NCES 2011-017
March 2011

Table A-9.  Estimated equations and model statistics for public elementary and secondary teachers

Dependent variable Equation1 R2 Breusch-Godfrey Serial Correlation LM test statistic2 Time period
Elementary ln(RELENRTCH) =   3.93 + .06 ln(RSALARY) - .25 ln(RSGRNTELENR) + .51 AR(1) 0.99 .03 (0.983) 1973 to
(35.037)   (3.532)   (-9.112)   (2.887)     2006

Secondary ln(RSCENRTCH) =   4.16 - .23 ln(RSGRNTSCENR) + .63 ln(RSCENRPU) + .52 AR(1) 0.99 .06 (0.969) 1973 to
(44.931)   (-16.147)   (5.631)   (3.095)     2006
 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. 2 Number 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. RELENRTCH = Ln of the ratio of public elementary school enrollment to classroom teachers (i.e., student/teacher ratio). RSCENRTCH = Ln of the ratio of public secondary school enrollment to classroom teachers (i.e., student/teacher ratio). RSALARY = Ln of the average annual teacher salary relative to the overall economy wage in 2000 dollars. RSGRNTELENR = Ln of the ratio of education revenue receipts from state sources per capita to public elementary school enrollment in 2000 dollars. RSGRNTSCENR = Ln of the ratio of education revenue receipts from state sources per capita to public secondary school enrollment in 2000 dollars. RSCENRPU = Ln of the ratio of enrollment in public secondary schools to the 11- to 18-year-old population. SOURCE: U.S. Department of Education, National Center for Education Statistics, Elementary and Secondary Teacher Model, 1973–2006. (This table was prepared February 2010.)