政府是否應允許商業銀行持有非金融業企業之股票？(1/2)

行政院國家科學委員會專題研究計畫 期中進度報告

政府是否應允許商業銀行持有非金融業企業之股票？(1/2)

計畫類別： 個別型計畫 計畫編號： NSC92-2416-H-002-033- 執行期間： 92 年 08 月 01 日至 93 年 07 月 31 日 執行單位： 國立臺灣大學財務金融學系暨研究所 計畫主持人： 陳業寧 計畫參與人員： 王衍智，林岳賢 報告類型： 精簡報告 處理方式： 本計畫可公開查詢

中 華 民 國 93 年 6 月 11 日

行政院國家科學委員會補助專題研究計畫

□ 成 果 報 告

X 期中進度報告

政府是否應允許商業銀行持有非金融業企業之股票？(1/2)

Banking and Commerce: Should Banks be Allowed to Hold

the Equity of Nonfinancial Firms? (Part I)

計畫類別： 個別型計畫

計畫編號：NSC 92-2416-H-002-033

執行期間：2003 年 8 月 1 日至 2004 年 7 月 31 日

計畫主持人： 陳業寧

共同主持人：

計畫參與人員： 王衍智、林岳賢

成果報告類型(依經費核定清單規定繳交)：精簡報告

執行單位：國立台灣大學財務金融學系

中 華 民 國 93 年 5 月 31 日

計畫中英文摘要

中文摘要 本計畫發展一理論模型以探討對銀行持有非金融業股票之管制（即限制銀行不得持有過 多非金融業企業股票）的福利效果。在該模型中，有可能倒閉的銀行在決定是否清算借 款公司之投資計畫時，其清算決策會過於寬鬆；也就是說，某些應被清算的計畫仍可繼 續執行。要求銀行僅能持有清償次序最優先的債權可能可以降低此問題之嚴重性。然 而，這樣的限制也有其福利成本：對於倒閉可能性很低的銀行，此限制將使其在決定是 否清算借款廠商之計畫時過於嚴苛。本計畫中也討論了在哪些情況下限制銀行僅能持有 最優先受償之債權較可能提高社會福利。此外，本計畫也指出：其他政策（如政府補貼 與銀行自有資本管制）也可能可以提高銀行清算決策之效率。故要限制銀行持有非金融 企業股票的前提條件之一是其為所有可能採行之政策中最有效率的政策。 關鍵詞：銀行綜合化經營、銀行持股管制、清算決策、政府補貼、銀行自有資本 管制 Abstract

This project develops a theoretical model to study the welfare implications of bank equity investment regulations, that is, the regulations limiting the extent to which banks can invest in the equity of non-financial firms. It finds that, if a bank may default, then it may be too lenient when deciding whether to liquidate the investment projects it finances. That is, it will allow some projects to be continued even if their continuation values are lower than their liquidation values. It also shows that requiring banks to hold only the most senior debt of the borrowing firms may alleviate this problem. However, these regulations have their costs. If a bank’s liquidation rule is efficient without the equity investment restrictions, then it will liquidate too often after the restrictions are imposed. This project discusses the conditions under which bank equity investment regulations will be welfare improving. It also studies the possibility of using other alternatives (such as governmental subsidies and bank capital ratio regulations) to improve banks’ liquidation decisions. It suggests that bank equity investment regulations can be justified only when they are more efficient than all the other possible alternatives.

Keywords: universal banking, bank equity investment regulation, liquidation decision,

government subsidy, bank capital ratio regulation I

計畫內容

1. Introduction

This project studies the welfare implications of the regulations that impose limits on banks’ investments in the equity of non-financial firms. Santos (1999) points out that many countries have this type of regulation. A common justification for these

regulations is that, since banks are highly leveraged, allowing banks to hold more equity will increase their incentive and ability to pursue high risk. However, several articles propose that bank equity investment regulations may result in inefficiencies. For example, Santos (1999) shows that, when the contract between the bank and the borrower affects the borrower’s effort choice, an equity investment restriction is never welfare improving. Park (2000) demonstrates that, when the contract between the bank and the borrowing firm affects the bank’s incentive to liquidate, the equity investment restriction should not be too tight. Otherwise, the bank may have too much incentive to liquidate the firm’s project.

In contrast to these papers that show the costs of bank equity investment

regulations, this project demonstrates that these regulations may be welfare improving under certain circumstances. The story of the project can be described as follows. Consider a bank which finances numerous projects. The cash flow that a project will generate depends on both the project’s quality and the state of the economy. Given the same project quality, the expected cash flow generated by a project is higher in the good state and is lower in the bad state. Moreover, the projects’ continuation values may fall below their liquidation values. After the bank finances the projects, it learns the projects’ qualities; it then uses this information to decide which projects to liquidate. However, it does not learn the state of the economy when it makes the decisions. It is shown that the efficiency of the bank’s liquidation decisions will depend on whether it faces default risk. More specifically, the bank’s liquidation rule will be efficient if it can always pay off the deposits, and will be too lax if it cannot pay off its deposits in the bad state.

