On average inflation targeting

Will the Fed switch to an average inflation targeting regime?

Yes, think Cecchetti and Schoenholtz because such shift would be a moderate step and will allow the Fed for some makeup of past misses:

In the chart below, taking the averaging window to be the previous three years, we plot the implied average annual inflation target over the two-year restoration period. (Note that this a static assumption: it does not take into account how the inflation process changes as the Fed adopts this five-year average inflation targeting approach.) Under these assumptions, the implied target since 2011 would have ranged between 2.20% and 3.04%, with an average of 2.65%. That is, with a three-year historical averaging window and a two-year restoration period, the Fed’s inflation target would have been 0.65 percentage points higher for the past decade. If this central bank behavior was both credible and anticipated, it would have lowered the average real short-term interest rate by 65 basis points; a welcome (if moderate) boost at the zero lower bound for nominal interest rates.

Average Inflation Targeting
By: Stephen G. Cecchetti, Kermit L. Schoenholtz – Brandeis University, New York University

Average inflation targeting without rational expectations

Nakata and al. use a New Keynesian with an occasionally binding lower bound on nominal interest rates and find that under rational expectations, assigning an average inflation targeting objective to the central bank, improves macroeconomic outcomes and increases people’s welfare when compared to standard inflation targeting. But under boundedly-rational expectations:

[I]f cognitive limitations are sufficiently strong, the optimal averaging window is finite, and the welfare improvement from abandoning standard inflation targeting in favor of average inflation targeting can be small. The effectiveness of makeup strategies such as average inflation targeting thus hinges on the extent to which people understand how these strategies make future monetary policy and macroeconomic outcomes contingent on current economic conditions.

Average Inflation Targeting and the Interest Rate Lower Bound
Authors: Taisuke Nakata, Sebastian Schmidt, Flora Budianto
From: Board of Governors of the Federal Reserve System, ECB, BIS

What is the optimal degree of history dependence or averaging window?

Amano and al. use a two agent New Keynesian model, where a fraction of firms have adaptive expectations and where the lower bound on nominal interest rates  binds 10% of the times, to study the effectiveness of average inflation targeting as compared to price- level targeting. They find:

• If the economy is subject to demand shocks, it is optimal for the central bank to target an average inflation rate calculated over a window of slightly less than two years. In this case, average-inflation targeting leads to outcomes that are very close to those generated by price-level targeting.
• If the economy is subject to cost-push shocks, the optimal window length declines substantially to about two quarters. In this case, average-inflation targeting with a long averaging window leads to greater volatility and lower welfare.

Average Is Good Enough: Average-Inflation Targeting and the ELB
Authors: Robert Amano, Stefano Gnocchi, Sylvain Leduc, Joel Wagner
From: Bank of Canada, Federal Reserve Bank of San Francisco