Department of Economics

Financial regulations and bank credit to the real

economy

James&Porter1,&Giulia&Iori1,&Giampaolo&Gabbi2,3,&Saqib&Jafarey1&1City&University&London&

2Universita&degli&Studi&di&Siena&3SDA&Bocconi&School&of&Management&

&&

Department of Economics Discussion Paper Series

No. 14/04

Financial regulations and bank credit to the real

economy

James Portera, Giulia Ioria, Giampaolo Gabbib,c, Saqib Jafareya,⇤

aDepartment of Economics, City University London, London, United Kingdom

bDepartment of Management and Law, Universita degli Studi di Siena, Siena, Italy

cSda Bocconi School of Management, Milan, Italy

Abstract

The modelling of interbank markets has typically focused on them in isola-tion. This leaves unanswered questions concerning the impact of financialregulation on real economic performance. We present a new agent-basedmodel focusing on the linkage between the interbank market and the realeconomy with a stylised central bank acting as lender of last resort. Usingthis model we address the tradeo↵ between stability and economic perfor-mance for di↵erent structures of the interbank market. We also explore thee�cacy of recent regulatory changes using our richer model.

Keywords: Financial Regulation, Bank Lending, Systemic RiskJEL: G21, G28, E32

IThe research leading to this paper has received funding from the European Union, Sev-enth Framework Programme FP7/2007-2013 under grant agreement CRISIS “ComplexityResearch Initiative for Systemic Instabilities”, nr. 288501. The authors thank TizianaAssenza, Jacob Grazzini, Alessandro Gobbi and Gabriele Tedeschi for helpful commentsand discussions. All remaining errors and omissions are our own.

⇤Corresponding author: e-mail: s.s.jafarey@city.ac.uk

Preprint submitted to Journal of Economic Dynamics and Control March 10, 2014

1. Introduction

Among the most commonly cited factors for the 2008 financial and eco-nomic crisis are the excessive leverage that banks had built up under theprevious Basel guidelines and the interconnectedness of the banking systemwhich gave it a systemic dimension. In the aftermath of the crisis, a consul-tative document published by the Basel Committee (2009) highlighted boththese factors. The document cited as one of the main reasons the economicand financial crisis became so severe, that the banking sectors of many coun-tries had built up excessive on- and o↵-balance sheet leverage. At the sametime, many banks were holding insu�cient liquidity bu↵ers to face stressedand contingency outflows in case of the evaporation of the funding sources.

The banking system therefore was not able to absorb the resulting sys-temic trading and credit losses nor could it cope with the re-intermediationof large o↵-balance sheet exposures that had built up in the shadow bankingsystem.

The document also identified as one of the main shortcomings of the pre-vious regulatory regime, that it placed too great a focus on idiosyncraticrisk, i.e. micro-prudential regulation, at the expense of systemic risk, whichwould call for macro-prudential regulation. The post-crisis regulatory regimewas therefore designed to include a significant macro-prudential component.The new proposals can be summarized as follows: ensuring that an adequateshare of a bank’s capital consists of ‘plain vanilla’ common equity, with fullloss-absorbing potential; simplification and consistency in the definitions ofboth Tier 1 and Tier 2 capital, focusing on financial instruments which canabsorb losses on a going concern basis and further international harmonisa-tion in the definition and regulation of hybrid and innovative capital.

The new (Basel III) leverage ratio is defined as as a minimum percentage(3%) of the capital measure to the exposure measure. The capital measureconsists of Tier 1 capital as defined by the risk-based capital framework. Theexposure measure is defined as the sum of the following exposures: (i) on-balance sheet exposures; (ii) derivative exposures; (iii) securities financingtransaction exposures; and (iv) o↵-balance sheet items. One of the impactsof this new approach is that it considerably widens the definition of whatconstitutes leverage in the banking system. Thus even without altering thestatutory leverage ratios, it would have considerably increased the burden onbanks to either increase their capital or reduce their intermediation activity.

The leverage ratio was disputed by Beltratti and Stulz (2012) since banks

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which experienced the strongest market value decrease were not correlatedwith those with the highest leverage ratio and because, substantially it repre-sents a strong deviation from the prudential regulation based on the capitaladequacy calibrated on the risk weighted assets. On the other hand, ac-cording to Blum (2007) the leverage ratio would reduce banks incentivesto understate their true risks by reducing the ex ante option value. Haldaneand Madouros (2012) empirically support the thesis that the leverage ratio, asimpler measures than those introduced within the first pillar of Basel 2 regu-lation, appears to have greater pre-crisis predictive power than risk-weightedalternatives.

While advocates of tougher regulation generally support this tightening,its critics point to the fact that it is going to push banks towards issuingmore equity which is a costlier form of financing than debt since equityholders require higher returns than debt holders. Cecchetti (2010) counter-argues that banks could meet the new rules by a combination of retainingmore of their earnings, decreasing remuneration rates on debt liabilities andreducing overhead costs including managerial compensation. In addition, ifthe reforms make the banking system safer, the cost of raising equity willcorrespondingly fall. Since many of these e↵ects are likely to take place overa longer term, whether or not they occur while depend on whether in theshort run, obliging banks to reduce their leverage ratio will increase systemicsafety more than it reduces the intermediating role of the banking system,which in e↵ect is the engine of growth for the real economy. If that occurs, itwill be more likely that the system will move into a longer term equilibriumwith higher safety and no sacrifice in e�ciency.

The aim of this paper is to study this question, using an agent basedmodel of the banking sector coupled to a simplified real sector. The modelof the banking sector used in this paper has been developed as part of alonger-term project on creating an agent-based model with endogenous de-termination of both the real macroeconomy and the financial sector. Whilethe complete articulation of the model is a work in progress, and our currentmodel cannot be used to examine all the ramifications of higher leveragerules, it is rich enough in terms of endogenising banks’ choices between howto invest their available funds between real sector lending, interbank lendingand cash reserves and indeed which sources to obtain leverage from (equityis considered fixed in the present model), that it can be used to address thebasic tradeo↵ between stability and e�ciency of the banking system.

A number of agent-based models have considered the interrelation be-

3

tween the credit market and the real economy and the possibly de-stabilisingrole of feedback loops between the two systems (Lenzu and Tedeschi (2012),Tedeschi et al. (2012), Battiston et al. (2012), DelliGatti et al. (2009)). How-ever, in these models the emphasis is on the behaviour of firms and house-holds, with banks providing credit following somewhat unrealistic rules ofthumbs. In our model we take the opposite approach. We provide an agent-based micro-foundation to the strategies of banks while simplifying the role ofhouseholds and firms, whose behaviour is captured by a stochastic processesfor deposit fluctuations and demand for loans.

The model builds on Iori et al. (2006) by endogenising (1) the allocationof a bank’s funds between firm-loans, inter-bank loans, and cash reserves; (2)counter-party rating schemes and interest adjustment models; (3) lending asdependent on counter-party credit risk; (4) learning and strategic behaviourof banks; (5) banks decision rules are made contingent on leverage require-ments and inter-bank exposure.

