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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, [...]