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Journal of Banking & Finance 31 (2007) 3885­3900 www.elsevier.com/locate/jbf

The cyclical effects of the Basel II capital requirements q

Frank Heid

*

Deutsche Bundesbank, Wilhelm-Epstein-Strasse 14, 60431 Frankfurt am Main, Germany Received 2 May 2006; accepted 2 March 2007 Available online 30 March 2007

Abstract Capital requirements play a key role in the supervision and regulation of banks. The Basel Committee on Banking Supervision is in the process of changing the current framework by introducing risk sensitive capital charges. Some fear that this will unduly increase the volatility of regulatory capital. Furthermore, by limiting the banks' ability to lend, capital requirements may exacerbate an economic downturn. The paper examines the problem of capital-induced lending cycles and their pro-cyclical effect on the macroeconomy in greater detail. It finds that the capital buffer that banks hold on top of the required minimum capital plays a crucial role in mitigating the impact of the volatility of capital requirements. Ó 2007 Elsevier B.V. All rights reserved.

JEL classification: E32; E44; G21 Keywords: Minimum capital requirements; Regulatory capital; Economic capital; Capital buffer

This paper represents the author's personal opinion and does not necessarily reflect the views of the Deutsche Bundesbank. I thank the members of the Research Task Force of the Basel Committee on Banking Supervision for their helpful comments. In particular, I thank Heinz Herrmann, Thilo Liebig, Dirk Tasche and two anonymous referees for their suggestions. The usual disclaimer applies. * Tel.: +49 69 9566 3357; fax: +49 69 9566 4275. E-mail address: [email protected] 0378-4266/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2007.03.004

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1. Introduction In 2004, the Basel Committee on Banking Supervision passed a revision of its accord on capital regulation, which came into force in 2007.1 The new accord, which is referred to as Basel II, seeks to better align regulatory capital with economic risk, sometimes also called economic capital. In contrast to the old framework, now often conveniently named Basel I,2 the capital charges of Basel II are based on asset quality rather than on asset type. Banks will be able to choose from among several approaches. The standardized approach is based on the borrower's public ratings by attributing specific risk weights to the respective rating classes. More sophisticated banks will be eligible for the two internal ratings based approaches (IRB), which permit the use of the banks' own internal rating systems to quantify the creditworthiness of their debtors. As in the old framework, total capital charges are 8% of risk-weighted assets. It is worth noting that the Basel Committee apparently believes that capital charges will on average stay at the current level. Aligning regulatory capital with economic risks has obvious microeconomic benefits mainly because it reduces the potential for regulatory arbitrage. On the other hand, by increasing the sensitivity to credit risk, the new accord will make required minimum capital more cyclical. This could potentially pose severe capital management problems to banks due to the fact that capital charges are likely to increase in an economic downturn at a time when banks are confronted with the erosion of their equity capital as a result of write-offs in their loan portfolios. However, the impact on the macroeconomy may be even more severe if capital constrained banks are forced to reduce their lending. With regard to the cyclicality of capital charges, many empirical studies on Basel II indeed expect significant swings in minimum capital over the course of a business cycle, though the variety of estimates is fairly large. Most of these studies assess the likely cyclical patterns of capital charges under Basel II by performing numerical simulations on hypothetical or real world portfolios. No adjustments on behalf of the bank are assumed over the observation period. Ervin and Wilde (2001), who assume a hypothetical portfolio of BBB-rated borrowers, conclude that a bank with an initial capital ratio of 8% in 1990 would have experienced a fall in regulatory capital to 6.8% under the IRB approaches in subsequent years.3 A similar approach is taken by Kashyap and Stein (2004), who base their simulation on a portfolio of borrowers who at the time had a public rating from S&P or KMV. Their results show that for an average portfolio the increase in capital charges would have been in the range of 30­45% over the period from 1998 to 2002. Rosch (2002) ¨ further differentiates between the default risk effect and the transition risk effect. Using S&P's transition and default rates from 1982 to 2000, he concludes that these effects may offset capital requirements and that Basel II might therefore be even less cyclical than the old accord. A different approach is taken by Carling et al. (2002) who directly estimate the quality distribution of a major Norwegian bank's credit portfolio. They show that

Basel Committee on Banking Supervision (2004). In the European Union Basel II was put into law by the Capital Requirements Directive. Some countries, however, postponed the adoption of the new accord. The United States, for example, are expected to implement Basel II not before 2008. 2 Basel Committee on Banking Supervision (1988). 3 Calculations were based on the proposed risk weight function as of 2001. As the risk weight function has since changed, the effect is likely to be smaller.

