NCES 2013-008
January 2013

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
per pupil
ln(CUREXP) =   2.51 + 0.49ln(PCI) + 0.18ln(SGRANT) + 0.97AR(1) 0.997 4.98 (0.08) 1973–74 to
(1.280)   (2.551)   (2.127)   (35.854)     2008–09

Education revenue
from state sources
per capita
ln(SGRNT) =   1.03 + 1.11ln(PCI) + 0.74ln(ENRPOP) + 0.56AR(1) 0.989 1.63 (0.44) 1973–74 to
(0.840)   (20.129)   (4.280)   (4.323)     2008–09
 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. Numbers in parentheses are t-statistics. 2 The number in parentheses is the probability of the Chi-Square 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% significance level for a two-tailed test or 10% 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. 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 2008–09; and Revenue Receipts from State Sources Model, 1973–74 through 2008–09. (This table was prepared March 2012.)