Releasing the countercyclical capital buffer under quantitative easing in a DSGE framework

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under Quantitative Easing in a DSGE Framework

Edi Vording

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15-8-2017

Universiteit van Amsterdam

Student number: 11384557

Abstract

The interaction between unconventional monetary policy and the release of the countercyclical capital buffers has not yet been researched extensively. Using a New Keynesian DSGE model featuring a banking sector and large scale asset purchases, we analyze the possible interplays between these two forms of policy by making an endogenous capital constraint more countercyclical, effectively turning it into a countercyclical buffer. Although no quantitative inference can be drawn from our model, we show that the countercyclical capital buffer can serve as a macroeconomic stabilizer from a qualitative point of view. Besides, the buffer may already be stabilizing if released but before actually being run down, through an expectations channel. Moreover, we show that there exists a degree of substitutability between unconventional monetary policy and countercyclical buffers. This link is in line with results already found between conventional monetary policy and countercyclical buffers. Finally, we find qualitative evidence that releasing countercyclical buffers under unconventional policy is relatively slightly less effective than under conventional policy.

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This thesis was part of an internship at De Nederlandsche Bank. I gratefully acknowledge both computational and conceptual help by my supervisor Kostas Mavromatis, Dennis Bonam, Gavin Goy, Gabriele Galati and all the others at the Economics and Research Department with whom I have had interesting discussions. The views expressed in this paper are solely those of the author, and do not necessarily reflect those of De Nederlandsche Bank. The Dynare file used for simulations is available on request, edi.vording@student.uva.nl

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Statement of Originality

This document is written by Edi Vording who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Introduction

The word ‘cycle’, from ancient Greek κυκλος, originally meant circle, but also circular motion. It illustrates the revolving nature of phenomena around some state. Cyclicality has always been part of the modern human’s environment; from the seasonal swings of nature, to the earliest forms of food storage; the first granaries were built in modern day Jordan, some 11 thousand (!) years ago, to store food for less abundant times (Kuijt & Finlayson, 2009). This notion of (economic) cyclicality was not exclusively present in material world, but also in the intangible one. The Roman proverb ‘’in times of peace, prepare for war’’ (si vis pacem, para bellum) beautifully illustrates this. Analogously, economists have, to some extent, come to the same realization ever since Keynes’ General Theory: in times of boom, prepare for bust. Consequently, the notion of countercyclicality, or ‘’leaning against the wind’’, gradually found its way into fiscal and monetary policy over the course of the 20th_{century. It took many more years and the largest}

financial breakdown since the Great Depression for economists to realize that this concept might also be applicable to financial regulation, which is largely captured in the developing literature on macroprudential policy.

First, the 2008 financial crisis and subsequent European sovereign debt crisis once more required economists to thoroughly reassess the structure of our economy. The crackdown of the financial system and large scale bank failures made policymakers and academics shift their focus to macroprudential policy, which aims at making the financial sector as a whole more resilient to shocks. One of the main policy tools recently developed addresses this cyclical nature of the financial system, and has become one of the cornerstones of Basel III: the countercyclical capital buffer. Its purpose is to make banks accumulate buffers in booms, so they can deplete them in busts, to shield the banking sector from the credit cycle. The crisis yet again showed the importance of the banking sector for a proper allocation of credit and the transmission of monetary policy. Therefore, the build-up of systemic risk within the financial sector needs to be addressed with respect to both its cross-sectional and time-varying dimension. This paper focuses on the latter dimension: how to deal with the build-up of systemic risk over time? This strand of literature on macroprudential policy is still in its infancy. There is a lot of work to be done to analyze both the sign and size of new macroprudential policy tools (Galati & Moessner, 2012). Moreover, there is no consensus yet. For example, Drehmann and Gambacorta (2012) find that countercyclical capital requirements indeed work countercyclically, by limiting credit growth in booms, and boosting it in busts. However, Repullo and Saurina (2011) argue that this form of capital buffers may actually work procyclically, depending on the leading indicator. The discussion is far from being settled.

Second, during but especially after the 2008 and subsequent debt crisis hit the European economy, the ECB pursued an increasingly aggressive strategy to safeguard financial stability, stepping in as lender of last resort for troubled banks by providing vast amounts of liquidity. Financial markets calmed in 2012 after Mario Draghi’s famous announcement2_{that he would do}

‘’whatever it takes’’ to save the Eurozone. Early 2013, stuck at the zero lower bound, the ECB ventured into unchartered waters by engaging in unconventional monetary policy, in an attempt to shore up dwindling inflation in the medium run. The use of the (Targeted) Long Term Refinancing Operations and Quantitative Easing were unprecedented. Although called unconventional, it is not unlikely that a combination of unconventional monetary policy and the

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The full quote reads: "Within our mandate, the ECB is ready to do whatever it takes to preserve the euro. And believe me, it will be enough."

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release of countercyclical capital buffers will be applied again in the (distant) future. Yet, to the best of our knowledge, the interaction between unconventional monetary policy and the countercyclical capital buffer has not been researched.

This paper aims at bridging that gap. We introduce a macroprudential countercyclical element to an endogenous capital constraint in a New Keynesian model, namely the Gertler & Karadi (GK from now on) model on large scale asset purchases (2013). It features a banking sector and a QE-type of unconventional monetary policy. We try to identify the possible channels through which macroprudential and unconventional policy interact in a crisis situation. We compare these results to baseline scenarios. Are they substitutes, complements or do they have contradicting effects? By answering these questions, this paper is relevant to both scholars and policy makers. Although this is a theoretical paper, it may have important implications for policy makers.

The rest of this paper is structured as follows. In the literature review, the definition and history of and the rationale behind (countercyclical) capital buffers will be discussed. The theoretical and empirical relation between monetary policy and (countercyclical) capital buffers will also be reviewed. In the subsequent section, the model will be outlined. Then, we will carry out several experiments and comment on the results. Finally, we acknowledge limitations, make suggestions for policy and future research and conclude.

Literature Review

In this section, we give an overview of the literature regarding (countercyclical) capital buffers. First, we will clarify what capital requirements and the countercyclical capital buffers are. Second, to see things in a broader perspective, we treat the historical development of capital requirements and why they were introduced in the first place. Third, we will dedicate a subsection on the potential trade-off between financial stability and the credit flow to the real economy. Fourth, the relation between monetary policy and countercyclical capital buffers will be analyzed.

