The network structure of the Malawi interbank market: implications for liquidity distribution and contagion around the banking system

Interbank markets have been classified as a unique type of money market since loans in these markets are both secured and unsecured. Because of this aspect, borrowing and lending in interbank markets depend on the trust that the market players have for each other. Interbank markets are, therefore, one of the key gauges of market tensions and expectations in many economies. This calls for intensive research on interbank network as such research contributes to the development of a stress testing framework for assessing systemic risk in the banking system. This is because the close relationships that exit in interbank markets are associated with complex financial institutional networks. The study focused on the interbank market network for Malawi, a relatively small but active market, with a view to analyze liquidity distribution and contagion around the banking system. The study reveals that the network for Malawi’s interbank market is fairly dense with a significantly high clustering and a small average path length, implying that liquidity is able to flow in a fairly efficient manner around the banking system. Following the relatively high connectivity of the interbank network, entry or exit of a bank, for most of the times, has little impact on the ability of other banks to lend and borrow from each other. The high connectivity of the network also implies that banks are able to monitor each other’s behaviour. This results into a situation where some banks withhold lending to other banks, forcing the liquidity deficient banks to get liquidity at a higher cost than the one prevailing on the market. The relatively high clustering and a small average path length further implies that the interbank participating banks are more vulnerable to contagion than in random networks. Since there is strong connectivity among the banks, the network may not be resilient to an operational shock affecting one or more of the banks. In this case, the impact of an operational shock may be felt not just on the connectivity of the network but rather on the availability of liquidity with which to make payments. 1 E-Mail: korismie@yahoo.co.uk. I acknowledge, without implication, funding by the UK Economic and Social Research Council (ESRC) and the UK Department for International Development (DFID) under a research grant, ESRC Reference: ES/N013344/2, on ‘Delivering inclusive financial development and growth’.


Background to the Study
The effects of the US subprime mortgage crisis of 2007 and the collapse of Lehman Brothers in 2008 on global financial markets have been well documented in literature, intensifying the crucial role played by interbank markets across economies. Specifically, activities and behaviours of different interbank markets have continued to attract a lot of attention among both academic researchers and financial markets experts following the unusual behaviour of interbank markets that was observed after the global financial crisis; a breakdown of liquidity in the normally robust financial markets and failure of central bank intervention to enhance liquidity were noticeable after the financial crisis (Brunetti et al, 2015). It was further observed that linkages among financial institutions were the main source of systemic risk (Sahabat et al, 2017). Such observations have raised awareness on the part of stakeholders, especially central banks, to begin analyzing the resilience of the financial system based on the connectedness patterns within the interbank network. Although such observations continue to raise interesting research questions in financial economics in general, much attention has been directed towards the financial linkages that exist among interbank participating banks and how such linkages are considered to have played an important role in transmitting serious losses during the crisis (Xu, 2016). Interbank markets have, consequently, quickly become one of the key gauges of market tensions and expectations in many economies. Due to this, research on interbank network analysis remains very important as it contributes to the development of a stress testing framework for assessing systemic risk in the banking system.
The interbank market has been classified as a unique type of money market due to one of its stand-alone features: loans in interbank markets are both secured and unsecured. Since some loans in the interbank markets are not collateralized, borrowing and lending in these markets, especially in the unsecured segment of the market, depend on the trust that the market players have for each other. Because of this aspect, interbank markets are associated with close relationships between participants. Because of such close relationships, interbank markets are associated with complex financial institutional networks. The patterns of such connectivity can be altered either due to endogenous factors such as internal management mismatches that impact on other institutions or exogenous factors due to pressures in the economy that are transmitted through interconnected financial linkages (Sahabat et al, 2017).
Due to such factors, interbank markets require formulation of specific policies, especially policies concerning the way in which liquidity is funded. As different markets continue to 2 evolve over time, these highlighted aspects of the interbank market are becoming more important from both a policy and research point of view.
As pointed out by Brink and Georg (2011), the financial crisis of 2007/08 highlighted, among other things, the necessity of macro prudential oversight on financial systems in addition to micro prudential supervision. To ensure stability of the financial system, it is important not only to monitor the strength of the individual financial institutions, but also to analyze the network structure that they form due to their various interlinkages. Because trading in interbank markets depends on trust, a well-functioning interbank market is able to put in place strong disciplining mechanisms among its participants. By providing/denying and pricing liquidity according to the riskiness of counterparts, interbank markets offer an additional hand to central banks' macro-prudential regulation which continues to be challenged by sophistications in the banking industry, information asymmetry, weak legal frameworks and government intervention, among other things. Thus, studying the network structure of an active interbank market can expose some of the hidden risks in the banking system and assist the central bank to take the necessary actions and be able, therefore, to avoid some potential crises within the system.
Among different forms of interconnections between banks, interconnections through interbank loans are among the most important ones due to two main reasons. Firstly, interbank interconnections are convenient for the enhancement of liquidity allocation. Interbank markets provide a remedy to liquidity-constrained banks which would otherwise pay hefty premia to get funds elsewhere. This is specifically true for smaller banks who, in most cases, have to pay hefty premia to get funds from larger peers or regulators in times of liquidity shortages.
Secondly, interbank interconnections are associated with risk sharing in the banking system.
While risk sharing may be good in some cases, it may also mean that some risks are allocated to market players who may not be able to bear their portion of risk. That situation may lead the to amplification of shocks in times of crisis. As interbank trading continues to be cross-border, risk sharing also goes beyond banks operating in a particular market.
The study documents the network structure of the interbank market in Malawi by analyzing the topological characteristics of the network structure of the market and discuss such structure and its implications in terms of liquidity and contagion in the banking system. That is implemented by describing and mapping the interbank network in Malawi and its evolution using a simple network model and discussing how central bank's policy can affect the network 3 structure of the market. Such analysis is important for discussion on financial stability since it has the potential of opening up new opportunities for systemic risk assessments of the Malawi's relatively small and active interbank market.
Studying Malawi's interbank market as network topology contributes specifically to an understanding of the stability and robustness of a network of liquidity flows in response to an operational disturbance. This is because different network properties may give rise to different degrees of resilience to such disturbances. In particular, the properties of an interbank network may have important implications for the flow of liquidity through the system in stressed circumstances, for example, when a bank is operationally unable to make payments. Holding all things constant, the higher the connectivity of the system, the faster liquidity is expected to flow to the stricken member(s). Generally, banks that exhibit a low in degree are likely to be more vulnerable to disturbances than other banks because the removal of one link will severely limit the flow of incoming funds. On the other hand, banks with high out degrees have, holding all things constant, the potential to affect more counterparties if their payment processing is disrupted. In a near-complete network, however, link weights, rather than node, degree and connectivity, play a larger role.

