Banking and Sovereign Debt Crises in a Monetary Union Without Central Bank Intervention

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The economic and environmental sequence of actions

In this small economy, only domestic investors are initially endowed with resources, including e units of formal goods, M0 units of money and nominal government bonds that mature at date 2 in B2 units of national currency. The money supply remains constant in the first period. At date 2, the government recovers the nominal assets (money and government bonds) that are not used to purchase products in the first period and then issues M2 units of money and nominal bond of the second period. The latter reaches its maturity at date 4 in B4 units of national currency.
Banks, as the intermediaries in financial transactions, are at the heart of the economy. All the banks in our model are identical and they do not have their own resources.5 Endowed with special human capital, banks collect resources and invest them in illiquid projects. To absorb the resources from domestic residents, banks issue demand deposits denoted by d0 that allow depositors to withdraw whenever they want. Besides, banks have access to international financial markets, in which they can borrow in the short term denoted by D∗ and issue common shares.
With funds available for investment, banks finance the projects of domestic entrepreneurs. The latter possess non-transferable technology with a constant return to scale. Without initial endowment, each entrepreneur possessing a project should borrow from a bank one unit of goods before date 0. There are two types of projects in the economy: a proportion α of the total projects maturing at date 2 are called early projects and the remaining projects, maturing at date 4, are late projects. However, at the time of investment, no one can distinguish the type of a project and this information will be revealed only at date 0. Regardless of the maturity date, a maturing project yields C(> 1) units of goods net of tax. The special ability of banks allows them to collect γC(γ < 1) units of goods from a maturing project, and the entrepreneur keeps the residual (1 − γ)C. In the event of a liquidity shortage, banks may choose to restructure illiquid projects prematurely. Restructuring each immature project delivers only c(< 1) units of goods.6 We summarize the relationship with the following inequality: c < 1 < γCt < Ct (2.1).
In this small economy, national currency and government bonds are issued at the initial date to boost the domestic production and they will be retrieved by the government through taxation. The government collects taxes with a rate τ from the output of production projects and the tax is paid only in national currency. Given that the general price level at date t is Pt, the nominal amount of tax collected from a maturing project at date t is thus τ 1 − τ CtPt.
However, if a project is restructured, the nominal amount of tax is decreased to τ 1 − τ cPt. Given condition (2.1), it is easy to see that the premature restructuring of illiquid projects is socially inefficient, because it not only induces losses for banks and entrepreneurs, but also leads the tax revenue to plummet.
We consider five dates or two periods in our setting. The time before date 0 is called the initial date, the time between date 0 and date 2 is the first period (or short term) and the time after date 2 corresponds to the second period (or long term).

Minimum capital requirement

The deposit is not negotiable. Depositors can withdraw on all dates following a sequential order until the banks deplete all their liquidity reserves and available assets. The holders of short-term debt have the right to request a refund when debts mature. Only the dividends are adjustable, since shareholders (capital) can only share the residual value with banks. These features imply that financing by capital permits the absorption of the losses, mitigates the negative impacts and improves the financial soundness of the banking system.
To ensure the stability of the banking system, the government of a small country impels its banks to respect a minimum capital ratio, denoted by k. This regulatory ratio prescribes that the proportion of the bank’s own funds (capital) should not be less than k per cent of the total resources collected by the bank. If the minimum capital level is not satisfied, banks cannot raise new funds.
Let du represent the total real value of the bank’s obligation, backed by one project maturing at date 4. Therefore, at date 4, the risk-neutral bank creditors require a value of du from γC and the shareholders (equity capital) equally share the residual value with the bank, each of them obtaining (γC − du)/2.13.
The ability of the bank to raise capital by issuing common shares is determined by the investors’ anticipation of the future profit of the bank.14 Specifically, investors will purchase common shares of banks if they anticipate that their return can at least compensate for their initial investment. Consequently, given the profitability of banks’ investment, the maximum capital ratio that a bank can hold is such that k = , 1 [γC + du] 2  1 [γC − du] 2 (2.9).
where the numerator on the right-hand side of (2.9) represents the value of capital at date 4 and the denominator stands for the bank’s total payment at date 4 to its shareholders and creditors.15 Backed by the return from a project maturing on date 4, the maximum amount of capital that the capital ratio is, the less important are the funds that a bank can collect. If we account for the international gross interest rate between date 2 and date 4 (i∗24), the maximum fund that a bank can collect at date 2 while respecting the minimum capital ratio is: γC (2.10) i∗24(1 + k).
Expression (2.10) implies that the ability of a bank to raise capital is also determined by the liquidity situation in the international financial market. An adverse shock on the international financial market can lead to higher interest rates, which will in turn reduce the amount that the bank can raise at date 2. We analyze the impacts of the minimum capital ratio in detail in the next section.

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The maximization problem of banks at date 2

Through the maximization problem of a representative bank at date 2, we examine several major factors affecting the stabilization of the banking system of a small open economy. Furthermore, we pay close attention to the negative impact of shocks from the international financial market and from the informal sector on banks’ balance sheet.

Banks’ maximization problem at date 2 without a currency mismatch

We first examine the liquidity crisis without a currency mismatch. The crisis is mainly due to the maturity mismatch between banks’ short-term debt and their long-term income. In this section, we assume that to avoid the banking fragility caused by monetary vulnerability, banks set all their contracts (both assets and liabilities) in real terms (equivalent to be in terms of foreign currency).17 In the next subsection, we will examine the case in which the contracts with domestic agents are in the national currency.

