Determinants of Cross-border Banking System Exposures

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Determinants of Cross-border Banking System Exposures



1. Literature review

As the global financial system becomes more interconnected, policymakers need new tools to quantify the impact of cross-border transactions on the local economy. The Bank for International Settlements provides valuable data for this type of analysis. Yet, the dynamics of risk transfers in shape of guarantees, credit derivatives and collateral remain understudied. The aim of this study is to fill this gap and estimate the model to approximate the driving forces behind increases and decreases in credit exposure that international banks decide to maintain to the destination economies. In order to achieve this aim, multiple steps are required. First, data wrangling, including obtaining data sets from various sources, filtering and adjusting them to be comparable and informative. Second, descriptive analysis, which, in our case, uses network analysis techniques to better understand the nature of data used, their structure and dynamics. Third, modelling of the data, i.e. using statistical models to establish links between various factors (covariates) and the target variable, which is the volume of exposure to a particular country.

The main subject of our research is risk transfer behavior of internationally active banks. The question behind this study is “what factors could explain international banks' decisions to increase or decrease the amount of risk transfers from a particular economy?”. Thus, the object under consideration is the statistical relation that might exist between the macroeconomic indicators for the particular economy and the exposure of international banks towards them.

Our research uses a multitude of statistical techniques. First, there is network analysis of the risk transfers data summarizing the changes in the network through a variety of centrality and density measures. Second, we use panel data regression to build a statistical model tying together macroeconomic covariates and the difference in exposure.

The hypothesis is tested in this model is that macroeconomic variables can indeed explain some of the changes in exposure maintained by the internationally active banks to a given economy. In practice, if the hypothesis is not rejected, the stress-testing frameworks used by central banks to assess the resiliency of the financial system in case of an internal or external shock could be augmented with the data about international banks' exposure to the country.

The paper structure is the following. The first section discusses the previous studies on this topic. The second section provides a detailed description of methods used in this study. It is followed by a thorough description of data collection and handling. The final section of this paper reports the findings.

The network analysis performed in this paper builds heavily upon a number of studies applying network theory to financial networks. Minoui and Reyes, 2013 construct global banking networks using the Bank for International Settlements locational banking statistics and trace a number of indicators from 1978 to 2010 on a quarterly basis to gain insights into the changes that occurred in the cross-border banking in this time period. The paper reports some interesting findings. First, total flows reached their all-time maximum values going into the 2008-2009 crisis, while connectivity and clustering measures are not significantly higher than the previous peaks. Second, the GFC affected density of the network most with its levels reaching historical minimums. Third, the density of the networks, while being pro-cyclical, decreased its rate of growth before the crisis. Fourth, lending and borrowing concentration index calculated in the paper increased significantly during the crisis, suggesting that instead of trying to diversify their risks, financial institutions started cutting off ties with the counterparties they trusted least and increased their dependency on the lower number of partners. The authors also study the distributions of indicators during the global cycles of capital flows to find statistical similarities between the dynamics prior to the Asian crisis of 1997-1999 and the global financial crisis of 2008-2009. A major finding there is that both in 1980 and 2007 the majority of flows were relatively weak and co-existed with a few high-intensity ones. Finally, the authors also determine which countries are the most central in the networks. Degree centrality shows that the most connected lenders are France, Germany, Switzerland, the UK, Japan and the US. Least diversified borrowers are Denmark, Japan and Sweden, while the most diversified ones are Luxembourg, Switzerland, and the UK.

The research by Minoui and Reyes, 2013 was instrumental in shaping the way this paper approaches data wrangling (both Minoui and Reyes, 2013 and this study list the Bank for International Settlements as the primary source of data) and network analysis. One of the key issues with large data sets which contain information on interactions between individual objects is that common descriptive analysis is not particularly informative. Minoui and Reyes, 2013 show how this kind of financial data can be better summarized if viewed as a network.

Another paper that also influenced this study to the same end is a Deutsche Bundesbank working paper by Roukny et al, 2014 . The authors build quarterly networks of interbank exposures of German banks using the data from a credit register. The authors use many of the indicators used in Minoui and Reyes,2013 and some new ones to study the changes in the interbank financial network from 2002Q1 to 2012Q2. They are also able to distinguish between the credit and derivative market transactions, which allows them to compare the structural evolution of both markets. They report that neither the GFC, nor the euro debt crisis seemed to have any impact on the interbank transactions taking place in Germany. The research also shows that the credit market has been slowly decreasing over time, while the derivatives market size is stable. Nonetheless, the size of the credit market is much bigger than the derivatives market. Both markets are relatively sparse, but the average number of counterparties for every financial agent seems to be increasing over time. The connectivity distributions for both markets are heterogeneous and have fat tails.

