Shaw was born at Ashton-under-Lyne, near Manchester, on 19 April 1865, and died at Enfield, near London on 15 April 1943. He was the son of James Shaw, who owned a manufacturing business, and his wife, Sarah Ann. After attending a local school Shaw went to Owens College, Manchester, where he studied political economy (BA 1883, MA 1886, DLitt 1892). He then worked for the Chatham Society as an editor before joining the Public Record Office in 1894. Here he worked on the Calendar of State Papers, Foreign, but then transferred to the Calendar of Treasury Papers, on which he worked for the remainder of his career.
From The Biographical Dictionary of British Economists in Oxford Reference.