## wp17136 ## Source details **Canonical URL:** [wp17136](https://www.imf.org/-/media/files/publications/wp/2017/wp17136.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2017/wp17136.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2017/wp17136.pdf.json) --- ### I. Introduction — purpose and high-level insights - Purpose: introduce ABBA, an agent-based model (ABM) for banking analysis to study dynamics of solvency, liquidity, and interconnectedness risk in response to shocks. - Key conceptual insight: adaptive, heterogeneous, and possibly sub-optimal microscopic agent behavior determines aggregate network characteristics (interconnectedness, centrality, systemic risk). - Comparative policy insight from simulations: - When capital requirements are too low relative to underlying credit risk, raising reserve requirements could lead to larger number of bank failures. - Higher capital requirements reduce counterparty risk but can be conducive to higher interconnectedness risk; this creates a potential systemic vulnerability in presence of tail events (a single bank failure could propagate). - Model design emphasis: endogenous formation of the interbank network as banks access it to meet liquidity needs; banks can take remedial actions (deleveraging, risk-weight optimization) instead of immediate failure when regulatory ratios fall. ### II. ABBA model architecture and agents - Implementation environment: NetLogo. - Agent types: - Savers: depositors spread across regions; proto-agents with heterogeneity and simple adaptive behavior. - Loans: modeled as agents; carry attributes loan amount, probability of default, risk weight, rating, recovery rate, fire-sale loss; proto-agents (heterogeneous). - Banks: full agents exhibiting adaptivity, learning potential, autonomy, heterogeneity; raise deposits, fund loans, manage provisions, reserves, equity, interbank lending, dividends, deleveraging, and portfolio rebalancing. - Spatial/region setup: - World divided in regions; initially each region dominated by a regional bank; banks may expand across regions over time. - Interbank linkages: - Single interbank exposure type: unsecured interbank loans. - Links (directed edges) form endogenously as creditor banks with excess reserves lend proportionally to illiquid banks' needs. - Liquidity rationing: banks access interbank loans sequentially, in random order; creditor contribution proportional to creditor’s share of aggregate excess reserves. ### III. Behavioral rules and mechanics (high-level, preserving technical terms) - Initial conditions and regulatory constraints: - Banks set initial loan portfolio and reserves so initial capital and reserve constraints are satisfied (equations (1) and (2) in text specify CAR and MRR checks). - Provisions against expected losses computed as sum over loans of p × (1 − recovery rate) × loan amount (equation (3)). - Lending rate for a loan set via a markup μ over fair price according to equation (4). - Period loop (per period bank lifecycle): 1. Evaluate bank solvency after loan portfolio defaults; compute net interest income (NII) and credit losses (equations (5)–(9)). 2. Compute second-round effects through interbank exposures (equations (12)–(14)); iterate until number of solvent banks stabilizes. 3. If solvent but undercapitalized (0 < E ≤ CAR × RWA), perform risk-weight optimization or deleverage (equations (15)–(18)). 4. Pay dividends subject to excess capital and excess reserves constraints (equations (19)–(21)); expand loan book if requirements remain satisfied. 5. Face liquidity shocks from deposit withdrawals; access interbank market; if unmet, potential bank runs and liquidation (fire-sale losses per equation (11)). - Risk-weight optimization: - Bank may retain subset of solvent loans to satisfy CAR constraint (equation (15)); change in equity and RWA from disposing loans computed via equations (16) and (17). - Optimization objective: arg max retained equity subject to RWA and CAR constraints (equation (18)); sequential enhancement alternative described when full optimization infeasible. - Dividends and reserve constraints: - Banks set internal targets: preferred reserve ratio = 1½ × minimum reserve ratio; preferred maximum capital ratio = 1½ × CAR. - Dividends paid as min(excess capital, excess reserves) per equation (21). ### IV. Second-round dynamics and systemic propagation - Interbank losses: - Interbank credit losses for bank i equal sum of exposures to defaulted counterparties (equation (12)). - Second-round