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We estimate a knowledge production function for university patenting using an individual effects negative binomial model. We control for Research and Development expenditures, research field, and the presence of a Technology Transfer Office. We distinguish between three kinds of researchers: faculty, postdoctoral scholars (postdocs), and PhD students. For the latter two, we also distinguish by visa status. We find patent counts to relate positively and significantly to the number of PhD students and number of postdocs. Our results also suggest that not all graduate students and postdocs contribute equally to patenting but that contribution is mediated by citizenship and visa status. (JEL C25, O31, O32, O34, O38)