Blanket guarantee, deposit insurance and restructuring decisions for multinational banks

Journal of Financial Stability 8 (2012) 84–95

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Blanket guarantee, deposit insurance and restructuring decisions for multinational banks Ville Mälkönen a , J.-P. Niinimäki b,c,∗ a

Government Institute for Economic Research, P.O. Box 1279, FI-00101 Helsinki, Finland Research Department, Bank of Finland, P.O. Box 160, FI-00101 Helsinki, Finland c Department of Economics, University of Turku, FI-20014 Turku, Finland b

a r t i c l e

i n f o

Article history: Received 30 June 2010 Received in revised form 21 February 2011 Accepted 25 February 2011 Available online 5 March 2011 JEL classification: G21 G28

a b s t r a c t This paper examines blanket guarantee, deposit insurance and restructuring decisions with respect to a multinational bank (MNB) using Nash bargaining when the threat of a bank panic motivates countries to make decisions quickly. Failure of the bank would unevenly distribute externalities across countries, influencing the restructuring incentives. In equilibrium, the bank is either liquidated or one of the countries – or both – recapitalizes it. A partition of the recapitalization costs is sensitive to the country-specific benefits and costs from recapitalization, panic and liquidation. The home regulator benefits from the advantage that it is the only entity that can legally liquidate the MNB. Rational expectations regarding the bargaining result affect the incentives to declare a blanket guarantee. © 2011 Elsevier B.V. All rights reserved.

Keywords: Blanket guarantee Deposit insurance Bank run Financial crises Bargaining

1. Introduction The emergence of large and complex multinational banks (MNBs) has raised concerns that national supervision and crisis management practices – such as national deposit insurance schemes – should be redesigned to meet the requirements of the contemporary international financial markets. These concerns follow directly from the observation that managing of financial stability is no longer a national issue, as most policies targeted to restructure a distressed MNB involve cross-border externalities. Cross-border issues are especially important in the unified European financial system, where the number of pan-European banks is increasing and the largest institutions have systemic importance for the financial markets of multiple countries.1

∗ Corresponding author at: Department of Economics, University of Turku, FI20014 Turku, Finland. Tel.: +358 2333 5399; fax: +358 2333 5893. E-mail addresses: [email protected], juhnii@utu.fi, [email protected] (J.-P. Niinimäki). 1 Schoenmaker (2009, p. 2) documents: ‘Average cross-border penetration in the EU has gradually increased from 11% in 1995 to 21% in 2007. Turning to individual banks, the European Central Bank has conducted a mapping exercise of EU banking groups with significant cross-border activity. While the number of banks included 1572-3089/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jfs.2011.02.005

The effects of an MNB failure vary among the countries concerned, which complicates cooperation, as national authorities pursue the policies they consider most beneficial for their country and their domestic financial system. The restructuring negotiations concerning Fortis in 2008 between the Belgian, Dutch and Luxembourg governments and central bankers offer a topical example. The unilateral closure of Lehman Brothers in the same year by the US authorities illustrates how the closure of a large and complex financial institution generates severe cross-border externalities. The restructuring decision might well have been different had there been cooperation between, for instance, the European and US authorities. History has demonstrated that regulators are unable to establish a credible pre-commitment to a given policy scheme during banking crises. A similar commitment problem applies to any international ex-ante agreement on crisis management of an MNB, as the regulators cannot feasibly control for all states of the world in the contract. The most plausible prediction is that a crisis in an MNB

in the analysis increased only slightly – from 41 to 46 between years 2001 and 2005 – the consolidated assets of the sample as a whole increased from 54% to 68% of overall consolidated EU banking assets.’

