We study the role of European Immigration on local and aggregate economic growth in the United States between 1880 and 1920. We employ a big data approach and link, at the individual-level, information from the Population Census, the universe of patents and millions of historical immigration records. We find that immigrants were more prolific innovators than natives, and document large differences in innovation potential across nationalities and regions in the United States. To measure the importance of immigrants for the creation of new ideas and economic growth, we develop a new spatial model of growth through dissemination of knowledge and workers’ mobility. The model allows us to use our micro and regional empirical findings to measure immigrants’ innovation human capital and the degree of knowledge diffusion which regulates scale effects. We quantitatively analyze the effects of imposing major immigration restrictions on American economic growth in the 19th and early 20th century. We find large, accumulating, losses from these restrictions. Both the scale effects and the exclusion of high-human capital immigrants contribute significantly to these losses.