NCES 2011-026
September 2011

Table A-15.  Estimated equations and model statistics for current expenditures per pupil in fall enrollment for public elementary and secondary schools, and education revenue from state sources per capita

Dependent variable Equation1 R2 Breusch-Godfrey
Serial Correlation LM
test statistic2
Time period

Current expenditures ln(CUREXP) =   0.58 + 0.64ln(PCI) + 0.21ln(SGRANT) + 0.93AR(1) 0.997 2.42 (0.30) 1973–74 to
per pupil       (0.371)   (3.814)   (2.456)   (18.176)     2007–08

Education revenue ln(SGRNT) =   0.85 + 1.12ln(PCI) + 0.73ln(ENRPOP) + 0.54AR(1) 0.988 2.31 (0.31) 1973–74 to
from state sources       (0.724)   (20.324)   (4.350)   (4.153)     2007–08
per capita

 1 AR(1) indicates that the model was estimated using least squares with the AR(1) process for correcting for first-order autocorrelation. To estimate the model, it was first transformed into a nonlinear model and then the coefficients were estimated simultaneously by applying a Marquardt nonlinear least squares algorithm to the transformed equation. For a general discussion of the problem of autocorrelation, and the method used to forecast in the presence of autocorrelation, see Judge, G., Hill, W., Griffiths, R., Lutkepohl, H., and Lee, T. (1985). The Theory and Practice of Econometrics. New York: John Wiley and Sons, pp. 315–318. 2 The number in parentheses is the probability of the Chi-Square(2) associated with the Breusch-Godfrey Serial Correlation LM Test. A p value greater that 0.05 implies that we do not reject the null hypothesis of no autocorrelation at the 5 percent significance level for a two-tailed test or 10 percent significance level for a one-tailed test, (i.e., there is no autocorrelation present). For an explanation of the Breusch-Godfrey Serial Correlation LM test statistic, see Greene, W. Econometric Analysis. New Jersey: Prentice-Hall, 2000. NOTE: R2 indicates the coefficient of determination. Numbers in parentheses are t-statistics. CUREXP = Current expenditures of public elementary and secondary schools per pupil in fall enrollment in constant 1982–84 dollars. SGRANT = Local governments' education revenue from state sources, per capita, in constant 1982–84 dollars. PCI = Disposable income per capita in constant 2000 chained dollars. ENRPOP = Ratio of fall enrollment to the population. SOURCE: U.S. Department of Education, National Center for Education Statistics, Elementary and Secondary School Current Expenditures Model, 1973–74 through 2007–08; and Revenue Receipts from State Sources Model, 1973–74 through 2007–08. (This table was prepared March 2011.)