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Projections of Education Statistics to 2019

NCES 2011-017
March 2011

Introduction to Projection Methodology: Postsecondary Degrees Conferred

Projections in this edition

This edition of Projections of Education Statistics presents projections of postsecondary degrees conferred by level of degree and sex of recipient for 2008Ė09 through 2019Ė20.

Overview of approach

Basic approach

Projections of associateís, bachelorís, masterís, and first-professional degrees for men and women were produced using forecasting equations that relate degrees conferred to full-time enrollment in degree-granting institutions by sex, student level (undergraduate or postbaccalaureate), and institution type (2-year or 4-year). Projections of doctorís degrees for men and women were produced using double exponential smoothing.

Degrees Conferred Model

Procedures used to project degrees

For all degree levels, projections of degrees conferred were made separately for men and for women. The projections for men and women were then summed to get projections of the total number of degrees.

Double exponential smoothing was used to project doctorís degrees, as described below. Multiple linear regression was used to project associateís, bachelorís, masterís, and first-professional degrees based on enrollment variables for men and women. The enrollment variables used for the different levels of degrees are briefly described below.

For details and results of the regression analyses used to project associateís, bachelorís, masterís, and first-professional degrees, see table A-28, under ďData and equations used to project degrees,Ē later in this section.

Associateís degrees. Projections were based on full-time undergraduate enrollment in 2-year institutions by sex.. Menís projections of associateís degrees were based on current full-time enrollment and full-time enrollment lagged 2 years. Womenís projections of associateís degrees were based on current full-time enrollment and full-time enrollment lagged 1 and 2 years.

Bachelorís degrees. Projections were based on full-time undergraduate enrollment in 4-year institutions by sex. For men and for women, bachelorís degree projections were based on current full-time enrollment and full-time enrollment lagged 2 years.

Masterís degrees. Projections were based on full-time postbaccalaureate enrollment by sex. Menís projections of masterís degrees were based on current full-time enrollment and full-time enrollment lagged 1 year. Womenís projections of masterís degrees were based on current full-time enrollment.

Doctorís degrees. Projections were obtained by double exponential smoothing of the historical data on doctorís degrees awarded by sex. A smoothing parameter of 0.4 was used.

First-professional degrees. Projections were based on full-time postbaccalaureate enrollment by sex. For men and for women, first-professional degree projections were based on current full-time enrollment and full-time enrollment lagged 1 and 2 years.

Data and equations used to project degrees

Enrollment data and projections for degree-granting institutions. Historical enrollment data by sex, level of student, and type of institution came from the NCES Integrated Postsecondary Education Data System (IPEDS). For the time period used for each level of degree, see table A-28 on page 138. The enrollment projections used are those produced for this edition of Projections of Education Statistics. For more information about the enrollment projections, see Section A.5. Enrollment in Postsecondary Degree-Granting Institutions, earlier in this appendix.

Data on degrees awarded at all levels. Historical data by level degree and sex of recipient came from the NCES Integrated Postsecondary Education Data System (IPEDS). Doctorís degrees were projected using data for 1960Ė61 to 2007Ė08. For the time periods used for the other degree levels, see table A-28 on page 138.

Estimated equations and model statistics. For details on the equations used to project associateís, bachelorís, masterís, and first-professional degrees, see table A-28 on page 138. The 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, the Breusch-Godfrey Serial Correlation LM test statistic, and residual plots.

Accuracy of projections

No MAPEs were calculated for degrees conferred as the current model used for producing their projections has been used for only one other edition of the Projections of Education Statistics.

For more information about MAPEs, see Section A.0. Introduction, earlier in this appendix.

