The purpose of this paper is to estimate the patent equation, an empirical counterpart to the knowledge-production function. Innovation output is measured through the number of European patent applications and the input by research capital, in a panel of French manufacturing firms. Estimating the innovation function raises specific issues related to count data. Using the framework of models with multiplicative errors, we explore and test for various specifications: correlated fixed effects, serial correlations, and weak exogeneity. We also present a first extension to lagged dependent variables.