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macroeconomic conditions have a significant impact on borrowers' probability of default (PD) and on regulatory capital under the Basel II IRB approaches. In any case, and whatever the cyclicality of capital charges, it would be premature to expect a bank's actual capital ratio to move in parallel with capital requirements since banks are likely to hold a certain capital buffer. Barrios and Blanco (2003) claim that banks hold a positive capital cushion even if economic capital is below the regulatory minimum. Other studies have tried to estimate the banks' optimal or target capital buffer. One early work is by Marcus (1983), who attempts to explain the dramatic decline in US commercial banks' capital from 1961 to 1978. A more recent study is by Ayuso et al. (2004), who estimate the relationship between the Spanish business cycle and the capital buffer held by Spanish commercial and savings banks. Other country studies are, among others, Estrella (2004), Lindquist (2004) and Rime (2001). Bikker and Metzemakers (2004) and Jokipii and Milne (2006) analyze the capital buffers in an international and a European context, respectively. All in all there is strong empirical evidence that capital buffers under Basel I exhibit significant cyclical patterns: They will increase during economic downturns and decrease during upturns. Some conclude that the cyclical behavior of capital buffers will further amplify the inherent cyclicality of Basel II caused by the risk sensitivity of capital charges. Others, however, point out that capital buffers will actually mitigate the cyclical effects of Basel II (Jokivuolle and Peura, 2004; Zicchino, 2005). This paper makes an important contribution to the discussion of the banks' capital buffer. First, it provides an explanation as to why under Basel I capital buffers tend to increase in an economic downturn, i.e. why they behave in an anti-cyclical manner. Second, it argues that capital buffers are nonetheless likely to move pro-cyclically under Basel II. These findings might help to explain diverging results in other studies. Importantly, it rules out any direct inferences ­ as other studies have done ­ from Basel I to Basel II without taking into account the very different nature of these two regulatory regimes. However, capital buffers will only partially mitigate the volatility in capital charges. On the whole, Basel II will have a pro-cyclical effect on lending. In contrast to other studies, I find that a significant pro-cyclical effect may exist even if banks are not capital constrained. Furthermore, this paper will result in a better understanding of the macroeconomic impact of Basel II, which has been largely neglected in the current debate on the cyclicality of the new capital accord.4 In one of the earlier studies of the cyclical effects of Basel I conducted by Blum and Hellwig (1995), they find that minimum capital requirements can have a significant macroeconomic impact. However, in their model equilibrium lending is solely determined by loan supply, which only makes sense if credit demand is rationed. Cecchetti and Li (2005) extend Blum's and Hellwig's model by incorporating loan demand into their model. However, both Blum and Hellwig (1995) and Cecchetti and Li (2005) fail to explain the cyclical effects of capital requirements in the case of banks which always hold a positive capital buffer. I find that a change in macroeconomic conditions can have an effect on the banks' lending supply even if banks have sufficient capital to meet the regulatory requirements at any time. I believe this feature to be highly relevant for the current debate since the actual regulatory capital of almost all banks is usually well above the required minimum. This is true even in economic downturns.

Related to this area is the question of how capital requirements affect monetary transmission channels (Van den Heuvel, 2002).

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The paper continues as follows. Section 2 presents a simple model of the banking industry. Section 3 assesses the cyclicality of the banks' capital ratio. Section 4 investigates the pro-cyclical effects of capital requirements on the macroeconomy. In Section 5, the model is calibrated to real world data. Section 6 concludes. 2. A model of the banking sector In the following, the banking industry is modelled by a representative bank which invests in riskless bonds (B) and loans (L) that are subject to default risk. A time horizon of one period (e.g. one year) is assumed. The bank finances its investments through equity capital (E) and customer deposits (D). The bank is unable to raise additional equity capital, which seems a reasonable assumption for the short-term horizon I have in mind. The only way the bank can increase its capital base is therefore by retained earnings. In addition, the amount of deposits is presumed to be an exogenous parameter to the bank that nevertheless depends on the riskless interest rate and GDP. The bank's investment decisions depend on interest rates, which are denoted by r for bonds and q for loans. The bank also takes into account the fact that a fraction s of its borrowers will have defaulted by the end of the period. For simplicity, I assume that the bank must write off the total amount of the loan if the borrower defaults.5 Ignoring any interest payments on deposits, the profit or loss at the end of the period is given by6 p = (q À s)L + rB. In addition, I assume that the precise realization of the future loss rate s is unknown at the beginning of the period. The loss rate is modelled as a random variable with an expected value of and a cumulative centered distribution function F. s In deciding on its optimal portfolio of bonds and loans, the bank also has to observe the solvency constraint and the (stricter) regulatory constraint. The latter requires that a bank's equity capital at the end of the period, E + p, must not be smaller than a fraction a of its risk-weighted assets. Without loss of generality, a risk weight of w is assumed for loans and 0 for riskless bonds. As a consequence, risk-weighted assets are given by w Æ L. It is convenient to normalize the bank's capital by L. With e representing the capital­ loan ratio E/L, the regulatory requirements (e + p/L > a Æ w) are stricter than the solvency requirements (e + p/L > 0). In fact, I argue that regulatory requirements shift the bank's default point from 0 to a Æ w. Since profits are random and a default on regulatory requirements is associated with large economic costs, the bank will make sure at the beginning of the period that e exceeds aw by some positive amount. However, decreasing the likelihood of default does not come free of cost, since, by investing in riskless bonds, the bank foregoes some lending margins. For the sake of simplicity I dispense with modelling the costs of default explicitly. Instead, I assume that the bank sets itself a target probability of its

Alternatively one may assume a fixed, positive recovery rate, but that would not change the subsequent analysis in any significant way. 6 In the following specification, it is assumed that interest is paid before a firm potentially defaults on the repayment of the loan. In other words, there is no loss of interest payments on behalf of the bank due to a firm's default. The alternative specification ­ interest payments fall due after a firm has defaulted ­ would not significantly change the results of the subsequent analysis.