The Network Theory and the Interbank Market
The network theory is generally associated with the study of graphs which are represented either as symmetric relation or asymmetric relation among discrete objectives. Such a representation has proved to be useful in different disciplines in the study of different relationships. In intelligence agencies, the theory is applied in identifying criminal and terrorist networks from traces of communication that they collect and then identifying the key players in these networks. In social network websites like Facebook, the network theory is used in identifying and recommending friends based on friends of friends. In epidemiology, the network theory is applied to track the spread of diseases like HIV/AIDS. In financial economics, especially following the financial crisis highlighted earlier, the network theory has specifically become useful in explaining the dynamics of the interbank market. From a financial market perspective, a network is defined as a set of nodes representing financial institutions in a particular market and set of links defining the relationships between those 4 nodes. Links may exist between the nodes and they may be directed or undirected. 1 While central banks have applied the network theory for mapping different interlinkages between financial institutions, the theory has become specifically useful in studying the structure of the banking system that is composed of banks that are connected by their interbank bilateral exposures.
Studying the interbank market as a network has proved to be helpful to both researchers and policy makers in aiding the understanding of how banks are related and the importance of each of the banks in the functioning of the interbank market. Using the network approach, stakeholders are able to find the degree of heterogeneity in the interbank market and use that to determine the disintegration of the network in the event of pressure. For instance, the network approach is able to show the interconnection structure differences between banks before and after a specific shock. This is done by measuring the distance of the connectedness within different time periods.
Although the network approach may not necessarily be used as a tool to identify potential future crises, by using the approach, the interbank connectivity pattern can be used in estimating the occurrence of pressures on the financial system in the future (early warning signals). Moreover, understanding of interconnectedness in the interbank market assists in identification of sources of potential crises in different markets. The network approach can be used to gauge financial contagion in the banking system since the structure of the network affects the degree and speed at which financial crises spread throughout the market. In addition, the network approach is favoured because of its ability to expose patterns in interbank relationships that may not be clearly observed numerically. For instance, the application of network theory has assisted in the understanding of the interconnectedness within the banking system which proved to be a key driver of systemic risk in the 2008 global financial crisis (Brunetti et al, 2015). Thus, using the network approach, stakeholders are able see some aspects that have become crucial for global financial stability. Such aspects include levels and changes in financial interconnectedness in such markets.

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The core-periphery model complements the network approach in the determination of the structure of the connectedness by classifying the group of banks acting as core/center or periphery. The theory was introduced by Borgatti and Everett (2000) but it was pioneered by Craig and von Peter (2014) in its application to interbank markets. According to the model, interbank market is split into two subsets; the core market and the periphery market. Although the unsecured segment of the interbank market is over-the-counter, the model presents the interbank market as a market that exhibits a core-periphery network structure. The 'core', consists of banks that are central to the system and are able to lend and borrow from all the other banks in the core and other banks outside the core while the other subset, the 'periphery' do not transact directly among themselves but depend on lending and borrowing from banks which are able to access the core market. In this set up, the core banks act as intermediaries.
The core-periphery setup implies that while some participants are able to trade with the market as a whole, there exists some parallel markets outside the general market, where liquidity can be supplied for the banks that, due to some reasons, are unable to tap into the liquidity that is available in the main interbank market. For instance, because the cost of trading in the core market may be relatively higher for small banks, such banks may resort to building relationships with the big banks and borrow indirectly through them. Because of that, the small banks may end up paying higher rates for liquidity than the rates prevailing on the core market.
Similarly, smaller banks may be receiving lower rates for their liquidity when they are on the liquidity surplus side. This means that some banks can borrow from the core market to lend to other banks in the relationship lending market and extracts rents from providing these services.
In markets where the core-periphery structure is in existence, many banks maintain long-term relationships and they trade with just a few banks. For instance, Chiu and Monnet (2016) highlighted that some banks possess a comparative advantage in overcoming information asymmetries, searching for counterparties or bargaining. Such differences, among other reasons, may lead to the birth of the core-periphery market structure and result into differences in borrowing and lending conditions for different banks. Moreover, such structure intensifies risk sharing as well as movement and spread of liquidity shocks in the market.

Related Literature
Earlier research on interbank market focused on importance of this type of market in hosting the first step of monetary policy transmission mechanism. Such literature includes the seminal work of Poole (1968). In more recent research, studies on interbank markets have gone deeper 6 to include interconnectedness in these markets and how such connections enhance risk sharing and amplification of shocks in times of crisis. The network approach has specifically been useful in that line of research. That has mainly followed the lessons from the 2007/2008 financial crisis since it has been documented that micro prudential supervision and regulation is inadequate on its own to identify potential route of contagion and assess the stability of financial system. It is no longer debatable, therefore, that the systemic importance of one bank depends not only on the properties of that bank, but also on the properties of the whole market.
This has brought in interest in interbank connections and these connections are looked at from different perspectives.
Brassil and Nodari (2018) applied the network approach to study interconnection in the Australian interbank market using aggregated loan-level data and constructed a network for each quarter for Australian banks for the period between 2005Q2 and 2016Q1. The results showed that out of the 42 participating banks in the Australian interbank market, on average, there existed 420 directed loan relationships. The results further showed that while the networks on the Australian interbank market have higher densities, the relationships were found to be sparse. Some researchers have concentrated on interbank connections and how such connections can affect the risk of the whole banking system. In Xu (2016) the network approach was applied to establish contagion in the US interbank market using message passing algorithm. The study used transactions between US banks for the period between 2006Q1 and 2010Q3. The results of the study showed that while dense networks and sparse networks perform differently in network properties and in contagions triggered by single-bank failures, the two perform the same when contagions are triggered by multiple-bank failures. In Brink and Georg (2011), the interbank market network for South African banking system was analyzed using the data from March 2005 to June 2010 by constructing an index that renders a particular bank's systemic significance less predictable and less constant. The study used a unique dataset of South African Multiple Options Settlements (SAMOS) system. The results showed that South African interbank system had been largely stable and resilient during the period covered in the study. That had been the case even in times of great distress on the international financial markets. In addition, the study concluded that the number of banks participating in the South African interbank market was almost constant and there was a high level of interconnectedness during the analyzed period. Because of the observed strong interconnectedness, the study established a high level of liquidity allocation and risk sharing in the South African interbank market. 7 Some studies have been interested in specific banks' positions in the market network and how such positions affect both liquidity access and provision. A study by Gabriel and Georg (2016) is one example of such studies. In Gabriel and Georg (2016) a dataset of all the European banks was used to study the liquidity reallocation among the banks. The study specifically, dwelt on how a bank's characteristics affect its ability to borrow and lend on the overnight interbank market. From the Ordinary Least Squares (OLS) estimations that were done in the study, the paper established that a bank's position in the interbank network, as measured by various measures of centrality in networks, has a significant impact on both liquidity provision and access. Precisely, banks with higher network centrality were found to provide more liquidity on the interbank market. Such banks are also willing to lend funds at cheaper prices. Similarly, banks with higher network centrality were found to have access to more liquidity and borrow funds on the interbank market at cheaper prices. This implies that a bank's position in the interbank network plays a role in the determination of both interbank traded volumes and rates.
The network approach has also been applied to compare the behaviour of banks during normal times and during times of financial crisis. Brunetti et al (2015) studied the behavior of the European interbank market before, during and after the financial crisis. The study established that while the two types of networks defined in the study, the correlation network 2 and the physical network 3 behaved the same way before the crisis, the correlation network showed an increase in interconnectedness during the crisis while the physical network highlighted a significant decrease in interconnectedness. It was further observed that physical networks were able to forecast liquidity problems while financial problems were better forecasted by correlation networks. The network approach has also been importantly used to understand how lending conditions in the interbank market are affected by the networking of banks. Blasques, Brauning and Lelyveld (2018), estimated the structural micro-founded dynamic network model on the network statistics of the Dutch unsecured interbank market using monthly data from February 2008 to April 2011. The study was specifically interested in the characteristics of interbank markets as can be explained by two main aspects of this type of market, namely, liquidity uncertainty and peer monitoring in interaction with counterparts. The study found that Dutch banks form long-term lending relationships that are associated with improved credit conditions and that the lending networks exhibits sparse core-periphery structure. The findings 2 Based on publicly traded bank returns 3 Based on interbank lending transactions 8 of the study support the crucial role played by lending/borrowing relationship in the determination of interbank traded volumes as well as the interbank rate. Those findings agree with Schumacher (2016), who applied the network approach in trying to understand how the lending conditions in the Swiss franc money market are affected by the networking of banks.
The findings in the study established that there is a difference in the lending conditions for the secured and the unsecured segments of the market. While clustering 4 is more pronounced in the unsecured segment of the market which serves as a social collateral, trust plays a minor role in the secured part of the market where physical collateral is involved. Generally, banks with stronger relationships in the interbank market (higher clustering coefficients) are offered better trading conditions in terms of both trading volume and rates.
The network approach has also been applied to establish the presence of core and periphery market structure in particular interbank markets and how such a structure affect lending and borrowing in interbank markets. Craig and von Peter (2014), studied the bilateral interbank exposures among 2000 German banks from 1999 to 2012. The study provided evidence that most banks in Germany do not lend to each other directly but through money center banks.
Such money center banks act as intermediaries for the interbank market. The study further confirmed a strong evidence of tiering in the German banking system and that such extent of tiering was not common in standard random networks.
The existence of core-periphery interbank market structure is associated with incompleteness, segmentation and inefficiency in interbank market and such characteristics are associated with the ineffectiveness of monetary policy. In Oduor et al. (2014), it is observed that incompleteness and segmentation in Kenyan interbank impede the effectiveness of monetary policy, especially in the short run and during periods of liquidity volatility. A similar observation was also noted in Colliard et al (2016) who documented the impact of segmentation between the core and the periphery markets in European interbank markets. In addition, it is highlighted that apart from raising the bargaining power of periphery banks that are connected to the core market, and raising the price dispersion in the interbank market, segmentation was found to raise inefficient resort to the central bank standing facilities. This implies that optimal monetary policy implementation may be hampered by increased levels of segmentation liked to the core-periphery structure. The existence of core-periphery structure may result from different bank characteristics that includes capital levels. This is observed in Green et al. (2016) 9 who established that banks with increased capital buffers enjoy lower costs of borrowing in the interbank market since highly-capitalized banks are perceived as less risky. Such banks can form the core of the market.
As can be noted from the reviewed literature, limited attention has been devoted to study the network structure of interbank markets of low-income countries like Malawi. Although most low-income economies like Malawi were not directly affected by the last financial crisis, contagion via the interbank market remains one of the key concerns of the central banks because possible chances of encountering such crises remain in such countries. It can also be recalled that low-income countries experienced a number of banking crises during the 1980s and 1990s which took longer to resolve than in other groups of countries. Moreover, chances of macroeconomic and banking system fragility still exist and crises can still arise following strides in financial deepening and sophistication of financial systems in these countries. In addition, due to relaxation in bank ownership restrictions observed in modern low-income banking sectors 5 , it has become more relevant than before, to study the interbank network structure of these markets in order to observe and analyze possible sources of crises, levels and the speed of such crises and discuss possible relevant policy actions that can be taken to make such markets resilient to possible identified shocks. Getting a better picture of the network structure is therefore a crucial step in developing systematic risk assessment of the interbank market.

