Duncan, G.J. et. Al. (2011). Does Money Really Matter? Estimating Impacts of Family Income on Young Children's Achievement With Data FromRandom-Assignment Experiments. Developmental Psychology, Vol47(5).p.p 1263-1279.

Social scientists do not agree on the size and nature of the causal impacts of parental income on children's achievement. We revisit this issue using a set of welfare and antipoverty experiments conducted in the 1990s. We utilize an instrumental variables strategy to leverage the variation in income and achievement that arises from random assignment to the treatment group to estimate the causal effect of income on child achievement. Our estimates suggest that a $1,000 increase in annual income increases young children's achievement by 5%-6% of a standard deviation. As such, our results suggest that family income has a policy-relevant, positive impact on the eventual school achievement of preschool children.