Leverage and risk weighted capitalrequirementsWorking Papers 2016

Leonardo Gambacorta | Sudipto Karmakar

Lisbon, 2016 • www.bportugal.pt

16

September 2016The analyses, opinions and findings of these papers represent the views of the authors, they are not necessarily those of the Banco de Portugal or the Eurosystem

Please address correspondence toBanco de Portugal, Economics and Research Department Av. Almirante Reis 71, 1150-012 Lisboa, PortugalT +351 213 130 000 | estudos@bportugal.pt

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Edition Economics and Research Department • ISBN 978-989-678-477-5 (online) • ISSN 2182-0422 (online)

Leverage and Risk Weighted Capital

Requirements

Leonardo GambacortaBank for International Settlements

& CEPR

Sudipto KarmakarBanco de Portugal

& UECE

September 2016

Abstract

The global �nancial crisis has highlighted the limitations of risk-sensitive bank capitalratios. To tackle this problem, the Basel III regulatory framework has introduced aminimum leverage ratio, de�ned as a bank's Tier 1 capital over an exposure measure,which is independent of risk assessment. Using a medium sized DSGE model that featuresa banking sector, �nancial frictions and various economic agents with di�ering degrees ofcreditworthiness, we seek to answer three questions: 1) How does the leverage ratio behaveover the cycle compared with the risk-weighted asset ratio? 2) What are the costs andthe bene�ts of introducing a leverage ratio, in terms of the levels and volatilities of somekey macro variables of interest? 3) What can we learn about the interaction of the tworegulatory ratios in the long run? The main answers are the following: 1) The leverageratio acts as a backstop to the risk-sensitive capital requirement: it is a tight constraintduring a boom and a soft constraint in a bust; 2) the net bene�ts of introducing theleverage ratio could be substantial; 3) the steady state value of the regulatory minimafor the two ratios strongly depends on the riskiness and the composition of bank lendingportfolios.

JEL: G21, G28, G32

Keywords: Bank Capital Bu�ers, Regulation, Risk-Weighted Assets, Leverage.

Acknowledgements: We would like to thank Pierre-Richard Agénor, Ingo Fender, GiovanniLombardo, Scott Nagel, Stefano Neri, Hyun Song Shin, Luca Sera�ni, Federico Signoretti,colleagues at the Bank of Portugal, and seminar participants at the BIS and the Bank ofEngland for helpful discussions and comments. The project was completed while SudiptoKarmakar was visiting the Bank for International Settlements under the Central BankResearch Fellowship Program. The views expressed are those of the authors and notnecessarily those of the Basel Committee on Banking Supervision, the BIS, the Banco dePortugal or the Eurosystem.

E-mail: Leonardo.Gambacorta@bis.org; Sudipto.Karmakar@bportugal.pt

Working Papers 2

1. Introduction

The global �nancial crisis has highlighted the limitations of risk-weighted bankcapital ratios (regulatory capital divided by risk-weighted assets). Despitenumerous re�nements and revisions over the last two decades, the weightsapplied to asset categories seem to have failed to fully re�ect banks' portfoliorisk causing an increase in systemic risk (Acharya and Richardson (2009),Hellwig (2010), and Vallascas and Hagendor� (2013)). To tackle this problemthe new regulatory framework of Basel III has introduced a minimum leverageratio, de�ned as a bank's Tier 1 capital over an exposure measure, which isindependent of risk assessment (Ingves (2014)).

The aim of the leverage ratio is to act as a complement and a backstopto risk-based capital requirements. It should counterbalance the build-up ofsystemic risk by limiting the e�ects of risk weight compression during booms.The leverage ratio is therefore expected to act counter-cyclically, being tighterin booms and looser in busts. If bank capital behaved in this way over the cycle,both the probability of a crisis and also the amplitude of output �uctuationswould be reduced.

The Basel III framework requires that the leverage ratio and the morecomplex risk-based requirements work together. The leverage ratio indicates themaximum loss that can be absorbed by equity, while the risk-based requirementrefers to a bank's capacity to absorb potential losses. The use of a leverage ratiois not new. A similar measure has been in force in Canada and the United Statessince the early 1980s (Crawford et al. (2009) and D'Hulster (2009)). Canadaintroduced the leverage ratio in 1982 after a period of rapid leveraging-up byits banks, and tightened the requirements in 1991. In the United States, theleverage ratio was introduced in 1981 amid concerns over bank safety due tofalling bank capitalization and a number of bank failures (Wall and Peterson(1987) and Wall (1989)). The introduction of a leverage ratio requirement forlarge banking groups was announced in Switzerland in 2009 (FINMA, 2009).Similar requirements have been proposed, more recently, in other jurisdictionsas well, with a view to implementing them by 2018 (BCBS, 2014b).

Motivated by these considerations this paper addresses the followingquestions:

1. How does the leverage ratio evolve over the cycle compared with the risk-weighted asset ratio?

2. What are the costs and the bene�ts of introducing a leverage ratio (in termsof level and volatility of some key variables)?

3. What can we learn about the interaction of the two regulatory ratios inthe long run?

To address these questions we embed the regulator's problem within amacroeconomic model. Speci�cally we build on the DSGE model developed

3 Leverage and Risk Weighted Capital Requirements

by Angelini et al. (2014) to examine the functioning and shortcomings of risk-based capital regulation and the role of the leverage ratio in mitigating thepro-cyclicality problem. This model features a simpli�ed banking sector andheterogeneity in the creditworthiness of the various economic agents. The modelalso features risk-sensitive capital requirements and a stylized countercyclicalcapital bu�er. We contribute by augmenting this model in two ways. First,we introduce a leverage ratio, independent of risk assessment, whose deviationfrom the minimum requirements produces additional capital adjustment costs.Second, we allow the risk weights on lending to households and non-�nancial�rms to be di�erent in the steady state. This modi�cation allows us to mimicthe real world setting and generates di�erent interest rates for the two classesof loans.

However, this framework has a few limitations. This setup does not allowfor bank defaults in equilibrium. It is for these reasons that we will conducta strictly positive analysis. We do not address normative questions such asthe optimality of the leverage ratio. Our contribution consists in the fact that,in contrast to earlier papers, we model the �nancial intermediaries such thatthey are subject to a minimum leverage requirement in addition to the risk-based capital requirement, in line with one of the main tenets of the Basel IIIguidelines. The aim is to study how these ratios interact over the business cycle.The costs and bene�ts analyzed are in terms of levels and standard deviationsof some key variables of interest. Our study does not assess the bene�ts of theleverage ratio in terms of reducing the frequency and severity of �nancial crises.

Our main results are as follows: (i) The leverage ratio is more counter-cyclical than the risk-weighted capital ratio: it is a tight constraint duringa boom and a soft constraint in a bust; (ii) The bene�ts of introducing theleverage requirement appear to be substantially higher than the associatedcosts; and (iii) the steady state values of the two ratios strongly depend on theriskiness and the composition of lending portfolios. The remainder of the paperis organized as follows. The next section discusses the issue of procyclicality andwhy bank capital regulation is important in making the �nancial system moreresilient. Section 3 describes Basel III regulation and presents some stylizedfacts on bank capital ratios. Section 4 describes the model, Section 5 presentsthe calibration while Section 6 discusses the results.