One of the key insights from the paper by Roukny et al, 2014 that was helpful in our research is the idea of building distinct networks for the derivatives data. Their research definitively shows that derivatives dynamics can be very different from the more traditional financial instruments, a finding that is proven to be true at the international level by our study.

The paper by Minoui and Reyes, 2013 and our research differ from the one by Roukny et al, 2014 in one very important aspect. Roukny et al, 2014 has access to position-level data of each financial agent in the network. They use anonymized data from the credit register. Minoui and Reyes, 2013 and us rely on international banking statistics. It leads to a much lower quality of the data underlying our research. The issues surrounding global banking statistics are best summarized in an IMF working paper by Cerutti et al, 2012 . The authors highlight three main challenges: lack of institutional mechanisms, which ensure coordination of national approaches, greater complexity in the international context, as well as scarcity of data. The authors call for better reporting of off-balance sheet assets and liabilities as well as collection of individual bank-level data. They argue that bilateral linkages are required for crisis management purposes. This concern about data quality translated into the G-20 Data Gaps Initiative and a proposal to establish a highly confidential data base holding bank-level data. Cerutti et al, 2012 mention that the latter was to be voted on as part of Early Warning Exercise, a joint research initiative between the Financial Stability Board and the IMF in 2011. The 2019 IMF Financial Surveillance Evaluation Report mentions Early Warning Exercise as confidential presentations of research findings that are “thought provoking and generate lively discussions by taking on outside-the-box issues” . It is not clear, whether the proposed data base was ever established, but it appears to not be publicly available.

Using with the data currently available, the choice of modelling framework for this research proved challenging. Network representation of the data calls for a family of models that can be estimated on the networks. There are multiple options available.

Exponential random graph model (ERGM) is one option. Kolaczyk and Csardi, 2014 provide a detailed description of ERGM models. In essence, they model the presence or absence of a connection between two participants of the network. One can include a variety of factors, upon which the binary variable will depend. The statistical software then starts simulating the connections in the network given the values of factors that are included. Obtained network is then compared to the actual connections present in the network showing the goodness of fit that can be obtained given the covariates used. There are also multiple examples of application of ERGM models to the financial networks. Engel et al, 2019a use exponential random graph model to reconstruct the connections present in the financial network using publicly available summary statistics. Since there is no publicly available data on individual connections, the authors use a combination of summary statistics that are available, not only as a way to put restrictions on the simulated data, but also to assess the goodness of fit for the model.

There are two key disadvantages to the application of ERGM model that make it impossible to use in our research. First, it models the presence or absence of a certain connection. In our case the majority of connections stay in place throughout the entire time period with varying weights. There is some progress in development of an ERGM model that could be used on a weighted network (e.g. Garlaschelli and Loffredo, 2009 ), yet this approach is not well-researched. The majority of textbooks on ERGM models stress the importance of this type of models applied to non-weighted graphs with a lot of variation in network structure (Ripley et al, 2015 , Newman, 2010 ). Second, the researchers highlight the fact that the model used does not take cross-border connections into account.

According to the recent working paper published by Engel et al, 2019b, the work to include an international aspect of financial connections is currently under way. This paper describes a block-structured model that first simulates the link-probability matrices using bivariate Bernoulli trials and then uses an ERGM models to assign weights. The authors claim that their approach simulates the network structure strongly resembling the real-life network and even use it to assess systemic risk within the European banking network using contagion models.

The use of block structured model in this paper was rejected, because this approach has not been thoroughly researched and the working paper describing it has not been peer reviewed as of the time of writing. Furthermore, the methodology developed in Engel et al, 2019b is geared towards the network of individual financial institutions, while our focus lies in the international dimension.

Another modelling approach is to include some of the network measures calculated on the network data as covariates in a different model. The paper by Peltonen et al, 2019 is an example of this approach. The authors attempt to link interconnectedness of the banking sector to the probability of a banking crisis occurring. Their research is based on the data from 2000Q1 to 2012Q1 for 14 European countries. The authors create networks of connections between institutional sectors at the country level: between non-financial companies, banks, insurance and pension funds, financial intermediaries, government and households. Various indicators are then calculated for these networks, reduced in dimension using principal component analysis and used as early-warning indicators for the crisis prediction model. The authors find that inclusion of network parameters in the model can improve its quality. The centrality of banking sector seems to have an impact on the probability of a crisis. Furthermore, credit risk appears to play the most important role (as proxied via financial instruments that carry the most credit risk). The paper also confirms the significant role of cross-border exposures; however, the results suggest that the role of the banking sector in the domestic economy is more important.

Gravity model, which is famous among international economists for its ability to explain trade flows, was also considered. The modification of this model for network data is described by Kolaczyk and Csardi, 2014 . The idea behind the gravity model is to estimate the strength of interaction between origin and destination objects as a function of their “size” and “distance” between them. According to Baier et al., 2014 , these models “dominated the international trade literature as the main econometric approach”. Gravity model was estimated using different measures of distance and trade flows. Its version for network analysis, however, is once again focused on the presence or absence of a connection between the two objects making it unsuitable for our analysis.

