%N 5 %X In this paper we develop a network model of international trade which is able to replicate the concentrated and sparse nature of trade data. Our model extends the preferential attachment (PA) growth model to the case of multiple networks. Countries trade a variety of goods of different complexity. Every country progressively evolves from trading less sophisticated to high-tech goods. The probability to capture more trade opportunities at a given level of complexity and to start trading more complex goods are both proportional to the number of existing trade links. We provide a set of theoretical predictions and simulative results. A calibration exercise shows that our model replicates the same concentration level of world trade as well as the sparsity pattern of the trade matrix. Moreover, we find a lower bound for the share of genuine missing trade links. We also discuss a set of numerical solutions to deal with large multiple networks. %D 2013 %L eprints1658 %A Rachele Foschi %A Massimo Riccaboni %A Stefano Schiavo %K JEL Codes: F14, F43. - Keywords: Multiple Networks, Trade Networks, Preferential Attachment, Missing Trade, Innovation and Trade %I IMT Institute for Advanced Studies Lucca %T Missing Links in Multiple Trade Networks