Psychologically, I'm not so sure. Loss aversion is a much stronger than not getting a benefit (think about not getting your bonus versus taking a pay-cut at work; even if the amounts are the same, I doubt you would feel the same about it) - so I think the explicit tax on childlessness would be more influential because of that.
Childless people between 20-50, both men and women, paid an extra 6% in taxes to the state.
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