Global Flow of Funds as a Network: Cross-Border Investment in G20

Abstract

This study measures global financial stability by constructing a global flow of funds (GFF) matrix model based on its inherent market mechanisms. We discuss the basic concept of GFF, integrate the data sources, establish a GFF statistical matrix, which can be used to evaluate the financial risks and influences among its members, and estimate bilateral exposures between countries for three different financial instruments within and across the G20 economies. Then, we use financial network analysis to construct the financial relationships between countries. Moreover, we employ the network theory to discuss an analytical method for the GFF and use countries in the G20 as the research sample to discuss the network centrality, mutual relationships, and the financial risk of foreign direct investment, portfolio investment, and cross-border bank credit among the United States, Japan, and China. This study establishes a GFF statistical matrix and introduces the network theory into the GFF analysis, which opens a new field for measuring and applying GFF.

Appendices

Appendix A: The Method for Constructing LBS Matrix

The process of converting BLS account data to a matrix is as follows.

Selection and Download of Relevant Data

Relevant data can be selected from LBS and its data source can see the Composition of Locational Banking Statistics (LBS).¹² It consists of two parts, Global tables and Country tables. Select A6.2 By country (residence) of counterparty and location of reporting bank from Country tables which shows the location of reporting bank.

Select Database

Select and download the G-20 data, and the countries are listed in 24 columns¹³ in order A, B, and C, etc., such as Canada in A6.2 (see Table A.1).

Table A.1 Canadian example

Setting of “Columns” and “Rows”

In the all Countries state, the columns of the matrix are set to assets (or liabilities), and the data in the columns are taken from the “Of which: loans and deposits” of all sectors in the liabilities side (or Assets side).¹⁴ Some countries, such as Argentina, China, India, Indonesia, Russia, Saudi Arabia, Singapore, and Turkey are not listed in the list of countries on the left of Table 2.1. Therefore, the above countries need to be inserted into the columns of the matrix in order of A, B, and C.

Refer to Table 2.1 and set relevant countries in the order of A, B, and C that was set with the “rows”. When some countries are not listed in Table 2.1, insert countries such as the above eight countries according to the order of the rows. Select the data on the asset side (or liabilities side) of A6.2 for these countries, and put them into the rows. Pay particular attention to the corresponding relationship between the column sequence and the row sequence of the object countries.

Handling of Row and Column Sums and the Items of “Others” and “Totals”

The data of other terms are calculated by subtracting the data of the observed country from the sum of columns or rows. Since the data of the above eight countries are inserted in the row, the items of “others” which is by total of countries in each column minus the observed country may have a negative number. Therefore, we may go to use three aggregate numbers to get the items of the “totals” such as the following ways:

• (1) BLS’A5 Location of reporting bank (All reporting countries). Positions reported by banking offices located in the specified country regardless of the nationality of the controlling parent. By instrument “Of which: loans and deposits”. Table A.2 shows the summary information from A5 and A6.2 of BLS, and the summary data of the asset side and the liability side are exactly the same in A5 and A6.2.Once the total items are determined, the other items are determined by subtracting the countries of observation from the totals.

• (2) All countries (total) in A6.2 (See Table A.1), A6.2’s data is the same as that of A5. But if there are no relevant country data in All countries (total) in A6.2, such as China, India, etc., then use the following method.

• (3) If there are no relevant national data in A6.2 all countries (total), such as the above 8 countries, select the total data of these countries in A6.2_Select a country. It needs to make sure that the data ranges of “Other” and “Total” for each country are consistent.

Appendix B: The Correspondence Between the Summarized Data in A5 and A6.2 of LBS

See Table A.2 in Appendix.

Table A.2 The correspondence between the summarized data in A5 and A6.2 of LBS

Appendix C: Calculation Method of PDI and SDI

The influence and sensitivity coefficients are defined as follows. We set the position of the two-way financial investment from country i (as a row) to country j (as a column) and set the number of observation objects as n. Then, Table A.3 in the Appendix is set by forms with matrix Y formed by n rows and n columns, as shown in Table A.3 in the Appendix.

$$\text{Set}\,T_{i} = T_{j} = \max \left(\sum\limits_{i = 1}^{n} {y_{ij}} , \sum\limits_{j = 1}^{n} {y_{ij} } \right), \quad \varepsilon_{j} = T_{j} - \sum\limits_{i = 1}^{n} {y_{ij} },\,\text{and}\, \rho_{i} = T_{i} - \sum\limits_{j = 1}^{n} {y_{ij} },$$

T is the total of rows or columns for the matrix Y of external assets/liabilities; the total of the rows equals the total of the columns of each country. Designating $\varepsilon_{i}$ as the net liabilities of country i, and $\rho_{j}$ as the net assets of country j, if the net assets of country i are nonnegative, $\varepsilon_{i} = 0$ and $\rho_{j} > 0$; and if the net assets of country i are negative, $\varepsilon_{i} > 0$, and $\rho_{j} = 0$. To illustrate the effect of the influence and sensitivity coefficients, we first need to define the input coefficient $c_{ij}$. The input coefficient $c_{ij}$ is the ratio of funds raised from country i to the total external financing of country j, i.e.,

$$c_{ij}=\frac{y_{ij}}{T_j}$$

From the direction of the rows in Table A.3 in the Appendix, we arrive at the following equilibrium equation:

$$\sum\limits_{j = 1}^{n} {y_{ij} + \varepsilon_{i} = \sum\limits_{j = 1}^{n} {c_{ij} T_{j} + \varepsilon_{i} = T_{i} } }$$

(2.15)

where C is the n × n matrix composed of the elements of $c_{ij}$. Thus, the equilibrium equations can be rewritten as

$$CT + \varepsilon = T$$

(2.16)

Solving for T yields.

$$T = (I - C)^{ - 1}$$

(2.17)

where Eq. (2.17) is the Leontief inverse. Denoting the inverse matrix as $\boldsymbol{\Gamma} =(\mathbf{I}-\mathbf{C})^{-1}$, which has elements $\gamma_{i,j}$, we can denote country j’s PDI as $\mu_{j}^{y}$ and its SDI as $\sigma_{i}^{y}$; then, they can be defined as follows. And the PDI and SDI of Tables A.3, A.4, A.5 and A.6 in the Appendix can be calculated separately using the same method.

$$\mu_{j}^{y} = \frac{{\sum\limits_{i = 1}^{n} {\gamma_{i,j} } }}{{\frac{1}{n}\sum\limits_{j = 1}^{n} {\sum\limits_{i = 1}^{n} {\gamma_{i,j} } } }}$$

(2.18)

$$\sigma_{i}^{y} = \frac{{\sum\limits_{j = 1}^{n} {\gamma_{i,j} } }}{{\frac{1}{n}\sum\limits_{i = 1}^{n} {\sum\limits_{j = 1}^{n} {\gamma_{i,j} } } }}$$

(2.19)

The numerator in Eq. (2.18) is the sum of the eigenvector of the column (asset side for a country) of the Leontief inverse, and its denominator is the average of the total of rows in Leontief inverse. We can derive the country j’s IC using Eq. (2.18). The numerator in Eq. (2.19) is the sum of the eigenvector of the row (liability side for a country) of the Leontief inverse, and the denominator is its average column total. We can derive the country i’s SDI using Eq. (2.19).

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Table A.3 FDI matrix (as of end-2018, millions of USD)

Table A.4 PI matrix (as of end-2018, millions of USD)

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Table A.5 Cross-border banking credit matrix (as of end-2018, millions of USD)

Table A.6 Cross-border banking credit matrix (as of end-2022, millions of USD)