- Email: [email protected]
Capital accumulation and regulation
The Quarterly Review of Economics and Finance 49 (2009) 760–771
Contents lists available at ScienceDirect
The Quarterly Review of Economics and Finance journal homepage: www.elsevier.com/locate/qref
Capital accumulation and regulation Ensar Yilmaz Yildiz Technical University, Economics, 34349 Istanbul, Turkey
a r t i c l e
i n f o
Article history: Received 1 April 2008 Received in revised form 11 December 2008 Accepted 15 February 2009 Available online 9 April 2009 JEL classification: G21 G28 E44
a b s t r a c t This paper sets up a dynamic model that analyzes a bank’s capital decision and the impact of this decision on her default risk and lending that affects aggregate output in the economy under regulation. The model shows that even though capital regulation may reduce the default risk of the bank, it may lead to credit crunch, hence the ensuing decline in output in the real sector. Furthermore, it appears that the risk-based capital requirement changes the composition of both liability and asset of the bank’s balance sheet. © 2009 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved.
Keywords: Regulation Capital requirement Credit crunch
1. Introduction The policy discussions on the regulation of banks have mainly been concerned with capital adequacy and this has been reinforced by the work of the Basel Committee that makes refinements of existing capital adequacy rules the core part of its regulatory reform work known as “Basel II”. The capital regulation suggested by “Basel II” is mainly intended to control the moral hazard (excessive risk-taking) induced by limited liability, which is a widely accepted explanation for the large number of bank failures that occurred in the 1980s and 1990s. The Basel II accord recognized that the risk sensitiveness of capital requirements should be enhanced to strengthen the soundness and stability of the banking system over the world. Hence it forces banks to hold minimum capital requirements with respect to the risk they undertake1 .
E-mail address: [email protected]. Value at Risk (VaR) is one of the most popular tools used in risk measurement. The concept of VaR has now been incorporated in the Basel II to measure especially credit risk. This approach includes not only the exposure of risk factors but also the volatility of the risk factors. Although there are some drawbacks of this approach (for this see Danielsson (2003)), it is expected that VaR based capital requirements provide a stronger incentive for well capitalized banks to reduce asset risk by rewarding low-risk banks with lower capital requirements. 1
1062-9769/$ – see front matter © 2009 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved.
doi:10.1016/j.qref.2009.02.004
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
761
However, the risk-based capital requirements have been criticized for not taking into account their impact on banks’ lending. Hence, in this paper, we are also concerned with the impact of revised capital regulation on lending, in addition to its impact on risk taking. Effects of capital adequacy rules on banks’ behavior have been analyzed in the literature before. Two strands of the literature try to clarify capital regulation-related issues. The first strand focuses on whether capital requirements are an effective tool for limiting the risk on an asset portfolio, which is analyzed in a static or dynamic framework. The static models mainly take bank capital as exogenous and abstracting from dividend and recapitalization choices. For example, for value-maximizing banks, while Furlong and Keeley (1989) demonstrate that capital requirements reduce risk-taking incentives, Flannery (1989), in contrast, concludes that the regulation may lead to higher risk taking. In a meanvariance framework, Kim and Santomero (1988), Kohen and Santomero (1980), and Rochet (1992) show that improperly chosen risk weights may increase the riskiness of banks. Some other authors argue that capital requirements reduce monitoring incentives, which reduces the quality of banks’ portfolios (e.g., Besanko & Kanatas, 1993; Boot & Greenbaum, 1993). However, static models do not consider the banks’ franchise value (expected future income) and, therefore, they give an incomplete explanation of banks’ capital. Hence dynamic models are more appropriate for analyzing the impacts of risk-based capital requirements. Taking into account the dynamic aspects of the problem, some studies show that capital requirement can be an effective tool for reducing risk-taking, while some other studies indicate that the capital regulation can induce risk-taking or have an ambiguous impact. For example, in a dynamic model, Hellmann, Murdock, and Stiglitz (2000) show that capital requirements force banks to have more of their own capital at risk so that they can be induced to invest in the prudent asset. Repullo (2004), following the main framework of Hellmann et al. (2000), finds out the similar results: if the capital requirement is imposed, the bank becomes more prudent, holding less risky assets. Similarly, Milne (2004) finds that in the short run, negative cash flow and higher capital requirements reduce risk-taking and lending, with greatest impact on severely undercapitalized banks. In contrast to these results, for example, Blum (1999) demonstrates that capital adequacy rules may increase the bank investment in the risky asset because raising equity may be excessively costly, the only possibility to increase equity tomorrow is to increase risk today under binding capital requirements. Pelizzon and Schaefer (2003), in a multi-period model under a VaR constraint, find the similar results to those of Blum (1999), i.e., capital regulation can induce a bank to undertake more risk due to her intertemporal concerns. However, Keppo, Kofman and Meng (2008) indicate that the impact of the capital regulation on default probability can be ambiguous. They find out that risk-based capital requirement may cause both positive (fall in the cash flow volatility) and negative (fall in the recapitalization level) effects on the default probability. That is, it is not guaranteed that the capital requirement has positive (or negative) effects on the default probability. The second strand of the literature analyzes the macroeconomic implications of capital requirements. One of the earliest attempts to examine the macroeconomic implications of bank capital regulation is Blum and Hellwig (1995). They show that since there is a bank lending channel of monetary policy, reductions in bank credit brought about by risk-based capital requirements can constrain real investment expenditures. Thakor (1996) also suggests that capital regulation potentially reduces the ability of monetary policy expansions to induce bank lending. In a different context, Kopecky and VanHoose (2004) conclude that binding capital requirements lead to a decline in aggregate loans and induce banks to hold more non-loan, security assets. Tanaka (2002) reaches an analogous conclusion within an IS-LM-style framework. He finds that the immediate effect of binding capital requirements is to alter the interest sensitivity and investment relationship and demonstrates that the monetary transmission mechanism is weakened if banks are poorly capitalized. On the other hand, Miyake and Nakamura (2006) provide a very different analysis of the macroeconomic effects of bank capital regulation. Utilizing a dynamic overlapping-generations model, they find that the imposition of bank capital regulation may lead to a reduction in equilibrium income. The second strand of the literature also provides an argument for linking capital requirements to the business cycle—the cyclicality issue. By cyclicality, it is commonly meant as the amplification of the business cycle due to the reduction in credit availability in recession periods (and vice versa in expansion periods). If the capital requirement is risk-sensitive, it is likely to increase during recessions
762
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
and decrease during expansions, tending to exacerbate the business cycle waves (e.g., Borio, Furfine, & Lowe, 2001; Estrella, 2004; Kashyap & Stein, 2004; Peura & Keppo, 2006). On the other hand, empirical studies also provide clues as to how the risk-based capital standards influence balance sheets of commercial banks. The empirical studies in this context mainly find that the implementation of risk-based capital standards resulted in banks’ decreasing lending. For example, to some studies (e.g., Brinkmann & Horvitz, 1995; Furfine, 2000; Thakor, 1996), the implementation of the risk based capital standards in the USA led to a slowdown in bank lending in the beginning of the 1990s. In the line with this, Chiuri, Ferri, and Majnoni (2001) find out that the enforcement of capital adequacy requirements negatively affects the supply of bank loans and the effect is stronger for less capitalized banks in emerging countries. Gambacorta and Mistrulli (2004) explore the same question using Italian banking data over the period 1992–2001. They find evidence of a bank capital channel in the monetary policy transmission mechanism, in which well capitalized banks are less constrained in their responses to monetary policy and other macroeconomic shocks than banks with relatively lower levels of capitalization. In a recent study, Brana and Lahet (2009) also find evidence that the implementation of the Basel risk-based capital ratio had a significant impact on Japanese banking behavior. The risk-based capital requirement reduced lending by internationally active Japanese banks which were subject to a more stringent capital adequacy regulation. However, a number of studies find less compelling evidence of a link between capital regulation and credit crunch. For example, using panel data for the USA states, Driscoll (2004) finds that shocks to the supply of bank loan do not affect output. This is possible since firms are not bank-dependent, and are able to substitute other forms of finance for bank loans. The main goal of this paper is to model a bank’s capital decision which is endogenously determined and effects of capital-based regulations. More precisely, the paper addresses the following questions for a representative bank in a dynamic model: (i) How does a bank’s risk-taking behavior depend on her capital position? (ii) How does a bank’s risk-taking and lending behavior depend on regulatory requirements? By addressing these questions we are able to assess the different effects of capitalbased regulations. In other words, we are able to account for the fact that banks with different capital positions will react differently to capital-based regulation. In the literature, such questions are not so often and simultaneously addressed in dynamic models. Addressing such questions in a more real setting also contributes to the ongoing discussion on the new Capital Accord, suggesting the fact that economies, which rely on bank credit, may have to consider the process of enforcement of a stricter bank capital discipline. This paper extends literature by studying the risk shifting effect in a setting where banks can choose multiple contracts – debt and equity which are substitutes – to finance firms in an endogenous capital setting under no capital requirement – the market model – and under capital requirement – the regulatory model – respectively. The model presented here incorporates capital requirements in a dynamic setting with endogenously raised bank equity or capital accumulation. In fact, we form a link between the first and second strand of the literature in a dynamic setting. That is, while capital requirements can be an effective tool for limiting the risk undertaken by the bank, they can also have macroeconomic repercussions through lending channel. The paper also tries to explain the observed association between the bank’s capitalization and propensity to take risks, and is in this respect parallel to the studies that suggest that higher capitalization restrains moral hazard (risk-taking) in banking. The regulator’s objectives in this paper are elucidated by risk and output loss. We find that there is a risk reducing effect of capital adequacy but this can only be achieved at the costs of restricting current bank lending that leads to output loss. Hence, the regulator is confronted with a difficult trade off: restrictive policies aimed at reducing the likelihood of bank failures tend to increase the probability of a credit crunch. The model shows that the response of the bank to capital regulation is mainly determined by the size of deposit market, which is a substitute for capital market. If deposit market is large enough, the risk-shifting effect is manifested in the bank’s adjustment of debt and equity she uses to finance firms in a way that motivates her to raise no new equity and to adopt a riskier behavior in the market model, allocating more fraction of funds to loans in comparison to the regulatory model. However, the bank responds to the capital regulation by reducing her default probability by raising new equity and shifting
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
763