V. Mälkönen, J.-P. Niinimäki / Journal of Financial Stability 8 (2012) 84–95

will lead to ex-post negotiations between the affected countries on appropriate restructuring policy and burden sharing. Most banking crises have demonstrated that once the first signs of distress in a bank emerge, the regulators have limited time to reach an agreement, because while the regulators are negotiating on appropriate intervention, uninsured depositors are likely to panic. The threat of panic motivates regulators to restructure banks quickly. The negotiations over Fortis provide a convincing example: ‘Belgium was desperate to prevent panic, because Fortis is the country’s biggest private sector employer and handles the bank accounts and insurance policies of 1.5 million Belgian households, or almost half the population.’ (Financial Times 29 October 2008) Take-over negotiations with other banks were unsuccessful, because the price offers were too low. Therefore, on September 28, 2008, Belgium, the Netherlands and Luxembourg organized a rescue plan worth of 11.2 billion euros to Fortis. Belgium promised to buy 49% of Fortis’ Belgian banking unit for 4.7 billion euros, while the Netherlands pays 4 billion euros for the Fortis’ Dutch banking business. Luxembourg provides a 2.5 million loan convertible into 49% of Fortis’ share in that country. The original plan, however, was later changed. This paper studies international cooperation in the design of restructuring policies of a failing MNB and its welfare implications. To this end, we develop a bargaining model where the countries try to find an agreement for restructuring the debt of an insolvent MNB and for sharing the associated costs. The outcomes of the game are dictated by three main features that are likely to emerge in such policy processes. The first feature is the allocation of regulatory responsibilities between the countries affected. The home-country regulator is the only entity with a legal right to liquidate the MNB. Another side of the same feature is that the closure of an MNB induces a cross-border externality in the form of real cost from the loss of value of uninsured deposits. The externality motivates the host country to participate in the costs conditional on the home country not liquidating the MNB, but agreeing to the recapitalization of the bank. The second feature is the limited time the regulators have to reach an agreement, as postponing the decision to a further round of negotiations increases the probability of panic. This feature affects the bargaining power of the regulators, as the likelihood that after the initial offer the bargainers can reconvene at the negotiation table becomes small. The third feature is related to the prevention of panic using a blanket guarantee. In many financial crises, regulators attempt to mitigate panic by extending deposit insurance coverage and declaring a blanket guarantee. Blanket guarantee is usually established when the first signs of distress emerge, but before the bank becomes legally insolvent. Again, the situation in the fall of 2008 provides an example: ‘The treasury was under pressure last night to guarantee the savings of all depositors in British banks after Germany announced it was following the lead of Ireland and Greece and offering a blanket guarantee on all savings.’ (Guardian, 6 October 2008) The main contributions of the paper illustrate that cooperation is welfare superior to unilaterally designed restructuring decisions regarding an MNB, but the cooperation outcomes allocate the welfare benefits unevenly among the countries. Firstly, we show that an optimal unilateral policy for the home country calls for liquidation, the bargaining equilibrium exhibits recapitalization, which maximizes the joint welfare of the countries. This result supports the argument that MNBs are more likely to become subjects of bailout policies when the regulators have the option to split the fiscal

