  Market impact is a key concept in the study of financial markets and several
models have been proposed in the literature so far. The Transient Impact Model
(TIM) posits that the price at high frequency time scales is a linear
combination of the signs of the past executed market orders, weighted by a
so-called propagator function. An alternative description -- the History
Dependent Impact Model (HDIM) -- assumes that the deviation between the
realised order sign and its expected level impacts the price linearly and
permanently. The two models, however, should be extended since prices are a
priori influenced not only by the past order flow, but also by the past
realisation of returns themselves. In this paper, we propose a two-event
framework, where price-changing and non price-changing events are considered
separately. Two-event propagator models provide a remarkable improvement of the
description of the market impact, especially for large tick stocks, where the
events of price changes are very rare and very informative. Specifically the
extended approach captures the excess anti-correlation between past returns and
subsequent order flow which is missing in one-event models. Our results
document the superior performances of the HDIMs even though only in minor
relative terms compared to TIMs. This is somewhat surprising, because HDIMs are
well grounded theoretically, while TIMs are, strictly speaking, inconsistent.