her portfolio away from risky assets, such as loans, and towards riskless assets, such as government securities, thus cutting her lending. These results are mainly compatible with the studies mentioned above which claim that capital regulation reduces risk-taking of banks. Although in different contexts, Milne (2004) and Kopecky and VanHoose (2004) also find out that binding capital requirements lead to a decline in aggregate loans and induce banks to hold more non-loan, security assets. These findings are also verified by several empirical studies mentioned above (e.g., Chiuri et al., 2001; Gambacorta & Mistrulli, 2004; Thakor, 1996). However, if deposit market is shallow, the bank tends to raise new equity besides collecting deposit. The size of equity to be raised – the capitalization level – may cause the regulation not to be binding. Hence, in this case, regulation may have no effect on risk and lending. This mainly implies that the financial structure in which the banks seek to find out funds like the extent of deposit markets maybe crucial for banks’ risk and lending conduct. Hence such structural constraints may be critical on aggregate behavior. The remainder of the paper is organized as follows. In Section 2, we lay out the basic structure and assumptions of our model. In Section 3, we analyze the optimal solution of the bank without capital regulation—the market model. Section 4 considers the response of the bank to the capital regulation—the regulatory model. Section 5 concludes. 2. Environment We consider a bank operating in a discrete-time infinite horizon environment. The banking firm enjoys market power in the loan market, but is a price taker in the deposit market with an amount constraint. The bank can attract the funds it needs to finance projects by both collecting deposits Dt and issuing new equity Et at the beginning of time t. At the start of each period, the bank has some capital carried over from the previous period Kt−1 . Although there exist perfect substitutes for bank liability, but this is not case for the bank assets. That is, collected funds are allocated to the safe asset, say government securities, St which has a deterministic gross yield, > 1 and to the risky asset, say loans, Lt whose repayments are stochastic. We assume that the bank invests a proportion ␣t of all the proceeds in loans, Lt , used to finance the projects of companies and the remaining proportion, 1 − ␣t , in risk-free securities St . Any short sales are ruled out. Thus, the financing constraint of the bank over time is Lt + St = Dt + Et + Kt−1
(1)
The stochastic component of return arises only from the risky loans. The expected net return on risky loans is R(Lt ) = t r(Lt )Lt
(2)
where r(·) is gross return on loans, and t is the expected repayment ratio. For notational simplicity, let Zt = r(Lt )Lt , thus R(Lt ) = t Zt . Following Taggart and Greenbaum (1978), we model the credit risk by means of a random variable t , with support [0,1], to denote the proportion of performing loans at the end of the period. Since the actual value of repayments to a bank at time t is only known at the end of each period when it is revealed and only some fraction of loans, t , is repaid at the end of time t. The remaining fraction 1 − t of the investment in the risky asset yields a return of 0, i.e., this fraction is lost (non-performing loans). Unexpected loan losses may be due to purely random shocks or asymmetric information in the lender–borrower relationship. We assume away any adverse selection and/or moral hazard problems pointed out by Stiglitz and Weiss (1981) which the bank might confront in setting its loan rate or loans. We also assume that the distribution of t is unaffected by the level of lending so that the degree of uncertainty per dollar of loans is constant. The fractional repayment ratio t is a random variable drawn from a distribution with a continuous and positive density function g() and cumulative distribution function G(). The bank faces a downward sloping demand for loans. This assumption would seem to fit in with empirical evidence and making this assumption helps guarantee an internal solution to the bank’s maximization problem. But a more satisfactory justification for a less than perfectly elastic demand
764
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
function comes from assuming that the bank has some specialized information on a set of borrowers. The bank-specific nature of the information required to effectively make loans to a group of potential borrowers gives each bank power to set their own rates on loans. Since the bank faces downward sloping demand for loan, we have ∂r(Lt )/∂Lt < 0. We also assume that ∂2 r(Lt )/∂Lt2 < 0, which is sufficient to ensure Z (Lt ) < 0. When the value of repayments of loans to a bank is sufficient to ensure her solvency, the full value of deposits is repaid at the end of each period. So long as the bank is not bankrupt, depositors’ gross gain is d Dt at the end of time t, where rd > 1 is the gross rate per one unit of deposit offered by the bank. The deposit rate rd is assumed to riskless rate because depositors do not act in accordance with the risk structure of the bank. They do not demand a higher deposit rate when the bank invests in more risky assets. This is because depositors are unable to assess the relative riskiness of the balance sheet of the bank and also because of the existence of deposit insurance. ¯ t. On the other hand, we assume that the supply of deposits is quantity constrained each period, D Deposit constraint can be explained to a large extent, by the existence of a customer base which is not too much changeable. In addition, for simplicity, the costs related to deposits – deposit insurance premium and operating costs – are assumed to be nonexistent. We have two capital-related costs that the bank faces. One is that since the bank holds capital, she suffers a holding cost that amounts to Kt−1 at time t, where is the opportunity cost rate of capital. The cost rate of holding capital is above the riskless rate of return in the market, > rd . The other cost related to capital for the bank is the cost of raising new equity. For simplicity, we also assume that cost of raising new equity is linear, thus Et , where is the equity raising cost rate, which is also higher than collecting deposits, > rd . There is a sizable theoretical (e.g., Myers & Majluf, 1984) and empirical literature (e.g., Calomiris & Hubbard, 1995) to support the assumption that issuing new equity can be quite costly. With raising new capital, Et , capital accumulates to the level, Kt = Et + Kt−1. In this paper, we assume that the bank does not use retained earning as a kind of internal financing but instead issues new equity within the relevant period. There is a substantial literature that has emerged to rationalize large dividend payouts to shareholders, positing a variety of signaling, tax, agency, and behavioral motivations. In fact adding retained earnings as a source of bank capitalization would only complicate the dynamics without adding much to the intuition derived from the model. Summarizing timing of the model: The bank collects deposits and raises equity at the beginning of the period t. Then she invests a proportion of these funds in riskless assets (securities), and risky assets (loans). Repayments of loans are known with certainty only at the end of the period, t. However, at the start of the period t, the bank is assumed to know the probability distribution of the period’s repayments, G( t ). Finally, at the end of the period t, if the bank can pay off her depositors, she survives and distributes the residual return on the bank’s investments to the bank’s shareholders. Otherwise, she fails and the regulator assumes the whole remaining liability of the bank. The bank aims at maximizing the total of the expected return net of paymerits to the bank’s shareholders by firstly making an optimal choice of Dt and Et each period and then choosing optimal allocation, ˛, of collected funds between risky (loans) and riskless (securities) assets: maxEt
∞
Dt ,Et
where
ˇt−1 t (·),
(3)
t=1
1
t =
(t Z(Lt ) + St − rd Dt )dG(t ) − Kt−1 − Et
(4)
tc
is the expected net return to the bank’s shareholders at the end of period t. If the net gain that is expressed in the integrand of (4) is positive, At = t Z(Lt ) + St − rd Dt > 0,
(5)
the bank survives and operates the next period. However, if At < 0, the bank ceases to exist and the deposit insurance agency pays off depositors after claiming the return on the bank’s asset portfolio due to the limited liability for the bank shareholders.
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
765
Note that the integrand At is the stochastic part of the profit under the probability distribution, G( t ). It determines a critical proportion of good loans, tc , below which a bank is insolvent is defined as tc =
rd Dt − St Z(Lt )
(6)
Thus the bank is in default whenever the total of realized returns on loans Lt and non-risky assets is less than deposits payments, i.e., whenever t < tc . Notice that tc is determined by only the integrand in (4), where c satisfies At = 0. Since the second term of (4), Kt−1 , is opportunity cost of holding capital, it does not influence the insolvency of the bank. The cost of raising new equity, Et , also does not affect the critical value of tc since issuing new equity is not like collecting deposits which requires the bank to pay out at the end of period. Furthermore, equity capital, being a “soft” claim upon which a default cannot occur, buffers a bank by affecting the threshold point of default which is embedded in St and Z(Lt ). This is why we excluded them from the integrand that determines the default probability, which is
G(tc ) =
tc
g(t )dt
(7)
0
The expression (7) suggests that the probability of the bank failure is related to how the bank finances (Dt and Et ) and how she allocates collected funds (Lt and St ). Hence the bank can affect the probability of failure, tc by choosing deposit and equity and their allocation given her knowledge of the distribution of t , i.e., the probability of bankruptcy is not exogenous to the bank. Therefore, it is easy to see that ∂G(tc )/∂Dt > 0, ∂G(tc )/∂Et < 0 and ∂G(tc )/∂˛t > 0. That is, when the bank increases her deposits, when everything is given, the default probability increases. However, an increase in capitalization leads the probability to fall. This state is compatible with the moral hazard literature, i.e., the probability of failure falls when there is an increase in the value of what the banker has at stake in case of bankruptcy—capital at risk effect. Larger capital accumulation absorbs more risk. And finally as the proportion of loans in total assets, ˛t , increases, the failure probability also increases. It seems that the bank becomes more vulnerable when investing in more risky assets. Furthermore, focusing on the partial impact of deposits on default probability, we see in (8) that the market power of the bank is crucial in terms of determining the degree of the effectiveness of the change in deposits on the default probability ∂G(tc ) ˛t [r · rd Kt + (r(·) − Z (·))(rd Dt − St )] = G (tc ) ∂Dt Z(·)2
(8)
If the bank has more monopoly power in the loan market, she can reduce an increase in failure probability followed by an increase in deposits to some extent due to the term inside (8) (r − Z (·)) = −r (Lt )Lt > 0
(9)
where r (Lt ) < 0 denotes the degree of market power. As the bank possesses more market power in the loan market, thus the lower r (Lt ) (in absolute terms), she can attenuate the rise in the failure probability arising from collecting deposits by affecting the bank interest margin. This is in line with the view that competition has traditionally been considered a source of excessive risk taking in banking—that is, the degree of moral hazard depends on the market power. In the following sections, we firstly elucidate the bank’s optimizing behavior in absence of capital regulation, which we call the market model. Then we analyze the behavior of the bank that is obliged by regulation to keep a minimum capital, which is in turn called the regulatory model. 3. The market model Under the market model in which there is no regulation, the optimal liability composition consisting of Dt and Et at period t, is determined along with the value function V(Kt−1 ), where the initial capital
766
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
Kt−1 is the state variable, as the solution to the dynamic programming problem V (Kt−1 ) = max{Et [t (Dt , Et ) + ˇV (Kt )]}
(10)
Dt ,Et
or more explicitly
1
¯ t) + ˇ (t Z(Lt ) + St − rd Dt )dG(t ) − Kt−1 − Et − t (Dt − D
V (Kt−1 ) = max{ Dt ,Et
1
tc
V (Kt )dG(t )} tc
(11)
where ˇ denotes the rate at which the bank discounts her future earnings. The maximand in (11) is understood as follows. The first term represents expected current-period earnings, since stockholders earn t (Dt , Et ) in the event of a favorable realization, t > tc , and earn zero otherwise. While the second and third terms represent the opportunity cost of holding capital and raising cost of equity, respectively, the fourth term is the quantity constraint in the deposit market faced by the bank. And finally the last term represents the continuation value when the bank survives at the end of the current period, weighted by the probability that this will be the case. Now we obtain the first order conditions of the expression (11) with respect to Dt and Et ,
1
(t Z (Lt ) + (1 − ˛t ) − rd )dG(t ) − t = 0, tc
1
1
(t Z (Lt ) + (1 − ˛t ))dG(t ) − + ˇ tc
(12)
V (Kt )dG(t ) = 0.
