Current Developments in Monetary and Financial Law, Volume 6
Chapter

Chapter 16: Counter-Cyclical Buffer of the Basel Capital Requirement and Its Empirical Analysis

Author(s):
International Monetary Fund. Legal Dept.
Published Date:
February 2013
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Author(s)
The authors would like to thank Ryozo Himino, Financial Services Agency, Japan, for his guidance on the research, and Kakeru Miura and Lowell Battles (Harvard Law School) for their helpful research assistance.

Introduction

The recent subprime loan crisis has taught various lessons. First, the procyclicality of the Basel capital requirement has been strongly recognized. It has caused Japan to suffer for so long after the burst of the bubble in 1991. When the economy was faced with a downturn, banks tended to lend less because their capital declined. A credit crunch was one of the causes of the slow recovery of the Japanese economy in the 1990s. Secondly, banks reduced their lending to small and medium sized enterprises (SMEs) and riskier businesses during the economic recession. For Asian countries, SMEs have formed quite an important sector. They have been mainly financed through the banking sector and are vulnerable to financial crises. Therefore, the stability of bank lending is quite important in Asian economies where bank loans dominate in the financial market.

This paper focuses on the role of the Basel capital requirement and proposes a new counter-cyclical measure based on a simple general equilibrium model. The question is: how could we make a Basel II counter-cyclical policy work? Some propose to raise the level of the minimum capital requirement by computing various risks associated with each asset. Others propose to raise minimum capital requirements in good times and reduce them in times of recession according to regulatory discretion. In contrast, there are different proposals to apply an adjustment factor to the Basel capital requirement ratio without discretion by regulators. For example, Ryozo Himino (2009) proposes a stock price index as an adjustment factor. The proposal is closely related to the thinking of market participants. As stock data are available in various countries and are based on an actively traded market, they can be extensively used in most countries.

This paper will explore adjustment factors based on various macroeconomic indicators, such as GDP growth, interest rates, a stock price index, and a real estate price index. Some of the previous proposals regarding the Basel capital requirement are based on a partial equilibrium model rather than on a general equilibrium model of the entire economy analyzed in this paper. Other proposals do not have a theoretical model at all.

This paper will address the following propositions.

  • (i) The Basel capital requirement ratio should depend on various economic factors such as GDP, stock prices, interest rates and land prices, based on a simple general equilibrium model. This paper uses a model with such adjustment factors. Recent discussions on Basel III require capital based on each asset class. This paper proposes to use macro economic variables to set up the optimal capital requirement because various risks of each asset are assumed to be related to macroeconomic fluctuations. Furthermore, the Basel minimum capital requirement rule should be different from country to country, since the economic structures are different. A simple general equilibrium model suggests that the optimal minimum capital requirement ratio does depend on the structure of the economy and bank behavior.

  • (ii) The Basel capital requirement ratio should vary during a period of economic boom and during a period of economic downturn since the coefficient obtained from the theoretical model varies.

  • (iii) Cross-border bank activity is analyzed by a two-country model. The minimum capital requirement ratio should follow the ratio where the assets are invested rather than the ratio where the capital originated.

Some restricted cases of empirical results are reported in this paper. Japanese data show that the minimum capital requirement should have been lowered by 2.20 percentage points during the period of 1998Q1–2008Q4. U.S. data shows that the minimum capital requirement ratio should have been increased by 4.42 percentage points during the boom period of 2002Q4–2007Q4, and it should have been lowered by 1.12 percent percentage points during the contraction period of 2001Q1–2002Q4.

This paper is organized as follows. Section 1 presents a simple model of profit maximization behavior by banks, which are faced with downward sloping demand for loans. A bank’s capital is assumed to be kept within the limit of the Basel capital requirement ratio. However, a bank has to pay a higher interest rate to attract funds from the market if its capital becomes closer to the binding minimum capital requirement ratio, since market participants expect the bank to face difficulties if it hits the binding condition for minimum capital requirement. Section 2 specifies the optimal Basel capital requirement ratio when the regulator seeks to stabilize bank lending. It shows that the optimal Basel minimum capital requirement ratio depends on the land price, the stock price, GDP and the interest rate.

