NCES 2011-026
September 2011

## Introduction to Projection Methodology: Elementary and Secondary Teachers

### Projections in this edition

This edition of Projections of Education Statistics presents projected trends in elementary and secondary teachers, pupil/teacher ratios, and new teacher hires from 2009 to 2020. These projections were made using two models:

• The Elementary and Secondary Teacher Model was used to project the number of public school teachers, the number of private school teachers, and the total number of teachers for the nation. It was also used to project pupil/teacher ratios for public schools, private schools, and all elementary and secondary schools.
• The New Teacher Hires Model was used to project the number of new teacher hires in public schools, private schools, and all schools.

### Approach for numbers of teachers and pupil/teacher ratios

Public schools. Multiple linear regression was used to produce initial projections of public school pupil/teacher ratios separately for elementary and secondary schools. The initial projections of elementary pupil/teacher ratios and secondary pupil/teacher ratios were applied to enrollment projections to project the numbers of elementary teachers and secondary teachers, which were summed to get the total number of public school teachers. Final projections of the overall public school pupil/teacher ratios were produced by dividing total projected public school enrollment by the total projected number of teachers.

### Assumptions underlying this method

This method assumes that past relationships between the public school pupil/teacher ratio (the dependent variable) and the independent variables used in the regression analysis will continue throughout the forecast period. For more information about the independent variables, see "Elementary and Secondary Teacher Model," later in this section of appendix A.

Private schools. Private school pupil/teacher ratios were projected by applying each year's projected annual percentage change in the overall public school pupil/teacher ratio to the previous year's private school pupil/teacher ratio. The projected private school pupil/teacher ratios were then applied to projected enrollments at private schools to produce projected numbers of private school teachers.

### Assumptions underlying this method

This method assumes that the future pattern in the trend of private school pupil/teacher ratios will be the same as that for public school pupil/teacher ratios. The reader is cautioned that a number of factors could alter the assumption of constant ratios over the forecast period.

### Approach for new teacher hires

The following numbers were projected separately for public schools and for private schools:

• The number of teachers needed to replace teachers who leave teaching from one year to the next. This number was estimated based on continuation rates of teachers by their age.
• The number of teachers needed to fill openings due to an increase in the size of the teaching workforce from one year to the next. This number was estimated by subtracting the projected number of teachers in one year from the projected number of teachers in the next year.

These two numbers were summed to yield the total number of "new teacher hires" for each control of school—that is, teachers who will be hired in a given year, but who did not teach in that control the previous year. A teacher who moves from one control to the other control (e.g. from a public to private school or from a private to a public school) is considered a new teacher hire, but a teacher who moves from one school to another school in the same control is not considered a new teacher hire.

### Elementary and Secondary Teacher Model

Projections for public schools were produced first. Projections for private schools were produced based partially on input from the public school projections. Finally, the public and private school projections were combined into total elementary and secondary school projections (not shown in the steps below).

### Steps used to project numbers of teachers and pupil/teacher ratios

Public school teachers. The following steps were used for the public school projections:

Step 1. Produce projections of pupil/teacher ratios for public elementary schools and public secondary schools separately. Two separate equations were used—one for elementary schools and one for secondary schools. The equations for elementary and secondary schools included an AR(1) term for correcting for autocorrelation and the following independent variables:

• Independent variables for public elementary school pupil/teacher ratios—(1) average teacher wage relative to the overall economy-level wage, and (2) level of education revenue from state sources in constant dollars per public elementary student.
• Independent variables for public secondary school pupil/teacher ratios—(1) level of education revenue from state sources in constant dollars per public secondary student, and (2) the number of students enrolled in public secondary schools relative to the secondary schoolage population.

To estimate the models, they were first transformed into nonlinear models and then the coefficients were estimated simultaneously by applying a Marquardt nonlinear least squares algorithm to the transformed equation.

For details on the equations, model statistics, and data used to project public school pupil/teacher ratios, see "Data and equations used for projections of teachers and pupil/teacher ratios," below.

Step 2. Produce projections of the number of teachers for public elementary schools and public secondary schools separately. The projections of the public elementary pupil/teacher ratio and public secondary pupil/teacher ratio were applied to projections of enrollments in elementary schools and secondary schools, respectively, to produce projections of public elementary teachers and public secondary teachers.

Step 3. Produce projections of the total number of teachers for public elementary and secondary schools combined. The projections of public elementary teachers and public secondary teachers were added together to produce the projections of the total number of public elementary and secondary teachers.

Step 4. Produce projections of the pupil/teacher ratio for public elementary and secondary schools combined. The projections of the total number of public elementary and secondary teachers were divided by projections of total enrollment in public elementary and secondary schools to produce projections of the overall pupil/teacher ratio in public elementary and secondary schools.

Private school teachers. The following steps were used for the private school projections:

Step 1. Produce projections of the private school pupil/teacher ratio. First, the projection of the private school pupil/teacher ratio for 2010 was calculated by multiplying the private school pupil/teacher ratio for 2009 (the last year of actual data) by the percentage change from 2008 to 2010 in the public school pupil/teacher ratio. The same method was used to calculate the projections of the private school pupil/teacher ratio for 2011 through 2020. That is, each year's projected annual percentage change in the public school pupil/teacher ratio was applied to the previous year's private school pupil/teacher ratio.

