In 1986, he joined Morgan Stanley, as Vice President for Technology in Nunzio Tartaglias automated proprietary trading group. In 1994, Shaw was appointed by President Clinton to the Presidents Council of Advisors on Science and Technology, where he was chairman of the Panel on Educational Technology. In 2000, he was elected to the board of directors of the American Association for the Advancement of Science served as its treasurer 2000–2010. In 2007, Shaw was elected as a fellow of the American Academy of Arts and Sciences. In 2009, he was appointed by President Obama again to the President's Council of Advisors on Science and Technology. In 2012, he was elected to the National Academy of Engineering and in 2014 was elected to the National Academy of Sciences.