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Influence of Petroleum and Gas Trade on EU Economies from The EPJ manuscript No. (will be inserted by the editor) Influence of petroleum and gas trade on EU economies from the reduced Google matrix analysis of UN COMTRADE data C´elestinCoquid´e1, Leonardo Ermann2, Jos´eLages1 and D.L.Shepelyansky3 1 Institut UTINAM, OSU THETA, Universit´ede Bourgogne Franche-Comt´e, CNRS, Besan¸con,France 2 Departamento de F´ısicaTe´orica,GIyA, CNEA, Av. Libertador 8250, (C1429BNP) Buenos Aires, Argentina. 3 Laboratoire de Physique Th´eorique,IRSAMC, Universit´ede Toulouse, CNRS, UPS, 31062 Toulouse, France Dated: February 5, 2019 Abstract. Using the United Nations COMTRADE database [1] we apply the reduced Google matrix (RE- GOMAX) algorithm to analyze the multiproduct world trade in years 2004-2016. Our approach allows to determine the trade balance sensitivity of a group of countries to a specific product price increase from a specific exporting country taking into account all direct and indirect trade pathways via all world countries exchanging 61 UN COMTRADE identified trade products. On the basis of this approach we present the influence of trade in petroleum and gas products from Russia, USA, Saudi Arabia and Norway determin- ing the sensitivity of each EU country. We show that the REGOMAX approach provides a new and more detailed analysis of trade influence propagation comparing to the usual approach based on export and import flows. PACS. XX.XX.XX No PACS code given 1 Introduction and poor countries have equal consideration) and also the PageRank and CheiRank algorithms take into account the The statistical data of UN COMTRADE [1] and the World whole chain of transactions incorporating the importance Trade Organization (WTO) Statistical Review 2018 [2] of specific network nodes. This is drastically different from demonstrate the vital importance of the international trade the simple bilateral transactions of import and export. between world countries for their development and pro- gress. Also the whole world economy deeply depends on Usually in directed networks, like WWW or Wikipedia, the world trade [3]. At present the UN COMTRADE data- the PageRank vector of the Google matrix plays the domi- nant role since its components are on average proportional base contains data for Nc = 294 UN countries with up to 4 to the number of ingoing links. For the WTN the ingoing Np ≈ 10 trade products. Thus the whole matrix of trade monetary flows reaches a large size N = N N ∼ 106. In flows are related to import. However, the outgoing flows, p c related to export, are also important for trade. Thus we fact for each year the commercial exchange between coun- ∗ tries represents the directed network with transactions of also use the Google matrix G , constructed from the in- various commodities (products) expressed in their US dol- verted transaction flows, with its PageRank eigenvector, lar (USD) values of the given year. called CheiRank vector [10,11]. The components of this It is clear that the recent research developments in the vector are on average proportional to the number of out- field of complex networks (see e.g. [4]) should find use- going links in the original WTN. The construction rules of arXiv:1903.01820v1 [q-fin.ST] 5 Mar 2019 ∗ ful applications for analysis of this multiproduct World G and G for the case of multiproduct WTN are described Trade Network (WTN). In [5,6] it was proposed to use in detail in [6]. the methods of the Google matrix G, PageRank and Chei- In many cases it is important to know the effective in- Rank algorithms for analysis of the WTN. The PageRank teractions of trade transactions for a specific region (i.e., algorithm had been invented by Brin and Page [7] for the for selected nodes of the global network) on which one ranking of nodes of the World Wide Web (WWW) be- wants to focus the analysis. This requires to know not ing at the foundation grounds of the Google search engine only direct links between nodes but also the indirect (or [7,8]. The applications of these methods to a variety of hidden) links which connect the selected nodes via the real directed networks are described in [9]. In contrast to remaining part of the global network. Recently the re- the usual economy approach based on bilateral import and duced Google matrix (REGOMAX) algorithm has been export flows, the Google matrix analysis treats all world invented in [12] and tested with various directed networks countries on equal grounds (since all columns with outgo- of Wikipedia [13,14] and protein-protein interactions [15] ing country flows of G are normalized to unity so that rich showing its