and van Wincoop, 2003, 2004). Finally, ��� is a set of _undirected_ country‐pair fixed effects that captures all the time‐invariant determinants of trade costs and addresses the endogeneity in the formation of PTAs (Baier and Bergstrand, 2007). To account for the presence of zeroes in trade flows, we estimate equation (1) using the Poisson pseudo maximum‐likelihood (PPML) estimator proposed by Santos Silva and Tenreyro (2006).

We analyze the effect of deep agreements on different types of trade. First, using data from WIOD, we define �������� as the total exports of goods and services from _i_ to _j_ . Second, we estimate equation (1) for export of goods and services separately to allow for heterogeneous effects of depth. Finally, we use the decomposition of gross trade into value added components proposed by Wang et al. (2016) to measure the effect of deep PTAs on GVC‐related trade.

The �������� variable comes from the content of PTAs data set constructed by Hofmann et al. (2016) and is defined as the count of legally enforceable provisions included in each agreement. To identify the effect of depth on exports, we include country‐pair fixed effects and exploit the within country‐pair variation, while controlling for any country‐year shocks. The coefficient �� in equation (1) captures the effect of signing the deepest agreement in the sample.<sup>8</sup> While the coefficient of the interaction term �� tests if the UK’s exports or imports are more or less sensitive to deep agreements than other countries. A positive (negative) and significant coefficient implies that for the same level of depth the UK exported or imported relatively more (less) than the average country in the sample. Both coefficients capture the average effect of depth after the agreements enter into force and assume linear effects on trade, with a percentage point increase in depth having similar effects for deep and shallow agreements.

Two caveats need to be kept in mind. First, the model assumes that the marginal effect of an additional provision is the same regardless of what type of provision is included. It is well possible that provisions in deep trade agreements have a different impact depending on how relevant they are for trade. Provisions on standards, investment or competition are likely to have a larger impact on trade than provisions that do not pertain to trade or economic cooperation (e.g. statistics, cultural cooperation). Second, we expect the short‐run impact to be smaller than in the longer term, because it takes time for trade flows to respond to changes in trade costs (Johnson and Noguera, 2014; Baier and Bergstrand, 2007).

# a. Goods and services trade

We begin our investigation from a more conventional analysis of gross trade flows. The first 3 columns of Table 4 report the PPML estimates of our baseline regressions of depth on gross trade. The gravity equation is augmented with the interaction of depth with a dummy that identifies observations for the UK as importer or exporter. The results in column 1 suggest that country pairs that signed the deepest PTA increased their total bilateral trade by 42 percent. The UK was not affected more than the average since the coefficient of the interaction is not significantly different from zero. In other words, the depth of UK trade agreements with the other EU members and with other partners with which the EU had signed PTAs increased UK trade by 42 percent –not differently from other countries.

The data in WIOD allow to split total trade into trade in goods and trade in services. Columns 2 and 3 report the coefficients of depth and the interaction with the UK dummy for goods and services

> 8 Since trade data from WIOD are limited to the 1995‐2011 period, the deepest agreement in our sample is the EC

> (27) Enlargement with 41 provisions.

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