One reason women are more likely to get a degree is that they get less value from non-degree qualifications than men. Combined with the fact that male coded jobs (plumber) have higher earnings than female coded jobs (nail salon), there are rational explanations for (some of) the HE participation gap
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Attending non-top third institutions is associated with a bigger earnings increase for women - around £6,600 for women compared to around £5,000 for men