We develop a new framework to study the welfare consequences of preferential trade agreements (PTAs) under global sourcing, incomplete contracts and endogenous matching. We uncover several new channels through which PTAs affect global welfare. There are effects stemmingfrom intensive margin changes---i.e., changes in investment and production in existing verticalchains---and from extensive margin relocations---i.e., due to the formation and destruction ofvertical chains. In each case, there are potential trade creating, trade diverting and relationship-strengthening forces. The first two are reminiscent of the classical Vinerian approach, but takedifferent forms under global sourcing. The third is entirely new in the regionalism literatureand arises because PTAs affect the severity of hold-up problems in sourcing relationships. Wecharacterize those forces and show circumstances when PTAs are necessarily welfare-enhancingor welfare-decreasing. In particular, we show that, because of the relationship-strengtheningeffect, PTAs can improve global welfare even when all types of trade creation forces are absent.