How should the Fed measure inflation?

In today's NY Times, Floyd Norris writes:

Since 1983, the government has measured the price of homes not by looking at house prices but by computing what it calls ''owner's imputed rent.'' That is the rental value of the house you own. It accounts for nearly a quarter of the entire Consumer Price Index.

When the change was made, the government provided statistics indicating that previous inflation rates would not have been very different under the new method, and that remained true until 1996.Since then the home price index maintained by the Office of Federal Housing Enterprise Oversight has doubled, while the imputed rent figure has risen by less than a third.

Had the government computed the Consumer Price Index using actual home prices since 1996, I estimate that it would have risen by an average of 4.1 percent a year, as opposed to the 2.5 percent reported. The core rate -- inflation excluding food and energy costs -- would be 4.2 percent, not 2.2 percent. Perhaps the Federal Reserve was too hesitant to raise rates, and thus allowed speculative bubbles to form, because it was seeing inflation through rose-tinted glasses.

Beyond the treatment of housing in particular, Norris's observation raises a broader question that has received too little attention from the community of research economists: If a central bank is to adopt inflation-targeting as a guide to policy, what inflation rate should it use?

The Fed seems to focus on core PCE inflation--that is, inflation in the prices of consumer goods and services excluding certain volatile sectors, such as food and energy. From the standpoint of practical monetary policy, this choice seems sensible. But it is hard to square this common-sense decision with standard monetary theory, which doesn’t readily yield a variable analogous to these empirical measures.

Steve Zeldes once observed that measures of core inflation are like the clues on the TV game show Jeopardy. The category is inflation. The answer is the CPI excluding food and energy. It is your job to figure out the question.

Some years ago, Ricardo Reis and I took a stab at this problem (published in the JEEA). We developed a framework for thinking about the issue and applied it to U.S. data. We found that the price of labor (that is, the nominal wage) should be given substantial weight in the index used for monetary policy. But I will be the first to admit that this conclusion was too tentative to take to the (central) bank.

Update: Mark Thoma points me to this recent summary by Mike Woodford of some of the relevant literature.