is there a statistically significant difference between birth rates
and birth order in developed countries? (i.e. do first borns have more
children on average than later borns?) More specifically, are the
percentage of Later borns or youngest children who do not have
children greater than the percentage of first borns who elect to not
have children? What is this difference 2% 25%, etc.

I love this question!  I'm a middle child (of 3), and I'm planning on
having 4-6 children (I have 2 now).  My older brother is planning on 2
(1 so far), and my younger sister isn't planning on having any.

I'm really interested to hear if there is any research on this.