(13)
tc
As seen in the optimal condition of deposits (12), the bank finds out optimal deposits within the current period, t, without having any intertemporal consideration. That is, the bank chooses a deposit level that equalizes its marginal benefit to deposit rate each period. However, the optimal capital accumulation decision of the bank, as seen in the condition (13), is an intertemporal decision. Hence the second optimality condition (13), using the envelope theorem, becomes
1
tc
(t Z (Lt )+(1−˛t ))dG(t )−+ˇ(1−G(tc )){
1
t+1 Z (Lt+1 )+(1−˛t+1 )dG(t+1 − )} = 0 c
t+1
(13a) This condition can be better understood in the following form,
1
tc
(t Z (Lt ) + (1 − ˛t ))dG(t ) + ˇ(1 − G(tc ))
1
t+1 Z (Lt+1 ) c
t+1
+ (1 − ˛t+1 )dG(t+1 ) = ε + ˇ(1 − G(tc ))
(13b)
While the left-hand side of the Eq. (13b) denotes the total of current and future marginal returns of capital accumulation respectively, the left hand side of (13b) represents the total of current and future marginal costs due to capital accumulation. The optimal capital to be raised, Et∗ , is to equalize them. We assume that the bank is not constrained in capital market when they issue new equity due to a highly attractive return rate of e that draws new shareholders. Turning back to the condition (12), if the constraint is not binding, t = 0, then the bank can collect deposits as much as she wants. She hence collects only deposits rather than raising equity. That is, even though the expected marginal returns of deposit and capital each period are the same, the cost of capital accumulation – the marginal cost of raising and holding capital – is higher than that of deposit. Therefore, a corner solution, Et∗ = 0 is obtained. This gives rise to the following observation: The bank is never willing to accumulate capital more under no regulation. This result is accordance with the existing literature.
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
767
However, if the constraint is binding, t > 0, the bank can collect deposits each period as much as ¯ t . Given that that amount of deposits, the bank will find out the remaining funds from raising Dt∗ = D ¯ t . The optimal amount capital. The optimality condition (13a) now works for the given deposit Dt∗ = D of equity at time t, is Et∗ > 0, which solves Eq. (13a). Hence, in the case of a shallow deposit market, raising capital becomes an important source for the bank. Given the optimal values of Dt∗ and Et∗ , we can now elucidate the optimal division of collected funds between risky and riskless assets and the impact of the bank’s capital accumulation on this. The first order condition of the objective function (3) with respect to ˛t yields
1
(t Z˛ (·) − )dG(t ) = 0
(14)
tc
Rearranging Eq. (14) gives
1
tc
t Z˛ (·)dG(t ) = (1 − G(tc ))
(15)
The bank allocates her funds in such a way that the expected return on the risky is equalized with the expected return on riskless assets at each period. Note that the term tc in (14) has the optimal value of ˛∗t that solves Eq. (14). Proposition 1. More capital accumulation leads the bank to decrease the proportion of risky assets (loans) in total assets. Proof.
Using implicit differentiation on Eq. (14), d˛∗t ∂2 t /∂˛t ∂Et =− <0 dEt ∂2 t /∂˛2t
since ∂2 t /∂˛t ∂Et < 0 and ∂2 t /∂2 ˛t < 0.
(16)
When the bank increases her capital accumulation, she allocates a smaller fraction of her portfolio to risky loans. It seems that she becomes more conservative when she has more to lose. As expected, without showing it, an increase in risk free return rate, , also leads the proportion of loans in total assets to decrease. The bank turns into safe assets, government securities. This development happened in many developing countries (Chiuri et al., 2001). Proposition 2. As the mean of loan repayments gets higher, the bank tends to allocate more of her funds to loans. Proof.
Eq. (14) can be rewritten as
Z˛ (·){¯ t −
tc
t dG(t )} − (1 − G(tc )) = 0
(17)
0
Hence, we d˛∗t Z˛ (·) =− > 0. ∂2 t /∂˛2t d¯ t
As the economy gets less stable, which is denoted by lower mean of repayments, ¯ t , the bank tends to allocate less of her funds to loans.2 These predictions of the model are broadly consistent with the lending patterns observed during the financial crises (Borensztein & Lee, 2002; Mishkin, 1999).
2 Various reasons surveyed in Bernanke and Gertler (1995) account for banks’ desire to reduce their loan supply following a negative shock to the economy.
768
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
4. The regulatory model Until now, we have looked at the bank’s capital problem from the perspective of the rational optimizing bank. That perspective would be sufficient and there would be no need for capital regulation in a perfect competitive equilibrium. Now, we also consider the perspective of the regulator, who forces the bank to maintain a level of capital above the mandatory (legal) regulatory minimum capital at the end of each period. We assume that the regulator is driven by two goals emanating from aspects of social welfare: to reduce the instability and social costs associated with bank failures and to avoid distortions away from the equilibrium level of output. The regulator tries to balance out between instability and efficiency. There is evidence that these goals are in fact important to the regulatory community (see Estrella, 2004). We now extend the model above by including these regulatory preferences and to elaborate the relationship between the default probability (risk), the supply of loans, and output. Recall that the optimizing bank chooses Dt∗ and Et∗ . Hence, the optimal failure probability is G∗ (tc (Dt∗ , Et∗ )) and total loans under no regulation is L∗ = ˛∗ (Dt∗ + Et∗ + Kt−1 )
(18)
Now we firstly suppose that the preferences of the regulator are guided by the failure risk of the bank (or financial stability). The failure risk (or probability) enters the social objective function in the form of u(G(tc )), where u(·) is a monotonically increasing transformation representing the utility of default risk for the regulator. The increase in capitalization decreases the failure risk, that is, uEt (·) < 0. On the other hand, the regulatory preference is also guided by production of firms in the economy. This is an aspect that is often neglected, when solvency regulation is under debate. Economic theory suggests and evidence shows a positive connection between bank lending and output. Bernanke and Blinder (1988) propose a model in which the output depends positively on bank loans. A downward shift in the proportion of bank lending leads to reductions in the equilibrium levels of both loans and output. Therefore, in line with this, we also assume that there is a positive association between the proportion of loans in the total assets and output, Qt , thus Qt = f(˛t ) and f (˛t ) > 0. The bank’s failure probability associated with the proportion of lending ˛t can be written as G(tc ) = (˛t ).
(19)
From here, we can pass on to the connection between output and default probability, Qt = Q (˛t ) = Q ( −1 (G(tc )))
(20)
q(G(tc )), where h(·) is a monotonically increasing transformation representing the value
Let h(Qt ) = of production for the regulator. The increase in capitalization decreases the proportion of lending, hence output, hEt (·) < 0. Consequently, the regulatory or social objective is to select a socially optimal level of G(tc ) at each period so as to maximize a welfare function taking into account both the failure risk and real production Wt = q(G(tc )) − u(G(tc ))
(21) q (G(tc ))
u (G(tc ))
G(tc )
G∗ (tc ),
There are two possible cases. First, suppose that > for all < so that the output cost of tightening the regulation is always higher than its benefit. Then the regulator prefers not to impose a binding capital requirement. In contrast, suppose that q (G(tc )) < u (G(tc )) for some G(tc ). Then there is an interior solution to the regulator’s problem and the optimal level of capital regulation that leads to G∗∗ (tc ) is given by the first-order condition is q (G∗∗ (tc )) = u (G∗∗ (tc )). If the regulator decides to impose a regulatory capital requirement, the requirement may be expressed in various equivalent ways. For example, one form of that is that the regulator can set an upper bound on the probability of failure, G(tc ) ≤ G∗∗ (tc ). Or an equivalent association between requirement capital level and loans can be set up. Now we will look at the response of the bank to regulation of this kind. We know that if deposit is not constrained by quantity, the bank does not accumulate capital under no regulation. However, if the regulator sets capital requirements, the bank is compelled to hold capital (raising equity) in this case.
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
769
The bank will choose a minimum amount of capital that is compatible with the capital requirement rule. This result is a direct consequence of the assumption that capital is more expensive than deposits. Proposition 3. If the deposit market is large enough, the default probability (risk) declines after the capital requirement regulation is set. Proof.
We know that the set of optimizing Dt∗ as described in (12) is
Dt∗ = {Dt |
1
(t Z (Lt ) + (1 − ˛t ) − rd )dG(t ) = 0}
(22)
tc
Applying implicit function theorem on Dt∗ reveals some insights about the reaction of the bank to the regulation,
1
c dDt∗ c t Z (Lt )dG(t ) − (∂t /∂Et ) t = − 1 dEt Z (L )dG( ) − (∂ c /∂D ) c
t
t
t
t
t
(23)
t
where t = (tc Z (·) + (1 − ˛) − d )g(tc ) < 0. Due to the fact ∂ c ∂tc r = d + t Zt (·) ∂Dt ∂Et
(24)
it can be easily seen that dDt∗ /dEt < −1. Hence we have dG(tc ) = G (tc ) dEt
∂ c ∂tc dDt∗ + t ∂Et ∂Dt dEt
< 0.