Section 3 analyzes cross border banking activities. A bank is assumed to lend money both in its domestic market and the overseas market. The overseas loans should comply with the minimum capital requirement of the target country rather than originating country. On the other hand, the domestic loans should comply with the domestic minimum capital requirement ratio. Section 4 contains our main results.

In this paper, the objective of the Basel capital requirement is assumed to be stable bank lending in light of the overexpansion of bank loans in a bubble economy. During the subprime loan crisis in the U.S., there was an overexpansion of housing loans. During asset price inflation in the late 1980s in Japan, there was an overexpansion of property loans. Therefore, this paper sets up stable bank lending as an objective of the Basel capital requirement policy. Recent papers by Farhi and Tirole (2011) and Diamond and Rajan (2011) analyze the optimal interest rate policy to achieve the maximum weighted average of consumer welfare. This paper implicitly assumes that the central bank monetary policy is set to achieve stable GDP and stable asset prices. Detailed mathematical analysis can be found in Yoshino and Hirano (2011 and 2009).

1. Bank behavior

Each bank is assumed to maximize profit. Each bank lends money to a risky sector and invests in risky loans and securities (denoted by L in Figure 1). A certain fraction of the risky loans and investments turn out to default and the default ratio is expected to be a ρe fraction of the total risky investment. The expected default ratio depends on macroeconomic variables, such as land prices, stock prices, GDP, and interest rates. A bank also invests in safe assets, such as government bonds (B). A bank is funded by deposits and from the short term money market (D), where the interest rate (im) will rise according to the proximity of the capital/credit risk ratio to the Basel minimum capital requirement.

Figure 1.Bank Balance Sheet

A bank pays the costs of lending, asset management and fund raising activities through payments for personnel, equipment, etc. A bank maximizes its profit (its revenue minus costs), namely,

Banks are maximizing their profits (Equation (1-1)) based on the budget constraint in Equation (1-2). This equation denotes the banks’ balance sheet, where banks make loans (L) and invest in safe assets (B), by absorbing funds from deposits (D) and stocks of capital (A(q2)) shown in Figure 1. The banks’ capital is shown as A(q2) which is assumed to depend on stock price q2.

The actual capital/credit risk ratio θ has to be higher than the minimum capital requirement ratio θ* (Equation (1-3)) where K{…} denotes the default risk asset and the demand for loans by firms (Equation (1-4)).

K{F[ρe(q1, q2, Y, iB)]} in Equation (1-3) denotes the default risk asset. The risk capital ratio, K, depends on macroeconomic factors, such as land prices (q1), stock prices (q2), GDP (Y), and the interest rate (iB). When the land prices and stock prices are rising, banks are faced with a lower default risk ratio for loans. Similarly, when the economy is booming and GDP (Y) is rising, banks will be faced with a lower default risk ratio. When the interest rate iB is rising, banks tend to invest more in the safe asset (B), which reduces the default risk. Therefore, the default risk ratio of K is denoted as K= K{F[ρe(q1, q2, Y, iB)]}. Equation (1-3) shows that banks must keep enough capital (A(q2)) and their “capital/credit risk asset” ratio must be greater than θ* (the Basel minimum capital requirement). Equation (1-3) denotes that the minimum capital requirement is required in order to keep an adequate capital to cope with various risks which could be faced by banks in the future as a constraint.

When corporations are maximizing their profits, the demand for bank loans by corporations depends on (a) the loan interest rate (iL), (b) the amount of output (Y) and (c) the land price (q1) as described in Equation (1-4).

The amount of bank loans is obtained by maximizing the bank’s profit (Equation (1-1)), subject to the balance sheet of the bank (Equation (1-2)), the Basel minimum capital requirement equation (Equation (1-3)), and the demand for bank loans. When banks are behaving in an inner solution, the following bank’s loan supply equation is obtained.

This equation states that the marginal rate of return on loans minus expected default minus interest on deposits minus the marginal cost equals zero.

Similarly, the bank’s demand for bonds is computed by maximizing the bank’s profit (equation (1–1)), subject to equation (1–2) as follows:

This equation states that the marginal rate of return on bonds minus the interest payment on deposits minus the marginal cost equals zero.

