Applying propensity score reweighting to Italian administrative data covering the period 1994-2012, we study the conditional distributions of injuries by wage of native and foreign workers and distinguish between the component that is explained by observable characteristics and the component that is instead attributable to the immigrant status. Our analyses highlight some stylized facts. Besides a substantial gap in wage and injury risk that cannot be attributed to differences in the characteristics, foreign workers face higher levels of risk by the same level of wages. The gap is significantly above the level predicted by their observable characteristics by remunerations that are close to the minimum wage level set by collective bargaining. After this threshold, injury rates decline, but less steeply for foreign workers than their observable characteristics would predict. We show that the hedonic wage model could explain the first result as a corner solution whereby workers with low wage potential are forced to accept higher levels of risk due to the lower bounds on minimum wage. The second results could simply be explained by assuming different utility functions for natives and foreigners. We also show that the hedonic wage model is compatible with the marked reduction in injury rates and in the gap that we observe in the recession years.