(25)
When the regulator sets a capital requirement rule, the bank substitutes capital for deposits. The bank reduces her deposits more than increased capital. The net impact on the default probability or the threshold value of tc is negative. That is, switching a unit of lending from being debt financed to being equity financed reduces the probability of failure. Proposition 4. Proof.
If the deposit market is large enough, the bank lends less under capital requirement.
Differentiating the expression (18) with respect to Et yields dLt∗ d˛∗t ∗ = (D + Et + Kt−1 ) + ˛∗t dEt dEt t
1+
∂Dt∗ ∂Et
(26)
Since (d˛∗t /dEt ) < 0 from (16) and ∂Dt∗ /∂Et < −1 from (23), we have dLt∗ <0 dEt
(27)
After the regulation is imposed, both the proportion of loans in total assets and the total collected funds (Et + Dt + Kt−1 ) decline. Thus the bank reacts to the capital requirement by lending less. This leads to charging higher interest rate of loans, i.e., r (Lt ) < 0. So, in any equilibrium with capital adequacy where capital adequacy is binding, the equilibrium loan interest rate is strictly higher than without capital adequacy. As a consequence, investment activity in the economy declines and banks will earn lower income from intermediation. This effect of capital adequacy regulation on production rests on two important assumptions. The first one is that equilibrium lending is solely determined by loan supply, which only makes sense if credit demand is rationed as in the model of Blum and Hellwig (1995). The second one is that firms do not have access to other sources of finance, once they are confronted with restriction in credit following capital adequacy regulation. Consideration of asymmetric information and evidence from studies of credit constrained firms (Hoshi, Kashyap, & Scharfstein, 1991) suggest that firms cannot
770
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
easily substitute other sources of finance for bank credit. In most countries, especially developing countries, bank finance is one of the most important sources of external finance. Thus far, we have assumed that the bank will hold no more capital than is required by regulation. However, if the deposit market is not large enough, the behavior of the bank concerning risk and lending changes as the following proposition claims. Proposition 5. If the deposit market is not large enough, the degree of capitalization will determine the impacts of regulation on risk and lending decisions of the bank. Proof. If the deposit constraint is binding, the optimal bank decision is changed. The bank will find out the optimal capital raised, Et∗ that solves (13a) given the maximum deposits that she can collect ¯ t . The optimal capital raised, E ∗ , can be higher or lower than the requirement level. If it each period, D t is lower than the requirement level, the gap will be closed by raising more equity for required capital. The bank in this case also reduces her lending. The extent of the gap between the required capital and market capital will determine the negative repercussion on the loans, hence the production level in the economy. This reaction will be greater if the bank is more undercapitalized. 5. Conclusion In this paper we modeled a large risk neutral bank in order to investigate consequences of a capital regulation that aims at both increasing the safety of the banking sector and decreasing its negative real repercussions on macro economy. That is, the solvency effect of capital adequacy requirements has to be balanced against negative consequences on current loan supply and the ensuing decline in output in the real sector. We analyzed two cases to explain the behavior of a bank when she chooses her capital. The first one – the market model – shows that there exists an optimal capital which maximizes the market value of firms depending on the extent of constraint on deposits. Shallowness degree of deposit market determines whether the bank applies to the capital market or not. This mainly follows from the fact that holding and extending equity is more costly than the risk free interest rate in the deposit market. However, since the optimal capitalization level of bank under the market model is typically below a legally required minimum level, we need to consider the second model—the regulatory model. In this case, the bank responds to the capital requirement in two ways: reducing her risk and constraining her lending. This paper extends the literature by studying the risk shifting effect of regulation in a setting where banks can choose multiple contracts – debt and equity – to finance firms. By regulation both the liability and asset composition is changed. The bank is forced to substitute capital for deposits (liability substitution). And the bank tends to allocate more to riskless assets and less risky assets (loans), adopting a less risky behavior (asset substitution). Overinvestment in risky investments – excessive risk taking – is rectified in comparison to the market model. This paper also contributes to the ongoing discussion on the new Capital Accord, stressing the fact that economies, which mostly rely on bank credit, may have to devote particular attention to the process of enforcement of a stricter bank capital discipline. The timing of the introduction of tight regulations is important: in a period of recession, too tight regulations could reduce the asset growth of banks. Several authors have claimed that the tightening of capital requirements – or their more stringent enforcement – contributed to the depth and length of the financial crisis of East Asian economies. References Bernanke, B. S., & Blinder, A. S. (1988). Credit, money, and aggregate demand. American Economic Review, 78(2), 435–439. Bernanke, B. S., & Gertler, M. (1995). Inside the Black Box: The Credit Channel of Monetary Policy Transmission. Journal of Economic Perspectives, 9, 27–48. Besanko, D., & Kanatas, G. (1993). Credit market equilibrium with bank monitoring and moral hazard. Review of Financial Studies, 6(1), 213–232. Blum, J. (1999). Do capital adequacy requirements reduce risks in banking? Journal of Banking and Finance, 23(5), 755–771.
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
771
Blum, J., & Hellwig, M. (1995). The macroeconomic implications of capital adequacy requirements for banks. European Economic Review, 39, 739–749. Boot, A., & Greenbaum, S. (1993). Bank regulation, reputation and rents theory and policy implications. In C. Mayer, & X. Vives (Eds.), Capital markets and financial intermediation (pp. 262–285). Cambridge: Cambridge University Press. Borensztein, E., & Lee, J. (2002). Financial crisis and credit crunch in Korea: Evidence from firm-level data. Journal of Monetary Economics, 49(4), 853–875. Borio, C., Furfine, C., & Lowe, P. (2001). Procyclicality of the financial system and financial stability: Issues and policy options. BIS Papers No. 1. Brana, S., & Lahet, D. (2009). Capital requirement and financial crisis: The case of Japan and the 1997 Asian crisis. Japan and the World Economy, 21(1), 97–104. Brinkmann, E. J., & Horvitz, P. M. (1995). Risk-based capital standards and the credit crunch. Journal of Money, Credit and Banking, 27, 848–863. Calomiris, C. W., & Hubbard, R. G. (1995). Internal finance and investment: Evidence from the undistributed profits tax of 1936–37. Journal of Business, 68(4), 443–482. Chiuri, M., Ferri, G., & Majnoni, G. (2001). The macroeconomic impact of bank capital requirements in emerging economies: Past evidence to assess the future. World Bank Policy Research Working Paper No. 2605. Danielsson, J. (2003). On the feasibility of risk based regulation. CESifo Economic Studies, 49, 157–179. Driscoll, J. (2004). Does bank lending affect output? Evidence from the U.S. states. Journal of Monetary Economics, 51(3), 451–471. Estrella, A. (2004). The cyclical behavior of optimal bank capital. Journal of Banking and Finance, 28, 1469–1498. Flannery, M. (1989). Capital regulation and insured banks’ choice of individual loan default rates. Journal of Monetary Economics, 24, 235–258. Furfine, C. (2000). Evidence on the response of U.S. banks to changes in capital requirements. Bank for International Settlements Working Paper, 88, 1–21. Furlong, F., & Keeley, M. (1989). Capital regulation and bank risktaking: A note. Journal of Banking Finance, 13, 701–718. Gambacorta, L., & Mistrulli, P. (2004). Does bank capital affect lending behavior? Journal of Financial Intermediation, 13(4), 436–457. Hellmann, T. F., Murdock, K. C., & Stiglitz, J. E. (2000). Liberalization, moral hazard in banking, and prudential regulation: Are capital requirements enough? American Economic Review, 90, 147–165. Hoshi, T., Kashyap, A., & Scharfstein, D. (1991). Corporate structure, liquidity and investment: Evidence from Japanese industrial groups. Quarterly Journal of Economics, 106, 236–247. Kashyap, A. K., & Stein, J. C. (2004). Cyclical implications of the Basel II capital standard. Economic perspectives. Federal Reserve Bank of Chicago. Keppo, J., Kofman, L., & Meng, X. (2008). Unintended consequences of the market risk requirement in banking regulation. Available at SSRN: http://ssrn.com. Kim, D., & Santomero, A. (1988). Risk in banking and capital regulation. Journal of Finance, 43, 1219–1233. Kohen, M., & Santomero, A. (1980). Regulation of bank capital and portfolio risk. Journal of Finance, 35, 1235–1244. Kopecky, K., & VanHoose, D. (2004). A model of the monetary sector with and without binding capital requirements. Journal of Banking and Finance, 28(3), 633–646. Milne, A. (2004). The inventory perspective on bank capital. Cass Business School Research Paper. Available at SSRN: http://ssrn.com. Mishkin, F. (1999). Global financial instability: Framework, events, issues. Journal of Financial Perspectives, 13(4), 3–20. Miyake, A., & Nakamura, T. (2006). A dynamic analysis of an economy with banking optimization and capital adequacy regulations. Journal of Economics and Business, 59(1), 14–27. Myers, S. C., & Majluf, N. S. (1984). Corporate finance and investment decisions when firms have information that investors do not have. Journal of Financial Economics, 13, 187–221. Peura, S., & Keppo, J. (2006). Optimal bank capital with costly recapitalization. Journal of Business, 79, 2163–2201. Pelizzon, L., & Schaefer, S. (2003). Do bank risk management and regulatory policy reduce risk in banking? Available at SSRN: http://ssrn.com. Repullo, R. (2004). Capital requirements, market power, and risk-taking in banking. Journal of Financial Intermediation, 13(2), 156–182. Rochet, J. C. (1992). Capital requirements and the behaviour of commercial banks. European Economic Review, 36, 1137–1178. Stiglitz, J., & Weiss, A. (1981). Credit rationing in markets with imperfect information. American Economic Review, 71(3), 393–410. Taggart, R., & Greenbaum, S. (1978). Bank capital and public regulation. Journal of Money, Credit and Banking, 10(2), 158–169. Tanaka, M. (2002). How do bank capital and capital adequacy regulation affect the monetary transmission mechanism? CESifo Working Paper No. 799. Thakor, A. V. (1996). Capital requirements, monetary policy, and aggregate bank lending: Theory and empirical evidence. The Journal of Finance, 51(1), 279–324.
