Gender Disparities in High
Academic Achievement
Nicole Fortin, Economics, UBC
Philips Oreopoulos, Economics, University of Toronto
Shelley Phipps, Economics, Dalhousie University
Social Interactions, Identity and Well-Being Program
Canadian Institute for Advanced Research (CIFAR)
June 2011
Gender Disparities in Academic Achievement
 Because women have come to far outnumber men among recent
college graduates in most industrialized countries, new questions
about gender disparities in educational attainment are emerging.
 Among OECD countries (OECD, 2006), the average share of the
student population accounted for by women reached 55% in 2005.
 Only four countries are likely not to achieve at least parity
between men and women by 2015: Korea, Turkey, Japan and
Switzerland.
2
Women now make up close to 60% of
university enrollment
Proportion of women in college/university enrollment
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
1947 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 2002 2007
Enrolment -United States
Enrolment -Canada
Source: Statistics Canada and NCES
BA Granted - United States
Degree Granted - Canada
3
Enrollment Rates in Degree Granting Institutions
1975
1980
1985
1990
Year
1995
Female
Female-Male Difference
-.05 .05
.4
Gender Difference in Rate
.5
of 18-24 year olds
.3
Enrollment Rate
Women’s university enrollment rates
continue to rise faster than men’s
2000
2005
2010
Male
Source: NCES Table 204, from October CPS 1967-2008
4
Gender Disparities in Academic Achievement
 Historically, girls have long obtained, on average, better grades in
school than boys.
 But because these achievements did not translate into higher levels
of educational attainment or better labor market outcomes for
women relative to men, much research has concentrated on
explaining the remaining gaps in women’s performance, e.g. in math
tests.
 The relative underperformance of boys is now attracting more
attention for several reasons.
5
1990s
2000s
Why should we care about the new gender
imbalance in higher education?
• As the manufacturing sector continues to shrink, there are less
“good jobs” than before for men with no post-secondary education
and a continuously increasing college premium for men.
• Consequences for potential labour shortage in occupations that do
not attract a lot of women, e.g. engineering, orthopedic surgeons.
• Consequences for the marriage market as college-educated women
will find fewer potential partners with the same level of education.
• Women may increasingly face the double-burden of family and
financial responsibilities.
• Parents are concerned about boys staying home until their early
30’s (i.e. delayed entry into adulthood).
9
Literature
• Causes of the lower participation of men in higher education
– Jacob (2002), Charles and Luoh (2003), Cho (2007), Frenette
and Zeman, (2007), Conger and Long (2008), Schwenkenberg
(2011)
– lower high school performance, less rigorous high school
classes
– lower parental aspirations, lower non-cognitive skills, behavioral
issues
– returns to college (greater variance among men) and other
related benefits higher for women
11
Literature
• Causes of the lower relative school performance of boys
– Machin and McNally (2005), Duckworth and Seligman (2006),
Buchmann, DiPrete, and McDaniel (2008), Lai (2009),
– Boys lower reading scores, as well as lower parental
expectations of boys’s reading skills
– Girls have higher levels of non-cognitive skills, including
attentiveness, and organizational skills (Farkas et al, 1990;
Jacob, 2002) self-discipline (Silverman, 2003; Duckworth and
Seligman, 2006) and persistence, they put more effort and are
less disruptive than boys (Downey and Vogt Yuan, 2005)
– Family resources and parental education
– Educational aspirations (Buchmann and Dalton, 2002)
12
Goal of the Paper
• The goal of this paper to study changes over the past three
(two) decades in some explanatory factors underlying the
gender disparities in educational achievement
– Three sets of changing factors include family environment, labor
market work during school, and planning for the future,
• The focus is on trends in high school performance
– self-reported grades by 12th, 10th and 8th graders
• using data from a long lived series of cross-sectional surveys
– the American “Monitoring the Future” Surveys conducted
yearly from 1976 (1991) to 2009
13
Goal of the Paper
• Decompose changes in the gender disparities across the
1980s, 1990s and 2000s to understand what changed?
• Warning! this is an accounting exercise, not “causal
inference”
• Not looking at the relationship between under-motivated or
under-performing boys and teachers (Dee, 2005, 2006) or
teaching styles (Algan, Cahuc, and Shleifer, 2010).