Step 2. Produce projections of the number of private school teachers. The projected pupil/teacher ratios were applied to projected private school enrollments to produce projections of private school teachers from 2010 through 2020.

For information about the private school teacher and enrollment data used for the private school projections, see "Data and equations used for projections of teachers and pupil/teacher ratios," below.

### Data and equations used for projections of teachers and pupil/teacher ratios

Public school data used in these projections were by organizational level (i.e., school level), not by grade level. Thus, secondary school enrollment is not the same as enrollment in grades 9 through 12 because some jurisdictions count some grade 7 and 8 enrollment as secondary. For example, some jurisdictions may have 6-year high schools with grades 7 through 12.

Data used to estimate the equation for public elementary school pupil/teacher ratios. The following data were used to estimate the equation:

• To compute the historical elementary school pupil/teacher ratios—Data on 197374 to 200809 enrollments in public elementary schools came from the NCES Common Core of Data (CCD). The proportion of public school teachers who taught in elementary schools was taken from the National Education Association and then applied to the total number of public school teachers from the CCD to produce the number of teachers in elementary schools.
• Data on 197374 to 200809 education revenue from state sources came from the CCD.

Estimated equation and model statistics for public elementary school pupil/teacher ratios. For the estimated equation and model statistics, see table A-11 on page 109. In the public elementary pupil/teacher ratio equation, the independent variables affect the dependent variable in the expected way:

• As the average teacher wage relative to the overall economy-level wage increases, the pupil/teacher ratio increases; and
• As the level of education revenue from state sources in constant dollars per public elementary student increases, the pupil/teacher ratio decreases.

Data used to project public elementary school pupil/teacher ratios. The estimated equation was run using projected values for teacher salaries and education revenues from state sources from 200910 through 202021. For more information, see Section A.0. Introduction, earlier in this appendix and Section A.4 Expenditures for Public Elementary and Secondary Education later in this appendix.

Data used to estimate the equation for public secondary school pupil/teacher ratios. The following data were used to estimate the equation:

• To compute the historical secondary school pupil/teacher ratios—Data on 197374 to 200809 enrollments in public secondary schools came from the NCES Common Core of Data (CCD). The proportion of public school teachers who taught in secondary schools was taken from the National Education Association and then applied to the total number of public school teachers from the CCD to produce the number of teachers in secondary schools.
• Data on 197374 to 200809 education revenue from state sources came from the CCD.
• To compute the historical secondary school enrollment rate—Data on the secondary school-age population from 197374 to 200809 came from the U.S. Census Bureau. Data on enrollments in public secondary schools during the same period came from the CCD, as noted above.

Estimated equation and model statistics for public secondary school pupil/teacher ratios. For the estimated equation and model statistics, see table A-11 on page 109. In the public secondary pupil/teacher ratio equation, the independent variables affect the dependent variable in the expected way:

• As enrollment rates (number of enrolled students relative to the school-age population) increase, the pupil/teacher ratio increases; and
• As the level of education revenue per secondary student increases, the pupil/teacher ratio decreases.

Data used to project public secondary school pupil/teacher ratios. The estimated equation was run using projections for education revenues, public secondary enrollments, and secondary schoolage populations from 200910 through 201920. Secondary enrollment projections were derived from the enrollment projections described in Section A.1. Elementary and Secondary Enrollment. Population projections were from the Census Bureau's 2008 National Population Projections by age and sex (August 2008), ratio-adjusted to line up with the most recent historical estimates.

Private school teacher and enrollment data. Private school data for 198990, 199192, 199394, 199596, 199798, 19992000, 200102, 200304, 200506, 200708, and 200910 came 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.

Private school enrollment projections. Private school enrollments from 2009 to 2020 came from the projections described in Section A.1. Elementary and Secondary Enrollment, earlier in this appendix.

### Accuracy of projections of numbers of teachers

Mean absolute percentage errors (MAPEs) for projections of public school teachers were calculated using the last 20 editions of Projections of Education Statistics. Table C, below, shows MAPEs for projections of the numbers of public school teachers. There was a change in the methodology for projecting private school teachers beginning with Projections of Education Statistics to 2017, and therefore there are too few years of data to present the MAPEs for private school teachers.

### New Teacher Hires Model

The New Teacher Hires 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.

A teacher is considered to be a new teacher hire for a control of school (public or private) for a given year if the teacher teaches in that control that year but had not taught in that control in the previous year. Included among new teachers hires are: (1) teachers who are new to the profession; (2) teachers who had taught previously but had not been teaching the previous year; and (3) teachers who had been teaching in one control the previous year but have moved to the other control. Concerning the last category, if a teacher moves from one public school to a different public school, that teacher would not be counted as a new 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 new teacher hire, since the teacher did not teach in a private school in the previous year.