2. Why is bank capital important?

Bank capital is the part of the bank's funds that is contributed by the owners orshareholders, as opposed to external sources of funding which include deposits,inter-bank funding and obligations. Minimum capital requirements are intendedto reduce bank insolvency risk. The main objective is to make sure thatbanks have su�cient internal resources to withstand adverse economic shocks

Working Papers 4

and to improve incentive distortions that are created by a number of marketimperfections in the banking sector.

2.1. Basel regimes

Over time, bank regulators have developed a sophisticated system of solvencyregulations that are intended to increase the safety of individual institutionsand the stability of the �nancial system. The �rst Basel Accord (Basel I) wasadopted in 1988 by the G-10 with the aim of harmonizing capital regulationacross countries and strengthening the stability of the international bankingsystem (BCBS, 1988). The framework was designed to encourage banks toincrease their capital positions and to make regulatory capital more sensitive tobanks' perceived credit risks. Accordingly, assets and o�-balance sheet activitieswere assigned risk weights between 0 and 100% according to their perceivedrisks, and banks were obliged to hold a minimal amount of capital relative tototal risk-weighted assets and o�-balance sheet activities.

The second Basel Accord (Basel II), which was �rst published in 2004and implemented in most industrial countries in 2007, can be seen as are�nement of Basel I that introduces a complementary three pillar concept ofbank regulation - minimum capital requirements, supervisory review (InternalCapital Adequacy Assessment Process) and market discipline (disclosurerequirements). Amongst other things, it enforced the existing standards byintroducing additional capital requirements for market risks, in particularinterest rate and exchange risks (BCBS, 2005). Basel II also allowed banks touse their own internal models to evaluate risk, once the models were validatedby the supervisory authority.

With the onset of the global �nancial crisis in 2008 and the perceptionof a number of weaknesses in the existing regulatory framework, the BaselCommittee on Banking Supervision developed the third Basel Accord (BaselIII) with the aim of implementing it in 2018 (BCBS, 2014b). It address theperception that the risk weights applied to asset categories have failed tofully re�ect banks' portfolio risk causing an increase in systemic risk. Totackle this problem, among other things, Basel III has introduced a minimumleverage ratio that is independent of risk assessment and treats all exposuresequally. As a result, the new capital regulation consists of three complementarycomponents: (i) the risk-weighted capital regulation in which capital adequacyis set in relation to a historical assessment of risks augmented by countercyclicalbu�ers (Drehmann et. al. (2010)); (ii) the stress-testing framework whichassesses banks' resilience to tail risks (BCBS, 2009b); and (iii) the leverageregulation that is independent of risk assessment.

It is important to note that the Basel III regulation requires the threecomponents to be in place concomitantly, since each of them addresses aparticular vulnerability. For instance, if the leverage ratio were used in isolation,then the information on individual asset risks would not be taken into account

5 Leverage and Risk Weighted Capital Requirements

when assessing capital adequacy. Banks might then be incentivized to shift theirinvestments from low-risk to high-risk assets. On the other hand, if there wereonly stress tests and risk-weighted capital requirements, banks would remainprone to model risk when classifying of particular assets into risk categories andin estimating future tail risks. Moreover, the problem that banks may leverageup their balance sheet by investing in assets that appear in the low-risk categorywould remain unaddressed.

To sum up, the leverage ratio is intended to act as a complement and abackstop to risk-based capital requirements. It should counterbalance the build-up of systemic risk by limiting the e�ects of risk weight compression duringbooms. The leverage ratio is therefore expected to act (more) countercyclicallythan the risk-weighted asset ratio, being tighter in booms and looser in busts.

2.2. What are the long term net bene�ts of bank capital regulation?

There is an intense debate between policymakers, industry lobbying groupsand academics about the costs and bene�ts of bank capital requirements.Earlier contributions by Harrison (2004) and Brealey (2006) analyze the BaselII package and conclude that no compelling arguments support the claim thatbank equity has a social cost. Focusing on the current crisis, Turner (2010)and Goodhart (2010) argue that a signi�cant increase in equity requirementsis the most important step regulators should take to achieve the broadermacroprudential goal of protecting the banking sector from period of excessaggregate credit growth. Acharya et al. (2011), Acharya et al. (2015) andGoodhart et al. (2010) suggest - in line with the actual implementation ofthe capital conservation bu�er - that regulators should impose restrictions ondividends and equity pay-outs as part of prudential capital regulation. Admatiet al. (2010) make a clear assessment of the applicability of standard corporate�nancial analysis and of the Modigliani-Miller propositions to understandingthe economic impact of the new bank capital regulation and conclude that thebene�ts are larger than the costs. However, the authors do not provide anyempirical quanti�cation of the net bene�ts.

There are other papers that try to assess the costs and bene�ts of highercapital requirements. One example is Miles et al. (2011) who derive the optimalcapital ratio for UK banks. They calculate costs using a two-step approach(�rst, estimate the impact of higher capital on lending spreads; next, estimatethe impact of higher lending spreads on output). The key result is that a 1percentage point increase in capital requirements causes output to fall by 0.02%(compared with 0.09 in Angelini et al. (2014) who use a similar set up). In thelong term, the increase in lending spreads caused by a 1 percentage point inthe capital requirement is equal to 0.8 basis points, smaller by a factor of16 than the estimate by King (2010) of 13 basis points. Given these costs andtaking into account that higher capital also reduces the probability of a bankingcrisis, their welfare analysis suggests that the optimal bank capital should be

Working Papers 6

around 20% of risk-weighted assets. Benes and Kumhof (2011) use a theoreticalmodel to analyze the impact of prudential rules and a countercyclical capitalbu�er requirement, similar to the reform proposed in Basel III, and �nd thattheoretically a bu�er requirement has the ability to increase overall welfareby reducing the volatility of output. More recently, Karmakar (2016) uses aDSGE model with a non-linear and occasionally binding capital requirementconstraint and shows that higher capital requirements reduce business cyclevolatility and raises welfare. He also derives an optimal capital requirement of16%, in line with the Basel guidelines.

The Institute of International Finance, (IIF 2011) argues that the economiccost of Basel III - in terms of foregone real GDP - will be signi�cant, about0.7% per year over the �ve years following the implementation of Basel III.The di�erence with respect to Miles et. al. (2011) depends on several factors,the most important one being the short time horizon and the lack of anyassessments of the bene�ts in the long run.

Corbae and D'Erasmo (2013) develop a dynamic model of banking industrydynamics to investigate banking regulations, and speci�cally Basel III, and theire�ect on industry dynamics. They �nd that a rise in capital requirements from4 to 6% leads to a rise in loan interest rates by about 50 basis points as wellas a lower level of GDP, while the cost of deposit insurance falls substantially.Generally similar results are obtained in the DSGE model presented by Aliaga-Diaz and Olivero (2012). When the capital requirement is raised by 2 percentagepoints in their model, loan rates rise by about 15 basis points, while outputfalls by slightly less than 1%. Consistently with these results, Drehmann andGambacorta (2012) �nd that the introduction of a countercyclical capitalbu�er helps to reduce credit growth during booms and attenuate the creditcontraction once it is released.