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own default, which is denoted by p. It is assumed that the bank maximizes its expected profits E½p ¼ ðq À ÞL þ rB under the funding and default constraint: s max½ðq À ÞL þ rB s

B;L

s:t: BþL¼DþE ðfunding constraintÞ ðdefault constraintÞ Prob½e þ p=L < aw 6 p

Note that there is a close relation between the target probability of default and the bank's target capital ratio. The smaller the target probability of default, the higher the target capital ratio, and vice versa. The fact that, in equilibrium, r is in general strictly smaller than the expected net return on loans q À , is easily shown. Assume, on the contrary, that r were larger than q À . s s Then, because of the monotonicity of expected profits in B, the bank would invest all of its assets in riskless bonds. This, however, cannot happen if the loan market is in equilibrium and loan demand is positive. It follows that r 6 q À . Equality can be ruled out as s a general case as it is not stable to small changes in loan demand. Under this condition and due to the monotonicity of E[p] in L, the default constraint in the maximization problem above becomes binding. After some transformations of the default constraints, one derives 1 À F ðe þ q þ rb À wa À Þ ¼ p s ð1Þ where b = B/L. Rearranging terms yields e ¼ kða þ wa À q þ r þ Þ s

A À1 rÞ E

ð2Þ

with k ¼ ð1 þ and a = F (1 À p). I define the bank's capital buffer (in levels) by the bank's excess capital over required capital at the beginning of the period. Accordingly, the bank's normalized capital buffer is given by the excess of the capital to loan ratio over regulatory requirements: D ¼ e À wa ¼ k ða À q þ r þ Þ þ ðk À 1Þwa s ð3Þ In the following, the term capital buffer is used in both ways (in levels and normalized) if the context is clear. Note, however, that the bank cannot set the capital buffer (in levels or normalized) directly. Instead it chooses its optimal mix of loans and bonds which in turn determines its capital buffer. Interestingly, banks will reduce their buffer if regulators increase the threshold value a (note that k < 1). In other words, the increase in the capital loan ratios will be smaller than the increase in capital charges. 3. The cyclical effects of capital requirements Basel II will introduce a dynamic feature into capital requirements which is not present in the old framework. Since credit quality is likely to decline when a firm's business outlook weakens, banks will face ­ ceteris paribus ­ higher capital charges during an economic downturn. Nonetheless, banks have some leeway to accommodate higher credit risk by actively managing their portfolio ­ in the present model by shifting their funds from loans to bonds.7 Thus, changes in actual capital ratios may turn out to be significantly smaller

7

À1

It is possible to generalize the model by incorporating a larger number of asset types.

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than those in a fixed portfolio of assets. Therefore, it is important in the present context to clearly separate between the cyclicality of capital charges and the cyclicality of actual capital ratios. Under the IRB approaches of Basel II, risk weights are determined by borrowers' probability of default (PD):8 w ¼ wðPDÞ ð4Þ I do not examine credit risk in greater detail here, as it has already been extensively analyzed in the literature. Instead I simply take for granted that the average PD is indeed subject to cyclical variations, i.e. PDy < 0 if y denotes GDP.9 Similarly, I assume y < 0 for the s expected default rate. For the ease of exposition, rather than writing w as a function of PD, and PD, in turn, as a function of y, I simply assume in the following that w is a direct function of y. In order to simplify the subsequent analysis even further, I impose the following linear structure on w(y): m wðyÞ ¼ w0 À ðy À y 0 Þ; m > 0 ð5Þ a In Eq. (5) y0 and w0 are interpreted as full capacity production and the respective risk weight. In the subsequent analysis y0 and w0 are used as reference points. The slope of w is stated in terms of a, as a result of which it does not affect the level of required capital at y = y0. This is useful in order to distinguish between a general rise in minimum capital requirements (indicated by an increase in a) and changes in their risk sensitivity (indicated by an increase in m).10 Rather than examining the cyclicality of minimum capital, the remainder of this section focuses on the cyclicality of the capital buffer and how it is affected by capital requirements. I define the cyclicality of the capital loan ratio as the sensitivity of e to changes in production y, and similarly for the capital buffer. By differentiation of Eq. (2), one derives ey ¼ e ky þ ky À km s k ð6Þ

From (6) it becomes clear that a distinction can be made between three different effects driving the cyclicality of capital loan ratios. The first term on the right hand side of Eq. (6) may be called the funding effect of bank lending. Note that from À1 À1 A D k ¼ 1þr ¼ 1þrþr ð7Þ E E one infers that it is negative provided that deposit supply is an increasing function of income (cf. Section 4). The second term in Eq. (6) ­ which is negative as well ­ describes the effect of credit risk on lending. The third term measures the cyclicality of capital charges

