According to Victor Canto, writing in the National Review, the answer is price-level targeters. Here's his claim, as picked up by pgl at Angry Bear:
While it’s true that the Fed has never disclosed its operating procedure, I have pointed out over the years that its policy behavior is consistent with the domestic price rule. What’s more, I have argued that the U.S. inflation rate was consistent with a price rule even prior to the Greenspan years.
OK then, lets go to the record. Here is how inflation, measured by the PCE chain-weight index, has behaved since 1983:
The picture is pretty clear. If you believe that the FOMC has had an implicit inflation target of about 2%, the data since about 1992 would give you no argument. You have a little more trouble going back to the Volcker/early-Greenspan years. Either you must assume that the implicit target was different in the earlier phase of the post-70s disinflation, or that the various incarnations of the FOMC in the 1980s were willing to accept a very long transition period to the preferred rate of inflation.
Which brings us to the key distinction between an inflation target and a price-level target. A central bank operating under an inflation target will let bygones be bygones: If inflation comes in above target is in any particular year, no conscious effort is made to undo the the effects on the level of prices by subsequently engineering inflation below the target.
Without assuming that the implicit inflation target was varying over the period since 1983, the proposition that the FOMC acted as if they were price-level targeters is a pretty tough sell. What about in the Greenspan years? It obviously depends on when you think the implicit 2% target became operative. If you contend that it was the objective since the beginning of Mr. Greenspan's tenure in August 1987, there is a very big distinction between the inflation targeting approach and the price-level targeting approach. If you are willing to start the clock at the end of the 1990-91 recession, or the beginning of 1992 (to get some distance away from the trough of the cycle), the FOMC looks like pretty successful inflation targeters (again assuming that a 2% annual increase in the price level is the goal):
The actual average rate of PCE inflation over the period since 1992 has been just a tad over 2%. As a simple matter of arithmetic, a price-level target that allows the price level to grow at 2% will look almost exactly like a successfully maintained average-inflation target of 2%. Whether or not you see the inflation-target vs. level-target approaches as amounting to distinctions without a difference depends on when you think history began.
If you are interested, here are the Power Point source for the pictures above:
UPDATE: In a follow-up, pgl correctly notes that observing a particular price-level trend in a small sample of years is not proof of a price-targeting central bank.