Dynamics of the Gender Gap in High Math Achievement

Glenn Ellison; Ashley Swanson

doi:10.3368/jhr.58.5.0620-10972R1

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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.
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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.
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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.
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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.
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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.

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Table 1

Summary Statistics—Participation and Scores

Grade Level	Number of Students	Statistics on AdjustedScore
Grade Level	Number of Students	Mean	SD	% ≥100	% ≥120
Girls
Grade 9	18,984	56.8	14.8	0.7	0.04
Grade 10	28,008	60.3	15.3	1.2	0.06
Grade 11	28,348	66.3	15.7	2.9	0.11
Grade 12	23,294	69.1	16.2	4.5	0.18
Boys
Grade 9	21,067	61.7	16.6	2.5	0.26
Grade 10	31,152	66.0	17.2	4.0	0.40
Grade 11	33,988	72.8	17.2	7.8	0.64
Grade 12	31,391	76.0	17.8	11.3	1.04

Notes: Table reports average annual AMC participation and scores by gender and grade level, weighting each year 1999–2007 equally.

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Table 2

Growth in Absolute Performance

Within-Grade Rank	Corresponding Overall Rank				Decrease in Overall Rank Necessary to Maintain Within-Grade Rank across Grade Transitions
Within-Grade Rank	Grade 9	Grade 10	Grade 11	Grade 12	9 → 10	10 → 11	11 → 12
5,000	52,554	32,686	15,654	11,395	38%	52%	27%
1,000	15,674	5,734	3,293	2,186	63%	43%	34%
500	8,350	3,234	1,738	1,356	61%	46%	22%
100	1,173	668	290	241	43%	57%	17%
50	875	310	152	106	65%	51%	30%

Notes: Table reports the full-population rank of the Nth-best student in each grade.

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Table 3

Average Achievement Gains as a Function of Initial Achievement

Variable	Dep. Var.: log(Rank_i,t+1) – log(Rank_it)
	10th → 11th		11th → 12th
	Coeff.	SE	Coeff.	SE
Constant	−0.50^***	(0.005)	−0.33^***	(0.005)
−[log (GradeRank_it − log(5000)]	−0.07^***	(0.004)	−0.05^***	(0.004)
Number of observations	81,430		100,270
Root MSE	0.92		1.01

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(GradeRank_it) instrumented with log(GradeRanki,_i,t−1).

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Table 4

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

Variable	Dep. Var.: log(GradeRank_i,t+1) – log(GradeRank_it)
Variable	Top 5,000 in Grade at t	Top 500 in Grade at t
Panel A
Female	0.31^*** (0.012)	0.32^*** (0.055)
log (GradeRank_it)	−0.25^*** (0.007)	−0.09^*** (0.024)
log(GradeRank_it)²	−0.02^*** (0.002)	0.01 (0.010)
Female × log(GradeRank_it)	−0.03^* (0.014)	0.01 (0.065)
Female × log(GradeRank_it)²	−0.01 (0.007)	0.01 (0.039)
Panel B
	1.51^*** (0.009)	2.18^*** (0.033)
	1.20^*** (0.015)	1.99^*** (0.078)
Number of observations	81,570	9,682

Notes: Regression sample is restricted to students in Grades 9,10, or 11 in the initial year and whose genders are nonmissing. The log(GradeRank_it) control is adjusted by subtracting the sample mean. Regressions also include unreported year and grade dummies, dummies for students taking the B-test (B-Date_it), and dummies for students taking both the A-test and B-test (Both_it). 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

Variable	Dep. Var.: Dropout t → t + 1
	Sample: Top 5,000 in Grade X in Year t				Top 500 All Grades
	All Grades	Grade 9	Grade 10	Grade 11	Top 500 All Grades
Female	0.023^*** (0.004)	0.005 (0.006)	0.021^*** (0.006)	0.045^*** (0.007)	0.002 (0.013)
log(GradeRank_it)	0.069^*** (0.002)	0.073^*** (0.004)	0.066^*** (0.004)	0.069^*** (0.004)	0.030^*** (0.006)
log(GradeRank_it)²	0.008^*** (0.001)	0.008^*** (0.001)	0.009^*** (0.001)	0.008^*** (0.001)	0.004 (0.002)
Female × log(GradeRank_it)	0.001 (0.005)	0.006 (0.008)	−0.004 (0.008)	−0.002 (0.008)	−0.005 (0.016)
Female × log(GradeRank_it)²	0.001 (0.002)	0.004 (0.004)	−0.005 (0.004)	0.001 (0.004)	0.007 (0.008)
Number of observations	119,325	39,284	39,747	40,294	12,020

Notes: Regression sample is restricted to students in Grades 9, 10, or 11 in the initial year and whose genders are nonmissing. The log(GradeRank_it) control is adjusted by subtracting the sample mean. Regressions also include unreported year and grade dummies, dummies for students taking the B-test (B-Date_it), and dummies for students taking both the A-test and B-test (Both_it). 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 6

Decomposition of Declines in Fraction Female in Top Rank Groups

Grade Level	Achievement Level	Change in % Female	Decomposition of Decline
Grade Level	Achievement Level	Change in % Female	Drop	Cont.	Grow	Entry	Mech.
Average	Top 5,000	−3.1	−0.4	−1.2	−3.6	−1.1	3.5
9 → 10	Top 5,000	−4.6	−0.1	−1.4	−2.9	−2.2	2.0
10 → 11	Top 5,000	−2.3	−0.4	−1.1	−3.7	−0.8	3.8
11 → 12	Top 5,000	−2.3	−0.9	−1.1	−4.3	−0.4	4.8
Average	Top 500	−1.9	−0.3	−1.0	−4.5	−0.4	4.1
Average	Top 50	−0.5	−0.3	−0.8	−3.0	0.2	3.1

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Table 7

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

Variable	Dep. Var.: Dropout t → t+1
	Sample:
	Within Two Answers	Optimal Bandwidth
	Within Two Answers	Male	Female
	Estimation:
	OLS	RD with Controls
Female × Grade 9	−0.006 (0.011)
Female × Grade 10	0.009 (0.008)
Female × Grade 11	0.038^*** (0.006)
Below AIME cutoff	0.037^*** (0.006)	0.034^*** (0.007)	0.042^*** (0.012)
Female × Below AIME cutoff	0.019^* (0.009)
Bandwidth	10/12	12.043	10.575
Number of observations	139,874	701,686	614,014

Notes: Standard errors in parentheses.
↵* p < 0.05,
** p < 0.01,
*** p < 0.001.

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Table 8

Reactions to Disappointment—Regression Discontinuity Evidence on Achievement Gains

Variable	Dep. Var.: log(GradeRank_i,t+1) – log(GradeRank_it)
	Sample:
	Within Two Answers	Optimal Bandwidth
	Within Two Answers	Male	Female
	Estimation:
	OLS	RD with Controls
Female × Grade 9	0.412^*** (0.030)
Female × Grade 10	0.309^*** (0.022)
Female × Grade 11	0.285^*** (0.017)
Below AIME cutoff	0.097^*** (0.017)	0.048^* (0.020)	0.048 (0.039)
Female × Below AIME cutoff	−0.067^** (0.025)
Bandwidth	10/12	13.041	8.156
Number of observations	85,545	324,325	247,507