The intuition behind this result is clear. In the bad state, the projects’ expected cash flows are lower, so more projects should be liquidated. However, when the bank cannot pay off the deposits in the bad state, it will care only about its payoff in the good state. As a result, it will adopt a more lax liquidation rule and allows some

projects whose continuation values are lower than their liquidation values to be continued.

The simple story stated above has several important policy implications. First, it suggests that regulations that impose limits on banks’ investment in the equity of non-financial firms may improve efficiency. By forcing banks to hold only the most senior debt, banks will become tougher when they make the liquidation decisions. In this sense, this model supports the traditional wisdom that bank equity investment regulations can reduce the banks’ incentive to pursue risks. On the other hand, this project also demonstrates that these regulations are not always welfare improving. They will reduce welfare if a bank’s liquidation rule is efficient without the regulations.

This project also implies that imposing equity investment limits on banks is more likely to be welfare improving when the banking industry is less profitable. The more profitable the banking industry is, the lower the probability that a bank will default, so the more efficient the bank’s liquidation rule will be. This result provides an

explanation for the observation that countries with a more concentrated banking industry are less likely to impose strict equity investment restrictions on banks. Finally, the model in this project implies that both government subsidy to banks and bank capital ratio regulations can be used to improve the banks’ liquidation decisions. This means that bank equity investment regulations can be justified only when they are more efficient than all the other possible alternatives.

It is interesting to compare the model of this project with those in Santos (1999) and Park (2000) because the conclusions of this project are different from those in the two papers. In Santos (1999), the contract between the bank and the borrower affects the borrower’s effort choice, while in my model the contract affects the bank’s liquidation decisions. In Santos (1999), when the borrower’s effort is unobservable, the second-best solution can be achieved by a combination of equity and debt

contracts. Requiring the bank to hold only debt in his model will raise the borrower’s payoffs in the better states and lowers her payoffs in the worse ones. As a result, the borrower’s effort will be distorted toward improving the probabilities that the better states will occur. In contrast, even under the optimal contract, in my model the bank’s liquidation decisions may still be too loose when it faces default risk. Requiring the bank to hold only the most senior debt will alleviate this problem. Complementing to Santos (1999), my model shows that the bank’s incentive problems should also be

considered when discussing the welfare effects of bank equity investment regulations. As to Park (2000), the bank in his model never defaults, so its liquidation

decision is efficient if (i) it need not play the role of the delegated monitor, and (ii) it always receives a constant proportion of the project’s realized cash flow.1 My model extends Park’s model by taking into account how default risk influences the bank’s behavior. It is shown that the liquidation decisions of a bank that may default may be too lenient, and that requiring the bank to receive more when the project is liquidated may alleviate this problem.2

The rest of the project is organized as follows. Section 2 introduces the basic model. Section 3 is the analysis of the basic model. Section 4 discusses the welfare implications of the bank equity investment restrictions. Section 5 extends the basic model to a repeated-game model. Concluding remarks are contained in Section 6.

2. The Model

Consider a model with a bank and numerous entrepreneurs and depositors. This is a three-date model (dates 0 to 2). All parties are risk neutral, and the risk free interest rate is zero. The bank is controlled by a manager who is the only equity holder of the bank.3 Entrepreneurs are identical at date 0. Each entrepreneur has an investment project. Each project requires one dollar invested at date 0, and matures at date 2. A project either succeeds or fails; it will yield R dollars if it succeeds and will yield nothing if it fails, where R > 1. For an entrepreneur i, the probability that her project will succeed is η pi, where h and pi are the random variables representing the

macroeconomic and firm-specific components of the success probability, respectively. Assume that the value of h is determined by the state of the economy, and there are only two possible states. With probability θ, the state is good and h = 1; with

probability 1 – θ, the state is bad and h = w, where 0 < w < 1. The assumption about η allows me to investigate how systematic risk affects the bank’s behavior. The pi

represents a project’s quality, and is continuously distributed on [0, 1] with probability density function f(pi) and cumulative density function F(pi). The qualities of any two

1 _{In Park (2000), when the bank need not play the role of the delegated monitor, its liquidation decision}

is efficient if it holds a constant proportion of the firm’s debt and equity. Under this arrangement, the bank always gets a constant proportion of the project’s realized cash flow.

2 _{In fact, in my model it can be easily shown that the liquidation decisions of a bank that may default}

will be too lenient if it receives a constant proportion of the projects’ realized cash flows.

3 _{Since the manager is the only equity owner of the bank, in this project I do not distinguish rigorously}

projects are independent. Although projects mature at date 2, they can be liquidated early. The date-1 liquidation value of a project is L dollars, where 0 < L < 1.

