The high-tech sector is increasingly concentrated in a small number of expensive cities, with the top ten cities in "Computer Science", "Semiconductors" and "Biology and Chemistry", accounting for 70%, 79% and 59% of inventors, respectively. Why do inventors tend to locate near other inventors in the same field, despite the higher costs? I use longitudinal data on top inventors based on the universe of US patents 1971 - 2007 to quantify the productivity advantages of Silicon-Valley style clusters and their implications for the overall production of patents in the US. I relate the number of patents produced by an inventor in a year to the size of the local cluster, defined as a city x research field x year. I first study the experience of Rochester NY, whose high-tech cluster declined due to the demise of its main employer, Kodak. Due to the growth of digital photography, Kodak employment collapsed after 1996, resulting in a 49.2% decline in the size of the Rochester high-tech cluster. I test whether the change in cluster size affected the productivity of inventors outside Kodak and the photography sector. I find that between 1996 and 2007 the productivity of non-Kodak inventors in Rochester declined by 20.6% relative to inventors in other cities, conditional on inventor fixed effects. In the second part of the paper, I turn to estimates based on all the data in the sample. I find that when an inventor moves to a larger cluster she experiences significant increases in the number of patents produced and the number of citations received. Conditional on inventor, firm, and city _ year effects, the elasticity of number of patents produced with respect to cluster size is 0.0662 (0.0138). The productivity increase follows the move and there is no evidence of pre-trends. IV estimates based on the geographical structure of firms with laboratories in multiple cities are statistically similar to OLS estimates. In the final part of the paper, I use the estimated elasticity of productivity with respect to cluster size to quantify the aggregate effects of geographical agglomeration on the overall production of patents in the US. I find macroeconomic benefits of clustering for the US as a whole. In a counterfactual scenario where the quality of U.S. inventors is held constant but their geographical location is changed so that all cities have the same number of inventors in each field, inventor productivity would increase in small clusters and decline in large clusters. On net, the overall number of patents produced in the US in a year would be 11.07% smaller.