Definition

The capital requirement (or capital adequacy) is both an important indicator to assess banks’ health and a regulatory tool. It specifies the amount of capital that a bank should maintain relative to its (nowadays risk-weighted) assets. However, many different definitions of these requirements have been in practice throughout the years. In the past, for example, capital-to-deposits and capital-to-assets were used to measure the shock-absorbing capacity of the banks. The definition of the countercyclical capital buffer is in its name. It comprises part of the total amount of capital banks have to maintain to be in accordance with statutory capital requirements, but countercyclical in nature. It is built up when excessive credit growth necessitates it, as to be able to release it in downturns, hopefully enhancing financial stability. Basel III in general aims at ensuring financial stability, which is also reflected in the new components of capital buffers for banks. Figure 1 illustrates the different tranches of regulatory capital.

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Figure 1

Core equity tier 1, besides having been raised to 4.5% compared to Basel II, is topped up by additional tier 1 capital and additional tier 2 (specific forms of debt, including CoCo’s). This is supplemented by a 2.5% capital conservation buffer, which serves as another layer of shock absorbing capacity, as was proposed by the Basel Committee on Banking Supervision (BCBS) to increase bank resilience (Repullo & Saurina, 2011). Even though the conservation buffer has to consist of the same type of equity as CET1, there is an important distinction. Whenever the conservation buffer is breached, special regulatory action is taken, which includes a limit on the amount of dividends and bonuses a bank can pay out (ESRB). Finally, the countercyclical capital buffer, amounting to a maximum of 2.5% of risk-weighted assets, serves to make the banking industry more robust to systemic risk build-up. Breaching it results in similar legal and regulatory action as with the capital conservation buffer. Not shown in the graph are the 1-2.5% buffers specific to G-SIFI’s (Global Systemically Important Financial Institutions), and the additional SIFI requirement at the national governments’ discretion3_{. Absent the national SIFI}

buffer, total capital requirements can thus add up to 15.5% of risk-weighted assets.

History

The concept of capital requirements has a long history. As early as 1864, US regulators introduced static minimum capital requirements based on local population sizes to assess the financial health of banks. However, it was difficult to quantify the requirements, and so these first attempts were unsuccessful (Norton, 1995). Then, regulators experimented using

3_{The national SIFI requirement was introduced to enable countries to specifically top up requirements for large}

important financial institutions in their country. Especially for small countries with a vast banking sector, additional prudential tools such as this one are important, as became painfully clear during e.g. the Icelandic and Cypriot banking crises.

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to-deposits and capital-to-total-assets, but these measures were repealed on the grounds of being ineffective. After and during the Great Depression, regulators shifted their attention to solvency, thus calculating capital adequacy as capital-to-assets (Alfriend, 1988). In the 1940’s, the US Federal Reserve introduced the system based on risk-weighted assets. It was spurred by rapid credit expansion in the years after WWII, which fueled concerns about financial stability. It has remained the standard in American and European legislation until today, after its formal international introduction in Basel I4_{(Basel Committee, 1988). The idea to weigh assets by risk}

was introduced to distinguish between different classes of securities banks invested in. Traditionally, cash holdings, interbank lending and government bonds were considered free, whereas e.g. commercial loans and mortgages carried higher weights. This way of risk-weighting remains an inherent part of the Basel III agreements, although significant changes have been made to the actual weights and types of assets included.

Until the 1980’s, the requirements were not formally quantified, and were used as ‘just’ one indicator within a broader range of measures. From then onwards, US regulators started formalizing capital requirements to replace the unclear arrangements that had been applied until then. Rather than treating it as just an indicator, they became front-line measures of solvency and financial health. Over time, the requirements became stricter and more coordinated across supervisors to minimize arbitrage from banks rechartering in another jurisdiction in the US (Posner, 2015). As the regime moved from ‘guidelines’ to a rule-based system, regulators decided on the exact amount of capital that banks should hold against the asset-side of their balance sheets. As Posner argues, many of the percentages were not based on scientific evidence. Regulators hardly ever supplied cost-benefit analyses of the proposed reforms, which they were formally required to do by law. They determined the requirements based on what Posner calls ‘norming’: look at the average, and cut out the outliers at the lower end. The regulators’ reasoning was: we are only imposing costs on the bottom 5 percent of the banking system. As the percentage is set by what we observe in the system, it should be adequate, implicitly assuming that only 5 percent of the banking sector was undercapitalized. Regarding the CCB, to our best knowledge there have been only two country to introduce it prior to the 2008 financial crisis: Spain and Uruguay5_{. Formally called a dynamic (loan loss) provision,}

its functioning is very similar to the CCB. We will treat the Spanish case more elaborately shortly.

Why we need capital requirements

One might wonder why we need capital requirements in the first place. In the view of the neoclassical school, the market is perfectly capable of regulating itself. Prices (and thus bank-specific interest rates) will signal the amount of risk underlying an institution or asset. In our view, disciplining the financial system cannot be (completely) left to the market, for there are several information asymmetries and moral hazards involved. For example, it is very costly and time consuming for depositors to monitor their banks, especially given the asymmetries in both expertise and inside factual knowledge. Specialized institutions overseeing and quantifying risk for the entire banking sector could fill the gap, but as we have seen during the recent financial

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According to the Basel Committee, its advantages comprised (i) better comparison of banks across countries, (ii) an easier way to include off-balance sheet activities and (iii) not discouraging banks to hold low-risk assets. All three goals were (to some extent) undermined in the following twenty or so years.

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The Uruguayan dynamic provisioning differs only in two technical respects from the Spanish scheme. Its specifics will not be discussed here. For an overview, see e.g. Wezel (2010).

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crisis, it turned out to provide depositors with a false sense of security6_{. Besides, if we leave}

discipline entirely to the markets and market failures do occur, the losses are substantial due to the key role of the financial system within our economy.

Considering the financial system, market discipline is often late, abrupt and it overshoots7_{. It is}

late in that it often only starts disciplining financial institutions once things have started to go south. It can also be very abrupt, as can be seen in the rapidly declining share values of major banks during banking crises (Strah et al., 2013). Moreover, it overshoots (Breuss, 2011), since poor judgment about risk, bubbles and speculation may exacerbate the (required) adjustment, which should be driven by fundamentals rather than irrational expectations (Bongini et al., 2002).

Theoretically, equity increases the shock absorbing capacity of a bank. If more capital makes banks safer, why are they not fully equity financed? The distinguishing characteristic of banks compared to other financial institutions and non-financial firms, is that they are deposit-takers. These deposits provide a convenience yield to depositors (and thus have a significant value to society), who use their accounts to store their holdings, earn interest and transfer funds to others. This argument does not hold for bank liabilities in the form of bonds, as they are by far not as liquid and carry more risk than insurance-protected deposits. However, under conventional wisdom, debt is cheaper than equity (although this is not undisputed, see e.g. Admati et al. (2013)). In contrast to the Modigliani-Miller theorem, bank debt is (assumed?) less costly, mainly due to favourable tax treatment and the inherent implicit government subsidy8_.