14
Preview of Findings
• Boys and girls are increasingly raised in somewhat different families,
that would seem to disadvantage girls
– Larger families (Angrist and Evans, 1998), more likely absent
father (Dahl and Moretti, 2008), less college educated parents,
mom more likely to work full-time
– Despite that girls with higher grades are largely “swimming
upstream” with regards to family characteristics
• In the 1980s, boys were more likely to work during school; by the
2000s, the gap had disappeared
– Working during high school is associated with academically high
achieving girls
15
Preview of Findings
• Factors associated with “Planning for the Future”
– Choice of high school (academic, general, vocational, etc.)
– Own expectations about type of post-secondary choices (military,
vocational, two-year college, four-year college, graduate school)
• are found to be the post powerful set of factors “accounting” for
changes over time in gender differences in high academic
achievement in secondary school.
– These factors have changed substantially over the past 30 years
– They are important as early as grade 8, and perhaps sooner!
16
Outline of the Talk
1.
Introduction
2.
Data
3.
Changes in Gender Differences in Academic Achievement
4.
Explanatory Factors: Changes in Family Environment, Working
during School and Planning for the Future
5.
Decomposition Methodology: OB with Reweighting
6.
Aggregate Decomposition Results
7.
Detailed Decomposition Results
8.
Conclusion
Data: ‘Monitoring the Future’ Surveys
• Our main data source are the ‘Monitoring the Future’ surveys
– an on-going study of the behaviors, attitudes, and values of
American secondary school students.
– conducted by the Institute for Social Research, University of
Michigan to monitor substance abuse in particular .
– We use the cross-sectional surveys of 8th, 10th, and 12th graders
conducted yearly from 1976 (1991 for 8th/10th ) to 2009.
– These data comprise 10,000 to 16,000 observations per grade
per year for the core questions.
– Many more attitudes and behavioral questions are asked of
students answering one of 6 modules.
– Focus on core sample.
18
Proportion of High School Students who say they
“Will Definitively Go to College”
.4
.2
0
Proportion
.6
.8
A. Proportion among U.S. 12th Graders by Gender
1975
1980
1985
1990
Year
1995
Female
Female-Male Difference
Source: Authors’ Computation, Monitoring the Future Surveys, 1976-2009
2000
2005
2010
Male
20
As early as 8th grade, girls are expecting to go
to college in greater numbers than boys
.3
.4
Proportion
.5
.6
.7
B. Relative Proportion of Female Students who will “Definitively go to College”
1975
1980
1985
1990
12th graders
8th graders
Year
1995
2000
2005
2010
10th graders
Source: Authors’ Computation, Monitoring the Future Surveys, 1976-2009
21
Girls have long obtained, on average, better
grades in school than boys
Gender Difference
3
0
.25
.5
2.5
Mean Grades
3.5
4
A. All 12th Graders
1975
1980
1985
1990
Year
1995
2000
Female
Female-Male Difference
Source: Authors’ Computation, Monitoring the Future Surveys, 1976-2009
2005
2010
Male
22
Consistent with trends from
High School Transcript Study
24
Descriptive Statistics:
Self-reported grades
12th grade
Self-reported grades
Index
D (69 or below) 1
C- (70-72)
1.7
C (73-76)
2
C+ (77-79)
2.3
B- (80-82)
2.7
B (83-86)
3
B+ (87-89)
3.3
A- (90-92)
3.7
A (93-100)
4
1976-1988
Boys
Girls
0.015
0.046
0.106
0.148
0.165
0.203
0.152
0.091
0.074
0.007
0.023
0.068
0.104
0.134
0.218
0.199
0.137
0.110
1989-1999
Boys
Girls
*
*
*
*
*
*
*
*
*
0.015
