Germany is a welfare state and yet children from poor parents perform worse in school.
https://i.imgur.com/JQfZ5vi.png
Inflation adjusted per capita income transfers have roughly doubled since 1990, from ~$4,400 to ~$8,600 in 2016.
I suspect that a big part of it is that money is being wasted (the Fed.Gov cannot negotiate drug prices!), and not reaching the intended beneficiaries. My perception is that there is an industrial-welfare complex that diverts the money.
A better question would be: Is the performance gap between poor students and middle class students lower in Germany?