## A4. Elementary and Secondary Teachers

Public Elementary and Secondary Teachers

The number of public elementary and secondary teachers was projected separately for the elementary and secondary levels. The elementary teachers were modeled as a function of local education revenue receipts from state sources per capita and elementary enrollment. Secondary teachers were modeled as a function of local education revenue receipts from state sources per capita (lagged 3 years) and secondary enrollment. Local education revenue receipts from state sources were in constant 1982-84 dollars.

The equations in this section should be viewed as forecasting rather than structural equations, as the limitations of time and available data precluded the building of a large-scale, structural teacher model. The particular equations shown were selected on the basis of their statistical properties, such as coefficients of determination (R2s), the t-statistics of the coefficients, the Durbin-Watson statistic, and residual plots.

The multiple regression technique will yield good forecasting results only if the relationships that existed among the variables in the past continue throughout the projection period.

The public elementary teacher model is:

ELTCH = b0 + b1SGRANT + b2ELENR

where:

ELTCH is the number of public elementary teachers.

SGRANT is the level of education revenue receipts from state sources per capita in constant 1982-84 dollars; and

ELENR is the number of students enrolled in public elementary schools.

Each variable affects the number of teachers in the expected way. As the state spends more money on education and as enrollment increases, the number of elementary teachers hired increases.

The public secondary teacher model is:

SCTCH = b0 + b1SGRANT3 + b2SCENR

where:

SCTCH is the number of public secondary teachers;

SGRANT3 is the level of education revenue receipts from state sources per capita in constant 1982-84 dollars, lagged 3 years; and

SCENR is the number of students enrolled in public secondary schools.

Each variable affects the number of teachers in the expected way. As the state spends more money on education and as enrollment increases, the number of secondary teachers hired increases.

Table A4.1 summarizes the results for the elementary and secondary public teacher models.

Enrollment is by organizational level, not by grade level. Thus, secondary enrollment is not the same as grade 9-12 enrollment because some states count some grade 7 and 8 enrollment as secondary. Therefore, the distribution of the number of teachers is also by organizational level, not by grade span.

Private Elementary and Secondary Teachers

Projections of private elementary and secondary teachers were derived in the following manner. For 1960 to 1998, the ratio of private school teachers to public school teachers was calculated by organizational level. These ratios were projected using single exponential smoothing, yielding a constant value over the projection period. This constant value was then applied to projections of public school teachers by organizational level to yield projections of private school teachers. This method assumes that the future pattern in the trend of private school teachers will be the same as that for public school teachers. The reader is cautioned that a number of factors could alter the assumption of constant ratios over the projection period.

The total number of public school teachers, enrollment by organizational level, and education revenue receipts from state sources used in these projections were from the Common Core of Data (CCD) survey conducted by NCES. The proportion of public school teachers by organizational level was taken from the National Education Association and then applied to the total number of teachers from CCD to produce the number of teachers by organizational level.

Projection Accuracy

An analysis of projection errors from the past 12 editions of Projections of Education Statistics indicated that the mean absolute percentage errors (MAPEs) for projections of classroom teachers in public elementary and secondary schools were 1.9 percent for 1 year out, 1.3 percent for 2 years out, 1.9 percent for 5 years out, and 4.6 percent for 10 years out. For the 2-year-ahead prediction, this means that one would expect the projection to be within 1.3 percent of the actual value, on the average. For more information on the mean absolute percentage errors, see table A2

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