0.037
0.087
0.127
0.149
0.202
0.159
0.117
0.106
0.007
0.019
0.053
0.088
0.121
0.200
0.196
0.164
0.154
2000-2009
Boys
Girls
*
*
*
*
*
*
*
*
0.014
0.031
0.065
0.099
0.129
0.187
0.175
0.154
0.147
0.005
0.016
0.039
0.068
0.103
0.169
0.190
0.203
0.207
*
*
*
*
*
*
*
*
25
Descriptive Statistics:
Self-reported grades
12th grade
Self-reported grades
Index
D (69 or below) 1
C- (70-72)
1.7
C (73-76)
2
C+ (77-79)
2.3
B- (80-82)
2.7
B (83-86)
3
B+ (87-89)
3.3
A- (90-92)
3.7
A (93-100)
4
1976-1988
Boys
Girls
0.015
0.046
0.106
0.148
0.165
0.203
0.152
0.091
0.074
0.007
0.023
0.068
0.104
0.134
0.218
0.199
0.137
0.110
1989-1999
Boys
Girls
*
*
*
*
*
*
*
*
*
0.015
0.037
0.087
0.127
0.149
0.202
0.159
0.117
0.106
0.007
0.019
0.053
0.088
0.121
0.200
0.196
0.164
0.154
2000-2009
Boys
Girls
*
*
*
*
*
*
*
*
0.014
0.031
0.065
0.099
0.129
0.187
0.175
0.154
0.147
0.005
0.016
0.039
0.068
0.103
0.169
0.190
0.203
0.207
*
*
*
*
*
*
*
*
26
But girls have increase their relative proportion
among high achievers
Female and Male Densities of Self-Reported Grades among 12th graders
Female - 2000-2009
1
2
3
4
.6
0
.2
.4
.6
.4
.2
0
0
.2
.4
.6
.8
Female - 1989-1999
.8
Female - 1976-1988
1
3
4
1
2
3
4
Male - 2000-2009
1
2
3
4
.6
0
.2
.4
.6
.4
.2
0
0
.2
.4
.6
.8
Male - 1989-1999
.8
Male - 1976-1988
2
1
2
3
4
Source: Authors’ Computation, Monitoring the Future Surveys, 1976-2009
1
2
3
4
27
But girls have increase their relative proportion
among high achievers
Female and Male Densities of Self-Reported Grades among 8th graders
Female - 1991-1999
Female - 2000-2009
1
2
3
4
.6
0
.2
.4
.6
.4
.2
0
0
.2
.4
.6
.8
Female - 1991-1999
1
3
4
3
4
3
4
.6
0
.2
.4
.6
.4
0
2
2
Male - 2000-2009
.2
.4
.2
0
1
1
Male - 1991-1999
.6
Male - 1991-1999
2
1
2
3
4
1
2
Source: Authors’ Computation, Monitoring the Future Surveys, 1976-2009
3
4
29
Gender gap in the proportion of students in
each grade bin is the dependent variable
-.04
-.02
0
.02
.04
.06
Female/Male Differences in School Grades of 12th Graders
1
1.3
1.7
2
2.3
2.7
School Grade Index
1976-1988
2000-2009
3
3.3
3.7
4
1989-1999
Source: Authors’ Computation, Monitoring the Future Surveys, 1976-2009
30
Gender gap in the proportion of students in
each grade bin is the dependent variable
0
-.04-.02
2
3
School Grade Index
4
1
2000-2009
2
3
School Grade Index
1991-1999
4
2000-2009
0
.02 .04 .06
/Male Difference in Proportions
0
.02 .04 .06
1991-1999
4-.02
B. 8th Graders
.02 .04 .06
A. 10th Graders
4-.02
1
Female/Male Difference in Proportions
-.04-.02
0
.02 .04 .06
Female/Male Differences in School Grades
Source: Authors’ Computation, Monitoring the Future Surveys, 1976-2009
31
Explanatory Factors
1) Family environment including parental education (SES) and family
structure, including absent dad/mom, mom working, no. of siblings
2) Labor market work during the school year, including hours and
wages
3) Planning for the future include type of school attended and
expectations for post-secondary studies, including army and
vocational
4) Controls for student endowments including race and smoking (as a
measure of time impatience), but excluding “totally” endogenous
behaviors such as leisure and study time
32
Gender and Academic Achievement
Students’
endowments
Male or
Female
Childhood
Family Size,
Divorce, Parents’
Education, Mom
working, etc.
Labor Market
Experience
Achievement in High
School
Youth’s
Decision to
pursue Higher
Education
Who do I want to be
when I grow up ?
33
Gender and Academic Achievement
Students’
endowments
Male or
Female
Childhood
Family Size,
Divorce, Parents’
Education, Mom
working, etc.