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burden of costly recapitalization. Second, the cost allocation is sensitive to country-specific bargaining power, which is determined by the expected costs from recapitalization, bank liquidation and those emerging from bank panic. The home regulator benefits from the privilege that it is the only entity that can legally liquidate the MNB. But the position of the home country becomes weaker when the share of insured deposits is high, as the host country has limited incentives to share the regulatory cost burden of the home country. In equilibrium, one of the countries may recapitalize the MNB alone, or the countries may jointly recapitalize it. Sometimes the optimal solution is achieved when the countries decide to liquidate the MNB. Third, if uninsured deposits are subordinated to insured deposits, the liquidation decision becomes more likely. The subordination decision also boosts the bargaining power of the home country. The results regarding blanket guarantees show that a blanket guarantee is optimal under certain conditions and, in a similar manner as in the ex-post restructuring decisions, efficient implementation of the policy calls for cooperation between the countries. The conditions where a blanket guarantee is optimal are the following. When the regulators anticipate that MNB will be recapitalized should it become insolvent, it is optimal to declare a blanket guarantee. Otherwise, a blanket guarantee is declared if the risk of bank insolvency is small and the probability of a costly panic is high. Efficient design of a blanket guarantee calls for cooperation, because the cross-border externalities diminish the incentives of the home country regulator to minimize the expected joint costs of a failure. This indicates that the countries should renegotiate over the partition of the recapitalization costs concurrently with the declaration of the blanket guarantee, even though the MNB is still solvent and may yet avoid failure. The paper is related to two strands in the literature. One strand is Nash’s (1950) classic bargaining theory. On these issues Muthoo’s (2002) provides an extensive survey. The second strand of the literature consists of analysis on banking crises and bank restructuring: e.g. Merton (1977), Mailath and Mester (1994), Aghion et al. (1999), Mitchell (2001), Repullo (2001, 2004, 2005), Hothausen and Ronde (2002), Holthausen and Ronde (2005), Acharya (2009), Niinimäki (2009, forthcoming), Dewatripont and Rochet (2009) and Borio et al. (2009). Repullo (2001), Calzolari and Loranth (2005) and Holthausen and Ronde (2005) present models on multinational banks.2 The paper extends the existing literature on the regulation of multinational banks in the following directions. Holthausen and Ronde (2005) examine closure regulation, when it is possible to close a bank or leave it open. Regulators in both countries have access to private information that is relevant to the closure decision. Our approach differs from that in Holthausen and Ronde (2005) in several aspects. In their analysis, regulators are asymmetrically informed and exchange information, whereas in our model regulators have perfect information about the financial status of the MNB, which is in line with the consolidated supervision principle within the EU. Asymmetric information in our model is between the regulators and the market and revealed to the market through exogenous technology. This emphasizes the feature that a rapid decision is required in efforts to solve banking crises, because market reactions exacerbate the problem. With respect to the equilibrium closure policies of a cheaptalk game between the regulators, Holthausen and Ronde find

2 Although theoretical and empirical research is scarce, the regulation of multinational banks has created active debate: e.g. Mayes and Vesala (1998), Calzolari and Loranth (2001), Eisenbeis and Kaufman (2008), Goodhart (2008) and Krimminger (2008).

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that the better aligned the regulators’ incentives, greater the efficiency. The bargaining results of this paper contradict this finding. We show that the outcome is a joint maximizing policy, regardless of the distribution of the externalities. Finally, Holthausen and Ronde focus on the problem of asymmetric information between the regulators. We believe that in the case of multinational banking crises, where the regulators must reach agreement rapidly, the results of the negotiations will be mainly driven by the risk of bank panic, deposit insurance and blanket guarantee. Repullo (2001) investigates the determinants of the takeover of a foreign bank by a domestic bank. The takeover is more likely to be realized if the foreign bank is relatively small, if it is relatively risky and if the deposit insurance premium is lower in the domestic bank’s home country. Since Repullo concentrates on the determinants of international takeovers based on the risk diversification motive, his study differs from our paper. Calzolari and Loranth (2005) compare regulators’ incentives to take disciplining regulatory actions with respect to two types of multinational bank: branches and subsidiaries. We explore only branch structure in a very different model setting. The present paper is organized as follows. Section 2 describes the economy and the policies of bank restructuring. Section 3 examines the Nash bargaining process in period 1. Section 4 gives a numeric example, whereas a blanket guarantee is analyzed in Section 5. Section 6 examines the robustness of the results and Section 7 concludes.

