NCES 2011-017
March 2011

Table A-13.  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 Current expenditures per pupil   Education revenue from state sources per capita Equation1 R2 Breusch-Godfrey Serial Correlation LM test statistic2 Time period ln(CUREXP) = 0.58 + 0.64ln(PCI) + 0.20ln(SGRANT) + 0.92AR(1) 0.996 2.60 (0.27) 1973–74 to (0.381) (3.892) (2.364) (17.622) 2006–07 ln(SGRNT) = 0.92 + 1.11ln(PCI) + 0.72ln(ENRPOP) + 0.55AR(1) 0.987 2.02 (0.37) 1973–74 to (0.749) (19.170) (4.237) (4.138) 2006–07
 1AR(1) indicates that the model included an AR(1) term 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. The Theory and Practice of Econometrics, New York: John Wiley and Sons, 1985, pp. 315–318. 2Number in parentheses is Prob. Chi-Square(2) associated with the Breusch-Godfrey Serial Correlation LM Test. A p value greater than 0.05 implies that we do not reject the null hypothesis of no autocorrelation at the 5 or 10 percent significance levels. For an explanation of the Breusch-Godfrey Serial Correlation LM test statistic, see Greene, W. (2000). Econometric Analysis. New Jersey: Prentice-Hall. 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 2006–07; and Revenue Receipts from State Sources Model, 1973–74 through 2006–07. (This table was prepared January 2010.)