Contents lists available at ScienceDirect
The Quarterly Review of Economics and Finance journal homepage: www.elsevier.com/locate/qref
Capital accumulation and regulation Ensar Yilmaz Yildiz Technical University, Economics, 34349 Istanbul, Turkey
a r t i c l e
i n f o
Article history: Received 1 April 2008 Received in revised form 11 December 2008 Accepted 15 February 2009 Available online 9 April 2009 JEL classification: G21 G28 E44
a b s t r a c t This paper sets up a dynamic model that analyzes a bank’s capital decision and the impact of this decision on her default risk and lending that affects aggregate output in the economy under regulation. The model shows that even though capital regulation may reduce the default risk of the bank, it may lead to credit crunch, hence the ensuing decline in output in the real sector. Furthermore, it appears that the risk-based capital requirement changes the composition of both liability and asset of the bank’s balance sheet. © 2009 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved.
Keywords: Regulation Capital requirement Credit crunch
1. Introduction The policy discussions on the regulation of banks have mainly been concerned with capital adequacy and this has been reinforced by the work of the Basel Committee that makes refinements of existing capital adequacy rules the core part of its regulatory reform work known as “Basel II”. The capital regulation suggested by “Basel II” is mainly intended to control the moral hazard (excessive risk-taking) induced by limited liability, which is a widely accepted explanation for the large number of bank failures that occurred in the 1980s and 1990s. The Basel II accord recognized that the risk sensitiveness of capital requirements should be enhanced to strengthen the soundness and stability of the banking system over the world. Hence it forces banks to hold minimum capital requirements with respect to the risk they undertake1 .
E-mail address: [email protected]. Value at Risk (VaR) is one of the most popular tools used in risk measurement. The concept of VaR has now been incorporated in the Basel II to measure especially credit risk. This approach includes not only the exposure of risk factors but also the volatility of the risk factors. Although there are some drawbacks of this approach (for this see Danielsson (2003)), it is expected that VaR based capital requirements provide a stronger incentive for well capitalized banks to reduce asset risk by rewarding low-risk banks with lower capital requirements. 1
1062-9769/$ – see front matter © 2009 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved.
doi:10.1016/j.qref.2009.02.004
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
761
However, the risk-based capital requirements have been criticized for not taking into account their impact on banks’ lending. Hence, in this paper, we are also concerned with the impact of revised capital regulation on lending, in addition to its impact on risk taking. Effects of capital adequacy rules on banks’ behavior have been analyzed in the literature before. Two strands of the literature try to clarify capital regulation-related issues. The first strand focuses on whether capital requirements are an effective tool for limiting the risk on an asset portfolio, which is analyzed in a static or dynamic framework. The static models mainly take bank capital as exogenous and abstracting from dividend and recapitalization choices. For example, for value-maximizing banks, while Furlong and Keeley (1989) demonstrate that capital requirements reduce risk-taking incentives, Flannery (1989), in contrast, concludes that the regulation may lead to higher risk taking. In a meanvariance framework, Kim and Santomero (1988), Kohen and Santomero (1980), and Rochet (1992) show that improperly chosen risk weights may increase the riskiness of banks. Some other authors argue that capital requirements reduce monitoring incentives, which reduces the quality of banks’ portfolios (e.g., Besanko & Kanatas, 1993; Boot & Greenbaum, 1993). However, static models do not consider the banks’ franchise value (expected future income) and, therefore, they give an incomplete explanation of banks’ capital. Hence dynamic models are more appropriate for analyzing the impacts of risk-based capital requirements. Taking into account the dynamic aspects of the problem, some studies show that capital requirement can be an effective tool for reducing risk-taking, while some other studies indicate that the capital regulation can induce risk-taking or have an ambiguous impact. For example, in a dynamic model, Hellmann, Murdock, and Stiglitz (2000) show that capital requirements force banks to have more of their own capital at risk so that they can be induced to invest in the prudent asset. Repullo (2004), following the main framework of Hellmann et al. (2000), finds out the similar results: if the capital requirement is imposed, the bank becomes more prudent, holding less risky assets. Similarly, Milne (2004) finds that in the short run, negative cash flow and higher capital requirements reduce risk-taking and lending, with greatest impact on severely undercapitalized banks. In contrast to these results, for example, Blum (1999) demonstrates that capital adequacy rules may increase the bank investment in the risky asset because raising equity may be excessively costly, the only possibility to increase equity tomorrow is to increase risk today under binding capital requirements. Pelizzon and Schaefer (2003), in a multi-period model under a VaR constraint, find the similar results to those of Blum (1999), i.e., capital regulation can induce a bank to undertake more risk due to her intertemporal concerns. However, Keppo, Kofman and Meng (2008) indicate that the impact of the capital regulation on default probability can be ambiguous. They find out that risk-based capital requirement may cause both positive (fall in the cash flow volatility) and negative (fall in the recapitalization level) effects on the default probability. That is, it is not guaranteed that the capital requirement has positive (or negative) effects on the default probability. The second strand of the literature analyzes the macroeconomic implications of capital requirements. One of the earliest attempts to examine the macroeconomic implications of bank capital regulation is Blum and Hellwig (1995). They show that since there is a bank lending channel of monetary policy, reductions in bank credit brought about by risk-based capital requirements can constrain real investment expenditures. Thakor (1996) also suggests that capital regulation potentially reduces the ability of monetary policy expansions to induce bank lending. In a different context, Kopecky and VanHoose (2004) conclude that binding capital requirements lead to a decline in aggregate loans and induce banks to hold more non-loan, security assets. Tanaka (2002) reaches an analogous conclusion within an IS-LM-style framework. He finds that the immediate effect of binding capital requirements is to alter the interest sensitivity and investment relationship and demonstrates that the monetary transmission mechanism is weakened if banks are poorly capitalized. On the other hand, Miyake and Nakamura (2006) provide a very different analysis of the macroeconomic effects of bank capital regulation. Utilizing a dynamic overlapping-generations model, they find that the imposition of bank capital regulation may lead to a reduction in equilibrium income. The second strand of the literature also provides an argument for linking capital requirements to the business cycle—the cyclicality issue. By cyclicality, it is commonly meant as the amplification of the business cycle due to the reduction in credit availability in recession periods (and vice versa in expansion periods). If the capital requirement is risk-sensitive, it is likely to increase during recessions
762
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
and decrease during expansions, tending to exacerbate the business cycle waves (e.g., Borio, Furfine, & Lowe, 2001; Estrella, 2004; Kashyap & Stein, 2004; Peura & Keppo, 2006). On the other hand, empirical studies also provide clues as to how the risk-based capital standards influence balance sheets of commercial banks. The empirical studies in this context mainly find that the implementation of risk-based capital standards resulted in banks’ decreasing lending. For example, to some studies (e.g., Brinkmann & Horvitz, 1995; Furfine, 2000; Thakor, 1996), the implementation of the risk based capital standards in the USA led to a slowdown in bank lending in the beginning of the 1990s. In the line with this, Chiuri, Ferri, and Majnoni (2001) find out that the enforcement of capital adequacy requirements negatively affects the supply of bank loans and the effect is stronger for less capitalized banks in emerging countries. Gambacorta and Mistrulli (2004) explore the same question using Italian banking data over the period 1992–2001. They find evidence of a bank capital channel in the monetary policy transmission mechanism, in which well capitalized banks are less constrained in their responses to monetary policy and other macroeconomic shocks than banks with relatively lower levels of capitalization. In a recent study, Brana and Lahet (2009) also find evidence that the implementation of the Basel risk-based capital ratio had a significant impact on Japanese banking behavior. The risk-based capital requirement reduced lending by internationally active Japanese banks which were subject to a more stringent capital adequacy regulation. However, a number of studies find less compelling evidence of a link between capital regulation and credit crunch. For example, using panel data for the USA states, Driscoll (2004) finds that shocks to the supply of bank loan do not affect output. This is possible since firms are not bank-dependent, and are able to substitute other forms of finance for bank loans. The main goal of this paper is to model a bank’s capital decision which is endogenously determined and effects of capital-based regulations. More precisely, the paper addresses the following questions for a representative bank in a dynamic model: (i) How does a bank’s risk-taking behavior depend on her capital position? (ii) How does a bank’s risk-taking and lending behavior depend on regulatory requirements? By addressing these questions we are able to assess the different effects of capitalbased regulations. In other words, we are able to account for the fact that banks with different capital positions will react differently to capital-based regulation. In the literature, such questions are not so often and simultaneously addressed in dynamic models. Addressing such questions in a more real setting also contributes to the ongoing discussion on the new Capital Accord, suggesting the fact that economies, which rely on bank credit, may have to consider the process of enforcement of a stricter bank capital discipline. This paper extends literature by studying the risk shifting effect in a setting where banks can choose multiple contracts – debt and equity which are substitutes – to finance firms in an endogenous capital setting under no capital requirement – the market model – and under capital requirement – the regulatory model – respectively. The model presented here incorporates capital requirements in a dynamic setting with endogenously raised bank equity or capital accumulation. In fact, we form a link between the first and second strand of the literature in a dynamic setting. That is, while capital requirements can be an effective tool for limiting the risk undertaken by the bank, they can also have macroeconomic repercussions through lending channel. The paper also tries to explain the observed association between the bank’s capitalization and propensity to take risks, and is in this respect parallel to the studies that suggest that higher capitalization restrains moral hazard (risk-taking) in banking. The regulator’s objectives in this paper are elucidated by risk and output loss. We find that there is a risk reducing effect of capital adequacy but this can only be achieved at the costs of restricting current bank lending that leads to output loss. Hence, the regulator is confronted with a difficult trade off: restrictive policies aimed at reducing the likelihood of bank failures tend to increase the probability of a credit crunch. The model shows that the response of the bank to capital regulation is mainly determined by the size of deposit market, which is a substitute for capital market. If deposit market is large enough, the risk-shifting effect is manifested in the bank’s adjustment of debt and equity she uses to finance firms in a way that motivates her to raise no new equity and to adopt a riskier behavior in the market model, allocating more fraction of funds to loans in comparison to the regulatory model. However, the bank responds to the capital regulation by reducing her default probability by raising new equity and shifting
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
763