The following analysis also holds true for the standardized approach of Basel II. In this case, the PD should be interpreted as a credit score attributed to a particular rating. 9 The cyclicality of the rating system depends on the methodology applied, in particular whether it is set on a ``through-the-cycle'' or ``point-in-time'' basis, cf. Gordy and Howels (2004). The new Basel accord is not explicit here. However, even if borrowers are rated on a ``through-the-cycle'' basis, which is less cyclical, rating assessments are still likely to be cyclical, cf. Amato and Furfine (2003). 10 Since the sensitivity of credit risk to the business cycle is likely to vary among banks, the parameter m can be heterogenous but is assumed constant for the purpose of our analysis of a representative bank.

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and is also negative. There is an interesting link to the macroeconomic literature on the bank lending channel of monetary policy transmission. In this context, a monetary tightening is assumed to have real effects on output because it affects the banks ability to lend (corresponding to the funding effect), as well as the borrowers' balance sheet conditions (corresponding to the credit risk effect). The third effect, the cyclicality of capital charges, is a new phenomenon of Basel II.11 Taken together, all three factors have a pro-cyclical effect on lending, because Ly/L = Àey/e > 0. In passing I wish to note that risk-weighted assets can move in the opposite direction due to the simultaneous change in risk weights: oy lnðwLÞjw¼w0 ¼ À m À ey =e> 0 < aw0 ð8Þ

It has been claimed in the literature that capital buffers absorb some of the volatility in capital charges, in other words, that awy and Dy have different signs (the first negative, the second positive). However, this is not true in general. In fact, if m is small, the buffer might actually decrease during an economic upturn. From Eq. (6): s Dy ¼ ky þ e ky þ ð1 À kÞm k ð9Þ

Whereas the first two terms on the right hand side are negative, the third term is positive (note that 0 < k < 1), leaving the overall effect ambiguous. In particular, Dy is negative if risk weights are insensitive to credit risk changes, such as under Basel I. Therefore, the cyclical behavior of the buffer ultimately depends on the size of m. I now analyze whether or not capital requirements increase the cyclicality of the capital loan ratios. Proposition 1. A rise in the risk sensitivity of risk weights or the threshold value of minimum regulatory capital, m or a respectively, increases the cyclicality of the capital loan ratio (in the sense that it increases jeyj). In particular om ey jy¼y 0 ¼ Àk < 0 oa ey jy¼y 0 ¼ k y w < 0 ði:e: om jey j > 0Þ ði:e: oa jey j > 0Þ ð10Þ ð11Þ

Proof. The proposition follows directly by differentiation of Eq. (6).

h

Interestingly, the capital buffer absorbs some (but not all) of the increase in the volatility of capital charges caused by a rise in m: om Dy ¼ 1 À k > 0 An increase in a has the opposite effect: oa Dy ¼ k y w < 0

11

ð12Þ ð13Þ

Kashyap and Stein (2004) identify the cost of default ­ which I implicitly in the bank's target probability of default ­ as a further source of cyclicality.

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It was mentioned that in the present model the bank can change its capital loan ratio e only through lending since its equity capital is fixed. By virtue of proposition 1, and since loan supply is given by L = eÀ1E (with E being fixed), a rise in m has therefore a pro-cyclical effect on loan supply: omLy > 0. To sum up the main results of this section, the model suggests that banks adjust their capital loan ratios in a cyclical way. Since capital is assumed to be fixed at the start of the period, they do so by modifying their loan supply. Capital requirements can have a significant impact on the cyclicality of the capital loan ratio and as a result also on loan supply. If capital charges are very sensitive to changes in GDP, i.e. if m is relatively large, capital buffers will absorb some of the volatility of capital charges. This finding has important consequences for the assessment of Basel II. First, it shows that it is not sufficient to only look at the prospective volatility in capital charges in order to assess potential changes in bank lending. In doing so one would ignore the dampening effects of capital buffers. Second, it would be wrong to make any direct inferences from the observed cyclicality of capital buffers under Basel I to the prospective cyclicality of capital buffers under Basel II. My findings in Section 5 below rather suggest that capital buffers are likely to behave quite differently under the two regimes: they are counter-cyclical under Basel I and most likely to be pro-cyclical under Basel II. 4. The pro-cyclical effect on the macroeconomy In the preceding Section 1 analyzed how the business cycle influences the banks' capital and lending decisions and to what extent these decisions depend on capital requirements. While this is an important question, it is at the same time part of a wider and potentially more severe problem due to potential feedback effects to the real sector. Blum and Hellwig (1995), who analyzed the macroeconomic effects of Basel I, highlighted the importance of drawing a clear distinction between transitory and permanent effects of a change in regulatory requirements. I follow their approach to analyze the permanent effects by investigating to what extent capital requirements amplify exogenous shocks to GDP. In the following, the banking model of the previous sections is extended by incorporating the macroeconomy more systematically into the general framework. This part of the model builds on the seminal work of Bernanke and Blinder (1988), who introduced a formal model of the bank lending channel. As regards the loan market, the representative bank's loan supply can be easily derived from its target capital ratio depicted in Eq. (2): Ls ðq; r; yÞ ¼ E Á eÀ1 ðq; r; yÞ ð14Þ

