The two gaps

Fix a setting and a threshold — say, the top 10% of the academic performance distribution. Two facts describe the STEM applicant pool at that threshold. First, who is in the high-achieving group: the share of students above the bar who are women. Second, what they do: among those students, how likely a woman and a man each are to rank a STEM program first.

The first is the pipeline gap, defined as the female-minus-male difference in representation among students above the threshold. The second is the choice gap, defined as the female-minus-male difference in the share of high-achieving students who rank STEM first or anywhere on the list. A percentage point (pp) is an absolute difference in probabilities: a gap of −20pp means that if 30% of qualifying men rank STEM first, 10% of qualifying women do.

Let T_g denote the number of students of gender g in the top group and s_g the share who rank the field first. The number of high-achieving applicants is A_g = T_gs_g. Taking logs of the ratio between men and women gives

ln(A_M / A_F) = ln(T_M / T_F) + ln(s_M / s_F) = P + C

The first term is the pipeline component P; the second is the choice component C. This is an accounting identity with no residual. Its orientation differs from the percentage-point figures: those report female minus male, whereas positive values of P or C favor men.

The two components are directly comparable in this form. The underlying percentage-point gaps are not: one is a difference in composition shares and the other a difference in application rates.

The male share among high-achieving applicants is Λ(P + C), where Λ(z) = 1 / (1 + e^−z). A value of zero maps to a male share of 50%.

Setting P to zero gives Λ(C): the male share that would obtain if the top group were gender balanced, holding the observed choice component fixed. Setting C to zero gives Λ(P): the share that would obtain if women and men applied at equal rates, holding the observed pipeline component fixed.

Each system also records the program every student is assigned to, so the identity extends by one factor. Let M_g be the number of top-group students of gender g assigned to the field and v_g = M_g / A_g. Then

ln(M_M / M_F) = P + C + V,  V = ln(v_M / v_F)

and the male share among high-achieving students assigned to the field is Λ(P + C + V). The assignment component V is a ratio of counts, not an admission probability: a student can be assigned to a program ranked below first, and v_g exceeds one for at least one gender in four settings.

In the data V is small and carries no systematic sign, so the gender composition of assigned cohorts is close to what the submitted lists imply. Pooled across settings, women are 51.2% of high achievers, 38.6% of those listing STEM anywhere, 34.0% of those ranking it first, and 34.7% of those assigned to STEM. These are group compositions, not individual acceptance rates; a small net component does not establish that otherwise identical applicants are treated alike. The paper reports the extension in Online Appendices E and F and the setting-by-setting counterfactuals in Online Appendix B.8.

The obvious objection to reading application lists as preferences is strategy. If a student expects to be rejected from her first choice, she might not list it. Then a list reveals a mixture of what she wants and what she thinks she can get, and a gender difference in the lists could be a gender difference in confidence about admission rather than in what students want to study.

All ten systems assign places through variants of deferred acceptance: students submit a ranked list, programs rank students by a performance score, and the algorithm repeatedly tentatively assigns and bumps applicants until the assignment is stable. Under this class of mechanism, ranking programs in true preference order generally gives applicants little incentive to misreport. This argument is weaker where lists are short, applications precede scores, or the mechanism is iterative; the paper treats these features as qualifications rather than assuming the systems are frictionless.

• All ten systems rank students on academic performance and assign places through variants of deferred acceptance.
• Deferred acceptance gives applicants little incentive to misreport, so the submitted list is informative about the ordering of programs they were willing to enter.
• List-length caps range from two programs in Brazil to a hundred in Taiwan, and Greece imposes no numerical limit at all.

The analysis concentrates on students near the top of each performance distribution because that is where the constraints that usually confound this comparison bind least. Students in the top decile are the applicants most likely to gain admission to and succeed in selective STEM programs. Restricting attention to this group reduces, but does not eliminate, differences in admission prospects.

The top-10% cutoff is a reporting convention. The appendix repeats the analysis at the top 5%, 20%, and 30% and across the full performance distribution; top-1% estimates are also available for nine settings.

The institutional design reduces the scope for several mechanical explanations, but it does not identify the process that generates the observed rankings.

Two further limits are worth stating plainly. The decomposition is descriptive — it allocates an observed gap between two margins, and does not estimate the effect of any intervention. And the comparability of the ten settings rests on the construction choices documented on each country page, including the performance measure, the sample definition, and, in Chile, the denominator. Chile's tables, its decomposition components, and Online Appendix Figures B.I and D.I use full top-decile totals (a top-10% choice gap of −23.1 percentage points), while panel (b) of Figures 2 and 5 and Online Appendix Figures B.V to B.VIII condition on top-decile students who submit a list (−24.6).

The choice component compares women and men within the top group rather than at an identical score. Where men sit higher within that group and application rates rise with performance, part of the component reflects within-group composition. Narrowing the threshold does not remove it: the choice component is positive in all ten settings at the top 5%, and at the top 1% in all nine where that group can be formed; across those nine its mean falls from +0.69 log points at the top 10% to +0.55 at the top 1%, and it is lower at the top 1% in eight of the nine. These threshold comparisons do not isolate the contribution of within-group score composition.