Alan Blinder, Bill Clinton's Vice Chair of the Federal Reserve, quoted and discussed here:
“Here is an interesting historical fact. Since Harry Truman, the growth rate has fallen every time a Republican president replaced a Democrat and has risen every time a Democrat has replaced a Republican.”
No, not every time, in either case.
Nixon/Ford current dollar GDP growth (Republican) was better than previous JFK/LBJ GDP (Democrat), up 100% vs. 80%.
And Obama current dollar GDP growth (Democrat) was worse following Bush GDP (Republican), up 30% vs. 39%.
For best growth of current dollar GDP in the post-war, Democrat presidents own positions one and four covering 12 years, but Republicans own positions two and three covering 16 years:
Four Republican administrations lasting 8 years each have averaged 8.2% in the post-war, and four Democrat administrations lasting 8 years each have averaged 7.5%.
Democrat Carter's 4 years at 13.5% easily beats Bush 41's 4 years at 6.0%, but this hardly offsets the better Republican performance over the long haul compared with the Democrat (see here for the figures).