Todd's primary areas of interest are the study of migration issues and the study of firm market power over workers. His recent work has shown that firm wage setting power increases during economic downturns and that firm market power may bias estimates of the substitutability of different types of workers. He has also studied the mobility of guest workers on H-1B visas and found a surprising amount of mobility of these workers, providing a check on firm market power over these workers.

He joined IZA as a Research Affiliate in January 2007 and became a Research Fellow in April 2010.