This table shows how some outcomes differ for rich and poor children. None of this is very surprising. To my knowledge, there is not any study that finds a negative relationship between parental income and children's outcomes -having rich parents evidently is just not bad for children. Nevertheless, numbers like these do not tell us that raising the income of poor parents would improve their children's outcomes. This is because poor parents are not the same as rich parents.
Poor parents have less education, have worse health, fewer skills and differ in many other ways.
When social scientists control relevant parental characteristics, they find that the effect of income on most outcomes declines. Studies that control several relevant parental characteristics find smaller effects than studies that control only a few such characteristics. Still, even when social scientists have used techniques intended to control all such parental characteristics, they have found positive effects on the outcomes they assess. The implication of this is that, if there were no costs associated with income redistribution and the income itself really improved children's outcomes, then and redistributing income from the rich to the poor would increase the average level of child well-being. There are two areas of controversy among social scientists.