Labor Market
Experience
Achievement in High
School
Youth’s
Decision to
pursue Higher
Education
Planning for the
Future
34
Gender Disparities in Family Structure
12th Grade
Selected Variables
1976-1988
Boys
Girls
Siblings not same household
Three or more siblings
Father not same household
Mother not same household
Mom working: No
Some of the time
Most of the time
All the time
Father education: less than primary
Some high school
Completed College
Graduate or professional
Mother education: less than primary
Some high school
Completed College
Graduate or professional
0.245
0.424
0.172
0.078
0.312
0.311
0.175
0.202
0.063
0.147
0.188
0.126
0.033
0.128
0.163
0.071
0.236
0.449
0.189
0.068
0.299
0.301
0.165
0.235
0.079
0.156
0.174
0.119
0.043
0.152
0.144
0.071
1989-1999
Boys
Girls
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
0.327
0.345
0.203
0.099
0.198
0.253
0.195
0.353
0.035
0.102
0.229
0.153
0.027
0.083
0.233
0.107
0.312
0.366
0.229
0.085
0.185
0.242
0.176
0.397
0.047
0.111
0.213
0.140
0.036
0.102
0.210
0.104
2000-2009
Boys
Girls
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
0.329
0.332
0.207
0.096
0.146
0.206
0.185
0.462
0.031
0.098
0.253
0.147
0.027
0.071
0.290
0.125
0.311
0.374
0.244
0.089
0.140
0.196
0.170
0.495
0.041
0.108
0.225
0.142
0.034
0.082
0.257
0.124
*
*
*
*
*
*
*
*
*
*
*
*
*
*
Gender Disparities in Family Structure
• In comparison with girls, boys are raised
– in smaller families,
– where the dad is more likely to live in the same household
– where the dad is more educated (higher proportion had
completed a college)
– where the mom is more likely not to have worked and less likely
to have worked “all of the time”
– where the mom is more educated (higher proportion had
completed a college)
• Over the time, there are more mom working “all the time”
• The gender gaps are similar in the sample without Blacks
36
Gender Disparities in Working for Pay
and Planning for the Future
12th grade
Selected Variables
1976-1988
Boys
Girls
Works for pay over school year
0.848 0.797
Average hours of work (mid)
15.189 12.900
Average earnings per week (mid) 42.050 33.538
Type of high school: Academic
0.478 0.504
General
0.302 0.311
Vocational
0.158 0.123
Other
0.061 0.063
Index of likeness to attend: (overall mean zero)
Army
0.090 -0.083
Vocational
0.028 -0.026
Two-year college
-0.014 0.013
Four-year college
0.000 0.000
Graduate or professional
0.002 -0.002
Number of observations
78616 84294
1989-1999
Boys
Girls
2000-2009
Boys
Girls
* 0.801 0.792 *
* 14.037 13.074 *
* 59.164 50.555 *
* 0.546 0.608 *
* 0.284 0.273 *
* 0.109 0.069 *
0.061 0.050 *
0.755 0.756
13.024 12.633 *
67.517 59.931 *
0.518 0.589 *
0.328 0.298 *
0.081 0.049 *
0.073 0.065 *
* 0.070
* 0.030
* -0.004
-0.030
* -0.031
61996
0.065
0.035
-0.001
-0.042
-0.043
50549
-0.065
-0.028
0.004
0.027
0.029
68192
*
*
*
*
*
-0.057
-0.031
0.001
0.037
0.038
57202
37
*
*
*
*
Gender Disparities in Working for Pay
and Planning for the Future
12th grade
Selected Variables
1976-1988
Boys
Girls
Works for pay over school year
0.848 0.797
Average hours of work (mid)
15.189 12.900
Average earnings per week (mid) 42.050 33.538
Type of high school: Academic
0.478 0.504
General
0.302 0.311
Vocational
0.158 0.123
Other
0.061 0.063
Index of likeness to attend: (overall mean zero)
Army
0.090 -0.083
Vocational
0.028 -0.026
Two-year college
-0.014 0.013
Four-year college
0.000 0.000
Graduate or professional
0.002 -0.002
Number of observations
78616 84294
1989-1999
Boys
Girls
2000-2009
Boys
Girls
* 0.801 0.792 *
* 14.037 13.074 *
* 59.164 50.555 *
* 0.546 0.608 *
* 0.284 0.273 *
* 0.109 0.069 *
0.061 0.050 *
0.755 0.756
13.024 12.633 *
67.517 59.931 *
0.518 0.589 *
0.328 0.298 *
0.081 0.049 *
0.073 0.065 *
* 0.070
* 0.030
* -0.004
-0.030
* -0.031
61996
0.065
0.035
-0.001
-0.042
-0.043
50549
-0.065
-0.028
0.004
0.027
0.029
68192
*
*
*
*
*
-0.057
-0.031
0.001
0.037
0.038
57202
38
*
*
*
*
Gender Disparities in Working for Pay
and Planning for the Future
• In the 1980s, boys were more likely than girls to work during school,
but that gap has disappeared in the 2000s
• Boys continue to work slightly more hours and have higher earnings
• In terms of types of school,
– The gap in favor of girls in the proportion attending an academic
high school has grown
– The gap in favor of girls in the proportion attending a general
high school has reversed
• In terms of post-secondary aspirations,
– A gap in favor of girls expecting to attend a 4-yr college has
opened while the gap for 2-yr college has closed
– The gap in favor of boys expecting to attend grad school has
reversed
39
Conditional Probability Model of
Academic Achievement
• Because we are interested in the gender gap in specific grades, we
specify a linear probability model
P(g) = Prob(Gig = g | X ) = Xig γg + ε ig
• where Gig is equal to 1 if the student’s grade is g and 0 otherwise.
