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Projections of Education Statistics to 2018

NCES 2009-062
September 2009

Projection Methodology: 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 number of public elementary teachers was projected using the public elementary student/teacher ratio. The ratio was modeled as a function of education revenue from state sources per student, and the level of elementary and secondary teacher wages relative to the overall economy–level wages. The number of public elementary teachers was obtained by applying the projected public elementary student/teacher ratio to the previously projected enrollment in public elementary schools. The number of public secondary teachers was projected using the public secondary student/teacher ratio. The ratio was modeled as a function of local education revenue from state sources per student and public secondary enrollment relative to the 11– to 18–year–old population. The number of public secondary teachers was obtained by applying the projected public secondary student/teacher ratio to the previously projected enrollment in public secondary schools.

The models were estimated using the AR(1) model for correcting for autocorrelation, and all variables are in log form. Local education revenue from state sources were in constant 2000 dollars.

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:

ln(RELENRTCHt) = b0 + b1 l n (RSALARYt) + b2 ln(RSGRNTELENRt)

where:

RELENRTCHt is the public elementary student/teacher ratio in year t;
RSALARYt is the average teacher wage relative to the overall economy–level wage in year t; and
RSGRNTELENRt is the level of education revenue from state sources deflated by the consumer prices chained–price index in constant 2000 dollars per public elementary student in year t.

Each variable affects the public elementary student/ teacher ratio in the expected way. As the average teacher wage relative to the overall economy–level wage increases, schools economize on teachers by increasing the student/ teacher ratio as teachers are now more expensive to hire. As the level of real grants per elementary student increases, the class size decreases. The more money being devoted to education, the more teachers are hired, thus decreasing the student/teacher ratio.

The public secondary teacher model is:

ln(RSCENRTCHt) = b0+ b1ln(RSGRNTSCENRt) + b2ln(RSCENRPUt)

where:

RSCENRTCHt is the public secondary student/teacher ratio in year t;
RSGRNTSCENRt is the level of education revenue from the state sources deflated by the consumer prices chained–price index in constant 2000 dollars per public secondary student in year t; and
RSCENRPUt is the number of students enrolled in the public secondary schools relative to the secondary school–age population in year t.

Each variable affects the public secondary student/teacher ratio in the expected way. As the level of real grants per secondary student increases, the student/teacher ratio decreases. The more money being devoted to education, the more teachers are hired, thus decreasing the student/ teacher ratio. As enrollment rates (number of enrolled students relative to the school–age population) increase, the ratio also increases: increases in the enrollment rate are not matched by increases in the number of teachers.

Table A–23 summarizes the results for the elementary and secondary public teacher models. Enrollment for this equation is by organizational level, not by grade level. Thus, secondary enrollment is not the same as grade 9–12 enrollment because some jurisdictions count some grade 7 and 8 enrollment as secondary.

Private Elementary and Secondary Teachers

Projections of private elementary and secondary teachers for this edition were derived using a different method than that used for the Projections of Education Statistics to 2018. In this edition, the projection of the private school pupil/teacher ratio for 2008 was calculated by multiplying the ratio for 2007 by the percentage change from 2007 to 2008 in the public school pupil/teacher ratio. The same method was then used to calculate the projections of the private school pupil/teacher ratio for 2009 through 2018. The projected pupil/teacher ratios were applied to the projected private school enrollments to produce projections of private school teachers from 2008 through 2018. This method assumes that the future pattern in the trend of private school pupil/teacher ratio will be the same as that for public school pupil/teacher ratio. 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 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 the CCD to produce the number of teachers by organizational level.

Data for private school teachers are from the biennial NCES Private School Universe Survey (PSS). Since the PSS is collected in the fall of odd numbered years, data for years without a PSS collection were estimated using data from the PSS.

New Teacher Hires

Projections of new teacher hires were produced using the Teacher Hires Model. The model was estimated separately for public and private school teachers. The model produces projections of the number of teachers who were not teaching in the previous year, but who will be hired in a given year. Teachers who move from teaching in one sector to the other sector are considered new teacher hires. If a teacher moves from teaching in one public school to a different public school, that teacher would not be counted as a teacher hire for the purposes of this model. On the other hand, if a teacher moves from a public school to a private school, that teacher would be counted as a private school teacher hire since the teacher is moving between sectors.