At date 0, entrepreneurs have no money, so they have to get funding from the bank to undertake the projects. The contract between the bank and an entrepreneur can be represented by (xR, xL). If the bank and an entrepreneur sign the contract, then

it has the right to liquidate the entrepreneur’s project at date 1. Moreover, the bank receives xR if the project succeeds at date 2, and receives xL if the project is liquidated

at date 1. The fact that entrepreneurs have no money at date 0 implies xR ≤ R and xL ≤

L.

At date 0, the bank proposes (xR, xL) to entrepreneurs, and entrepreneurs either

accept or reject the contract. When determining the contract, the bank maximizes its expected profit. Let u0 > 0 denote the entrepreneurs’ reservation utility, that is, an

entrepreneur will not undertake the project unless her payoff from doing so is no lower than u0. The u0 can be interpreted as the bargaining power of entrepreneurs

against the bank. The higher the u0, the more bargaining power entrepreneurs have

(and the less bargaining power the bank has). In the rest of the paper, I will say that the bank has more bargaining power when u0 is lower. Note that under this setting, the

contract between the bank and entrepreneurs is general, and is not limited to debt or equity contracts.4

The bank’s only assets are its claims to entrepreneurs. For each dollar it uses to finance an entrepreneur’s project, the bank raises Z dollars by issuing deposits and the manager contributes the remaining 1 – Z dollars as bank capital. To simplify the exposition, assume that the manager will inject the necessary capital into the bank at date 0. The condition under which the manager will voluntarily do so will be stated later. In this model, Z is exogenously given with L < Z < 1. The value of Z reflects the government’s regulation on the bank’s capital ratio. For example, if the government requires that the bank’s capital ratio must be no lower than 0.08, then Z = 1 – 0.08 = 0.92. The deposits are fully protected by governmental deposit insurance, and depositors have no other investment opportunities, so the interest rate on deposits is zero. For simplicity, assume that deposit insurance is free, which means the bank need not pay any deposit insurance premium.

4 _{It can be shown that, if the contract between the bank and entrepreneurs is limited to a combination}

of debt and equity contracts, then xR – xL must be no larger than R – L. The qualitative results of this

The qualities of the projects are revealed at date 1, and the value of h is realized date 2. At date 1, after the information about the projects (that is, pi) is realized, the

bank decides which projects to liquidate. Let pˆ denote the bank’s cutoff point of pi,

that is, it will liquidate the projects with pi lower than pˆ . Note that the bank does not

observe the value of h when it makes the liquidation decisions. The sequence of moves can be summarized as follows.

Date 0 The bank collects deposits, and the manager contributes the bank capital. The bank then signs the contract (xR, xL) with atomistic entrepreneurs.

Date 1 The values of the projects’ pi are revealed. The bank decides which

projects to liquidate. It receives xL from each entrepreneur whose project is

liquidated.

Date 2 The value of h is revealed. According to pi and h, the projects which are

not liquidated at date 1 either fail or succeed. The cash flows are distributed according to the contract. If possible, the bank pays off the deposits.

3. The Analysis of the Basic Model

This section analyzes the optimal (xR, xL) the bank will choose. Let h0 denote the

expected value of h. We have h0 ≡ h + (1 – h) w. Given pi, the continuation and

liquidation values of a project are h0 pi R and L, respectively. Therefore, the first-best

liquidation rule is to liquidate a project if and only if

R L p p_i 0 * η ≡ < . … (1) Define

∫

+ ≡ 1 ˆ 0 ( ) ) ˆ ( ) ˆ ( ppdF p R L p F p PV η . … (2)

The PV( pˆ ) defined in (2) is a project’s expected cash flow given a cutoff point pˆ . It can be easily shown that PV is maximized when pˆ = p*. From the above description, a project can never be financed if PV(p*) < 1 + u0.

The optimal contract is solved backwards. I will first study the bank’s choice of

pˆ at date 1 given (xR, xL). I will then find the optimal contract that the bank will

pˆ can be written as5 } ) ( ) ˆ ( , 0 max{ ) 1 ( } ) ( ) ˆ ( , 0 max{ 1 ˆ 1 ˆ pdF p Z F p x wx pdF p Z x x p F p R L p R L+

∫

− + −θ +

∫

− θ . … (3) The above expression reflects the fact that the bank has limited liability when it cannot pay off the deposits. Define

R L L R x x x x p 0 1( , )≡_η , … (4) R L L R x x x x p₂( , )≡ , … (5) Z p dF p x x x x p F x x L Rx x p R L L R L R B ≡ + − Π

_∫

1 ) , ( 0 1 1 1 ) ( )) , ( ( ) , ( η , … (6) ] ) ( )) , ( ( [ ) , ( 1 ) , ( 2 2 2 Z p dF p x x x x p F x x L Rx x p R L L R L R B ≡ + − Π θ

∫

. … (7)

The following lemma states the bank’s choice of pˆ . All the proofs of the lemmas and propositions are available from the author upon request.