• Advantages: Does not rely on the assumptions of normality of
residuals and estimation of nuisance parameter (σε2).
– By comparison with an ordered probit model, this model allows the
educational responses to be different by school grade
– By comparison with a multinomial logit, there is no need to linearized
the responses.
• Disadvantages: The predicted probabilities are not bounded
between 0 and 1. In practice, there are some under-predictions (<0),
but the predicted probabilities over all grades sum to 1.
Conditional Probability Model of
Academic Achievement : Estimates
12th graders - 2000-2009
SelectedExplanatory
Boys
Variables
Race: Black
13.731 (19.23)
Smoked cigarettes per day: None (base)
Less than one-half pack 7.710 (16.43)
One to 1½ pack
8.673 (7.66)
Father not same household 2.663 (5.31)
Mother not same household 1.464 (2.13)
Mom Working: All the time 3.982 (6.80)
Father education: less than primary
3.230 (2.44)
Completed College
-2.104 (-3.76)
Graduate or professional -2.262 (-3.18)
Mother education: less than -2.630
primary (-1.85)
Completed College
-2.340 (-4.33)
Graduate or professional -2.356 (-3.20)
C+ (77-79): 2.3
Boys as Girls X's
Girls
Boys
A (93-100): 4
Boys as Girls X's
Girls
15.266 (25.34) 11.243 (20.63)
-14.390 (-20.56) -16.050 (-25.59) -16.436 (-25.74)
7.301 (15.61) 8.436 (20.66)
8.347 (6.69) 11.808 (10.96)
2.769 (6.05) 2.159 (5.38)
0.165 (0.24) 1.079 (1.81)
4.087 (7.14) 3.168 (6.38)
4.256 (3.78) 3.368 (3.50)
-1.561 (-2.84) -0.591 (-1.25)
-2.799 (-4.05) -1.397 (-2.36)
-2.147 (-1.73) 1.915 (1.81)
-2.314 (-4.32) -3.655 (-7.88)
-2.330 (-3.25) -2.738 (-4.44)
-10.737 (-23.35) -12.137 (-24.93) -12.657 (-26.45)
-12.794 (-11.53) -13.839 (-10.66) -14.511 (-11.49)
-1.628 (-3.32) -2.661 (-5.59) -2.921 (-6.21)
-0.959 (-1.42) -0.897 (-1.27) -2.610 (-3.73)
-4.452 (-7.76) -4.334 (-7.27) -5.289 (-9.09)
-1.011 (-0.78) -3.594 (-3.07) -3.093 (-2.74)
2.134 (3.90) 1.583 (2.76) 3.168 (5.70)
3.839 (5.51) 3.324 (4.62) 4.176 (6.03)
0.207 (0.15) -0.137 (-0.11) -4.727 (-3.80)
2.795 (5.27) 3.784 (6.78) 4.599 (8.46)
1.829 (2.53) 2.726 (3.65) 3.444 (4.76)
Note: T-statistics in parentheses
41
Conditional Probability Model of
Academic Achievement : Estimates
12th graders - 2000-2009
Selected Explanatory
Variables
Boys
Type of high school:
Academic
-10.187
General
0.861
Vocational
-4.549
Other (base)
Index of likeness to attend:
Army
3.896
Vocational
1.901
Two-year college
14.943
Four-year college
-13.714
Graduate or professional -12.229
Constant
22.347
R-squared
0.133
Number of observations
50549
C+ (77-79): 2.3
Boys as Girls X's
A (93-100): 4
Girls
Boys
Boys as Girls X's
Girls
(-12.99) -10.230 (-13.05) -13.407 (-19.62)
(1.11) 0.675 (0.85) -1.231 (-1.78)
(-4.62) -4.949 (-4.41) -4.750 (-4.96)
12.301 (16.01) 11.914 (14.60) 15.265 (19.06)
-0.701 (-0.92) -1.618 (-1.96) -0.385 (-0.47)
5.736 (5.94) 6.432 (5.50) 5.191 (4.62)
(5.97)
(2.77)
(26.38)
(-18.20)
(-17.55)
(20.17)
-3.893
-4.900
-15.843
10.191
18.600
39.579
0.180
50549
3.302
1.141