The results of our model provide some support, albeit qualified, to theconcerns raised by critics of the recent tightening of regulatory capital re-quirements under the new Basel framework. While low ceilings on leverageratios can protect banks from idiosyncratic as well as systemic risk, theydo have an anti-competitive e↵ect which hurts borrowers in the real econ-omy, especially in times when the demand for bank credit is high. At thesame time, relaxed leverage ceilings can make banks particularly vulnerableto systemic failure in times when demand for bank credit is low, so whilecounter-cyclical leverage constraints, as proposed by some observers, mightencourage the banking system to extend cheaper credit to the real sectorit also exposes it to greater systemic risk especially when it is already vul-nerable to such risk. Other results include the possibility that greater bankconnectivity can have a non-monotonic e↵ect on bank stability, first increas-ing the risk of contagion and then decreasing it. Finally, there appears tobe no “one-size-fits-all” solution to financial regulation as both the economicperformance of the banking system (by which we mean its role in provid-ing credit to the real economy) and its stability vary in relation to demandconditions, the structure of the interbank market and regulatory settings.

The rest of the paper is structured as follows. Section 2 covers relatedliterature; Section 3 describes the model; Section 4 presents results frombaseline simulations meant to ensure that the model produces sensible results.Section 5 discusses the e↵ects of regulatory ceilings on the allocations of bankfunds, interest rates on various kinds of loans, profitability of banks and firms

4

and the stability of the banking system. Section 6 concludes and draws policyimplications.

2. Literature Review

The literature on systemic risk in credit markets has developed over sev-eral dimensions. Some authors have analysed the relationship between thenetwork structure of the interbank market and its resilience to di↵erent kindof shocks (Iori et al. (2006); Battiston et al. (2012); Lenzu and Tedeschi(2012); Georg (2013); Gai et al. (2011)). Others have focused on the e↵ectsof asset fire-sales, roll-overs of risk and portfolio overlaps (Nier et al. (2007),Caccioli et al. (2012); Anand et al. (2012)) as sources of contagion. A fewstudies have considered the possible feedback loops between the macroecon-omy and the financial sector (Lenzu and Tedeschi (2012), Tedeschi et al.(2012), Battiston et al. (2012), DelliGatti et al. (2009)).

Broadly, two di↵erent approaches have been adopted. One type of modelassumes the network of exposure among market participants as given, possi-bly calibrated to real market data. Stress scenarios are simulated by applyingidiosyncratic, or system-wide shocks, and their e↵ects are monitored in theparameter space. The second type of models assign behavioural rules, eitherad hoc or micro-founded, to economic agents and organisations. Balancesheet and reciprocal exposures are endogenously determined by the portfo-lio allocation strategies. Defaults events are endogenously generated in thiscontext, even if the dynamics of the system are driven by exogenous riskfactors.

Gai and Kapadia (2010) is an influential example of the first type ofmodel. The authors explore how the probability and potential impact ofcontagion is influenced by aggregate and idiosyncratic shocks, changes in net-work structure, and asset market liquidity. The authors show, via impulseresponse exercises, that the interbank market presents a robust-yet-fragileproperty: while the probability of contagion might be low, the e↵ects canbe extremely widespread when they occur. Caccioli et al. (2012) extend themodel of Gai and Kapadia (2010) to account for a number of empiricallyobserved properties of financial networks, namely heterogeneous degree dis-tribution, heterogeneous assets distribution and degree correlations amongconnected banks. An heterogeneous distribution of assets increases the prob-ability of contagion even with respect to random failures. An increase of thecapital bu↵er of a few big banks can significantly reduce the contagion prob-

5

ability of highly connected networks. A policy targeted to increase in thecapital bu↵er of the most connected bank is ine↵ective. Correlations, de-pending on their direction, can either increase or decrease the probabilityof contagion. Networks with heterogeneous degree distributions are moreresilient to contagion triggered by the random failure of a single bank, butmore vulnerable to contagion triggered by the failure of highly connectedbank nodes. A power law distribution of balance sheet size is shown to in-duce ine�cient diversification making the system more prone to contagion.Dis-assortative mixing is shown to enhance the stability of the system.

Caccioli et al. (2012) analyse a model of financial contagion driven by com-mon asset holdings. The relevant parameters for the model are the averagediversification (the average number of assets held by banks) and the initialleverage of banks. Contagion occurrences are non-monotonic in the diversi-fication parameter while increasing leverage increases the overall instabilityof the system, and there is a critical level of leverage below which global cas-cades do not occur for any value of diversification or crowding. Anand et al.(2012) analyse how the role of macroeconomic fluctuations, asset market liq-uidity and network structure in determining contagion and aggregate lossesin a stylised financial system. Calibrating the model using publicly availabledata from advanced-country banking sectors, they illustrate how macroeco-nomic fluctuations and asset price feedback e↵ects intertwine to generate fattailed distributions of banks losses and make large-scale financial disruptionpossible.

Iori et al. (2006) introduce one of the first agent-based models of con-tagion via interbank lending within a dynamical framework that leads toendogenously generated interbank exposures. In the model banks face riskfree, but random, investment opportunities and exchange reserves in theovernight interbank to counteract exogenous deposit fluctuations and to sat-isfy their reserve requirements. Iori et al. (2006) highlight the importance ofagents’ heterogeneity in explaining the e↵ects of interbank linkages on sys-temic risk. With homogeneous banks, an interbank market unambiguouslystabilizes the system, with heterogeneity, knock-on e↵ects become possible.The stabiliyzing role of interbank lending remains in the sense that idiosyn-cratic banks defaults become less likely, but when they occur their systemicimpact is stronger, revealing the robust-yet-fragile property of Gai and Ka-padia (2010). Moreover the authors distinguish between direct or indirectcontagion. A direct e↵ect arises via knock-on from a failing bank to its di-rect creditors. An indirect e↵ect arises when, following the defaults of one or

6

several banks, the interbank market liquidity is depleted, reducing the oppor-tunities for interbank funding. In the model indirect e↵ects are much moreimportant than the direct ones. The indirect contagion e↵ect provides analternative explanation to the credit crunch aspect of the liquidity hoardinghypothesis.

Ladley (2013) extends the model of Iori et al. (2006) in a partial equi-librium setting in which banks’ portfolios and the inter-bank interest rateare determined endogenously. The author investigates the e↵ects of the mar-ket connectivity structure on contagion, under both individual and systemicshocks, and assesses a number of mechanisms for mitigating the impact ofsystemic risk. The author recognises that when shocks are economy-wide,interbank linkages spread systemic instability. On the contrary when shocksare limited, interbank linkages improve the stability of the system. The ef-fect of interbank linkages on systemic stability thus varies with the nature ofthe shock and there is no optimal network structure resistant to all kind ofshocks.