Lemma 1. Suppose that the bank signs the contract (xR, xL) with atomistic

entrepreneurs at date 0.

(a) The optimal pˆ for the bank is p1(xR, xL) if

ПB1(xR, xL) ≥ ПB2(xR, xL), … (8a)

and is p2(xR, xL) if

ПB1(xR, xL) ≤ ПB2(xR, xL). … (8b)

The bank is indifferent between p1 and p2 if ПB1(xR, xL) = ПB2(xR, xL).

(b) A sufficient condition for the bank to set pˆ = p2(xR, xL) is

0 ) ( ) ( L+wR

_∫

1 pdF p −Z ≤ R w L F R w L . … (9)

Lemma 1 can be explained as follows. By (3), the bank’s expected profit is ПB1(xR, xL) if it can always pay off the deposits, and is ПB2(xR, xL) if it can pay off the

deposits only in the good state. It can be shown that the bank will set pˆ = p1(xR, xL)

5 _{For simplicity, the capital the manager contributes at date 0 (whose value is 1 – Z) is not included}

when the bank’s expected profit is calculated. It will be considered later when I discuss the condition under which the manager will set up the bank at date 0.

if it maximizes ПB1(xR, xL), and will set pˆ = p2(xR, xL) if it maximizes ПB2(xR, xL).

Lemma 1 says that the bank will choose between p1 and p2 depending on whether

ПB1(xR, xL) is larger or smaller than ПB2(xR, xL). Note that p1 > p2 given any (xR, xL),

which implies that the bank will choose a looser liquidation rule when it cannot pay off the deposits in the bad state. Intuitively, if the bank knew which state would be realized, it would enforce a stricter liquidation rule in the bad state because projects have lower success probabilities in this state. When the bank can pay off the deposits in both states, its choice of pˆ will maximize the sum of its profits in the two states weighted by the probabilities of the states. On the other hand, when the bank cannot pay off the deposits in the bad state, it cares only about its profit in the good state. As a result, it will choose a looser liquidation rule when it may default. This result is consistent with the well known fact in the corporate finance literature that debtors who do not care about the downside risk have excessive incentives to pursue risks. Part (b) of the lemma states a sufficient condition for the bank to choose p2 over p1.

When (9) holds, the bank can never pay off the deposits in the bad state even if (xR, xL)

= (R, L). Therefore, it will set pˆ = p2(xR, xL). It can be easily shown that (9) will

hold when w is low.

In the above discussion, the contract (xR, xL) is assumed given. I next study the

optimal (xR, xL) the bank will offer at date 0. Because the bank’s choice of pˆ

depends on whether (8a) and (8b) hold,6 these two cases should be discussed

separately. First consider the case where (8a) holds. The optimization program in this case can be stated as follows.

Program 1: ₁( , ) ,x B R L x x x Max L R Π … (10) subject to (8a),

∫

≥ − + − 1 ) , ( 0 0 1 1 ) ( ) ( ) ( )) , ( ( L R x x p R L L R x L x R x pdF p u x p F η , … (11a) xL ≤ L, … (12) and xR ≤ R. … (13)

Condition (11a) is the entrepreneur’s individual rationality condition, which states that an entrepreneur will not undertake the project unless her payoff for doing so is no

6 _{Note that the sets of (x}

R, xL) that satisfy (8a) and (8b) are not exclusive. When ПB1(xR, xL) = ПB2(xR,

lower than u0. Equations (12) and (13) are the feasibility conditions saying that the

amount that the bank receives cannot exceed the realized cash flow of the project. The optimization problem when (8b) holds can be written in a similar way. It is stated as follows. Program 2: ₂( , ) ,x B R L x x x Max L R Π … (14) subject to (8b), (12), (13), and

∫

≥ − + − 1 ) , ( 0 0 2 2 ) ( ) ( ) ( )) , ( ( L R x x p R L L R x L x R x pdF p u x p F η . … (11b)

(11b) is an entrepreneurs’ individual rationality condition when the bank sets pˆ = p2(xR, xL).

To find the optimal contract, the bank has to solve both programs 1 and 2, and then chooses a contract that gives it the highest expected profit. Since there are four constraints in each optimization problem, it is very difficult to find the optimal contract for the general case. Instead of doing so, I will discuss the solutions in two special cases that have interesting policy implications. Define

) (0 * * p PV u R xR≡ − , … (15) R L p PV u L x_L ) (0 * *_{≡ − . … (16)}

The following proposition finds a sufficient condition under which the bank’s liquidation rule will be efficient.

Proposition 1. Suppose that (i) Π_B1(x*_R,x_L*)>Π_B2(x_R*,x_L*), and (ii) for all the (xR, xL)

that satisfy(8b),

∫

> − + − 1 ) , ( 0 0 2 2 ) ( ) ( ) ( )) , ( ( L Rx x p R L L R x L x R x pdF p u x p F η .

