We develop a novel methodology for the proxy variable identification of firm productivity in the presence of productivity-modifying learning and spillovers, which facilitates a unified internally consistent analysis of the spillover effects among firms. Contrary to the popular two-step empirical approach, ours does not postulate contradictory assumptions about firm productivity across the estimation steps. Instead, we explicitly accommodate cross-sectional dependence in productivity induced by spillovers, which facilitates identification of both the productivity and spillover effects simultaneously. We apply our model to study cross-firm spillovers in China's electric machinery manufacturing, with a particular focus on productivity effects of inbound FDI.