What is the bank instability problem. Understand the Bryant and Diamond models o

Question

What is the bank instability problem. Understand the Bryant and Diamond models of bank runs. I want you to understand the quantitative logic of the problem. Memorizing formulas is not the point here. Be able to understand how my decision about whether to wait for my return or not depends on what I expect others to do. Notice that information problems are important in fully understanding the problem. What are the solutions to the bank instability problem? Understand how they work. What is the role of asymmetric information in creating the bank instability problem. Explain the connection between the solution to the bank instability problem that we have adopted and the necessity for bank regulation. Relate to the problem of moral hazard in debt finance.

Explanation / Answer

Bank instability is an outcome of the conflict of interests a bank faces acting as a financial intermediary between borrowers and depositors. Banks engage in two principal-agent relationships – one with borrowers where it acts as principal and one with depositors where it acts as agent. As such, a bank necessarily finds itself in competing and potentially compromising relationships. Because bank activities take place within the tangible and intangible structure of institutions and because behavior is affected by the incentives or disincentives they create, institutions – legal, political, sociologic, economic, and banking – can shape, in part the outcome of the transactions. Bank regulation and supervision measures as well as corruption and ethnic heterogeneity impact bank instability. The Basel Accord also gives a set of international banking guidelines for the express purpose of avoiding bank instability that can emerge when banks act as borrower and lender. These models have the feature that the economy has multiple equilibria, so that the functioning of the economy can respond to non-fundamental shifts such as “panics” “consumer confidence”, etc.

(1) a higher degree of corruption raises bank instability;

(2) deposit insurance raises bank instability;

(3) a higher degree of ethnic heterogeneity is associated with higher bank instability;

(4) restrictions on bank participation in securities activities reduce bank instability;

and at the bank-specific level, disclosure of offbalance sheet items, disclosure of risk management practices, and the imposition of sanctions on bank management and directors for infractions of cease and desist-type orders reduce bank instability.

Bryant model of bank run

According to Bryant, a run occurs because the bank’s assets, which are liquid but risky, no longer cover the nominally fixed liability (demand deposits), so depositors withdraw quickly to cut their losses. The real losses are indirect, through the loss of collateral caused by falling prices.

We start with an example due to Bryant.

There are N workers.

Each worker has ¯e units of labor, and works ei [0, e¯].

His utility function is: Ui = ci ei, where ci is his consumption.

Each agent produces an identical good, so consumption is simply equal to output. Each agent’s production function exhibits complementarities or spillovers.

ci = min[e1, e2, e3, . . . , eN ], where > 1 .

Coordination failure means two things:

1. There are multiple (Nash) equilibria

2. The equilibria are Pareto-rankable, or at least one equilibrium is Pareto superior to another.

Here, the equilibrium in which everyone selects ¯e is Pareto superior to any other equilibrium. If all of the agents could get together and sign contracts on how much they will work, they would all agree to pick ¯e. But if they cannot, they may find themselves at another, inferior equilibrium. Where there are multiple equilibria in a macro model, a few other things can appear:

1. Self-fulfilling prophecies: if everyone guesses that no one will work tomorrow, no one will, so the guess was correct. This sort of model can explain things like currency crises, bank runs, stock market bubbles, etc. Maybe it also explains recessions.

2. Sunspots: a factor which has no intrinsic relevance to the economy becomes a driving force. For example, suppose that everyone in the economy believes that no one will work tomorrow if Fed chairman wears a gray suit, and everyone will work if he wears a blue suit. It will turn out that this belief is correct, and Frs Chairman’s clothing will determine the path of the economy.

Diamond's model of bank runs

The Diamond–Dybvig model is an influential model of bank runs and relatedfinancial crises. The model shows how banks' mix of illiquid assets (such as business or mortgage loans) and liquid liabilities (deposits which may be withdrawn at any time) may give rise to self-fulfilling panics among depositors.