A Brief Description of the Market
Network properties are market-specific across different countries because of the different characteristics of specific markets. The interbank market in Malawi is relatively small, but has been active for its entire life period. Trading in Malawi's interbank market started in 2001 and since then, trading, in terms of volumes, has generally been increasing (chart 1).

Source: Author's computation based on available Reserve Bank of Malawi (RBM) data
Generally, banks lend or borrow from the interbank market in relation to their predicted excess reserves that is calculated as any amount of liquidity that is above or below the Liquidity Reserve Requirement (LRR) prescribed by the RBM from time to time. Consequently, the amount of funds traded on the interbank market, to a certain extent, reflects the liquidity condition in the banking system and the monetary policy stance of the central bank, the RBM. This is shown in chart 2. as well as the pricing of interbank loans, therefore, reflect a bank's perceived level of risk. Such a disciplining role points towards the potential for the market to support to macro-prudential regulation by the central bank.

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In general terms, a network consists of nodes and links. In this study, each node stands for a bank and each link connecting two nodes bears interbank trading relationship between the two corresponding banks. Although a network can be either directed or undirected, the study was interested in the directed network for the analysis of the interbank market in Malawi. Node characteristics and the links associated with individual nodes have different implications depending on whether a bank is a borrower or a lender. The study models Malawi's interbank loan flows as a directed network. This is because directed network brings out good discussions for policy making of central banks.
In the study, banks are represented as nodes in the network and traded volumes between banks form the links between these nodes. We define these links as being 'directed' in such a way that if bank X only lends (but does not borrow) funds to bank Y then there would be a directed link from X to Y but not one from Y to X. In a situation where both banks X and Y extended loans to each other, we have two directed links, one in each direction. The weight attached to a link is proportional to the value or volume of interbank loans passing through that link. The design of the interbank market in Malawi has been in such a way that all banks and discount houses can technically borrow and lend to all other banks and discount houses. Malawi's interbank market can therefore, in principle, be modelled as a complete network. The empirical work analyzed the extent to which each of these links is used in practice and hence discuss the implications of that on the flow of liquidity and contagion around the banking system.

Data
The study uses aggregated interbank loan amounts to construct a network of the banks operating in Malawi given the small size of the interbank market in the country. For the full analysis of the network structure of Malawi's interbank market, the study uses network constructed in such a manner for the last quarter of 2018. To understand the interconnections and the evolution of such interconnections, the study further uses aggregated interbank loan amount data to construct a network for each quarter for banks operating in Malawi for the period 2010Q1 to 2018Q4. Comparing a number of network characteristics for different periods is important in this study because there has been a number of policy changes ranging from LRR percentage, the observance period to how the LRR has been calculated during the period. It is of interest therefore, to learn how such changes affect the interbank network and its characteristics and implication of such changes on financial stability. Moreover, there has been changes to the number of banks operating in Malawi in different periods. It is of interest 13 therefore, to analyze how entry and exit of banks from the system affect the strength of the network. The descriptive statistics of the data for the 32 quarters of interest is presented in table 1.

Network Characteristics of Malawi's Interbank Market
For the empirical analysis of the study, network measures of the directed network are used.

Nodes, Links and Degree
The number of nodes defines the size of a network. For the sample period used in the study, the number of nodes varies from 10 to 13. Chart 3 plots the number of banks participating in Malawi's interbank market as at 2018Q4 as borrowers and/or lenders. It is observed that as at 2018Q4, there were 10 registered LRR complying institutions (9 banks and 1 discount house) in Malawi and all of the institutions were participating in the interbank market during the quarter. Chart 4 indicates that there have been variations in the number of participating banks during the study period. The average size of the Malawi interbank network on any given quarter is 12 nodes. The largest network is that of 13 banks and that appeared in 20 different quarters.
14 The smallest network is that of 10 banks and appeared in each of the last three quarters of the sample period (2018Q2, 2018Q3 and 2018Q4).

