Over at Fangraphs, Alex Remington wrote this about a week ago:

In 2003, MLB instituted the "bereavement list." Now also known as the "Family Medical Emergency List," it allows players to take time off for family emergencies, including the death of a relative. And in 2011, MLB instituted both the seven-day DL for concussions and the "paternity leave list," which allows players to leave their teams for the birth of a child. Colby Lewis was the first person to use the list to attend the birth of his child in mid-April, and seven more players have made use of it since then: Grant Balfour, David Purcey, Ian Desmond, Kurt Suzuki, Jason Bay, Ross Gload and most recently Ian Kinsler.

Link (emphasis added)

I had not previously realized that bein' a daddy was the new market inefficiency.