The paper answers two questions simultaneously. What is the effect of offshoring on firms' total factor productivity? What is the effect of offshoring on skill-biased technological change? We estimate a model of firm production that allows for the effect of offshoring on both total factor productivity and relative skilled labor productivity, and for spillovers between the two. The model is fitted to Swedish firm-level data between 2001-2011. We find positive effects of offshoring intensity on total factor productivity, particularly of small domestic firms and large foreign-owned firms, and on skill-biased technological change in production of firms with low offshoring intensity. Initiating offshoring results in skill-biased technological change in non-production activities of large domestic firms. We show that evaluating the impact of offshoring in a unified framework has implications for the estimation results.