Chart 3: Size of the Malawi's Interbank Network as at 2018Q4
Turning to the evolution of the network over time, charts 4, 6, 7 and 8 illustrate that the characteristics of the interbank network has not been stable even in times when the number of market participants has been stable. For instance, although the number of participating banks did not change between 2010 and 2013, the number of links has been changing and has been volatile during that period. This is against findings of some studies of similar nature. For instance, Soramaki et al (2006) found that USA interbank connectivity patterns change when there is a disruption to a number of financial systems and infrastructure. The Malawi interbank network structure does not support the change in connectivity due to the number of banks trading in the market. However, it may be the case that connectivity has been changing due to change in infrastructure.

Chart 4: Changes in the Number of Nodes and Links in Malawi's Interbank Network
(2010Q1-2018Q4) 16 Chart 5 provides a visualisation of the Malawi's interbank network on a sample quarter (2018Q4). The thickness of the links is proportional to their weight, defined as the value of the interbank loan passing through the link. It is clear that interbank trading between participating banks forms a fairly well-connected network. The high level of connectivity is confirmed by the descriptive statistics presented in Table 2. The network displays both a fair connectivity (68.9%) and a short average path length (1.322), implying that most banks have directed links with most banks in the market and the average degree 6 of a node is 6.2; that is, on average, more than six links originated from each node and more than 6 links ended at each node.
However, the network could be classified as less complete compared to the interbank payment flows of the United Kingdom 7 where connectivity was found to be as high as 88%, with the average path length of 1.1 (Becher et al, 2008). Maximum/ Average/ Minimum out degree 9/6.2/3 Maximum/ Average/ Minimum in degree 8/6.2/5 Average path length 1.322 Average clustering Coefficient 0.707

Completeness of the Network
The degree of completeness of a network in this study is measured by the number of links It is generally noted that connectivity in Malawi's interbank market changes with the tightness of monetary policy. One of the ways by which the central bank alters the liquidity levels in the market is to make changes to the LRR. When the central bank has taken a tight monetary policy stance, it reduces liquidity in the banking system by making sure that banks are depositing a higher part of their total deposits with the central bank. This reduces the supply of liquidity in the market and pushes the interbank rate up. The increase in interbank rate is expected to affect other interest rates in the market and results into increased lending rates. Increase in interest rates, holding all things constant, reduces the inflation rate. The opposite is also true in terms of a loose monetary policy stance. Appendix 1 shows the main changes that have been made to the LRR during the study period. It is noted that when LRR is higher and the observance period is shorter (daily), connectivity between banks increases. As can be observed from chart 4, although the number of nodes (participating banks) remained unchanged between 2010Q1 18 and 2013Q3, activity, as shown by the number of links has been changing. It is further noted that there was a consistent increase in number of links between 2012Q3 and 2013Q4. This increase in connectivity in the interbank market was associated with the tight monetary policy that was being implemented by the RBM. A bigger part of the period is associated with the period that the RBM set the LRR ratio at twofold: at 15.5% to be observed fortnightly and 12.0% to be observed daily. Because banks were supposed to keep 12.00% of the total deposits with the central bank daily while at the same time making sure they meet the 15.5% fortnight LRR, banks could not afford keeping extra cash untraded as demand for such cash was there most of the times. Likewise, when the RBM revised the LRR to 7.5% observed daily (from the 12.00% that was being observed daily) in November 2015, we notice a significant drop in connectivity in 2015Q4.
Changes in network completeness for Malawi interbank market network during the sample period is in shown in chart 6.

Chart 6: Changes in Malawi Interbank Network Completeness (2010Q1-2018Q4)
Chart 6 shows a general increasing trend in network completeness during the sample period.
The average density is 0.528. The lowest density of 0.282 is observed in 2012Q3 while the highest density of 0.756 is observed in 2018Q3. As at 2018Q4, density for the Malawi interbank market stood at 0.689. This implies that the interbank network in Malawi is relatively dense, with a degree of completeness averaging 52.80% compared to the extremely sparse fed funds network (Bech and Atalay, 2010) and the network of Fedwire payments (Becher et al., 2007) with a degree of completeness less than 1%. As can be observed from chart 6, the interbank network completeness was increasing continuously from 2012Q3 until 2014Q1.

Clustering
Clustering is a measure of the degree to which two banks, which are connected to a specific bank, are also connected to each other. In this study, the neighborhood of a node (a bank) is defined as the set of nodes that are connected to that node. If every node in the neighborhood of a particular node is connected to every other node in the neighborhood of that node, then the neighborhood is said to be complete and will have a clustering coefficient of 1. However, if no nodes in the neighborhood of a particular node are connected, then the clustering coefficient will be 0. The average clustering coefficient over all nodes in the network determines the network clustering. Analysis of interbank network clustering helps to understand the extent of liquidity flows in the banking system and how contagious a crisis can be. The actual distribution of links between banks affects the stability of the banking system and the possible contagion after a main shock. If all banks are connected to all other banks (a complete network), a shock to a single bank can easily be shared between the banks and the stability of the system is likely to be safeguarded. On the other hand, when the network is clustered, spillover of some of the banks can become considerable.
During the study period, the average clustering coefficient for the whole interbank market was

Centrality
Centrality measures the importance of a node in a network. In the case of interbank markets, centrality assists to understand not only the importance of a bank in terms of the volumes of liquidity coming from or going into it, but also on how important is a bank to the whole banking system. Centrality measures are used to compare banks with respect to their respective systemic importance as participants in the market. That is important in analyzing the smoothness of liquidity distribution in a given banking system as well as the levels of contagion in the market in times of a liquidity shock.
The study compares centrality of the banks in the network using degree centrality and betweenness centrality 9 . Degree centrality shows how many links come from and go into a node. That shows the connectivity of a node and the distribution of the degree centrality can give implication on properties of the network structure. Since interbank networks are directed, the distributions of in-degree and out-degree are analyzed in the study. The individual bank clustering coefficients take into account the borrowing and lending activity of each of the banks and its counterparts. They therefore determine the relative importance of a bank within the network. Using this measure, banks that are important to the flow of funds are the ones that are counterparts to other banks. Such banks obtain a higher centrality score. Thus, a systemically important bank will be identified as a bank that is active in the interbank market by trading with other banks in the interbank market.

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Betweenness centrality is a measure of node's importance to the network than just connectivity.
It measures the number of shortest paths from all nodes to others passing through a node, particularly indicating the importance of the node in information transmission. Unlike individual banks clustering coefficient, betweenness centrality considers both direct and indirect relationships. Betweenness measures are based on the link structure of the network and measures the importance of a bank as intermediary in the network. The betweenness centrality of a node is therefore the probability that the node is used as an intermediary on the shortest path between any two other nodes. That measures the importance of a node in terms of the flows between other nodes in the network in both lending and borrowing. The more paths a node handles, therefore, the more central is this node in the network. Centrality betweenness is calculated as the fraction of shortest paths between all nodes that go through this node. Hence the higher the betweenness centrality measure, the more important the bank is as an intermediary in the network.

Average Path Length
Interbank networks are associated with the small-world property where most nodes can be reached from the others via a small number of links. That indicates that the degree of intermediation between net demanders of funds and net suppliers is small (Bech and Atalay, 2010). In the study of interbank networks, path helps to measure how close nodes are to one another at any given time. A path is a sequence of nodes and links beginning and ending with nodes, where any link or node is not included more than once.
The length of a path is measured by its number of links and reflects the course that liquidity or contagion could follow. The distance between a pair of nodes is the length of the shortest path connecting them. Average shortest path is defined as the average number of links to reach any other bank in the network on the shortest path. Longest-path-length-in/out provide further descriptions of the distance between nodes. The Longest-path-length of a node is length of the longest path originating in the node. The Longest-path-length can provides an indication of how easily or quickly an event affecting one node could potentially affect the other nodes in the network. For example, if one participant fails to send payments, participants with direct relationships with it might find themselves short of liquidity sooner than those who have only indirect relationships with that participant.
As can be seen from chart 9, the shortest average paths length of 1.244 is observed in 2018Q3 while the longest average path length of 1.842 is observed 2010Q4. As at 2018Q4 the average path length stood at 1.322. That means that, on average, banks in the interbank market expect funds to switch hands up to 0.322 (1.322-1) more times.