This creates an environment in which banks will take on debt as well as equity. However, due to the leverage effect, banks have perverse incentives to decrease their equity and increase their debt9_{. Also, bank shareholders like to have less ‘skin-in-the-game’. They are protected by limited}

liability at the bottom, and deposit-insurance on the top. These conditions encourage shareholders to make the bank operate on thinner and thinner equity cushions, which could provide serious negative externalities to the economy if left unchecked by the regulator.

On the other hand, ignoring the convenience yield to depositors for a moment, higher bank capital does not guarantee bank solvency and a low probability of (systemic) failures in case of a crisis. Perotti et al. (2011), constructing a purely theoretical model, argue that higher bank equity poses two risks, both related to tail risk. First, hits incurred under a sufficiently high realization of the tail risk loss can wipe out almost any realistic level of capital, hence it can provide a false sense of security. The ‘’skin-in-the-game’’ argument no longer holds, because shareholders lose their money no matter how high the initial level of capitalization. Second, based on anecdotal evidence from before the crisis, banks with strong equity positions may in fact be more risk-taking. The reason is that given their strong equity position above the regulatory minimum, they can compliantly take on very tail risky projects with a low threat of

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The three big rating agencies Moody‟s, Standard & Poor‟s and Fitch all rated Lehman Brothers with at least an A until its collapse in September 2008.

7_{We thank Aerdt Houben for pointing us to this argument.}

8_{This implicit subsidy stems from government intervention in case of bank failures. Especially regarding}

(Global) Systemically Important Banks, or (G)SIBS, government bailouts were almost inevitable in case of bank insolvency. Since bank debt holders are aware of this expected bailout, the cost of debt falls, as (a large) part of the risk is borne by the sovereign, rather than by private investors themselves. To prevent this in the future, significant progress has been made in the form of the European Banking Union.

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Companies can increase their return-on-equity by simply levering up, substituting equity for debt, even if the return-on-assets is unchanged.

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capital adjustment costs. These costs occur when banks (almost) breach statutory requirements, and may take the form of loss of confidence by market participants or the inability to raise new funds. These banks can survive the impact if low (but non-tail risk) returns materialize. The authors do not argue that capital requirements are futile. Rather, they stress the importance of special monitoring of well capitalized banks by the regulator. This stresses the need for tailored supervision on top of raising capital requirements.

So far, we have only discussed the rationales behind and specifications of static capital requirements. Treating the systemic risks to the banking sector as something static was an important flaw in the design of pre-2008 financial regulation. It ignores the cyclical nature of the economy. Inadequately low equity cushions are one of the causes for the large-scale banking failure during the 2008-2009 financial crisis (Demirguc-Kunt et al., 2013). Moreover, these low equity levels may propagate concerns or even panics about counterparty solvency and reliability (Perotti et al., 2011). That is why we now turn to the supplementary countercyclical buffers.

Why capital requirements should be countercyclical

Countercyclical capital buffers constitute an important part of Basel III. Banks have little trouble raising capital in good times, but it can become difficult in bad times. Monte dei Paschi di Siena, the oldest surviving bank in the world, is a clear example. Finding itself severely undercapitalized in 2016, it was unable persuade market participants to buy its equity (Za & Fonte, 2016). Introducing a tranche of capital that is countercyclical may reduce this problem: banks build up equity in good times, when it is cheap, and face lower requirements in bad times, when they are more balance sheet constrained.

The development of the notion that bank capital should ‘’lean against the wind’’ can be traced back to experience from both Basel I and II. Following regulatory arbitrage under Basel I, its successor introduced the risk-weighted capital requirements based on internal-rating based (IRB) approach. Compliant10_{banks were allowed to use their own risk parameters to calculate}

regulatory capital. The BCBS’s rationale was that by empowering banks to do this on their own account and using their own expertise, risk models would become more accurate. After all, banks will want to minimize their required capital.

Although Basel II capital requirements were supposed to prevent regulatory arbitrage and procyclicality, the result were quite the opposite. Evidence shows that the (IRB) capital requirement under Basel II actually had a procyclical effect for two reasons. First, as banks face adverse economic circumstances, they can start making negative profits, which drains equity. Especially when the capital requirement becomes (almost) binding, credit to real activity is cut. Second, the IRB calculations rely positively on probability of default (PD) and loss given default (LGD). Under financial distress, both go up, effectively raising capital requirements per euro of outstanding loans (depending on the risk class), which constrains lending, and vice versa in an upturn (Heid, 2007; Repullo & Saurina, 2008; Kashyap & Stein, 2003).

To address this issue, the BCBS proposed the countercyclical capital buffer, which reacts to the state of the financial cycle, to make bank capital lean against the wind: let banks build up shock absorbing capacity when the credit markets are booming, and release these buffers when they are in a rut. Hence, the primary objective of the CCB is financial stability in the banking sector, by

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Banks had to fulfill certain requirements, minimum conditions, and needed approval from their national regulator.

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shielding it from excessive credit growth that often precedes banking crises. The CCB has another potential benefit; by requiring banks to hold more equity in upturns, the regulator is essentially discouraging the extension of additional credit. As a marginal euro extended as a loan now has to be backed by a larger amount of capital, credit growth may be slowed down when the buffer requirements are increased, which may help prevent excessive credit growth in the first place. However, it is important to stress that the latter is regarded as a side-effect of the CCB, and not as its main objective.

Another rationale behind the CCB is related to risk-taking (and particularly, risk-shifting). During booms, commercial banks have perverse incentives to increase their leverage and to engage in risk-shifting, i.e. investing in too risky assets. Their potential payoff increases and their own value at stake is small (they are protected by limited liability). Requiring banks to hold more equity in good times may decrease these risk-shifting incentives (Jensen & Meckling, 1976; Holmstrom & Tirole, 1997), which may lower the amount of debt overhang banks face after a financial shock has occurred. The reduction in debt overhang may in turn limit the drop in lending to the real economy, as banks are less financially constrained. Besides, loosening capital requirements may also lower the need of excessive risk-taking by banks in downturns in search

for yield, when interest rates are kept low. Jiménez et al. (2014) actually find evidence of

increased risk-taking by low-capitalized banks when short rates are low. The CCB can potentially mitigate this effect, by giving banks more breathing space.

As of yet, Switzerland (2013), Sweden (2015), Norway (2015), the Czech Republic (2015) and Hong Kong (2015) are the only entities to have raised their CCB’s in response to financial stability concerns; Switzerland, Sweden and Hong Kong out of concern for real-estate market (and thus mortgage debt) overheating, Norway and the Czech Republic because of rising credit-to-GDP growth and household debt. To our best knowledge, no empirical studies on the other three cases exist as of today.