An overall assessment of the net bene�ts (bene�ts minus costs) of BaselIII are reported in the Long-term Economic Impact study (the so-called LEIreport, see BCBS, 2010b). In particular, this study indicates that the economiccosts associated with tighter capital and liquidity standards are considerablylower than the estimated positive bene�t that the reform should have byreducing the probability of banking crises and their associated banking losses.However, none of the DSGE models used in this study feature credit risk andthe possibility of default, so that the main bene�ts of the reform are calculatedby considering the reduction in output volatility (see Angelini et al. (2014)).This is a limitation of our study as too.1

1. Most models used in the LEI's exercise are of the dynamic stochastic general equilibrium(DSGE) family. However, following a `diversi�cation' approach, a limited number ofalternative models (example: semistructural and vector error correction models (VECM))were also used (see Angelini et al., 2015).

7 Leverage and Risk Weighted Capital Requirements

3. Stylized facts about the risk-weighted capital and leverage

requirements

One aspect that remains to be assessed is if the side-by-side application of risk-weighted capital and leverage requirements could be of help in preventing theoccurrence of a fragile boom and smoothing the cycle. One of the lessons fromthe recent �nancial crisis is that the banks built up a substantial amount ofleverage while apparently maintaining strong risk-based capital ratios. Whenthe �nancial markets forced the banks to deleverage rapidly, this put a strongdownward pressure on asset prices. This in turn brought about a decline inbank capital and eventually a credit squeeze that exacerbated the problem.

Typically, during booms, risk materialization is low and hence banks have anincentive to engage in pro�t-making opportunities. It is precisely at this time,that risk weights are low, giving the impression that banks are su�cientlycapitalized and in sound �nancial health. Overoptimistic assessment of riskweights lead to large-scale extension of credit and hence decline in lendingstandards. The reduction of risk weights could be particularly strong in a periodin which interest rates are low. This is the so-called the risk-taking channel(Borio and Zhu (2008), Adrian and Shin (2014), Altunbas et al. (2014)) andworks not only through a "search for yield" mechanism but also through theimpact of low interest rates on valuations, incomes and cash �ows. A reductionin the policy rate boosts asset and collateral values, which in turn can modifybank estimates of probabilities of default, loss given default and volatilities.For example, low interest rates by increasing asset prices tend to reduce assetprice volatility and thus risk perceptions. Since higher stock prices increasesthe value of equity relative to corporate debt, a sharp increase in stock pricesreduces corporate leverage and could thus lessen the risk of holding stocks.All this has a direct impact on value-at-risk methodologies for economic andregulatory capital purposes (Danielsson et al. (2004)). As volatility tends todecline in rising markets, it releases the risk budgets of �nancial �rms andencourages leveraged position-taking. A similar argument is provided in themodel by Adrian and Shin (2014), who stress that changes in measured riskdetermine adjustments in bank balance sheets and leverage conditions and thatthis, in turn, ampli�es business cycle movements.

When loan quality starts to deteriorate, capital is used to absorb the losses.It is mainly for this reason that we need a non risk based measure that willcomplement the risk based capital requirements. The leverage ratio indicatesthe maximum loss that can be absorbed by equity. The opposite happensduring economic downturns. During such times, risk weights are high and hencethe capital requirement constraint tightens but the leverage requirement isuna�ected by the changes in risk weighting and it will be satis�ed. The mainpoint is that the two capital requirements need to work together to limit aboom-bust cycle.

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It must be noted that a necessary condition for the minimum LRrequirement to act as a cyclical backstop to the RWRs is that thebanks' exposure expands more strongly during a �nancial boom than thecorresponding increase in its' risk-weighted assets. This should make the LRwork countercyclically. Indeed, using a large data set covering internationalbanks headquartered in 14 advanced economies, Brei and Gambacorta (2016)�nd that the Basel III leverage ratio is signi�cantly more countercyclical thanthe risk-weighted regulatory capital ratio: it is a tighter constraint for banksin booms and a looser constraint in recessions. The main results of Brei andGambacorta (2016) are summarised in Table A.1. A 1% point increase in realGDP growth is associated with a reduction of the LR of 5 basis points, whilethe risk-weighted ratio does not react to GDP movements. Similar results areobtained using a �nancial measure of the cycle, the credit gap (the di�erencebetween the credit to GDP ratio and its trend).

The Basel Committee on Banking Supervision sets out that the leverageratio is intended to:

1. Avoid excessive build-up of leverage so that rapid deleveraging, in the eventof a crisis, does not destabilize both the �nancial and real sectors.

2. Complement the risk-based measures with a simple, non risk-based�backstop� measure.

The Basel III leverage ratio (LR) is de�ned as a capital measure over totalexposure,2

LeverageRatio =Capital

Exposure

In this paper, we will explore if the leverage requirement really acts asa backstop to the capital requirements. Despite the fact that the minimumleverage ratio has already been set at 3%, we cannot use this as a minimumrequirement to calibrate the model because the composition of the creditportfolio of our banks is quite simpli�ed: it does not include interbank loansand more importantly government bonds (our model does not feature a publicsector).3

2. The total exposure is given by total assets and other commitments. A detailedexplanation of the de�nition of capital and total exposures can be found in BCBS (2014a).

3. Refer the Group of Central Bank Governors and Heads of Supervision (GHOS)press release dated 11th January, 2016. (http://www.bis.org/press/p160111.htm). Thereis still an ongoing debate about the possibility of a leverage surcharge for globalsystemically important banks (G-SIBs). Most of the existing leverage ratio frameworksindicate an additional surcharge of 1-2% (Bank of England, Financial Stability Report,2016). The additional surcharge for G-SIBs on the risk-weighted capital ratio has beenalready designed by the Basel III regulation following a bucket approach from 1-3.5%(http://www.bis.org/publ/bcbs255.pdf). For simplicity, we do not consider such bu�ers inour model.

9 Leverage and Risk Weighted Capital Requirements

Following Fender and Lewrick (2015), a useful concept in calibrating theLR in a manner consistent with the existing RWRs (i.e. by taking possibleinteractions into account) is the "RWA density" or "density ratio" (DR),de�ned as the ratio of RWA to the LR exposure measure. The density ratiodenotes the average risk weight per unit of exposure for any given bank orbanking system. The relationship between the LR and the DR can be obtainedby expanding the LR de�nition as follows:

LR =Capital

RWA∗ RWA

Exposure= RWR ∗DR (1)

The LR can thus be expressed as the product of the risk-weighted capitalratio (RWR= Capital/Risk-weighted assets) and the DR. This relationship canhelp us calibrate a consistent minimum LR requirement.

