They've done a number of studies. Here's a nice meta-analysis.
I will add that there are some advantages to having wealth/power concentrated. Mainly, they can direct/power that wealth towards a single larger purpose that might not have been achievable without it. Musk couldn't have made SpaceX without several billion behind him, and China couldn't have built their wind farms, and Britan couldn't have eliminated smallpox. Spread that money/power out, and everyone will work for themselves, each with their own idea of how to do things. Everyone need to take the vaccine to eliminate a disease, for instance, even those against it.
Still, you need healthy and educated workers to accomplish those things. You can't build pyramids with weak and starving slaves. Or start a mars colony without a lot of college graduates.
Of course, the wealth could just as easily be squandered on something stupid. Like war. Or writing your name so big you can see it from space (http://www.huffingtonpost.com/2011/07/20/hamad-sheikh-name-private-island_n_904635.html). So it's no guarantee of money well spent.