Xiaodong Gong and I have a paper in the latest issue of the Australian Economic Review. Abstract below.

Does Maternal Age Affect Children’s Test Scores?
Andrew Leigh and Xiaodong Gong
We estimate the relationship between maternal age and child outcomes, using indices aimed at measuring overall outcomes, learning outcomes and social outcomes. In all cases,we find evidence that children of older mothers have better outcomes. Not only do children born to mothers in their twenties do better than children born to teen mothers, but children born to mothers in their thirties do better than children born to mothers in their twenties. However, when we control for other socioeconomic characteristics, such as family income, parental education and single parenthood, the coefficients on maternal age become small and statistically insignificant. The only exception is an index of social outcomes, which is positively associated with maternal age, even controlling for socioeconomic factors. For cognitive outcomes, young motherhood appears to be a marker, not a cause, of poor child outcomes.

An easy way to see the result is to compare the relationship between maternal age and child outcomes first without any socioeconomic controls:

(strong positive relationship, mostly statistically significant)

…and then with socioeconomic controls:

(virtually no relationship, generally statistically insignificant).