Investments returns are long-term, while consumption needs are uncertain and subject to idiosyncratic shocks. As long as consumption shocks are not perfectly correlated across individuals, banks may efficiently invest savings long-term, providing depositors with insurance against idiosyncratic consumption shocks.

The economy lasts three periods, t = 0, 1, 2, and produces one good.

There is a continuum of agents of measure 1 each endowed with one unit of good at time 0.

Agents get utility from consumption and are sufficiently risk averse u 0 (c) > 0; u 00(c) < 0; cu0 (c) u 00(c) > 1 cu0 (c) c < 0;

At t = 1 agents experience a consumption shock and learn whether they are ”impatient”, i.e., they derive utility only from consumption at t = 1, or are ”patient”, i.e., they derive utility only from consumption at t = 2.

Liquidity shocks are not publicly observable and an insurance market cannot open.

The probabilities of being impatient and patient (the shares of impatient and patient in the population) are p and 1 p

With no discounting, the expected utility of each individual at t = 0, as well as the social welfare, is U = pu(c1) + (1 p)u(c2) p is common knowledge;

consumption shocks are unobservable.

The good can be stored or can be invested in an amount 0 I 1 in a long-run technology.

The investment provides R > 1 units of consumption at t = 2, but L < 1 units of consumption if it’s terminated early at t = 1

max c1,c2 U = pu(c1) + (1 p)u(c2) s.t. pc1 = 1 I (1 p)c2 = IR

max c1,c2 L = pu(c1) + (1 p)u(c2) [pc1 + (1 p) c2 R 1]

L c1 = pu0 (c1) p = 0

L c2 = (1 p)u 0 (c2) (1 p) R = 0

L = pc1 + (1 p) c2 R 1 = 0

u 0 (c1) = Ru0 (c2)

Given that R > 1 and u 00(·) < 0

c 1 < c 2

Given that cu0 (c) c < 0 1 · u 0 (c1) > R · u 0 (R) Therefore, given that u 00(·) < 0 1 < c 1 < c 2 < R

c1 = 1 I + LI = 1 (1 L)I 1 c2 = 1 I + RI = 1 + (R 1)I R

Consumers cannot replicate the optimal allocation

Assume that after the liquidity shocks occur a financial market opens where agents can trade their present and future goods.

Let B be a bond which yields with certainty a unit of good at t = 2 and b its price c1 = 1 I + bRI c2 = 1 I b + RI

If b > 1/R (i.e., if bR > 1) all agents prefer to invest long-term and sell the bond when they know to be impatient.

If b < 1/R (i.e., if 1/b > R) all agents will prefer to store their goods and buy the bond when they know to be patient

In equilibrium: b = 1/R Therefore c1 = 1 c2 = R Financial markets cannot replicate the optimal allocation.

The optimal allocation can be implemented by a bank offering the following deposit contract D : In exchange for one unit of good at time 0, pay c 1 on deposits withdrawn at t = 1 and c 2 on deposits withdrawn at t = 2

Impatient investors have no interest to withdraw at t = 2 and patient have no interest to withdraw at t = 1

The contract D and the asset allocation reported in the balance sheet are a Nash equilibrium

When there is uncertainty concerning p, R or there is lack of confidence in the bank, another possible equilibrium is all depositors withdraw at t = 1 Assume that a patient investor believes that a fraction x of other patient investors wants to withdraw at t = 1 He anticipates that the bank will be forced to liquidate part of its long-term investments at a loss in order to pay c 1 at t = 1 and, hence, that it cannot pay c 2 to 1 x patient depositors The optimal strategy for patient and impatient investors is to withdraw at t = 1, and the Nash equilibrium is ”bank run” (all consumers withdraw at t = 1 and the bank is liquidated).

Remedies against bank run.

1.Narrow banking - Narrow banking has 3 interpretations

a. Enough liquidity to pay all depositors in case of a bank run )100 per cent reserve ratio

(1-I)> C1

C2 < IR

Bankís problem max U = 1u(C1) + 2u(C2) s.t. (1 I) C1, C2 < IR

Result: C1 = 1-I, C2 = IR. All depositors can withdraw C1 at t = 1.

No run! But as liquidity insurance, this is more expensive than autarky

2. Enough liquidity after liquidation of long term assets that it can meet a run

(1-I) + lI > C1

C2 <RI + 1- I.

Result: C1 = (1- I) + lI, C2 = RI + 1- I.

No run! Same as autarky.

3. Obtain enough liquidity to meet a run after securitization of its long term assets, i.e., sell them but not as an emergency in t = 1.

Same as the bond market: At t = 1 the bank sells claims (at t = 2) on its long term assets to patient consumers, just enough to Önance withdrawals at t = 1:

Essentially the same as the bond market. C1 = 1, C2 = R

No run, but not as good as the good NE in fractional reserve banking.

In general, these guarantees of stability prevent the Örst best good equilibrium.

2. Suspension of convertibility

If the bank knows the proportion of impatient consumers 1 it declares it will suspend paying out deposits at t = 1 when 1C1 has been withdrawn. Then all type 2 will wait until t = 2. But, the bank will normally not know the true 1. ñ If it errs on the low side, a number of truly impatient consumers will be denied liquidity insurance. ñ Because it may err on the high side, type 2 consumers may still have an incentive to run.

3. Deposit insurance

Introduce an institution (government) that can levy a tax on banks in t = 1 based on the realized 1. Unlike the bank which at t = 0 commits to paying C1 at t = 1 and C2 at t = 2, the deposit insurer levies this tax on withdrawals in t = 1 when the insurer observes the true value of 1 denoted b1. The tax is decided in period 1 when the deposit insurer observes b1. Given b1, it can then realize the Örst best after tax consumption solution C 1 (b1), C 2 (b1) by setting the right tax rate. Proceeds from the tax is channeled back to the bank to make sure the bank has enough liquid assets that all b1 who choose to withdraw at t = 1 can actually get C 1 (b1). Since all depositors who want to withdraw at t = 1 can withdraw, and type 2 now knows that with tax Önanced deposit insurance they will always get C2 > C1 by waiting, only the true type 1 choose to withdraw at t = 1, and the Örst best solution is realized. But in the real world another problem: if a bank through costly e§ort can ináuence R, deposit insurance causes moral hazard.

4. Interbank market

So far, have abstracted from interbank market where benks can lend and borrow liquidity Interbank market ) less likely a bank will have to liquidate long run assets to pay depositors ) run against the bank less likely. But, contagion of a liquidity shock through interbank market is possible.

5. Lender of last resort (LLR)

Bagehot (1873): Central banks should lend in an emergency to illiquid but solvent banks. But at penalty rate.

Goodhart: Clearcut distinction between illiquidity and insolvency is a myth. LLR can in practice be risky, should be approved by Treasury.

Norges Bank: LLR shall not be solvency assistance to banks. Hence LLR normally against collateral or guarantees when the stability of the Önancial system as such is at stake. Normally consulting with the Treasury. Look at borrowing bankís solvency. LLR at a penalty rate.

Role of asymmetric information in creating the bank instability problem

Factors that may lead to instability: i) Increases in interest rates ii) Increases in uncertainty iii) Asset market effects on balance sheets iv) Problems in the banking sector All of these lead to a worsening of asymmetric information problems. Financial instability may result in a crisis through the slowing down of information flows which reduce financial intermediation activity. A financial crisis results in the sorting out of insolvent firms from healthy firms, and this will reduce uncertainty in financial markets, and reduce the potential for adverse selection and moral hazard problems. This will be essential for a subsequent recovery.

Financial instability occurs when shocks to the financial system interfere with information flows so that the financial system can no longer do its job of channeling funds to those with productive investment opportunities. Without access to these funds, individuals and firms cut their spending, resulting in a contraction of economic activity, which can sometimes be quite severe. In order to prevent financial instability from occurring, policymakers need to understand what causes it to happen. The asymmetric information analysis we have used to understand the structure of the financial system suggests that there are four categories of factors that lead to financial instability: increases in interest rates, increases in uncertainty, asset market effects on balance sheets, and problems in the banking sector.

A crucial impediment to the efficient functioning of the financial system is asymmetric information, a situation in which one party to a financial contract has much less accurate information than the other party. For example, borrowers who take out loans usually have much better information about the potential returns and risk associated with the investment projects they plan to undertake than lenders do. Asymmetric information leads to two basic problems in the financial system: adverse selection and moral hazard.

Adverse selection is an asymmetric information problem that occurs before the transaction occurs when potential bad credit risks are the ones who most actively seek out a loan. Thus, the parties who are the most likely to produce an undesirable (adverse) outcome are most likely to be selected. For example, those who want to take on big risks are likely to be the most eager to take out a loan because they know that they are unlikely to pay it back. Since adverse selection makes it more likely that loans might be made to bad credit risks, lenders may decide not to make any loans even though there are good credit risks in the marketplace. This outcome is a feature of the classic “lemons problem” analysis first described by Akerlof (1970). Clearly, minimizing the adverse selection problem requires that lenders must screen out good from bad credit risks. Moral hazard occurs after the transaction takes place because the lender is subjected to the hazard that the borrower has incentives to engage in activities that are undesirable (immoral) from the lender’s point of view—that is, activities that make it less likely that the loan will be paid back. Moral hazard occurs because a borrower has incentives to invest in projects with high risk in which the borrower does well if the project succeeds but the lender bears most of the loss if the project fails. Also the borrower has incentives to misallocate funds for her own personal use, to shirk and just not work very hard, or to undertake investment in unprofitable projects that increase her power or stature. The conflict of interest between the borrower and lender stemming from moral hazard (the agency problem) implies that many lenders will decide that they would rather not make loans, so that lending and investment will be at suboptimal levels.2 In order to minimize the moral hazard problem, lenders must impose restrictions (restrictive covenants) on borrowers so that borrowers do not engage in behavior that makes it less likely that they can pay back the loan; then lenders must monitor the borrowers’ activities and enforce the restrictive covenants if the borrower violates them.

necessity for bank regulation

Bank regulation is a form of government regulation which subjects banksto certain requirements, restrictions and guidelines, designed to createmarket transparency between banking institutions and the individuals andcorporations with whom they conduct business, among other things.

Given the interconnectedness of the banking industry and the reliance that the national (and global) economy hold on banks, it is important for regulatory agencies to maintain control over the standardized practices of these institutions.

Among the reasons for maintaining close regulation of banking institutions is the aforementioned concern over the global repercussions that could result from a bank's failure; the idea that these bulge bracket banks are "too big to fail". The objective of federal agencies is to avoid situations in which the government must decide whether to support a struggling bank or to let it fail. The issue, as many argue, is that providing aid to crippled banks creates a situation of moral hazard. The general premise is that while the government may have prevented a financial catastrophe for the time being, they have reinforced confidence for high risk taking and provided an invisible safety net. This can lead to a vicious cycle, wherein banks take risks, fail, receive a bailout, and then continue to take risks once again.

problem of moral hazard in debt finance

moral hazard arises in debt financing. Equity holders can expropriate bond holders by inducing them to lend at a lower rate of interest than the ex post risk of the firm deserves, either by misleading them as to true nature of the firm’s risk (asymmetric information) or by changing the risk of the firm after the loan is made and before it is paid off (asset substitution). One approach to mitigating moral hazard risk is to attempt to prevent the equity holders from engaging in actions that would result in expropriation. Thus, bonds may include covenants that attempt to preclude risk-increasing corporate actions (e.g., mergers), or that ensure that the firm maintains certain financial ratios. An alternative to contractually constraining managerial risk taking is to design contracts to reduce the incentives of managers to take unanticipated risks.

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