Cerutti, 2014 uses panel regression and reduced-form models to explore cross-border exposures during the crisis. The author combines BIS data with bank-level data to find statistical links between changes in exposure to a destination country and a number of bank-level and global covariates. The model from the creditor's perspective considers the link between exposure growth and a number of covariates, including GDP growth in the borrower countries, the presence of banking crisis in the creditor country, the ratio of deposits to loans, the share of direct cross-border lending in the total claims, as well as a number of global variables: interest rate spread between 3 months LIBOR and the treasuries with the same maturity, volatility index (VIX) and fixed effect dummy. The presence of a systemic banking crisis in the creditor country was shown to be the most significant one, while the interest rate spread and VIX index were significant in times of a crisis as well.

Cerutti, 2014 also reports the summary of a model from the borrower country's perspective. In this case the change of exposure to the borrower country was a dependent variable, while the covariates included GDP growth, the presence of banking crisis in the creditor country, share of direct borrowing in the country's total foreign borrowing, deposit to loans ratio in the borrower country, as well as the same global covariates that were mentioned above. A larger number of factors were proven to be significant in this case. Systemic banking crisis in the creditor country was proven to be significant, as well as the share of direct cross-border borrowing in the total, and an interest rate spread.

Our research adopts the research design of Cerutti, 2014 focusing on the model for the borrower country and focusing on the role of macroeconomic covariates in the decisions to increase or decrease exposure to the borrower country. The next section provides a detailed description of methods used in this study.



2. Methods

2.1 Network analysis

Graph G(V,E) is usually defined as a mathematical structure containing a set V of vertices and a set of E edges. A number of vertices and edges are sometimes referred to as order and size of a graph. The graphs that are created for the analysis described in this paper are more sophisticated than a simple set of vertices and edges. We use weighted, directed graphs. Weighted graphs have a numerical value associated with every edge. In a classical social network application these values represent the strength of connections between people, e.g. a number of messages exchanged in a certain time period. In our case they will be the dollar amounts of risk transfers taking place between banking systems of different countries. Directed graphs take into account not only the presence of connection between two vertices, but also the direction of these connections. This type of graph is very useful when the edges are not reciprocal. An example from the classical network theory would be if person A sends person B 200 messages per month, while B never replies, or if person A sends 50 messages and receives only 10 replies.

It is still quite common to explore network graphs by plotting them. However, given the size and the quantity of the networks used in this research, it is hard to draw any analytical conclusions from the plots of graphs. Therefore, we use a set of indicators to compare networks, nodes and vertices with each other.

2.1.1 Vertex degree and centrality measures

Four indicators fall into this category. The first is vertex strength, which represents the sum of weights w_v of edges incident to v. We also compute the average strength of all immediate neighbours of a given vertex. This indicator is denoted as knn_v^s. For each indicator distribution function can be estimated. We can also analyze their relationship for each graph.

When it comes to centrality measures, we take into account that the graphs we deal with are disconnected. Therefore, we calculate weighted betweenness centrality, defined as

where у(s,t|v) is the number of weighted shortest paths between vertices s and t that pass through vertex v, and у(s,t) is the strength of v. We also normalize this indicator by multiplying it by 2/(n^2-3n+2), where n is the number of vertices to make it comparable across different graphs.

We also estimate a different measure of centrality that tries to capture the idea that a vertex connected to “central” vertices should by itself be also considered “central.” In mathematical terms, it requires that the eigenvalue problem Ac_(E_i )=б^(-1) c_(E_i ) needs to be solved for c_(E_i ). A denotes the adjacency matrix of the graph in question and б is the largest eigenvalue of this matrix; hence, c_(E_i ) is the corresponding eigenvector. We then calculate the following centrality measure:

The value of c_(E_i ) lies between 0 and 1 due to eigenvector orthonormality, thus no further normalization is needed.

2.1.2 Edge betweenness

Edge betweenness is calculated the same way as the vertex betweenness centrality. However, computation of edge betweenness can be computationally expensive, so it requires an optimized algorithm. A relatively recent paper provides such an algorithm that is implemented in the igraph package for R programming language, which is used for the majority of computations in this paper. Brandes describes the implementation of Dijkstra's shortest path algorithm in the computation of edge betweennwss. This algorithm begins with setting the distance from start vertex to start vertex to 0, then setting the distance for all other vertices to the infinity. It then repeats the following steps until the list of unvisited vertices is empty:

Visit the unvisited vertex with the smallest known distance from the start vertex;

For the current vertex:

2.1 Examine its unvisited neighbours;

2.2 Calculate the distance from each neighbour to the start vertex;

If the calculated distance is less than the known distance, update the shortest distance;

Update the previous vertex for each of the updated distances;

Add the current vertex to the list of visited vertices.