Capital requirements and bank lending to the real economy

There is an active discussion on whether higher capital requirements in general reduce lending to firms and households. With the credit-crunch that followed the 2008-2009 financial crisis still reverberating in the economy, many ask whether it is prudent to increase capital requirements now. Berrospide and Edge (2010), using panel data, find only a modest response to lending resulting from increased capital requirements. Gambacorta and Mistrulli (2004), based on the Italian banking sector, argue that the effect of increasing capital requirements on lending is situational. Banks that are not well capitalized may find it difficult to raise equity in times of distress, and therefore have to cut lending to the real economy in order to meet the new, more stringent requirements. Bridges et al. (2014) investigate the effect of increasing capital requirements on bank lending to different sectors using UK data between 1990 and 2011. Their general result is that banks increase their capital buffers over about a three year period following a one percentage point increase in capital requirements. Banks generally maintain buffers at a level slightly higher than the statutory requirement. Hence, it takes them about three years to achieve a capital ratio that is somewhat above the requirement. Critically, to do so they cut lending to the real economy. This results in temporary reductions in loan growth to households of about a year. Interestingly, the largest decrease in credit growth occurs in lending to commercial real estate. It suggests that if raising capital requirements results mostly in (temporary) decreases in real estate credit growth, the CCB might be an effective tool to deal

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with overheating real estate markets and potentially entire credit markets in general. Sweden is currently engaging in this form of prudential policy, on which we will elaborate more shortly. Unfortunately, all studies just mentioned focus on increases in capital requirements, while we are especially interest in decreases. The problem is that throughout history, static capital requirements have, to our best knowledge, rarely been lowered. The effects on bank lending are thus difficult to quantify. Even though there is broad evidence in the literature that increasing requirements decreases (certain forms of) lending, we cannot readily assume that the opposite also holds.

There is, however, some evidence on releasing the CCB and its lending effects. The only CCB policy experiment in the pre-2008 crisis economic system was conducted in Spain. As mentioned, the Banco d’España introduced a dynamic provision11_{to make sure banks built up}

buffers in good times, to be able to run them down in bad times. Naturally, this provisioning received academic attention following the heated debate on macroprudential policy (ironically, it did so only after the Great Recession had occurred). Jiménez et al. (2012) study the impact of the dynamic provision on credit supply to firms and consumers in the 2000-2010 period, thereby capturing (i) the introduction of the CCB in 2000, (ii) a slight loosening of the CCB in 2005 and (iii) the 2008 financial crisis. They find that the dynamic provisions served their secondary purpose, in that they slowed down the extension of credit by individual banks in a boom. However, in good times firms found other sources of funding (e.g. at another, less constrained bank), which undermined the brake on total amount of credit supplied. Banks that were operating at the margin of their capital requirement cut credit by much more than the banks that were well provisioned in downturns. They conclude that even though the dynamic provisions were not (high) enough to prevent large scale banking failure in Spain, they did serve their purpose in terms of the side-benefit: limiting credit in booms, and easing it in busts. This argument is supported by Lozano-Vivas and Martinez-Alba (2017), who find evidence that the scheme smoothed the Spanish credit cycle, based on a 1995-2016 sample.

In 2013, Switzerland was the first country to activate the countercyclical capital buffer as it was envisioned in Basel III (as opposed to the similar Spanish provisioning scheme), albeit in a rather specific form: Swiss banks were required to hold an additional 1% of capital stock on their risk-weighted mortgage assets. The Swiss authorities implemented the CCB regulation as proposed by the Basel committee, but added a subtlety. Normally, the CCB targets all risk-weighted assets for the specific jurisdiction in which the bank operates, but the Swiss government can target specific asset classes on banks’ balance sheets, as to be able to slow credit growth in some sectors, while not distorting others. The aim of activating the CCB was twofold, following rising concerns about the booming Swiss residential real estate market: to increase loss-absorbing capacity and to tamper credit growth. Basten and Koch (2015) show that the activation of the CCB leads to higher mortgage prices, as can be expected. Since banks now have to hold more (expensive) equity against their newly issued mortgages, they charge their customers a higher price. Comparing their results to Jimenez et al. (2012) provides some intriguing similarities. In an upturn, they find that banks operating at the margin of their

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A dynamic loan loss provision is conceptually very similar to the CCB. It is designed as a tranche of loss absorbing capacity that builds up as the economy moves up the credit cycle. Forcing banks to maintain extra provisions naturally raises lending rates, so a side effect can be a cool-down of credit supply in upturns. The main difference with the CCB is that dynamic provisions do not target bank capital specifically, even though it is front-line loss absorbing capacity.

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requirement after the activation of the CCB raise prices by more than their well-capitalized competitors, which we can call a price effect. During a downturn, Jimenez et al. find that the marginal bank cuts credit by more than better capitalized banks, which we can call a quantity

effect. Even though the conclusions from both papers cannot be compared on a one-to-one basis,

the result is still interesting, for it seems that there exists homogeneity in marginal banks’ responses after a policy increase/decrease of the CCB, either through prices and/or quantities.

Interaction between CCB and monetary policy

The goal of our analysis is to understand the interplay between CCB’s and unconventional monetary policy. To gain an understanding of the mechanisms at work, it is necessary to start from the metaphorical beginning. In this subsection, we analyze the interaction between (counter)cyclical capital and (un)conventional monetary policy in the following order:

- Conventional monetary policy and (static) bank capital (requirements) - Conventional monetary policy and countercyclical bank capital requirements - Unconventional monetary policy and countercyclical bank capital requirements Then, we will also briefly approach the interaction from an institutional perspective.

Before analyzing these interactions, let us briefly reconsider the objectives of both forms of policy. As just mentioned, the CCB’s primary objective is to make bank capital buffers more resilient to fluctuations in the credit cycle, thereby enhancing financial stability. The objective of unconventional monetary policy (QE/LSAP in our analysis), at least in the Eurozone, is to restore inflation to a level close to but below 2 percent, by stimulating lending and thus investment and consumption in the real economy. In other words, the ECB strives for price stability..

The literature has brought forward two (actually three) hypotheses that are part of the credit

channel of monetary policy transmission12_{: the bank lending channel and the bank capital} channel, which will be briefly reviewed in that order.