equity and reserves adjust for interbank losses and interest flows (equations (13) and (14)). - Cascade mechanism: - Insolvency of a bank triggers liquidation of solvent loans at fire-sale values, potentially rendering savers insolvent (first-come, first-serve payout). - Second-round failures may follow iteratively until stable set of solvent banks achieved. - Modeling assumption noted: - ABBA assumes creditor banks honor interest payments on interbank loans even if insolvent (can be relaxed in modular extensions). ### V. Simulation exercise: design assumptions and key parameter values - Simulation objective: analyze impact of capital and reserve ratio requirements on bank failures, profitability, and interconnectedness risk. - Savers (explicit parameters): - There are 10,000 savers distributed evenly across 10 regions. - Savers hold bank deposits with a unit balance. - The bank pays a deposit rate of 1 percent. - Interest on deposits is consumed upon receipt so the balance remains constant and equal to one. - A saver withdraws deposits and changes banks with a probability sampled from a discrete uniform distribution with values in the set {0, 0.01, ..., 0.20}. - Loans (explicit parameters): - Number of available loans: 20,000, evenly distributed across 10 regions. - Loan amount is set equal to 1. - Recovery rate given default is constant and equal to 40 percent. - Each loan’s probability of default sampled from discrete uniform distribution {0, 0.1, 0.2 ... 0.10}. - Loan risk weight = 0.5 + 5 × Probability of default, with range [0.5, 1]. - Fire-sale loss (percent of face value) sampled from discrete uniform distribution {0, 0.1, 0.2 ... 0.10}. - Loan rate quoted by bank set according to equation (4). - Banks (explicit parameters): - There are 10 banks. - Initial equity of each bank set equal to 100. - Banks prefer reserve ratio equal to 1½ times the minimum reserves ratio requirement. - Upper bound / maximum capital ratio preferred by the bank is 1½ times the CAR; whenever upper bound exceeded, excess capital distributed as dividends if deposits permit. - Interbank loans are unsecured and used only to meet liquidity needs (not to fund assets). - Liquidity and interbank market rules: - Liquidity shocks arise from saver withdrawals; in the basic model aggregate system liquidity is neutral since withdrawals are offset by deposit inflows elsewhere, but idiosyncratic bank runs can occur if withdrawals exceed reserves. - Interbank lending is rationed; creditor contribution proportional to creditor’s share of aggregate excess reserves; illiquid banks last in queue may receive insufficient interbank funding and require emergency liquidity assistance in extended versions (ELA not included in basic ABBA). - Simulation protocol: - Capital requirements (measured as equity to risk-weighted assets) allowed values: 0.04, 0.08, 0.12, 0.16. - Minimum reserve ratio allowed values: 0.03, 0.045, 0.06. - Simulations: One hundred simulations, each comprising 240 periods, were performed for each of the twelve combinations of capital requirement and reserve requirement. This corresponds roughly to weekly observations over a period of 4 years. - Interbank loans and Emergency Liquidity Assistance (ELA) (section III specifics): - Interbank loan rate is set equal to 1 percent. - All banks enjoying excess reserves lend to well capitalized but illiquid banks. - A lending bank lends an amount proportional to its share in total excess reserves in the banking system. - Undercapitalized but solvent banks borrow enough deposits from the ELA facility at a zero interest rate. - Solvent banks return funds to the ELA facility in the next period. - There are no penalties if failed banks do not return funds; costs to ELA are not accounted explicitly. ### VI. Main findings — Bank failures: the interplay of solvency and liquidity requirements - At low capitalization levels, banks are more vulnerable to credit shocks and are more likely to be undercapitalized. - Banks unable to meet the regulatory capital requirement would have their access to the interbank market curtailed, raising liquidity risk. - When the capital requirement is 4 percent: - It is difficult for banks to keep their reserve ratio at the target level set at 50 percent above the minimum reserve ratio. - After a number of periods, banks on average are not able to meet the minimum reserve ratio and have to rely on the ELA facilities. - When capital requirements are 8 percent or above: - Banks on average can