With further improvements by Brandes this greedy algorithm helps calculate both edge and vertex betweenness swiftly.

2.1.3 Graph density

In order to estimate the density of the graph in question, we use two measures. The first one, density is a frequency of realized edges relative to potential edges. For a directed graph G it is calculated as

den(G)=(|E_G |)/(|V_G |(|V_G |-1)), ( 3)

where E and V are the number of edges and vertices, respectively.

We also calculate the transitivity measure, which is an example of clustering coefficients that can be calculated for a graph.

cl_T (G)=(3фД(G))/(ф_3 (G)), ( 4)

where фД(G) is the number of triangles in graph G and ф_3 (G) is the number of subgraphs of three vertices connected with two edges present in a graph.

This set of indicators gives us a lot of information about any graph and thus can be used to compare a set of different graphs to each other.

2.2 Panel regression

After completion of network analysis of the risk transfers data, we turn our attention to modelling of cross-border exporures. The cross-border exposures have two different dimentions: there are separate objects (weighted edges of our networks) that change in time. This dimensionality allows for the use of panel data respresentation and modelling approaches associated with it. In its simplest form a one-way error component regression model has the following specification:

y_it=б+X_it^' в+м_i+н_it,where ( 5)

i denotes individual entities (in our case these entities will be directed exposures), t denotes time period, б is a scalar, в is a KЧ1 vector of coefficients. X_it is the observation of ith object at time t and corresponding K covariates. One-way error component assumes that the model errors can be broken down into an unobservable individual specific effect м_i and the remainder н_it.

One way to estimate the parameters of a panel regression is by applying ordinary least squares estimate to the raw data. This approach is called a “pooling” regression. However, in the context of panel data OLS is not the best linear unbiased estimator (BLUE) and other methods should be applied.

Fixed-effects or “within” estimator is the most suitable for a model, which focuses on individual effects present in the data. To obtain the fixed-effects estimator, raw data is pre-multiplied by the matrix W:

W=I_NT-I_N?J_T/T=I_NT-B,where ( 6)

I is an identity matrix with the dimensions given by a subscript, J_T is a square matrix of ones with the dimensions TЧT, T denotes the number of observations and N the number of objects.

The fixed-effects model specification can be written as

Wy=бj+Xв+?=WXв+Wн,where ( 7)

y is a dependent variable, j is a column-vector of ones, X is a matrix of covariates, в is a column-vector of coefficients в in the model and ? is the sum of vector н of length NT (idiosyncratic part) and vector з (individual effect) of length N, for which each element is repeated T times.

This model can then be estimated using the OLS estimator. It is important to mention that fixed-effects estimator removes covariates that do not exhibit intra-individual variation. However, our covariates do not include any binary variables meaning that “filtering out” of covariates should not decrease the quality of the model.

We also estimate the two-ways effect modification of this model. The one-way effect model described above can only incorporate the individual effect present in the model. Two-way effect models also include a time-invariant constant м, which is responsible for any time effect present in the data. The time effect is incorporated in the model using additional dummy variables for time. As a result, the number of degrees of freedom in the model significantly increases making such model fit less reliable.

R package plm is used to perform panel regression analysis for this paper.

3. Data

We use risk transfer data from the Consolidated banking statistics (CBS) data base. Risk transfers in this case are defined as “credit risk mitigants that shift a bank's credit exposure from the immediate counterparty to a guarantor, to another counterparty or collateral that guarantees the claim.” The guarantor is then defined as the party that has to make sure the contract is honored in case of default by intermediate counterparty. There are four types of risk transfers included:

Parent guarantees to branches;

Explicit guarantees by parents and third parties;

Credit derivatives;

Collateral.

An important point to clarify is that only credit derivatives that provide similar credit protection, as explicit guarantees are included in the data base. Any derivatives present in the trading book are ignored.

The value of risk transfer is assumed to be equal to its face value, unless it exceeds the value of the underlying claim. In the latter case the value of the underlying claim is used. For credit derivatives notional value is used.

This paper uses the claims on the guarantor basis that are calculated in the following way:

Claims_(i,j)^G=Claims_(i,j)^immediateCP+(RT_(i,j)^IN-RT_(i,j)^OUT) ( 8)

We limit our sample to the 15 core countries that historically shared larger amounts of information with the Bank for International Settlements. These countries are Austria, Belgium, Canada, Denmark, France, Germany, Ireland, Italy, Japan, Luxembourg, the Netherlands, Sweden, Switzerland, the United Kingdom and the United States. Minoui and Reyes, 2013 found that in a related Locational Banking Statistics (LBS) data base about 96% of all data were reported by the aforementioned countries.

