Every month, Brandeis professor Steve Cecchetti (co-founder, with Mike Bryan, of the Cleveland Fed's median CPI), weighs in with his thoughts on the Consumer Price Index report.  Steve's reaction to the September numbers:

That brings us to the big question:  Will energy price increases feed into the other prices, leading to higher trend inflation?  If they do, watch out.  So far, the news is good.  Core service price inflation (services excluding energy services) are up 1.5% (a.r.) this past month, and 2.5% for the past 12 months.   Looking forward, we can divide services into two types: housing and those based primarily on labor inputs. As for housing, things are moving along at a 2.3% clip (over the past 12 months).  While this might rise somewhat, there are reasons to be optimistic that owner-equivalent rent, and other rental-based measures of shelter costs, will not rise at a rate in excess of 2.5% in the near future.  What about other services?  Here, we need to figure out if wages are likely to rise in response to price increases. My guess is that the answer is no.  Or, at least not much.  American workers don't seem to have much bargaining power, so they are unlikely to be able to recover the real wage losses created by the new energy prices.

At the aggregate level, there is reason for optimism as well. Inflation in the US does not seem to be terribly persistent.  That is, higher inflation today does not seem to portent higher inflation in the future.  Instead, inflation tends to return quickly to the levels we have recently seen.  Today, that means in the neighborhood of 2%.

Steve also has some advice for the Fed (for whom he served as research director at the Federal Reserve Bank of New York from 1997 to 1999):

It is important that the FOMC increase the target federal funds rate by more than the increase in inflation.  That is, they have to drive real interest rates up. We found out in the 1970s what happens when the Fed doesn't go far enough: inflation takes off.  To get some sense of the magnitude of the challenge facing policymakers today, we can look at the path of the realized (ex post) three-month real interest rate over the past few years.  Eighteen months ago, when the fed funds target was still 1%, the one-month real interest rate was about -1%.  One year ago, after three 25 basis point increases, it rose to zero.  Today, with inflation over 5% (the all-items CPI is the right index to use here), we are back below zero.   In other words, after a series of eleven increases in the target federal funds rate, the real interest rate today is lower than it was two years ago.  Now, I am surely overstating the case.  But with headline inflation above 4% and the equilibrium real interest rate near 2.5% (or higher)... well, you can do the math. 

There.  You have your assignment.

I've included the archive of Steve's past inflation updates in the "useful links" section of this page.