  Immigrants are always accused of stealing people's jobs. Yet, by assumption,
standard immigration models -- the neoclassical model and
Diamond-Mortensen-Pissarides matching model -- rule out displacement of native
workers by immigrants. In these models, when immigrants enter the labor force,
they are absorbed by firms without taking jobs away from native jobseekers.
This paper develops a more general model of immigration, which allows for
displacement of native workers by immigrants. Such generalization seems crucial
to understand and study all the possible effects of immigration on labor
markets. The model blends a matching framework with job rationing. In it, the
entry of immigrants increases the unemployment rate of native workers.
Moreover, the reduction in employment rate is sharper when the labor market is
depressed because jobs are scarcer then. On the plus side, immigration makes it
easier for firms to recruit, which improves firm profits. The overall effect of
immigration on native welfare depends on the state of the labor market.
Immigration always reduces welfare when the labor market is inefficiently
slack, but some immigration improves welfare when the labor market is
inefficiently tight.
