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Research ArticleArticles
Open Access

Dynamics of the Gender Gap in High Math Achievement

View ORCID ProfileGlenn Ellison and View ORCID ProfileAshley Swanson
Journal of Human Resources, September 2023, 58 (5) 1679-1711; DOI: https://doi.org/10.3368/jhr.58.5.0620-10972R1
Glenn Ellison
Glenn Ellison is a professor of economics at MIT.
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Ashley Swanson
Ashley Swanson () is an associate professor of economics at the University of Wisconsin–Madison.
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  • For correspondence: [email protected]
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  • Figure 1
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    Figure 1

    Percent Female by Grade and Achievement Level

    Notes: Figure reports the average percent female, for each achievement group, across the six cohorts that we observe for all four of their high school years during 1999–2007.

  • Figure 2
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    Figure 2

    Persistence in Math Performance—Forward Transition Matrix

    Notes: Figure reports the forward transition probability of each year-within-grade rank group for students in each year-within-grade rank group.

  • Figure 3
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    Figure 3

    Early Performance of Top Math Students—Backward Transition Matrix

    Notes: Figure reports the probability of each within-ninth-grade rank group for students in each within-12th-grade rank group.

  • Figure 4
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    Figure 4

    Gender Composition of AMC Entry

    Notes: Figure reports the gender composition of highly ranked students new to the AMC in comparison with students in the rank group in the previous year. All calculations are simple unweighted averages of the means for each grade–year cell.

  • Figure 5
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    Figure 5

    Reactions to Disappointment—“Dropout” Rates

    Notes: Figure reports the raw probability that students with scores around the AIME cutoff “drop out” of participating in the next year, by gender. Running variable is distance between the student’s score on the first test they took in a given year and the AIME cutoff for that test–year. Lines indicate linear fit within 24 points of cutoff.

Tables

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    • View popup
    Table 1

    Summary Statistics—Participation and Scores

    Grade LevelNumber of StudentsStatistics on AdjustedScore
    MeanSD% ≥100% ≥120
    Girls
    Grade 918,98456.814.8  0.70.04
    Grade 1028,00860.315.3  1.20.06
    Grade 1128,34866.315.7  2.90.11
    Grade 1223,29469.116.2  4.50.18
    Boys
    Grade 921,06761.716.6  2.50.26
    Grade 1031,15266.017.2  4.00.40
    Grade 1133,98872.817.2  7.80.64
    Grade 1231,39176.017.811.31.04
    • Notes: Table reports average annual AMC participation and scores by gender and grade level, weighting each year 1999–2007 equally.

    • View popup
    Table 2

    Growth in Absolute Performance

    Within-Grade RankCorresponding Overall RankDecrease in Overall Rank Necessary to Maintain Within-Grade Rank across Grade Transitions
    Grade 9Grade 10Grade 11Grade 129 → 1010 → 1111 → 12
    5,00052,55432,68615,65411,39538%52%27%
    1,00015,674  5,734  3,293  2,18663%43%34%
    500  8,350  3,234  1,738  1,35661%46%22%
    100  1,173    668    290    24143%57%17%
    50    875    310    152    10665%51%30%
    • Notes: Table reports the full-population rank of the Nth-best student in each grade.

    • View popup
    Table 3

    Average Achievement Gains as a Function of Initial Achievement

    VariableDep. Var.: log(Ranki,t+1) – log(Rankit)
    10th → 11th11th → 12th
    Coeff.SECoeff.SE
    Constant−0.50***(0.005)−0.33***(0.005)
    −[log (GradeRankit − log(5000)]−0.07***(0.004)−0.05***(0.004)
    Number of observations81,430100,270
    Root MSE0.921.01
    • Notes: Standard errors in parentheses.

    • ↵* p < 0.05,

    • ** p < 0.01,

    • *** p < 0.001.

    • Table reports the results of IV regressions of growth in absolute performance as a function of initial performance relative to cohort. log(GradeRankit) instrumented with log(GradeRanki,i,t−1).

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    Table 4

    Gender Differences in Within-Cohort Rank Dynamics for High-Achieving Students

    VariableDep. Var.: log(GradeRanki,t+1) – log(GradeRankit)
    Top 5,000 in Grade at tTop 500 in Grade at t
    Panel A
    Female0.31***
    (0.012)
    0.32***
    (0.055)
    log (GradeRankit)−0.25***
    (0.007)
    −0.09***
    (0.024)
    log(GradeRankit)2−0.02***
    (0.002)
    0.01
    (0.010)
    Female × log(GradeRankit)−0.03*
    (0.014)
    0.01
    (0.065)
    Female × log(GradeRankit)2−0.01
    (0.007)
    0.01
    (0.039)
    Panel B
    Embedded Image1.51***
    (0.009)
    2.18***
    (0.033)
    Embedded Image1.20***
    (0.015)
    1.99***
    (0.078)
    Number of observations81,5709,682
    • Notes: Regression sample is restricted to students in Grades 9,10, or 11 in the initial year and whose genders are nonmissing. The log(GradeRankit) control is adjusted by subtracting the sample mean. Regressions also include unreported year and grade dummies, dummies for students taking the B-test (B-Dateit), and dummies for students taking both the A-test and B-test (Bothit). The latter variables are intended to control for unobserved differences in students’ commitment to the contests. Standard errors in parentheses.

    • ↵* p < 0.05,

    • ** p < 0.01,

    • ↵*** p < 0.001.

