Brennan coauthored Alternating Currents: Electricity and Public Policy, which looks at the complex economic and regulatory policy issues raised by the restructuring of the electricity industry.

Brennan is a professor of public policy and economics at the University of Maryland-Baltimore County. Previously, he served as an economist for the Antitrust Division of the U.S. Department of Justice. During 2003 to 2005, he served as a staff consultant to the Bureau of Economics of the Federal Trade Commission, and during 2006 held the T.D. MacDonald Chair in Industrial Economics at the Canadian Competition Bureau. From 1996 to 1997, Brennan served as a senior economist for the Council of Economic Advisers.