Further narrowing our sample, we only keep the claims reported on the guarantor basis. We only use the data for domestic banks, excluding their domestic positions,

The data are reported every quarter. Our sample has a first set of observations in the fourth quarter of 2004. At the time of this writing the latest available data is for the third quarter of 2019.

It is important to mention that the share of entries labelled as “Not available” (NA's) has been decreasing continuously decreasing from 39% of observations in 2005Q1 to 3% in 2019Q3 (see figure 1). It is also clear that the data from 2004Q1 has to be eliminated from the sample.



Figure 1: Share of NAs in the sample

All the entries in CBS data base are reported in billions of US dollars. FX adjustments are made by the data base maintainers at BIS. Inflation adjustments, on the other hand, have to be performed by the researchers. We use consumer price index for urban areas published by Federal Reserve Bank of St. Louis and accessed using Quantmod R package.

The construction of networks is implemented using igraph R package. Instead of wrangling data to construct weighted adjusted matrices of risk transfers, the data is sliced into dataframes containing “from”, “to” and “weights” columns, where weights differ from quarter to quarter. This data frame is then used to create igraph network objects.

To perform panel data analysis in section 5 a number of different indicators were accessed from Organisation for Economic Cooperation and Development (OECD) Data warehouse and Bank for International Settlements. The following indicators were used:

GDP growth . This indicator represents percentage change in real GDP from quarter to quarter and is adjusted for inflation and seasonality.

Producer price index (PPI) . Used as a measure of inflation, this indicator reflects an increase or decrease in price levels of products sold in the domestic market. Available at quarterly frequency.

General government debt (Debt to GDP ratio) . The indicator reflects the gross debt of the government measured as a percentage of GDP. Debt to GDP ratio is published annually.

Household net worth is calculated as the total value of households' financial and non-financial assets less their liabilities. The indicator is available as a percentage of household net disposable income on an annual basis.

Banking sector leverage is calculated as a share of currency, deposits, debt securities and loans in total equity of the banking sector. It is published as a percentage of net value added on an annual basis.

Long-term interest rate is a yield of 10-year government bonds implied by their prices in the marketplace averaged over a quarter.

Short-term interest rate is a 3-months money market rate, where available. If such information is unavailable it is replaced with short-term government paper yields or intrabank credit rate. The money market rates are averaged over a quarter.

Return of share price index. A return on a basket of currencies is usually calculated by the national stock exchange. In some cases central banks calculate it instead.

Effective exchange rate index is calculated by BIS. In this case monthly nominal exchange rate based on a narrow index was used.

Some indicators were modified or calculated for use in the panel regression. Long- and short-term interest rates were used to calculate interest rate spread. Share price index was used to obtain a measure of quarterly stock market volatility. Effective exchange rate was modified to obtain quarterly averages.



3. Descriptive analysis

3.1 Total risk transfers

We start by examining the patterns of countries' banking systems accumulating risk from the other countries using the in-strength indicator. The mean dollar amount of risk taken on by countries peaks right before the Global Financial Crisis. This peak can also be seen in cross-border flows data examined in the research by Minoui and Reyes (2013). After the crisis the amount of risk transfers levelled off in the range between 800 and 850 trillion US dollars. Since 2017 the mean amount of risk transfers started growing again (see figure 2), which points to an increase in risk-appetite of banks in the core countries.

Figure 2: Average in-strength of networks.

Zooming in at the in-strength for individual countries gives a more detailed breakdown of demand for risk in the global financial system. There are four countries that consistently take on over 950 trillion dollars of risk transfers. These countries are Germany, France, Great Britain and the United States (Panel A of appendix A.4). Out of these four countries the United States is the only one that started significantly increasing its exposure to the foreign economies in 2017.

The amount of risk transfers that each of the other 14 countries receives differs widely from quarter to quarter (Panel B of appendix A.4). However, the financial system of Japan appears to increase its exposure to the other core countries most actively. Other countries' financial institutions also seem to be more active in taking on risk from the system (with the exception of Denmark, Austria and Sweden).

Out-strength indicator shows financial institutions in which countries are the most likely to seek guarantees from other countries. Some countries do not report the assets that are guaranteed by financial institutions in other countries (Denmark and Luxembourg), while others started reporting it later than 2005Q1 (Canada since 2007Q3, Ireland since 2006Q2, Sweden since 2005Q2). Despite these deficiencies, some conclusions can be drawn from this indicator. First, the financial institutions in the countries that intake the largest amounts of risk from the financial system are also the most likely to insure their assets with an exception of Japan. The largest share of risk-transfers originates in Japan, followed by France, Great Britain and the United States. Germany accounts for the lowest share among the top countries by out-strength (Panel A of appendix A.5).

