To identify wage impacts of immigration, we use licensing requirements in the Norwegian construction sector that give rise to exogenous variation in immigrant employment across trades. Individual panel data reveal lower wage growth in trades with rising immigrant employment shares, with a 10% increase in immigration predicted to reduce wages by 0.6%. Selective attrition masks the causal wage impact if neglected. For low and semi-skilled workers, wage effects are comparable for natives and older immigrant cohorts, consistent with perfect substitutability between native and immigrant labour within trade. Price data indicate that wage and cost reductions are passed on to consumers.