Uncovering Offshore Financial Centers: Conduits and Sinks in the Global Corporate Ownership Network

Multinational corporations use highly complex structures of parents and subsidiaries to organize their operations and ownership. Offshore Financial Centers (OFCs) facilitate these structures through low taxation and lenient regulation, but are increasingly under scrutiny, for instance for enabling tax avoidance. Therefore, the identification of OFC jurisdictions has become a politicized and contested issue. We introduce a novel data-driven approach for identifying OFCs based on the global corporate ownership network, in which over 98 million firms (nodes) are connected through 71 million ownership relations. This granular firm-level network data uniquely allows identifying both sink-OFCs and conduit-OFCs. Sink-OFCs attract and retain foreign capital while conduit-OFCs are attractive intermediate destinations in the routing of international investments and enable the transfer of capital without taxation. We identify 24 sink-OFCs. In addition, a small set of five countries – the Netherlands, the United Kingdom, Ireland, Singapore and Switzerland – canalize the majority of corporate offshore investment as conduit-OFCs. Each conduit jurisdiction is specialized in a geographical area and there is significant specialization based on industrial sectors. Against the idea of OFCs as exotic small islands that cannot be regulated, we show that many sink and conduit-OFCs are highly developed countries.

In the second step, all companies with more than 1000 employees were grouped together. We considered company A subsidiary of a company B (with consolidated accounts) if their values of revenue were within 25% of each other. We then iteratively substracted the operating revenue of the subsidiaries. This approach corrects for duplicated information among large companies 1 .

Normalization of ownership
Since the information is collected by different country-level agencies and merged by Orbis, the sum of the stakes of the shareholders do not always add up to 100%. We corrected by collecting all direct ownership stakes. When the sum of the direct ownership stakes was below 100% we added total ownership up to 100%, when it was above we normalized the ownership to sum up to 100%.

Mathematical formulation of country chains
The paper provides an explanation of the process from ownership links to country chains based on the different construction steps. Here we outline the theoretical definitions of the concepts obtained in each of these steps.
In the global corporate ownership network N = (F, E), firms are represented as a set F of size n = |F|. The set of ownership relations E ⊆ F × F contains a total of m = |E| pairs (i, j) indicating that there is a directed ownership relation between firms i, j ∈ F. Here, firm j owns i and thus value may flow from i to j. The link weight w(i, j) ∈ [0; 1] or in short w i j represents the ownership percentage of a relation (i, j) ∈ E. For example, the value of w i j is equal to 0 for non-existing links, equal to 1 for fully owned subsidiaries of j and 0.3 in case of 30% ownership. The value of a node i, denoted R(i) or in short R i , represents the (always positive) value of firm i. Here we use the revenue of the firm.
Multiple ownership relations may together form an ownership path: an ordered sequence of firms in which each subsequent pair of firms is connected through an ownership link. So, for a path p of length = |p| with firms p = (v 1 , v 2 , . . . , v ) it holds that (v i , v i+1 ) ∈ E for 1 ≤ i < . For brevity, in the paper such as a path is denoted v 1 |v 2 | . . . |v . A simple path has no repeated nodes, i.e., no cycles. The notion of multiplicative ownership w(p) or in short w p models the ownership weight relation w(v i , v ) along a particular ownership path p = (v 1 , v 2 , . . . , v ) of length = |p| as the multiplication of weights of the links between the subsequent nodes in the path, i.e., The value V (p) of a path p, in short V p , is defined as the value that flows from the first to the last node in the path, i.e., the product of the value of this first node and the multiplicative ownership of the path: An ownership chain of a firm v is an ownership path p which satisfies four criteria: it starts at node v, it is a simple path (has no repeated nodes), it has a multiplicative ownership value of at least threshold θ , i.e., w p ≥ θ and is maximal in length, i.e., cannot be extended by adding another node. Experiments with different values θ are discussed in the section 'Sensitivity analysis' of 2/11 the Supplementary Information. A node typically starts more than one ownership chain, and the set of all ownership chains starting at node v ∈ F is denoted C(v) or in short C v . Ultimately, C represents the set of all ownership chains in the network: Each chain p ∈ C in the set of ownership chains is in fact a path of length = |p|. From an ownership chain, we can generate all possible subpaths of length 2, 3, . . . , , which together we call the set of ownership chunks, denoted H. The set of ownership chunks of length x is denoted H x . Each chunk q ∈ H has an associated value V p (q) or in short V p q . This value depends on the value of the first node in the ownership chain p that chunk q originated from, as well as the path followed from that node to chunk q.
For each node v, a function φ (v) → I indicates the country c ∈ I in which firm v is based. The function can be applied to both paths and individual nodes. For each previously obtained chunk q = (v 1 , v 2 , . . . , v ), we create a country chain in two steps.
First, we map each node in the chunk to its respective country, obtaining: Note that in the main text of the paper, for brevity when we talk about country chains we use the ISO 2-letter country codes combined with the shorthand notation discussed above, e.g., NL|LU|KY . Second, we merge any two subsequent nodes of the This results in country chain g. The valuation function V φ (g) of a country chain g ∈ G sums the weights of the ownership chunks that map to this particular country chain. For brevity, in the main text of the paper we again use V g when it is clear from the context that we consider a country chain g. Note that as a result of the second step, the length of a resulting country chain may be shorter than the length of the originating ownership chunk. Furthermore, multiple ownership chunks may result in the same country chain. Applying this process to all ownership chunks in H results in the full set of country chains G. Analogously to before, we denote the set of country chains of length x as G x . These chains are the basis for the definitions of sink-OFC and conduit-OFC centrality proposed in the main text of the paper.

