capture the trade impact of the EEA as the average effect of the trade agreement between the European Economic Community and the EFTA countries, signed in 1973, and the EEA of 1994.<sup>13</sup> A more recent study by Dhingra et al. (2016), based on a general equilibrium trade model à la Costinot and Rodriguez‐Clare (2013), finds that the losses associated with Brexit range between 1.28 percent and 2.61 percent of GDP. Combining our reduced form results and estimates on the elasticity of income to trade in goods by Feyrer (2009), we find that Brexit would imply larger impacts on the UK’s income: a decrease by 3 percent in the “Norway” scenario and by 13 percent in the no‐agreement case. A possible interpretation of the difference is that the reduced form estimates deliver a higher impact because they capture both the dynamic and static effects, while the structural model only accounts for static effects due to the increase in trade barriers (Dhingra et al., 2016).<sup>14</sup> Our focus is on UK‐EU trade relations, but Brexit will also impact trade relations the UK has with countries that have singed a PTA with the EU. What would be the trade effect if Brexit also implied the exit of the UK from all the EU’s PTAs? The average number of provisions included in these agreements is around 14. The group of the UK’s non‐EU PTA partners account for 14 percent of the UK’s total export of goods, of which the most important partners are Switzerland, South Africa, Turkey and Norway that together account for 11 percent of exports.<sup>15</sup> By exiting all the non‐EU PTAs, the UK would decrease its exports to these countries by 17 percent, equivalent to $12.212 billion. Obviously, the UK could re‐negotiate these agreements seeking deeper integration or decide to pursue deep trade agreements with other important trade partners such as the US, Canada and China.

# 5. Conclusions

This paper studies the role of deep trade agreements in UK‐EU trade relations. We first look at the impact that membership of the EU had on trade of the UK with its partners and then use this information to predict future trade relations based on different scenarios. We find that EU membership had a strong impact on UK‐EU trade and that it contributed particularly to the rise of UK services exports and its integration in global value chains. While there is substantial uncertainty on the content of a future agreement between the UK and the rest of the EU, our scenario analysis indicates that there is a clear trade‐off between the depth of such agreement and the intensity of future UK‐EU trade. In particular, a shallower agreement will have a stronger negative impact on the UK’s services trade and GVC integration, which have relied more on the deep arrangements of the EU.

A number of questions remain open. First, the analysis does not account for the possibility that the UK after Brexit may choose to sign new trade agreements with other trade partners and for the EU to continue its process of “ever closer union” by further deepening its integration. Both scenarios would impact future UK‐EU trade relations going forward in ways that are difficult to predict, as the effects will depend on the specific content of these agreements. But the trade‐off between PTA depth and trade intensity uncovered in this analysis will still likely delimit future policy choices. Policy makers can either

> 13 Baier et al. (2008) code the dummy EEA equal to 1 from 1973 onwards if one of the countries is in the EU and the other is in EFTA.

> 14 Similarly, a recent study by Kee and Nicita (2016) focusing on tariff changes finds that leaving the EU would lead to a 2 percent decrease in the UK’s exports in the short run.

> 15 Given the limited coverage of WIOD, we compute these statistics using data from COMTRADE.

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