Inflation and attention thresholds
In this paper Korenok et al. study the level of inflation which triggers households and businesses to alter their behavior as internalization of inflation can lead to a significant inflation acceleration:
One of the dangers of high inflation is that it can cause firms and households to pay close attention to it. This internalization of inflation can lead to an accelerationist regime, making inflation harder to control. We empirically assess the relationship between attention and the level of inflation for 37 countries. Our measures of attention are constructed either from internet search behavior or the popularity of inflation mentions on Twitter. We find evidence that attention thresholds do exist for the majority of countries in our sample. We also find interesting variability across countries.

Inflation and attention thresholds
Authors: Oleg Korenok, David Munro, Jiayi Chen
From: Virginia Commonwealth University, Middlebury College
How UK firms set prices during the current inflationary period
In this paper, Bunn et al. use firm-level data from the Decision Maker Panel (a large and representative survey of firms in the UK) to study inflation dynamics and how firms have set prices during the period of 2016-2022 Q2. Two of their findings:
Inflation rates across firms have become more dispersed and skewed since the start of the pandemic. We find that average price inflation is positively correlated with the dispersion and skewness of the distribution.
During the early part of the Covid pandemic, this measure of subjective price uncertainty increased by less than subjective sales uncertainty. But since the start of 2021, as uncertainty about sales was mostly declining, uncertainty about inflation rose. Price uncertainty reached a new peak in 2022 following the Russian invasion of Ukraine.
Firming up price inflation
Authors: Philip Bunn, Lena Anayi, Nicholas Bloom, Paul Mizen, Gregory Thwaites, Ivan Yotzov
From: Bank of England, University of Nottingham