meet their target reserve ratios. - Interaction of capital and reserve requirements at low capital (4 percent): - Higher reserve requirements force banks to hold more reserves, reducing the impact of liquidity shocks and their associated failures. - However, when banks are undercapitalized, higher reserve requirements prevent banks from performing risk-weight optimization (which requires running down the reserves), leading to an increase in the number of credit failures that offsets the lower number of liquidity failures. - Dividend distribution constraint: - Simulations assume banks target capital ratio 50 percent higher than the minimum requirement (example: with a CAR of 8 percent, a bank will start distributing dividends if its capital ratio exceeds 12 percent). - The amount of reserves held by the bank constrains its ability to distribute dividends. - When capital requirement is low (4 percent), banks are more reluctant to pay dividends since they need to rebuild their capital base; paying dividends becomes more difficult as reserve ratios increase. ### VII. Key statistics and reported figures (preserved as in source) - Capital adequacy ratios considered: 4 percent, 8 percent, 12 percent, 16 percent. - Minimum reserve ratios considered: 3.0 percent, 4.5 percent, 6.0 percent. - Percent failures reported (excerpt): - Panel A (Minimum capital adequacy ratio = 4 percent), Failures, in percent: 43.8, 38.2, 46.8 for reserve ratios 3 percent, 4.5 percent, 6 percent respectively. - Panel B (Minimum capital adequacy ratio = 8 percent), Failures, in percent: 8.6, 0.0, 0.0 for reserve ratios 3 percent, 4.5 percent, 6 percent respectively. - Panel C (Minimum capital adequacy ratio = 12 percent), Failures, in percent: 6.0, 0.0, 0.0 for reserve ratios 3 percent, 4.5 percent, 6 percent respectively. - Panel D (Minimum capital adequacy ratio = 16 percent), Failures, in percent: 6.4, 0.0, 0.0 for reserve ratios 3 percent, 4.5 percent, 6 percent respectively. - Breakdown "of which (in percent)" for Panel A (CAR = 4 percent): - For reserve ratio 3 percent: 27.5 (liquidity), 16.3 (credit). - For reserve ratio 4.5 percent: 14.7 (liquidity), 23.5 (credit). - For reserve ratio 6 percent: 16.0 (liquidity), 30.8 (credit). ### VIII. Profitability - When banks are required to hold capital ratios of 8 percent or above: - Bank profitability (measured as return on equity) appears driven mainly by regulatory capital requirements and only slightly affected by the reserve requirement ratio. - For high capital ratios, return on equity is higher the lower capital requirements are. - Higher reserve requirements encourage banks to hold higher reserve levels (banks target a buffer above the regulatory requirement), which enhances capacity to distribute dividends and raise return on equity. - Exception when capital requirements are low: - When banks target a low capital ratio it becomes more difficult to pay dividends, which hurts the return on equity. - Figure 6 mirrors results in Figure 5 (mean capital ratio patterns). ### IX. Interconnectedness - Interconnectedness arises endogenously as banks facing liquidity pressures borrow reserves in the interbank market. - NetLogo visualization notes: - Red lines show interbank loans from banks with excess reserves to banks facing liquidity problems. - Example: each borrowing bank receives loans from four banks (in-degree of four); lending banks have an out-degree of two. - Dynamics and averages: - On average, the in-degree of a bank is zero ninety percent of the time. - On average, the out-degree of a bank is zero about seventy percent of the time. - When banks are net creditors, they lend on average to one bank twenty percent of the time, and to two banks the remaining ten percent of the time. - In-degree values of six and higher realize with certain frequency at about seven to nine percent of the time, especially when reserve requirements do not exceed 4½ percent. - The maximum number of out-degrees for a single bank seldom exceeds three during the simulations. - Paradoxical effect: - An increase in capital requirement could increase interconnectedness when initial capital levels are low, because higher capital ratio targets make it less likely banks are undercapitalized, facilitating access to the interbank market when facing liquidity shortages. - Holding the capital requirement constant, higher reserve requirements induce higher reserve targets, reducing the need for interbank borrowings and interconnectedness. ### X. Conclusions