we measure for every shareholder and affiliate country and sector its degree of upstreamness as well as downstreamness. Due to the country-sector variation of the aforementioned measures, their main effects will be absorbed by the country-sectortime fixed effects. However, their interaction effects with PTA-Measures _ij,t_ can be identified.

As indicated above, we will present results regarding the firm-to-firm ownership at two types of extensive margins: the frequency of ownership links and the propensity of any ownership link. Table 4 presents the results for the ownership-link frequency. In the first column, we employ a binary indicator for PTA membership, while in the remaining columns we employ alternative measures of PTA depth. Clearly, the results suggest that PTAs have a positive and stronger effect on vertical ownership links (that is, if either the shareholder or the affiliate is situated up or down the stream of the value chain of each other). The effects appear to be bigger for upstream ownership links, which is possible, because ownership may be more or less concentrated.<sup>3</sup> The positive effects on vertical ownership tend to be bigger with deeper PTAs. However, there is one exception with regard to the latter: deep PTAs appear to have a weaker effect on the acquisition of upstream affiliates.

Table 4: Frequency of Ownership Links: Upstreamness and Downstreamness within GVCs

|log(Number of Firm-to-Firm Connections (_CF _<sup>_rs_</sup><br>_ij,t_<sup>))</sup>|PTA|Total depth|Core depth|WTO-X depth|
|---|---|---|---|---|
|PTA-Measures_ij,t_|_−_1_._338<sup>_∗∗∗_</sup>|_−_1_._917<sup>_∗∗∗_</sup>|_−_1_._442<sup>_∗∗∗_</sup>|_−_2_._122<sup>_∗∗∗_</sup>|
||(0_._047)|(0_._072)|(0_._052)|(0_._085)|
|PTA-Measures_ij,t ×_ upstreamness afliate<sup>_r_</sup><br>_i_|0_._025<sup>_∗∗∗_</sup>|0_._022|0_._020<sup>_∗_</sup>|0_._024|
||(0_._009)|(0_._014)|(0_._01)|(0_._017)|
|PTA-Measures_ij,t ×_ upstreamness parent<sup>_s_</sup><br>_j_|0_._045<sup>_∗∗∗_</sup>|0_._072<sup>_∗∗∗_</sup>|0_._051<sup>_∗∗∗_</sup>|0_._087<sup>_∗∗∗_</sup>|
||(0_._009)|(0_._013)|(0_._009)|(0_._015)|
|PTA-Measures_ij,t ×_ downstreamness afliate<sup>_r_</sup><br>_i_|0_._230<sup>_∗∗∗_</sup>|0_._375<sup>_∗∗∗_</sup>|0_._263<sup>_∗∗∗_</sup>|0_._435<sup>_∗∗∗_</sup>|
||(0_._013)|(0_._021)|(0_._015)|(0_._025)|
|PTA-Measures_ij,t ×_ downstreamness parent<sup>_s_</sup><br>_j_|0_._313<sup>_∗∗∗_</sup>|0_._429<sup>_∗∗∗_</sup>|0_._324<sup>_∗∗∗_</sup>|0_._479<sup>_∗∗∗_</sup>|
||(0_._013)|(0_._02)|(0_._014)|(0_._023)|
|BIT_ij,t_|0_._018<sup>_∗_</sup>|0_._018<sup>_∗_</sup>|0_._018|0_._018<sup>_∗_</sup>|
||(0_._011)|(0_._011)|(0_._011)|(0_._011)|
|Country-pair FE|✓|✓|✓|✓|
|Industry-pair FE|✓|✓|✓|✓|
|Shareholder-country-industry-year FE|✓|✓|✓|✓|
|Subsidiary-country-industry-year FE|✓|✓|✓|✓|
|Domestic-year FE|✓|✓|✓|✓|
|Obs.|985,731|985,731|985,731|985,731|
|R<sup>2</sup>|0.568|0.568|0.568|0.568|

Standard errors are clustered at country-industry pairs level and reported in parentheses. Downstreamness have been scaled by 10<sup>_−_3</sup> * _p <_ 0 _._ 1, ** _p <_ 0 _._ 05, *** _p <_ 0 _._ 01 In Table 5 we use the same structure as in Table 4 but now focus on the propensity

> 3Several shareholders may be involved in one affiliate. Conversely, one shareholder my hold ownership in several affiliates, etc.

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