Georg (2013) considers an interbank market that includes both commer-cial banks and a central bank. Commercial banks optimise their portfoliosbetween risky investments and riskless reserves. Banks are subject to twosources of uncertainty: fluctuating deposits and risky investments. Illiquidbanks can borrow both on an un-collateralized interbank market and throughcollateralized central bank loans. Georg (2013) shows that the interbanknetwork structure plays little role on systemic stability during normal times,while it becomes crucial during periods of financial distress (captured by ahigher volatility of deposit fluctuations and returns on investments). Duringa crisis period networks with large average path length are more resilient tofinancial distress. Central bank intervention can alleviate financial distressin the short run. However if the central banks accepts a large proportion ofbanks assets as collateral, it causes a crowding-out e↵ect reducing volumeson the interbank market.

3. The Model

The economy consists of four types of players: commercial banks (orsimply banks), firms, households and a Central Bank. Households are thesource of bank deposits and firms are the primary recipient of loans. Thesupply of deposits from households to firms is assumed to be constant and isredistributed each period amongst existing banks by means of an exogenously

7

specified zero-sum stochastic process. Firms generate demands for loans frombanks and this too follows a random process. Each firm has a fixed andexogenous probability of default on loans. The Central Bank stands ready tosupply liquidity as needed by banks as well as to accept excess reserves frombanks at rates that it sets. These rates also establish the corridor betweenwhich bank lending to firms and to each other takes place. Figure 1 belowdescribes the system.

Firm

Firm

Macroeconomy

Bank

Bank CentralBank

Lending/depositLending

Deposits

IB

Firm

Firm

Macroaggregate

Bank

Bank CentralBank

Lending/depositLending

Deposits

IB

Macro-link

Figure 1: A schematic overview of the economy.

3.1. Balance sheets

There are NB commercial banks, NF firms and one Central Bank. Theassets of commercial bank j are defined as:

Aj(t) = Rj(t) + Lj(t)

Lj(t) = L

fj (t) + L

bj(t),

L

fj (t) =

NFX

i=1

L

fj,i(t)

L

bj(t) =

NBX

k=1

I

`j,k(t)

where Rj(t) are cash reserves, if any, held by bank j with the central bankat time t L

fj,i(t) is the book value at time t of a loan extended from bank j

8

to firm i, and I

`j,k(t) is the book value at time t of a loan extended from bank

j to bank k (I`j,j(t) = 0).The liability side of the bank’s balance sheet is given by:

Lj(t) = Dj(t) +NBX

k=1

I

bj,k(t) + Cj(t),

where Lj(t) represents the liabilities of bank j at time t; Dj(t) is the value ofdeposits held at bank j, Ibj,k(t) is the book value at time t of a loan extendedfrom bank k to bank j and Cj(t) is the value of any funds borrowed fromthe Central Bank at time t. Note that in any period t, either Cd

j (t) � 0 andC

bj (t) = 0 or Cb

j (t) � 0 and C

dj (t) = 0.

By definition the equity of the bank is:

Ej(t) = Aj(t)� Lj(t),

Banks choose a leverage ratio � that determines the proportion of loansto equity in their portfolio Lj(t) = �jEj(t). This ratio cannot exceed themaximum leverage ratio allowed by regulators, but it might be less than that.We assume, for simplicity, that if banks wish to increase leverage (withoutviolating the regulatory constraint) they can always find funds by makinguse of the Central Bank window although the costs of these funds will benormally higher than borrowing from other banks.

3.2. Beginning of day regulatory check

At the beginning of the trading day banks pay interest at the constantand exogenous rate r

D to depositors, repay their interbank loans (if any) atthe rate rbj,k(t� 1), loans from the Central Bank (if positive) at the constantand exogenous rate rH , receive repayment on loans from each borrowing firmi at the rate 1+ r

fj,i(t� 1) (unless firm i defaults) and each borrowing bank j

at the rate 1+ r

`j,k(t�1) (unless bank j defaults), and receive interest on the

cash deposited (if positive) in its central bank account at the rate r. Bank’sequity is adjusted as follow

Ej(t) = Ej(t� 1) + dEj(t)where

dEj(t) = Rj(t�1)(1+r

L)⇥I�Cj(t�1)(1+r

H)⇥(1�I)+NFX

i=1

L

fj,i(t�1)[(1+r

fj,i(t�1))+

9

NBX

i=1

I

`j,i(t�1)(1+ r

`j,i(t�1))�

NBX

i=1

I

bj,i(t�1)(1+ r

bj,i(t�1)�Dj(t�1)(1+ r

D).

where I is an indicator function which takes on the value 1 if Rj(t� 1) > 0,Cj(t� 1) = 0 and 0 if Rj(t� 1) = 0, Cj(t� 1) > 0. If bank equity becomesnegative at this point the bank goes into default.

3.3. Lending to firms

Banks receive demands for loans from firms. Firms can only borrow frombanks with which they share a connection. Lending to firms is the mainsource of both reward and risk to the banking system. Reward, becausefirms are able to exploit investment opportunities that provide real returnsto the economy and risk, because these opportunities are idiosyncraticallyrisky and might lead the firm to default on its loan.

The probability that a firm defaults is ⇢ which is exogenous, identicalacross firms and known to banks. The demand size is random, distributedaccording to �(2, d/2), where d is the average demand for loans. Loans tofirms are for one period. For simplicity we assume that firms either pay o↵the loan o↵ in full (with interest) or do not pay at all (default). Firms havea stepwise demand function in each period. They will borrow all of theirdemand at any rate up to this maximum, but once the rate is higher theyborrow nothing.1

The lending rate to firm is updated so to try and achieve the targetleverage level. Thus if the bank has not been able to lend all the desired levelto firms it reduces the rate otherwise it increases it. The rate is boundedfrom below by the bank’s marginal funding cost cj(t) per unit of funds. cj(t)varies with the source of funding as will be explained below:

The reservation (lowest) price at which bank j is willing to lend to firmi taking into account the risk of default is described by the condition

(1 + r

minij (t))(1� ⇢) + �⇢ � (1 + cj(t)) 8j, (1)

1These rates are heterogeneous leading to a downward sloping demand curve. Oneway to justify this is to assume that firms are perfectly competitive, risk-neutral profitmaximisers that receive idiosyncratic investment opportunities i that pay ⇧i > 0 withprobability 1� ⇢ and 0 with probability ⇢. The maximum interest rate that firm i wouldthen be willing to pay would be the one that makes it break even in expectation.

10

or

r

minij (t) =

1 + cj(t)]� �⇢

1� ⇢

� 1, (2)

where rminij (t) is the minimum rate at which bank j will lend to firm i and � is

the recovery rate in case of default (for simplicity in the case of simulations,we assume that � = 0).

The above condition states that a bank will not lend to a firm at aninterest rate which lies below its expected cost of funds cj(t). cj(t) is in turna weighted average of interest rates paid by the bank on previous borrowings,where the weights represent the di↵erent sources of funds.

cj(t) = !

Dj (t)r

D + !

bj(t)E[rbj(t)] + !

