It is important to note that with the inclusion of a PTA dummy in columns 6 and 7 of Table 3, we capture the effect of depth due to variations within country-pairs and within PTAs. The PTA dummy could be interpreted either as a trade agreement fixed effect or as an interaction variable that captures the effect of an agreement with zero provisions. Therefore, a positive and significant coefficient indicates that country-pairs with deep agreements trade more with respect to those that have shallower agreements. This suggests that results in the first four columns are not merely due to the presence of a PTA. Moreover, results are robust to the inclusion of bilateral tariffs as well, which suggests that the finding that deep trade agreements increase bilateral trade is not driven by tariff liberalization.

Our baseline specification could suffer from several econometric problems. On the one hand, the relatively small effects of ����h on trade we find in Table 3 compared to the literature may suggest a downward bias in our coefficients.<sup>26</sup> On the other hand, the potential endogeneity of deep agreements and trade could bias our estimates in the opposite direction. More specifically, a first econometric issue could be that trade flows tend to adjust slowly to trade cost changes and by using annual data without lags we may not capture the full effect of trade agreements.<sup>27</sup> The issue may be particularly relevant for deep agreements as they tend to have longer implementation phases, which could bias downwards the estimates of depth. Second, coefficients of the anticipation effects of PTAs may also be a confounding factor in our regression analysis. If trade flows increase in anticipation of the agreement even before its entry into force, we would fail to assign these effects to the agreements when using contemporaneous variables. Evidence of anticipatory effects could also raise concerns about the identification strategy and causality because of the difficulty in distinguishing between anticipation effects and pre-existing trends. Finally, a third concern is that the absence of intrabetween China and Hong Kong SAR, China. The coefficient on old PTAs in column 5 is 0.18 which suggests that older PTAs increased bilateral trade by around 20 percent on average during the 2002-2014 period. This impact is equivalent to signing an agreement that includes 30 legally enforceable provisions and reflects the depth of EU pre-accession agreements.

> 26 According to a meta-analysis of the effect of trade agreements on trade by Head and Mayer (2014), the median coefficient of a PTA dummy is 0.28. In the case of deep trade agreements such as the EU, the coefficient found in the literature is 0.98, which is higher than our estimate for the trade effect of the agreement with highest depth.

> 27 Trefler (2004) suggests that trade flows adjust slowly to changes in trade costs and criticizes the use of yearly data. Therefore, we use 3-year intervals to allow more time for trade to adjust to changes in depth of trade agreements. We find that results in Table A3, in Appendix A, are qualitatively and quantitatively similar to results obtained using consecutive years, with the exception for core depth which becomes statistically insignificant. In the rest of the paper, we favor yearly data over 3-year intervals because it is more common in the gravity literature.

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