His most well known research is on the minimum wage and immigration, The work is somewhat controversial in that the results show small negative effects from raising the minimum wage and from increasing immigration. In my view that is a sign of an economist who is willing to let the evidence do the talking, and that is a good trait to have in this job.
He has also worked in many other areas, including occupational licensing, the economics of terrorism, and more recently on job search in periods when unemployment is high, including how job search is affected by things such as unemployment insurance. But that is just a small taste of the large amount of research he has done.
Finally, it's important to recognize what the CEA does:
Over the years, the CEA has provided objective and professional economic advice at the highest levels in the White House. ... A hallmark of the ethos of the CEA is the pride that its staff members take in providing objective analysis. ... Because the CEA has retained its small size over the years, it can be quick and nimble in ways that are difficult for some larger agencies. Moreover, because the CEA is viewed as a neutral agency without ties to any particular constituency, the CEA often has played an important role on interagency committees and working groups... Along those lines, perhaps the most important role of the CEA has been to scuttle many of the more adventuresome ideas that inevitably bubble up through the machinery of government. ...In my view, his wide-ranging theoretical skills and his level-headed demeanor should serve him very well in this role. Again, I believe this is an excellent choice.