Among the other countries Canada, China, Ireland and Italy are the top sources of risk transfers taking place. These countries, as well as Japan, France, Great Britain and the United States, increased the amount of risk transfers since 2017.

We can also explore how much a given country relies on the largest players of the global financial system using the average neighbor strength. Austria, Belgium, Ireland, Sweden and Denmark appear to be the countries that rely on the `strongest' banking systems in the global financial system. Knn indicator for Denmark and Sweden also points to a significant increase in the average strength of their immediate neighbors in 2017 (Panel A of appendix A.6).

The other ten countries either have immediate neighbors with strength that differs widely, pushing the knn indicator down, or mostly rely on the countries with lower strength (Panel B of appendix A.6). There is also very little variance in the average strength of immediate neighbors of the majority of countries.

Having looked at the volumes of risk transfers taking place between countries, as well as the choice of partners approximated via the knn indicator, we turn our attention to the issue of vertex and edge centrality. These two indicators suggest, which countries and which connections are the most essential in the existing network.

Weighted betweenness centrality points to Austria as the most essential vertex in the network, followed by Sweden and Ireland. Panel A of appendix A.7 shows weighted betweenness scores for countries with positive score in at least one quarter. There is a lot of volatility in the betweenness score for all countries.

Eigenvector centrality measure paints a different picture (see panel B of appendix A.7). This indicator suggests that Luxembourg is the most essential country in the network, followed by Ireland and Denmark. In this case the proximity of a given `central' country to the other `central' country increases its centrality score. When it comes to contagion effects in a financial network, it is plausible to assume that eigenvector centrality is a better measure of a country's importance in the network as a whole.

To find out which edges have historically been the most significant in the network the following algorithm was implemented. First, edge betweenness for each edge in each network was estimated. Then the top 5 edges by their betweenness score were selected from each network and put together into a single data set. Then using the capabilities of the dplyr package , the number of occurrences of each edge, as well as summary statistics for their betweenness scores were calculated. The result is presented in table 1.

The edge betweenness data are consistent with the vertex betweenness scores. In 9/10 most important edges Austria is either the source or a destination of a risk transfer. The connections between Ireland, Sweden and Austria are not only some of the most frequent in the data set of the most central edges, but also some of the `strongest' in a sense that they have the largest volumes of risk transfers going through them.

Table 1: The most significant edges in the networks

Finally, we turn our attention to the measures of network density. Up to the GFC the density of the risk transfers network kept rising. Since then density indicator first slightly decreased after the crisis, but pretty much stayed at the same level. Transitivity measure shows even less volatility than the density indicator and has also stayed at about the same levels as at the dawn of the crisis in 2008 (figure 3).

Figure 3: Network density and transitivity.



3.2 Derivatives risk transfers

Risk transfers that take place in the form of derivatives display entirely different patterns. The average amount of risk that countries were ready to accept peaked in the beginning of 2015 at around 210 trillion dollars and has been decreasing since. (see figure 4) There are some noticeable increases in the beginning of 2016 and in the middle of 2019. Yet, at the lowest point the average amount of risk transfers fell to about 90 trillion dollars.

Figure 4: Average in-strength of derivatives networks.

The data for individual countries clearly shows the separation into three groups (see figure 5). The two countries that receive the majority of risk transfers are the USA and Great Britain. At the peak in 2015Q2 the two countries were on the receiving end of 60% of all risk transfers in form of derivatives. The second most active group of countries consists of Germany and France. They accounted for about 20% of transactions. The Netherlands, Italy and Japan collectively reported the risk transfers corresponding to roughly 11% of the total.

In 2019Q3 the concentration of risk transfers decreased with the share of the USA and Great Britain at 45%, Germany and France at 16% and the Netherlands, Italy and Japan at under 10%.



Figure 5: Strength (in) of individual countries estimated on derivatives data.

The amount of risk being shifted abroad has also been falling since 2013 in almost all countries (see figure 6). Germany is the country, where the most risk transfers originated. Switzerland used to be the second largest source of risk transfers using derivatives, but it was surpassed by Great Britain in 2015Q2 and held 3rd place since. The top three countries are also the ones that experienced the largest drop in volumes of risk transfers. The United States is also close to this group of countries, even though the volumes of risk transfers originating in the country are about 1/3 of Germany's.

France, Canada and Japan form the second distinct group of countries, which have substantial volumes of risk transfers with very low volatility.



Figure 6: Strength (out) of individual countries.

The average neighbor strength for the derivatives network shows some curious patterns (see figure 7). The countries that are connected to the most active banking systems of the derivatives network are Austria and Ireland. Switzerland's knn indicator showed exceptional growth towards the end of 2018, which could result from either new connections to the “strong” vertices or break of connections to the “weak” ones. Denmark and Belgium are the only other countries, for which average neighbor strength is higher than 100 billion USD.

