and tariffs, and the consequent aggregation bias produces tariff elasticity that are smaller in magnitude (Redding and Weinstein, 2019).<sup>16</sup> Using the simple count of provisions to approximate the RTAs’ depth implicitly gives the same importance to any type of provision. One may want to assign relatively higher value of depth to those RTAs including rare provisions. So, as a robustness check, in Table 4 we show results by using weighted count to approximate the depth of RTAs (the weight is equal to one minus each provision’s frequency in the matrix of the RTAs mapped by the World Bank Deep Trade Agreements database). The resulting index weights relatively more RTAs containing rare provisions. Results, reported in Table 4, support the robustness of our baseline results. Interestingly, the estimations coefficients in Table 4 point to a stronger impact of deep RTAs on exports when approximated by a weighted sum. This suggests that the inclusion of rare provisions in RTAs is a good signal of the extent of trade costs reductions associated to deep RTAs between member countries.

The effect of RTA depth is robust to the inclusion of dummies for the presence of a RTA between country _i_ and _j_ at time _t_ . See results reported in Table A6. To take into account the presence of non-mapped active RTAs (i.e. those RTAs not included in the World Bank database), in Table A6 we take the list of RTAs from CEPII and assign a value of depth respectively equal to one (see columns 1-2), or equal to the closest (in time) country-pair’s RTA depth to nonmapped active RTAs (see columns 3-4). As expected, the presence of an empty (active) RTA – i.e. a RTA with zero depth – has null effect on the export of firms (see coefficient on RTA _adjusted_ in table A6 columns 1-3). The presence of a RTA has positive effects on export only if the agreement has some depth (i.e. positive number of provisions) - see columns (1),(2) and (3). While reassuring, results in Table A6 must be taken _cum grano salis_ because of the high collinearity between the RTA dummy and the measure of depth in regional trade agreements. As a last robustness check, we estimate equation (1) on the sub-sample of country-pairs that change RTA status during the period 2000-2020. Results, reported in Table A7 support the robustness of our baseline results.

The baseline and the robustness check regressions discussed so far suggest that deep RTAs have a statistically significant positive effect on the exports of firms in developing countries. However such a positive effect may hide strong heterogeneity across firms of different types, and dynamic effect after the change in depth of a RTA. We dig more into the heterogeneous effects

> 16The negative and significant coefficients on applied tariffs reassure us on the accuracy of our estimations. This accuracy is also supported by point estimates on standard gravity controls reported in appendix Tables A4 and A5. In these appendix tables we remove country-pair fixed effects and include standard gravity model controls (such as distance, colony, common language and border) to have a benchmark with previous literature on gravity controls’ coefficients (Head and Mayer, 2014). These variables have the expected sign and magnitude in line with previous studies.

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