In this case, the optimal (xR, xL) is (x*R,xL*), and the bank’s liquidation rule is efficient,

that is, it will liquidate a project if and only if pi < p*.

It can be verified that the condition stated in Proposition 1 will hold when Z is not high and u0 is low. Intuitively, when the bank has more bargaining power (u0 is

lower) or less debt burden (Z is lower), it is more likely to be able to pay off the deposits in both states. In this case, it will internalize all the efficiency gains and

losses, so its liquidation decisions will be efficient.

I next show it is possible that the bank will enforce a suboptimal liquidation rule. Let p denote the pˆ that satisfies

0 ) ) ˆ ( ( ) ( ˆ ) ˆ ( ) ( ˆ ) ˆ ( ˆ 1 0 ˆ 0 1 ˆ ₌           − + +

∫

∫

u p PV p dF p p p F p dF p p p F p d d p p η , … (17) and define

∫

+ − ≡ ₁ 0 0 ) ( ˆ ) ( ) ( p R p dF p p p F u p PV x η , … (18) L x ≡ p x_R. … (19)

The following proposition suggests that the bank’s liquidation rule may be too loose compared with the first best one.

Proposition 2. Suppose that (9) holds, x_R≤ R, and x_L≤ L. In this case, the optimal

(xR, xL) = (xR,xL), and the bank liquidates a project if and only if pi < p . Moreover, p < p*.

The following numerical example illustrates the results in Proposition 2.

Example 1. Suppose that R = 3, L = 0.8, θ = 0.75, w = 0.4, Z = 0.9, u = 0.1, and f(p)

= p. In this case, 0 0333 . 0 ) ( ) ( L+wR

∫

1 pdF p −Z =− < R w L F R w L ,

so (9) holds. Moreover, xR = 2.82533 < R, xL= 0.67432 < L, and p = 0.238669 <

p* = 0.313725. It can also be shown that (8b) is satisfied when (xR, xL) = (xR,xL). The

bank will liquidate a project if and only if pi < p . A project’s expected cash flow

realized under this liquidation rule is PV( p ) = 1.39331.

Before leaving this section, I briefly discuss the condition under which the

manager of the bank will voluntarily contribute the bank capital at date 0. Let (xRs, xLs)

denote the optimal contract that the bank will offer, and assume that the required rate of return for the manager is the risk free rate. The manager will inject capital if

max{ПB1(xRs, xLs), ПB2(xRs, xLs)} ≥ 1 – Z.

The left-hand side of the above expression is the bank’s expected profit for each dollar it invests, and the right-hand side is the bank capital it has to contribute for one

dollar’s investment. If the above inequality does not hold, the manager will not have the incentive to set up the bank at date 0.

4. Welfare Implications of Bank Equity Investment Regulations

In the previous section, I show that the bank may adopt a loose liquidation rule that allows projects whose continuation values are lower than their liquidation values to be continued. In this section, I will demonstrate that bank equity investment regulations may alleviate this problem. Since the contract form (xR, xL) is general and is not

limited to the combinations of equity and debt contracts, in this project it is not appropriate to impose an upper bound on the proportion of a borrowing firm’s equity that the bank can hold.7 Instead, I explain the bank equity investment restriction as the requirement that the bank can hold only a fixed-amount claim on the project and this claim has to be senior to all the other claims. The justification for this setting is that it fits the spirit of bank equity investment regulations, which is to reduce the volatility of the bank’s payoff. To simplify the exposition, I will sometimes refer to this restriction as “asking the bank to hold only the most senior debt”. By forcing the bank to receive more when a project is liquidated, this restriction increases the bank’s incentive to liquidate projects, thus inducing the bank to enforce a stricter liquidation rule.

Let D denote the face value of the bank’s claim when bank equity investment regulations are imposed. Given the assumption that L < 1, it is obvious that xL = L and

xR = D in this case, so the contract between the bank and entrepreneurs can be

represented by D.

The process for solving the optimal contract in this case is the same with that stated in Section 3 except that now (12) is binding. Let pD2 denote the pˆ that

satisfies 0 0 1 ˆ ( ) ) ˆ ( η u p dF p p L R p = −

∫

. … (20)

7 _{As Santos (1999) points out, this type of regulation usually limits a bank’s investment in the equity of}

I will show the optimal contract in the case where (9) holds to demonstrate the point that bank equity investment regulations can be welfare improving.

Proposition 3. Suppose that (9) holds. If the bank is allowed to hold only the most

senior debt, then the optimal face value of the bank’s claim is L/pD2. At date 1, the

bank will liquidate a project if and only if pi < pD2. Moreover, pD2 > p if

] ) ( ) ( )[ ( ) ( ) ( ) ( 1 1 0 0

∫

∫

+ < − R L R L p pdF R L R L F R L f R L p pdF R L F u R L PV u . … (21)

Example 2. Suppose that the parameter values are just the same with those in

Example 1. Moreover, assume that the bank is allowed to hold only the most senior debt. The optimal face value of the bank’s claim is 2.74283, and the bank will liquidate a project at date 1 if and only if pi < pD2, and

p = 0.238669 < pD2 = 0.29167 < p* = 0.313725.