Cj (t)r

H (3)

where E[rbj(t)] is the expected cost of borrowing on the interbank market,given by

E[rbj(t)] =T bX

⌧=1

r

bj(t� ⌧)

I

bj (t� ⌧)

PT⌧=1 I

bj (t� ⌧)

(4)

which is the weighted average of past borrowings from the interbank marketby bank j with T

b being the length of memory of past rates. If in some periodt � ⌧ the bank did not borrow then r

bj(t � ⌧) = 0. !

ij(t) are the respective

shares of source i in bank j

0s total financing (i = D, I

b, C)) in recent history

immediately preceding time t, rD and r

H are known constants.Note that the bank may not achieve the desired level of lending to firms.

L

fj (t) represents the actual amount of loans to firms provided by banks j at

time t.

3.4. Shocks to deposits

After banks have committed to lend to firms they receive an exogenousshock on deposits dDj((t) . This is a re-distributive shock that proxies for de-positors’ partiality for successful banks: a proportion of each bank’s depositsis reallocated to another bank, with the likelihood of selection proportionalto equity size (this allows us to mimic depositors as moving to profitablebanks without modeling the competition for deposits in detail).

In case the shock on deposit on bank j is negative and large enough that|dDj((t)| > Rj((t) then bank j enters the interbank market and requests aninterbank loan of size

I

bj ((t) = dDj(t)�Rj((t) (5)

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On the contrary, if the shock on deposits is positive, or if it is su�cientlysmall that the bank’s reserves remain positive, Rj(t) > 0, the bank will tryand lend Rj(t) in the interbank market.

3.5. The interbank market

In case banks end up with negative positions on their central bank ac-counts after the shock, they enter the interbank market. Lending on theinterbank market does not bear liquidity risk and banks are willing to lendall their excess cash, as long as they can make an expected profit (accountingfor the risk of default of borrowers) at least comparable to leaving reserveswith the Central Bank. Banks set borrowing rates which they o↵er to payto lending banks in the interbank market. This is constrained by the centralbank corridor and all loans are overnight. The rate is updated by an adjust-ment mechanism (depending on their past ability to borrow, banks eitherincrease or decrease the rate).

Lenders’ reservation rates are determined by the conditions

(1 + r

`j,k((t))(1� p

bk) + �p

bk = (1 + r

L) 8j, k (6)

Lender j accepts any o↵er from a borrower k as long as its reservation priceis lower that the rate o↵ered by the borrower:

r

`j,k((t) =

(1 + r

L � �p

bk)

1� p

bk

� 1 < r

bk((t)) (7)

Borrowers compete for liquidity and they post bids at the rate

r

bk(t) =

(1 + r

L � �p

bk)

1� p

bk

� 1 + rk((t) (8)

where rj(t) is a mark-up o↵ered by borrower k over a lender’s reservationlevel. The premium is specific to borrower k and takes into account theriskiness that lending to that borrower entails.

Borrowers post their bids and lenders, in random order: observe theirneighbours borrowers bids, compute the profitability of each bid as

⇡i,j(t) = [rbj(t)� r

`i,j(t)] (9)

rank them and fill them in order of profitability.

12

We assume that lending is restricted to an exogenous pre-determinednetwork (to mimic OTC lending). This is currently done via a fixed (foreach simulation) Erdos-Reyni random graph. This allows us to go from theextreme of an anonymous fully connected market to a very weakly connectedmarket.

3.6. Central Bank

Failing to borrow all they need from the interbank market, solvent butilliquid banks can borrow from the Central Bank at the rate rH . We assumethat the Central Bank accepts loans to firms as collateral without charginga haircut. Thus a solvent bank’s liquidity needs will always be satisfied bythe Central Bank. For a more realistic version of the model, it would beimportant to model funding constraints explicitly, for example as done inGeorg (2013).

Banks with excess liquidity earn interest r

L on central banks account,while banks that borrow liquidity from the Central Bank pay r

H> r

L.In addition, borrowing from the Central Bank facility carries a stigma e↵ectwhich makes it more di�cult for the bank to borrow on the interbank marketin future periods.

3.7. Bank defaults

We assume two di↵erent scenarios to estimate the probability of defaultby bank. In the first case we assume that the probability of default of eachbank is common knowledge in the market. In practice we make two simpli-fying assumptions about this probability. First that, given the amount ofloans committed to firms and the bank’s equity, the probability of defaultby a bank is calculated from the probably of defaults by its debtor firms(i.e. probability that losses on firm lending exceed equity). In this sense,banks ignore contagion e↵ects on each other’s defaults and only concentrateon ‘fundamental’ defaults. Second, we use a normal approximation to thebinomial distribution of losses which assumes that each bank-firm loan is ofequal size, has the same probability of default, and the defaults are inde-pendent. This is consistent with the Basel approach to estimating defaultprobability.2

2In the case of correlated defaults, one could use the one factor Vasicek model used tocalculate the Internal Ratings-Based (IRB) approach of Basel II

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The probability of default by bank k with loans to N

fk (t) firms is

p

bk = P

�N

�k (t)L

f> Ek(t)

�(10)

where L

f is the standardised size of a loan and N

�k are the number of bank

k

0s non-performing loans (N �k (t) < N

fk (t)).

The second approach assumes that banks cannot estimate each other’sdefault probability and lending banks start with a uniform prior over allborrowing banks, which is equal to the historical average rate of default inthe interbank market over the past T

h periods. But if a bank goes to theCentral Bank to seek funds, its borrowing is observed by other participantswho then update their prior about that bank and deny it loans over a fixednumber of future periods, T g.

In the event of a bank defaulting, its available funds are distributed firstto depositors, then to pay back Central Bank loans if any, and finally to paywhatever is left over to its interbank creditors in proportion to their loans.In order to keep the number of banks constant, we assume that for eachdefaulting bank, a new bank is created by the regulator whose initial size isa fraction of the initial size of the original banks. The resources to set up thenew bank are raised by a proportionate tax on the equity of existing banks.In this way the banking system as a whole su↵ers a loss beyond the unpaiddebts of the defaulting back. This mechanism also reflects some of the newproposals for resolving bank failures.

3.8. Learning

For rate bidding behaviour in the firm bank market or the interbankmarket, we assume that banks use simple threshold adjustment mechanisms.If they have been successful in past bidding they decrease the competitive-ness of their o↵er by trying to extract a bigger surplus, whereas if they havebeen unsuccessful they make their o↵er more competitive. Rates are furtherconstrained by the costs and benefits of pursuing alternative scenarios (for ex-ample, borrowing from the Central Bank or placing deposits with it). Whilethe threshold levels are arbitrary they are calibrated to meet the bank’s maintarget, which is its target leverage ratio.

