I am continually surprised as to the size of the post doc world especially in engineering. In a recent Nature article they report a drop in the total post docs. They state:
From 1979 to 2010 the number of US postdocs in the biomedical
sciences has risen steadily, from just over 10,000 to more than 40,000.
But in the past three years, the tide has turned, according to official
statistics. The population of US biomedical
postdocs fell 5.5% between 2010 and 2013, to just under 38,000, with
losses getting bigger each year, notes a study published on 6 October — although the number of new graduates with science PhDs continues to rise
The above is from Nature as referenced. What is interesting is the ratio of new PhDs to Post Docs, it appears to be dramatically different in Bio from Sci and Engr. That is a measure of the length of time as a post doc.
The true measure is that post docs are all too often used to replace technicians. The techs are employees and get paid more and have benefits. The post doc is at best a journeyman level position with no security.
Also there is a problem of lumping Science and Engineering. I would suspect that most PhDs in Engineering get jobs, for that is where one learns one's craft especially in engineering. Most Engineering Post docs seem to be foreign students being used as super techs. Then they return to wherever.