No more sticky prices
Alberto Caballo argues that in the past 10 years online competition has increased both the frequency of price changes and the degree of uniform pricing across locations. He adds that this higher frequency of change can increase the sensitivity of prices to aggregate shocks such as gas prices and exchange rates.
For monetary models and empirical work, my results suggest that the focus needs to move beyond traditional nominal rigidities: labor costs, limited information, and even “decision costs” (related to inattention and the limited capacity to process data) will tend to disappear as more retailers use algorithms to make pricing decisions.

Some preliminary evidence on other countries

More Amazon Effects: Online Competition and Pricing Behaviors
Author: Alberto Cavallo
From: Harvard University
Focus on unemployment
Erceg and al. argue that in today’s environment where the Phillips curve is relatively flat and the prevalence of supply-side shocks means that inflation volatility is likely, reacting strongly to inflation tends to induce a high degree of volatility in the (true) unemployment gap. Their results show that retaining a significant response to the unemployment gap—even if mismeasured—tends to perform better in achieving dual mandate goals than does shifting toward aggressive stabilization of inflation.

Some Implications of Uncertainty and Misperception for Monetary Policy
Authors: Christopher Erceg, James Hebden, Michael Kiley, David Lopez-Salido, and Robert Tetlow
From: Federal Reserve Board