Equation (1) shows how the LR and the RWRs complement each otherfrom a cross-sectional point of view. If, all else equal, a bank's risk modelunderestimates its risk weights, this will bias the Tier 1 capital ratio upwards.Yet, at the same time, the DR is biased downwards, making a minimumLR requirement relatively more constraining. Conversely, for a given LRrequirement, a bank with a relatively low DR will have an incentive to shift itsbalance sheet towards riskier assets to earn more income - a type of behaviorthat the RWRs would constrain. This suggests that banks' risk-weighted capitalratios and the LR provide complementary information when banks' resilienceis assessed.

The coherence between the LR and the RWR requirement, set by the BaselIII regulation at 8.5%, implies the calculation of a plausible value for the DR inthe steady state.4 In the context of our model, banks lend only to householdsand non-�nancial �rms and we have to reconstruct a plausible density ratiotaking into account: (a) the risk weights for loans to households and non-�nancial �rms and (b) the proportion of bank loans to these two sectors in thelong run.

The �rst point can be solved using information in EBA (2011) that reportsthe average risk weights implied by the internal models of European banks.In particular, weights are 0.37 for household lending and 0.92 for lending tonon-�nancial �rms. These weights are very similar to those implied by thestandardized approach in Basel I, which are, respectively, 0.35 and 1.00. As forthe second point, we can simply rely on the long-term share of loans to thenon-�nancial sector in the euro area that is approximately 60% to householdsand 40% to �rms. Taking these values into account the density ratio is equalto 0.59 (0.37*0.6+0.92*0.4) and from equation (1) it is possible to derive a

4. New Basel III regulation has tightened risk-weighted capital requirements. Banks haveto meet a 6% Tier 1 capital ratio (comprising a more broadly de�ned Tier 1 capital elementas numerator); and (ii) maintain an additional capital conservation bu�er of 2.5% (in termsof CET1 capital to RWA). The new minimum could be considered to be 8.5%

Working Papers 10

plausible value for the minimum LR approximately equal to 5% (8.5*0.59). Inour numerical results, we will use this as a baseline case for the minimum LRrequirement. It is worth stressing that this value is coherent with the calibrationof our speci�c model and should not be interpreted as a benchmark for thecalibration of the actual minimum requirement in the euro area.

4. The model

We build on the model by Gerali et al. (2010) and Angelini et al. (2014). Thereare some trade-o�s to using this framework. The framework allows us to studya non-naive �nancial sector, besides incorporating credit frictions, borrowingconstraints and a set of real and nominal rigidities. The borrowing constraintsare modeled as Iacoviello (2005) while the real and nominal rigidities aresimilar to the ones developed in Christiano, Eichenbaum and Evans (2005) andSmets and Wouters (2003). The borrowing constraints and the bank regulatoryconstraints are always binding and not occasionally binding. In this section, wediscuss the main features of the model. For further details, we would like torefer the reader to Angelini et al. (2014).

4.1. A brief overview

The �owchart in Figure A.1 shows the interactions between the di�erent agentsin the economy. There are two types of households (patient and impatient)who consume, supply labor, accumulate housing (in �xed supply) and eitherborrow or lend. The two types of households di�er in their respective discountfactors (βP > βI). The di�erence in discount factors leads to positive �nancial�ows in equilibrium. The patient households sell deposits to the banks whilethe impatient households borrow, subject to a collateral constraint. Theentrepreneurs hire labor from the households, and buy capital from the capitalgoods producers, to produce a homogeneous intermediate good.

The banks accept deposit and supply business and mortgage loans. Similarto the impatient households, the entrepreneur also faces a collateral constraintwhile drawing a loan from the bank. Another useful feature of this model is thatthe banks are monopolistically competitive. In other words, they set lendingand deposit rates to maximize pro�ts. The banks can only accumulate capitalthrough retained earnings i.e. we do not allow for equity issuance.

On the production side, there are also monopolistically competitive retailersand capital goods producers. The retailers buy intermediate goods from theentrepreneurs, di�erentiate and price them, subject to nominal rigidities. Thecapital goods producers help us introduce a price of capital to study asset pricedynamics.

The model also features a monetary authority and a macroprudentialauthority. The monetary authority sets policy rates and follows a standard

11 Leverage and Risk Weighted Capital Requirements

Taylor rule. The macroprudential authority sets the minimum risk based capitaland leverage requirements. We now study the individual agents in greater detail.

4.2. The patient households

The representative patient household `i' chooses ct, lt, ht and dt to maximizethe expected utility

E0

∞∑t=0

βtP

[(1 − aP )εzt log(cPt (i) − aP cPt−1) + εht logh

Pt (i) − lPt (i)1 + ϕ

1 + ϕ

]

subject to the following budget constraint (in real terms)

cPt (i) + qht ∆hPt (i) + dPt (i) ≤ wPt lPt (i) +

(1 + rdt−1)dPt−1(i)

πt+ tPt (i), (2)

where πt = PtPt−1

is the rate of in�ation. The expected utility depends on current

and lagged consumption cPt , housing hPt and labor hours lPt . There are external

habits in consumption. The household utility is subject to two preferenceshocks. The shock to consumption is εzt and the shock to housing demandis εht . They follow independent AR(1) processes. Equation (2) is the budgetconstraint. The expenses include consumption, accumulation of housing andselling one period deposits to the banks. The receipts are in the form of laborincome, gross return on last periods deposits and some lump-sum transfers tt.The real house price is qht and wPt is the real wage rate.

4.3. The impatient households

The representative patient household `i' chooses ct, lt, ht and bIt to maximize

the expected utility

E0

∞∑t=0

βtI

[(1 − aI)εzt log(cIt (i) − aP cIt−1) + εht logh

It (i) −

lIt (i)1 + ϕ

1 + ϕ

]subject to the following budget constraint (in real terms)

cIt (i) + qht ∆hIt (i) +(1 + rbHt−1)bIt−1(i)

πt≤ wIt l

It (i) + bIt (i) + tIt (i) (3)

and the borrowing constraint,

(1 + rbHt )bIt (i) ≤ mItEt

[qht+1h

It (i)πt+1

](4)

Similar to the patient households, the expected utility of the impatienthouseholds depends on consumption cIt , housing h

It and hours worked l

It and are

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subject to the same preference shocks. The budget constraint in this case lookssomewhat di�erent from the earlier case. The expenses consists of consumption,accumulation of housing and servicing of debt bIt−1. The receipts comprise laborincome, new loans and lump-sum transfers.

Equation (4) above represents the households borrowing constraint. Thisstates that the household can borrow up to the expected value of their housingand mI

t is the stochastic LTV ratio for mortgages.

4.4. The entrepreneurs

Each entrepreneur `i' maximizes his expected utility that depends only onconsumption cEt (i).

