Inflation persistence
The source of inflation persistence is a longstanding question. Most studies have tried to attribute inflation inertia to indexation to past inflation, an assumption that has been controversial because a) it relies on non-optimizing price-setting behavior and b) implies that all prices change every period, an assumption contradicted by micro evidence which shows that many individual prices remain unchanged for several months.
In this paper, Kurozumi and Van Zandweghe use a DSGE model with a) staggered price and setting and b) Kimball (1995)-type aggregators of individual differentiated goods and labor which relax the requirement of a constant elasticity of substitution (CES) between goods or labor. Their model provides a theory of inflation persistence without relying on ad hoc backward-looking price and wage setting behavior. The calibrated version of their model shows that inflation exhibits a persistent, hump-shaped response to monetary policy shocks, as documented by the empirical literature. The intuition behind their model:
Nonzero trend inflation affects inflation dynamics in the model because in each period some prices remain unchanged in line with micro evidence.4 Then, under staggered price setting, the Kimball-type non-CES aggregator of individual goods gives rise to a variable real marginal cost of aggregating the goods, which becomes a driver of inflation. Moreover, the real marginal cost consists of an aggregate of the goods’ relative prices, which depends on current and past inflation rates, thereby generating intrinsic inertia in inflation. Likewise, under staggered wage-setting, the non-CES aggregator of labor leads to intrinsic inertia in wage inflation, which enhances the persistence of price inflation.
A Theory of Intrinsic Inflation Persistence
Authors: Takushi Kurozumi, Willem Van Zandweghe
From: Bank of Japan, Federal Reserve Bank of Cleveland
Inflation persistence in a low and a high inflation regime
In this paper, Borio et al. highlight the usefulness of characterizing the inflation process in terms of two regimes: with one regime characterized by low inflation and the other by high inflation, and with self-reinforcing transitions from low to high. Some interesting observations:
The more limited pass-through of relative price changes into inflation in low-inflation regimes is also consistent with yet another well-known stylised fact: the persistence of inflation falls with the level of inflation.
[T]the degree to which the general price level becomes relevant for individual decisions increases with the level of inflation.
When inflation settles at a low level, it loses traction on agents’ behaviour. When it increases from those levels, it tends to feed on itself. And when it becomes persistently higher, it can more easily spin out of control.

The two-regime view of inflation
Authors: Claudio Borio, Marco Lombardi, James Yetman, Egon Zakrajšek
From: BIS