2. The model Consider two countries, A and B. The banking sectors of the countries involve national banks and a multinational bank (MNB). The operations of the national banks are limited to the country in question. The MNB has a branch structure. It has headquarters in country A and a branch in country B. The MNB is therefore treated as a single legal entity that has received its operating licence from the regulators of country A. In line with current EU legislation (see Eisenbeis and Kaufman, 2008), the regulator of country A supervises the MNB and insures its deposits. He can also declare a blanket guarantee on deposits. The regulators share information regarding the MNB, but the regulator of country B cannot liquidate it. Liquidation is possible only by the regulator of country A (regulator A). Both regulators can, however, inject more equity capital into the MNB and in this way recapitalize it. The timing of the events is the following. At period 0 the first signs of financial downturn emerge in both countries. The MNB is still solvent, but there is a risk that it fails in the following period. Negative news generates concerns about the financial condition of the MNB, which generates a risk of a panic. At this point the regulators have two options. They can wait and engage in a gamble that involves three outcomes: panic, insolvency and solvency. An alternative is to implement a blanket guarantee that insulates the bank against a run and may reduce the cost of restructuring in the case of insolvency. At the second period, if the MNB is insolvent, the regulators design a restructuring policy that maximizes domestic welfare. The policies involve liquidation or recapitalization. The restructuring decision is modelled as a bargaining game that determines whether the countries engage in restructuring the MNB unilaterally or in cooperating so that where the countries also share the costs. We solve the model using backward induction. We focus first on period 1 and derive the equilibrium restructuring policies (Sections 2–4). Thereafter, we turn to period 0 and investigate negotiations regarding the blanket guarantee (Section 5).

The other assumptions regarding the economies are the following. The MNB has no equity capital and uses deposits to fund its operations. The deposit insurance scheme covers a share ˛ of deposits. The bank must therefore pay positive interest rud only on uninsured deposits.3 The initial bank size is Dini = D(˛ + (1 − ˛)/(1 + rud )) at the start of each period as long as the bank is successful. At the end of a period, the volume of deposits, principal and interest, amounts to D = DA + DB where subscript A (B) is used to denote deposits collected from country A (B). If bank lending is successful, the value of bank assets is Dini + Rsuc > D at the end of a period, where Rsuc denotes the liquid loan income that is spent to pay interest on uninsured deposits and dividends. In the case of bank failure, the value of bank assets is R < D. Liquidation of bank assets entails costs and the liquidation value of the assets satisfies L < R. To simplify analysis, we assume that the ratios of uninsured deposits and bank assets in countries A and B are equal to the ratio of bank deposits, DA /DB . The net value of an insolvent MNB at the start of period 1 is V = R − D < 0. The regulators choose a cost-minimizing restructuring policy,  p . Subscript p denotes the restructuring policies available to regulators: recapitalization ( r ) and liquidation ( l ). The regulators may also be unable to reach an agreement ( 0 ). The costs and benefits from each restructuring policy are next analyzed. The aim of the regulators is to minimize the regulatory costs they incur. They do not care about the losses of the uninsured depositors. The assumption is arguably restrictive. If the regulators were to maximize social welfare, they would pay attention to the losses of the uninsured depositors. Yet, if the regulators fully internalize the losses of the uninsured depositors in our model, it is obvious that recapitalizing a bank is more profitable than liquidating it. Then, division of the recapitalization costs is the only focus of the bargaining process, not the decision whether to recapitalize/liquidate. Obviously, this type of model would be relatively simple. The subject is further discussed in Section 6.2. The outcome of the bargaining game is dictated by policy options available for the regulators and how the costs of their implementation are allocated between the countries. These policies also constitute the outside options in the bargaining game when a country decides to implement a policy on unilateral basis. The following subsections describe the policies and the implications of a panic. 2.1. Liquidation If regulator A chooses liquidation,  l , it closes the MNB. The combined payoffs the countries incur for the liquidation policy are given by ˘(l ) = A (l ) + B (l ),

(2.1)

where i ( l ) < 0 is the payoff for regulator i. The payoff consists of the following factors

 i (l ) =

¯ A ) − C e (DA ) ˛(L − D) − CAn (ˇ A ¯ B ) − C e (DB ) −CBn (ˇ B

for i = A . for i = B

(2.2)

3 We do not model how the deposit interest rate of uninsured deposits is calculated, because the exact level of the interest rate is irrelevant for our analysis. We simply assume that the deposit interest rate is endogenous and the uninsured deposits are priced correctly. If the MNB is rescued in all circumstances – for example, it is too big to fail – the interest rate of uninsured deposits is zero. If the MNB is rescued under certain circumstances, the deposit interest rate of uninsured deposits is positive. Hence, it is rational that the deposit interest rate of a rescued bank is positive (includes a risk premium).

