A6. Expenditures of Institutions of Higher Education
One current-fund expenditure model and one educational and general expenditure model were estimated for each of three types of higher education institutions-public 4-year, public 2-year, and private 4-year. In each case, econometric techniques were used. Due to the lack of a consistent database for private 2-year schools, the last actual values, for 1995-96, were used as constants. These values for private 2-year schools were used in the tables for expenditures in all institutions (tables 46 and 47.)
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.
Similar econometric models were developed for the three types of institutions. While there has been significantly less work by economists studying the factors influencing higher education finance data than those influencing elementary and secondary finance data, there have been some valuable studies. This body of work was used in building these models.
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.
The Public 4-Year Institutions Expenditure Models
The public 4-year institutions current-fund expenditure model is:
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 1995-96. 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 U.S. Quarterly Model of Standard & Poor's DRI (DRI). 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 1.4 percent and 3.1 percent from 2000-01 to 2009-10. In the low set of alternative projections, the revenues of state and local governments per capita increase at rates between -0.7 percent and 2.0 percent. In the high set of alternative projections, the revenues of state and local governments per capita increase at rates between 2.6 percent and 4.7 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 1998-99 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 1998-99 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.
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:
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 Private 4-Year Institutions Expenditure Models
The private 4-year institutions current-fund expenditure model is:
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 DRI's U.S. Quarterly Model.
In the middle set of projections, disposable income per capita rises each year from 2000-01 to 2009-10 at rates between 1.8 percent and 2.7 percent. In the low set of projections, disposable income per capita increases at rates between 0.5 percent and 2.4 percent. In the high set of projections, disposable income per capita increases at rates between 2.6 percent and 3.9 percent.
In the middle set of projections, the inflation rate varies between 2.2 percent and 2.7 percent. In low set of projections, it varies between 1.7 percent and 2.7 percent, and in the high set of projections, it varies between 0.7 percent and 2.1 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.
The Private 2-Year Institutions Expenditure Models
Unlike the other higher education variables, econometric methods were not used for either private 2-year current-fund expenditures or private 2-year educational and general expenditures. This was due to a change in the sample universe for private 2-year institutions. The period for which the private 2-year universe is relatively consistent, from 1982-83 to 1995-96, has only fourteen observations. This is too short a period for econometric techniques, so another means of projecting private 2-year institution expenditures was required. To compute national totals for all institutions despite this deficiency, another method of estimation was used. Both current-fund expenditures per student and educational and general expenditures per student were assumed to stay constant at the last year for which there are data, 1995-96. These values for private 2-year schools were used in the tables for expenditures in all institutions (tables 37 and 38.)
This is the ninth time in the past twelve years that Projections of Education Statistics has contained projections of higher education expenditure data. The other eight editions were the Projections of Education Statistics to 2009, Projections of Education Statistics to 2008, Projections of Education Statistics to 2007, Projections of Education Statistics to 2006, Projections of Education Statistics to 2005, Projections of Education Statistics to 2004, Projections of Education Statistics to 2003 and Projections of Education Statistics to 2000. The projections that appeared in the seven most 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 different models.
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 six of the last eight 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. No projections from the Projections of Educations Statistics to 2009 could be evaluated as there has been no additional higher education expenditure data since the publication of that edition.
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 separate average for each lead time. These means are the MAPEs of each variable for each lead time which are presented in table A6.2.
The current-fund expenditure data and the educational and general expenditure data are from the "Financial Statistics of Institutions of Higher Education" and 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 numbers 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 a component 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 Universitie" 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 next year.