Conclusion
From the interbank network characteristics analyzed in the study, we observe that Malawi's interbank market network has not been stable between 2010Q1 and 2018Q4 although the number of participating banks have been stable in most cases. Generally, the network for Malawi's interbank market is fairly dense with a significantly high clustering and a small average path length. The implication of this network structure is that liquidity is able to flow efficiently around the banking system. The network characteristics further unveils that entry or exit of a bank for most of the times has little impact on the ability of other banks to lend and borrow from one another. The high connectivity of the network will have contributed to this resilience. However, changes to central bank's monetary policy stance has a significant impact on the connectivity of the interbank network.
The network structure also shows that failure of the one bank to supply liquidity to the system may not result into serious disruption in payments elsewhere in the network. This, however, also depends on the amount of liquidity available in the market (as a whole) at the specific The fact that the market is not a fully connected network may be an indication that some banks withhold lending to other banks. This is also in support of the situation where some bank access the central bank's standing facility even when some banks have the liquidity. This is indicative of the ability of interbank participating banks to monitor each other's behavior which may also be aided by the small membership of registered banks in the country. That may also be due to the fact that individual banks have bilateral limits to how much they can lend or borrow from each other in the interbank market. On the other hand, the relatively high clustering and a small average path length makes the interbank participating banks more vulnerable to contagion than random networks. Because of the strong connectivity, the network may not be resilient to an operational shock affecting one of the banks. In that case, the impact of an operational shock may be felt not just on the connectivity of the network but rather on the availability of liquidity with which to make payments. This may be hazardous to the whole banking system.

Date Main Reform
June 2001

The network structure of the Malawi interbank market: implications for liquidity distribution and contagion around the banking system
Esmie Koriheya Kanyumbu 1

Abstract
Interbank markets have been classified as a unique type of money market since loans in these markets are both secured and unsecured. Because of this aspect, borrowing and lending in interbank markets depend on the trust that the market players have for each other. Interbank markets are, therefore, one of the key gauges of market tensions and expectations in many economies. This calls for intensive research on interbank network as such research contributes to the development of a stress testing framework for assessing systemic risk in the banking system. This is because the close relationships that exit in interbank markets are associated with complex financial institutional networks. The study focused on the interbank market network for Malawi, a relatively small but active market, with a view to analyze liquidity distribution and contagion around the banking system. The study reveals that the network for Malawi's interbank market is fairly dense with a significantly high clustering and a small average path length, implying that liquidity is able to flow in a fairly efficient manner around the banking system. Following the relatively high connectivity of the interbank network, entry or exit of a bank, for most of the times, has little impact on the ability of other banks to lend and borrow from each other. The high connectivity of the network also implies that banks are able to monitor each other's behaviour. This results into a situation where some banks withhold lending to other banks, forcing the liquidity deficient banks to get liquidity at a higher cost than the one prevailing on the market. The relatively high clustering and a small average path length further implies that the interbank participating banks are more vulnerable to contagion than in random networks. Since there is strong connectivity among the banks, the network may not be resilient to an operational shock affecting one or more of the banks. In this case, the impact of an operational shock may be felt not just on the connectivity of the network but rather on the availability of liquidity with which to make payments. Due to such factors, interbank markets require formulation of specific policies, especially policies concerning the way in which liquidity is funded. As different markets continue to 2 evolve over time, these highlighted aspects of the interbank market are becoming more important from both a policy and research point of view.
As pointed out by Brink and Georg (2011), the financial crisis of 2007/08 highlighted, among other things, the necessity of macro prudential oversight on financial systems in addition to micro prudential supervision. To ensure stability of the financial system, it is important not only to monitor the strength of the individual financial institutions, but also to analyze the network structure that they form due to their various interlinkages. Because trading in interbank markets depends on trust, a well-functioning interbank market is able to put in place strong disciplining mechanisms among its participants. By providing/denying and pricing liquidity according to the riskiness of counterparts, interbank markets offer an additional hand to central banks' macro-prudential regulation which continues to be challenged by sophistications in the banking industry, information asymmetry, weak legal frameworks and government intervention, among other things. Thus, studying the network structure of an active interbank market can expose some of the hidden risks in the banking system and assist the central bank to take the necessary actions and be able, therefore, to avoid some potential crises within the system.

Among different forms of interconnections between banks, interconnections through interbank
loans are among the most important ones due to two main reasons. Firstly, interbank interconnections are convenient for the enhancement of liquidity allocation. Interbank markets provide a remedy to liquidity-constrained banks which would otherwise pay hefty premia to get funds elsewhere. This is specifically true for smaller banks who, in most cases, have to pay hefty premia to get funds from larger peers or regulators in times of liquidity shortages.
Secondly, interbank interconnections are associated with risk sharing in the banking system.
While risk sharing may be good in some cases, it may also mean that some risks are allocated to market players who may not be able to bear their portion of risk. That situation may lead the to amplification of shocks in times of crisis. As interbank trading continues to be cross-border, risk sharing also goes beyond banks operating in a particular market.
The study documents the network structure of the interbank market in Malawi by analyzing the topological characteristics of the network structure of the market and discuss such structure and its implications in terms of liquidity and contagion in the banking system. That is implemented by describing and mapping the interbank network in Malawi and its evolution using a simple network model and discussing how central bank's policy can affect the network 3 structure of the market. Such analysis is important for discussion on financial stability since it has the potential of opening up new opportunities for systemic risk assessments of the Malawi's relatively small and active interbank market.
Studying Malawi's interbank market as network topology contributes specifically to an understanding of the stability and robustness of a network of liquidity flows in response to an operational disturbance. This is because different network properties may give rise to different degrees of resilience to such disturbances. In particular, the properties of an interbank network may have important implications for the flow of liquidity through the system in stressed circumstances, for example, when a bank is operationally unable to make payments. Holding all things constant, the higher the connectivity of the system, the faster liquidity is expected to flow to the stricken member(s). Generally, banks that exhibit a low in degree are likely to be more vulnerable to disturbances than other banks because the removal of one link will severely limit the flow of incoming funds. On the other hand, banks with high out degrees have, holding all things constant, the potential to affect more counterparties if their payment processing is disrupted. In a near-complete network, however, link weights, rather than node, degree and connectivity, play a larger role.