and policy implications - ABBA is a simple modular agent-based model for analyzing risks and interactions in the banking system that accounts for heterogeneity and adaptive behavior. - The model accommodates endogenous bank networks through interbank loans and dynamic bank balance sheet adjustment via risk-weight optimization, dividend payments, and loan book expansion. - Policy-relevant implications: - Capital and reserve requirements interact nonlinearly with bank behavior: tightening one requirement can have counterintuitive effects when another requirement or underlying credit risk is binding. - Raising reserve requirements when capital requirements are too low relative to portfolio risk can increase number of bank failures. - Higher capital requirements reduce direct counterparty risk but may increase interconnectedness, raising systemic vulnerability to tail events. - Allowing remedial actions (deleveraging, risk-weight optimization) alters system responses relative to models that force immediate failure upon breaching regulatory minima. - Modeling utility and extensions: - ABBA provides a computational laboratory to analyze what-if scenarios for competing policy proposals, capturing agent heterogeneity, endogenous network formation, and second-round propagation channels. - Straightforward extensions include wholesale investors, collateralized loans with collateral asset proto-agents and price dynamics, and richer depositor behavior; these could better fit dynamics of banking systems like those in the United Kingdom and the United States. *Source: wp17136 - References.* ### References ............................................................................................................. ### References ................................................................................................................................31 ### Figures - 1.Savers’ behavioral decisions .................................................................................................10 - 2. Loans payoffs .......................................................................................................................11 - 3. Bank’s actions and interactions with other agents ...............................................................13 - 4. Average reserve ratio for different regulatory requirements ...............................................21 - 5. Mean capital ratio for different regulatory requirements .....................................................23 - 6. Mean return on equity under different regulatory requirements, in percent ........................24 - 7. NetLogo implementation of ABBA showing interbank loans .............................................25 - 8. In-degree and Out-degree dynamics for a representative bank ...........................................26 - 9. Percent of times out-degree of a bank exceeds one .............................................................27 ### Tables - 1. Credit and liquidity failures for different regulatory requirements, in percent ....................22 - 2. Banks’ in-degree for different regulatory requirements, in percent ....................................28 *wp17136 - References* ### 3. Banks’ out-degree for different regulatory requirements, in percent ..................................29 ### 3. Banks’ out-degree for different regulatory requirements, in percent ..................................29 ### I. Introduction — purpose and high-level insights - Purpose: introduce ABBA, an agent-based model (ABM) for banking analysis to study dynamics of solvency, liquidity, and interconnectedness risk in response to shocks. - Key conceptual insight: adaptive, heterogeneous, and possibly sub-optimal microscopic agent behavior determines aggregate network characteristics (interconnectedness, centrality, systemic risk). - Comparative policy insight from simulations (summarized in text): - When capital requirements are too low relative to underlying credit risk, raising reserve requirements could lead to larger number of bank failures. - Higher capital requirements reduce counterparty risk but can be conducive to higher interconnectedness risk; this creates a potential systemic vulnerability in presence of tail events (a single bank failure could propagate). - Model design emphasis: endogenous formation of the interbank network as banks access it to meet liquidity needs; banks can take remedial actions (deleveraging, risk-weight optimization) instead of immediate failure