International sourcing, complementary inputs, and the structure of trade agreements: Deep, shallow, narrow, and wide

We analyze Preferential Trade Agreement (PTA) formation among a subset of members of a multilateral agreement when imported inputs are complementary to one another. A shallow (focused only on border policies) multilateral agreement does not place countries on the efficiency frontier. Furthermore, no subset of countries will form a shallow PTA. Alternatively, a deep PTA that addresses behind‐the‐border policies increases each country's welfare. This result suggests that the recent proliferation of PTA formation is driven by a need for deep integration. Although these deep PTAs increase welfare over a shallow multilateral agreement the efficiency frontier can only be reached by a deep multilateral agreement that covers both border and behind‐the‐border policies. Whether a deep PTA can generate consensus approval for further multilateral‐deep integration depends on the structure of the PTA and the success of the multilateral‐shallow agreement in lowering tariffs.