Once one of my wife's law professors polled her class on birth order. "How many of you are first-borns?" Two-thirds of the students raised their hands. Clear evidence that first-borns are achievers, right?
Hardly. An alternative hypothesis is that law students come from affluent families with few kids. Imagine that birth order has nothing to do with law school attendance. If half the students are only children, and half come from two-child homes, then three-quarters will be first-borns.
I decided to race these hypotheses using the General Social Survey. If you regress real income on birth order, you get the same pattern as my wife's law school class. The first-born averages $1900 more than the second-born, who averages $1900 more than the third-born, and so on.
However, if you regress real income on birth order AND family size, you get a totally different picture. Birth order makes essentially no difference (in fact, the sign reverses), but average income falls by about $2400/child in your family. First-born only child? You'll make more than average. First-child child in a big family? You'll do no better than the fifth-born child - maybe a little worse!
Does this show that big families hurt incomes? Possibly, but the simpler story is more plausible: Poor people have more kids, and kids of poor people tend to be poor themselves.