The expected present value of a project given this liquidation rule is PV(0.29167) = 1.39987 > PV( p ) = 1.39331.

Proposition 3 and Example 2 together imply that the equity investment restriction does induce the bank to adopt a stricter liquidation rule, and it can be welfare improving. However, bank equity investment regulations are not always welfare improving. If the bank adopts the efficient liquidation rule without bank equity investment regulations, then its liquidation decisions will become too strict after the regulations are imposed. The following proposition demonstrates this point.

Proposition 4. Suppose that (i) Π_B1(x*_R,x_L*)>Π_B2(x_R*,x_L*), and (ii) for all the (xR, xL)

that satisfy(8b),

∫

> − + − 1 ) , ( 0 0 2 2 ) ( ) ( ) ( )) , ( ( L Rx x p R L L R x L x R x pdF p u x p F η .

If the bank is allowed to hold only the most senior debt, then the optimal face value of the bank’s claim is L/(η0 pD1), where pD1 is the pˆ that satisfies

0 0 1 ˆ 0 ) ( ) ˆ ( η η u p dF p p L R p = −

∫

. … (22)

The bank will liquidate a project if and only if pi < pD1. Moreover, pD1 > p*.

5. A Repeated-Game Model

Up to now, I assume that the bank collects the deposits and makes the liquidation decisions only once. Such a setting cannot be used to investigate how future

profitability affects banks’ behavior. As pointed out in the literature, the banks’ moral hazard problems will become less serious when they care about charter value, which is defined as the sum of the discounted future profits that a bank can earn if it is not closed. To study this issue, this section discusses the bank’s liquidation rule when the game stated in Section 2 is repeatedly played.

Suppose that the game stated in Section 2 is repeatedly played with the following modifications. If the bank is never closed, then what happen at date 0, 1, and 2 in the basic model happen at date 2t, 2t+1, and 2t+2 for any non-negative integer t.

Entrepreneurs are short-term players in the sense that an entrepreneur born at date 2t die at date 2t+2. For any integer t > 0, at date 2t, all the entrepreneurs born at date 2t – 2 die, and a new generation of entrepreneurs are born. The number of entrepreneurs born in each generation is kept constant.

In the rest of this section, the time span between date 2t to 2t+1 or between date 2t+1 to 2t+2 will be call a stage; the two consecutive stages from date 2t to 2t+2 will be called a period. The risk free interest rate per stage is r > 0 rather than 0. A project undertaken at date 2t will yield R’ at date 2t+2 if it succeeds, and will yield L’ at date 2t+1 if it is liquidated early. Define R = R’/(1 + r)2, and L = L’/(1 + r). In the modified model, R and L are the present values of a project’s realized cash flows when it succeeds and when it is liquidated early, respectively.8 The contract (xR, xL) can be

reinterpreted in a similar way, where xR is the present value of the bank’s proceeds

from a project when the project succeeds, and xL is the present value of the bank’s

proceeds from a project when the project is liquidated at date 2t+1.9 The definition of Z does not change. However, since the risk free interest rate is r rather than zero, for Z dollars’ deposits received at date 2t, the bank has to pay Z(1+r)2 at date 2t+2.

Suppose that the bank is supervised by a government. At every date 2t, the

8 _{The present values are estimated at the date when the project is undertaken.} 9 _{More specifically, for a project financed at date 2t, the bank receives x}

R’ at date 2t+2 if it succeeds,

and receives xL’ at date 2t+1if it is liquidated. Define xR = xR’/(1+r)2 and xL = xL’/(1+r). Given these

definitions, xR is the present value of the bank’s proceeds from a project when the project succeeds, and

government decides whether to close the bank. The closure rule adopted by the government is simple: the bank will be closed if and only if it cannot repay all the deposits due at date 2t. There are two funding sources that the bank can use to repay the deposits. The first is the payments it receives from entrepreneurs born at date 2(t–1), and the second is the new capital contributed by the manager at date 2t. The bank is not allowed to issue new deposits before it pays off the old ones. Once the old deposits are paid off, the bank is then allowed to continue for one more period.

Intuitively, the bank will have less incentive to choose a loose liquidation rule under the modified setting. If future profitability is not low, the manager will inject new capital to pay off the deposits when losses occur, which means he no longer enjoys limited liability and has to suffer the losses. As a result, he is more likely to adopt an efficient liquidation rule. Define

1 ) 1 ( ₊ 2₋ ≡ r δ , … (23) where δ is the discount rate for two stages (that is, one period). The following lemma states the bank’s choice of pˆ in the revised infinite-period model.

Lemma 2.

