What I really would like to see is a historical trend analysis seeing whether BLS and nongovernment estimates (public or private) start to decouple about now.

What I really would like to see is a historical trend analysis seeing whether BLS and nongovernment estimates (public or private) start to decouple about now. If you have enough sources you presumably at least can start to make observations about which sources agree and which disagree. Actually I presume something like this already exists, but I'm not an economist so I don't know.