- Inflation falls if there is significant spare capacity.
- If the central bank can consistently hit its inflation target there is no spare capacity.
- If there is no spare capacity, there is no policy problem.
- There is only a problem if inflation is below target AND the central bank cannot raise the inflation rate.
- If the central bank cannot raise the inflation rate, and inflation is below target, it cannot hit a higher inflation target.
Raising the inflation target cannot be a solution to 4. If the CB cannot hit its current inflation target, it cannot hit a higher one (5). If it can hit its current inflation target, there is no problem (2 & 3).
It should be noted that prior to 4 occurring, a higher inflation target might reduce the probability of 4 occurring, but once 4 has occurred, raising the inflation target cannot be a solution.
Also, if 4 is occurring, the central bank cannot hit a nominal GDP target at will (this only requires the additional assumption that if the CB cannot raise the inflation rate it cannot hit a nominal GDP target at will). Therefore nominal GDP targeting cannot be a solution, either.
To believe that raising the inflation target or nominal GDP targeting are policy solutions to 4, one has to believe that one of more of 1-3, and/or 5, are false.
For a detailed explanation of 1-4, this by Simon Wren-Lewis is spot on. For a defence of raising the inflation target, read Brad DeLong and Tony Yates. I think Brad advocates a higher target precisely to reduce the probability of 4 occurring, rather than as a solution once it has occurred. The ever-insightful David Beckworth argues for regime change and nominal-GDP targets here. For denial of the futility of using current tools to raise the inflation rate, this by Frances Coppola is superb.