Figure 7: Average neighbor strength of individual countries (estimated on derivatives network).



The most central vertices in the derivatives network can be determined based on the figure 8. In 2014-2016Q2 there were multiple countries that could be considered to be the most central in the network: Ireland, Switzerland and Austria. However, Austria's centrality measure decreased substantially leaving Ireland and Switzerland as the most central countries. In 2018Q2 its weighted betweenness centrality started a steep climb and surpassed both Ireland and Austria by the end of 2019.

Figure 8: Weighted betweenness centrality of individual countries (estimated based on derivatives network.

In terms of edge centrality, the most central edges are determined using the same algorithm that was used on the total flows data. Some of the most central connections in the network include the links between large financial centers, such as Ireland, Austria and Switzerland. Links that lead to or originate in Japan appear to be quite central to the network as a whole as well.



Table 2: The most significant edges in the derivatives networks.

Multiple observations should be made regarding the total exposure and derivatives data analyzed above. First, the data suggest that after the global financial crisis there has been some deleveraging in the financial system. This observation is consistent with the findings made by Minoui and Reyes (2013). However, in the past 2 years we can see many indicators showing sharp rise. Despite the fact that their levels do not reach the peaks seen before the financial crisis, this trend should be worrisome to the financial authorities.

Second, the data shows that the density of financial connections has not changed since the great recession. This fact might suggest that the same patterns of contagion could repeat themselves in the future. Therefore, rigorous stress-testing of financial institutions and vast capital buffers are required to make sure that the contagion can be stopped without capsizing the system as a whole.

Third, network analysis shows the financial centers that have outsized influence at the system as a whole. They fall into two categories: large, well-connected economies that can be considered systemically important because of the sheer size of risk transfers, and relatively small economies, that are nonetheless highly connected and could spread the shock to the multitude of their counterparties. The first category contains of the USA, Japan, Great Britain, France and Germany. Austria, Luxembourg, Ireland and Sweden fall under the second category.

Fourth, network analysis also points to certain connection as central in the financial network as a whole. Additional cooperation between the countries on both sides of these connections would ensure their stability and prevent any sharp changes or breakdowns in them.

The analysis performed above does not only summarize some of the descriptive characteristics of the data set this research is based on, but also suggest a path forward for the analysis performed using panel regression. It is clear that the volume of risk transfers can be used to estimate the path of financial contagion in case of large shock incurred by the economy of one of the countries in the network. However, in order to estimate which shocks are likely to affect the network of risk transfer, additional analysis is required. The next section is dedicated to estimation of statistical links between the macroeconomic indicators characterizing the economic situation in the creditor and borrower countries.



5. Panel regression

The main hypothesis of this paper is that the dynamics of cross-border exposures is driven by the changing parameters of the borrowers' economy. We differentiate two types of effects: scale and perceived risk. Unlike Cerutti, we do not aggregate the exposures and do not consider “demand” and “supply” models separately. Instead, panel data is created, in which every “object” is an edge from the network graph, i.e. an exposure of country A to country B. Since the networks for multiple time period are available, we are able to observe the change in this exposure from one quarter to another.

Due to the fact that a change in exposure can reflect change at either side of an edge, scale effects have to be accounted for not only for the borrower country, but also for the creditor country. Perceived riskiness of the economy affects both sides as well. If the domestic economy situation is assessed as risky, financial institutions might opt for lending abroad. Another consideration is the foreign exchange conversion rate change. It can also affect the dollar amount of exposure and is also controlled for in the model.

Each effect can be further classified on the basis of the sector of the economy. The scale effects are captured by the following variables:

Real sector

GDP growth, GDP, captures the increase in the size of the economy of the borrower and creditor countries. The size of the economy directly affects demand for risk that the country's banking system shows through higher risk-appetite and larger overall value of assets for investment. It is also linked to the supply of risk. A growing economy requires a steady supply of credit to keep growing, shifting risk to the cross-border lender. An expected sign for GDP.from, GDP growth in the creditor country, is positive. The same is true for the GDP growth in the borrower country, GDP.

Financial sector

Financial leverage or equity multiplier, EQMULT shows the stability of financial institutions and serves as a proxy variable for the risk appetite of the economy. It can reflect the ability of the creditor country to provide funds to the borrower (EQMULT.from), as well as the ability of the borrower country (EQMULT) to absorb more risk in the domestic economy. An expected sign for both is negative, since higher financial leverage is associated with lower availability of credit.

Return on stock index, STOCKS, reflects the size of the corporate sector of the economy. Positive sign is expected for both STOCKS.from and STOCKS reflecting the stock index return in creditor and borrower countries, respectively.

Network-based measures

Node degree, DEGREEOUT.from and DEGREEIN, are network-based measures that capture the overall number of borrowers for the creditor country and the number of creditors for the borrower, respectively. These measures are control variables, which are meant to capture the choices the country faces, while solving a diversification problem in investment and acquiring funding, respectively.