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    Table 5

    Gender Differences in Dropout Rates for High-Achieving Students

    VariableDep. Var.: Dropout t → t + 1
    Sample: Top 5,000 in Grade X in Year tTop 500
    All Grades
    All GradesGrade 9Grade 10Grade 11
    Female0.023***
    (0.004)
    0.005
    (0.006)
    0.021***
    (0.006)
    0.045***
    (0.007)
    0.002
    (0.013)
    log(GradeRankit)0.069***
    (0.002)
    0.073***
    (0.004)
    0.066***
    (0.004)
    0.069***
    (0.004)
    0.030***
    (0.006)
    log(GradeRankit)20.008***
    (0.001)
    0.008***
    (0.001)
    0.009***
    (0.001)
    0.008***
    (0.001)
    0.004
    (0.002)
    Female × log(GradeRankit)0.001
    (0.005)
    0.006
    (0.008)
    −0.004
    (0.008)
    −0.002
    (0.008)
    −0.005
    (0.016)
    Female × log(GradeRankit)20.001
    (0.002)
    0.004
    (0.004)
    −0.005
    (0.004)
    0.001
    (0.004)
    0.007
    (0.008)
    Number of observations119,32539,28439,74740,29412,020
    • Notes: Regression sample is restricted to students in Grades 9, 10, or 11 in the initial year and whose genders are nonmissing. The log(GradeRankit) control is adjusted by subtracting the sample mean. Regressions also include unreported year and grade dummies, dummies for students taking the B-test (B-Dateit), and dummies for students taking both the A-test and B-test (Bothit). The latter variables are intended to control for unobserved differences in students’ commitment to the contests. Standard errors in parentheses.

    • ↵* p < 0.05,

    • ** p < 0.01,

    • *** p < 0.001.

    • View popup
    Table 6

    Decomposition of Declines in Fraction Female in Top Rank Groups

    Grade LevelAchievement LevelChange in % FemaleDecomposition of Decline
    DropCont.GrowEntryMech.
    AverageTop 5,000−3.1−0.4−1.2−3.6−1.13.5
        9 → 10Top 5,000−4.6−0.1−1.4−2.9−2.22.0
        10 → 11Top 5,000−2.3−0.4−1.1−3.7−0.83.8
        11 → 12Top 5,000−2.3−0.9−1.1−4.3−0.44.8
    AverageTop 500−1.9−0.3−1.0−4.5−0.44.1
    AverageTop 50−0.5−0.3−0.8−3.00.23.1
    • View popup
    Table 7

    Reactions to Disappointment—Regression Discontinuity Evidence on “Dropout” Rates

    VariableDep. Var.: Dropout t → t+1
    Sample:
    Within Two AnswersOptimal Bandwidth
    MaleFemale
    Estimation:
    OLSRD with Controls
    Female × Grade 9−0.006
    (0.011)
    Female × Grade 100.009
    (0.008)
    Female × Grade 110.038***
    (0.006)
    Below AIME cutoff0.037***
    (0.006)
    0.034***
    (0.007)
    0.042***
    (0.012)
    Female × Below AIME cutoff0.019*
    (0.009)
    Bandwidth10/1212.04310.575
    Number of observations139,874701,686614,014
    • Notes: Standard errors in parentheses.

    • ↵* p < 0.05,

    • ** p < 0.01,

    • *** p < 0.001.

    • View popup
    Table 8

    Reactions to Disappointment—Regression Discontinuity Evidence on Achievement Gains

    VariableDep. Var.: log(GradeRanki,t+1) – log(GradeRankit)
    Sample:
    Within Two AnswersOptimal Bandwidth
    MaleFemale
    Estimation:
    OLSRD with Controls
    Female × Grade 90.412***
    (0.030)
    Female × Grade 100.309***
    (0.022)
    Female × Grade 110.285***
    (0.017)
    Below AIME cutoff0.097***
    (0.017)
    0.048*
    (0.020)
    0.048
    (0.039)
    Female × Below AIME cutoff−0.067**
    (0.025)
    Bandwidth10/1213.0418.156
    Number of observations85,545324,325247,507
    • Notes: Standard errors in parentheses.

    • ↵* p < 0.05,

    • ↵** p < 0.01,

    • ↵*** p < 0.001.

Additional Files

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  • Free alternate access to The Journal of Human Resources supplementary materials is available at https://uwpress.wisc.edu/journals/journals/jhr-supplementary.html

    • 0620-10972R1_supp.pdf
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Journal of Human Resources: 58 (5)
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1 Sep 2023
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Dynamics of the Gender Gap in High Math Achievement
Glenn Ellison, Ashley Swanson
Journal of Human Resources Sep 2023, 58 (5) 1679-1711; DOI: 10.3368/jhr.58.5.0620-10972R1

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Dynamics of the Gender Gap in High Math Achievement
Glenn Ellison, Ashley Swanson
Journal of Human Resources Sep 2023, 58 (5) 1679-1711; DOI: 10.3368/jhr.58.5.0620-10972R1
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  • Article
    • ABSTRACT
    • I. Introduction
    • II. The High-Achievement Gender Gap in AMC Scores
    • III. Dynamics of Achievement among High-Achievers
    • IV. Gender Differences in Dynamics and a Decomposition
    • V. Potential Mechanism: Reactions to Disappointment
    • VI. Conclusions
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