What's up with Inflation?

As we have watched FED go on a spree of interest rate cuts to bring back the economy to its equilibrium growth path, inflation has been creeping on us. It is no secret, nor rocket science which we learned during our years in college that there is a trade-off between GDP growth and Inflation. After the publication of the Barro-Gordon model and a series of papers by Prescott it has become a general concensus that central banks are able to stimulate economic growth through interest rate cuts, but only in the short-run. In the long-run (3+ years) this will bring nothing but higher inflation.
So is FED on a suicidal mission? Maybe! Or maybe it sees a 2nd great depression if it does not act accordingly, where high inflation is a peanuts trade-off.
ECB (European Central Bank) has been acting differently and in line with its mandate (maintain medium-term inflation close, but above 2%) coinciding with most scientific recommendations.
Anyway for anyone interested in finding more about optimal monetary policy rules, one can consult a benchmark manual by "Walsh", or the original paper by Barro-Gordon.

Predicted inflation rates for next year in US should be +4% and in Europe somewhere close to 4%. What I have found during this last week is that there are some market instruments that are pricing only 1.5% inflation for both economies, which seems quite unlikely.

Investment Strategy: Long French & US 1 year Inflation Linked Bonds and Short French & US government bonds

The yield between inflation linked bonds and government bonds is interpreted as the expected inflation rate which for these two countries is currently at 1.5% and much below the expected value, so I would expect for this spread to widen to at least 3-4% meaning that the inflation linked bond price should go down in relation to the government bonds.