A novel empirical test reveals that natives living in cities with a substantial Mexican-born population are insulated from the effects of local labor demand shocks compared to those in cities with few Mexicans. The reallocation of the Mexican-born workforce among these cities reduced the incidence of local demand shocks on low-skilled natives’ employment outcomes by more than 40 percent.
That is from Brian C. Cadena and Brian K. Kovak. Here is a related post from Modeled Behavior. You can think of the mobile Mexican labor as providing risk insurance for low-skilled labor markets. It is a further interesting question what this result implies for the aggregate impact of immigration on low-skilled wages, but I don’t see that there is a ready answer a priori, at least not based on the results of this paper. The local geographic swings could be significant, while the aggregate impact could be either high or low.