To identify relative wage impacts of immigration, we make use of certification and licensing requirements in the Norwegian construction sector that give rise to exogenous variation in immigrant employment shares across trades. Individual panel data reveal substantially lower wage growth for workers in trades with rising immigrant employment than for other workers. Selective attrition from the sector masks the causal wage impact unless accounted for by individual fixed effects. For low and semi-skilled workers, effects of new immigration are comparable for natives and older immigrant cohorts, consistent with perfect substitutability between native and immigrant labor within trade. Finally, we present evidence that immigration reduces price inflation, as price increases over the sample period were significantly lower in activities with growth in the immigrant share than in activities with no or small change in immigrant employment.