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¯ i ) and C e (Di ) denote the costs the regulaThe functions Cin (ˇ i tors bear for restructuring the other banks in country i. That is, the liquidation of the MNB implies cost to the regulator, due to the potential systemic importance of the MNB. Since the deposits of the MNB are insured by the home country, regulator A pays the difference, ˛(D − L) > 0. The rest of the liquidation proceeds, (1 − ˛)L, are channelled to uninsured depositors. The parameter ¯ i = (D − L)(1 − ˛)Di /D > 0 denotes the losses country i’s uninˇ sured depositors’ due to the liquidation of the MNB. Here, D − L is the volume of the lost deposits resulting from the liquidation of the MNB and (1 − ˛)Di /D is country i’s share of the uninsured deposits. ¯ i ), can The restructuring costs of the other domestic banks, Cin (ˇ be interpreted in the following manner. Since the proceeds from the MNB liquidation do not cover its total uninsured deposits, these depositors bear losses.4 In practice, interbank loans constitute a substantial share of the uninsured deposits. The MNB’s failure to repay other banks may have a contagious effect, due to the lost interbank deposits. Regulators must then extend the restructuring policies and the magnitude of the losses thus depends on the MNB’s position in the interbank market.5 To formalize this we assume that 0≤

¯ i) ∂Cin (ˇ ¯i ∂ˇ

< 1.

(2.3)

This expression implies that the restructuring costs related to other banks in the economy increase when the share of uninsured deposits increases in the MNB. However, this also implies that the total restructuring costs of domestic banks in country i, due to the failure of the MNB, are less than the amount of country i’s depos¯ i ) < (1 − ˛)Di for all itors’ uninsured deposits with the MNB, Cin (ˇ ¯ˇi .6 Intuitively, the MNB obviously has uninsured deposits from multiple investors and only a fraction of those are other domestic banks. Since the initial wealth of the banking sector in the country is positive, the restructuring costs the regulator incurs from the MNB’s failure to repay uninsured depositors should be lower than the value of uninsured deposits in the MNB. Other costs of the regulator resulting from the closure of the MNB, Cie (Di ), involve, for example, those costs related to disturbances to the payment system in country i. We assume that ∂Cie (Di ) ∂Di

> 0,

(2.4)

as it is plausible that the effect increases with the volume of the MNB’s operations in country i. 2.2. Recapitalization The second policy option for the regulator is recapitalization of the insolvent multinational bank, where regulators inject fresh

4 In the European Union, ‘. . . the system must provide deposit insurance coverage of 20 thousand euros, must exclude coverage of interbank deposits, . . .,’ Eisenbeis and Kaufman (2008, p. 177) 5 The insolvency of Continental Illinois in 1984 gives an interesting example. Davison (1998, p. 250) reports: ‘With regard to the Continental Illinois, the regulator’s greatest concern was systemic risk, and therefore handing Continental through a payoff and liquidation was simply not considered a viable option. Continental had an extensive network of correspondent banks, almost 2,300 of which had funds invested in Continental; more than 42 per cent of those had invested funds in excess of $100,000, with a total investment of almost $6 billion. The FDIC determined that 66 of these banks, with total assets of almost $5 billion, had more than 100 per cent of their equity capital invested in Continental and that an additional 113 banks with total assets of more than $12 billion had between 50 and 100 per cent of their equity capital invested.’ The liquidation of Continental Illinois would have triggered a surge of bank failures. 6 We do not study how the national banks are restructured. We simply assume that the restructuring process is optimal.

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equity capital into the MNB so as to boost its value from negative to zero. The MNB can then be resold to private investors. Essentially, recapitalization is a bail-out policy that insulates all depositors – whether or not their deposits are insured – from the losses they would incur if the regulators were to close the bank. The policy therefore eliminates cost terms Cin (ˇi ) and Cie (Di ). The financial costs of the recapitalization may, however, turn out to be high relative to liquidation. The total payoff of recapitalization is7 ˘(r ) = R − D < 0.