The Network Theory and the Interbank Market
The network theory is generally associated with the study of graphs which are represented either as symmetric relation or asymmetric relation among discrete objectives. Such a representation has proved to be useful in different disciplines in the study of different relationships. In intelligence agencies, the theory is applied in identifying criminal and terrorist networks from traces of communication that they collect and then identifying the key players in these networks. In social network websites like Facebook, the network theory is used in identifying and recommending friends based on friends of friends. In epidemiology, the network theory is applied to track the spread of diseases like HIV/AIDS. In financial economics, especially following the financial crisis highlighted earlier, the network theory has specifically become useful in explaining the dynamics of the interbank market. From a financial market perspective, a network is defined as a set of nodes representing financial institutions in a particular market and set of links defining the relationships between those 4 nodes. Links may exist between the nodes and they may be directed or undirected. 1 While central banks have applied the network theory for mapping different interlinkages between financial institutions, the theory has become specifically useful in studying the structure of the banking system that is composed of banks that are connected by their interbank bilateral exposures.
Studying the interbank market as a network has proved to be helpful to both researchers and policy makers in aiding the understanding of how banks are related and the importance of each of the banks in the functioning of the interbank market. Using the network approach, stakeholders are able to find the degree of heterogeneity in the interbank market and use that to determine the disintegration of the network in the event of pressure. For instance, the network approach is able to show the interconnection structure differences between banks before and after a specific shock. This is done by measuring the distance of the connectedness within different time periods.
Although the network approach may not necessarily be used as a tool to identify potential future crises, by using the approach, the interbank connectivity pattern can be used in estimating the occurrence of pressures on the financial system in the future (early warning signals). Moreover, understanding of interconnectedness in the interbank market assists in identification of sources of potential crises in different markets. The network approach can be used to gauge financial contagion in the banking system since the structure of the network affects the degree and speed at which financial crises spread throughout the market. In addition, the network approach is favoured because of its ability to expose patterns in interbank relationships that may not be clearly observed numerically. For instance, the application of network theory has assisted in the understanding of the interconnectedness within the banking system which proved to be a key driver of systemic risk in the 2008 global financial crisis (Brunetti et al, 2015). Thus, using the network approach, stakeholders are able see some aspects that have become crucial for global financial stability. Such aspects include levels and changes in financial interconnectedness in such markets.

5
The core-periphery model complements the network approach in the determination of the structure of the connectedness by classifying the group of banks acting as core/center or periphery. The theory was introduced by Borgatti and Everett (2000) but it was pioneered by Craig and von Peter (2014) in its application to interbank markets. According to the model, interbank market is split into two subsets; the core market and the periphery market. Although the unsecured segment of the interbank market is over-the-counter, the model presents the interbank market as a market that exhibits a core-periphery network structure. The 'core', consists of banks that are central to the system and are able to lend and borrow from all the other banks in the core and other banks outside the core while the other subset, the 'periphery' do not transact directly among themselves but depend on lending and borrowing from banks which are able to access the core market. In this set up, the core banks act as intermediaries.
The core-periphery setup implies that while some participants are able to trade with the market as a whole, there exists some parallel markets outside the general market, where liquidity can be supplied for the banks that, due to some reasons, are unable to tap into the liquidity that is available in the main interbank market. For instance, because the cost of trading in the core market may be relatively higher for small banks, such banks may resort to building relationships with the big banks and borrow indirectly through them. Because of that, the small banks may end up paying higher rates for liquidity than the rates prevailing on the core market.
Similarly, smaller banks may be receiving lower rates for their liquidity when they are on the liquidity surplus side. This means that some banks can borrow from the core market to lend to other banks in the relationship lending market and extracts rents from providing these services.
In markets where the core-periphery structure is in existence, many banks maintain long-term relationships and they trade with just a few banks. For instance, Chiu and Monnet (2016) highlighted that some banks possess a comparative advantage in overcoming information asymmetries, searching for counterparties or bargaining. Such differences, among other reasons, may lead to the birth of the core-periphery market structure and result into differences in borrowing and lending conditions for different banks. Moreover, such structure intensifies risk sharing as well as movement and spread of liquidity shocks in the market.

Related Literature
Earlier research on interbank market focused on importance of this type of market in hosting the first step of monetary policy transmission mechanism. Such literature includes the seminal work of Poole (1968). In more recent research, studies on interbank markets have gone deeper 6 to include interconnectedness in these markets and how such connections enhance risk sharing and amplification of shocks in times of crisis. The network approach has specifically been useful in that line of research. That has mainly followed the lessons from the 2007/2008 financial crisis since it has been documented that micro prudential supervision and regulation is inadequate on its own to identify potential route of contagion and assess the stability of financial system. It is no longer debatable, therefore, that the systemic importance of one bank depends not only on the properties of that bank, but also on the properties of the whole market.
This has brought in interest in interbank connections and these connections are looked at from different perspectives.
Brassil and Nodari (2018)  showed that South African interbank system had been largely stable and resilient during the period covered in the study. That had been the case even in times of great distress on the international financial markets. In addition, the study concluded that the number of banks participating in the South African interbank market was almost constant and there was a high level of interconnectedness during the analyzed period. Because of the observed strong interconnectedness, the study established a high level of liquidity allocation and risk sharing in the South African interbank market.

7
Some studies have been interested in specific banks' positions in the market network and how such positions affect both liquidity access and provision. A study by Gabriel and Georg (2016) is one example of such studies. In Gabriel and Georg (2016) a dataset of all the European banks was used to study the liquidity reallocation among the banks. The study specifically, dwelt on how a bank's characteristics affect its ability to borrow and lend on the overnight interbank market. From the Ordinary Least Squares (OLS) estimations that were done in the study, the paper established that a bank's position in the interbank network, as measured by various measures of centrality in networks, has a significant impact on both liquidity provision and access. Precisely, banks with higher network centrality were found to provide more liquidity on the interbank market. Such banks are also willing to lend funds at cheaper prices. Similarly, banks with higher network centrality were found to have access to more liquidity and borrow funds on the interbank market at cheaper prices. This implies that a bank's position in the interbank network plays a role in the determination of both interbank traded volumes and rates.
The network approach has also been applied to compare the behaviour of banks during normal times and during times of financial crisis. Brunetti et al (2015) studied the behavior of the European interbank market before, during and after the financial crisis. The study established that while the two types of networks defined in the study, the correlation network 2 and the physical network 3 behaved the same way before the crisis, the correlation network showed an increase in interconnectedness during the crisis while the physical network highlighted a significant decrease in interconnectedness. It was further observed that physical networks were able to forecast liquidity problems while financial problems were better forecasted by correlation networks. The network approach has also been importantly used to understand how lending conditions in the interbank market are affected by the networking of banks. Blasques, Brauning and Lelyveld (2018), estimated the structural micro-founded dynamic network model on the network statistics of the Dutch unsecured interbank market using monthly data from February 2008 to April 2011. The study was specifically interested in the characteristics of interbank markets as can be explained by two main aspects of this type of market, namely, liquidity uncertainty and peer monitoring in interaction with counterparts. The study found that Dutch banks form long-term lending relationships that are associated with improved credit conditions and that the lending networks exhibits sparse core-periphery structure. The findings 2 Based on publicly traded bank returns 3 Based on interbank lending transactions 8 of the study support the crucial role played by lending/borrowing relationship in the determination of interbank traded volumes as well as the interbank rate. Those findings agree with Schumacher (2016), who applied the network approach in trying to understand how the lending conditions in the Swiss franc money market are affected by the networking of banks.
The findings in the study established that there is a difference in the lending conditions for the secured and the unsecured segments of the market. While clustering 4 is more pronounced in the unsecured segment of the market which serves as a social collateral, trust plays a minor role in the secured part of the market where physical collateral is involved. Generally, banks with stronger relationships in the interbank market (higher clustering coefficients) are offered better trading conditions in terms of both trading volume and rates.
The network approach has also been applied to establish the presence of core and periphery market structure in particular interbank markets and how such a structure affect lending and borrowing in interbank markets. Craig and von Peter (2014), studied the bilateral interbank exposures among 2000 German banks from 1999 to 2012. The study provided evidence that most banks in Germany do not lend to each other directly but through money center banks.
Such money center banks act as intermediaries for the interbank market. The study further confirmed a strong evidence of tiering in the German banking system and that such extent of tiering was not common in standard random networks.
The existence of core-periphery interbank market structure is associated with incompleteness, between the core and the periphery markets in European interbank markets. In addition, it is highlighted that apart from raising the bargaining power of periphery banks that are connected to the core market, and raising the price dispersion in the interbank market, segmentation was found to raise inefficient resort to the central bank standing facilities. This implies that optimal monetary policy implementation may be hampered by increased levels of segmentation liked to the core-periphery structure. The existence of core-periphery structure may result from different bank characteristics that includes capital levels. This is observed in Green et al. (2016) 9 who established that banks with increased capital buffers enjoy lower costs of borrowing in the interbank market since highly-capitalized banks are perceived as less risky. Such banks can form the core of the market.
As can be noted from the reviewed literature, limited attention has been devoted to study the network structure of interbank markets of low-income countries like Malawi. Although most low-income economies like Malawi were not directly affected by the last financial crisis, contagion via the interbank market remains one of the key concerns of the central banks because possible chances of encountering such crises remain in such countries. It can also be recalled that low-income countries experienced a number of banking crises during the 1980s and 1990s which took longer to resolve than in other groups of countries. Moreover, chances of macroeconomic and banking system fragility still exist and crises can still arise following strides in financial deepening and sophistication of financial systems in these countries. In addition, due to relaxation in bank ownership restrictions observed in modern low-income banking sectors 5 , it has become more relevant than before, to study the interbank network structure of these markets in order to observe and analyze possible sources of crises, levels and the speed of such crises and discuss possible relevant policy actions that can be taken to make such markets resilient to possible identified shocks. Getting a better picture of the network structure is therefore a crucial step in developing systematic risk assessment of the interbank market.

