[eng] The increase in the foreign-born population is one of the main socio-economic changes that has been seen in many developed
countries over the last decades. In the United States, the share of foreign-born individuals increased from 9.2% of the population
in 1990 to 14.3% in 2010. More striking examples can be found in Europe. In Italy, over the same period, the share of foreign
residents rose from 2.5% to 9.7%, whereas in Spain it increased from 2.1% to 14.4%. In these economies, the Great Recession
took place contemporaneous to this context of large immigrant inflows. As a result of rigid labour markets, in Spain and Italy,
the economic downturn triggered by the Great Recession led to a large increase in unemployment rather than substantial wage
reductions (Font et al., 2015; Adamopoulou et al., 2016). Many papers have tried to estimate the impact of immigration on the
labour market outcomes of host countries (see Dustmann et al., 2016 for a review of several important recent findings). Most
of these papers either abstract from search frictions (Ottaviano and Peri, 2012; Dustmann et al., 2013; Peri and Sparber, 2009;
Moreno-Galbis and Tritah, 2016; Llull, 2018) or focus on steady-state comparisons (Chassamboulli and Palivos, 2014; Battisti et al.,
2018), and consequently, little is known about the impact of immigration in non-stationary environments or during the transition
from steady-states.