3.8.1. Bank rates to firms

The lending rate to firms is updated so to try and achieve the targetlevel Lf

j (t). Banks calculate how much they managed to lend to firms in the

14

previous period, Lfj (t � i), compare it to their target L

fj (t) and adjust the

rate as follows:

r

lk(t) =

(1 + r

L � �p

bk)

1� p

bk

� 1 + r

lk(t) (11)

where:

r

lk(t) = r

lk(t� 1) +�r

lU(0, 1) if L

fj (t� 1) < ⌘

l0L

fj (t� 1)

r

lk(t) = r

lk(t� 1) if L

fj (t� 1)) 2 (⌘l0L

fj (t), ⌘

l1L

fj (t� 1)))

r

lk(t) = max[cj(t), r

lk(t� 1)��r

lU(0, 1), 0] if L

fj (t� 1) > ⌘

l1L

fj (t� 1)

where ⌘

l0 and ⌘

l1 (⌘l0 < ⌘

l1) are threshold proportions of fulfilled supply from

the previous period.

3.8.2. Interbank market spreads

Spreads on interbank market are updated following a similar rule as ap-plies to bank lending to firms. Things are a little more complex as bankshave di↵erent probabilities of defaults which are taken into account. Theyactually bid in terms of a premium on top of a rate which makes lending (inexpectation) equivalent to the risk free central bank deposit facility.

Borrowing banks calculate how much they managed to borrow in the lastperiod in which they were borrowers (and did not make use of the CentralBank), t� ⌧ , Ibk(t� ⌧), compare it to their target liquidity demand I

bk(t� ⌧),

and adjust the rate as follows.

r

bk(t) =

(1 + r

L � �p

bk)

1� p

bk

� 1 + r

bk((t) (12)

where:

r

bk(t) = r

bk(t� ⌧) +�r

bU(0, 1) if I

bk(t� ⌧) < ⌘

b0[I

bk(t� ⌧)]

r

bk(t) = r

bk(t� ⌧) if I

bk(t� ⌧) 2 (⌘b0I

bk(t� ⌧), ⌘b1I

bk(t� ⌧))

r

bk(t) = max[rbk(t� ⌧)��r

bU(0, 1), 0] if I

bk(t� ⌧) > ⌘

b1I

bk(t� ⌧)

where ⌘b0 and ⌘

b1 (⌘0 < ⌘1) are threshold proportions of fulfilled demand from

the last time bank k borrowed on the interbank market (that time is denotedby t � ⌧ . Note that although not explicit in the above formula, bank k willnever o↵er a mark-up that makes its overall borrowing rate rbk(t) exceed r

H ,which is the cost of borrowing from the Central Bank.

15

3.8.3. Leverage Target

Banks initially choose randomly a leverage target �i in an interval � 2(�m,�m + ��,�m + 2��, · · · ,�M) and update it at regular intervals T� inorder to maximise their profitability. At the beginning of each period (unlessthey default) banks look at the target level achieved in the previous previous,�, (which may be smaller than their target level) round it to closest possiblevalue target �j and update the profitability of �j as follow

⇧(�j) = ⇧(�j)e�� +Rj(t� 1)(1 + r

L)⇥ I � Cj(t� 1)(1 + r

H)⇥ (1� I)+

NFX

i=1

L

fj,i(t� 1)[(1 + r

fj,i(t� 1)) +

NBX

i=1

I

`j,i(t� 1)(1 + r

`j,i(t� 1))

�NBX

i=1

I

bj,i(t� 1)(1 + r

bj,i(t� 1)�Dj(t� 1)(1 + r

D).

where � is a memory decay rate.After each T� steps banks select a new leverage ratio �i with probability

p(�i) =e

�⇧(�i)

Pk e

�⇧(�k)(13)

4. Simulations

For our simulations we fix the number of banks at 100 as it is roughlyin line with the number of banks in several Eurozone economies and allowsfor a non-trivial interbank market. The central bank lending and borrowing(deposit facility for banks) have rates rH , rL which are fixed for each simu-lation; the latter o↵ers a risk-free return for banks. Banks choose a leveragelevel (determined by their strategy) � which is a multiple of their equity andthis becomes their target to lend to firms. Bank are initialised with a levelof equity Ej(0) and deposits Dj(0).

4.1. Basic Tests

We first consider a simple version of the model, where the deposit raterd = 0 and the probability of default is low (⇢ = 1%). We want to ensurethat the model is well-behaved.

Figure 2 depicts the average performance of the system for varying levelsof the size of the real economy (proxied by the ratio of firms to banks) over 25

16

runs of 1000 periods each.3 Model I refers to the interbank scenario in whichbanks have complete information (the scenario with limited information islabelled Model II).

The left panel of Figure 2 shows how banks allocate on average theirfunds in terms of both destination and source: loans to firms, loans to eachother, reserves held at the Central Bank and loans taken from it. The rightpanel depicts the interest rates associated with each of these allocations.The results are not surprising: as the number of firms per bank increases,banks lend more to them. Initially they also lend more to each other asthe interbank market helps to spread the underlying demand for liquidityacross the system. This lending plateaus at some point indicating that aftera point, each bank has enough of its own real sector borrowers. At thispoint banks begin to make use of the Central Bank facility. This leads toa steady increase in the cost of borrowing as the Central Bank facility isthe most expensive source of funds and this is passed on as higher interestrates charged to firms. The use of the Central Bank reserve facility steadilydiminishes in this process.4

Figure 3 compares the baseline behaviour of the economy in a single runof the model, comprising 1000 periods, for three discrete scenarios concerningthe ratio of firms to banks: low, medium and high respectively. These plotsalso reflect results that are largely expected. In each scenario, the economytends to have a stable steady state, with smaller economies showing lesslending to the real sector than larger ones. Bank rates for lending to firmsalso increase with the size of the economy, reflecting both the greater capacityof the economy to generate real returns and the greater competition amongreal sector borrowers for credit.

One interesting feature of the plots is that the medium and large economiestend towards cyclical behaviour. Note that the firm-bank ratios in both these

3Averaging over a greater number of runs does not qualitatively change the nature ofthe plots.

4The interbank lending rate appears to behave non-monotonically, falling and thengradually rising again. This seems to reflect the fact that initially, when the number offirms per bank is low, there are more banks that are not getting any loan o↵er acceptedand are competing against each other in lending to the banks that are lining up loancommitments to firms. Once the size of the economy is large enough, there remain fewbanks with spare funds to lend on the interbank market and they can extract higher ratesfrom borrowing banks.

17

Figure 2: Allocations and interest rates with varying sizes of the real economy: Model I.Firm Lending (Blue), Interbank Lending (Red), Central Bank Reserves (Green), Central Bank Borrowing (Turquoise),Average Cost of Funds (Purple).

cases lie along the flat portion of the interbank lending line in the left panelof Figure 2. This suggests that the average amount lent by banks to eachother does not vary with greater demand for interbank loans by the banksthat are lending to firms.

