Do rich kids do better?

A US economist plans to investigate whether family income is directly linked to children’s educational attainment. He will give a random group of low income, single mothers $4,000 each, for the first three years of their children’s lives.
Will it make a difference?
Well, this is pre-school, so the better question might be “How will it make a difference?”
They could learn to count the banknotes.
They could learn how many romper suits you can buy for $12k.
They could learn how many hours of babysitting it pays for.
They could learn how many detectives you could hire to find the father.
Or how many lawyers, once you’ve found him. (Not many.)
Or contract killers, depending on whether the split was amicable or not.
Or maybe the money could just be put into schools instead…