The bank lending channel is built on the assumption of bank debt market imperfections. The channel functions as follows. Following a monetary tightening (e.g. open market sales by the central bank), interest rates go up and bank reserves fall. The reserve requirement then becomes (more) binding, and thus deposits fall13_{. Because of imperfections in the market for}

bank debt, banks cannot elastically substitute deposits for bank debt14_{. Eventually, the decrease}

in liabilities lowers the amount of assets the bank can maintain, thus reducing the amount of credit to the real economy (Bernanke & Blinder, 1988; Bernanke & Gertler, 1995). Moreover, as Gambacorta and Mistrulli (2004) point out, weakly capitalized banks with a lower creditworthiness face even tougher conditions in raising new liabilities after a monetary tightening, which brings us to the second hypothesis.

12_{A third one, the financial accelerator/balance sheet mechanism, will not be treated here for simplicity.}

Essentially, it entails the fact that increases in market rates lower asset prices, thus pushing down the ability of borrowers to post collateral. This reduces lending, potentially leading to a prolonged spiral of decreasing asset prices and decreasing lending. See e.g. Bernanke et al. (1999). Another, similar form of financial accelerator exists in the model presented in this paper, as will be shown in the next section.

13_{Alternatively, according to the monetary view, one can argue that due to an increase in interest rates, output}

falls and therefore the amount of deposits eventually decreases, thus limiting the bank‟s ability to lend funds.

14

Note that this substitutability need not be absent for a friction to arise. As soon as demand for deposits and bank debt are not perfect substitutes, a friction emerges following a contractionary monetary policy.

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The bank capital channel hypothesis relies on three important assumptions. First of all, the market for bank equity features frictions; monitoring costs and tax issues make issuing new equity costly. Second, banks face interest rate risk inherent in their business of maturity transformation. Third, banks have to obey statutory requirements. After an increase in open market rates (due to a tightening), the maturity mismatch in banks’ balance sheets makes the rates on deposits (short-term) rise faster than the rates on loans (long-term)15_{. It results in}

lower bank profitability (or even losses) and thus hurts equity via retained earnings. Even when the capital constraint is not binding, banks may lower the amount of outstanding credit. (Van den Heuvel, 2002; Gambacorta & Mistrulli, 2004). This is due to the fact that it is costly for a bank to break capital adequacy rules, both in terms of regulatory action and a potential loss of faith among market participants (Gambacorta & Marquez-Ibanez, 2011). Naturally, we are more interested in the effects following a monetary expansion (as we consider unconventional monetary policy). This literature is more limited in size. Still, Some research provides clues. For example, Van den Heuvel (2002), using a DSGE approach, finds that expansionary monetary policy especially increases lending by poorly capitalized banks through the bank capital channel, a symmetric effect of the mechanism following a monetary contraction just described. Tanaka (2002), based on an extended theoretical IS-LM framework, argues that well-capitalized banks and low capital requirements increase the effectiveness of monetary policy transmission. However, because interest rates have been close to zero for many years now and real activity has sluggish, banks have a hard time remaining profitable. In short, the debate on the bank capital channel is far from being settled.

Admittedly, many of the papers just mentioned date back more than a decade now. Although Bernanke and Gertler (1995) already argued that the influence of the bank lending and capital channel had diminished in the years prior to their paper, recent evidence shows that these channels played a large role in both the build-up to and unwinding of the financial crisis (Gambacorta & Marques-Ibanez, 2011). They contend that factors including deregulation, the growing influence of private investors and financial innovation contributed to the changing nature of monetary policy transmission through the bank lending channel. Their conclusions contain two key points worth mentioning in light of our analysis. First, they find that bank capital (Tier 1) is an important determinant of loan supply. Second, protracted periods of low interest rates can increase lending. Both statements are captured by the model of this paper, which will become clear shortly.

While the preceding analysis has been mostly empirical, the more recent debate on the relation between conventional monetary policy and CCB’s features more macro-modelling elements, which can be attributed, to a certain extent, to the rise of dynamic stochastic general equilibrium (DSGE) models and the lack of real-life experience with the CCB. Angelini, Neri and Panetta (2011) study this interaction, using such a model with both macroprudential and monetary policy. They conclude that macroprudential policy is not very effective at stabilizing the economy in normal times. However, in case of financially driven crises (that result in loan supply constraints for banks), macroprudential policy strengthens the tackling impact of monetary policy in terms of a reduction in the volatility of output and the loan-to-output ratio, at the expense of a more volatile interest rate and fluctuating capital requirements. This is due to the fact that the central bank can help out a friend in need, by deviating from its own policy objective

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Short-term debt is negotiated more often than long-term loans. Thus, as the bank faces a new, higher interest rate, it will have to pay its creditors a higher rate, whereas the rate on its loans remains unchanged.

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(price stability) if properly coordinated. A lack of cooperation between the central bank and the macroprudential authority may lead to conflicting and volatile responses in interest rates and capital requirements, through what Charles Bean (Bank of England) calls an I push you pull effect. This need for coordination stems from the fact that both authorities influence the same or closely related variables, but with different objectives. The macroprudential authority tries to minimize the capital-gap, which therefore boosts output and inflation. This is counteracted by the CB, who has a strong inflation target, raising interest rates. This, in turn, hurts bank profitability (because the risk-free rate goes up), thus potentially widening the bank capital gap, etc. Unifying the two authorities under a single policymaker’s banner, has a more stabilizing impact. Interestingly, depending on their calibration, they find redistributive effects of macroprudential policy, possibly favoring savers over borrowers. Benes and Kumhof (2015) analyze the issue in a DSGE framework with non-contingent returns on loan portfolios. Therefore, banks have to maintain precautionary capital conservation buffers, resulting in additional capital on top of the requirement. They find that by introducing a CCB, significant welfare gains can be achieved through the absorbing impact when losses actually materialize. Finally, they argue that monetary policy need not be as countercyclical in the presence of CCB’s, implying some substitutability In contrast, Angeloni and Faia (2009) conclude that capital ratios should be mildly countercyclical, combined with a monetary policy that does respond to asset prices. Cecchetti (2009) finds that they are, in fact, substitutes. The stronger the monetary policy response, the weaker the macroprudential response can be. He argues that there should be a good coordination mechanism between these two forms of policy. This is partly contradicted by Svenson (2014), who argues that the process of monetary and macroprudential policy making should be a Nash equilibrium, rather than a coordinated equilibrium, following from their distinct objectives: price and financial stability respectively. The (strong) underlying assumption is that macroprudential policy is effective at financial stabilization, whatever monetary policy is pursued. Bean et al. (2010), using an adapted version of Gertler & Karadi (2009/2011), find that macroprudential policy is better at leaning against the wind than monetary policy, as long as one considers bank capital and leverage to be the main drivers of risk-taking. This, again, implies some sort of substitutability, rather than complementarity, in managing systemic risk. Like Angelini et al. (2011), they find potential sources of conflict between the macroprudential and monetary authorities. Our analysis is to some extent similar to Bean’s. We depart from their analysis through several dimensions. They consider the interaction between conventional monetary policy and the CCB. We, on the other hand, employ GK 2013, which features a more QE-like unconventional monetary policy. Another important difference is the way we model the CCB. They consider a levy/subsidy on the evolution of banker net worth, which depends on the state of the business/credit cycle. It is financed by lump-sum taxes, and flows back to households through transfers. In reality, the CCB is not financed out of taxpayer money, a fact they, and Angelini et al. (2011), readily acknowledge16_{. Moreover, rather than including the}

macroprudential element in the equation for the evolution of banker net worth, we incorporate it directly into the leverage/capital constraint. All of this will become clear shortly, in the model section.