when regulatory ratios fall. ### II. ABBA model architecture and agents - Implementation environment: NetLogo. - Agent types: - Savers: depositors spread across regions; proto-agents with heterogeneity and simple adaptive behavior. - Loans: modeled as agents; carry attributes loan amount, probability of default, risk weight, rating, recovery rate, fire-sale loss; proto-agents (heterogeneous). - Banks: full agents exhibiting adaptivity, learning potential, autonomy, heterogeneity; raise deposits, fund loans, manage provisions, reserves, equity, interbank lending, dividends, deleveraging, and portfolio rebalancing. - Spatial/region setup: - World divided in regions; initially each region dominated by a regional bank; banks may expand across regions over time. - Interbank linkages: - Single interbank exposure type: unsecured interbank loans. - Links (directed edges) form endogenously as creditor banks with excess reserves lend proportionally to illiquid banks' needs. - Liquidity rationing: banks access interbank loans sequentially, in random order; creditor contribution proportional to creditor’s share of aggregate excess reserves. ### III. Behavioral rules and mechanics (high-level, preserving technical terms) - Initial conditions and regulatory constraints: - Banks set initial loan portfolio and reserves so initial capital and reserve constraints are satisfied (equations (1) and (2) in text specify CAR and MRR checks). - Provisions against expected losses computed as sum over loans of p × (1 − recovery rate) × loan amount (equation (3)). - Lending rate for a loan set via a markup μ over fair price according to equation (4). - Period loop (per period bank lifecycle): 1. Evaluate bank solvency after loan portfolio defaults; compute net interest income (NII) and credit losses (equations (5)–(9)). 2. Compute second-round effects through interbank exposures (equations (12)–(14)); iterate until number of solvent banks stabilizes. 3. If solvent but undercapitalized (0 < E ≤ CAR × RWA), perform risk-weight optimization or deleverage (equations (15)–(18)). 4. Pay dividends subject to excess capital and excess reserves constraints (equations (19)–(21)); expand loan book if requirements remain satisfied. 5. Face liquidity shocks from deposit withdrawals; access interbank market; if unmet, potential bank runs and liquidation (fire-sale losses per equation (11)). - Risk-weight optimization: - Bank may retain subset of solvent loans to satisfy CAR constraint (equation (15)); change in equity and RWA from disposing loans computed via equations (16) and (17). - Optimization objective: arg max retained equity subject to RWA and CAR constraints (equation (18)); sequential enhancement alternative described when full optimization infeasible. - Dividends and reserve constraints: - Banks set internal targets: preferred reserve ratio = 1½ × minimum reserve ratio; preferred maximum capital ratio = 1½ × CAR. - Dividends paid as min(excess capital, excess reserves) per equation (21). ### IV. Second-round dynamics and systemic propagation - Interbank losses: - Interbank credit losses for bank i equal sum of exposures to defaulted counterparties (equation (12)). - Second-round equity and reserves adjust for interbank losses and interest flows (equations (13) and (14)). - Cascade mechanism: - Insolvency of a bank triggers liquidation of solvent loans at fire-sale values, potentially rendering savers insolvent (first-come, first-serve payout). - Second-round failures may follow iteratively until stable set of solvent banks achieved. - Modeling assumption noted: - ABBA assumes creditor banks honor interest payments on interbank loans even if insolvent (can be relaxed in modular extensions). ### V. Simulation exercise: design assumptions and key parameter values - Simulation objective: analyze impact of capital and reserve ratio requirements on bank failures, profitability, and interconnectedness risk. Full numerical details in companion paper (Chan-Lau (2014) referenced in source). - Savers (explicit parameters): - There are 10,000 savers distributed evenly across 10 regions. - Savers hold bank deposits with a unit balance. - The bank pays a deposit rate of 1 percent. - Interest on deposits is consumed upon receipt so the balance remains constant and equal to one. - A saver withdraws deposits and changes banks with a probability sampled from a discrete uniform distribution with values in the set {0, 0.01, ..., 0.20}. - Loans (explicit parameters): - Number of available loans: 20,000, evenly distributed across 10 regions. - Loan amount is set equal to 1. - Recovery rate given default is constant and equal to 40 percent. - Each loan’s probability of default sampled from discrete uniform distribution {0, 0.1, 0.2 ... 