A Brief Description of the Market
Network properties are market-specific across different countries because of the different characteristics of specific markets. The interbank market in Malawi is relatively small, but has been active for its entire life period. Trading in Malawi's interbank market started in 2001 and since then, trading, in terms of volumes, has generally been increasing (chart 1).

Chart 1: Interbank Traded Volume (2010-2017)
Generally, banks lend or borrow from the interbank market in relation to their predicted excess reserves that is calculated as any amount of liquidity that is above or below the Liquidity as well as the pricing of interbank loans, therefore, reflect a bank's perceived level of risk. Such a disciplining role points towards the potential for the market to support to macro-prudential regulation by the central bank.

12
In general terms, a network consists of nodes and links. In this study, each node stands for a bank and each link connecting two nodes bears interbank trading relationship between the two corresponding banks. Although a network can be either directed or undirected, the study was interested in the directed network for the analysis of the interbank market in Malawi. Node characteristics and the links associated with individual nodes have different implications depending on whether a bank is a borrower or a lender. The study models Malawi's interbank loan flows as a directed network. This is because directed network brings out good discussions for policy making of central banks.
In the study, banks are represented as nodes in the network and traded volumes between banks form the links between these nodes. We define these links as being 'directed' in such a way that if bank X only lends (but does not borrow) funds to bank Y then there would be a directed link from X to Y but not one from Y to X. In a situation where both banks X and Y extended loans to each other, we have two directed links, one in each direction. The weight attached to a link is proportional to the value or volume of interbank loans passing through that link. The design of the interbank market in Malawi has been in such a way that all banks and discount houses can technically borrow and lend to all other banks and discount houses. Malawi's interbank market can therefore, in principle, be modelled as a complete network. The empirical work analyzed the extent to which each of these links is used in practice and hence discuss the implications of that on the flow of liquidity and contagion around the banking system.

Data
The study uses aggregated interbank loan amounts to construct a network

Network Characteristics of Malawi's Interbank Market
For the empirical analysis of the study, network measures of the directed network are used.

Nodes, Links and Degree
The number of nodes defines the size of a network. For the sample period used in the study, the number of nodes varies from 10 to 13. Chart 3 plots the number of banks participating in Malawi's interbank market as at 2018Q4 as borrowers and/or lenders. It is observed that as at 2018Q4, there were 10 registered LRR complying institutions (9 banks and 1 discount house) in Malawi and all of the institutions were participating in the interbank market during the quarter. Chart 4 indicates that there have been variations in the number of participating banks during the study period. The average size of the Malawi interbank network on any given quarter is 12 nodes. The largest network is that of 13 banks and that appeared in 20 different quarters.
14 The smallest network is that of 10 banks and appeared in each of the last three quarters of the sample period (2018Q2, 2018Q3 and 2018Q4).

Chart 3: Size of the Malawi's Interbank Network as at 2018Q4
Turning to the evolution of the network over time, charts 4, 6, 7 and 8 illustrate that the characteristics of the interbank network has not been stable even in times when the number of market participants has been stable. For instance, although the number of participating banks did not change between 2010 and 2013, the number of links has been changing and has been volatile during that period. This is against findings of some studies of similar nature. For instance, Soramaki et al (2006) found that USA interbank connectivity patterns change when there is a disruption to a number of financial systems and infrastructure. The Malawi interbank network structure does not support the change in connectivity due to the number of banks trading in the market. However, it may be the case that connectivity has been changing due to change in infrastructure. Changes in network completeness for Malawi interbank market network during the sample period is in shown in chart 6.

Chart 6: Changes in Malawi Interbank Network Completeness (2010Q1-2018Q4)
Chart 6 shows a general increasing trend in network completeness during the sample period.
The average density is 0.528. The lowest density of 0.282 is observed in 2012Q3 while the highest density of 0.756 is observed in 2018Q3. As at 2018Q4, density for the Malawi interbank market stood at 0.689. This implies that the interbank network in Malawi is relatively dense, with a degree of completeness averaging 52.80% compared to the extremely sparse fed funds network (Bech and Atalay, 2010) and the network of Fedwire payments (Becher et al., 2007) with a degree of completeness less than 1%. As can be observed from chart 6, the interbank network completeness was increasing continuously from 2012Q3 until 2014Q1.

Clustering
Clustering is a measure of the degree to which two banks, which are connected to a specific bank, are also connected to each other. In this study, the neighborhood of a node (a bank) is defined as the set of nodes that are connected to that node. If every node in the neighborhood of a particular node is connected to every other node in the neighborhood of that node, then the neighborhood is said to be complete and will have a clustering coefficient of 1. However, if no nodes in the neighborhood of a particular node are connected, then the clustering coefficient will be 0. The average clustering coefficient over all nodes in the network determines the network clustering. Analysis of interbank network clustering helps to understand the extent of liquidity flows in the banking system and how contagious a crisis can be. The actual distribution of links between banks affects the stability of the banking system and the possible contagion after a main shock. If all banks are connected to all other banks (a complete network), a shock to a single bank can easily be shared between the banks and the stability of the system is likely to be safeguarded. On the other hand, when the network is clustered, spillover of some of the banks can become considerable.
During the study period, the average clustering coefficient for the whole interbank market was

Centrality
Centrality measures the importance of a node in a network. In the case of interbank markets, centrality assists to understand not only the importance of a bank in terms of the volumes of liquidity coming from or going into it, but also on how important is a bank to the whole banking system. Centrality measures are used to compare banks with respect to their respective systemic importance as participants in the market. That is important in analyzing the smoothness of liquidity distribution in a given banking system as well as the levels of contagion in the market in times of a liquidity shock.
The study compares centrality of the banks in the network using degree centrality and betweenness centrality 9 . Degree centrality shows how many links come from and go into a node. That shows the connectivity of a node and the distribution of the degree centrality can give implication on properties of the network structure. Since interbank networks are directed, the distributions of in-degree and out-degree are analyzed in the study. The individual bank clustering coefficients take into account the borrowing and lending activity of each of the banks and its counterparts. They therefore determine the relative importance of a bank within the network. Using this measure, banks that are important to the flow of funds are the ones that are counterparts to other banks. Such banks obtain a higher centrality score. Thus, a systemically important bank will be identified as a bank that is active in the interbank market by trading with other banks in the interbank market.