(a) Suppose that at date 2t, the bank offers (xR, xL). Moreover, suppose that the bank’s

date-2t charter value is C. The optimal pˆ for the bank is p1(xR, xL) if

ПB1(xR, xL) + (1 – θ) C ≥ ПB2(xR, xL), … (24a)

and is p2(xR, xL) if

ПB1(xR, xL) + (1 – θ) C ≤ ПB2(xR, xL). … (24b)

The bank is indifferent between p1 and p2 if (24a) and (24b) are binding.

(b) Suppose that the bank always offers (xR, xL) to atomistic entrepreneurs in all the

periods when it is not closed. The optimal pˆ for the bank is p1(xR, xL) if

ПB1(xR, xL) ≥ δ θ δ + − ) 1 ( ПB2(xR, xL), … (25a) and is p2(xR, xL) if ПB1(xR, xL) ≤ δ θ δ + − ) 1 ( ПB2(xR, xL). … (25b) The bank is indifferent between p1 and p2 if (25a) and (25b) are binding.

Comparing Lemmas 1 and 2, the condition under which the bank will set pˆ = p1(xR, xL) is relaxed in the infinite-period model. Applying the same logic, it should

be obvious that the bank’s liquidation rule is more likely to be efficient in the infinite-period game. This result is shown in Proposition 5.

Proposition 5. Suppose that

) , ( ) 1 ( ) , ( * * 2 * * 1 R L B R L B x x > _{− +} Π x x Π δ θ δ , and that for all the (xR, xL) satisfying (25b),

∫

> − + − 1 ) , ( 0 0 2 2 ) ( ) ( ) ( )) , ( ( L Rx x p R L L R x L x R x pdF p u x p F η .

The optimal (xR, xL) for the bank is (x*R,x*L), and the bank’s liquidation rule is

efficient, that is, it will liquidate a project if and only if pi < p*.

One implication of Lemma 2 and Proposition 5 is that a governmental subsidy to the banking industry may improve banks’ liquidation decisions. To see this, consider the policy that the government gives the bank a subsidy b in the beginning of the period if the bank has not been closed yet, where b > 0. If the bank always offers (xR,

xL) in all the periods, then it can be shown that under this policy, the bank will choose

p1 as the cutoff point if and only if

b x x x x_{R L B R L} B θ δ θ δ θ δ + − − − Π + − ≥ Π ) 1 ( 1 ) , ( ) 1 ( ) , ( ₂ 1 . … (26)

By (26), the bank is more likely to set pˆ = p1(xR, xL) when b increases. This result is

consistent with the idea in Chan, Greenbaum, and Thakor (1992) that subsidizing banks with under-priced deposit insurance can alleviate the banks’ moral hazard problems.

The results in this section have two interesting policy implications. First, bank equity investment regulations are less likely to be beneficial when the banking industry is more profitable. When the banking industry is more profitable, the charter value C is higher. By Lemma 2 and Proposition 5, in this case the bank is more likely to set pˆ = p*_{. This result provides an explanation for the observation that countries}

association between banking and commerce.10 Second, in addition to bank equity investment regulations, there exist other alternatives for improving the banks’ liquidation rules. This project suggests two. The first is the governmental subsidy discussed above. The second is bank capital ratio regulations. From Lemma 2 and Proposition 5, the value of Z may affect the bank’s choice of pˆ , which implies that capital ratio regulations also have an impact on banks’ liquidation decisions.11 To justify bank equity investment regulations, it has to be shown that they are more effective (or less costly) than other possible alternatives.

6. Concluding Remarks

In this project, I develop a simple model to study the welfare implications of bank equity investment regulations. It is found that these regulations may be either welfare improving or decreasing. The conditions under which they can improve welfare are discussed. The model can be extended in several directions. First, in this project it is assumed that the bank automatically acquires the information about projects (that is, the values of pi). However, in the real world banks need expend efforts to get the

information about borrowers, and the contracts between banks and borrowing firms will affect banks’ information acquisition decisions. It will be interesting to see whether the results of my model will change when monitoring by the bank is costly. Second, the model in this project can be applied to study the welfare effects of bank capital ratio regulations. As mentioned above, the value of Z will affect the bank’s liquidation decisions. To formally study this issue, the fact that bank capital is more costly than deposits should be taken into consideration. It will be a promising topic to compare bank capital ratio regulations and bank equity investment regulations in terms of their effectiveness in improving banks’ liquidation decisions. Finally, this project does not discuss how the concern for the borrowing firms’ control rights will affect the welfare effects of bank equity investment regulations. One important purpose of bank equity investment regulations is to prevent banks from acquiring the control rights of non-financial firms. To study this issue, the model in this project should be extended so that (i) borrowing firms have multiple projects, and (ii) the project choice of a firm is made by the party who owns the most shares of the firm.