0.10}. - Loan risk weight = 0.5 + 5 × Probability of default, with range [0.5, 1]. - Fire-sale loss (percent of face value) sampled from discrete uniform distribution {0, 0.1, 0.2 ... 0.10}. - Loan rate quoted by bank set according to equation (4). - Banks (explicit parameters): - There are 10 banks. - Initial equity of each bank set equal to 100. - Banks prefer reserve ratio equal to 1½ times the minimum reserves ratio requirement. - Upper bound / maximum capital ratio preferred by the bank is 1½ times the CAR; whenever upper bound exceeded, excess capital distributed as dividends if deposits permit. - Interbank loans are unsecured and used only to meet liquidity needs (not to fund assets). - Liquidity and interbank market rules: - Liquidity shocks arise from saver withdrawals; in the basic model aggregate system liquidity is neutral since withdrawals are offset by deposit inflows elsewhere, but idiosyncratic bank runs can occur if withdrawals exceed reserves. - Interbank lending is rationed; creditor contribution proportional to creditor’s share of aggregate excess reserves; illiquid banks last in queue may receive insufficient interbank funding and require emergency liquidity assistance in extended versions (ELA not included in basic ABBA). ### VI. Policy-relevant findings and implications (from model description and simulation overview) - Regulatory interactions: - Capital and reserve requirements interact nonlinearly with bank behavior: tightening one requirement can have counterintuitive effects when another requirement or underlying credit risk is binding. - Specific model-derived policy implications: - Raising reserve requirements when capital requirements are too low relative to portfolio risk can increase number of bank failures (reserve tightening can force asset sales or liquidity shortfalls). - Higher capital requirements reduce direct counterparty risk but may increase interconnectedness as healthier banks engage more in interbank activity; elevated interconnectedness can raise systemic vulnerability to tail events. - Allowing banks remedial actions (deleveraging, risk-weight optimization) changes system responses compared to models that force failure once ratios breach regulatory minima — enabling analysis of credit supply effects of stricter capital requirements. - Modeling utility: - ABBA provides a computational laboratory to analyze what-if scenarios for competing policy proposals, capturing agent heterogeneity, endogenous network formation, and second-round propagation channels. *Source: wp17136 - 3. Banks’ out-degree for different regulatory requirements, in percent ..................................29* ### section III. ### wp17136 - section III ### Interbank loans and Emergency Liquidity Assistance (ELA) - Interbank loan rate is set equal to 1 percent. - All banks enjoying excess reserves lend to well capitalized but illiquid banks. - A lending bank lends an amount proportional to its share in total excess reserves in the banking system (see section III for details). - Undercapitalized but solvent banks borrow enough deposits from the ELA facility at a zero interest rate. - Solvent banks return funds to the ELA facility in the next period. - There are no penalties if failed banks do not return funds; costs to ELA are not accounted explicitly. ### Regulatory requirements - Capital requirements (measured as equity to risk-weighted assets) were allowed to take values in [0.04, 0.08, 0.12, 0.16]. - The minimum reserve ratio was allowed to take values in [0.03, 0.045, 0.06]. - Simulations: One hundred simulations, each comprising 240 periods, were performed for each of the twelve combinations of capital requirement and reserve requirement. This corresponds roughly to weekly observations over a period of 4 years. ### Simulation sequence (per period) - Credit losses in the loan portfolio, net income and provisions are evaluated. - If banks become insolvent, second-round effects (i.e. credit losses from interbank loans) on other banks are evaluated. If the second-round effects prompt additional bank failures, their impact on surviving banks is reassessed. - Well capitalized banks pay dividends. - If banks become undercapitalized, they perform risk-weight optimization (reduce balance