We study the distributional effect of the massive exodus of Venezuelans in Colombia and how public policy can shape its impact. Using RIF-regressions in an instrumental variables approach, we find that the exodus had a larger negative effect on the lower tail of the natives’ wage distribution, increasing inequality in the host economy. We propose downgrading as the driving mechanism: due to formal restrictions, immigrants ended up working in more routine and lower-paying jobs than natives with similar characteristics. Finally, we show that a large-scale amnesty program reduced the magnitude of downgrading, mitigating the unequalizing impact of the exodus.

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