Using a statistical model of an evolving multiplex network, we study tie formation in global production chains within and across developed countries, their trade activities with developing economies in the intermediate goods market, and the mutual dependencies between these relationships. Our model approaches these dynamics from the perspective of individual nodes and thus identifies the driving forces behind the tie formation process. The empirical value of our approach is demonstrated by fitting the model to a panel data set from the OECD Inter-Country Input-Output Tables between 2005 and 2015. Based on these data, we find that (i) geography, two-sided heterogeneity of buyers and sellers, trade costs, as well as structural characteristics of the production network determine the formation of trade linkages between OECD country-sectors, (ii) some of these determinants have an asymmetric effect on import and export ties between OECD and non-OECD countries, and (iii) intra-OECD trade and import and export ties with non-OECD economies are mutually dependent.