This paper estimates the effects of immigration on wages of native workers at the national U.S. level. Following Borjas (2003) we focus on national labor markets for workers of different skills and we enrich his methodology and refine previous estimates. We emphasize that a production function framework is needed to combine workers of different skills in order to evaluate the competition as well as cross-skill complementary effects of immigrants on wages. We also emphasize the importance (and estimate the value) of the elasticity of substitution between workers with at most a high school degree and those without one. Since the two groups turn out to be close substitutes, this strongly dilutes the effects of competition between immigrants and workers with no degree. We then estimate the substitutability between natives and immigrants and we find a small but significant degree of imperfect substitution which further decreases the competitive effect of immigrants. Finally, we account for the short run and long run adjustment of capital in response to immigration. Using our estimates and Census data we find that immigration (1990-2006) had small negative effects in the short run on native workers with no high school degree (-0.7%) and on average wages (-0.4%) while it had small positive effects on native workers with no high school degree (+0.3%) and on average native wages (+0.6%) in the long run. These results are perfectly in line with the estimated aggregate elasticities in the labor literature since Katz and Murphy (1992). We also find a wage effect of new immigrants on previous immigrants in the order of negative 6%.