I do not impose any particular structural form on loan demand, Ld, apart from the usual assumptions on elasticities, i.e. Ld < 0 and Ld > 0. The equilibrium loan rate q* is deterq y mined by the market clearing condition on the loan market, i.e. Ls ðqà ; r; yÞ ¼ Ld ðqà ; r; yÞ ð15Þ

Clearly, q* is a function of y and r. In order to simplify the subsequent presentation, I assume that output y is fully driven by real aggregate demand. This restriction is not material, as the supply side can be easily accommodated in the analysis. As in Bernanke's and Blinder's model, I assume that aggre-

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gate demand yd depends on current output as well as the riskless interest rate r and the loan rate q. y d ¼ y d ðq; r; yÞ ð16Þ

Since a demand-driven model is assumed, equilibrium in the output market is defined (for any given values for q and r) as the fixed point of aggregate demand, i.e. y à ¼ y d ðq; r; y Ã Þ ð17Þ

Money demand is modelled in the standard way, assuming that it is a function of income and the riskless interest rate. At the same time, total deposits are taken to be a fixed fraction of money demand. Hence D ¼ Dðr; yÞ ¼ sMðr; yÞ ð18Þ

In the following, I assume that the riskless interest rate r is exogenously set by the central bank. This permits an analysis of the cyclical effects of capital regulation on the macroeconomy in isolation from any potential countermeasures by the central bank. In reality the central bank might choose a monetary policy that mitigates economic fluctuations arising from capital requirements. However, the objectives of prudential supervision might be in conflict with the goal of maintaining high and stable growth. Cecchetti and Li (2005) have shown (in their specific framework) that it is possible to derive an optimal monetary policy that reinforces prudential capital requirements and at the same time stabilizes aggregate economic activity. Further research, however, is needed to determine the optimal monetary policy in the Basel II framework. The following lemma provides an analytical expression for the elasticity of the equilibrium loan rate, and equilibrium lending with respect to changes in y: Lemma 1. The elasticity of the equilibrium loan rate with respect to changes in output is given by qà ¼ Àðely þ ey Þðelq À kÞÀ1 where l = lnLd. The elasticity of equilibrium lending y with respect to y is positive and it is given by Là =Là ¼ ðey lq þ kly Þðk À elq ÞÀ1 . y Proof. Inserting (14) into the market clearing equation for loans (15) and taking the logarithm on both sides of the equation yields ln E À ln e ¼ l Implicit differentiation of Eq. (19) with respect to y yields: ÀeÀ1 ðey þ eq qÃ Þ ¼ ly þ lq qà y y ð20Þ ð19Þ

Since eq = À k Eq. (2), one derives the first part of the lemma by solving the equation above for qy. The second part follows directly from inserting the expression for qà into y oy ln Ld ðqà ðyÞ; yÞ ¼ ly þ lq qà y à ð21Þ

Note that while Là =Là is positive, the sign of qà is ambiguous. However, this will not be y y crucial for the subsequent analysis. More important in our context is how qà is affected y by a change in regulatory requirements.

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Proposition 2. A rise in the risk sensitivity of capital requirements decreases the output sensitivity of the equilibrium loan interest rate, i.e. qà < 0. Furthermore, it has a proym cyclical effect on equilibrium lending, i.e. om Là =Là > 0. y Proof. It was shown in the lemma above that qà ¼ À y ely þ ey elq À k ð22Þ

Note that the target capital ratio e and hence the equilibrium value of the loan interest rate do not depend on m if production is at full capacity (y = y0). Since eym = À k (Eq. (10)) one derives qà ¼ ym k <0 elq À k ð23Þ

Similarly, differentiating the expression for Là =Là that was provided in the lemma above y yields om Là klq y >0 à ¼ L elq À k à ð24Þ

I now turn to the question to what extent business fluctuations are affected by a rise in m. In Fig. 1, the IS curve describes the equilibria on the goods market and the LL curve those on the loan market. Overall equilibrium is attained at Z0, where the IS and the LL curve intersect. Now assume a positive aggregate demand shock, which shifts the IS curve to the right. The new equilibrium is attained at Z1. If the income sensitivity of equilibrium lending increases, which I expect will happen under Basel II (cf. proposition 2), the LL curve becomes flatter (LL 0 ). Under this scenario, the post-shock equilibrium would be attained at Z 01 , which is located to the right of Z1. In other words, a rise in m has a pro-cyclical effect on production.

LL IS Z1 Z'1

LL'

Z0

y

Fig. 1. Aggregate demand and loan interest rate.