The New Teacher Hires Model measures the demand for teacher hires. Due to difficulties in defining and measuring the pool of potential teachers, no attempt was made to measure the supply of new teacher candidates.

### Steps used to project numbers of new teacher hires

The steps outlined below provide a general summary of how the New Teacher Hires Model was used to produce projections of the need for new teacher hires.

First, the whole series of steps outlined below was used to produce projections of public school new teacher hires. Then, the same steps were used to produce projections of private school new hires. Finally, the public and private new teacher hires were combined to produce projections of total new teacher hires.

Step 1. Estimate the age distribution of full-time-equivalent (FTE) teachers in 2007. For this estimate, the age distribution of the headcount of school teachers (including both full-time and part-time teachers) in 2007 was applied to the national number of FTE teachers in the same year.

Step 2. Estimate the number of new FTE teacher hires needed to replace those who left teaching between 2007 and 2008. In this step

• Age-specific continuation rates for 2004 were applied to the FTE count of teachers by age for 2007, resulting in estimates of the number of FTE teachers who remained in teaching in 2008 by individual age.
• The FTE teachers who remained in teaching by individual age were summed across all ages to produce an estimate of the total number of FTE teachers who remained teaching in 2008.
• The total number of remaining FTE teachers in 2008 was subtracted from the total FTE teacher count for 2007 to produce the estimated number of FTE teachers who left teaching.

Step 3. Estimate the number of new FTE teacher hires needed due to the overall increase in the teacher workforce between 2007 and 2008. The total number of FTE teachers in 2007 was subtracted from the total number of FTE teachers in 2008 to determine the overall increase in the teaching workforce between 2007 and 2008.

Step 4. Estimate the total number of new FTE teacher hires needed in 2008. The number of FTE teachers who left teaching from step 2 was added to the estimated net change in the number of FTE teachers from step 3 to estimate the total number of new FTE teacher hires needed in 2008.

Step 5. Estimate the FTE count of teachers by age for 2008. In this step

• The age distribution for the headcount of newly hired teachers in 2007 was applied to the estimated total number of new FTE teacher hires in 2008, resulting in the estimated number of new FTE teacher hires by age.
• For each individual age, the estimated number of new FTE teacher hires was added to the estimated number of remaining FTE teachers (from step 2, first bullet) to produce the estimated FTE count of teachers by age for 2008.

Step 6. Repeat steps 2 to 5 for each year from 2009 through 2020.

• In step 2
• For public school teachers ages 22 through 66 and private school teachers ages 21 through 65, projections of age-specific continuation rates were used. A separate smoothing constant, chosen to minimize the sum of squared forecast errors, was used to calculate the projected progression rate for each age. (For a general description of the exponential smoothing technique, see Section A.0. Introduction, earlier in this appendix.)
• For all other ages, the age-specific continuation rates for 2008 (the last year of actual data) were used.
• In step 3, projections of the numbers of FTE teachers were used for all years in which there were no actual teacher numbers. The projections of FTE teachers are described under "Elementary and Secondary Teacher Model," earlier in this section of appendix A.

### Assumptions underlying this method

A number of assumptions are made in order to make these projections. They include that (1) the age distribution of FTE teachers in 2007 was 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 2008 through 2020 are similar to either the projections produced using single exponential smoothing or the values for 2008, depending on the age of the teachers (step 2); (3) the age distribution for newly hired FTE teachers from 2008 through 2020 is similar to that of newly hired full-time and part-time teachers in 2007 (step 3); (4) the actual numbers of FTE teachers for each year from 2008 through 2020 are similar to projections of FTE teachers shown in table 16 on page 53; and (5) no economic or political changes further affect the size of the teaching force.

### Data used for projections of new teacher hires

Data on numbers of public school teachers. Numbers of FTE teachers for 2008 came from the NCES Common Core of Data (CCD).

Data on numbers of private school teachers. Private school data on the numbers of FTE teachers in 200304, 200506, 200708, and 200910 came 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.

Data on the age distribution of public and private school teachers. Data on the age distribution of full-time and part-time public and private school teachers came from the 200708 NCES Schools and Staffing Survey (SASS). These data and their standard errors are shown in table A-12 on page 110.

Data on the age distribution of public and private new teacher hires. Data on the age distribution of newly hired full-time and part-time public and private school teachers came from the 200708 NCES Schools and Staffing Survey (SASS). These data and their standard errors are shown in table A-13 on page 110.

Data on and projections of age-specific continuation rates of public and private school teachers. The 2008 continuation rates came from the 200809 NCES Teacher Follow-Up Survey (TFS). Data from the 199495, 200001, and 2004-05 TFS were also used in the projection of age-specific continuation rates. The actual data, their standard errors, and the projections are shown in table A-14 on page 111.

Projections of the numbers of public and private elementary and secondary school teachers. These projections are described under "Elementary and Secondary Teacher Model," earlier in this section of appendix A.

### Accuracy of projections of new teacher hires

Because this is the fourth edition of Projections of Education Statistics to include projections of new teacher hires, there are too few years of data to present the MAPEs for new teacher hires.