sheet) in order to increase their capital ratio. - Insolvent banks are shut down and unwind their loan portfolios. - Banks experience either net positive and liquidity shocks as savers shift deposits from one bank to another. - Well capitalized but illiquid banks access the interbank market, borrowing from banks with excess reserves. - Solvent but undercapitalized banks access emergency liquidity assistance. - Banks facing a run fail and unwind their loan portfolios. ### Main findings — Bank failures: the interplay of solvency and liquidity requirements - At low capitalization levels, banks are more vulnerable to credit shocks and are more likely to be undercapitalized. - Banks unable to meet the regulatory capital requirement would have their access to the interbank market curtailed, raising liquidity risk. - When the capital requirement is 4 percent: - It is difficult for banks to keep their reserve ratio at the target level set at 50 percent above the minimum reserve ratio. - After a number of periods, banks on average are not able to meet the minimum reserve ratio and have to rely on the ELA facilities. - When capital requirements are 8 percent or above: - Banks on average can meet their target reserve ratios. - Interaction of capital and reserve requirements at low capital (4 percent): - Higher reserve requirements force banks to hold more reserves, reducing the impact of liquidity shocks and their associated failures. - However, when banks are undercapitalized, higher reserve requirements prevent banks from performing risk-weight optimization (which requires running down the reserves), leading to an increase in the number of credit failures that offsets the lower number of liquidity failures. - Dividend distribution constraint: - Simulations assume banks target capital ratio 50 percent higher than the minimum requirement (example: with a CAR of 8 percent, a bank will start distributing dividends if its capital ratio exceeds 12 percent). - The amount of reserves held by the bank constrains its ability to distribute dividends. - When capital requirement is low (4 percent), banks are more reluctant to pay dividends since they need to rebuild their capital base; paying dividends becomes more difficult as reserve ratios increase. ### Key statistics and reported figures (preserved as in source) - Capital adequacy ratios considered: 4 percent, 8 percent, 12 percent, 16 percent. - Minimum reserve ratios considered: 3.0 percent, 4.5 percent, 6.0 percent. - Percent failures reported in a summary table (excerpted): - Panel A (Minimum capital adequacy ratio = 4 percent), Failures, in percent: 43.8, 38.2, 46.8 for reserve ratios 3 percent, 4.5 percent, 6 percent respectively. - Panel B (Minimum capital adequacy ratio = 8 percent), Failures, in percent: 8.6, 0.0, 0.0 for reserve ratios 3 percent, 4.5 percent, 6 percent respectively. - Panel C (Minimum capital adequacy ratio = 12 percent), Failures, in percent: 6.0, 0.0, 0.0 for reserve ratios 3 percent, 4.5 percent, 6 percent respectively. - Panel D (Minimum capital adequacy ratio = 16 percent), Failures, in percent: 6.4, 0.0, 0.0 for reserve ratios 3 percent, 4.5 percent, 6 percent respectively. - Breakdown "of which (in percent)" for Panel A (CAR = 4 percent): - For reserve ratio 3 percent: 27.5 (liquidity), 16.3 (credit). - For reserve ratio 4.5 percent: 14.7 (liquidity), 23.5 (credit). - For reserve ratio 6 percent: 16.0 (liquidity), 30.8 (credit). ### Profitability - When banks are required to hold capital ratios of 8 percent or above: - Bank profitability (measured as return on equity) appears driven mainly by regulatory capital requirements and only slightly affected by the reserve requirement ratio. - For high capital ratios, return on equity is higher the lower capital requirements are. - Higher reserve requirements encourage banks to hold higher reserve levels (banks target a buffer above the regulatory requirement), which enhances capacity to distribute dividends and raise return on equity. - Exception when capital requirements are low: - When banks target a low capital ratio it becomes more difficult to pay dividends, which hurts the return on equity. - Figure 6 mirrors results in Figure 5 (mean capital ratio patterns). ### Interconnectedness - Interconnectedness arises endogenously as banks facing liquidity pressures borrow reserves in the interbank market. - In the NetLogo implementation, red lines show interbank loans from banks with excess reserves to banks facing liquidity problems. - Example: