effect of PTAs is positive.

Interestingly, conditional on PTA membership, BITs tend to reduce the propensity of any ownership in this table.

Table 7: Ownership Propensity: Vertical integration in Global Value Chains

|1(Number of Firm-to-Firm Connections (_CF _<sup>_rs_</sup><br>_ij,t_<sup>))</sup>|PTA|Total depth|Core depth|WTO-X depth|
|---|---|---|---|---|
|Backward<sup>_rs_</sup><br>_j_ <sup>(</sup><sup>_ars_</sup><br>_j,t_|_−_0_._006<sup>_∗∗∗_</sup>|_−_0_._017<sup>_∗∗∗_</sup>|_−_0_._015<sup>_∗∗∗_</sup>|_−_0_._013<sup>_∗∗∗_</sup>|
||(0_._002)|(0_._002)|(0_._002)|(0_._002)|
|Forward<sup>_rs_</sup><br>_j_ <sup>(</sup><sup>_brs_</sup><br>_j,t_<sup>)</sup>|0_._039<sup>_∗∗∗_</sup>|0_._034<sup>_∗∗∗_</sup>|0_._035<sup>_∗∗∗_</sup>|0_._037<sup>_∗∗∗_</sup>|
||(0_._002)|(0_._002)|(0_._002)|(0_._002)|
|PTA-Measures_ij,t_|_−_0_._004<sup>_∗∗∗_</sup>|_−_0_._008<sup>_∗∗∗_</sup>|_−_0_._005<sup>_∗∗∗_</sup>|_−_0_._009<sup>_∗∗∗_</sup>|
||(0_._000)|(0_._000)|(0_._000)|(0_._000)|
|PTA-Measures_ij,t ×_ Backward<sup>_rs_</sup><br>_j_|0_._120<sup>_∗∗∗_</sup>|0_._287<sup>_∗∗∗_</sup>|0_._190<sup>_∗∗∗_</sup>|0_._343<sup>_∗∗∗_</sup>|
||(0_._003)|(0_._005)|(0_._004)|(0_._007)|
|PTA-Measures_ij,t ×_ Forward<sup>_rs_</sup><br>_j_|0_._085<sup>_∗∗∗_</sup>|0_._202<sup>_∗∗∗_</sup>|0_._131<sup>_∗∗∗_</sup>|0_._244<sup>_∗∗∗_</sup>|
||(0_._002)|(0_._004)|(0_._003)|(0_._006)|
|BIT_ij,t_|_−_0_._001<sup>_∗∗∗_</sup>|_−_0_._001<sup>_∗∗∗_</sup>|_−_0_._001<sup>_∗∗∗_</sup>|_−_0_._001<sup>_∗∗∗_</sup>|
||(0_._000)|(0_._000)|(0_._000)|(0_._000)|
|Country-pair FE|✓|✓|✓|✓|
|Industry-pair FE|✓|✓|✓|✓|
|Shareholder-country-industry-year FE|✓|✓|✓|✓|
|Subsidiary-country-industry-year FE|✓|✓|✓|✓|
|Domestic-year FE|✓|✓|✓|✓|
|Obs.|111,505,680|111,505,680|111,505,680|111,505,680|
|R<sup>2</sup>|0.193|0.194|0.194|0.194|

Standard errors are clustered at country-industry pairs level and reported in parentheses. * _p <_ 0 _._ 1, ** _p <_ 0 _._ 05, *** _p <_ 0 _._ 01 Table 7 suggests that, across all three measures of PTA depth, the propensity of any ownership link being present rises, and more strongly so in the backward rather than the forward-integration direction.

In Tables 8 and 9 we further scrutinize on the ownership margin results, using triple interaction terms between the PTA-depth measures, the GVC measures, and a measure of the specificity of inputs. The latter reflects the degree to which inputs are customized and cannot be easily substituted for when traded between firms, and it is defined by following Rauch (1999) in classifying the average products belonging to a supplying sector at stake.<sup>4</sup> In discussing the results, we focus on the coefficient on the interaction effect between PTA depth and input specificity and the triple-interaction terms.

We start presenting the results where the dependent variable is the log( _CFij,t_<sup>_rs_),</sup> i.e., the ownership count, in Table 8. This table suggests that a high specificity of – inputs which are supplied by the shareholder or the affiliate, depending on the direction of ownership – increases the integration frequency in the forward direction, while it reduces it in the backward direction.

> 4Rauch (1999) product classification is based on the SITC 5-digit level. The association between 5-digit SITC-product categories and 2-digit ISIC sectors as used to cluster firms follows the concordance tables provided by UNCTAD.

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