Mumford is an assistant professor in the Economics Department at Purdue University. He teaches courses in econometrics, public finance, and labor economics. His masters-level econometrics course covers standard regression methods, basic time series methods, panel data methods, and instrumental variables estimation. His PhD-level labor economics course covers labor demand, labor supply, and taxation. It focuses on common applied microeconometric tools including matching methods, difference-in-differences, regression discontinuity, instrumental variables, quantile regression, and panel methods.

His research has focused on taxation, fertility and families, labor supply, poverty, and the role of human capital in measuring national wealth (economic sustainability). He has received research grants from the Purdue Research Foundation, the Institute for Research on Poverty, the Upjohn Institute for Employment Research, the John M. Olin Program in Law and Economics, and the Alfred P. Sloan Foundation. In 2010, he was awarded the John and Mary Willis Young Faculty Scholar Award.

Mumford lives in West Lafayette, Indiana with his wife Darcia and they have four young children, Bryson, Kaitlyn, Alyssa, and Hailey.