her portfolio away from risky assets, such as loans, and towards riskless assets, such as government securities, thus cutting her lending. These results are mainly compatible with the studies mentioned above which claim that capital regulation reduces risk-taking of banks. Although in different contexts, Milne (2004) and Kopecky and VanHoose (2004) also find out that binding capital requirements lead to a decline in aggregate loans and induce banks to hold more non-loan, security assets. These findings are also verified by several empirical studies mentioned above (e.g., Chiuri et al., 2001; Gambacorta & Mistrulli, 2004; Thakor, 1996). However, if deposit market is shallow, the bank tends to raise new equity besides collecting deposit. The size of equity to be raised – the capitalization level – may cause the regulation not to be binding. Hence, in this case, regulation may have no effect on risk and lending. This mainly implies that the financial structure in which the banks seek to find out funds like the extent of deposit markets maybe crucial for banks’ risk and lending conduct. Hence such structural constraints may be critical on aggregate behavior. The remainder of the paper is organized as follows. In Section 2, we lay out the basic structure and assumptions of our model. In Section 3, we analyze the optimal solution of the bank without capital regulation—the market model. Section 4 considers the response of the bank to the capital regulation—the regulatory model. Section 5 concludes. 2. Environment We consider a bank operating in a discrete-time infinite horizon environment. The banking firm enjoys market power in the loan market, but is a price taker in the deposit market with an amount constraint. The bank can attract the funds it needs to finance projects by both collecting deposits Dt and issuing new equity Et at the beginning of time t. At the start of each period, the bank has some capital carried over from the previous period Kt−1 . Although there exist perfect substitutes for bank liability, but this is not case for the bank assets. That is, collected funds are allocated to the safe asset, say government securities, St which has a deterministic gross yield, > 1 and to the risky asset, say loans, Lt whose repayments are stochastic. We assume that the bank invests a proportion ␣t of all the proceeds in loans, Lt , used to finance the projects of companies and the remaining proportion, 1 − ␣t , in risk-free securities St . Any short sales are ruled out. Thus, the financing constraint of the bank over time is Lt + St = Dt + Et + Kt−1
(1)
The stochastic component of return arises only from the risky loans. The expected net return on risky loans is R(Lt ) = t r(Lt )Lt
(2)
where r(·) is gross return on loans, and t is the expected repayment ratio. For notational simplicity, let Zt = r(Lt )Lt , thus R(Lt ) = t Zt . Following Taggart and Greenbaum (1978), we model the credit risk by means of a random variable t , with support [0,1], to denote the proportion of performing loans at the end of the period. Since the actual value of repayments to a bank at time t is only known at the end of each period when it is revealed and only some fraction of loans, t , is repaid at the end of time t. The remaining fraction 1 − t of the investment in the risky asset yields a return of 0, i.e., this fraction is lost (non-performing loans). Unexpected loan losses may be due to purely random shocks or asymmetric information in the lender–borrower relationship. We assume away any adverse selection and/or moral hazard problems pointed out by Stiglitz and Weiss (1981) which the bank might confront in setting its loan rate or loans. We also assume that the distribution of t is unaffected by the level of lending so that the degree of uncertainty per dollar of loans is constant. The fractional repayment ratio t is a random variable drawn from a distribution with a continuous and positive density function g() and cumulative distribution function G(). The bank faces a downward sloping demand for loans. This assumption would seem to fit in with empirical evidence and making this assumption helps guarantee an internal solution to the bank’s maximization problem. But a more satisfactory justification for a less than perfectly elastic demand
764
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
function comes from assuming that the bank has some specialized information on a set of borrowers. The bank-specific nature of the information required to effectively make loans to a group of potential borrowers gives each bank power to set their own rates on loans. Since the bank faces downward sloping demand for loan, we have ∂r(Lt )/∂Lt < 0. We also assume that ∂2 r(Lt )/∂Lt2 < 0, which is sufficient to ensure Z (Lt ) < 0. When the value of repayments of loans to a bank is sufficient to ensure her solvency, the full value of deposits is repaid at the end of each period. So long as the bank is not bankrupt, depositors’ gross gain is d Dt at the end of time t, where rd > 1 is the gross rate per one unit of deposit offered by the bank. The deposit rate rd is assumed to riskless rate because depositors do not act in accordance with the risk structure of the bank. They do not demand a higher deposit rate when the bank invests in more risky assets. This is because depositors are unable to assess the relative riskiness of the balance sheet of the bank and also because of the existence of deposit insurance. ¯ t. On the other hand, we assume that the supply of deposits is quantity constrained each period, D Deposit constraint can be explained to a large extent, by the existence of a customer base which is not too much changeable. In addition, for simplicity, the costs related to deposits – deposit insurance premium and operating costs – are assumed to be nonexistent. We have two capital-related costs that the bank faces. One is that since the bank holds capital, she suffers a holding cost that amounts to Kt−1 at time t, where is the opportunity cost rate of capital. The cost rate of holding capital is above the riskless rate of return in the market, > rd . The other cost related to capital for the bank is the cost of raising new equity. For simplicity, we also assume that cost of raising new equity is linear, thus Et , where is the equity raising cost rate, which is also higher than collecting deposits, > rd . There is a sizable theoretical (e.g., Myers & Majluf, 1984) and empirical literature (e.g., Calomiris & Hubbard, 1995) to support the assumption that issuing new equity can be quite costly. With raising new capital, Et , capital accumulates to the level, Kt = Et + Kt−1. In this paper, we assume that the bank does not use retained earning as a kind of internal financing but instead issues new equity within the relevant period. There is a substantial literature that has emerged to rationalize large dividend payouts to shareholders, positing a variety of signaling, tax, agency, and behavioral motivations. In fact adding retained earnings as a source of bank capitalization would only complicate the dynamics without adding much to the intuition derived from the model. Summarizing timing of the model: The bank collects deposits and raises equity at the beginning of the period t. Then she invests a proportion of these funds in riskless assets (securities), and risky assets (loans). Repayments of loans are known with certainty only at the end of the period, t. However, at the start of the period t, the bank is assumed to know the probability distribution of the period’s repayments, G( t ). Finally, at the end of the period t, if the bank can pay off her depositors, she survives and distributes the residual return on the bank’s investments to the bank’s shareholders. Otherwise, she fails and the regulator assumes the whole remaining liability of the bank. The bank aims at maximizing the total of the expected return net of paymerits to the bank’s shareholders by firstly making an optimal choice of Dt and Et each period and then choosing optimal allocation, ˛, of collected funds between risky (loans) and riskless (securities) assets: maxEt
∞
Dt ,Et
where
ˇt−1 t (·),
(3)
t=1
1
t =
(t Z(Lt ) + St − rd Dt )dG(t ) − Kt−1 − Et
(4)
tc
is the expected net return to the bank’s shareholders at the end of period t. If the net gain that is expressed in the integrand of (4) is positive, At = t Z(Lt ) + St − rd Dt > 0,
(5)
the bank survives and operates the next period. However, if At < 0, the bank ceases to exist and the deposit insurance agency pays off depositors after claiming the return on the bank’s asset portfolio due to the limited liability for the bank shareholders.
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
765
Note that the integrand At is the stochastic part of the profit under the probability distribution, G( t ). It determines a critical proportion of good loans, tc , below which a bank is insolvent is defined as tc =
rd Dt − St Z(Lt )
(6)
Thus the bank is in default whenever the total of realized returns on loans Lt and non-risky assets is less than deposits payments, i.e., whenever t < tc . Notice that tc is determined by only the integrand in (4), where c satisfies At = 0. Since the second term of (4), Kt−1 , is opportunity cost of holding capital, it does not influence the insolvency of the bank. The cost of raising new equity, Et , also does not affect the critical value of tc since issuing new equity is not like collecting deposits which requires the bank to pay out at the end of period. Furthermore, equity capital, being a “soft” claim upon which a default cannot occur, buffers a bank by affecting the threshold point of default which is embedded in St and Z(Lt ). This is why we excluded them from the integrand that determines the default probability, which is
G(tc ) =
tc
g(t )dt
(7)
0
The expression (7) suggests that the probability of the bank failure is related to how the bank finances (Dt and Et ) and how she allocates collected funds (Lt and St ). Hence the bank can affect the probability of failure, tc by choosing deposit and equity and their allocation given her knowledge of the distribution of t , i.e., the probability of bankruptcy is not exogenous to the bank. Therefore, it is easy to see that ∂G(tc )/∂Dt > 0, ∂G(tc )/∂Et < 0 and ∂G(tc )/∂˛t > 0. That is, when the bank increases her deposits, when everything is given, the default probability increases. However, an increase in capitalization leads the probability to fall. This state is compatible with the moral hazard literature, i.e., the probability of failure falls when there is an increase in the value of what the banker has at stake in case of bankruptcy—capital at risk effect. Larger capital accumulation absorbs more risk. And finally as the proportion of loans in total assets, ˛t , increases, the failure probability also increases. It seems that the bank becomes more vulnerable when investing in more risky assets. Furthermore, focusing on the partial impact of deposits on default probability, we see in (8) that the market power of the bank is crucial in terms of determining the degree of the effectiveness of the change in deposits on the default probability ∂G(tc ) ˛t [r · rd Kt + (r(·) − Z (·))(rd Dt − St )] = G (tc ) ∂Dt Z(·)2
(8)
If the bank has more monopoly power in the loan market, she can reduce an increase in failure probability followed by an increase in deposits to some extent due to the term inside (8) (r − Z (·)) = −r (Lt )Lt > 0
(9)
where r (Lt ) < 0 denotes the degree of market power. As the bank possesses more market power in the loan market, thus the lower r (Lt ) (in absolute terms), she can attenuate the rise in the failure probability arising from collecting deposits by affecting the bank interest margin. This is in line with the view that competition has traditionally been considered a source of excessive risk taking in banking—that is, the degree of moral hazard depends on the market power. In the following sections, we firstly elucidate the bank’s optimizing behavior in absence of capital regulation, which we call the market model. Then we analyze the behavior of the bank that is obliged by regulation to keep a minimum capital, which is in turn called the regulatory model. 3. The market model Under the market model in which there is no regulation, the optimal liability composition consisting of Dt and Et at period t, is determined along with the value function V(Kt−1 ), where the initial capital
766
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
Kt−1 is the state variable, as the solution to the dynamic programming problem V (Kt−1 ) = max{Et [t (Dt , Et ) + ˇV (Kt )]}
(10)
Dt ,Et
or more explicitly
1
¯ t) + ˇ (t Z(Lt ) + St − rd Dt )dG(t ) − Kt−1 − Et − t (Dt − D
V (Kt−1 ) = max{ Dt ,Et
1
tc
V (Kt )dG(t )} tc
(11)
where ˇ denotes the rate at which the bank discounts her future earnings. The maximand in (11) is understood as follows. The first term represents expected current-period earnings, since stockholders earn t (Dt , Et ) in the event of a favorable realization, t > tc , and earn zero otherwise. While the second and third terms represent the opportunity cost of holding capital and raising cost of equity, respectively, the fourth term is the quantity constraint in the deposit market faced by the bank. And finally the last term represents the continuation value when the bank survives at the end of the current period, weighted by the probability that this will be the case. Now we obtain the first order conditions of the expression (11) with respect to Dt and Et ,
1
(t Z (Lt ) + (1 − ˛t ) − rd )dG(t ) − t = 0, tc
1
1
(t Z (Lt ) + (1 − ˛t ))dG(t ) − + ˇ tc
(12)
V (Kt )dG(t ) = 0.
