I think there were three important contributory factors to what happened in the 1970s that are just not present today. First, our knowledge of inflation output trade-offs, although hardly complete now, was much weaker back then. Second, the Fed and other monetary policy makers did not have clear inflation targets that they were publicly committed to. Third, there appeared to be an alternative instrument for dealing with inflation: direct controls on prices and wages. The 1970s really was a different world in terms of the understanding of macroeconomic policy.
I think the argument for publicly stated inflation targets has the same vulnerability as the argument for a single mandate. The Fed did not state an inflation target until recently. I might be ignorant but I think there have been two Fed statements on inflation targets the December 12 up to 2.5% is ok so long as unemployment is over 6.5% and a 2% target stated the previous year.
I just googled [greenspan inflation target]. The second link is entitled "Greenspan Rejects Inflation Targets"
"'A specific numerical inflation target would represent an unhelpful and false precision,' Mr. Greenspan said." I submit that Mr Greenspan managed to avoid high inflation in spite of specifically rejecting your advice.
The first hit says that Bernanke is for inflation targetting, but I think a FOMC chaired by him first announced a target well after 2010 (I think in 2012).
The search (not that it should be hard to reproduce) http://bit.ly/ZjTxwW
OK now I google [Bernanke inflation target" and get
"By Jonathan Spicer
Wed Jan 25, 2012 6:35pm EST
(Reuters) - The Federal Reserve took the historic step on Wednesday of setting an inflation target, a victory for Chairman Ben Bernanke that brings the Fed in line with many of the world's other major central banks." Yep 2012 (but close whew).
I'd also say that there was very little discussion of wage and price controls in the USA during the period of high inflation. There were wage and price controls in 1973 *before* the oeriod of high inflation. My sense during the 70s is that they were considered to have been one of Nixon's mistakes. I can't believe that faith in wage and price controls was a significant factor affecting policy.
update: Staff at the IMF and Ryan Avent too. The IMF staff wrote "when central banks whipped inflation in the early 80s and set low targets for it." Ryan Avent quotes the historical claim without comment here (RA is identified as Ryan Avent here). Again, the FOMC set a target for inflation on January 25 2012.
Warning big pdf. I was not sure that Paul Volcker never declared an inflation target. I'm afraid the best link I can find is to this pdf entitled "Inflation Targetting in the United States ?" it is a chapter from a conference book from 2003 called "The Inflation Targetting Debate" edited by Ben Bernanke and Michael Woodford (who know a bit about monetary policy and have views on inflation targetting).
Note the question mark in the title. It was not agreed in 2003 that the USA had had inflation target since the early 80s. The question was whether it should have a target. The discussant of the chapter argued that it definitely did not have an inflation target in the mid 80s -- inflation and forecast inflation were over 2% and the FOMC didn't do anything about it or much discuss doing anything about it.
Of course it is possible that Volcker had a target which just happened to be over 2%. Perhaps he considers a 2 % target too low and supports a higher target. (please do click those links).
It is obvious that Volcker accepted 4% inflation not because that was his target (such a target is, to quote Volcker "nonsense") but because he wasn't targetting inflation but was rather balancing an obviously weak desire for low unemployment with a desire for inflation to be as low as possible.
It was argued, ad nauseum, that clear simple verifiable rules were key to successful monetary policy. That argument was repeatedly rejected by Volcker [and Greenspan*] by their words and Volcker's deeds. The advocates of simple rules don't conclude that Volcker doesn't know how to handle inflation so some of them have rewritten history.