E0

∞∑t=0

βtE[log(cEt (i) − aEcEt−1)

]The entrepreneurs choose consumption cEt , physical capital k

Et , loans b

Et ,

and the labor inputs lE,Pt and lE,It . The budget constraint for the entrepreneursis given by:

cEt (i) +wPt lE,Pt (i) +wIt l

E,I(i) +1 + rbEt−1

πtbEt−1(i) + qkt k

Et (i) (5)

=yEt (i)

xt+ bEt (i) + qkt (1 − δ)kEt−1(i),

where δ and qkt are the depreciation and price of physical capital,respectively. The competitive good is produced by the technology,

yEt (i) = aEt[kEt−1(i)

]α [lEt (i)

]1−αThe relative competitive price of the good is 1/xt = PWt /pt, a

Et is the

stochastic TFP and lEt = (lE,Pt )µ(lE,It )1−µ, where µ is the share of patienthouseholds labor.5

Further, the entrepreneurs are also subject to borrowing constraints. Theycan also borrow up to the expected value of their undepreciated capital i.e.

(1 + rbEt )bEt (i) ≤ mEt Et

[qkt+1(1 − δ)kEt (i)πt+1

], (6)

where mEt is the stochastic LTV on entrepreneurial loans. Following Iacoviello

(2005) and Gerali et al. (2010), we choose the value of shocks such that theborrowing constraints always bind in the neighborhood of the steady state.

5. A detailed discussion can be found in Iacoviello and Neri (2010).

13 Leverage and Risk Weighted Capital Requirements

4.5. The banks

The banks have market power in setting lending and deposit rates. They adjustloans and deposits in response to cyclical conditions of the economy whilesatisfying the balance sheet identity and the regulatory requirements. Eachbank consists of a wholesale unit that manages bank capital and two retailunits that accept deposits and make loans.

4.5.1. The wholesale branch. The wholesale branch operates under perfectcompetition. On the liabilities side, it combines the bank capital, Kb

t , with theretail deposits, Dt, while on the asset side, it provides funds to the retail branchto extend di�erentiated loans, BHt and BEt . There is also a cost associatedwith the wholesale activity. We assume that the banks incurs quadratic costswhenever it deviates from a required leverage and a risk-weighted asset ratio.These requirements are �xed by the regulator and hence the bank takesthese targets as exogeneously given while solving the optimization problem.The exogenous target incorporates the accelerator mechanism as described byAdrian and Shin (2010). Essentially, the bank tries to stay close to a constantleverage and risk-weighted asset ratio and there are costs to deviating fromthese targets.

There is no equity issuance in the model and therefore bank capital isaccumulated through retained earnings only. The law of motion for bank capitalis as follows:

Kbt+1(j) = (1 − δb)Kb

t (j) + Jbt ,

where Jbt−1 represents the overall pro�ts of the banking group. The wholesalebranch chooses loans and deposits to maximize pro�ts:

E0

∞∑t=0

ΛP0,t[(1 +RBHt )BHt (j) + (1 +RBEt )BEt (j) − (BHt+1(j) +BEt+1(j))+

Dt+1(j) − (1 +Rdt )Dt(j) + (Kbt+1(j) −Kb

t (j))

−κKb2

(Kbt (j)

ωHt BHt (j) + ωEt B

Et (j)

− νbt )2Kbt (j)−

κLb2

(Kbt (j)

BHt (j) +BEt (j)−ϕb)2Kb

t (j)]

subject to the balance sheet identity, BHt (j) +BEt (j) −Dbt (j) = Kt(j)

The last two terms in the above expression show the quadratic costs incurredon deviating from the capital and leverage requirements, respectively. Thesecosts are parametrized by κKb and κLb. The �rst-order conditions yield arelationship between the capital position of the bank and the cost of funds.We can write the FOCs for any bank, j, as follows:

Working Papers 14

RBHt −Rdt = −κKb(Kbt

ωHt BHt + ωEt B

Et

− νbt )(Kbt

ωHt BHt + ωEt B

Et

)2ωHt −

κLb(Kbt

BHt +BEt− ϕb)(

Kbt

BHt +BEt)2 (7)

RBEt −Rdt = −κKb(Kbt

ωHt BHt + ωEt B

Et

− νbt )(Kbt

ωHt BHt + ωEt B

Et

)2ωEt −

κLb(Kbt

BHt +BEt− ϕb)(

Kbt

BHt +BEt)2 (8)

It can be seen that equations (7) and (8) are identical if the risk weights aresame i.e. RBHt = RBEt , if ωEt = ωHt . The left-hand side shows the marginalpro�ts from increasing lending (equal to the spread) while the right-handside shows the costs of deviating from the minimum requirements. FollowingAngelini et al. (2014), we model risk weights as follows:

ωit = (1 − ρi)ωi + (1 − ρi)χi(Yt − Yt−4) + ρiωit−1, i = H,E

In the above equation, ωi corresponds to the steady-state risk weights onhousehold and entrepreneurial lending. χi < 0 which means the risk weightstend to be low during booms and high during recessions. The cyclicality ofthe risk weights is what di�erentiates a bank's regulatory capital ratio from itsleverage ratio, following the discussion in Section 3. The law of motion for riskweights helps us capture the di�erence between the capital and leverage ratiosover the business cycle.

4.5.2. The retail branch. A Dixit-Stiglitz framework is assumed for the retailcredit and deposit markets. The elasticities of loan and deposit demand comingfrom households and entrepreneurs is given by εbs and εd, where s = H,E.These terms will be a major determinant of spreads between bank rates andthe policy rate. We maintain the assumption in Gerali et al. (2010) that eachof these elasticity terms is stochastic. Innovations to interest rate elasticities ofloans and deposits can be interpreted as innovations to bank spreads arisingindependently of monetary policy. The retail branch takes the loan and depositdemand schedules as given and then chooses the interest rates to maximizepro�ts. The loan and deposit demand schedules, facing bank j, can be derivedas follows:

bst (j) =

(rbst (j)

rbst

)−εbstbst dPt (j) =

(rdt (j)

rdt

)−εdtdt, s = H,E (9)

15 Leverage and Risk Weighted Capital Requirements

We observe that the aggregate demand for loans at bank j by impatienthouseholds or entrepreneurs depends on the overall volume of loans tohouseholds or entrepreneurs and on the interest rate charged on loans relativeto the rate index for that speci�c type of loan. A similar relationship is obtainedfor the deposits as well.

