AEI is a private, non-profit institution. While it's address is a Washington, D.C., address, it is not a government institution.
It does want to influence thinking, and its ideas are, for the most part, politically conservative. So Wolfowitz will be at home there.
So, they're going to have him work on "entrepreneurship and development issues, Africa and public-private partnerships"...well, there goes Africa
It's a shame that Wolf had so much influence re Iraq policy

Before the war he was so dismissive of the US military and post war planning. The
river of his ideas met the river of an increase in executive power and secrecy to produce a catastrophic event.
After it became clear that the war in Iraq left the country in shambles, he went around blaming others, without any mention of how they were just
following his ideas, from start to non-finish. (I don't mean to imply that Wolf
wanted either a war without end or an Iraq in shambles, but that he was so far off on military needs and post war plans.)
Hopefully, if he continues to espouse his views through AEI, no one in power in US gov't will listen this time around.