Incremental state higher education expenditures.(ORIGINAL PAPER)

Introduction

This study analyzes various measures of state expenditures on higher education using a panel of data from 45 states for the years 1986 through 2005. (1) Results of panel stationarity tests indicate that each measure of state higher education spending is non stationary. Specifically, each series contains a unit root. It is shown that a unit root in higher education spending is consistent with the incremental model of government spending. The incremental theory argues that current expenditures on a government program are equal to expenditures in the previous period plus a marginal adjustment for changes in some set of economic, demographic, or political factors. To avoid problems associated with the use of non-stationary dependent variables in regression analysis, all measures of state higher education expenditures are differenced to induce stationarity. Panel regressions then are used to identify factors that significantly explain annual increments or changes in state higher education spending.

The regression analysis of increments to state higher education spending addresses several issues raised in previous papers. However, it is unclear if these prior studies used stationary dependent variables in their regressions. For example, Kane et al. (2003) provide evidence that increases in state Medicaid spending have "crowded out" or reduced state higher education expenditures. (Weerts and Ronca 2006) find that increases in elementary education and healthcare spending are associated with greater expenditures on higher education. (2) Kane et al. as well as Tandberg (2008) find that state higher education expenditures are procyclical. In Tandberg's study, a larger proportion of the population of a state either in poverty or above the age of 65 years is associated with lower higher education expenditures. Benton (1992) concludes that total state spending (net of federal funds) was directly related to federal aid to states for some time periods.

Results of this study indicate that stationary increments to state higher education spending are significantly procyclical. In addition, it is shown that the business cycle appears to have a larger effect on higher education spending than on overall state spending. Coefficient estimates are consistent with full adjustment of state higher education expenditures to population growth and over-adjustment of these expenditures to CPI inflation. (3) Larger state governments are associated with significantly greater increments to per capita real higher education expenditures. Federal higher education funds provided to states have a significant direct effect on increments to state funded higher education expenditures as a percentage of the adjusted state budget. This last result provides some support for the findings of Benton.

No significant support is found for the conclusion of prior studies that state Medicaid spending crowds out higher education spending. Similarly, no evidence is found that state spending on elementary education has any significant effect on higher education expenditures. States with a larger percentage of their population categorized as impoverished are found to experience significantly larger annual increments to per capita real higher education expenditures. These differences in results from those of previous investigations may be due to a variety of causes, including differences in the sample periods examined and the use of stationary data in this study.

Measuring State Higher Education Expenditures

Two measures of state higher education expenditures are examined for each of the 45 states. The measures are per-capita real higher education expenditures (PCRHE) and the percentage of the state budget allocated to higher education (PHE). (4) Two versions of each measure are examined. The first version includes federal higher education funds provided to the states and is referred to as gross expenditures. The second version excludes the federal funds and is referred to as net expenditures.

The two measures of state higher education spending are closely related, with an average correlation between increments to the two measures across all states of 0.747 for unadjusted expenditures and 0.693 for adjusted expenditures. However, the two measures potentially offer somewhat different information regarding adjustments to higher education spending. Examination of increments to PCRHE identifies significant influences on the absolute size of state higher education expenditures, while examination of increments to PHE identifies factors that significantly affect the relative size of state higher education expenditures compared to the total of all other state budget items. In addition, the two measures do not move closely together for all states. Correlations of these measures for individual states are as low as 0.228 for increments to unadjusted expenditures and -0.259 for increments to adjusted spending.

The average correlation across all states between adjusted and unadjusted expenditures is quite high (0.917 for PCRHE and 0.885 for PHE). However, it is interesting to examine whether there are differences in influences on higher education spending funded only by state sources (adjusted expenditure) and spending that is partially funded by federal money (unadjusted expenditures). Also, the correlations between versions vary widely across the individual states, with a correlation between adjusted and unadjusted PCRHE as low as 0.343 and a correlation between adjusted and unadjusted PHE as low as 0.2584.