The retail loan branch j chooses the interest rate on loans to maximize:

E0

∞∑t=0

ΛP0,t[rBHt (j)bHt (j) + rBEt (j)bEt (j) − (RBHt BHt (j) +RBEt BEt (j))

−κbH2

(rbHt (j)

rbHt−1(j)− 1)2rbHt bHt − κbE

2(rbEt (j)

rbEt−1(j)− 1)2rbEt bEt ], (10)

subject to the loan demand forthcoming from households and entrepreneurs(Equation (9)). The �rst two terms are simply the returns from lending tohouseholds and entrepreneurs. The next term re�ects the cost of remuneratingfunds received from the wholesale branch. The last two terms are the costsof adjusting the interest rates. After imposing a symmetric equilibrium, the�rst-order conditions for interest rates yield:

1− εbst + εbstRbstrbst

−κbs(rbstrbst−1

− 1)rbstrbst−1

+Et[Λpt+1κbs(

rbst+1

rbst− 1)(

rbst+1

rbst)2Bst+1

Bst] = 0

(11)The discount factor is equal to the one of patient households because they ownthe bank. It can be seen that the retail rates depend on the markup and thewholesale rate (the marginal cost for the bank) which in turn depends on thebanks capital position and the policy rate. A similar equation can be derivedfor the deposit retail branch:

−1 + εdt − εdtRt

rdt− κd(

rdtrdt−1

− 1)rdtrdt−1

+Et[Λpt+1κd(

rdt+1

rdt− 1)(

rdt+1

rdt)2dt+1

dt] = 0

(12)It can be seen from equations (11) and (12) that when prices are perfectly�exible, the lending rates are simply a markup over the policy rate while thedeposit rate is a markdown on the policy rate, i.e.,

rbst =εbst

1 − εbstRbst rdt =

εdtεdt − 1

Rdt , s = H,E

Finally, the total pro�ts of the banking group, j, can be written as follows:6

6. Retail and wholesale branches taken together and ignoring within group transactions.

Working Papers 16

Jbt = rBHt bHt + rBEt bEt − rdt dt −κKb

2(

Kbt

ωHt BHt + ωEt B

Et

− νbt )2Kb

t

−κLb2

(Kbt

BHt +BEt−ϕb)2Kb

t −κbH

2(rbHt (j)

rbHt−1(j)− 1)2rbHt bHt − κbE

2(rbEt (j)

rbEt−1(j)− 1)2rbEt bEt

(13)Thus total bank pro�ts are total receipts from retail loans less deposit costs,

costs of deviating from the leverage and capital requirement regulations, andinterest rate adjustment costs.

4.6. Retailers and capital goods producers

Capital goods producers buy undepreciated capital from entrepreneurs and �nalgoods from retailers to produce new capital which is sold back to entrepreneurs,at price Qkt . This process of transforming the �nal goods into capital goodsentails adjustment costs. Following Bernanke et al. (1999), the retail goodsproducers are assumed to be monopolistically competitive. They face nominalrigidities and their price is indexed to a combination of past and steadyin�ation. They face quadratic adjustment costs to change prices beyond whatis allowed by indexation.

4.7. Monetary and macroprudential policy

There are a few more ingredients that warrant discussion, namely the monetaryauthority and the macroprudential authority.

The monetary authority sets policy rates according to a standard Taylorrule:

(1 + rt) = (1 + r)1−ϕR(1 + rt−1)ϕR(πtπ

)ϕπ(1−ϕR)(yty

)ϕy(1−ϕR)

εrt ,

where ϕy and ϕπ are the weights attached to output and in�ation growthrespectively and εrt is a white noise monetary policy shock.

The macroprudential setup is di�erent in this paper with respect toAngelini et al. (2014). The macroprudential authority sets a time-varyingcapital requirement and a �xed leverage requirement, that banks must complywith at all times. As discussed earlier, there are costs to deviating from theseexogenously set targets. Time-varying capital requirements follow:

νt = (1 − ρν)ν + (1 − ρν)

[χν

(BtYt

− B

Y

)]+ ρννt−1,

where χν > 0 would imply the presence of a countercyclical capital bu�er. Theobjective of having such time-varying capital requirements is to increase bank

17 Leverage and Risk Weighted Capital Requirements

capital when the loan to output ratio deviates away from its steady-state level(Drehmann and Gambacorta (2012)).

5. Calibration

Most of the parameters used are the ones estimated in Gerali et al. (2010). Themain parameters are reported in Table A.2. The discount factor is identical forthe impatient households and the entrepreneurs. The steady-state risk-weightedcapital requirement is set at 8.5% which includes a core Tier 1 requirement of6% and a conservation bu�er of 2.5%. As discussed earlier, the model calibrationof the leverage ratio is sensitive to the steady-state risk weights. To illustratethis point a bit further, we use Figure A.2 to plot equation (1). On the x andy axis, we alter the risk-weights on mortgage and �rm lending while on the zaxis we plot the leverage ratio. As is intuitive, the leverage ratio is increasing ineither of the steady-state risk weights. In terms of equation (1), this is becausean increase in either of the two risk weights increases the risk weight density,thereby increasing the minimum leverage requirement. Intuitively, when theoverall economic scenario is more risky, it is prudent to hold more capital.Our baseline calibration corresponds to steady-state risk weights of 0.37 onhousehold lending and 0.92 on entrepreneurial lending. Given that the steady-state risk-weighted capital ratio requirement and that the share of lending tohouseholds vs. �rms is 60-40, we calibrate the leverage ratio to be 5%. We alsoreport the results of using the standardized risk weights for the calibration i.e.0.35 and 1.00 for mortgage to households and �rm lending respectively.

The depreciation of capital (δ) is set to get an annual depreciation of 10%.The mark-ups in the goods and labor markets are assumed to be 25% and20% yielding values of εl = 5 and εy = 6 respectively. The weight of housingin the utility function is taken from Iacoviello and Neri (2010) and is set atεh = 0.2. The LTV ratio on entrepreneurial lending is set at 70% and for thehousehold lending, it is 35%. The calibration of the TFP shock is standard, asit is adopted from the business cycle literature.

Regarding the parameters of the law of motion for the risk weights, we usethe estimated parameters from Angelini et al. (2011).7 The parameters χH ,χE , ρH , and ρE are set at, respectively, -10, -15, 0.94, and 0.92. Regardingthe steady-state risk weights, we experiment with two sets of values. The �rstset corresponds to the European Banking Authority �gures (ωH = 0.37 and

7. They use data on delinquency rates on loans to households and non-�nancialcorporations in the US as proxies for the probabilities of default on these loans (similardata for the euro area were not available). They input these time series into the BaselII capital requirements formula, and, using a series of assumptions concerning the otherkey variables of the formula, they back out the time series for the risk weights. Next theyestimate the law of motion for the risk-weights equation to obtain the parameters. For moredetails, we refer the reader to Appendix 1 of Angelini et al. (2011).

Working Papers 18

ωE = 0.92) while the second set corresponds to the standardized risk weightingapproach (ωH = 0.35 and ωE = 1.00).

6. Results

We will analyze the response of the economy to two shocks, namely a positivetechnology shock and a shock to the loan-to-value ratio for entrepreneuriallending. We will also conduct some exercises with alternative values of theleverage ratio to understand the costs and bene�ts of the same.

