NCES 2011-026
September 2011

Table A-11.  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) =   3.81 + .07 ln(RSALARY) - .23 ln(RSGRNTELENR) + .32 AR(1) 0.99 .03 (0.985) 1973 to
(40.307)   (5.102)   (-10.551)   (1.989)     2009

Secondary ln(RSCENRTCH) =   4.14 - .24 ln(RSGRNTSCENR) + .49 ln(RSCENRPU) + .63 AR(1) 0.99 .18 (0.912) 1973 to
(41.407)   (-16.565)   (4.293)   (4.383)     2009

 1AR(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 G. Judge, W. Hill, R. Griffiths, H. Lutkepohl, and T. Lee, The Theory and Practice of Econometrics, New York: John Wiley and Sons, 1985, 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. (2000). Econometric Analysis. New Jersey: Prentice-Hall. NOTE: R2 indicates the coefficient of determination. Numbers in parentheses are t-statistics. RELENRTCH = Ratio of public elementary school enrollment to classroom teachers (i.e., pupil/teacher ratio). RSCENRTCH = Ratio of public secondary school enrollment to classroom teachers (i.e., pupil/teacher ratio). RSALARY = Average annual teacher salary relative to the overall economy wage in 2000 dollars. RSGRNTELENR = Ratio of education revenue receipts from state sources per capita to public elementary school enrollment in 2000 dollars. RSGRNTSCENR = 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, 1973–2009. (This table was prepared March 2011.)