This observation is consistent with the period-by-period time path forinterbank lending in Figure 3, which shows a roughly constant mean in bothmedium and large economies. Thus, as bank loans to firms grow, banksmake increasing use of central bank funds (this is more obvious for the largeeconomy than the medium one) and this pushes up borrowing costs for bankswhich are then passed on to firms. This kicks o↵ a downturn due to a decreasein borrowing by firms. This chain of e↵ects is most clear in the bottom mostplot at and near the period, t = 600. Notice the upturn in Central Banklending before the downturn in firm borrowing at this time and in the righthand panel, notice the upward swing in lending rates to firms at the sametime. In this case, the downturn in loans to the real sector is from about65,000 to about 58,000 an overall drop of about 11%.

In the next set of plots, Figure 4, we see the behaviour of the average allo-cation of funds and of interest rates in response to changes in the underlyingprobability of firm default.

The left panels show allocations and the right ones show interest rates.As expected, higher probabilities of firm default induce less lending to firms,thus less interbank lending which is essentially derived from firm lending andgreater accumulation of the safe asset. Interest rates on firm lending rise inline with the greater risk premium. Note that at low default probabilitiesbanks make use of Central Bank funds but this decreases as the probability

18

Figure 3: Allocations and interest rates in a single run of 1000 periods: Model I Low=20(Top), Medium=50 (Centre), High = 100 (Bottom); Firm Lending (Blue), Interbank Lending (Red), Central Bank Reserves(Green), Central Bank Borrowing (Turquoise).

19

Figure 4: Average allocation and interest rates with varying probability of firm default:Model I. Firm Lending (Blue), Interbank Lending (Red), Central Bank Reserves (Green), Central Bank Borrowing(Turquoise), Average Cost of Funds (Purple).

20

of firm default rises. This explains why the average cost of funds for bankstends to go down with default probabilities.

The behaviour of interbank rates, especially in low-demand economies, issomewhat surprising, as they are inverse U-shaped in the underlying defaultprobability. Conventional wisdom would suggest that inter-bank rates shouldrise monotonically with fundamental risk as seems to happen in economieswith medium and large real sectors. It appears that controlling for the sizeof an economy, there are two e↵ects on interbank rates: a counter-partyrisk e↵ect and a competition e↵ect. With higher probability of firm default,banks that lend to firms inherit some of the riskiness of their clients and thispushes up the price of interbank loans made to them. At the same time,with higher probability of firm default, there is a decrease in bank-to-firmlending so that the number of banks seeking funds on the interbank marketbecomes smaller relative to banks willing and able to lend. This tends todrive interbank interest rates down.

In the small economy, when the probability of default is low and thus theproportion of banks that lend to firms is relatively high (given the size of theeconomy), the first e↵ect dominates while at higher probability of default andless lending to firms the second e↵ect comes to dominate. The reason in turnfor the second e↵ect could be that in the small economy, there are more banksrelative to the size of demand from the real sector. As the number of banksthat lends to that sector shrinks, the competition amongst banks to lendon the interbank market goes up. Thus the competition e↵ect on the inter-bank market becomes more important as the underlying default probabilityexceeds a threshold. In the larger two economies, this threshold does not arisewithin the range of probabilities considered because the number of banks thatget directly exposed to firm risk is greater at every level of risk.

Note also that the sensitivity of the interbank rate to an increase in firmrisk is also greater (at low default probabilities) in the the small economy thanin the other two: the slope of the interbank rate line is steeper in this economyand much more gradual in the other two. This suggests that counter-partyrisk is more important at the margin in smaller sized economies than inlarger ones. This hypothesis is further supported by Figure 6, discussedlater, which shows that, at the benchmark default probability of 1%, thelikelihood of bank failures decreases with the size of the economy. Indeed,in the high-demand (large) economy, the rate of bank failures is an orderof magnitude lower than in the small one and this helps explain why theinter-bank lending rate slopes so gradually upwards in that economy.

21

5. Regulation

5.1. Regulatory changes

In this section we carry out a study of the e↵ect of regulatory changes inleverage ratios on bank performance and systemic stability. As stated in theIntroduction, this is the main aim of the present paper. Recall that banksare able to optimise their leverage while remaining within the Central Bank’sregulatory constraint, Our main experiments in this section will consist ofvarying (i) the maximum leverage allowed by regulators and (ii) the degree ofconnectedness of the interbank market at discrete settings of the regulatoryconstraint.

5.2. Leverage constraints

In Figure 5 we can see the consequences on market outcomes of varyingthe maximum leverage ratio on banks. And in Figure 6 we see the conse-quences on bank defaults.

The plots show the e↵ect of firm demand (a proxy for the size of thereal economy) on allocation of funds and market rates. In the top-mostplot we can see how the available demand for credit is quickly exhaustedwhen firm demand is low, so increasing the leverage ceiling beyond 20 (whichequals a capital adequacy ratio of 5%) has little e↵ect on firm lending orother allocations. The bottom-most plot shows that with high demand thehigher leverage levels may not be exhausted, there is increasing interbanklending and more use of the central bank deposit facility; indeed lending tofirms becomes partially supported by the central bank. This also leads toa U-shaped relationship between the average cost of funds and the leverageceiling: at low thresholds, interbank charges are high but decline with greaterleverage and increasing lending to firms; at high leverage ratios, Central Bankfunding for real sector loans is increasingly sought and this pushes up thecost of funds again.

A noteworthy feature of the plots is that for each size of the real economy,there is a point after which relaxing leverage constraints has little or noe↵ect on market volumes or prices. For the small economy there appearsto be no e↵ect beyond a ceiling of 20, and for the high-demand economy,there is diminishing e↵ect after a ceiling of 30. Although our numericalresults are only suggestive they could illustrate the verity real possibilitythat if regulators set leverage constraints that are not tight enough, thebanking sector’s activities will be barely a↵ected even with a high degree of

22

Figure 5: Average allocations and interest rates with varying leverage constraints: ModelI. Firm Lending (Blue), Interbank Lending (Red), Central Bank Reserves (Green), Central Bank Borrowing (Turquoise),Average cost of funds (Purple).I

23

turnover between the banking and the real sector. This in turn lends supportto the call for leverage constraints to be set counter-cyclically. However,a di↵erent policy implication arises when we look at the e↵ect of varyingleverage constraints on bank defaults.

This e↵ect is captured in Figure 6. As expected, in each state of marketdemand, the rate of bank defaults increases along with the maximum lever-age ratio. Rather surprisingly, banks in the low demand economy seem to bemore vulnerable to failure than in the high demand one, with the mediumdemand one coming in the middle. The gap also grows with the leverage con-straint, implying that not only is the low demand economy more vulnerablein absolute terms it is also marginally more susceptible to bank defaults fora given increase in the allowable leverage ratio. Thus, as the ratio increasesfrom 10 to 40, the mean rate of bank failure increases from one every 1000periods to one every 35 periods.

Figure 6: Mean default per bank with varying leverage ratios and three firm-bank scenar-ios: Model I. Low (Blue), Medium (Green), High (Red).