Still, a potential synergic interaction may exist. White and Borio (2003) state that protracted periods of low interest rates may fuel excessive risk taking in search for yield. This result is supported by Gambacorta and Marques-Ibanez (2011). We argue that the CCB has the potential

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of mitigating this to some extent. By allowing more breathing room, banks have less dire need to seek very risky projects, ‘’gambling for resurrection’’. Macroprudential policy may thus alleviate some of the (negative) externalities originating from monetary policy.

The relation between unconventional monetary policy and the CCB has, to our best knowledge, not yet produced any empirical literature for two reasons. First, empirical/quantitative research on the CCB in general is still in its infancy, as it has only been applied in a handful of countries up to this day. Second, the simultaneous implementation of QE and the use of the CCB has only occurred in one country so far: Sweden, and in another composition than in our setup. Although still stimulating real activity with QE, they raised, rather than released, the CCB to prevent overborrowing by Swedish households for real-estate purposes17_.

Due to the limited literature in the interaction between QE and the CCB, we have our own conjectures. Essentially, the distinct difference between conventional and unconventional monetary policy, is that the latter can be used once the zero lower bound (ZLB) is reached. Both aim at boosting inflation (and potentially output). Whereas conventional monetary policy does so through lowering short-term rates, unconventional policy targets long-term rates (as to flatten the yield curve). This, in turn, with the objective of increasing inflation expectations by explicitly keeping interest rates low for an extended period. Although a (conventional) monetary easing can increase lending through the capital channel, especially considering poorly-capitalized banks (Van den Heuvel, 2002; Tanaka 2002), sustained periods of low interest rates may hurt bank profitability to such an extent that banks get into trouble. On the other hand, the sheer sized acquisitions of assets under QE boosts their asset side. Also, although returns on investments have been quite low due to lower economic activity, the long period of low interest rates provided banks with the opportunity of much-needed deleveraging. This was certainly necessary, and for many banks mandatory following stricter capital regulation. In a future crisis, however, it might be more prudent to reduce the size or abruptness of this deleveraging, as it might be at the expense of bank lending to the real economy. This reduction can be achieved by the release of the CCB, thus preventing financial accelerator spirals.

Looking at the institutional perspective, the ECB’s only policy objective is price stability (the by now classical ‘’below but close to 2 percent’’). However, the recent financial crisis and sovereign debt crisis proved that the ECB has taken on a more (pro) active role. Voices are raised to change the rigid objective of price stability, and to let the monetary stance respond to other indicators of economic performance as well (see e.g. the discussion on long-term rates in the Taylor rule by Carlstrom, Fuerst and Paustian (2017)). Most importantly, the systemic risk inherently building up in het financial system could be taken account of in setting interest rates.

On the other hand, the European Systemic Risk Board (ESRB) is the authority which monitors and reacts to systemic risk. Therefore, there may be interactions or conflicts between the ECB and the ESRB, even though the former is the parent agency of the latter (and the chairman of the ESRB is the president of the ECB). Concerning the CCB specifically, the decision on whether to increase or release the buffer is at the national governments’/central banks’ discretion. The

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In fact, this is not at all that strange. First, only a handful of countries has started to build up the CCB in the first place. Second, the increases in asset prices that QE can produce, especially in real-estate, can be threatening from a macroprudential perspective. Lending to non-financial firms has recovered in Sweden, and credit supply is accelerating (Finansinspektionen, 2015). Macroprudential policy, in this case the CCB, can then lean against the „‟asset-price wind‟‟, allowing for a more tailored, yet possibly conflicting, policy mix.

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ESRB merely has an advisory role. In our opinion, this raises two concerns. First, it may lead to moral hazard if two conditions are met: an internationally integrated financial system and a peak in the credit cycle. A country may then decide not to raise the CCB, even if this is justified by indicators/fundamentals, to attract more financial intermediation, thus actively enabling regulatory arbitrage vis-à-vis a country that does raise it. Second, despite the fact that the ECB and ESRB are under the same roof, the fact that CCB decisions are ultimately at the governments’ discretion may complicate the coordination process. Especially political motives threaten the effectiveness of macroprudential measures in general, and the CCB in particular. To use the words of former Federal Reserve Chairman Martin: ‘’nobody wants to take away the punch bowl just as the party starts to get merry’’.

To see how the CCB and unconventional monetary policy interact, we adapt the Gertler & Karadi (2013) model on large scale asset purchases and implement the countercyclical capital buffer. The model will be described in the next section.

The model

Households

The model’s economy is populated by a continuum of identical households of measure unity. Households consume, supply labour, pay lump-sum taxes and transfer funds intertemporally. Concerning the latter, they can hold deposits at financial intermediaries and potentially also lend funds to the central bank (CB).

Within each household, a fraction 1-f of household members are workers, who work in production, and a fraction f act as bankers, who run financial intermediaries. Members switch occupation over time, which occurs according to a random process. Specifically, the probability that a member who is a banker in period t will still be a banker in period t+1 is given by . Hence, the average survival time for a banker is ⁄ 18_{. Therefore, every period an amount}

exits the banking industry, transferring their accumulated retained earnings back to the household. An equal proportion enters the banking industry, as to keep the ratio bankers/workers fixed. New bankers receive start-up funds from their households of size per banker, in which denotes the aggregate value of start-up funds provided.

Using conventional notation, denote consumption by and labor by , the habit parameter by

h, the inverse Frisch elasticity of labor supply by and the utility weight of labor by .

Household utility is then given by: ∑

( 1 )

with , and .

Real money balances do not enter the utility function19_{, following Woodford (2003). In the limit,}

the economy becomes cashless, hence consumers do not gain utility from these holdings.

18_{GK introduce a finite horizon for bankers to prevent a situation in which bankers accumulate sufficient}

retained earnings to be able to finance investment out of capital only.

19

Woodford‟s argument for this cashless economy is twofold: first, the use of physical currency may become redundant in the future, as it will be replaced by electronic currency. He does not consider this to be very likely.

