This paper proposes a general method to extend a standard input-output (IO) table to incorporate firm heterogeneity when portraying the domestic segment of global value chains in a country. We develop a quadratic optimization model to estimate an extended IO table that reports inter-sector transactions between different types of firms in an economy, using information from standard IO tables along with various linear constraints implied by sector-level statistics and firm-level data. The proposed method permits the computation of standard errors of all values in the estimated IO tables, inferred from bootstrapped samples of the underlying firm-level data. As an illustration, we implement our model using Chinese IO tables and firm census data. We then use the estimated IO tables to compute the direct and indirect domestic value added in exports of different firm types in China. Based on our reconciled data sets for 2007 and 2010, we find that both state-owned enterprises (SOE) and small and medium enterprises (SME) in China have much higher value-added exports (VAX) to gross exports ratios, compared to the rest of the economy. While the VAX ratio of China’s aggregate exports increased by about 9% between 2007 and 2010, SOE’s and SME’s VAX increased by 47% and 27%, respectively.
value-added trade global value chains quadratic optimization intra-national trade