2. Optimal value of the minimum capital requirement

In order to obtain the optimal value for the minimum capital requirement set by the Basel Committee, we assume that stable bank lending is the objective of the Basel minimum capital requirement. Equation (1-3) denotes that the minimum capital requirement forces banks to retain enough capital to cope with expected future default losses accrued from asset management as a constraint. Monetary policy focuses on a stable rate of inflation and stable business conditions, such as stable GDP growth. On the other hand, the Basel capital requirement is assumed to be focused on stability in banking activities, more specifically, the stability of bank lending.

The optimal value for θ is set as follows. The bank regulator determines the optimal value for the minimum capital requirement by minimizing the fluctuations of bank loans based on the equilibrium value for bank loans obtained as follows:

subject to equations 1-4 and 1-5.

The optimal value for θ* (the Basel minimum capital requirement) will be expressed as follows:

Total differentiation of equation (2-2) yields,

where the optimal changes for the value for the Basel capital requirement (dθ*) depends on the following variables: (a) the target level of the bank lending (L*); (b) the land price (q1); (c) the stock price (q2); (d) GDP (Y); and (e) the interest rate (im).

To close the model, we need to write down the equilibrium condition of other markets such as the land market, the stock market, the goods market, and interest rate. As indicated earlier, detailed mathematical explanations may be found in Yoshino and Hirano (2009, 2011).

3. The optimal value for the Basel minimum capital requirement ratio: A numerical example

Suppose the land price is affected by some shock (α). According to this land market shock, the stock price (q2), interest rate (iB) on bonds and GDP (Y) will change. What is the value for θ* when the bank regulator aims to stabilize bank loans in response to the land price shock (α)? The amount of bank loans is obtained from the profit maximization behavior of banks (Equation (1-4)). The bank loan supply is determined such that the banks’ marginal rate of return for additional loan supply becomes equal to the marginal costs associated with the additional increase in bank lending.

To stabilize bank loans in response to various economic shocks, the Basel capital requirement ratio should be adjusted according to the impact of the land price, stock price, GDP and the market interest rate as follows:

  • (i) The land price shock will affect both the bank loan behavior and the expected default risk ratio. Banks’ costs will also change due to their changes in credit analysis. etc. In order to keep the bank loans stabilized, the Basel capital requirement has to be adjusted to cope with the macroeconomic shock that comes from the land price shock. Banks expand their loans when they are faced with rising land price since the collateral value rises. The supply of bank loans shifts to the right and the total amount of bank loans increases. If bank regulators would like to reduce bank loans in order to cope with a future increase of risky assets held in banks, the Basel minimum capital has to be adjusted so as to reduce banks’ aggressive lending behavior. The amount of θ*, which is the optimal Basel capital ratio is theoretically obtained as depending on the land price, stock price, GDP and interest rate.

During the period of economic recess, the demand for bank loans will also decline, which can be shown as a decline in d0 in equation (1-4) and as a shift of the demand curve to the left. In order to keep bank loans unchanged, the minimum capital requirement ratio θ has to be lowered much further to cope with the sluggish demand for loans.

In equation 2–4, the desired amount of bank loans is set to a constant value so that dL* = 0. Therefore, θ* (the optimal minimum capital requirement ratio) should vary based on the land price (q1), the stock price (q2), GDP (Y) and the market interest rate (iB) because the default risk ratio is dependent on all these macroeconomic factors.

A numerical example based on Japanese quarterly data (1996Q1-2008Q4) is as follows. The optimal value for minimum capital requirement (θ*) can be computed by estimating the equation for the default risk ratio.

The first term in Equation (3-1) is the magnitude of adjustment for the minimum capital requirement ratio when the land price (q1) changes (namely, a coefficient of −0.00238), the second term is the impact from the stock price (q2) fluctuations (a coefficient of 0.299 – (–0.00853)), the third term is the impact from GDP (Y) (a coefficient of −0.0369), and the last term is the impact from the market interest rate. The second term’s coefficient is divided into two parts, i.e., its impact on capital (A) (0.299) and its impact on the risk ratio (K) (–0.00853). The preliminary estimates show that the biggest impact comes from the impact from the stock price on banks’ capital (A), as indicated by the coefficient of 0.299.

To what extent should the minimum capital requirement be adjusted in total? If we take period of 1998Q1 and 2008Q4 in Japan as an example, the Basel minimum capital requirement ratio should be lowered by 2.20 percentage points to ensure that bank lending does not contract (Table 1).