(2.5)

Obviously, the individual countries’ payoffs sum up to ˘( r ). The payoffs are determined by the Nash bargaining game in Section 3. 2.3. Disagreement (break down) Muthoo (2002, p. 152) determines the disagreement problem as follows: “..in the bargaining situation considered here there are three possible ways in which the players fail to reach agreement: through perpetual disagreement, when a player opts out and when the negotiations break down in a random manner. As such there are three possible payment pairs associated with a failure to reach agreement, namely the impasse point, the outside option point and the breakdown point. Corollary 6.3 states that the disagreement point in the Nash’s set up should be identified with the impasse point.” An impasse point is the payoff obtainable if each player always rejects any offer made to him. Yet, in our model the impasse point is equal to the breakdown point (Muthoo, 2002, p. 75). Hence, in our model there are only two possible alternatives associated with a failure to reach agreement: outside options and a breakdown point in which the negotiations break down in a random manner. Now the disagreement point in the Nash’s set up should be identified with the breakdown point. It is necessary to determine the breakdown point. In period 1 the MNB is insolvent and this fact becomes public rapidly. A panic occurs and the MNB fails, breaking up the negotiations (an information based panic). If the negotiations take time, a panic occurs with certainty. Thus, the payoff pair of a panic is the disagreement point in Nash bargaining. When a panic occurs, the MNB liquidates its assets to meet the demands of the depositors.8 The losses of uninsured deposits are D ˇi = (1 − ˛)Di − i L. D

(2.6)

The constraint (2.3) is also satisfied for ˇi .9 The losses of uninsured depositors are smaller under a panic than under liquidation: ¯ i . This follows from the fact that under liquidation the uninˇi < ˇ sured depositors’ share of the bank’s liquidation proceeds is 1 − ˛, whereas under a panic they have access to the full amount of these ¯ i implies C n (ˇ ) ≤ C n (ˇ ¯ i ). proceeds. Now ˇi < ˇ i -i i -

7 We focus on two policies, liquidation and recapitalization, since the costs from recapitalization are almost the same as those costs from other methods: nationalization, the purchase and assumption method and a merger with a solvent bank. In each case, uninsured depositors do not (usually) lose their deposits and the regulators use fresh funds so that the value of the insolvent bank’s assets equals the value of its deposits. 8 Two main views on bank panics exist. According to the first view, e.g. Diamond and Dybvig (1983) and Niinimäki (2003, 2010), panics are pure panics but the second view, e.g. Jacklin and Bhattacharya (1988) and Chen and Hasan (2008), rests on the idea of information based runs. Empiric research, e.g. Wicker (1996), supports both views. 9 Here ˇ > 0, because we implicitly assume that (1 − ˛)D > L : the volume of i

uninsured deposits exceeds liquidation value of the bank assets. We have also investigated the opposite case.

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The restructuring payoff of national banks due to the failure of the MNB is likely to be lower under a panic than under liquidation, because a panic implies a smaller volume of lost interbank deposits. The panic payoffs represent the disagreement point in Nash bargaining:



Ci (0 ) =

−˛D − CAn (ˇA ) − CAe (DA ) −CBn (ˇB ) − CBe (DB ) -

for i = A . for i = B

(2.7)