6.1. Response to a positive technology shock:

We analyze the response of some key variables in response to a unit standarddeviation shock to total factor productivity. Figure A.3 illustrates the mainmechanism of the model. The left-hand panel shows how the risk weightsdecline during booms. The decline in risk weights could encourage excessiverisk taking during booms and this is precisely what the leverage ratio aims tocorrect. The right panel shows how the leverage ratio and the risk-sensitivecapital ratio evolve after the incidence of the shock. The mechanism is thefollowing. During booms, lending to households and �rms increases, drivingdown the leverage and the capital ratio. However, risk weights also decline andtherefore the decline in the leverage ratio (non-risk-sensitive) is larger than thecapital-to-RWA ratio. This increases costs for the bank because it deviates morefrom the regulatory requirements. In the absence of the leverage requirement,the bank would continue to expand lending. It is in this way that the leverageratio restricts a credit cycle boom. It is intuitive to see that the opposite wouldhappen in an economic downturn. In that scenario, the capital ratio would bethe more binding constraint as the risk weights also tend to increase. Thusthe leverage ratio is intended to be the constraining ratio in booms and themilder constraint in a downturn. In Figure A.4 we report the impulse responseof some other key variables of the model. In the top panels, we show theIRFs of loan to output ratio and the total lending: precisely the variables themacroprudential instruments target. In the lower panel, we show the two mostimportant real variables, namely, output and investment. These �gures clearlyhighlight the bene�ts of introducing the leverage ratio requirement in additionto the risk weighted ratio requirement. Volatility in the credit cycle is reducedsubstantially, which also translates into a moderation of the real series.

Although there are clear gains from introducing the minimum leveragerequirement for banks, there are also some associated costs. Table A.3 addressesthis question. Following the literature, we base our analysis on the impacton output (Gerali et al. (2010) and Angelini et al. (2014)). We show theleverage requirement's e�ect in reducing the steady-state level and volatilityof output. For the sake of robustness, this analysis is done for two di�erent

19 Leverage and Risk Weighted Capital Requirements

sets of steady-state risk weights. The �rst set of values corresponds to theEuropean Banking Authority �gures (ωH = 0.37 and ωE = 0.92) while thesecond set corresponds to the standardized risk weighting approach (ωH = 0.35and ωE = 1.00). The EBA risk weights would imply a minimum leveragerequirement of approximately 5% while the standardized approach would imply5.20%.8 We observe that, conditional on the choice of steady-state risk weights,the leverage requirement generates a loss in steady-state output in the rangeof 0.7 − 1.7%. On the other hand, the reduction in output variability is quitesubstantial (24 − 28%). To put these magnitudes in perspective, we make acomparison with the long-term impact study conducted in BCBS (2010). TheLEI report �nds that a 1% increase in risk-weighted capital requirements leadsto a reduction in the steady-state output of 9bps and in output volatility of1.3%. Our numbers are qualitatively similar and imply that the bene�ts fromintroducing the minimum leverage requirements are substantially larger thanthe costs.

6.2. A shock to the loan-to-value ratio

In this section, we conduct an alternative check by analyzing the response to ashock to the LTV ratio for entrepreneurial loans. More speci�cally, we analyzea one-time rise in the LTV ratio by 20 percentage points. We present resultsfor the shock to the LTV on entrepreneurial lending but the shock to LTV onmortgage lending was also analyzed and the results are qualitatively similar.Figures A.5 - A.6 and Table A.4 present the results. Figure A.5 presents theimpact on the risk weights and the regulatory ratios, after the incidence ofthe shock, with both the regulatory minima operating. Similar to the case ofthe TFP shock, we �nd that the leverage ratio declines much more than therisk-weighted capital ratio, causing the leverage requirement to bind earlier.This is once again driven by the decline in risk weights and because the bankaccumulates capital relatively slowly. On impact, the lending responds �rst,leading to a decline in both ratios. This is the almost instantaneous volumee�ect. But with the higher LTV, interest rates are also higher. Once interestrates start increasing, the banks pro�ts and capital also start increasing. Thisleads to a gradual recovery in the regulatory ratios. Figure A.6 once againreports the impulse response of the main variables following the shock. Notethat in contrast to the TFP shock, the risk weights in this case decline muchless and this is partly due to the way the risk weights have been modeled:The productivity shock a�ects output and risk weights directly but this is notthe case in the present scenario. Table A.4 represents the cost-bene�t analysisin this scenario. The main insights are similar to the ones presented in Table

8. Assuming that the minimum risk-weighted capital requirement is 8.5% and the shareof mortgage lending to households is 0.6.

Working Papers 20

A.3. We represent the theoretical moments from the simulation of the model,with the LTV shock operative. The last column highlights the fact that thereduction in the volatility is substantially higher than the reduction in levels.This is all the more evident in the lending variables. This is intuitive as theprincipal aim of imposing the minimum leverage requirement is to reduce thevolatility of the credit cycle. It should be mentioned here that we are notanalyzing a shock to house prices separately, as the dynamics of a house priceshock are qualitatively similar to the LTV shock, in the model. A rise in houseprices would relax borrowing constraints, which would lead to higher creditgrowth. The bene�ts of introducing the leverage ratio in such a situation willbe identical.

6.3. Altering the sensitivity of risk weights to output

The main reason for introducing the leverage ratio requirement is that riskweights tend to be cyclical and that, during booms, the risk-weighted capitalratio may not be a good indicator of a bank's capital situation. Therefore,a natural question to ask is: how does the role of the leverage ratio changeas the cyclicality of risk weights is altered? Table A.5 reports the standarddeviations of the loan-to-output ratio, total loans, output, and consumption.The baseline case corresponds to the calibration by Angelini et al. (2014). Thesecond case is a thought experiment where we increase the sensitivity by afactor of ten.9 We report the theoretical second moment from a 1000 periodsimulation conditional on the occurrence of the productivity shock. We �ndthat, when risk weights tend to be highly countercyclical, the introduction ofthe leverage ratio is much more e�ective in controlling the volatilities in thesystem. The decline in standard deviations is quite large and more so for thelending variables, which is precisely what the leverage ratio aims to control.

7. Conclusion

The main bene�t of bank capital requirements is to make the �nancial systemmore resilient, reducing the probability of banking crises and their associatedoutput losses. However, the global �nancial crisis has highlighted the limitationsof risk-sensitive bank capital ratios (regulatory capital divided by risk-weightedassets). Despite numerous re�nements and revisions over the last two decades,the weights applied to asset categories seem to not have been able to fullyre�ect banks' portfolio risk. To tackle this problem the Basel III regulatoryframework has introduced a minimum leverage ratio, de�ned as a bank's Tier1 capital over an exposure measure, which is independent of risk assessment.

9. Note that this is just a thought experiment to gain intuition. One could experimentwith any other sensitivities as well.

21 Leverage and Risk Weighted Capital Requirements

This paper seeks to answer three questions: 1) How does the leverage ratiobehave over the cycle compared with the risk-weighted asset ratio?; 2) Whatare the costs and the bene�ts of introducing a leverage ratio?; 3) What can welearn about the behavior of the two ratios in the long run and their optimalcalibration? To this end, we have used a medium sized DSGE model thatfeatures a banking sector, �nancial frictions, and economic agents with di�eringdegrees of creditworthiness as a means of evaluating the regulator's problem.In particular, we built on the model by Angelini et al. (2014), augmenting it intwo ways. First, we introduce a leverage ratio, independent of risk assessment,whose deviation from the minimum requirements produces additional capitaladjustment costs. Second, we allow the risk weights on lending to householdsand non-�nancial �rms to be di�erent in the steady state. This modi�cationallows us to mimic the real characteristics of the evolution of bank-risk-settingbehavior and to generate di�erent interest rates for the two classes of loans.The main results are the following: 1) The leverage ratio acts as a backstopto the risk-sensitive capital requirement: it is a tight constraint during a boomand a soft constraint in a bust; 2) the net bene�ts of introducing the leverageratio could be substantial; 3) the steady state value of the regulatory minimafor the two ratios strongly depends on the riskiness and the composition ofbank lending portfolios.