10 _{Usually the banking industry is more profitable when it is more concentrated.}

11 _{To investigate this alternative, the cost of bank capital need be specified, otherwise the optimal}

Investigating such a case will broaden our knowledge in how bank equity investment regulations should be designed.

參考文獻

Banerji, S., A. H. Chen and S. C. Mazumdar, 2002, Universal banking under bilateral information asymmetry, Journal of Financial Services Research, 22, 3, 169-187. Berlin, M., K. John and A. Saunders, 1996, Bank equity stakes in borrowing firms and

financial distress, Review of Financial Studies, 9, 889-919.

Bhattacharya, S. and F. Lafintaine, 1995, Double-sided moral hazard and nature of share contracts, The Rand Journal of Economics, 761-782.

Bhattacharya, S. and A. Thakor, 1993, Contemporary banking theory, Journal of

Financial Intermediation, 3, 2-50.

Boyd, J., C. Chang and B. Smith, 1998, Moral hazard under commercial and universal banking, Journal of Money Credit and Banking, 30, 3, 426-468.

Chan, Y., S. Greenbaum, and A. Thakor, 1992, Is Fairly Priced Deposit Insurance Possible? Journal of Finance 47, 227-246.

Delong, B., 1991, Did J. P. Morgan’s men add value? an economist’s perspective on financial capitalism, In Inside the Business Enterprise: Historical Perspectives on

the Use of Information, ed. Peter Temin, Chicago: University of Chicago Press for

NBER, 205-236.

Gorton, G. and Frank A. S., 2000, Universal banking the performance of German firms, Journal of Financial Economics, 58, 29-80.

Hoshi, T., A. Kashyap and D. Scharfstein, 1990, The role of banks in reducing the costs of financial distress in Japan, Journal of Financial Economics, 27, 67-88. Hoshi, T., A. Kashyap and D. Scharfstein, 1991, Corporate structure, liquidity, and

investments: evidence from Japanese industrial groups, Quarterly Journal of

Economics, 106, 33-60.

Jensen, M. and W. Meckling, 1976, Theory of the firm: managerial behavior, agency costs and ownership structure, Journal of Financial Economics, 3, 306-360.

John, K., T. A. John and A. Saunders, 1994, Universal banking and firm risking-taking,

Journal of Banking and Finance, 18, 307-323.

Kaplan, S. and B. Minton, 1994, Appointments of Outsiders to Japanese boards: determinants and implications for managers, Journal of Financial Economics, 36, 225-258.

Krainer, J., 2000, The separation of banking and commerce, Economic Review, Federal Reserve Bank of San Francisco, 15-25.

Kroszner, R. S. and R. G. Rajan, 1994, Is the Glass-Steagall Act justified? a study of the U.S. experience with universal banking before 1933, American Economic

Review, 84, 810-832.

Park, S., 1997, Risk-taking behavior of banks under regulation, Journal of Banking

and Finance, 21, 491-507.

Pozdena, R. J., 1991, Why banks need commerce powers, Federal Reserve Bank of

San Francisco Economic Review, 18-30.

Prowse, S., 1990, Institutional investment patterns and corporate financial behavior in the U.S. and Japan, Journal of Financial Economics, 27, 43-66.

Santos, J. A. C., 1999, Bank capital and equity investment regulations, Journal of

Banking and Finance, 23, 1095-1120.

Saunders, A., 1994, Banking and commerce: an overview of the public policy issues,

計畫自評

This project is the first part of a two-year project. Judging from its results, this project has achieved most of the original goals specified in the research proposal. The model in this project is tractable and can be extended in several directions. As mentioned in Section 6 of the contents of the project, the bank’s monitoring effort can be included in the model. Also, the model can be applied to compare the welfare effects of bank equity investment regulations and those of bank capital ratio regulations. Most importantly, this model can be extended to study how the concern for the borrowing firms’ control rights will affect the welfare implications of bank equity investment regulations. Among these three possible extensions, the last two have important policy implications, and will be my focus in my second year’s project.

One thing worth mentioning is that the model in this project has a nice feature that is not planned in the original research proposal. In the model, the bank finances numerous rather than one project. One may think that, when the bank can finance many projects, it can diversify away all the risk (as is done in Diamond (1984)),12 _so

its liquidation decision on any single project should be efficient. In fact, one referee of the research proposal claimed that discussing the relationship between one bank and one borrowing firm is misleading because each bank finances many firms in the real world. This project shows that, even if a bank finances numerous projects, its liquidation decisions may still be inefficient if it cannot diversify away the default risk. To include this feature (that is, the bank finances multiple firms) into the model and to keep the model simple, I assume that each firm has only one project and that the bank can acquire the information about projects without any cost. Based on the results of the current model, I think the model will still be tractable if these assumptions are relaxed. Therefore, these assumptions will be relaxed in the second part of the two-year project.

12 _{Please see Diamond, D. W., 1984, “Financial Intermediation and Delegated Monitoring,” Review of}