Professor Hatfield's primary research interest is the field of matching theory, a field of economics that studies markets in which agents have explicit preferences over whom they buy from and sell to, not just over the underlying goods bought and sold. Examples of such economies include the markets for medical residency positions, the assignment of students to public schools, and the formation of collaborative research enterprises. His research has expanded the frontiers of matching theory, offering a sharp characterization of when equilibria exist in such markets, as well as constructing mechanisms to find those equilibria and identifying those mechanisms' strategic properties. This work has been applied in understanding the effect of price controls, allocating West Point cadets to branches of the U.S. Army, and ascertaining the incentive effects of different public school choice mechanisms.

Professor Hatfield also pursued a separate line of research into federalism, in order to understand how the assignment of tax and expenditure powers to either local or central governments affects economic policy. His ongoing work details the advantages (and disadvantages) of competition between local governments.