The impact of the informal sector and open market policy

The open market operation is efficient in stabilizing the nominal interest rates and in alleviating banks’ debt burden in a closed economy (Diamond and Rajan, 2006). In this section, we examine the effect of such a policy in the context of a small open economy. Through the following example, we study first how the informal sector affects the volatility of the nominal interest rate.26 Then, we analyze whether or not the open market policy can reduce or eliminate the volatility of the nominal interest rate and thus enhance banks’ resilience to the shock from the informal sector.
Numerical Example 3: Now we assume that all the contracts signed with domestic agents are denominated in national currency. Different from example 1, we now measure banks’ balance sheet in terms of national currency. All the other variables and parameters are equivalent to those in example 1.27 We already know that banks’ income from maturing projects is inadequate with respect to the liquidity demand. When banks finance through borrowing, the real value of financial assets held by banks at date 2 is 17.286 and the price level at date 2 is P12 = 1,157. Thus, the value of the money used for paying the tax is M0 n τ(eP0+E0(K∗+D1∗) [αC + (1−α)c ]o = 12, 9645. However, with the same amount of money M0+B2 1−τ i24.
(M0 = 15), consumers can now buy a quantity of informal goods equal to q1 = 14. As the informal goods and formal products are perfect substitutes, the banks must adjust the nominal gross interest
rate on deposits to i02 = q1/(M0/P12) = 1, 0799. According to the purchasing power parity, the nominal exchange rate on date 1 increases to E1 = P02/P∗ = (M0/q1)/P∗ = 1, 0714, and the exchange rate at date 2 climbs upward to E2 = P12/P∗ = 1, 157. Given that E1/E2 = i∗02/i02 → 1, 0714/1, 157 = 1/1, 0799, these solutions satisfy the uncovered interest rate parity (2.8). Banks’ revenue from both early and late entrepreneurs measured in nominal terms at date 2 equals [P0e + E0(K∗ + D∗)] [αγC + (1 − α)γC/i∗24] = 63 units of national currency.
Accordingly, the total value of banks’ assets at date 2 is 63 + M0 + B2 = 83 units of national currency. On the liability side, the foreign short-term debt corresponds to 30 units of foreign currency, or 34.71 units of national currency, and the national deposits are worth i02d0P0 = 52, 065 units of national currency. Finally, the liabilities and assets of the banks at date 2 are respectively 86.775 and 83 units of national currency. According to condition (2.15), the banking system becomes insolvent at date 2. It is necessary to notice that all the information is taken into account by economic agents at date 0. Therefore, the bank run will take place immediately at date 0 and all the projects will be prematurely restructured, including the early projects maturing at date 2. This situation is socially inefficient since at least part of the restructuring is not necessary.

Table of contents :

Chapter 1 General Introduction
1.1 Several Major Features of Eurozone Crisis
1.2 The Outline of the Ph.D. Thesis
Chapter 2 Money and Banking crisis in a small open economy
2.1 Introduction
2.2 The framework
2.2.1 Basic assumptions
2.2.2 The economic and environmental sequence of actions
2.2.3 Currency
2.3 The maximization problem of banks at date 2
2.3.1 Banks’ maximization problem at date 2 without a currency mismatch
2.3.2 Banks’ maximization problem at date 2 with a currency mismatch
2.4 Economic policies
2.4.1 Intervention in project restructuring
2.4.2 Minimum capital ratio
2.4.3 The impact of the informal sector and open market policy
2.5 Conclusion
Chapter 3 The banking crisis with interbank market freezes
3.1 Introduction
3.2 Related literature
3.3 The model
3.3.1 The environment
3.3.2 Market discipline in the interbank lending market
3.3.3 The maximization problem of banks
3.4 Crises in the interbank market
3.4.1 Pure confidence crisis
3.4.2 Foreign debt crisis and the domestic interbank market
3.4.3 Asymmetric information and the interbank market
3.5 The government’s crisis response
3.5.1 Bailout during a pure confidence crisis
3.5.2 Bailout during a crisis resulting from a foreign debt crisis
3.5.3 Preventive policy to avoid a crisis due to gambling behavior
3.6 Conclusion
Chapter 4 Banking and Sovereign Debt Crises in a Monetary Union Without Central Bank Intervention
4.1 Introduction
4.2 A small economy model with a banking system
4.2.1 The environment
4.2.2 The optimal allocation (normal times)
4.3 The financial safety net: regulatory measures and government deposit guarantee
4.3.1 The unregulated economy (α = 0)
4.3.2 Liquidity regulation : α > 0
4.3.3 Government deposit guarantee
4.4 The financial safety net in a sovereign debt crisis
4.4.1 Role of investors’ expectations
4.4.2 Twin banking and sovereign debt crisis
4.4.3 Potentially perverse effects of regulation
4.5 Policy issues
4.5.1 Role of credit rating agencies
4.5.2 Contagion
4.5.3 Eurobonds
4.6 Conclusion
Chapter 5 Banking Crisis, Moral Hazard and Fiscal Policy Responses
5.1 Introduction
5.1.1 Relationship to the literature
5.2 Basic framework
5.3 Fiscal policy ignoring the potential bailout
5.4 Fiscal response to the crisis
5.4.1 Commitment
5.4.2 Discretion
5.5 Crisis resolution through public lending
5.6 Conclusion
Chapter 6 Conclusion
6.1 Summary
6.2 Extensions
Bibliography

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