“The unemployment resulting from wage rigidity and job rationing is sometimes called structural unemployment.” — Mankiw’s intermediate text
“Frictional unemployment [w.a. where the only other kind of unemployment they mention is cyclical unemployment] is the unemployment that exists when the economy is at full employment.” — Dornbusch, Fischer and Startz
“The part of unemployment associated with the institutional features of an economy, including hiring and firing costs and the structure of the unemployment compensation system.” — Jones’ intermediate text
There may be confusion about this term because there seems to be such a multitude of definitions (wikipedia’s definition talks about skill mismatch). I like Jones’ definition the best, but the point I want to make is that the lefty bloggers are reading more into these definitions than necessary.
There’s no reason to think the relationships between “wage rigidity”, “full employment”, “institutions” or “skill mismatch” and unemployment are constant over the business cycle. You can make good arguments that the mechanisms producing these relationships are responsive to overall conditions in the economy (I won’t). And… and!… estimates of structural unemployment suggest that it is time-varying: higher during recessions and lower during booms (anyone have a good cite for an estimate of time-varying NAIRU?).
When the Fed folks say structural unemployment is high right now (e.g. Altig or Kocherlakota), they’re not saying its permanently high. They’re not trying to pull an inception making us feel like permanent high unemployment is ok. They’re observing momentarily high structural unemployment that fits in a pattern consistent with historic experience.