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The authors seem to suppose that tax rates affect the distribution of household work. But they need to say what tax rate for men would encourage them to throw up their hands with respect to the market and start doing dishes instead. A 100% tax rate would have that effect.
Studies would need to be done on the influence that a proposed gender-differential tax rates would have on workforce participation and leisure.
If the distribution of household and market work is unaffected by tax rates, then lowering tax res for women will act as a disincentive for them to work.
ResidentM