Lemma 1 compares the costs of a panic and liquidation. The proof is in Appendix A.10 Lemma 1. The cost of a bank panic is globally (and for country A) higher than the cost of liquidation. The cost of a panic is, however, lower than the cost of liquidation for country B.11 We have detailed the costs and benefits from three types of restructuration policies: liquidation, recapitalization and disagreement. Next we examine which policy will be chosen. 3. Nash bargaining in period 1 When bargaining about the allocation of costs that arise from restructuring of an insolvent MNB there can be three outcomes. In a burden sharing equilibrium the countries agree to recapitalize the MNB and simultaneously approve how the costs will be shared. The following subsections characterize the potential cost sharing equilibria. Two outside options exist: recapitalization by one’s self or liquidation. Since the liquidation option is available only to the home country, the outside options of the host country are limited to recapitalization. Here it is worth noting that if a country utilizes its outside option to recapitalize the MNB alone, the costs to other country are zero. If the home country unilaterally liquidates the bank, the foreign country incurs the costs related to uninsured deposits. 3.1. Equilibrium At the start of period 1, the MNB is insolvent and the regulators begin negotiations on a restructuring policy under a threat of a panic. Since the regulators’ incentives are not perfectly aligned, both countries have an incentive to negotiate. We begin with the following observation. Lemma 2. Recapitalization is a joint welfare-maximizing policy, ˘( r ) > A ( l ) + B ( l ), when the value of bank assets is high, the liquidation value of the assets is low and the share of insured deposits is high. If the deposit insurance coverage is 100%, the MNB is recapitalized.

Proof.

The results just derived indicate that a bargaining situation emerges only when recapitalization is a joint welfare-dominating policy. We model the policy negotiations as Nash bargaining. The assumption is plausible, because the bargaining outcome is identical to that of Rubinstein’s (1982) model, when the time period between the bargaining rounds approaches zero. This feature is quite realistic in the restructuring negotiations where the time the regulators use to decide on policies regarding the restructure of a large bank is counted in hours rather than in days. Furthermore, timing of the negotiations is usually allocated to weekends and holidays, when the financial markets and banks are closed. We solve the Nash equilibrium in two steps. First, we consider the problem without outside options. Thereafter, we examine a game in which the countries have outside options. The analysis of the game with outside options builds on the results derived in the first step. This is analytically plausible, because outside options do not affect the disagreement point. Solving for the equilibrium in two steps adds little to the results of the analysis, because the true negation process has only one phase and the outside options are present from the very beginning. However, this methodological strategy simplifies the exposition and interpretation of the results. The bargaining equilibrium, x¯ A , x¯ B = ˘(r ) − x¯ A , is a solution to the problem max(xA − dA )(xB − dB ), xa ,xb

(3.1)

where dA = CA ( 0 ), dB = CB ( 0 ). Here xA and xB are the payoffs of regulator A and regulator B, whereas dA and dB denote the utilities from the disagreement point. The equilibrium satisfies ˘( r ) = xA + xB < 0 because the recapitalization payoffs of the regulators must add up to the costs of recapitalization. Proposition 1, below, illustrates the equilibrium of the bargaining process in two phases. First we illustrate the outcome under the assumption that the regulators do not have outside options. This is presented in (i) below. The second phase adds the outside options. First, in (ii), we have an equilibrium when the option to recapitalize the MNB alone (weakly) welfare-dominates the equilibrium / [˘(r ), 0]. without the outside options. This occurs when x¯ A , x¯ B ∈ Finally, in (iii) we add the county A’s option to liquidate the MNB. Proposition 1. (i) The equilibrium of the Nash bargaining process without outside options is x¯ A =

˘(r ) + CA (0 ) − CB (0 ) , 2

x¯ B =

10

Continental Illinois gives a good example regarding the speed and scale of a panic. Billions of dollars were withdrawn from the bank very quickly. The panic started on May 9, 1984, and by May 11 Continental had to borrow $3.6 billion at the Federal Reserve’s discount window to make up for its lost deposits. During the following weekend, Continental aimed to solve its problems by creating a $4.5 billion loan package provided by 16 banks, but this was insufficient to stop the panic. The volume of withdrawn deposits during the panic exceeded $10 billion (Davison, 1998). 11 The result: ‘The cost of a panic is. . .lower than the cost of liquidation for country B’ may be surprising. It is based on the uninsured depositors’ ability to withdraw a lot of funds from the MNB during a panic. Thus, regulator B favours a panic to liquidation. This type of effect could be avoided if the liquidation value of assets was sufficiently lower under a panic than under standard liquidation. For simplification, we have not made this kind of assumption. We also simplify the study by assuming that the MNB’s assets are exhausted in a panic. In reality, regulator A might close the doors of the bank when the panic has continued for a while. The simplification does not affect the key ideas of this paper.

