You have data on all individuals in Sweden, including their family size (i.e. their number of children) and their earnings. You want to estimate the effect of family size on earnings, but you suspect...

You have data on all individuals in Sweden, including their family size (i.e. their number of children) and their earnings. You want to estimate the effect of family size on earnings, but you suspect your regression will be biased as you do not have information on preferences for how many children people want to have.

a) You have information on gender of all children. You have heard that people
who have two children of the same gender are more likely to have a third child. Would you be able to use gender composition of the first two children as an instrument for family size? Discuss the assumptions needed for such a model (assume treatment effects are constant). Set up the assumptions mathematically and explain in words what they mean.

b) How would you test if the assumptions in b) hold? Is it likely that they hold? (Assume gender composition of the first two children is the only instrument you have access to.)