I pile up some data sources here for myself and others.
US Census: Monthly import and output data of the US
USITC DataWeb: Detailed trade data of the US, like by types of use, commodity, etc.
Two very interesting and recent papers on productivity slowdown:
A Theory of Falling Growth and Rising Rents – Philippe Aghion et al.
Low Interest Rates, Market Power, and Productivity Growth – Ernest Liu et al.
Both contribute productivity slowdown to market concentration, yet via different mechanisms (entry cost for Aghion et al. and low interest rate for Ernest Liu et al.).