He graduated from Ottawa University, from the University of Kansas with an M.A. in 1953, and a Ph.D. in 1954. He taught at Ottawa University from 1959 to 1985. He was elected to the Kansas State House of Representatives, in 1960. He ran for the U.S. House of Representatives in 1966 and the U.S. Senate in 1978, losing in the Republican primaries to Larry Winn and Nancy Landon Kassebaum, respectively.
He served as the Governor of the Federal Reserve Board from 1986 to 1994. He left to become a Chief Economist and Senior Managing Director for Bear Sterns & Co., Inc., where he served until 2002. He opened a consultancy, Angell Economics.
He is a frequent economics commentator on CNBC's "Kudlow & Company", "Fast Money", and has appeared on "Charlie Rose". A chair in economics has been named for him at Ottawa University. He lives with his wife Betty Angell in Arlington, Virginia. They have four children and nine grandchildren.