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Therefore, there exists no cash in this model. However, households use assets to transfer funds intertemporally. They can save in the form of deposits held at financial intermediaries, or invest in sovereign debt. Both assets are real one period bonds that yield a gross real return of from period t-1 to t. These assets are riskless and therefore perfectly substitutable. We denote the total amount of short-term debt the household holds , the real wage , net profits from entrepreneurial activity in both non-financial and financial firms and lump sum taxes . This yields the following household budget constraint:

, ( 2 )

denotes the marginal utility of consumption. The households standard first order conditions

for labour supply and intertemporal substitution of consumption are:

, ( 3 ) in which , and , ( 4 ) in which . Financial intermediaries

The model’s financial sector, as previously noted, consists of a continuum of identical banks run by a banker. They funnel funds from household to non-financial firms, through deposits and business loans respectively. In the process, they engage in maturity transformation: the banks borrow short term (deposits)20_{and lend long term (business loans). They are also able to hold}

(long term) government bonds. The model’s banking sector serves as a proxy for the entire banking sector; both commercial and investment banking.

The intermediaries hold two types of assets: short-term business loans and long-term government bonds. Let the net period income flow from a loan that is financing a unit of capital by the bank be denoted by , the market value of the claim by , the depreciation rate of capital by and a disturbance term by . It follows that the rate of return for the bank equals

Second, and most predominantly, he shows that for the analysis of (effective) monetary policy it is not a necessity to consider money holdings in the utility function, which can greatly simplify the model. For a more profound analysis, see his book.

20_{In reality, deposits are a relatively stable source of funding, hence considering them as short-term liabilities}

may seem strange. However, the fact that they are callable on short notice justifies it. Moreover, they serve as a proxy for short-term bonds within the model, to mimic the reliance of modern banks on debt rollover.

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, ( 5 )

Note that the real return on private assets is thus increasing in its net income flow, increasing in the market value of the claim that remains after depreciation the next period, and decreasing in negative realizations of the random disturbance, all relative to its current market value.

Government bonds in the model are held by both banks and by households directly21_{. Sovereign}

bonds take the form of a perpetuity that yields one euro per period indefinitely. The price of the bond is denoted by and is the price level. It follows that the real rate of return equals

⁄ ( 6 )

Note that the real return on bonds is thus decreasing in the price level, and increasing in development in the bond price.

Now consider the financial intermediary’s balance sheet. In period t, a financial intermediary/banker j is funded by deposits denoted by , and equity –or net wealth- denoted by . The value of its private assets (business loans) is , the quantity of financial claims to the non-financial sector it holds, multiplied by , their relative price. It also holds government bonds on its asset side, denoted by , whose relative price is . More formally:

( 7 )

For now, it suffices to exclude central bank intermediation in the credit supply of banks.

As mentioned, households earn a certain real gross return on deposits held at the financial intermediary at time t of at time t+1. Intermediary private assets yield a stochastic return of over this period. Note that both and are determined endogenously. The

evolution of the bank’s equity is thus determined by the difference between the interest bankers earns on their assets and the interest they pay on deposits. Formally:

( 8 )

Bank equity can only be built up or replenished out of retained earnings. The reason is twofold. First, including other forms of capitalization (issuance of common stock, state support etc.) would make the model quite complex. Second, it is not necessary for our analysis, as macroprudential policy comes in useful when issuance of stock is problematic and state support is no longer an option.

The banker seeks to maximize his discounted stream of profits, in which the discount factor is the household’s intertemporal marginal rate of substitution, given by .

As long as the bank earns a profit or at least breaks even on its activities (i.e. the interest it earns on its assets is at least as large as the interest it pays its depositors), the banker will stay in business until he is randomly forced to exit; i.e. it is beneficial to keep retaining earnings until exiting. Therefore, the banker seeks to maximize his expected terminal wealth, given by:

21

We do not describe the derivation of household direct bond holdings in this paper. We will elaborate on it shortly.

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∑ ( 9 )

Whenever the risk adjusted discounted premium is positive, the banker is incentivized to expand his assets indefinitely. To solve this issue, GK propose a moral hazard problem: each period, the banker has two options. Either he stays in business or he robs the bank, i.e. he diverts a fraction of private sector assets on his bank’s balance sheet to his own household. However, following such a diversion, the depositors force the bank into bankruptcy, thereby recovering a fraction of 1- of private assets. It is too costly for depositors to recover the fraction diverted by the banker. Moreover, the banker can divert only a smaller fraction of its holdings of government bonds, in which . This difference aims at capturing the notion that private loan portfolio is more subject to banker misconduct22_{than its government bond portfolio, which}

is based on the assumption that it is more difficult to monitor the private portfolio than the bond portfolio for depositors (or the financial regulator). Alternatively, consider the fact that purchases of private assets free up more bank capital than purchases of government bonds, which will become clear later.

Hence, to ensure a situation in which depositors willingly provide funds to the banker, the following incentive constraint must be satisfied:

. ( 10 )

This states that the ongoing franchise value of the bank/terminal value of the banker’s wealth (the left side) should always be bigger or equal to the amount he can earn by diverting assets (the right side), thereby effectively closing the bank.

We briefly return to the discount factor. The ‘augmented’ stochastic discount factor, which comprises of the product of the household discount factor and a multiplier , is then

given by

̃ . ( 11 )

Here, denotes the shadow value of a unit of net worth to the banker at time t+1. This augments the discount factor by averaging the marginal value of an additional unit of net worth across exiting and continuing bankers:

( 12 )

The first argument on the right hand side entails the marginal gain of net worth of one, as the banker simply pays out all accumulated net worth to the household. If the banker continues, with probability , the marginal value is simply the derivative of net worth one period ahead with respect to the ongoing value of the bank. Indeed, whenever the spread is positive, this derivative is larger than one.

Let be the Lagrange multiplier on the incentive constraint. Taking the first order conditions, the expected excess returns on assets satisfy

22

GK‟s reasoning is that private loan portfolios are more likely to be subject to perversely incentivized risk taking.

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̃

( 13 )

̃ ( 14 )

Financial markets are frictionless in case the incentive constraint is non-binding. This occurs when equals zero for all t. Banks then keep expanding assets until their discounted return on assets is simply equal to the rate they pay on deposits. Also, equals one is this instance: the

product of the households discount rate and excess returns equals zero.

If the constraint binds, excess returns occur in equilibrium. This is one of the key features of the model. The binding incentive constraint results in limits to arbitrage: banks cannot outcompete, in which case financial markets are no longer frictionless, and thus a spread arises. The more binding the constraint, the larger the spread will be. In the general equilibrium of the model this occurrence of excess returns implies a higher price of capital. This yields a sub-optimal equilibrium, in which investment and industrial capital are below their potential value in a frictionless environment. In a crisis, a rise in the spread thus leads to a contraction in investment and thus output.

