Amazing!!! Thanks to www.advancednflstats.com for doing all the leg-work. Highly recommend their site too. Their in-game win probability statistics are always a must-have for me on game-day ^_^
http://www.advancednflstats.com/2009/09/4th-down-study-part-...
The tl;dr version can be found at:
http://www.advancednflstats.com/2010/05/4th-down-briefs.html
The conclusion is that teams should go for it on 4th down much more often than they currently do.
He also has a calculator where you can get the exact values:
http://www.math.toronto.edu/mpugh/Teaching/Sci199_03/Footbal...
I also believe Belichek/Adams have funded some football economics research.