interaction term of depth with UK for foreign value added exports identifies the impact of EU membership on the UK’s backward linkages in GVCs.

The domestic value added in gross exports increased on average by 14 percent for the country‐pairs that signed the deepest PTA. The effect for the UK is larger by an additional 21 percent. Splitting the UK dummy into importer and exporter suggests that the effect of deep PTA increased both the UK’s value added imports and exports. Deep PTAs are also found to have a positive effect on intermediates value added. Signing the deepest PTA increased domestic intermediates value added by 14 percent on average and by an additional 17 percent for the UK. The close similarity of these coefficients with those for domestic value added and the fact that intermediates represent around two‐thirds of UK’s value added in exports (Figure 6) suggest that deep agreements increased the relative importance of value added of intermediate goods with PTA members. In other words, the depth of the UK’s trade agreements with the EU and with the third‐countries the EU had signed PTAs largely contributed to the UK’s forward integration into GVCs.

The estimates for re‐exported value added and foreign value added shed more light on the structure of UK GVCs. Comparing the coefficient of the interaction term in column 3 with that in column 5 indicates that the additional increase in domestic intermediate value added for the UK is driven by the value of intermediates that are directly absorbed by the importer. In fact, the left hand side variable of columns 5 and 6 is a subset of on the variable in columns 3 and 4 since it includes only the value of intermediates that are re‐exported by the importer to third countries or returned home. Deep PTAs increased the foreign value added content of UK exports by 37 percent.<sup>9</sup> Column 8 shows that depth had an additional effect on both the foreign content of UK exports and imports. This result suggests that the UK used more foreign inputs to produce its exports after signing deeper PTAs and, at the same time, also countries that export to the UK increased foreign value added in their exports to the UK.

_Table 5:_ Value added trade and depth

||(1)|(2)|(3)|(4)|(5)|(6)|(7)|(8)|
|---|---|---|---|---|---|---|---|---|
|VARIABLES|D|VA|Intermed|iates VA|Re‐exp|orted VA|F|VA|
|Depth|0.130**|0.131**|0.127**|0.127**|0.176***|0.177***|0.0786|0.0786|
||(0.0548)|(0.0548)|(0.0626)|(0.0626)|(0.0672)|(0.0672)|(0.0545)|(0.0545)|
|Depth*UK|0.189***||0.160***||0.0436||0.315***||
||(0.0582)||(0.0594)||(0.0600)||(0.0814)||
|Depth*UK exporter||0.169**||0.152**||0.0337||0.309***|
|||(0.0749)||(0.0762)||(0.0821)||(0.109)|
|Depth*UK importer||0.213***||0.172**||0.0599||0.318***|
|||(0.0745)||(0.0849)||(0.104)||(0.0913)|
|Observations|26,520|26,520|26,520|26,520|26,520|26,520|26,520|26,520|

The estimator is PPML. All specifications include bilateral fixed effects and country‐time fixed effects. Robust standard errors, clustered by country‐pair, are in parentheses.

*** p<0.01, ** p<0.05, * p<0.1

9 The results in the last columns of the table suggest that on average deep PTAs did not increase foreign value added in gross exports. This may be due to the fact that in our data we do not know the origin of foreign value added in the bilateral relationship.

17