Working Papers 22

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[51] Smets, F., and R. Wouters, (2003), "An estimated dynamic stochasticgeneral equilibrium model of the euro area". Journal of the EuropeanEconomic Association, vol. 1, Issue 5, pp. 1123 - 1175.

[52] Turner, A., (2010), "What do banks do? Why do credit booms and bustsoccur and what can public policy do about it?". In Turner A. et al., TheFuture of Finance: The LSE Report, Ch. 1, London School of Economics.

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[54] Wall, L., (1989), "Capital requirements for banks: A look at the 1981and 1988 standards". Federal Reserve Bank of Atlanta Economic Review(March/April), pp. 14-29.

[55] Wall, L. and D. Peterson, (1987), "The e�ect of capital adequacy guidelineson large bank holding companies". Journal of Banking and Finance, vol.11, pp. 581-600.

Working Papers 26

Appendix: Figures and Tables

Patient Hhs

Impatient Hhs

Banks (Wholesale + Retail)

Entrepreneurs

Capital Goods Producers

Retailers

D Rd

Bh

Rh

Be Re

Lp Wp Li

Wi

h_bar = hp + hi hp hi

Buy (1-δ)k-1 at price qk

Sell back new k at price qk

It

Pt

Y (int) P (int)

Central bank conducting monetary

policy

Macroprudential Authority setting

capital and leverage

requirements

Y= c + I + adjustment costs

Figure A.1: Flowchart of Agents

0.920.94

0.960.98

11.02

1.041.06

1.081.1

1.12

0.240.26

0.280.3

0.320.34

0.360.38

0.40.42

4.4

4.6

4.8

5

5.2

5.4

5.6

5.8

6

Firm Lending Risk WeightsMortgage Risk Weights

Leve

rage

Rat

io

Figure A.2: Leverage Ratio and Steady State Risk Weights

27 Leverage and Risk Weighted Capital Requirements

(a) Risk Weights (b) Leverage and Capital Ratios

Figure A.3: Risk Weights, Capital and Leverage Ratio (TFP Shock)

(a) Loan to Output Ratio (b) Total Lending

(c) Output (d) Investment

Figure A.4: IRF in response to a 1 standard deviation positive TFP shock

Working Papers 28

(a) Risk Weights (b) Leverage and Capital Ratios

Figure A.5: Risk Weights, Capital and Leverage Ratio (LTV Shock)

(a) Loan to Output Ratio (b) Total Lending

(c) Output (d) Investment

Figure A.6: IRF in response to the LTV shock

29 Leverage and Risk Weighted Capital Requirements

Models Business Cycle Financial Cycle(Real GDP growth) (Credit Gap)

LR = Tier1EM

RWR = Tier1RWA

LR = Tier1EM

RWR = Tier1RWA

Baseline model -0.052** -0.048 -0.005* -0.003(0.026) (0.038) (0.003) (0.004)

Controlling for di�erent regimes -0.055** -0.045 -0.005* 0.004of capital regulation (0.026) (0.037) (0.003) (0.004)

Table A.1. Cyclicality of capital Ratios

Source: Brei and Gambacorta (2016). (1) The empirical speci�cation in the baseline modelincludes bank-speci�c controls, bank-�xed e�ects and a lagged value of the dependentvariable. The model is estimated with GMM and allows for the presence of a structuralbreak during the global �nancial crisis. (2) The second model controls for (i) the shift fromBasel I to Basel II, and (ii) the presence of an additional leverage ratio requirement inCanada and US. The �gures show the impact after one year of a 1% increase in the cyclemeasure (1995-2007).

Parameter Symbol Value Target/Source

Discount Rate Patient βP 0.99 Annual risk free rate of 4%Discount Rate Impatient βI 0.975 Iacoviello (2005)%

Discount Rate Entrepreneurs βE 0.975 Iacoviello (2005)%SS Capital Requirement νb 0.085 Basel committee guidelinesLeverage Requirement ϕb 0.05 Basel committee guidelines

Depreciation δ 0.025 Annual 10%Share of Capital α 0.25 StandardRisk Aversion ϕ 1.5 Standard

Goods mkt. markup εh 6 Gerali et. al (2010)Lab. mkt. markup εl 5 Gerali et. al (2010)

Inverse of Frisch Elasticity of labor supply ϕ 0.5 Labor supply elasticity = 2Utility fn. weight of housing εht 0.2 Iacoviello & Neri (2010)

LTV household mIt 0.7 Calza et. al. (2009)

LTV �rms mEt 0.35 Gerali et. al. (2010)

Markdown deposits εd −1.46 Gerali et. al. (2010)Markup Mortgage εbH 2.79 Gerali et. al. (2010)Markup Frims εbE 3.12 Gerali et. al. (2010)

Persistence of TFP shock ρA 0.90 Std. business cycle literatureVolatility of TFP shock σ2u 0.01 Std. business cycle literature

Mean of TFP A 1.00 Std. business cycle literaturePersistence of house pref. shock ρεh 0.96 Iacoviello & Neri (2010)Volatility of house pref. shock σεh 0.043 Iacoviello & Neri (2010)

Table A.2. Calibration

Working Papers 30

ωH = 0.35, ωE = 1.00 ωH = 0.37, ωE = 0.92⇒ ϕb = 0.052 ⇒ ϕb = 0.050

Yss σY Yss σYK 0.2196 0.0839 0.2232 0.0796

K+L 0.2180 0.0605 0.2194 0.0599% decline 0.70 28.48 1.70 24.75

Table A.3. Costs Vs Bene�ts

Variable Moments K K+ L % decline

Output Mean 0.2566 0.2514 2.02SD 0.0391 0.0371 5.11

Consumption Mean 0.1353 0.1311 3.10SD 0.0323 0.0307 4.96

Loan to Output Mean 0.9260 0.9250 0.11SD 1.2093 1.1085 8.33

Total Loans Mean 1.1826 1.1772 0.46SD 1.2204 1.1175 8.46

Table A.4. Shock to the LTV ratio on entrepreneurial loans

Baseline Case High SensitivityK K+L % decline K K+L % decline

Loan to Output Ratio 0.186 0.161 13.44 0.235 0.166 29.37Total Loans 0.186 0.162 12.90 0.263 0.177 32.69Output 0.085 0.061 28.23 0.086 0.056 34.88

Consumption 0.070 0.054 22.85 0.071 0.052 26.76

Table A.5. Altering the sensitivity of risk weights to output

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