Not a lot of research in economics has been done using ML (Machine Learning, not Maximum Likelihood!), but numbers are growing. I believe, we will see a exponential growth in near future.
Bringing cutting-edge machine learning methods into econometrics is currently an active area. Leading economists who are active in machine learning include:
Victor Chernozhukov: http://web.mit.edu/~vchern/www/
Alex Belloni: https://faculty.fuqua.duke.edu/~abn5/belloni-index.html
Christian Hansen: http://faculty.chicagobooth.edu/christian.hansen/research/
Susan Athey: https://www.gsb.stanford.edu/faculty-research/faculty/susan-athey
In this page, I will try to compile a list of already published work in economics that used ML and make a list of possible areas in economics where ML can be used successfully.