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Women are more likely to use methods of suicide with a high degree of failure like taking a large amount of pills(which means they can get their stomach pumped or otherwise treated if caught) while men are more likely to simply use a gun and other more violent and immediate methods which have a far higher fatality rate. Thus we would expect in an increase in suicide attempts in young women and a decrease in suicide attempts among young men would lead to a net decrease in suicides because young women consistently fail at committing suicide while young men are far more successful.

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But it's not clear from this experimental technique whether school closure/opening reduces suicides just delays/accelerates it.

Without doubt school is stressful for adolescents and return to school increases suicidal ideation. But school is only one potential source of this. I hated school at times but never dreamed of suicide while lots of adolescents kill themselves for reasons unrelated to schooling.

If school holidays were very short or didn't exist then you wouldn't see this seasonal pattern. But it's not clear to me that this would reduce the underlying adolescent suicide rate.

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