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The above findings can also be shown in a formal way. Suppose a shock to aggregate demand equal to . The new equilibrium on the goods market is attained at point y*, which is the solution of the following equilibrium equation y à ¼ y d ðq; r; y Ã Þ þ Differentiating (25) with respect to yields the multiplier y à ¼ ð1 À y d À y d qy Þ y q

À1

ð25Þ

ð26Þ

Under standard assumptions,12 y à is positive (and usually larger than 1). Proposition 3. A rise in the risk sensitivity m of capital requirements increases the multiplier y à . Proof. Upon inspection of Eq. (26), it is clear that in the present model capital requirements can influence the multiplier y à only via the income sensitivity of loan interest rates, qy. In proposition 2, I showed that qym is negative. Therefore, by virtue of (26) om y à ¼ y 2 y d qym > 0 q 5. Calibration In this section, I run a calibration exercise to analyze whether the cyclical effects established in the previous section are significant in magnitude. The simulation study is based on balance sheet data drawn from Bankscope of Bureau van Dijk for banks operating in OECD countries in the year 2004. The total number of observations was 945 and includes commercial banks, savings banks and credit cooperatives. Table 1 provides an overview of key financial ratios for small, medium-sized, and large banks. Note that both weighted and unweighted capital ratios depend negatively on the size of the credit institution. Furthermore, larger institutions have smaller loan-to-equity ratios than small and medium-sized banks, which calls for a distinction between different size classes in the subsequent analysis (see Table 2). The starting point of the simulation study is a bank's target capital loan ratio, calibrated on the basis of available balance sheet information. Recall that À1 A e ¼ kða À q þ r þ þ waÞ where k ¼ 1 þ r s : ð28Þ E In Section 3, I found that the cyclicality of e is largely driven by k and w. Note that k depends on the leverage ratio of a bank, which ­ for a particular point of time ­ can be derived from its balance sheet data. It also depends on the riskless interest rate r, which is set at 5% in the remainder of this section. For the average risk weight w, I used the average risk weight of each bank in the sample as of year-end 2004, which is given by the ratio of risk-weighted assets to non-weighted assets. The risk parameter a can be derived in an indirect way by solving Eq. (28). In doing so, I assumed that, as a first approximation,

12

Ã

ð27Þ

In particular: 0 < y d < 1, y d < 0 and qy > 0. y q

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Table 1 Capital ratios of international banks Small banks Balance sheet ratios (in %) Tier 1 ratio (weighted) Total capital ratio (weighted) Equity over total assets Equity over cross loans Key parameters of target capital Average risk weight w Sensitivity parameter k Risk parameter a PD (normal distribution) PD (log-normal distribution) 13.0 14.0 9.7 13.8 0.99 0.66 0.11 0.01 0.08 Medium-sized banks 10.9 12.7 8.5 12.9 1.02 0.63 0.10 0.00 0.04 Large banks 8.5 11.5 5.9 10.2 0.89 0.54 0.80 0.00 0.00

Table 2 Scenario analysis: capital ratios and risk-weighted assets Scenario 1 pch av. risk weight pch total assets ch capital loan ratio ch regulatory capital ratio pch risk-weighted assets pch total loans À À10 +0.4/+0.5/+0.5 +0.4/+0.5/+0.5 À3/À3/À4 À3/À3/À4 Scenario 2 +30 À +1.6/+1.5/+1.1 À2/À1.8/À1.7 +17/+16/+17 À10/À11/À10 Scenario 3 30 À10 +2/+2/+1.7 À1.6/À1.4/À1.2 +13/+12/+12 À13/À14/À14

pch, percentage change; ch, change; results reported for small/medium-sized/large banks.

the expected net return on the loan portfolio is approximately equal to the riskless rate, i.e. q À À r % 0.13 Then, by virtue of (28): s e ð29Þ a ¼ À wa k In order to check whether the results for the parameter a are reasonable, I converted them into the respective probability values of the underlying loss distribution. Please recall that I defined F as the (centered) distribution of s À . I define by F* the (standardized) distribus s tion of sÀ where r denotes the standard deviation of s. r Note that a = FÀ1(1 À p), where p is the bank's target probability of its own default. In terms of the normalized distribution p can be written as a p ¼ 1 À FÃ ð30Þ r The solution of (30) heavily depends on the choice of the distribution function F *. The normal distribution is taken as a first approximation here. However, it is a well-known fact that loan loss data can be very skewed and exhibit fat tails. Therefore I also provide the results for the log-normal distribution. Obviously, the resulting values for the target

This simplification is not material, because even if the spread is positive, it is likely to be small compared with the other parameters in (28).