16.272
-13.350
-11.748
22.013
0.140
50549
(3.52)
(1.65)
(31.83)
(-16.96)
(-18.24)
(20.10)
3.409
2.243
10.918
-11.363
-7.126
19.579
0.136
57202
(4.21)
(3.78)
(23.80)
(-16.90)
(-12.69)
(20.54)
(-6.09)
(-7.29)
(-28.53)
(13.80)
(27.23)
(36.46)
-2.026
-4.264
-17.652
9.514
17.459
41.681
0.177
50549
(-2.07)
(-5.92)
(-33.16)
(11.61)
(26.03)
(36.56)
-1.270
-3.364
-16.354
10.763
13.728
47.680
0.187
57202
(-1.34)
(-4.84)
(-30.43)
(13.66)
(20.86)
(42.70)
Note: T-statistics in parentheses
42
Decomposition Methodology
• Goal of the exercise is to
• 1) determine what portion of the gender gap in grades is attributable
o to differences in the characteristics of boys and girls
o to gender differences in the educational response to these
characteristics
 Aggregate decomposition
• 2) determine which explanatory factors and responses to these
explanatory factors are relatively more important
 Detailed decomposition
• Warning! This is an accounting exercise and not a causal
determination
43
Decomposition Methodology
• The classic Oaxaca-Blinder (1973-74) methodology is based on the
construction of a counterfactual state of world.
• Assuming that grades (G) can be modeled as a linear function of
characteristics (X) that is different for girls (F=1) and boys (F=0)
E [G|X,F = 1] = E [X|F = 1]β1 and E [G|X,F = 0] = E [X|F = 0]β0 ,
under the zero conditional mean assumption, E[ε| X,F]=0.
• We can ask “What would boys’ grades be if they had the same
characteristics as girls?” or “What would girls’ grades be if they had
the same educational response as boys?”
E [Gc] = E [X|F =1]β0
44
Decomposition Methodology
• We could write the differences between the average grades of girls
(F=1) and boys (F=0) as
ΔμO = E [G|F = 1] - E [G|F = 0] + E[Gc] - E [Gc]
= E [X|F = 1]β1 - E [X|F = 0]) β0 + E [X|F = 1] βo -E [X|F = 1] β0
= (E [X|F = 1] -E [X|F = 0]) β0 + E [X|F = 1](β1-β0)
=
Δ μX
+
Δ μE
composition effect
educational response effect
• But , if the true conditional expectation is not linear, the OB
decomposition is biased (Barsky et al., 2002).
• We address this issue by using a modified decomposition.
45
Reweighted Decomposition
• We reweight the sample of boys so that the distribution of their
characteristics (X) is similar to that of girls, using the reweighting
function
Ψ(X)= [Prob(X | F =1 ) / Prob(X | F =0)]
= [Prob(F =1 | X) / Prob(F =0 | X)] • [ Prob(F =0)/ Prob(F =1)]
• The counterfactual coefficients β01 will be estimated on the
reweighted sample {X0, Ψ(X0) },
• then the difference β1- β01 reflects the true gender gap in
educational responses
• And the counterfactual means X 01 = Σi Ψ(Xi) • Xi
X1
Reweighted Decomposition
• The reweighted decomposition uses the terms from the
reweighted sample as counterfactuals,
ΔμO,R = E [X|F = 1]β1 - E [X0|F = 1]) β01 + E [X0|F = 1] β01 - E [X|F = 0] β0
=
ΔμE,R
+
ΔμX,R
• to obtain a decomposition as the sum of an educational
response composition effect and a composition effect.
• This is called an aggregate decomposition.