22
Betweenness centrality is a measure of node's importance to the network than just connectivity.
It measures the number of shortest paths from all nodes to others passing through a node, particularly indicating the importance of the node in information transmission. Unlike individual banks clustering coefficient, betweenness centrality considers both direct and indirect relationships. Betweenness measures are based on the link structure of the network and measures the importance of a bank as intermediary in the network. The betweenness centrality of a node is therefore the probability that the node is used as an intermediary on the shortest path between any two other nodes. That measures the importance of a node in terms of the flows between other nodes in the network in both lending and borrowing. The more paths a node handles, therefore, the more central is this node in the network. Centrality betweenness is calculated as the fraction of shortest paths between all nodes that go through this node. Hence the higher the betweenness centrality measure, the more important the bank is as an intermediary in the network. Table 3 shows that there is significant variation in importance of individual banks in terms of liquidity distribution. In 2018Q4, two banks borrowed from up to 8 banks in the Malawi interbank network while only one bank lent to all the remaining 9 institutions in the market.
This shows that while some banks have a wide choice of where to borrow from and lend to, some banks have narrower choice. This implies that the real impact of a liquidity shock to the whole market depends on which banks are affected. Similarly, bank 4 has the highest betweenness centrality of about 7.3 compared to bank 1 with the lowest betweenness centrality of just 0.2. This shows that, while some banks are more important as intermediaries in the Malawi interbank market, some banks are less important.

Average Path Length
Interbank networks are associated with the small-world property where most nodes can be reached from the others via a small number of links. That indicates that the degree of intermediation between net demanders of funds and net suppliers is small (Bech and Atalay, 2010). In the study of interbank networks, path helps to measure how close nodes are to one another at any given time. A path is a sequence of nodes and links beginning and ending with nodes, where any link or node is not included more than once.
The length of a path is measured by its number of links and reflects the course that liquidity or contagion could follow. The distance between a pair of nodes is the length of the shortest path connecting them. Average shortest path is defined as the average number of links to reach any other bank in the network on the shortest path. Longest-path-length-in/out provide further descriptions of the distance between nodes. The Longest-path-length of a node is length of the longest path originating in the node. The Longest-path-length can provides an indication of how easily or quickly an event affecting one node could potentially affect the other nodes in the network. For example, if one participant fails to send payments, participants with direct relationships with it might find themselves short of liquidity sooner than those who have only indirect relationships with that participant.
As can be seen from chart 9, the shortest average paths length of 1.244 is observed in 2018Q3 while the longest average path length of 1.842 is observed 2010Q4. As at 2018Q4 the average path length stood at 1.322. That means that, on average, banks in the interbank market expect funds to switch hands up to 0.322 (1.322-1) more times.

Conclusion
From the interbank network characteristics analyzed in the study, we observe that Malawi's interbank market network has not been stable between 2010Q1 and 2018Q4 although the number of participating banks have been stable in most cases. Generally, the network for Malawi's interbank market is fairly dense with a significantly high clustering and a small average path length. The implication of this network structure is that liquidity is able to flow efficiently around the banking system. The network characteristics further unveils that entry or exit of a bank for most of the times has little impact on the ability of other banks to lend and borrow from one another. The high connectivity of the network will have contributed to this resilience. However, changes to central bank's monetary policy stance has a significant impact on the connectivity of the interbank network.
The network structure also shows that failure of the one bank to supply liquidity to the system may not result into serious disruption in payments elsewhere in the network. This, however, also depends on the amount of liquidity available in the market (as a whole) at the specific period in time. In situations where liquidity levels are limited, banks are able to make use of alternative sources of liquidity. Such sources include discounting of securities and accessing the central bank's Lombard facility. However, because the banks are different in importance, there is possibility that the operational disruption of some banks, especially if they are net 25 suppliers of liquidity to the system, would have a more severe impact on the payment network than disruption of some less important banks.
The fact that the market is not a fully connected network may be an indication that some banks withhold lending to other banks. This is also in support of the situation where some bank access the central bank's standing facility even when some banks have the liquidity. This is indicative of the ability of interbank participating banks to monitor each other's behavior which may also be aided by the small membership of registered banks in the country. That may also be due to the fact that individual banks have bilateral limits to how much they can lend or borrow from each other in the interbank market. On the other hand, the relatively high clustering and a small average path length makes the interbank participating banks more vulnerable to contagion than random networks. Because of the strong connectivity, the network may not be resilient to an operational shock affecting one of the banks. In that case, the impact of an operational shock may be felt not just on the connectivity of the network but rather on the availability of liquidity with which to make payments. This may be hazardous to the whole banking system.

Date Main Reform
June 2001 RBM set the Minimum Liquidity Reserve Requirements at 30 percent and each depository institution (Commercial banks and discount houses) were supposed to maintain minimum cash balances in relation to the preceding month's total deposit liabilities (including government deposits). The Liquidity Reserve Requirement consisted of balances in the main account with the Reserve Bank, call deposit account balances with licensed discount houses and vault cash. However, balances with discount houses to be considered as part of the LRR was not to exceed 25 percent of the LRR. The minimum LRR specified above was to be maintained as a simple one week (Monday -Sunday) average.

February 2006
The RBM set the Minimum Liquidity Reserve Requirements at 25 percent and each depository institution was to maintain minimum cash balances in relation to the preceding week's total local currency deposit liabilities, including government deposits. In the case of discount houses, the LRR was to apply to non-collaterised deposits from the corporate sector. Non-collaterised deposits with discount houses to be considered as part of LRR was not to exceed 10.0 percent of the LRR. The minimum LRR specified above was to be maintained as a simple one week (Monday -Sunday) average. Monitoring of compliance was to be effective from the first business day of the week.

2008
The LRR ratio was set at 15.5 percent and had be observed as a simple one week (Monday -Sunday) average.
June 2010 Each depository institution was supposed to maintain required reserves in relation to the preceding fortnight's total deposit liabilities, including Government deposits, repurchase agreements, foreign currency deposits and any other liabilities as the Reserve Bank of Malawi was to define from time to time. LRR observance on foreign currency deposits was set at a minimum of US$200,000-00 equivalent and the LRR ratio was set at 15.5%.
The LRR was set to be observed as a simple two week (Monday of the first week -Sunday of the second week of the observance period) average.

January 2014
The RBM introduced a Lombard Facility at its discount window. The Lombard Rate was set at 2 percentage above the Monetary policy rate. In addition, the RBM revised the guidelines on the Rediscount Facility and introduced a Foreign Exchange Swap Facility to provide banks with alternative avenues (other than the Lombard Facility) for managing their Malawi Kwacha liquidity. The LRR ratio was set twofold: at 15.5% to be observed fortnightly and 12.0% to be observed daily.