The higher education 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.
In Chapter 7, some of the factors that are historically associated with the level of expenditures are discussed. These are: (1) the state of the economy; (2) the inflation rate; and (3) enrollments. Each of the models presented here contains variables measuring at least two of these three factors. Either disposable income per capita or revenues of state and local governments per capita was used to measure the state of the economy. Two measures of the inflation rate were considered: the rate of change in the inflation rate; or a dummy for years with inflation rates greater than 8 percent. In each equation, 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 ex-post mean absolute percent errors. The final specification of each model has the dependent variables and some of the independent variables as first differences.
DPUTCUR4= b0 + b1DSTREV1 + b2DPUFTE4 + b3DUMMY
where:
DPUTCUR4 is the change from the previous year in current-fund expenditures per student in full-time-equivalent (FTE) enrollment in public 4-year institutions in constant 1982-84 dollars;
DSTREV1 is the change from the previous year in the sum of personal tax and nontax receipts to state and local governments and indirect business taxes and tax accruals, excluding property taxes, to state and local governments, per capita, in constant 1982-84 dollars lagged one year;
DPUFTE4 is the change from the previous year in FTE enrollment in public 4-year institutions in thousands of students; and
DUMMY is a dummy variable equaling 1 when the inflation rate 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 1994-95. Ordinary least squares was used to estimate all the public institution models.
The results for this model are in table A6.1. 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 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 WEFA Group's Mark 11 Quarterly Model of the U.S. Economy. The development of these alternative sets of projections is discussed in Appendix A5.
In the middle set of alternative projections, the revenues of state and local governments per capita increase at rates between 1.2 percent and 2.2 percent. In the low set of alternative projections, the revenues of state and local governments per capita increase at rates between 0.5 percent and 1.8 percent. In the high set of alternative projections, the revenues of state and local governments per capita increase at rates between 1.7 percent and 2.7 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 1995-96 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. All the higher education total expenditure projections, all expenditure projections in 1995-96 dollars, and all the current dollar projections were calculated in similar fashion.
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:
DPUED4= b0 + b1DSTREV1 + b2DPUFTE4 + b3DUMMY
where: DPUED4 is the change from the previous year 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 A6.1.
As with current-fund expenditures, each variable affects expenditures in the expected way.
DPUTCUR2 = b0 + b1DSTREV1 + b2DPUFTE2
where:
DPUTCUR2 is the change from the previous year in current-fund expenditures per student in FTE enrollment in public 2-year institutions in constant 1982-84 dollars; and
DPUFTE2 is the change from the previous year in FTE enrollment in public 2-year institutions in thousands of students.
The results for this model are in table A6.1. Again, DSTREV1 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 expenditures counterpart. It is:
DPUED2= = b0 + b1DSTREV1 + b2DPUFTE2
where:
DPUED2 is the change from the previous year 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 A6.1.
DPRTCUR4 = b0 + b1DPCI + b2DPRFTE4 + b3ININCR
where:
DPRTCUR4 is the change from the previous year in current-fund expenditures per student in FTE enrollment in private 4-year institutions in constant 1982-84 dollars;
DPCI is the change from the previous year in disposable income per capita in 1992 dollars;
DPRFTE4 is the change from the previous year in FTE enrollment in private 4-year institutions to the population in thousands; and
ININCR is the rate of change in the inflation rate measured by the Consumer Price Index.
The model was estimated using the AR1 method for correcting for autocorrelation.
The three alternative sets of projections for current-fund expenditures were produced using varying assumptions about the growth paths for disposable income and the rate of change in the inflation rate measured by the Consumer Price Index. These disposable income and inflation rate projections were also developed using the WEFA Group's Mark 11 Quarterly Model of the U.S. Economy.
In the middle set of projections, disposable income per capita rises each year from 1997-98 to 2007-08 at rates between 1.1 percent and 1.9 percent. In the low set of projections, disposable income per capita increases at rates between 0.7 percent and 1.7 percent. In the high set of projections, disposable income per capita increases at rates between 1.4 percent and 2.3 percent.
In the middle set of projections, the inflation rate varies between 2.5 percent and 3.3 percent. In low set of projections, it varies between 2.5 percent and 3.7 percent, and in the high set of projections, it varies between 2.3 percent and 3.0 percent.
The private 4-year institutions educational and general expenditure model is:
DPRIED4= b0 + b1DPCI + b2DPRFTE4 + b3ININCR
where:
DPRIED4 is the change in educational and general expenditures per student in FTE enrollment in private 4-year institutions in constant 1982-84 dollars.
The results of this model appear in table A6.1.
There are several commonly used statistics which can be used to evaluate projections. The values for one of these, the mean absolute percentage error (MAPE), are presented in table A6.2. MAPEs are presented for current-fund expenditures and for educational and general expenditures by several different breakdowns. Two alternative sets of MAPEs are presented: with one set, the projections from the last five editions of the Projections of Education Statistics were used in the calculations; with the other, the projections from the Projections of Education Statistics to 2000 were also included.
To calculate the MAPEs presented in table A6.2, 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 seperate average for each lead time. These means are the MAPEs. Hence, in table A6.2, there are a series of MAPEs for each variable with a different MAPE for each lead time.
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. Full-time-equivalent enrollment was derived by adding one-third of the part-time students to the number of full-time students for those three years.
The projected values for disposable income and the revenues of state and local governments per capita were developed using the WEFA Group's Mark 11 Quarterly Model of the U.S. Economy. Projected values of the Bureau of Labor Statistics' Consumer Price Index for all urban consumers, which were used for adjusting the higher education finance data, and the implicit price deflator for personal consumption expenditures, which was used for adjusting disposable income per capita, were also developed using the Quarterly Model of the U.S. Economy. The WEFA Group supplied the historic values for these variables.
Both the historic and projected values for the population were supplied by the U.S. Bureau of the Census.
The Higher Education Price Index was considered as a replacement for the Consumer Price Index for placing the higher education expenditures in constant dollars. As projections of the price index are required for placing the forecasts into current dollars, and as there are no projections of the Higher Education Price Index, the Consumer Price Index was used.
The values of all of the variables from The WEFA Group were placed in academic-year terms. The data were available in quarterly format so the academic-year numbers were calculated by taking the average of the last 2 quarters of 1 year with the first 2 of the next year.
