I have made most of these comments as comments on Econbrowser and Angry Bear (an excellent post by Robert Waldman), as well as on Econbrowser in response to a serious post by Jeffrey Frankel. I note that pgl has added useful comments on this matter in the other blogs.
So it was 1990 that the New Zealand central bank became the first in the world to impose an inflation target of 0-0.002. It worked out pretty well for NZ, and in general it has not done too badly in general where applied, well beyond the US. Of course, global inflation has declined, with a handful of exceptions.
In the mid-90s the US grew better than it had previously, and in the middle of the decade there was an important moment regarding policy. There was no inflation directive but Fed Chair Greenspan was facing a de facto such directive based on central Fed estimates that there was a known "natural rate of unemployment (=NAIRU) that must not be passed.
As it was then Fed Gov Janet Yellen in the mid 90s convinced Greenspan not to raise interest rates partly because of a paper by her husband, Noblelist George Akerlof. This famous paper from 1996 out of Brookings where George was due to Janet being at the Fed,
His now famous paper with Dickens and Perry redefined this whole debate. So the hard empirical fact is that that nominal wages do not decline. The Akerlof et al paper shows that there is no downard movement in nominal wages. His group said that given no wage downs, those gaining will push wages up.
George (yes, an old very close friend), has coauthored with his wife, Janet Yellen, on why workers do not accept nominal wage decreases. It is a matter of social relations within workers, with A and Y publishing numerous papers on why that no wages going down.
So, in 1990 the New Zealand central bank worked out OK In the mid-90s Yellen convinced Greenspan to lay back because there is no NAIRU or natural rate of unemployment, although there has never been a credible argument that the"natural rate of employment equals the NAIRU."