Shah served as Executive Director of the Royal Statistical Society from 2011 to 2019. Under his leadership the Society developed several new initiatives, including the celebration of Statistics of the Year, the Data Manifesto and the development of Statistical Ambassadors. The 10-point data manifesto was published after the 2015 election, intended to communicate the significance of certain statistics with politicians and the general public. The manifesto emphasised the need to use reliable evidence in public debate. Statistical Ambassadors act to support charities and the media, pairing them with statisticians trained in public engagement. Shah called for more care to be taken when companies disclose their gender pay gap; claiming that some could be "gaming the system" by incorrectly reporting their mandatory declarations. He has also called for the Public Administration and Constitutional Affairs Select Committee to stop having evidence sessions that consistently feature all male panels. In 2018 he worked with the Institute and Faculty of Actuaries to investigate the implications of big data. Shah believes that the public may become mistrustful of commercial use of their data in the same way they queried genetically modified food. In 2019 it was announced that Shah would join the British Academy as Chief Executive in 2020.
Non executive roles
Shah is Vice Chair of the Ada Lovelace Institute and Chair of the Friends Provident Foundation. The Ada Lovelace Institute is a think-tank that looks to ensure all data and artificial intelligence serves to benefit all members of society. The think-tank was established after a Royal Statistical Society workshop on big data, when participants questioned what ethics and governance organisations could use. The Ada Lovelace Institute support both the public and private sector, and are independent of government or corporate interests. The Friends Provident foundation is a grant making trust that looks to promote a more fair economy. He is a Visiting Professor at King's College London and was a member of the IPPR Commission on Economic Justice. He was also a member of the independent Social Metrics Commission chaired by Baroness Phillipa Stroud which recommended a new way of measuring poverty in the UK.