each borrowing bank receives loans from four banks (in-degree of four); lending banks have an out-degree of two. - Over time, in-degree of a bank changes randomly; borrowing banks may switch to lending and vice-versa. - In several dates, there can be as many as seven creditor banks in a system with only ten banks. - Average connectivity statistics: - On average, the in-degree of a bank is zero ninety percent of the time. - On average, the out-degree of a bank is zero about seventy percent of the time. - When banks are net creditors, they lend on average to one bank twenty percent of the time, and to two banks the remaining ten percent of the time. - Long-run perspective: - Interconnectedness is typically low, though occasionally the system becomes highly connected with a few banks connected to a large number of creditor banks. - In-degree values of six and higher realize with certain frequency at about seven to nine percent of the time, especially when reserve requirements do not exceed 4½ percent. - Interconnectedness arises mainly because many banks lend to a single bank rather than several banks borrowing from a single bank. - The maximum number of out-degrees for a single bank seldom exceeds three during the simulations. - Paradoxical effect: - An increase in capital requirement could increase interconnectedness when initial capital levels are low, because higher capital ratio targets make it less likely banks are undercapitalized, facilitating access to the interbank market when facing liquidity shortages. - Holding the capital requirement constant, higher reserve requirements induce higher reserve targets, reducing the need for interbank borrowings and interconnectedness. ### Conclusions - ABBA is a simple modular agent-based model for analyzing risks and interactions in the banking system that accounts for heterogeneity and adaptive behavior. - The model accommodates endogenous bank networks through interbank loans and dynamic bank balance sheet adjustment via risk-weight optimization, dividend payments, and loan book expansion. - ABBA can support policy guidance on financial regulation and evaluate risks associated with what-if scenarios; numerical simulations uncover linkages between regulatory requirements and solvency, liquidity and interconnectedness risk. - The current formulation captures dynamics of a traditional banking system (banks raise deposits, interbank loans meet liquidity shortages). - Extensions are straightforward in ABBA (e.g., wholesale investors as different agents, collateralized loans requiring a collateral asset proto-agent and price dynamics, richer depositor behavior driven by group dynamics). - These extensions could better fit dynamics of banking systems like those in the United Kingdom and the United States and complement models such as Bookstaber, Paddrik, and Tivnan (2014). *Source: Author’s calculations.* ### References ### References ### Agent-based models, simulation methods, and computational tools - Anselmo, P. and M. Planck, 2012, “Solvency Dynamics of an Evolving Agent-Based Banking System Model,” Working Paper, New Mexico Institute of Mining and Technology. - Axtell, R., D. Farmer, J. Geanakoplos, P. Howitt, E. Carella, B. Conlee, J. Goldstein, M. Hendrey, P. Kalikman, D. Masad, N. Palmer, and C. Yang, 2014, “An Agent-Based Model of the Housing Market Bubble in Metropolitan Washington D.C.” mimeo., (George Mason University, Oxford University, Yale University and Brown University). - Aymanns, C., and J.D. Farmer, 2015, “The Dynamics of the Leverage Cycle,” Journal of Economic Dynamics and Control 50, Special Issue: Crisis and Complexity, CRISIS Workship 2013, pp. 155–179. - Bookstaber, R., 2012, “Using Agent-Based Models for Analyzing Threats to Financial Stability,” Office of Financial Research, Working Paper No, 0003 (U.S. Department of the Treasury). - Bookstaber, R., and M. Paddrik, 2015, “An Agent-Based Model for Crisis Liquidity Dynamic,” Office of Financial Research, WP 15-18, U.S. Department of the Treasury (Washington, D.C.) - Bookstaber, R., M. Paddrik, and B. Tivnan, 2014, “An Agent-Based Model for Financial Vulnerability,” Office of Financial Research, WP 14-05, U.S. Department of the Treasury (Washington, D.C.) - Ismail, O., 2012, “An Agent-Based Computational Model for Bank Formation and Interbank Networks,” Ph.D. dissertation, School of Computational Engineering and Science, McMasters University. - North, M., and C.M. 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