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Table A-28. Estimated equations and model statistics for degrees conferred, by degree type and sex

Dependent variable Equation1 R2 Breusch-Godfrey Serial Correlation LM test statistic2 Time period
Associate's degrees, men DASSOCM =   1,758 + 79DUGFT2M + 58DUGFT2ML2     0.52 0.10 (0.951) 1980–81 to
2007–08
      (2.3)   (4.1)   (3.3)        
                           
Associate's degrees, women DLOGASSOCW =   # + 0.7DLOGUGFT2WS3 + .5MA(1)     0.59 0.07 (0.964) 1980–81 to
2007–08
      (†)   (3.8)   (2.8)        
                           
Bachelor's degrees, men DBACHM =   640 + 85DUGFT4M + 140DUGFT4ML2     0.81 1.49 (0.475) 1980–81 to
2007–08
      (0.6)   (3.4)   (5.7)        
                           
Bachelor's degrees, women DBACHW =   3620 + 96DUGFT4W + 103DUGFT4WL2     0.62 0.64 (0.726) 1980–81 to
2007–08
      (1.6)   (2.8)   (3.0)        
                           
Master's degrees, men PCHMASTM =   # + 0.6PCHGFTM + 0.6PCHGFTML1 + 0.4AR(1) 0.66 2.84 (0.241) 1970–71 to
2007–08
      (†)   (3.57)   (4.26)   (2.62)    
                           
Master's degrees, women PCHMASTW =   # + 0.4PCHGFTW + 0.6AR(1)     0.60 1.03 (0.596) 1974–75 to
2007–08
      (†)   (2.25)   (3.84)        
                           
First-professional degrees,
men
DFPROM =   101 + 163DFPFTML1 + 89DFPFTML2     0.61 3.34 (0.188) 1971–72 to
2007–08
      (0.6)   (5.1)   (3.0)        
                           
First-professional degrees,
women
DFPROW =   136 + 122DFPFTWL1 + 153DFPFTWL2     0.51 2.75 (0.25) 1971–72 to
2007–08
      (0.7)   (2.7)   (3.6)        
# Rounds to zero.
† Not applicable.
1 AR(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 is the coefficient of determination. Numbers in parentheses are t-statistics. There are no equations for doctor's degrees for men and women as projections of those items were obtained using double exponential smoothing.
DASSOCM = First difference of associate's degrees awarded to men.
DLOGASSOCW = First difference of the log of associate's degrees awarded to women.
DBACHM = First difference of bachelor's degrees awarded to men.
DBACHW = First difference of bachelor's degrees awarded to women.
PCHMASTM = Percentage change in master's degrees awarded to men.
PCHMASTW = Percentage change in master's degrees awarded to women.
DFPROM = First difference of first-professional degrees awarded to men.
DFPROW = First difference of first-professional degrees awarded to women.
DUGFT2M = First difference of full-time male undergraduate enrollment in 2-year institutions.
DUGFT2ML2 = First difference of full-time male undergraduate enrollment in 2-year institutions, lagged two periods.
DLOGUGFT2WS3= First difference of the sum of the full-time female undergraduate enrollment in 2-year institutions over the present year and the previous 2 years.
DUGFT4M = First difference of full-time male undergraduate enrollment in 4-year institutions.
DUGFT4ML2 = First difference of full-time male undergraduate enrollment in 4-year institutions, lagged two periods.
DUGFT4W = First difference of full-time female undergraduate enrollment in 4-year institutions.
DUGFT4WL2 = First difference of full-time female undergraduate enrollment in 4-year institutions, lagged two periods.
PCHGFTM = Percentage change in full-time male graduate enrollment.
PCHGFTML1 = Percentage change in full-time male graduate enrollment lagged one year.
PCHGFTW = Percentage change in full-time female graduate enrollment.
DFPFTML1 = First difference of full-time male first professional enrollment lagged one year.
DFPFTML2 = First difference of full-time male first professional enrollment lagged two years.
DFPFTWL1 = First difference of full-time female first professional enrollment lagged one year.
DFPFTWL2 = First difference of full-time female first professional enrollment lagged two years.
SOURCE: U.S. Department of Education, National Center for Education Statistics, Degrees Conferred Model, 1970–71 through 2007–08. (This table was prepared February 2010.)

 

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