita were used to measure the state of the economy, and a dummy for years with inflation rates greater than 8 percent was used in the models for public 4-year institutions. In each model, an enrollment variable was included.

For each dependent variable, a number of alternative specifications were examined. In each case, the choice of the final specification was made after considering such factors as the coefficients of determination, the t-statistics of the variables, residual plots, and expost mean absolute percentage errors. The final specification of each model has the dependent variables and some of the independent variables as first differences.

Public 4-Year Institutions Expenditure Models

The public 4-year institutions current-fund expenditure model is:

DPUTCUR4t = b0 + b1DDSTREVt + b2DPUFTE4t + b3DUMMYt

where:

DPUTCUR4t is the change from the year t-1 to year t in current-fund expenditures per student in full-time-equivalent (FTE) enrollment in public 4-year institutions in constant 1982–84 dollars;

DDSTREVt is the change from the year t-2 to year t-1 in the sum of personal tax and nontax receipts for state and local governments and indirect business taxes and tax accruals, excluding property taxes, for state and local governments, per capita, in constant 1982–84 dollars;

DPUFTE4t is the change from the year t-1 to year t in FTE enrollment in public 4-year institutions in thousands of students; and

DUMMYt is a dummy variable equaling 1 if the inflation rate in year t is greater than 8 percent and 0 otherwise.

This model and the other econometric models were estimated using a sample period from 1968–69 to 2000–01. Ordinary least squares was used to estimate all the public institution models.

The results for this model are in table A19. Each variable affects current-fund expenditures in a logical fashion. The more revenues that state and local governments receive, the more expenditures they can make for public institutions of higher education. In a year with high inflation (DUMMY equals 1), current-fund expenditures in constant dollars are lower than they would have been otherwise. The more students in public 4-year institutions, the less money is available to be spent per student.

Three projections were produced: the middle alternative set of projections, the low alternative set of projections, and the high alternative set of projections. Each set of projections was based on a different set of assumptions for the revenues of state and local governments per capita. The projections for revenues of state and local governments per capita and the other economic variables used to produce the higher education expenditure projections were produced using the U.S. Quarterly Model of the economic consulting firm, Global Insight, Inc.

In the middle set of alternative projections, the revenues of state and local governments per capita increase at rates between 1.4 percent and 5.6 percent from 2003–04 to 2013–14. In the low set of alternative projections, the revenues of state and local governments per capita increase at rates between 0.9 and 5.5 percent. In the high set of alternative projections, the revenues of state and local governments per capita increase at rates between 2.5 percent and 6.9 percent.

Projections for total current-fund expenditures were made by multiplying the projections for current-fund expenditures per student in FTE enrollment by projections for FTE enrollment. Projections were developed in 1982–84 dollars and then placed in 2002–03 dollars using projections for the Consumer Price Index. Current dollar projections were produced by multiplying the constant dollar projections by projections for the Consumer Price Index.

A model for educational and general expenditures of public 4-year institutions was developed using the same variables as the current-fund expenditure model. The model is:

DPUED4t = b0 + b1DDSTREVt + b2DPUFTE4t + b3DUMMYt

where:

DPUED4t is the change from the year t-1 to year t in educational and general expenditures per student in FTE enrollment in public 4-year institutions in constant 1982–84 dollars.

This model is also shown in table A19.

As with current-fund expenditures, each variable affects expenditures in the expected way.

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Public 2-Year Institutions Expenditure Models

The public 2-year institutions current-fund expenditure model has a form similar to the public 4-year institutions current-fund expenditure model, except that the public 2-year institutions model does not contain any inflation variables. The model is:

DPUTCUR2t = b0 + b1DDSTREVt + b2DPUFTE2t

where:

DPUTCUR2t is the change from the year t-1 to year t in current-fund expenditures per student in FTE enrollment in public 2-year institutions in constant 1982–84 dollars; and

DPUFTE2t is the change from the year t-1 to year t in FTE enrollment in public 2-year institutions in thousands of students.

The results for this model are in table A19. Again, DDSTREV has the expected positive effect on expenditures, and the FTE enrollment variable has the expected negative impact.

The public 2-year institutions educational and general expenditure model is virtually identical to its current-fund expenditure counterpart. It is:

DPUED2t = b0 + b1DDSTREVt +b2DPUFTE2t

where:

DPUED2t is the change from the year t-1 to year t in educational and general expenditures per student in FTE enrollment in public 2-year institutions in constant 1982–84 dollars.

The results of this model appear in table A19.

Projection Accuracy

The majority of editions of Projections of Education Statistics in the past two decades had projections of expenditures of postsecondary institutions data. The projections that appeared in recent editions of Projections of Education Statistics were developed using the same methodology as that presented here. Those that appeared in Projections of Education Statistics to 2000 were produced using substantially different models.

Several commonly used statistics can be used to evaluate projections. The values for one of these, the mean absolute percentage error (MAPE), are presented in table A2. MAPEs are presented for current-fund expenditures in public 4-year and public 2-year institutions. The MAPEs were calculated using projections from the last nine editions of the Projections of Education Statistics.

To calculate the MAPEs, the projections of each variable were first grouped by lead time; that is, all the projections of each variable that were a given number of years from the last year in the sample period were grouped together. Next, the percent differences between each projection and its actual value were calculated. Finally, for each variable, the mean of the absolute values of the percent differences were calculated, with a separate average for each lead time. These means are the MAPEs.

Sources of Data

The current-fund expenditure data and the educational and general expenditure data are from the Integrated Postsecondary Education Data System (IPEDS) ''Finance'' surveys of the National Center for Education Statistics (NCES). One manipulation of the educational and general expenditures was required. From 1968–69 to 1973–74, student-aid expenditures were a separate component of current-fund expenditures. From 1974–75 on, scholarships and fellowships have been components of educational and general expenditures. Hence, for the period 1968–69 to 1973–74, student aid was added to the published numbers for educational and general expenditures.

The full-time-equivalent (FTE) enrollment data are from the ''Fall Enrollment in Colleges and Universities'' surveys of NCES. The FTE enrollment figures for 1968–69, 1969–70, and 1970–71 were estimated using part-time and full-time enrollment data. FTE enrollment was derived by adding one-third of part-time enrollment to total full-time-enrollment.

Between the Projections of Education Statistics to 2013 and this year's edition to 2014, there were some redefinitions in Global Insight’s U.S. Macro Model. In the government sector, tax receipts no longer include social insurance contributions/taxes. Total taxes are the sum of personal and corporate income taxes, and taxes on production and imports. Thus, the old total tax receipt concepts are more comparable to current total receipts than to total tax receipts. Personal tax receipts have been reduced by the shift of some receipts from taxes to personal current transfers. Receipts formerly classified as negative expenditures have been reclassified as receipts. Thus, both receipts and expenditures are higher than before. Net government saving has not changed. These changes affected the levels of the state revenue variable used in both the 2-year and 4-year current expenditure models; however, both the historical and forecast data were revised such that the data used throughout the models are consistent over time. The newly defined variables have the same desired effect on expenditures as the earlier models.

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