(13)
tc
As seen in the optimal condition of deposits (12), the bank finds out optimal deposits within the current period, t, without having any intertemporal consideration. That is, the bank chooses a deposit level that equalizes its marginal benefit to deposit rate each period. However, the optimal capital accumulation decision of the bank, as seen in the condition (13), is an intertemporal decision. Hence the second optimality condition (13), using the envelope theorem, becomes
1
tc
(t Z (Lt )+(1−˛t ))dG(t )−+ˇ(1−G(tc )){
1
t+1 Z (Lt+1 )+(1−˛t+1 )dG(t+1 − )} = 0 c
t+1
(13a) This condition can be better understood in the following form,
1
tc
(t Z (Lt ) + (1 − ˛t ))dG(t ) + ˇ(1 − G(tc ))
1
t+1 Z (Lt+1 ) c
t+1
+ (1 − ˛t+1 )dG(t+1 ) = ε + ˇ(1 − G(tc ))
(13b)
While the left-hand side of the Eq. (13b) denotes the total of current and future marginal returns of capital accumulation respectively, the left hand side of (13b) represents the total of current and future marginal costs due to capital accumulation. The optimal capital to be raised, Et∗ , is to equalize them. We assume that the bank is not constrained in capital market when they issue new equity due to a highly attractive return rate of e that draws new shareholders. Turning back to the condition (12), if the constraint is not binding, t = 0, then the bank can collect deposits as much as she wants. She hence collects only deposits rather than raising equity. That is, even though the expected marginal returns of deposit and capital each period are the same, the cost of capital accumulation – the marginal cost of raising and holding capital – is higher than that of deposit. Therefore, a corner solution, Et∗ = 0 is obtained. This gives rise to the following observation: The bank is never willing to accumulate capital more under no regulation. This result is accordance with the existing literature.
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
767
However, if the constraint is binding, t > 0, the bank can collect deposits each period as much as ¯ t . Given that that amount of deposits, the bank will find out the remaining funds from raising Dt∗ = D ¯ t . The optimal amount capital. The optimality condition (13a) now works for the given deposit Dt∗ = D of equity at time t, is Et∗ > 0, which solves Eq. (13a). Hence, in the case of a shallow deposit market, raising capital becomes an important source for the bank. Given the optimal values of Dt∗ and Et∗ , we can now elucidate the optimal division of collected funds between risky and riskless assets and the impact of the bank’s capital accumulation on this. The first order condition of the objective function (3) with respect to ˛t yields
1
(t Z˛ (·) − )dG(t ) = 0
(14)
tc
Rearranging Eq. (14) gives
1
tc
t Z˛ (·)dG(t ) = (1 − G(tc ))
(15)
The bank allocates her funds in such a way that the expected return on the risky is equalized with the expected return on riskless assets at each period. Note that the term tc in (14) has the optimal value of ˛∗t that solves Eq. (14). Proposition 1. More capital accumulation leads the bank to decrease the proportion of risky assets (loans) in total assets. Proof.
Using implicit differentiation on Eq. (14), d˛∗t ∂2 t /∂˛t ∂Et =− <0 dEt ∂2 t /∂˛2t
since ∂2 t /∂˛t ∂Et < 0 and ∂2 t /∂2 ˛t < 0.
(16)
When the bank increases her capital accumulation, she allocates a smaller fraction of her portfolio to risky loans. It seems that she becomes more conservative when she has more to lose. As expected, without showing it, an increase in risk free return rate, , also leads the proportion of loans in total assets to decrease. The bank turns into safe assets, government securities. This development happened in many developing countries (Chiuri et al., 2001). Proposition 2. As the mean of loan repayments gets higher, the bank tends to allocate more of her funds to loans. Proof.
Eq. (14) can be rewritten as
Z˛ (·){¯ t −
tc
t dG(t )} − (1 − G(tc )) = 0
(17)
0
Hence, we d˛∗t Z˛ (·) =− > 0. ∂2 t /∂˛2t d¯ t
As the economy gets less stable, which is denoted by lower mean of repayments, ¯ t , the bank tends to allocate less of her funds to loans.2 These predictions of the model are broadly consistent with the lending patterns observed during the financial crises (Borensztein & Lee, 2002; Mishkin, 1999).
2 Various reasons surveyed in Bernanke and Gertler (1995) account for banks’ desire to reduce their loan supply following a negative shock to the economy.
768
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
4. The regulatory model Until now, we have looked at the bank’s capital problem from the perspective of the rational optimizing bank. That perspective would be sufficient and there would be no need for capital regulation in a perfect competitive equilibrium. Now, we also consider the perspective of the regulator, who forces the bank to maintain a level of capital above the mandatory (legal) regulatory minimum capital at the end of each period. We assume that the regulator is driven by two goals emanating from aspects of social welfare: to reduce the instability and social costs associated with bank failures and to avoid distortions away from the equilibrium level of output. The regulator tries to balance out between instability and efficiency. There is evidence that these goals are in fact important to the regulatory community (see Estrella, 2004). We now extend the model above by including these regulatory preferences and to elaborate the relationship between the default probability (risk), the supply of loans, and output. Recall that the optimizing bank chooses Dt∗ and Et∗ . Hence, the optimal failure probability is G∗ (tc (Dt∗ , Et∗ )) and total loans under no regulation is L∗ = ˛∗ (Dt∗ + Et∗ + Kt−1 )
(18)
Now we firstly suppose that the preferences of the regulator are guided by the failure risk of the bank (or financial stability). The failure risk (or probability) enters the social objective function in the form of u(G(tc )), where u(·) is a monotonically increasing transformation representing the utility of default risk for the regulator. The increase in capitalization decreases the failure risk, that is, uEt (·) < 0. On the other hand, the regulatory preference is also guided by production of firms in the economy. This is an aspect that is often neglected, when solvency regulation is under debate. Economic theory suggests and evidence shows a positive connection between bank lending and output. Bernanke and Blinder (1988) propose a model in which the output depends positively on bank loans. A downward shift in the proportion of bank lending leads to reductions in the equilibrium levels of both loans and output. Therefore, in line with this, we also assume that there is a positive association between the proportion of loans in the total assets and output, Qt , thus Qt = f(˛t ) and f (˛t ) > 0. The bank’s failure probability associated with the proportion of lending ˛t can be written as G(tc ) = (˛t ).
(19)
From here, we can pass on to the connection between output and default probability, Qt = Q (˛t ) = Q ( −1 (G(tc )))
(20)
q(G(tc )), where h(·) is a monotonically increasing transformation representing the value
Let h(Qt ) = of production for the regulator. The increase in capitalization decreases the proportion of lending, hence output, hEt (·) < 0. Consequently, the regulatory or social objective is to select a socially optimal level of G(tc ) at each period so as to maximize a welfare function taking into account both the failure risk and real production Wt = q(G(tc )) − u(G(tc ))
(21) q (G(tc ))
u (G(tc ))
G(tc )
G∗ (tc ),
There are two possible cases. First, suppose that > for all < so that the output cost of tightening the regulation is always higher than its benefit. Then the regulator prefers not to impose a binding capital requirement. In contrast, suppose that q (G(tc )) < u (G(tc )) for some G(tc ). Then there is an interior solution to the regulator’s problem and the optimal level of capital regulation that leads to G∗∗ (tc ) is given by the first-order condition is q (G∗∗ (tc )) = u (G∗∗ (tc )). If the regulator decides to impose a regulatory capital requirement, the requirement may be expressed in various equivalent ways. For example, one form of that is that the regulator can set an upper bound on the probability of failure, G(tc ) ≤ G∗∗ (tc ). Or an equivalent association between requirement capital level and loans can be set up. Now we will look at the response of the bank to regulation of this kind. We know that if deposit is not constrained by quantity, the bank does not accumulate capital under no regulation. However, if the regulator sets capital requirements, the bank is compelled to hold capital (raising equity) in this case.
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
769
The bank will choose a minimum amount of capital that is compatible with the capital requirement rule. This result is a direct consequence of the assumption that capital is more expensive than deposits. Proposition 3. If the deposit market is large enough, the default probability (risk) declines after the capital requirement regulation is set. Proof.
We know that the set of optimizing Dt∗ as described in (12) is
Dt∗ = {Dt |
1
(t Z (Lt ) + (1 − ˛t ) − rd )dG(t ) = 0}
(22)
tc
Applying implicit function theorem on Dt∗ reveals some insights about the reaction of the bank to the regulation,
1
c dDt∗ c t Z (Lt )dG(t ) − (∂t /∂Et ) t = − 1 dEt Z (L )dG( ) − (∂ c /∂D ) c
t
t
t
t
t
(23)
t
where t = (tc Z (·) + (1 − ˛) − d )g(tc ) < 0. Due to the fact ∂ c ∂tc r = d + t Zt (·) ∂Dt ∂Et
(24)
it can be easily seen that dDt∗ /dEt < −1. Hence we have dG(tc ) = G (tc ) dEt
∂ c ∂tc dDt∗ + t ∂Et ∂Dt dEt
< 0.