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probability p will be higher for the log-normal distribution owing to fat tails. Since the standard deviation of the distribution might vary between large and small banks (Peura and Keppo, 2006), I used the cross-sectional empirical standard deviation of each of the respective size classes. All in all, the results show reasonable probability values. After deriving the parameters of the capital loan function, I was able to simulate the changes in capital and lending under different hypothetical scenarios. As I already mentioned above, the cyclical effects mainly stem from changes in required capital (i.e. in aw) and changes in the banks' total funds (A), which determine the parameter k. In the following, I present the results of three different scenarios. In scenario 1, I analyzed a 10% drop in total assets while keeping the required capital constant. This scenario might be interpreted as a reflection of capital regulation under Basel I with fixed risk weights. In scenario 2, I assumed a 30% change in the capital requirement in line with previous studies on Basel II (cf. Section 1). In scenario 3, I assessed the combined effect of a rise in required capital and a drop in total assets. The results show that even under the old regulatory regime lending is likely to be cyclical, which seems to correspond to empirical evidence.14 Note, however, that previous research often did not clearly separate between supply and demand effects. Therefore, it remains unclear to what extent cyclical variations in equilibrium lending are determined by changes in loan demand rather than changes in loan supply. The findings above, however, suggest that loan supply effects can be important. Under Basel II, cyclicality will most probably increase. Under scenario 2, lending would drop by 10%, in scenario 3 by 14%, whereas in scenario 1 it would only drop by 3%. It is instructive to look at the cyclical patterns of the capital ratios and the differences between scenarios 1 and 3. In both scenarios the capital loan ratio goes up as a result of reduced lending. This is also the case for the regulatory capital ratio in scenario 1. In scenario 3, however, the increase in risk weights overcompensates the reduction in lending. As a result, the regulatory capital ratios decrease. I now analyze the effects of capital requirements on the demand multiplier y as defined in Eq. (26). I simulate a rise in the risk sensitivity of risk weights, m, by 0.1­0.3 starting from an initial value of 0.15 Note that the relative change in the multiplier can be approximated by Dy % y dm ¼ y À1 y d qym dm q where, by virtue of Eq. (23), qym ¼ Z À1 k

Ld q Ld

ð31Þ

ð32Þ

with Z ¼ e À k. Since Z < À k, the value for qym is smaller than 1 in absolute terms. In the following, I assume that jqymj % 1, which is justified if the capital loan ratio is small compared to the absolute value of interest rate elasticity of loan demand. It should be noted though that in doing so the potential pro-cyclical effect will be overestimated. From Eq. (31) it is clear that the relative change in the multiplier also depends on y and y d . Further research is needed to estimate these parameters. Results can therefore only be q stated as multiples of the product term y À1 y d . As a rough estimate one might assume that q

14 15

Stolz and Wedow (2005). The values for m were derived by the author's own calculations, which are available on request.

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y À1 y d is close to 1. Obviously, the range of results for the pro-cyclical effect is fairly large. If q the change in m falls in the range of 0.1­0.3, the multiplier will increase by 10­30%. To sum up, the simulation exercise shows that the macroeconomic effect can be significant depending on the sensitivity of capital requirements to changes in business conditions. More research is needed to determine more accurately the size of the macroeconomic effect for different countries. 6. Conclusion The problem of cyclicality of the Basel II minimum capital requirements is currently the subject of an intense discussion in the financial and supervisory community. This paper provides two important contributions to the debate. First, whereas previous research has largely focused on fluctuations in capital charges only, it finds that the behavior of capital buffers is crucial to assess the impact of capital requirements on bank lending. Second, it provides an analysis of macroeconomic consequences emphasizing the conceptual difference between the cyclicality of regulatory capital ratios and lending and their procyclical effect on the real economy. With regard to the cyclicality of lending I find that the capital buffers are likely to mitigate the impact of changes in capital charges. I find that by ignoring this effect one might substantially overestimate any potential lending volatility. At the same time, the capital buffer will only partially absorb the fluctuations in minimum capital (roughly by 50%). It is worth noting that the cyclical effects of regulatory capital on lending are not unique to Basel II, but that they are also present in the old framework with time invariant risk weights. While pro-cyclical effects occur or are to be expected under the old and the new framework, the capital buffer is found to differ completely. Under the old framework this paper predicts an increase in the capital buffer during an economic downturn due to a reduction in lending (which is in line with previous empirical research). Under Basel II, however, the capital buffer will actually decrease, because the rise in the average risk weights will usually overcompensate the reduction in lending. I think that this finding has important implications for further empirical research on Basel II. In my view, it would be wrong to look at the movements of capital buffers under the old framework and assume a similar pattern under Basel II, as some previous papers seem to suggest. As to macroeconomic fluctuations, the impact of Basel II on aggregate demand can be significant ­ even if banks hold significant capital buffers ­ in particular for economies where bank lending plays an important role in the firms' investment decisions. However, the pro-cyclical effects on macroeconomic fluctuations will vary among countries. In general, bank-based economies will most probably experience the biggest effects, while the effects in financial markets-based economies will be smaller. The magnitude of any such pro-cyclical effect will depend on various factors, which are not specifically modelled in this paper, such as the firms' access to outside capital for instance. Among other things, the average size of firms, the sectoral specialization of a particular economy, its accounting framework and the competitive condition in the banking industry play an important role in this regard.16

16

See Jackson et al. (1999) and Borio et al. (2001).