The spread on sovereign bonds will always be smaller than the one on private loans. Recall that this occurs because of the lower fraction that bankers can acquire. Thus, the limits to arbitrage are smaller for government bonds than for private loan portfolios.

To formalize the above, let the following expressions illustrate the source of the limits to arbitrage, coming from the incentive constraint. It specifies the link between the size of the bank’s portfolios (private and public) and its capital.

( 15 )

( 16 )

in which

̃

̃ . ( 17 )

Equation (17) pins down the bank’s leverage. The size of depends on several factors. First, it depends negatively on the diversion parameter ; the higher the fraction of assets the banker can divert, the lower the amount depositors are willing to lend the bank, for this raises the banker’s incentive to do so. Second, it depends positively on the discounted risk-free rate

̃ . A rise in the risk-free rate increases the ongoing value of the bank . Third, and

likewise, an increase in the excess return/spread also increases the ongoing value, and hence makes depositors willing to lend more funds to the bank. The banker’s incentive to divert assets is decreased, through the higher discounted terminal value of the bank.

Going back to constraint (15) and (16), one can observe that the maximum amount of assets a given banker can acquire depends on the amount of capital he/she has, multiplied by the leverage . The leverage thus endogenously determines a capital constraint. When the constraint binds (i.e. ), the incentive to divert assets is exactly equal to the ongoing value of the bank. Throughout the remainder of this paper, we will use the terms leverage and capital

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constraint/requirement interchangeably. When talking about the capital requirement, we mean the inverse of the leverage23_.

Because none of the factors influencing the adjusted leverage ratio are bank-specific, one can readily aggregate the leverage constraint to the entire financial sector, which is given by

. ( 18 )

As before, but now in the aggregate, leverage constrains the amount assets the banking sector can accumulate. If the constraint binds, a shock to capital (a financial crisis) will sharply decrease , which immediately lowers the amount of loans supplied. This mimics real financial crises, in which losses on portfolios directly destroy part of the bank’s equity, after which it is constrained to lend to the real economy.

The dynamics of net worth are given by the sum of retained earnings by the fraction of surviving bankers and the start-up funds that new bankers receive from their household, X:

*

+ . ( 19 )

Note that the main determinants of developments in net worth are the spread between the private portfolio and deposits and government bonds and deposits. The size of the fluctuations is increasing in the leverage, which is given here by

, as assets over net worth. The countercyclical capital buffer

Our contribution to the literature, as noted earlier, is to analyze the interplay between countercyclical capital buffers and unconventional monetary policy. To this extent, we change the endogenous leverage constraint to reflect a macroprudential element. Even though the endogenous leverage/capital constraint in the model is already (mildly) countercyclical by construction, the addition of a stronger countercyclical force helps to identify the effect of CCB’s compared to the baseline model. GK do not explicitly stress the mildly countercyclical behavior of their leverage constraint. Since they parametrize their model to grasp important features of an economy in crisis and subsequent LSAP policy response, it seems justified to make the leverage constraint even more countercyclical to proxy a CCB. Recall the equation for the economy-wide leverage, but note the introduction of a time subscript to

̃

̃ . ( 20 )

To make (more) countercyclical, we endogenize the diversion parameter . To this end, we assume that it is given by the following

. ( 21 )

Here, denotes the steady state value of the diversion variable (which is equal to the

calibration GK use), is a sensitivity parameter that determines the size of the adjustment, denotes the amount of productive capital (which is equal to the amount of outstanding loans)

23

When we, for example, state that leverage goes up, this implies that the capital requirement goes down, as it is the inverse of the leverage ratio within this model.

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and is the steady-state amount of capital. The term on the right hand side reflects the capital gap, defined here as the difference between industrial capital in period t and the steady-state, long-run stock of capital. Whenever the gap is negative (i.e. current capital is below the trend/long-run stock), this term is multiplied by the sensitivity parameter and subtracted from the steady state diversion rate. This lowers , which relaxes the constraint: increases for a given risk-free rate and spread. Hence, we proxy the CCB in a simple yet effective way. The Financial sector-wide leverage/capital constraint immediately responds to drops in capital below the steady-state.

Note that theta is endogenized only in the capital requirement, and it only responds to deviations from the steady state. The addition of a countercyclical element to this variable therefore does not affect the steady state of the model. Neither does it change the dynamics of other equations that include the ‘’standard’’ diversion parameter as G&K calibrated it. Also note that whereas the CCB needs to be built-up in reality before being able to be released, in our model we simply assume that there is no need for that. Incorporating such a structure would be cumbersome, and would probably not improve the qualitative analysis. Thus, assuming that the buffer is fully built-up when we conduct our crisis experiment shortly is not too strong an assumption.

Whenever the credit/capital gap is negative, the fraction bankers can divert goes down. This relaxes the constraint, because depositors become more willing to lend their funds to the bank. The bank, in turn, uses these deposits to issue new loans/rollover existing loans. However, this mechanism does not function in the opposite direction. By construction, the CCB only loosens the leverage when the Lagrange multiplier on the incentive constraint is binding. When this is not the case, for example under a positive shock, the CCB simulations do not yield sensible results.

This notion of a changing divertible fraction may seem rather stylized and unrealistic. However, instead of thinking of it as some arbitrary fraction the banker can divert, consider it as a measure of risk that bankers are allowed to take, dictated by the financial regulator or macroprudential authority. Here, we mean overall bank risk, i.e. the probability that the bank goes under given an exogenous shock of a particular size. The lower this risk variable, the higher the leverage. If in a crisis situation the macroprudential authority lowers the risk measure , it effectively permits bankers to take on more risk for a given risk-free rate and spread/excess return, if we define this ‘’risk’’ as the leverage that results from this measure24_{. Implicitly, capital}

requirements are a measure of bank riskiness that the regulator tolerates. Hence, releasing the CCB is equivalent to this higher risk tolerance, which functions through the diversion parameter

.

It is important to stress the limitations of this approach. First, the CCB as it is being implemented now is discretion-based instead of rule-based. Currently, both the build-up and the release of the CCB are at the national governments’ discretion, based on a guideline prescribing suitable

24_{This line of reasoning relies on the assumption that bank riskiness is increasing in its leverage. Gains, but most}

importantly losses, are amplified by a higher the leverage ratio. We stress that we do not link risk to the amount of assets the banker can divert directly; intuitively, lowering this fraction lowers the risk for depositors of the banker diverting assets.