Table 1.Estimates of Optimal Minimum Capital Requirement Ratios for Japan, United States and Canada
(1) Japan
θ* = -2.20%1998 Q1 - 2008 Q4
(2) USA
θ* = +4.42%2002 Q4 - 2007 Q4
θ* = -1.116%2001 Q1 - 2002 Q4
(3) Canada
θ* = +0.37%2003 Q1 - 2004 Q4
θ* = +0.96%2006 Q1 - 2007 Q4

Changes in the land price, stock price, GDP and interest rate will all affect the expected default risk of banks and the banking behavior. Thus, the minimum capital requirement has to be adjusted in order to stabilize bank loans. Of course, the impact of various shocks will differ according to which market created the initial shock in the economy. Sometimes, the shock arises from the property market (α), as is the case of the recent subprime loan problem.

According to Revankar and Yoshino (2008), bank lending in Japan was significantly affected by the Basel minimum capital requirement. The decline in bank lending in Japan after the burst of the bubble can be explained by the Basel minimum capital requirement ratio, which was set to 8 percent for all the time rather than changing in value as formulated in this paper.

In other examples, U.S. data in Table 1 shows that the minimum capital requirement ratio should have been increased by 4.42 percentage points during the boom period of 2002Q4–2007Q4, and it should have been lowered by 1.12 percentage points during the contraction period of the 2001Q1–2002Q4. The Canadian case shows that the minimum capital requirement ratio should have been increased by 0.96 percentage points during the 2006Q4–2007Q4 period and it should have been lowered by 3.88 percentage points during the 2007Q4–2008Q4 period.

4. The case of cross-border banks

Figure 1 presents the case where a bank is operating its business in two countries (namely country A and country B). Let assume that the country A is in a boom and the country B is in a recession. Based on Section 1, the Basel minimum capital requirement ratio in county A (say, A percent) should be set higher than that of country B (say, B percent) in order to keep bank loans stable.

A bank prefers to set up its main office in the country B since its minimum capital requirement ratio is smaller than the country A. As is shown in Figure 2, a bank sets up its main headquarters in country B and extends its lending to country A. In this case, the bank should apply the minimum capital requirement ratio based on the country A’s minimum standard rather than the one in the originating country (B). Its lending in country B denoted by arrow 2 should follow the minimum capital requirement ratio of country B. If the lending in country A comes from country B, denoted by arrow 3 in Figure 3, it should follow the minimum capital requirement ratio in country A even though the funds come from country B. If the bank lending that originated from country B would follow the minimum capital requirement ratio of country B, the lending in country A would have expanded much more than desired and would have caused a bubble in country A.

Figure 2Two country model (Cross-Border)

Figure 3Two country model (Cross-Border)

The regulator has to monitor a bank’s lending behavior carefully as to the origin of funds. To find an easier way to monitor, banks will separate its accounts into two, based on the origin of funds. The account whose origin of funds is its own country is denoted by arrow 1 in Figure 2. The other account whose funds come from country B is denoted by arrow 3. Both categories of funds which are lent in country A should have the minimum capital adequacy ratio of country A.

Conclusion

This paper presented a model of counter-cyclical adjustment of the Basel capital requirement ratio in response to economic shocks, when banks would like to keep their bank loans in stable. As too much expansion of bank loans caused bubbles in Japan and the U.S., it would be appropriate to determine the optimal capital requirement to achieve stable bank loans. The value of the capital requirement to cope with various risks of bank assets is used as a constraint on banking behavior. The optimal Basel capital requirement ratio depends on (i) how banks behave, (ii) how macroeconomic factors, such as land price, stock price, GDP and the market interest rate, react to each other and (iii) how they are influenced by economic shocks.

This paper concludes that the optimal Basel capital requirement should depend on banking behavior, the macroeconomic structure in each country, and the impact of economic shocks on each economy. Since economic structures and banking behavior are different from country to country, it concludes that the optimal minimum capital requirement should depend on various economic variables, such as land price, stock price, GDP and the market interest rate. The paper provided numerical examples and showed how to adjust the Basel capital requirement in order to keep bank lending unchanged in times of economic shock.

Cross-border bank lending should follow the minimum capital requirement ratio where the bank lending is going on rather than where the funds originated.

The model in this paper is a very simple version, but other cases are being considered and the associated econometric models are also under estimation.

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