pr(child 2=boy|child 1 = boy) - pr(child 2 = boy|child 1=girl) = ?

Okay, so shout-outs to this blog have previously proven extremely useful for when I've needed, say, obscure mp3s or emergency HTML advice. Let's try something more difficult and even work related: I am trying to figure out (preferably for a contemporary population in a developed country like the United States) whether/how much the probability of one's second child being a boy/girl is affected by whether one's first child is a boy/girl. Basically, is the second child more likely to be of the same sex as the first child, and, if so, how large is the effect? I've been surprisingly flummoxed in my efforts, leading to this post. Does anyone have any ideas for tracking this down?

(I know, I am an affiliate in a demography center, so you'd think I could just send an e-mail to one of them. Which I might. But, given the interests of the ones I know well, they're usually more helpful for questions about death statistics than birth statistics.)