The risk effects are captured by the following variables:

Real economy

Inflation, PPI in the borrower country. High levels of inflation usually suggest structural deficiencies in the economy, while low inflation is usually associated with increased risk appetite in the financial markets. The expected sign is negative.

Debt to GDP ratio, GOVDEBT. High levels of debt might suggest instability of the economy. Increased perceived risk is likely to cause a decrease in exposure to the borrower.

Net household wealth, HHWEALTH and non-financial corporations' debt to surplus ratio, DEBTNONFIN, are measures of the resilience of households and non-financial corporations to economic downturns. Higher household wealth and lower debt to surplus ratios in the corporate world signal lower risks, suggesting positive and negative signs respectively.

Financial sector

Interest rate spread, INTDIFF, is a proxy for a yield structure in the economy. Short- and long-term interest rates reflect the markets' assessment of the economic prospects. Narrowing or negative interest rate spread is a sign of high perceived riskiness of the economy. Negative interest rate spread is also commonly used as a forward-looking indicator of a recession. We expect to see a positive sign for INTDIFF, interest rate in the borrower country, and negative sign for INTDIFF.from, the interest rate spread in the creditor country.

Volatility(variance) of a stocks index, VAR, shows the stability of the capital markets and is another market measure of confidence in the economy. Higher volatility is associated with higher risk, thus expected sign for VAR is negative, while a positive sign in front of VAR.from is expected.

5.1 Pair regressions

Table 3. Expected signs and pair regression estimated signs for total exposures data.



Table 3 summarizes the expected signs and the sign obtained in a pair regression model using fixed-effects estimator. Complete model summary is available in appendix A.1. Two covariates showed the signs contrary to the expectations. Interest rate spread in the borrower country appears to be negatively correlated with the change in exposure. The sign before household net wealth is also negative. This finding suggests that our hypothesis regarding these covariates could be rejected. However, it is important to include them in the model, to see, whether expected sign can be observed there.

Table 4. Expected signs and pair regression estimated signs for derivatives data.

In the derivatives data signs estimated in the pair regressions defy our expectations in almost every case (see table 4 for signs and appendix A.2 for model summaries). The sign is confirmed for GDP and stocks index growth in the creditor country, as well as for stocks index, interest rate spread and inflation in the borrower country. The overall quality of pair regressions estimated on the derivatives data is also lower.

5.2 Complete models

We estimate 4 models in total, all of them with the same specification given below. First two are estimated using the total exposure data and one- and two-way fixed-effects estimators, while the second two are fitted to the derivatives data.

diff(Volume)=lag(GDP.from)+EQMULT.from+lag(STOCKS.from)+lag(INTDIFF.from)+lag(VAR.from)+DEGREEOUT.from+lag(GDP)+lag(PPI)+DEBTNONFIN+GOVDEBT+HHWEALTH+EQMULT+lag(INTDIFF)+lag(STOCKS)+lag(VAR)+diff(FX)+DEGREEIN

We then use F-test to estimate the presence of time effects. Null hypothesis for this test states that there are no significant time effects in the data. For the total exposure data p-value is equal to 2.2e^(-16), meaning that the null hypothesis is strongly rejected. For the derivatives data p-value is 1.3e^(-9), rejecting the hypothesis as well.

F test shows that the most accurate models are reported in columns 2 and 4 of table 6. The results suggest that for both data sets inflation and interest rate spread in the borrower country, as well as foreign exchange conversion rate are significant covariates. Inflation has contradicting effect: in the total exposures data higher inflation in the borrower country is associated with lower volume of exposures, while in derivatives data this relationship is reversed. Narrowing interest rate spread in the borrower country is linked to higher volume of exposure to the borrower economy.

The total exposure data also shows the financial leverage in the creditor country plays a role in the changing exposure. Higher financial leverage is associated with lower volume of exposure. The same relationship is estimated between the borrower country banking sector financial leverage and debt to GDP ratio. Stock index growth, on the other hand, is shown to be inversely correlated with the volume of exposure.

5.3 Findings

Estimated model give us multiple insights into the driving forces behind financial exposures (model summaries available in appendix A.3). First, the factors that influence total cross-border exposures and derivatives exposures between the countries are not the same. Furthermore, even if the covariates are significant in models estimated with both data sets, they can still have the opposite signs. This finding further proves that derivatives data does not just follow the pattern set by the total exposures on a smaller scale, but has its own unique nature. Future research should incorporate this knowledge by developing different model specifications for the derivatives data.

Second, despite the fact that business press has been pronouncing inflation dead for two decades now (see, for example the Economist, 1999 and Forbes, 2020 ), it is still one of the most important factors impacting investment decisions even in the developed countries.

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