In order to produce the projections of the number of new teacher hires, data were drawn from a number of sources: the 200304 Schools and Staffing Survey (SASS); 200405 Teacher Follow-Up Survey (TFS); the Common Core of Data (CCD); the Private School Universe Survey (PSS); and the projections of the numbers of public and private elementary and secondary school teachers. The teacher numbers coming from SASS and the TFS are for full-time and part-time teachers, while those for the other surveys are for full-time-equivalent (FTE) teachers.

The following is a general summary of the Teacher Hires Model used to produce the projections for new teacher hires in public schools. A similar process was used for the projections of new teacher hires in private schools. A more thorough presentation can be found in section II of Hussar (1999). As already noted, this model measures the demand for teacher hires. Due to difficulties in defining and measuring the pool of potential teachers, there were no attempts to measure the supply of new teacher candidates.

In step 1 of the Teacher Hires Model, the age distributions of the headcounts of public school teachers from the 200304 SASS are applied to the national number of FTE teachers in 2003 from the CCD.

In step 2, the age-specific continuation rates from the 200405 TFS are applied to the 2003 FTE count of teachers by age, the results being an estimate of the number of FTE teachers who remained teaching in 2004 by individual age. Summing these remaining teachers over all ages produces the estimate of those who remained teaching in 2004. Subtracting the remaining teachers from the total FTE teacher count for 2003 produces an estimate of the number of new FTE teacher hires needed to replace those leaving teaching.

In step 3, the total number of FTE teachers in 2003 is subtracted from the number of FTE teachers for 2004 from the CCD to produce an estimate of the number of new FTE teacher hires that are needed due to the overall increase in the teaching workforce.

In step 4, the number of new FTE teachers needed to replace those leaving teaching from step 2 are added to the estimated net change in the number of FTE teachers from step 3, to get an estimate of the total number of new FTE teacher hires needed in 2004.

In step 5, the age distribution for newly hired full-time and part-time teachers from the 200304 SASS is applied to the estimate of total number of new FTE teacher hires needed in 2004 to produce an estimate of the number of new FTE teacher hires by age. In step 6, for each individual age, the estimate of the number of remaining FTE teachers from step 2 is added to the estimate of the number of newly hired FTE teachers from step 5 to produce estimates of the total number of FTE teachers by age in 2004.

Steps 2 through 6 are then repeated for each year from 2005 through 2018, so that the Teacher Hires Model can produce projections for the number of new teacher hires. Projections of the age-specific continuation rates for public school teachers ages 28 through 66 and private school teacher ages 23 through 65 were used in step 2. These projections were produced using exponential smoothing with a smoothing constant of 0.4. For all other ages, the continuation rates from the 200405 TFS were used in step 2. Projections of the numbers of FTE teachers were used in step 3 for those years in which there were no CCD teacher numbers (2007 through 2018). Three alternative sets of projections of new teacher hires were produced, one set for each of the alternative sets of FTE teacher projections.

A number of assumptions are made in order to make these projections. They include that: (1) the age distribution of FTE teachers in 2003 is similar to that of full-time and part-time teachers in that year (Step 1); (2) the age-specific continuation rates for FTE teachers for each year from 2004 through 2018 are similar to either the projections produced using exponential smoothing or the values from the 200405 TFS depending on the age of the teachers (Step 2); (3) the age distribution for newly hired FTE teachers from 2004 through 2018 is similar to that of newly hired full-time and part-time teachers in the 200304 SASS (Step 3); (4) the actual numbers of FTE teachers for each year from 2006 through 2018 are similar to projections of FTE teachers on table 32; and (5) no economic or political changes further affect the size of the teaching force.

Table A–24 shows the age distributions for full–time and part–time teachers; table A–25 shows age distributions of new teacher hires; and table A–26 shows actual and projected continuation rates of teachers.

Projection Accuracy

An analysis of projection errors from the past 18 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 1.0 percent for 1 year out, 1.5 percent for 2 years out, 3.2 percent for 5 years out, and 6.1 percent for 10 years out. For the 2-year-ahead prediction, this means that one would expect the projection to be within 1.5 percent of the actual value, on average. For more information on the MAPEs, see table A-2.

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