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Finally, I need to mention some other qualifications of the model presented above. First, it assumes that the riskless interest rate remains constant over the business cycle. This assumption was made to separate the pro-cyclical effects of Basel from any potential counter-cyclical measures of the central bank. In the present context this means that the central bank needs to accommodate any income-induced changes in money demand in order to keep the interest rate fixed, and this has an additional effect on real demand. Further research is necessary to assess the interdependence of the prudential regulation of banks and monetary policy. Secondly, the model is not explicitly dynamic but makes interpretations that are dynamic in nature. However, augmenting the model with a dynamic specification is unlikely to change the basic results in principle unless one assumes very high portfolio adjustment costs on behalf of the bank.17 Deviating from the assumption of full flexibility in the portfolio adjustment ­ for example if assets are illiquid ­ it suffices to assume that a sufficiently large fraction of loans expires every year. References

Amato, J.D., Furfine, C.H., 2003. Are credit ratings procyclical? BIS Working Papers 129, Bank for International Settlements. ´ Ayuso, J., Perez, D., Saurina, J., 2004. Are capital buffers pro-cyclical? Evidence from Spanish panel data. Journal of Financial Intermediation 13, 249­264. Barrios, V.E., Blanco, J.M., 2003. The effectiveness of capital adequacy requirements: A theoretical and empirical approach. Journal of Banking and Finance 27 (10), 1935­1958. Basel Committee on Banking Supervision, 1988. International Convergence of Capital Measurement and Capital Standards, Bank for International Settlement. Basel Committee on Banking Supervision, 2004. International Convergence of Capital Measurement and Capital Standards: A Revised Framework, Bank for International Settlement. Bernanke, B.S., Blinder, A.S., 1988. Credit, money, and aggregate demand. American Economic Review 78 (Supplement), 435­439. Bikker, J., Metzemakers, P., 2004. Is bank capital procyclical? A cross-country analysis. DNB Working Paper 9/ 2004, Dutch National Bank. Blum, J., Hellwig, M., 1995. The macroeconomic implications of capital adequacy requirements for banks. European Economic Review 39, 739­749. Borio, C., Furfine, C., Lowe, P., 2001. Procyclicality of the financial system and financial stability: Issues and policy options. BIS Papers No. 1. ´ Carling, K., Jacobson, T., Linde, J., Roszbach, K., 2002. Capital charges under Basel II: Corporate credit risk modelling and the macroeconomy. Sveriges Riksbank Working Paper Series 142. Cecchetti, S.G., Li, L., 2005. Do capital adequacy requirements matter for monetary policy? NBER Working Paper 11830. Chami, R., Cosimano, T.F., 2001. Monetary policy with a touch of Basel. IMF Working Paper 01/151, International Monetary Fund. Ervin, D.W., Wilde, T., 2001. Pro-cyclicality in the new Basel accord. Risk 14, 28­32. Estrella, A., 2004. The cyclical behavior of optimal bank capital. Journal of Banking and Finance 28, 1469­1498. Gordy, M.B., Howels, B., 2004. Procyclicality in Basel II: Can we treat the disease without killing the patient? Journal of Financial Intermediation 15, 395­417. Jackson, P., Furfine, C., Groeneveld, H., Hancock, D., Jones, D., Perraudin, W., Radecki, L., Yoneyama, M., 1999. Capital requirements and bank behaviour: The impact of the Basle Accord. Basle Committee on Banking Supervision Working Papers 1, BIS. Jokipii, T., Milne, A., 2006. The cyclical behaviour of European bank capital buffers. Bank of Finland Research Discussion Papers 17.

See, for example Chami and Cosimano (2001). An application of this model to Basel II can be found in Zicchino (2005). These models do not, however, model the costs of failure on regulatory requirements.

17

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Jokivuolle, E., Peura, S., 2004. Simulation based stress tests of banks' regulatory capital adequacy. Journal of Banking and Finance 28 (8), 1801­1824. Kashyap, A.K., Stein, J.C., 2004. Cyclical implications of the Basel II capital standard. Economic Perspectives, Federal Reserve Bank of Chicago. Lindquist, K.G., 2004. Banks' buffer capital. How important is risk? Journal of International Money and Finance 23, 493­513. Marcus, A.J., 1983. The bank capital decision: A time series-cross section analysis. The Journal of Finance XXXVIII (4), 1217­1232. Peura, S., Keppo, J., 2006. Optimal bank capital with costly recapitalization. Journal of Business 79, 2163­2201. Rime, B., 2001. Capital requirements and bank behaviour: Empirical evidence for Switzerland. Journal of Banking & Finance 25, 789­805. Rosch, D., 2002. Mitigating Pro-cyclicality in Basel II. Unpublished Working Paper. Faculty of Business and ¨ Economics, University of Regensburg. Stolz, S.,Wedow, M., 2005. Banks' regulatory capital buffer and the business cycle: Evidence for German savings and cooperative banks. Deutsche Bundesbank Discussion Paper Series 2: Banking and Financial Studies, No. 07/2005. Van den Heuvel, S.J., 2002. The bank capital channel of monetary policy, Unpublished Working Paper. The Wharton School, University of Pennsylvania. Zicchino, L., 2005. A model of bank capital, lending and the macroeconomy: Basel I versus Basel II. Bank of England Working Paper No. 270.

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