• Inasmuch as grade dummies can be averaged out, we obtain
results on the additional assumptions of common support and
conditional independence , F ║ ε|X
Aggregate Decomposition: 12th graders
-.04
-.02
0
.02
.04
.06
Aggregate Decomposition 1976-1988
1
1.3
1.7
2
2.3
2.7
3
School Grade Index
Educational Structure
Total Gender Gap
3.3
3.7
4
Composition Effects
48
Aggregate Decomposition: 12th graders
-.04
-.02
0
.02
.04
.06
Aggregate Decomposition 1989-1999
1
1.3
1.7
2
2.3
2.7
3
School Grade Index
Educational Structure
Total Gender Gap
3.3
3.7
4
Composition Effects
49
Aggregate Decomposition: 12th graders
-.04
-.02
0
.02
.04
.06
Aggregate Decomposition 2000-2009
1
1.3
1.7
2
2.3
2.7
3
School Grade Index
Educational Structure
Total Gender Gap
3.3
3.7
4
Composition Effects
50
Aggregate Decomposition: 8th graders
-.04
-.02
0
.02
.04
.06
Aggregate Decomposition 2000-2009
1
1.3
1.7
2
2.3
2.7
3
School Grade Index
Educational Structure
Total Gender Gap
3.3
3.7
4
Composition Effects
51
Reweighted Decomposition
• Each term of the reweighted decomposition can be further
broken down into the “pure” effect and a residual term
ΔμX,R = E [X0|F = 1]) β01 - E [X|F = 0] β0 + E [X0|F = 1] βo - E [X0|F = 1])β0
= (E [X0|F = 1] -E [X|F = 0]) βo + E [X0|F = 1]) ](β01 – βo)
ΔμX,p
=
ΔμX,e
+
pure composition effect
specification error
ΔμE,R = E [X|F = 1]β1 - E [X0|F = 1]) β01 - E [X|F = 1]) β01 + E [X|F = 1]) β01
= E [X|F = 1]) ](β1 – β01) + (E [X|F = 1] - E [X0|F = 1] )β01
=
ΔμE,p
pure response effect
+
ΔμE,e
reweighting error
Reweighted Decomposition
• The specification error ΔX,e =E [X0|F = 1](β01 - β0) corresponds to the
difference in the composition effects estimated by reweighting and
using simple regressions, where E [X0|F = 1] is the mean of the
reweighted sample.
• The reweighting error ΔE,e =(E [X|F =1]- E [X0|F = 1]) β01 goes to zero
in a large sample.
• The detailed reweighted decomposition can thus be obtained by
running two Oaxaca-Blinder decompositions:
– OB1) with sample 1 and sample 01 to get the pure wage structure
effect,
– OB2) with sample 0 and sample 01 to get the pure composition
effect.
Detailed Decomposition: 2000-2009
Selected Grades
12th graders - 2000-2009
C+ (77-79): 2.3
A (93-100): 4
3.115 (0.005)
-5.963 (0.007)
8th graders - 2000-2009
C+ (77-79): 2.3
A (93-100): 4
1.521 (0.005)
-6.032 (0.007)
Total Explained
Race
Family Structure
Work
Parental Education
Type of High School
Smoking, SMSA
Post-secondary
expectations
1.024
-0.238
-0.106
0.036
-0.092
0.257
0.013
0.733
-0.125
-0.031
0.122
-0.157
0.166
-0.026
1.153 (0.002)
-2.001 (0.003)
0.783 (0.002)
-2.100 (0.003)
Specification Error
-0.052 (0.006)
0.085 (0.007)
0.138 (0.006)
-0.120 (0.007)
Total Differential
(0.003)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.000)
-2.007
0.224
0.167
-0.104
0.173
-0.375
-0.090
(0.004)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.003)
(0.000)
(0.001)
(0.001)
(0.001)
(0.001)
(0.000)
-2.271
0.146
0.069
-0.107
0.261
-0.592
0.051
(0.004)
(0.001)
(0.001)
(0.001)
(0.001)
(0.001)
(0.000)
Note: Total Explained = (E [X0|F = 1] -E [X|F = 0]) βo + E [X0|F = 1]) ](β01 – βo)
54
Detailed Decomposition: 2000-2009
Selected Grades
12th graders - 2000-2009
C+ (77-79): 2.3
A (93-100): 4
3.115 (0.005)
-5.963 (0.007)
8th graders - 2000-2009
C+ (77-79): 2.3
A (93-100): 4
1.521 (0.005)