Comparison of our data with Foreign Direct Investment (FDI)
FDI reflects controlling ownership stakes in all the companies in one country by all the companies located in another country. In order to further assess the quality of our data, we compared the value of transnational ownership ties of firms from a particular country against the foreign direct investment (FDI) of that country, as provided by the IMF. Since some countries systematically under-report inward FDI, we kept for each country the maximum value between the value reported by the country, and the sum of outward FDI to that country as reported by the counterpart economies. The weighted ownership matches well with FDI data ( Figure S1).

Null model for Figure 3
Companies own stakes of other firms across the world. When these stakes are aggregated at the country level, we obtain a fully connected network where the weight of the link corresponds to the sum of value flowing between the pair of countries. In order to keep only significant links, we created a null model where the weight between two countries was set to the product of the GDP of both countries. We kept only those edges with a weight 10 times larger than in the null model -after normalizing both networks to have the same sum of edge weights.

Sector specialization
Starting from the global corporate ownership chains of size three (G 3 ) we mapped each company to its corresponding sector code (NACE Rev. 2) as provided by Orbis. We then grouped all sectors according to their dominant position in chains of size three: the first position (source), second (conduit) and third (sink), finding six categories: only source, only conduit, only sink, source+conduit, source+sink, conduit+sink and source+conduit+sink, by using the criteria in Table S2.
Finally, the weight of a sector within a category (e.g., sink) was calculated as the sum of the value of the chains where the sector participates in its category (sink) minus the sum of the value of the chains where the sector participates in other categories (conduit or source). The weight was further normalized by the sum of the value of companies that participate in the network in such category.

Sensitivity analysis
We investigated the effects of variating the thresholds used in Methods.
Multiplicative ownership of 0.001: We calculated the sink-OFCs and conduit-OFCs using thresholds for the multiplicative ownership equal to 0.1 and 0.01 ( Figure S2). For the threshold of 0.1 two small sink-OFCs (Nauru and Monaco) fell out of this category, and three small sink-OFC were found (Aruba, Guernsey and Saint Kitts and Nevis. Figure S2A). A new small conduit-OFC was also found (Austria. Figure S2B). For the threshold of 0.01 we found the same classification of territories into sink and conduit-OFCs that we found using our original threshold (0.001), which indicates that we achieved convergence S c > 10: We classified countries as sink-OFCs when the value remaining in the country was larger than ten times the GDP of the country (S c > 10). The sink-OFC classification varies with the S c threshold as reflected in Table S3. The countries identified as conduit-OFCs vary with the S c threshold as reflected in Table S4. Importantly, the five large conduit-OFCs are found independently of the S c threshold studied (Table S4). When the S c threshold is increased to 100, several sink-OFCs (Luxembourg, Cyprus, Hong Kong, Marshall Islands, Gibraltar and Bahamas) become conduit-OFCs (Table S4 and Fig. S3), which indicates a double role of those jurisdictions as sink and conduit-OFCs.  Belgium to be the only countries identified as conduit-OFCs ( Figure S3C). However, we hypothesized that the set of identified conduit-OFCs constitute a homogeneous cluster. In order to test this, we clustered the territories using the KMeans algorithm from the sklearn Python package. We found that all big five conduit-OFCs are always found in the same cluster when we asked the algorithm to find two to six clusters ( Figure S4). Moreover, Austria, Panama, Isle de Man, and Barbados are also often in the same cluster than the conduit-OFCs, which is expected since have been considered tax havens. We found that a group of countries composed by The Netherlands, Belgium, Ireland, Singapore, United Kingdom and Switzerland always constitute their own cluster with threshold C c(in/out) = 1. This cluster is different from the cluster of sink-OFCs (higher values of C c ) and the cluster(s) of other countries (lower values of C c ). Thus, we found that the division between conduit-OFCs and other countries occur naturally around C c(in/out ) = 1.

Euroclear and Belgium as a conduit-OFC, Panama and Guernsey
From the set of conduit-OFCs the peripheral position of Belgium stands out. Closer inspection of the underlying data reveals that Belgium derives its conduit-OFC status foremost from the ownership chains SHELL NL → Euroclear NL → Euroclear BE → Euroclear LU (Euroclear is a large custodian, which means that in this case there are no data available on the ultimate owners of this stake in Shell). Two other peripheral conduit-OFCs are Panama and Guernsey, since many GCOCs going to sink-OFCs go through the countries in comparison to their GDP. However, both jurisdictions are very small actors.

Comparison of sink-OFC and conduit-OFC centrality with other rankings of offshore financial centers and tax havens
We compared our ranking (based on the value entering the sink) of offshore financial centers to previous rankings and lists of countries (Table S5)