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

Where did the gains from deep PTAs for the UK come from? Did deep PTAs increase trade with the original members of the EU or the new members? In order to address these questions, we add additional interaction terms to equation 1. The interaction of depth with UK exporter dummy is further interacted with a dummy equal to one if the partner is one of the founding EU members (Belgium, France, Germany, Italy, Luxemburg and the Netherlands). The coefficient of the triple interaction tests for differences between the UK’s exports to the original and newer EU members as depth increases. A positive coefficient would suggest that the UK exported disproportionally more to the founding EU members as the EU agreement deepened. Similarly, we also add the triple interaction of depth with the UK importer and the original EU importer dummies. The results in columns 8 and 9 suggest that the deepening of the EU was particularly important for exports of services directed to the original members that in turn exported relatively more goods to the UK.

# b. GVC trade

A body of economic literature suggests that the rise of deep agreements and the increasing importance of GVCs are tightly related. Intuitively, the unbundling of stages of production across borders creates new forms of cross‐border policy spillovers and time‐consistency problems. This, in turn, generates a demand for deeper forms of integration as certain national policies need to be disciplined in PTAs for GVCs to operate smoothly. Lawrence (1996), Baldwin (2010) and WTO (2011) are some of the first studies that look at how deep PTAs are related to GVCs from an informal theoretical perspective. A first formal model of how GVCs affect the design of trade agreements is presented in Antras and Staiger (2012). More recently, a number of studies have also provided empirical evidence of such relationship (Orefice and Rocha, 2014; Johnson and Noguera, 2014; Osnago, Rocha and Ruta, 2015).

Here we build on Osnago et al. (2016) and estimate the specific effect of deep PTAs on different measures of trade in value added for the UK. We estimate the gravity equation (1) for four left hand side variables of trade in value added with country‐pair, importer‐year and exporter‐year fixed effects. From WIOD, we use the decomposition of gross exports in value added components by Wang et al. (2016) to measure the domestic value added of exports (i.e. the total value produced in the exporting country), intermediates value added (i.e. the value of all intermediate goods created in the exporting country), re‐exported value added (i.e. the value produced in the exporting country that is processed by the importing country and re‐exported to third countries or to the source country) and foreign value added (i.e. the total value produced by foreign countries included in exports).

As before, the coefficient of depth is the average effect of signing the deepest PTA in our sample. The interaction of depth with dummies identifying the UK tells whether the UK increased GVC‐trade more or less than the average country by signing deep PTAs. The PPML estimates of the gravity equation are reported in Table 5. Odd columns are results for the UK independently of it being an importer or an exporter; even columns instead distinguish the additional effect of deep PTAs for the UK as exporter and importer. The comparison of the effects of depth on domestic value added with the effects of depth on intermediates value added sheds light on the importance of forward linkages in GVCs for the UK. The 16