This blog post establishes some links between housing scarcity and immigration:
Only the wealthiest, best-educated immigrants move [to California], and most refugee resettlement agencies no longer place families in San Francisco because of the city’s high housing costs. The city accepts 95% fewer refugees than just a few years ago. Who actually welcome immigrants and refugees? Cities like Houston, Phoenix, and Atlanta that have lower costs of living.
Empirically, we leverage an EU legal directive that resulted in an exogenous increase in the intensity of competition between immigrants and natives over public housing in Austria. Our findings indicate that support for anti-immigrant parties is highly responsive to perceived scarcity resulting from immigrant receipt of in-kind benefits.
This blog post establishes some links between housing scarcity and immigration:
Cavaille and Ferwerda (2017) provide a well-identified channel: