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A Monetary Model of Banking Crises

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Therefore, bank runs can occur as a balance of sunspots due to panic in the market, and banks become insolvent due to bank runs. This process continues on the date-(t−1) night market and bank balance sheets expand until the reserve requirements are committed.

Social Welfare

In this line of interpretation, the banking crisis (or bank runs) can be considered in this model as a model of "flight to quality" observed during the 2007-2008 financial turmoil.

Sequence of decisions

In the j submarket, a seller produces units of the intermediate goods and sells them to the buyers. A buyer buys qb units of the intermediate goods and chooses cash, mnb, and a bank deposit, dnb, to carry to the night market.

The night market

Then she chooses cash, mns and a bank deposit, dns, which she takes to the night market. In the night market, bank deposits grow to (1 +in)dns for a seller and (1 +in)dnb for a buyer, respectively.

The day market

Because kandq is traded competitively in the night market, equilibrium prices are determined by. In the equilibrium where the banks are active, it must be the case that ddb > 0. In this article we focus on the equilibrium allocation for the case where id > 0.

Finally, banks' expectations regarding withdrawals and redeposits in the j-submarket are determined as follows. The exact withdrawn amount is re-deposited by sellers in the same sub-market to the banks. Social welfare with and without banks: It is easy to verify that the social welfare of an economy with a banking sector is the same as that of a cash economy without banks.

Possibility of a bank run due to a herd behavior

The equilibrium output is essentially the same as in the case of a banking crisis in the models of Sections 3 and 4. In the basic model, the central bank can prevent bank runs by setting in>0. In our baseline model, where we assume full loan enforcement and no bank insolvency shock, there is no need for any other government intervention.

By the way, if i=id=in = 0, that is, if the Friedman rule is implemented, the first best assignment can be achieved in the basic model.

3 Bank Insolvency Shock

  • The night market
  • The day market
  • Equilibrium
  • Policy implications

Therefore, buyers never deposit their remaining cash in banks when the economy is hit by a bank insolvency shock. Therefore, the total production of intermediate goods in the case of a banking crisis is Γ(1−n)qbs. Friedman's rule: Note that real damage from a banking crisis also occurs when i = id = in = 0.

Fiscal policy: When the buyers fail to buy the intermediate goods due to the shortage of cash during a banking crisis, the government itself can buy the goods in the day market and sell them in the night market. The similar decrease in loan demand in the banking crisis will be shown if we assume that when the traders buy the intermediate goods in the day market, they can buy them on credit with probability π and pay cash for the material goods with probability 1−π . The government can issue cash to finance the fiscal policy in the day market, which can be redeemed in the night market by selling the intermediate goods to the buyers.

Suspension of convertibility: This policy can be interpreted in our model as a withdrawal ban in the day market. Whatever method is taken, the government must restore public expectations of banks' solvency.

4 Incomplete Loan Enforcement and Collateral Constraint

Equilibrium

The optimization problems for sellers and buyers are identical to those in the model of Section 3. Because δ is small, the value of ϕddb is approximated by (59), the value in the base model. About the direct sale of assets: In our model, there is no direct sale of collateralized assets (i.e. the machines,k) during a banking crisis.

The downward spiral of asset prices due to fire sales by financial institutions is called the fire-sale externality, which is probably the main rationale for banking regulation (see Brunnermeier, et al. [2009]). Although the fire-sales externality is not present in our model, it should be easily incorporated into our model by some modifications, which we leave to future research. Therefore, it is a puzzle that the downward spiral of a fire sale could continue on a significant scale and cause extensive damage to the economy.

Policy implications

This upper limit is clearly insufficient to restore normal production of intermediate goods. Thus, the real damage of the banking crisis can be completely eliminated by this policy. Moreover, the price of the asset increases in response to the increase in the production of intermediate goods.

Therefore, the solvency of the banking system is restored through the guarantee of bank liabilities, and the government incurs no costs to implement the guarantee afterwards. But if we change the setting of the model slightly so that the government can only partially substitute the buyers, it turns out that the fiscal policy cannot restore the solvency of the banks and cannot stop the bank runs. Fiscal policy cannot restore the solvency of banks or the production of consumer goods, while the amount of intermediate goods produced can be completely restored.

Extension of the model: Productivity shock and the business cycle As the Lagos-Wright monetary model is embedded in a standard business cycle model

As we saw above, monetary easing may not be able to stop a financial crisis as long as central banks only provide liquidity and do nothing to restore the solvency of the financial system. Stimulating demand through fiscal measures can only be a good policy to stop the crisis and restore market confidence and the solvency of the banking system if governments can effectively act as substitutes for liquidity-constrained firms (i.e. buyers) in corporate chains. of production in private economies. As is likely, if governments are ineffective substitutes for private buyers, neither market confidence nor the solvency of the financial system can be restored, and fiscal stimulus will not stop the crisis from worsening further.

What is most needed are the banking reforms that explicitly aim to restore the solvency of the financial system, which entails decisive policy initiatives for strict asset assessments of financial institutions, complete divestment of bad assets, and adequate capital increases from either private investors, taxpayers' money, or both. Therefore, a (small) shock in productivity, A, can induce a significant fluctuation in economic activities through the occurrence of a banking crisis. This feature of the model may be useful for further understanding the amplification mechanism of business cycles and the current global financial crisis.

5 Conclusion

A Alternative specification of banking sector

As Freixas and Rochet (2008) show, this is a convex problem and the solutions are determined by . The central bank can implicitly determine ρ (> 0) by setting ir and ip such that 0≤ir< id< ip. If the total amount of cash in the economy (deposited at the central bank) is determined by the central bank, the deposit rate, id, is determined in equilibrium such that the demand for deposits from depositors is equal to the supply of deposits from banks.

As we argue in the text, the lending rate, i, is determined in equilibrium by monetary policy, i.e. the money growth rate. This alternative model of the banking sector is compatible with optimizations by sellers and buyers in the text.

B Idiosyncratic shock, bank runs, and contagion

Setting

Third, we assume that the intermediate good, q, must be installed and combined with the machine during the day market. A buyer who has purchased q units of an intermediate good can install only q units of the good in his machine. Therefore, a night market buyer can sell his machine together with an embedded intermediate good, q.

We also assume that there exists q (>0) such that the production of the consumer goods by the machine is y=Aqθ ifq ≥q and y= 0 if q < q. If a buyer fails to purchase the semi-finished products at the day market, her machine cannot produce anything at the night market. The main consequence is that a bank cannot recover its bank loan from the borrower if it is a buyer who has failed to buyq (≥q) on the overnight market because the value of its collateral is zero and it can walk away and leaves the worthless behind. collateral held by the bank.

Equilibrium

Each bank i receives an independent shock ˜ωi,t, which takes the value 1 with probability 1−δ and ω (<1) with probability δ. This means that a buyer who borrows from a bank deposits the borrowed money in the lender's bank. If a borrower deposits the borrowed money in another bank, an idiosyncratic shock can lead to bank run contagion.

This is because the collateral value of the machines becomes zero for 1−ρ depositors and the bank cannot recover their loans that exceed the value of their collateral. The optimization problems and equilibrium conditions are quite similar to those in Sections 3 and 4. Since the shocks are idiosyncratic, the equilibrium price is unique and the liquidity constraints imply that qsb =qnb ≡qb (andqbf = 0).

Contagion

Since bank 1's depositors are bank 2's borrowers, bank 1's outflow generates the public's expectation that bank 2 will become insolvent. The bank run on bank 2 in turn makes bank 1 bankrupt because bank 2's depositors are bank 1's borrowers. Thus, a sunstroke on bank 1 causes bank outflows on both banks and makes both banks bankrupt in a self-fulfilling way.

This model implies that in general a run on one bank can cause different types of contagion leading to other bank runs, depending on the structure of the financial network or the way in which a particular bank's borrowers deposit their borrowed money. in that bank or other banks.

C On the condition for δ

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