integrated in regional value chains. For instance, the share of intermediates value added on total domestic value added in UK exports (the majority of which goes to the EU) is close to 70 percent.

We first investigate the extent to which the depth of the EU contributed to boost trade between the UK and other EU members. We use data from the World Input Output Database (WIOD) on goods, services and value added trade and the World Bank data on the content of deep agreements to estimate a gravity equation augmented with a measure of depth for the period 1995‐2011. By interacting the depth of PTAs with dummies identifying the UK, we can quantify the effect of the depth of trade agreements on UK imports and exports of goods, services and value added. Deep trade agreements are found to increase goods and services trade by 42 percent on average. The depth of the UK’s trade agreements strongly increased trade in services: as a result of its EU membership and its participation in deep PTAs signed by the EU with third countries, UK services trade more than doubled. Deep PTAs also increased domestic value added in gross exports of the UK. This effect is mainly driven by stronger GVC relationships of the UK with its EU partners: the UK’s intermediates value added in gross exports (forward linkages) increased by 31 percent thanks to deep PTAs. In addition, foreign value added in UK exports (backward linkages) was boosted by EU membership by 37 percent. Finally, breaking down the EU into “new” and “founding” members reveals that EU membership has been particularly important to increase UK exports of services directed to the latter.

We then analyze the impact that changes in the UK‐EU trade agreement can have on UK‐EU trade relations going forward. This is a difficult task, as the only certainty on the future institutional setting is its uncertainty. We address this problem by considering three distinct scenarios, with decreasing depth of the future agreement between the UK and the rest of the EU. The first scenario assumes that the PTA between the UK and the EU will be as deep as the agreement the EU has with Norway. In the second scenario, the UK and the EU will sign a PTA as deep as the average PTA the EU currently has with third countries. Finally, the third scenario has no agreement. We find that bilateral UK‐EU trade declines under all scenarios and that this drop is sharper the lower the depth of the future arrangement relative to the depth of the EU agreement. In terms of value added trade, the decline ranges from 6 percent of the “Norway” scenario to 28 percent of no agreement. In all scenarios, the largest declines are for UK services and GVC trade with the rest of the EU. These predictions should be seen as average effects. As it takes time for trade flows to respond to changes in trade costs, we expect the impact in the short‐run to be smaller than in the longer term.

Our work is closely related to two strands of economic literature. The first is the large body of literature that investigates the impact of trade agreements on members’ trade relations, which has recently been summarized in Limão (2016). As many of these studies, we use a gravity framework to guide our analysis of the trade effects of PTAs. Second, our work also relates to the small and recent literature that focuses on the economic and trade effects of Brexit (e.g. Dinghra et al., 2016 and Kee and Nicita, 2016). Our paper differs from others in two main respects. First, we employ an explicit new measure of depth based on the content of PTAs. Second, we do not just focus on goods (or total) trade, but assess the impact of UK membership of the EU and its exit on goods, services and value added trade. Our study also relates to the economic literature that aims at assessing the economic effects of European economic and political integration (e.g. Brou and Ruta, 2011, and Campos, Coricelli, Moretti, 2014). Differently from this literature, we focus on EU trade‐related institutions and trade effects.

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