(25)
When the regulator sets a capital requirement rule, the bank substitutes capital for deposits. The bank reduces her deposits more than increased capital. The net impact on the default probability or the threshold value of tc is negative. That is, switching a unit of lending from being debt financed to being equity financed reduces the probability of failure. Proposition 4. Proof.
If the deposit market is large enough, the bank lends less under capital requirement.
Differentiating the expression (18) with respect to Et yields dLt∗ d˛∗t ∗ = (D + Et + Kt−1 ) + ˛∗t dEt dEt t
1+
∂Dt∗ ∂Et
(26)
Since (d˛∗t /dEt ) < 0 from (16) and ∂Dt∗ /∂Et < −1 from (23), we have dLt∗ <0 dEt
(27)
After the regulation is imposed, both the proportion of loans in total assets and the total collected funds (Et + Dt + Kt−1 ) decline. Thus the bank reacts to the capital requirement by lending less. This leads to charging higher interest rate of loans, i.e., r (Lt ) < 0. So, in any equilibrium with capital adequacy where capital adequacy is binding, the equilibrium loan interest rate is strictly higher than without capital adequacy. As a consequence, investment activity in the economy declines and banks will earn lower income from intermediation. This effect of capital adequacy regulation on production rests on two important assumptions. The first one is that equilibrium lending is solely determined by loan supply, which only makes sense if credit demand is rationed as in the model of Blum and Hellwig (1995). The second one is that firms do not have access to other sources of finance, once they are confronted with restriction in credit following capital adequacy regulation. Consideration of asymmetric information and evidence from studies of credit constrained firms (Hoshi, Kashyap, & Scharfstein, 1991) suggest that firms cannot
770
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
easily substitute other sources of finance for bank credit. In most countries, especially developing countries, bank finance is one of the most important sources of external finance. Thus far, we have assumed that the bank will hold no more capital than is required by regulation. However, if the deposit market is not large enough, the behavior of the bank concerning risk and lending changes as the following proposition claims. Proposition 5. If the deposit market is not large enough, the degree of capitalization will determine the impacts of regulation on risk and lending decisions of the bank. Proof. If the deposit constraint is binding, the optimal bank decision is changed. The bank will find out the optimal capital raised, Et∗ that solves (13a) given the maximum deposits that she can collect ¯ t . The optimal capital raised, E ∗ , can be higher or lower than the requirement level. If it each period, D t is lower than the requirement level, the gap will be closed by raising more equity for required capital. The bank in this case also reduces her lending. The extent of the gap between the required capital and market capital will determine the negative repercussion on the loans, hence the production level in the economy. This reaction will be greater if the bank is more undercapitalized. 5. Conclusion In this paper we modeled a large risk neutral bank in order to investigate consequences of a capital regulation that aims at both increasing the safety of the banking sector and decreasing its negative real repercussions on macro economy. That is, the solvency effect of capital adequacy requirements has to be balanced against negative consequences on current loan supply and the ensuing decline in output in the real sector. We analyzed two cases to explain the behavior of a bank when she chooses her capital. The first one – the market model – shows that there exists an optimal capital which maximizes the market value of firms depending on the extent of constraint on deposits. Shallowness degree of deposit market determines whether the bank applies to the capital market or not. This mainly follows from the fact that holding and extending equity is more costly than the risk free interest rate in the deposit market. However, since the optimal capitalization level of bank under the market model is typically below a legally required minimum level, we need to consider the second model—the regulatory model. In this case, the bank responds to the capital requirement in two ways: reducing her risk and constraining her lending. This paper extends the literature by studying the risk shifting effect of regulation in a setting where banks can choose multiple contracts – debt and equity – to finance firms. By regulation both the liability and asset composition is changed. The bank is forced to substitute capital for deposits (liability substitution). And the bank tends to allocate more to riskless assets and less risky assets (loans), adopting a less risky behavior (asset substitution). Overinvestment in risky investments – excessive risk taking – is rectified in comparison to the market model. This paper also contributes to the ongoing discussion on the new Capital Accord, stressing the fact that economies, which mostly rely on bank credit, may have to devote particular attention to the process of enforcement of a stricter bank capital discipline. The timing of the introduction of tight regulations is important: in a period of recession, too tight regulations could reduce the asset growth of banks. Several authors have claimed that the tightening of capital requirements – or their more stringent enforcement – contributed to the depth and length of the financial crisis of East Asian economies. References Bernanke, B. S., & Blinder, A. S. (1988). Credit, money, and aggregate demand. American Economic Review, 78(2), 435–439. Bernanke, B. S., & Gertler, M. (1995). Inside the Black Box: The Credit Channel of Monetary Policy Transmission. Journal of Economic Perspectives, 9, 27–48. Besanko, D., & Kanatas, G. (1993). Credit market equilibrium with bank monitoring and moral hazard. Review of Financial Studies, 6(1), 213–232. Blum, J. (1999). Do capital adequacy requirements reduce risks in banking? Journal of Banking and Finance, 23(5), 755–771.
E. Yilmaz / The Quarterly Review of Economics and Finance 49 (2009) 760–771
771
Blum, J., & Hellwig, M. (1995). The macroeconomic implications of capital adequacy requirements for banks. European Economic Review, 39, 739–749. Boot, A., & Greenbaum, S. (1993). Bank regulation, reputation and rents theory and policy implications. In C. Mayer, & X. Vives (Eds.), Capital markets and financial intermediation (pp. 262–285). Cambridge: Cambridge University Press. Borensztein, E., & Lee, J. (2002). Financial crisis and credit crunch in Korea: Evidence from firm-level data. Journal of Monetary Economics, 49(4), 853–875. Borio, C., Furfine, C., & Lowe, P. (2001). Procyclicality of the financial system and financial stability: Issues and policy options. BIS Papers No. 1. Brana, S., & Lahet, D. (2009). Capital requirement and financial crisis: The case of Japan and the 1997 Asian crisis. Japan and the World Economy, 21(1), 97–104. Brinkmann, E. J., & Horvitz, P. M. (1995). Risk-based capital standards and the credit crunch. Journal of Money, Credit and Banking, 27, 848–863. Calomiris, C. W., & Hubbard, R. G. (1995). Internal finance and investment: Evidence from the undistributed profits tax of 1936–37. Journal of Business, 68(4), 443–482. Chiuri, M., Ferri, G., & Majnoni, G. (2001). The macroeconomic impact of bank capital requirements in emerging economies: Past evidence to assess the future. World Bank Policy Research Working Paper No. 2605. Danielsson, J. (2003). On the feasibility of risk based regulation. CESifo Economic Studies, 49, 157–179. Driscoll, J. (2004). Does bank lending affect output? Evidence from the U.S. states. Journal of Monetary Economics, 51(3), 451–471. Estrella, A. (2004). The cyclical behavior of optimal bank capital. Journal of Banking and Finance, 28, 1469–1498. Flannery, M. (1989). Capital regulation and insured banks’ choice of individual loan default rates. Journal of Monetary Economics, 24, 235–258. Furfine, C. (2000). Evidence on the response of U.S. banks to changes in capital requirements. Bank for International Settlements Working Paper, 88, 1–21. Furlong, F., & Keeley, M. (1989). Capital regulation and bank risktaking: A note. Journal of Banking Finance, 13, 701–718. Gambacorta, L., & Mistrulli, P. (2004). Does bank capital affect lending behavior? Journal of Financial Intermediation, 13(4), 436–457. Hellmann, T. F., Murdock, K. C., & Stiglitz, J. E. (2000). Liberalization, moral hazard in banking, and prudential regulation: Are capital requirements enough? American Economic Review, 90, 147–165. Hoshi, T., Kashyap, A., & Scharfstein, D. (1991). Corporate structure, liquidity and investment: Evidence from Japanese industrial groups. Quarterly Journal of Economics, 106, 236–247. Kashyap, A. K., & Stein, J. C. (2004). Cyclical implications of the Basel II capital standard. Economic perspectives. Federal Reserve Bank of Chicago. Keppo, J., Kofman, L., & Meng, X. (2008). Unintended consequences of the market risk requirement in banking regulation. Available at SSRN: http://ssrn.com. Kim, D., & Santomero, A. (1988). Risk in banking and capital regulation. Journal of Finance, 43, 1219–1233. Kohen, M., & Santomero, A. (1980). Regulation of bank capital and portfolio risk. Journal of Finance, 35, 1235–1244. Kopecky, K., & VanHoose, D. (2004). A model of the monetary sector with and without binding capital requirements. Journal of Banking and Finance, 28(3), 633–646. Milne, A. (2004). The inventory perspective on bank capital. Cass Business School Research Paper. Available at SSRN: http://ssrn.com. Mishkin, F. (1999). Global financial instability: Framework, events, issues. Journal of Financial Perspectives, 13(4), 3–20. Miyake, A., & Nakamura, T. (2006). A dynamic analysis of an economy with banking optimization and capital adequacy regulations. Journal of Economics and Business, 59(1), 14–27. Myers, S. C., & Majluf, N. S. (1984). Corporate finance and investment decisions when firms have information that investors do not have. Journal of Financial Economics, 13, 187–221. Peura, S., & Keppo, J. (2006). Optimal bank capital with costly recapitalization. Journal of Business, 79, 2163–2201. Pelizzon, L., & Schaefer, S. (2003). Do bank risk management and regulatory policy reduce risk in banking? Available at SSRN: http://ssrn.com. Repullo, R. (2004). Capital requirements, market power, and risk-taking in banking. Journal of Financial Intermediation, 13(2), 156–182. Rochet, J. C. (1992). Capital requirements and the behaviour of commercial banks. European Economic Review, 36, 1137–1178. Stiglitz, J., & Weiss, A. (1981). Credit rationing in markets with imperfect information. American Economic Review, 71(3), 393–410. Taggart, R., & Greenbaum, S. (1978). Bank capital and public regulation. Journal of Money, Credit and Banking, 10(2), 158–169. Tanaka, M. (2002). How do bank capital and capital adequacy regulation affect the monetary transmission mechanism? CESifo Working Paper No. 799. Thakor, A. V. (1996). Capital requirements, monetary policy, and aggregate bank lending: Theory and empirical evidence. The Journal of Finance, 51(1), 279–324.