This paper uses data from the Young Lives study.  The author's summary reads as follows:

This paper examines the relationship of birth order with time use and parental educational aspirations for school-age children between 4-17 years old. It inspects the role of birth order in time investments, using extensive (school enrolment and child work binary outcomes) and intensive margins (continuous time use outcomes). It also investigates if parental aspirations vary by birth order as potential mechanism explaining time use allocation. Results indicate that being the second born sibling in two-child families has a significant and negative effect on child work. The youngest sibling is 10.8 percentage points less likely to participate in child work and spending 0.81 hours (about 49 minutes) less in care activities of other household members. The results on child work are robust to differences in family size, observed endowments (birthweight and cognitive score), and families with “complete” fertility decisions. I found no conclusive evidence of birth order effects for school participation, time spent in educational activities (school or studying), and time spent in leisure. Notwithstanding the negative result between higher birth order siblings and child work, parents are equally likely to aspire for the highest level of education, a University/Postgraduate degree for both children.