A possible explanation is that at low levels of market demand, althoughfew banks are exposed to firm risk, those that are exposed are more vulnerableto failure. For one thing, competition between banks drives down the firmlending rate (it is around 5% for the low demand economy as opposed to7% for the high-demand one) and reduces profit margins, skewing the risk-

24

return frontier towards more risk per unit of return. Less profits also meanlower equity which results in a higher likelihood of negative deposit shocks asdepositors seek out more profitable banks. This squeezes profit margins evenmore given that deposits are the cheapest source of funding. An increasein leverage ratios then leads to a movement along the skewed risk-returntowards seeking higher returns, at the cost of a higher probability of failure.

In this sense, if the aim of financial regulation is to prevent bank failures,the above analysis can be interpreted as undermining the case for counter-cyclical leverage constraints. In times of high market demand, banks arebetter insulated from idiosyncratic defaults while in bad times, they becomemore vulnerable. While constraints that move counter-cyclically might pro-mote more lending in bad times and restrain it in good times (as suggestedby Figure 5), it would have the opposite e↵ect on the risk of banks failing.5

5.3. Systemic risk

In this sub-section we consider the role of connectivity within the inter-bank market on contagion and systemic risk. Iori et al. (2006) among others,have shown that increasing interbank connectivity can, depending on circum-stances, either enhance the risk-sharing role of the interbank market or makeit a source of contagion. We are therefore interested in seeing how changesin interbank connectivity interact with regulatory changes in a↵ecting themarket outcomes and stability of the system.

5.3.1. Market outcomes and rates:

Figures 7 and 8 both depict market outcomes as functions of connectivityfor high demand scenarios at three di↵erent levels of regulatory leverage.Figure 7 pertains to Model I while Figure 8 pertains to Model II. Bothfigures tell qualitatively similar stories exept that there appears to be greaterdiversity in individual outcomes for the banks in Model II, especially at lowleverage ceilings.

Comparing the left hand plots in both figures, we can see that the lowleverage ceiling leads to a negative relationship between connectivity and

5Our banks are myopic profit-maximisers in that they do not take into account theconsequences of their own default. If they did, they might choose more prudent lendingstrategies in bad times given that their risk-return frontier deteriorates. In this sense, ouranalysis provides a rationale for why risk-averse banks might choose not to lend more evenif permitted to do so in bad times and calls into question the e↵ectiveness of counter-cyclical ratios.

25

lending on both markets, with Central Bank reserves soaking up the excessfunds. For the high ceiling the relationship between firm lending and connec-tivity slopes upwards while that between interbank lending and connectivitybecomes flat with Central Bank funding picking up the slack. An explana-tion is provided by the plots on market rates. At the low ceiling, it appearsthat due to the high demand for loans from firms, most banks end up fillingtheir order book with loans to the real sector and few banks are left withfunds to lend on the interbank market. Increasing connectivity then sim-ply links the banks that do have funds available to lend on the interbankmarket to a larger number of borrowing banks and this pushes up interbankinterest rates. These then lead to higher rates on firm loans (notice the up-ward trends in both rates in the top right plot) and this acts as a dampeneron those loans. In this situation, allowing individual banks to take on morefirm lending paradoxically increases the availability of funds on the interbankmarket.6

6Recall that firm loans are discretely sized so having larger leverage ratios allows asingle bank to commit loans to more firms while another bank may have none. Thisimbalance of service to the real sector helps promote balance between the two sides of theinterbank market.

26

Figure 7: Average allocations and interest rates for varying connectivity: Model I - HighDemand. Low Max Leverage = 10% (Top), Medium Max Leverage = 20% (Middle), High Max Leverage = 40%(Bottom); Firm Lending (Blue), Interbank Lending (Red), Central Bank Reserves (Green), Central Bank Borrowing(Turquoise), Average Cost of Funds (Purple).

27

Figure 8: Average allocations and interest rates for varying connectivity: Model II -High Demand. Low Max Leverage = 10% (Top), Medium Max Leverage = 20% (Middle), High Max Leverage =40% (Bottom), Firm Lending (Blue), Interbank Lending (Red), Central Bank Reserves (Green), Central Bank Borrowing(Turquoise), Average Cost of Funds (Purple).

28

5.3.2. Systemic profitability and stability:

Figures 9 and 10 display the average profits of the banking system andthe average rate of bank defaults at varying levels of connectivity, comparingresults across three leverage scenarios. In both case, a medium-sized realeconomy is chosen as it produces the most interesting variations across theregulatory scenarios. Figure 9 refers to Model I while Figure 10 refers toModel II. Once again, the two figures show qualitatively similar results exceptfor the fact that there is greater variation around the means in Model II thanin Model I.

In all cases depicted, bank profits are inversely related to bank defaultsas connectivity increases. This is expected. But what is striking is thatbank profits (resp: defaults) tend to increase (resp: decrease) with interbankconnectivity when leverage ceilings are low, to decrease (resp: increase) withconnectivity when leverage ceilings are high and to be U-shaped (resp: in-verse U-shaped) in connectivity under medium default ceilings. These rela-tionships can be explained by first taking into account the dual nature of therisk-sharing role of the interbank market, either as stabilising or a source ofcontagion, and then accounting for the e↵ect of leverage on individual banks’riskiness. Under conditions of low leverage, individual banks are already rel-atively safe (especially when the real economy is not too small relative tothe banking sector as in the case under consideration). Expanding interbanklending diminishes risk even further and makes them even safer. However,when banks are individually risky, then expanding interbank exposure canlead to contagion.

In the case of low leverage, the first e↵ect dominates. With medium lever-age, the initial expansion of interbank connectivity actually spreads contagionas a small number of lending banks get exposed to risky borrowing banksand thus face greater vulnerability to the latter’s failure, but as the poolof potential lenders in the interbank market grows relative to the numberof exposed banks, this helps bring about the stabilisation e↵ect. A similarinverse U-shaped relationship between bank failure and connectivity is foundby Caccioli et al. (2012).

In the case of high leverage, individual banks are too exposed to firm riskto allow su�cient risk-sharing even at high levels of connectivity. Thus thestabilising role of interbank lending never arises in an absolute sense.7

7Note that in Model I, the rate of bank failures does show a tendency to level out as

29

Figure 9: Average bank profits (Left) and probability of default (Right): Model I - MediumDemand. Low Max Leverage = 10% (Top), Medium Max Leverage = 20% (Middle), High Max Leverage = 40%(Bottom).

30

Figure 10: Average bank profits (Left) and probability of default (Right): Model II -Medium Demand. Low Max Leverage = 10% (Top), Medium Max Leverage = 20% (Middle), High Max Leverage= 40% (Bottom).

31

In the next set of plots, Figure 11 shows profits for banks, firms and thesum of the two as functions of interbank connectivity in various scenariosinvolving the level of real sector demand and leverage ceilings. Total profitsare a proxy for economic performance as a whole. A few points stand out.First, an economy with more real sector demand for loans delivers moreaggregate profits. This is not surprising.