Unit Roots in State Higher Education Expenditures

The first step in the analysis is to test for the presence of unit roots in the expenditures series. A variety of statistical tests for non-stationarity exist. One of the most popular is the augmented Dickey-Fuller (ADF) test. A standard specification for an ADF test is:

[DELTA][S.sub.i,t] = [[alpha].sub.i] + [[delta].sub.i][S.sub.i,t=1] + [j.summation over (j=1)] ([[lambda].sub.i,j] [DELTA][S.sub.i,t-j]) + [[epsilon].sub.i,t]. (1)

The dependent variable in the test equation is the differenced expenditures series at time t in the i'th state ([DELTA][S.sub.i,t]). The explanatory variables are a constant, one lag of the (not differenced) expenditures series ([DELTA][S.sub.i,t-1]), and a number (J) of lagged differenced expenditures included to eliminate serial correlation from the error term ([[epsilon].sub.i,t]). The [[alpha].sub.i], [[delta].sub.i], and ([[lambda].sub.i,j]s are coefficients to be estimated. The expenditures series contains a unit root under the null hypothesis:

[H.sub.0] : [[delta].sub.i] = 0. (2)

Rejection of the null hypothesis implies that the series is stationary.

Unfortunately, the twenty year time span of the expenditures series used in this study is so short that separate ADF tests for each state would have extremely low power. However, Levin and Lin (1993) have developed a test procedure with the potential of improving the power of the unit root test by exploiting the additional information offered by panel data sets. The Levin & Lin procedure allows the [[alpha].sub.i], and ([[lambda].sub.i,j] coefficients to vary across states, but imposes the restriction that the coefficient of interest, [[delta].sub.i], is equal for all states. The null hypothesis of the test is that all individual series contain a unit root ([[delta].sub.i] = 0 for all states), while the alternative hypothesis is stationarity of all individual series ([[delta].sub.i] < 0 with equality of [[delta].sub.i] for all states). The test statistic asymptotically follows a standard normal distribution. Results of this test for each version of the two state higher education expenditures series are presented in the second row of Table 1. A unit root cannot be rejected for any of the state higher education expenditures measures whether they include or exclude federal funding. A second round of tests rejects a unit root in both versions of each differenced expenditures measure. (5)

One potential weakness of the Levin & Lin procedure is that the test imposes the restriction of equal [[delta].sub.i] coefficients for all states. As an alternative, Maddala and Wu (1999) propose that a test first introduced by Fisher (1932) be used instead. This test combines the information from individual tests of the unit root hypothesis to form the following test statistic:

-2 [N.summation over (i=1)] 1n([pi].sub.i]). (3)

Here, ([pi].sub.i]) is the p-value obtained from a unit root test, as shown in equation (1), for the i'th individual state. The test statistic follows a chi-square distribution with 2*N degrees of freedom. The null hypothesis is the same as in the Levin & Lin test. The alternative hypothesis again is stationarity; however, the [[delta].sub.i] coefficients are allowed to differ across states. Results for this test are reported in the third row of Table 1. (6) A unit root cannot be rejected for either version of the two expenditures measures. Results for this test for the differenced expenditures series reject a unit root for both versions of each measure. (7)

The next section of this paper demonstrates that these results are consistent with the incremental model of government expenditures. The test results also imply that changes in the state higher education spending measures should be used as the dependent variables in the panel regressions estimated later in the paper.

Incremental Government Expenditures

The incremental theory of government spending argues that government policies and programs tend to be systematic with only relatively small changes from 1 year to the next. (8) Rather than using cost-benefit analysis to annually set an optimal level of spending for existing programs, government tends to renew previous budgets with marginal adjustments for changes in economic, demographic, or political conditions. Incremental spending may result from a lack of complete information regarding costs and benefits, the costliness of conducting cost-benefit analysis, or bureaucratic inertia.

Print Get the Mag Weekly Updates