efficiency. This algorithm originates from the 2 C. Coquid´e et al.: Influence of petroleum and gas trade on EU economies 0 scattering theory of nuclear and mesoscopic physics and with country indexes c; c = 1;:::;Nc and product index the field of quantum chaos. In this work, using the COM- p = 1;:::;Np. For future notation we also define TRADE data, we apply the REGOMAX algorithm to an- p X p ∗p X p alyze the influence on European Union (EU) countries of Vc = Mc;c0 ;Vc = Mc0;c: (2) petroleum and gas trade from Russia (RU), USA (US), c0 c0 Saudi Arabia (SA) and Norway (NO). With this approach p ∗p which are the volume of imports (Vc ) and exports (Vc ) we are able to measure the sensitivity of EU countries to for a given country c and a given product p. The global the supply of petroleum and gas from one of these four import and export volumes are given by V = P V p and countries taking into account the global WTN, i.e., tak- c p c ∗ P ∗p ^ ing into account all direct and indirect transactions of 61 Vc = p Vc . Thus the ImportRank (P ) and Export- major products with the rest of the world. Rank (P^∗) vector probabilities are given by the normal- We note that there is a variety of papers with network ized import and export volumes methods applied to financial and trade networks (see e.g. P^ = V p=V ; P^∗ = V ∗p=V ; (3) [16,17,18,19,20,21]). However, the applications of the Pa- i c i c geRank algorithm to the WTN is rarely used (see e.g. one where i = p + (c − 1)Np 2 f1;:::;N = NcNpg is the of the first cases in [22]) but the outgoing flows with the index associated to the country c { product p couple, and CheiRank analysis were not considered apart from [5,6]. P p P p the total trade volume is V = p;c;c0 Mc;c0 = p;c Vc = The analysis of hubs and authorities is performed in [23] P ∗p p;c Vc . but in our opinion this approach has lower performance The list of 61 products and 227 countries are given in comparing to the Google matrix methods. Thus for the [6]. bitcoin transaction network the Google matrix methods demonstrate the existence of oligarchy type structure [24]. Till present the matrix methods are rather rarely used in 2.1 Google matrix construction for the WTN the field of transactions even if it was shown that the Ran- dom Matrix Theory finds useful applications for financial The Google matrices G for the direct trade flow and G∗ and credit risk analysis [25,26]. The methods of statistical for the inverted trade flow have the size N = NcNp = mechanics also demonstrated their efficiency for analysis 227 × 61 = 13847 and are constructed as it is described in of market economies [27]. However, the flows considered [6]. By the definition the sum of elements in each column in [25,26] are non-directional while the WTN typically de- is equal to unity. The Google matrices have the form scribes directed flows. Due to these reasons we hope that G = αS + (1 − α)v ; the REGOMAX algorithm will find further useful applica- ij ij i (4) G∗ = αS∗ + (1 − α)v∗; tion for the treatment of trade and financial transactions. ij ij i ∗ The paper is constructed as follows: in Section 2, we where α 2]0; 1] is the damping factor, and vi and vi construct the Google matrix for the World Trade Network are components of positive column vectors called person- P P ∗ and introduce the REGOMAX method. In Section 3, we alization vectors with i vi = i vi = 1 [8]. In this present the network structure of petroleum and gas trade work we fix α = 0:5, its variation in the range [0:5; 0:9] in EU exhibiting direct and indirect effects of petroleum does not significantly affect the results. The PageRank P and gas trade between EU economies and non EU major and CheiRank P ∗ vectors have each an eigenvalue λ = actors as Russia, Saudi Arabia and USA. We also inves- 1 since GP = P and G∗P ∗ = P ∗. According to the tigate the EU countries trade balance sensitivity to Rus- Perron-Frobenius theorem the components fPigi=1;:::;N ∗ sian, Saudi Arabian, and US petroleum and to Russian and fPi gi=1;:::;N are positive and give probabilities to and Norwegian gas over the time period 2004-2016. find a random surfer (seller) traveling on the network of N nodes. The PageRank K and CheiRank K∗ indexes are defined from the decreasing ordering of probabilities of Pa- geRank vector P and of CheiRank vector P ∗ as P (K) ≥ P (K + 1) and P ∗(K∗) ≥ P ∗(K∗ + 1) with K; K∗ = 2 Methods 1;:::;N. A similar definition of ranks from import and export trade volume can be also done via probabilities ^ ^∗ ^ ^∗ ^ ^∗ ^ Pp, Pp , Pc, Pc , Ppc, Ppc and corresponding indexes Kp, We collected the multiproduct (multicommodities) trade K^ ∗, K^ , K^ ∗, K^ , K^ ∗.
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