Second, lower leverage ratios actually benefit bank profitability at theexpense of firm profitability. In each of the demand scenarios, an increase inleverage ratios raises firm profits and lowers bank profits. The explanationwould be that by placing more tightly binding limits on leverage, regulatorsactually reduce competition among banks in their loans to the private sector.This e↵ect is in line with some of the traditional concerns about the anti-competitive e↵ects of regulation and the potential for incumbents to use itfor what is known as regulatory capture.

Third, and perhaps more surprisingly, allowing banks to leverage them-selves more has ambiguous e↵ects on economic performance. This can beseen by comparing plots that are directly above each other. In low demandeconomies, increasing leverage does not seem to have much e↵ect on aggre-gate. In the medium demand case, it raises aggregate profits by moving fromthe low to the medium ceiling, but raising it further does not seem to havemuch more e↵ect. Finally, and most strikingly, in the high-demand economy,increasing leverage has a non-monotonic e↵ect on performance. Going fromlow to medium leverage raises aggregate profits but going further to highleverage actually lowers them. The explanation for these e↵ects appears tolie in the tradeo↵ between competitive e�ciency and stability of the bank-ing system. Allowing banks to leverage themselves more encourages greatercompetition which benefits the real economy, but it also leads to a higherrisk of financial instability. The way this tradeo↵ works is most clearly seenin the high-demand economy: as the maximum leverage ratio increases from

connectivity increases. This suggests that at least at the margin, the risk-sharing e↵ectof greater connectivity does seem to work even in the high-leverage case. While this doesnot happen in Model II, that could be because in that model, the marginal lender isless discriminating about the true riskiness of the borrower than is the marginal lenderin Model I. This not only leads to an adverse selection problem in the interest rate oninterbank loans it also exposes lenders to greater risk of contagion and this risk increasesthe more systemically risky the market already is. This could explain the convex shape ofthe relationship between bank defaults and connectivity in Model II.

32

10% to 20%, the pro-competitive e↵ect dominates but in the next step, from20% to 40% the systemic risk factor becomes too large and this results in adecline in aggregate performance.

Fourth, increasing interbank connectivity in a given scenario does not leadto an unambiguous increase in profits for any of the two types of institutionsor for the aggregate level of profits. Profits either flatten out or start decreas-ing with increasing connectivity. In fact the only scenario in which there iseventual decrease in profits at either the institutional or aggregate level is inthe high-demand economy for a medium level of the leverage ceiling.

It appears that in our model, the medium leverage ratio of 20% appearsto be optimal as it improves overall performance in the high-demand andmedium-demand scenarios without a↵ecting it in the low-demand. Again,this is a suggestive number rather than a prescriptive one. The general pointappears to be that indeed, too much focus on risk-minimisation can leadto adverse e↵ects both in terms of overall economic performance and, moreimportantly, in benefiting the real sector, which is the source of an economy’sproductivity and welfare and is therefore normally the intended beneficiaryof financial regulation.

33

Figure 11: Economy-wide profits at varying levels of connectivity: Model I. Low Demand(Left), Medium Demand (Centre), High Demand (Right); Low Max Leverage = 10% (Top), Medium Max Leverage = 20%(Middle), High Max Leverage = 40% (Bottom); Firms (Blue), Banks (Red), Aggregate (Green).

34

6. Conclusions

We developed a model of a banking system connected to a simplifiedreal economy consisting of a productive firm sector with both banks andfirms optimising their behaviour on credit markets. We found that both thecontribution of banks to the performance of the real sector and the stabilityof the credit system depend on both market demand, which can be cyclical,and regulatory constraints. While bank lending to the real sector tends tomove pro-cyclically in our model, the risk of bank failure changes counter-cyclically. In addition, the degree of interbank connectivity has ambiguouse↵ects on both economic performance and the possibility of systemic failure,depending again on market demand and regulatory constraints.

We also explored the impact of the new regulations that have been pro-posed to minimise the probability of bank default and reduce contagionwithin the financial system.

We found that loan pricing strongly depends not only on demand butalso on the leverage ratio threshold. The relationship between the averagecost of funds and the leverage ceiling appears to be non-linear (U-shaped).One important conclusion of our research is that the principle “one size fitsall” does not apply. The e↵ectiveness of regulatory measures in improvingfinancial stability will depend on the size of the real economy and the levelof credit demand. We found that the bite of regulatory leverage ceilings inrestricting bank activity can become quite weak unless the ceiling is fairlylow, even with a high degree of turnover between the banking and the realsector.

On the one hand, this possibility lends support to the proposal for cal-ibrating the regulatory constraint counter-cyclically. On the other hand,adopting a counter-cyclical leverage ratio would negatively a↵ect the prob-ability of bank defaults as in times of recession when real sector activity islow, banks become especially vulnerable to systemic failure in both absoluteterms and as a result of marginal increases in their leverage. In other words,in choosing a variable leverage ratio regulators might be facing a tradeo↵between improving the banking sector’s overall contribution to the real econ-omy and protecting it from systemic risk.

Our model estimated the impact of leverage constraints on bank prof-itability: again, in choosing between stability and e�ciency, regulators shouldtake into account the possibility that leverage ceilings have a non-monotonice↵ect on performance: bank profits increase when the ratio ranges between

35

low to medium values, while the impact is inverted when the leverage is fixedto higher levels.

The policy implications of our results are that the building block approachto correct the Basel 2 Capital Accord after the crisis did not pay su�cientattention to the cross-e↵ects of di↵erent measures. More specifically, theintroduction of a uniform leverage ratio can produce asymmetric and non-linear e↵ects on the credit intermediation function of the banking system,depending on the macro-economic cycle and on the economy size. Moreover,the capability to minimize systemic risk, which depends on the stability ofglobal systemically important financial institution (G-SIFI), is also explainedby dynamics of the bank network as induced by the mis-calibrated leverageratio.

36

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Appendix A. Configuration of Model

Appendix A.1. ParametersBelow we present the main model parameters with their default values

used for the results presented above.

• Target update frequency, how frequently leverage target is updated.Default: 10

• Number of firms per bank. Default: 25/50/100 for ‘Low”/“Medium”/“High”demand.

• Mean firm loan demand size. Default: 20.

• Number of banks each firm approaches. Default: 5.

• Connectivity, how likely it is for any two banks to be connected oninterbank market. Default: 0.2.

• rH , Central Bank Lending Rate. Default: 0.09

• rL, Central Bank Lending Rate. Default: 0.02

• Probability of firm loan default. Default: 0.01.

• Number of Banks. Default: 100.

• Initial deposit. Default: 500.

• Initial equity. Default: 100.

• Deposit volatility, weight for proportion of deposits withdrawn and al-located to another bank (in proportion to equity). Default: 0.1.

The adjustment thresholds below were selected because they seemed towork reasonably well. There qualitative results seemed to be una↵ected bytheir precise level. A lower threshold was selected for the interbank marketto account for its higher period to period volatility.

• ⌘

l0 = 0.8

• ⌘

l1 = 0.9

• ⌘

b0 = 0.5

• ⌘

b1 = 0.9

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