Question

Suppose the Fed pursues a policy with a (geometric) average ination target of 2%

over a three-year period (that is, from t to t + 1, from t + 1 to t + 2, and from t + 2 to

t+3). However, imagine now that the rst year's ination rate (the ination rate from

t to t + 1) ends up being below target, at 0%. What will the next two years' in

rates have to be for the Fed to live up to its ination policy?

Answer 1

Geometric average = nth root of the product of n numbers.

Fed's target is 2% inflation (geometric mean over three years)

In the given case, there are three periods with value zero in the first period, implying that the values in the the isecond and third period could be mathemetically 2 or 0 for both years. In both the scenarios the geometric mean fo three years would be 0.

Therfore, Fed would keep target for 2nd and 3rd year as 2% as per the original target instead of keeping at zero for these years and act accordingly.