-6.032 (0.007)
Total Responses
Race
Family Structure
Work
Parental Education
Type of High School
Smoking, SMSA
Post-secondary
expectations
Constant
2.079
0.317
-0.054
-0.212
0.026
0.894
0.037
0.539
0.279
-0.351
0.059
-0.411
0.123
-0.100
-0.133 (0.002)
1.203 (0.030)
0.109 (0.003)
-0.281 (0.042)
-0.068 (0.002)
1.009 (0.020)
0.113 (0.002)
-1.240 (0.027)
Reweighting Error
0.065 (0.001)
0.162 (0.003)
0.110 (0.001)
-0.230 (0.003)
Total Differential
(0.005)
(0.002)
(0.016)
(0.009)
(0.010)
(0.020)
(0.010)
-3.879
0.204
0.321
-1.560
-1.340
-2.827
1.496
(0.007)
(0.003)
(0.022)
(0.012)
(0.014)
(0.027)
(0.013)
(0.005)
(0.002)
(0.011)
(0.004)
(0.011)
(0.006)
(0.009)
-3.411
-0.090
0.135
-0.625
-1.278
-1.566
1.140
(0.007)
(0.003)
(0.014)
(0.006)
(0.015)
(0.008)
(0.013)
Note: Total Responses = E [X|F = 1]β1 - E [X0|F = 1]) β01 - E [X|F = 1]) β01 + E [X|F = 1]) β01
Detailed Decomposition: 12th Graders
-.04
-.02
0
.02
.04
.06
Detailed Decomposition 2000-2009 - Family
1
1.3
1.7
2
2.3
2.7
3
School Grade Index
Due to B-Diff in Family
Total Gender Gap
3.3
3.7
4
Due to X-Diff in Family
58
Detailed Decomposition: 8th Graders
-.04
-.02
0
.02
.04
.06
Detailed Decomposition 2000-2009 - Family
1
1.3
1.7
2
2.3
2.7
3
School Grade Index
Due to B-Diff in Family
Total Gender Gap
3.3
3.7
4
Due to X-Diff in Family
59
Detailed Decomposition: 12th Graders
-.04
-.02
0
.02
.04
.06
Detailed Decomposition 2000-2009 - Labor Market Work
1
1.3
1.7
2
2.3
2.7
3
School Grade Index
Due to B-Diff in Work
Total Gender Gap
3.3
3.7
4
Due to X-Diff in Work
60
Detailed Decomposition: 8th Graders
-.04
-.02
0
.02
.04
.06
Detailed Decomposition 2000-2009 - Labor Market Work
1
1.3
1.7
2
2.3
2.7
3
School Grade Index
Due to B-Diff in Work
Total Gender Gap
3.3
3.7
4
Due to X-Diff in Work
61
Detailed Decomposition: 12th Graders
-.04
-.02
0
.02
.04
.06
Detailed Decomposition 2000-2009 - Planning
1
1.3
1.7
2
2.3
2.7
3
School Grade Index
Due to B-Diff in Planning
Total Gender Gap
3.3
3.7
4
Due to X-Diff in Planning
62
Detailed Decomposition: 12th Graders
-.04
-.02
0
.02
.04
.06
Detailed Decomposition 1976-1988 - Planning
1
1.3
1.7
2
2.3
2.7
3
School Grade Index
Due to B-Diff in Planning
Total Gender Gap
3.3
3.7
4
Due to X-Diff in Planning
63
Detailed Decomposition: 8th Graders
-.04
-.02
0
.02
.04
.06
Detailed Decomposition 2000-2009 - Planning
1
1.3
1.7
2
2.3
2.7
3
School Grade Index
Due to B-Diff in Planning
Total Gender Gap
3.3
3.7
4
Due to X-Diff in Planning
64
Summary of Decomposition Results
• High achieving girls are “swimming upstream” disadvantageous
family environment
• In the 2000s, “Planning for the Future” are most important set of
explanatory factors accounting for girls better grades, even among
8th graders
– Important enough to account for all of the increase of 2.4% ,from
1980s to 2000s, in gender difference in the percentage of
students earnings A’s
• Boys’ lower grades are consistent with greater expectations about
going to the army and to 2 yr-college
65
What have we learned?
• Plans for the future are more strongly associated with grades than
usually anticipated in the literature!
• It is not a surprise that plans for the future may lead student to target
grades, and vice versa, but this underlines the need to act early!
Expectations
about going to
army
C+
Expectations
about going to
grad school
A-, A
66
Thank you!