This is easy to see from ˘( r ) − A ( l ) − B ( l ). 

˘(r ) + CB (0 ) − CA (0 ) . 2

(ii) When the options to recapitalize the MNB alone are recognized, we have

 x¯ i∗

=

0 ˘(r ) xi

if x¯ i > 0 . if x¯ i < ˘(r ) if 0 ≤ x¯ i ≤ ˘(r )

(iii) Two cases appear, depending on whether regulator A’s option to liquidate the MNB is binding: ∗ ≥  ( ), then x∗ = x ∗ , x∗ = x ¯A ¯ B∗ . (a) When x¯ A A l B A ∗ <  ( ), then x∗ =  ( ) and x∗ = ˘( ) − (b) When x¯ A r A l A l B A A (l ).

V. Mälkönen, J.-P. Niinimäki / Journal of Financial Stability 8 (2012) 84–95 ∗ , x∗ denote the true partition of the recapitalization costs. Here xA B

In the equilibrium without outside options, in (a), a regulator may end up with a positive payoff, x¯ A or x¯ B > 0. That is, he earns a profit from the recapitalization. This is possible only if the payoff of the counterparty is smaller than the total payoff of the recapitalization, x¯ i < ˘(r ) < 0. The counterparty instead recapitalizes the MNB alone. This is detailed above in (ii). In (iii), regulator A’s outside option to liquidate the MNB is also recognized. He never uses the option, because the recapitalization of the MNB is now optimal. ∗ <  ( ), he can threaten to use Yet, when the option is binding, x¯ A A l it to boost his payoff. If the option is not binding, it has no effect. So far we have investigated a case in which recapitalization represents the optimal solution. Suppose now that liquidation is the optimal policy. This produces the following result. Lemma 3. If liquidation of the MNB is a joint welfare-maximizing policy, the MNB is liquidated at once. Proof. Liquidation is a joint cost-minimizing policy when ˘( r ) < A ( l ) + B ( l ). It is easy to observe that any partition of the recapitalization costs such that xA + xB = ˘( r ), when xA ≥ A ( l ), xB ≥ B ( l ) is impossible. The Nash bargaining solution cannot be achieved. Country A knows this, opts out and liquidates the MNB (recall A ( 0 ) < A ( l )).  Put differently, it is possible to interpret the negotiations using the Rubinstein’s model in which the time period between the bargaining rounds approaches zero. Regulator A makes the first offer knowing the bargaining model completely. First, he analyzes whether liquidation is a joint cost-minimizing policy. If it is, he knows that he cannot make such a recapitalization offer, which is acceptable to both regulators. He liquidates the MNB and the bargaining process is over. Otherwise, he moves to the following stage. Second, regulator A compares his payoff under three alternatives: (i.) negotiation payoff without the outside options, (ii.) recapitalize ∗ =  ( ) alone or (iii.) threaten to liquidate and promise to pay xA A l for the recapitalization. If (ii.) is the best alternative for regulator A, he recapitalizes the MNB alone and the bargaining process is over. Otherwise, he moves to the next stage. Third, regulator A compares his payoffs from (i.) and (iii.), chooses a better one and offers it to regulator B. Fourth, regulator B compares the offer to his outside option to recapitalize the MNB alone. If the latter is more profitable to regulator B, he rejects the offer and recapitalizes the MNB alone. Otherwise, he accepts the offer and the MNB is jointly recapitalized. If the accepted offer is (i.) regulator A pays x¯ A and regulator B pays the rest, x¯ B . Otherwise, the accepted offer is (iii.), regulator A pays ∗ =  ( ) and regulator B pays the rest. The solution is achieved xA A l at once and a costly panic is avoided. 3.2. Comparative statistics Next we explore how sensitive the results are to assumptions regarding the size of the MNB and the deposit insurance coverage. We focus on the burden-sharing equilibrium. Using the notation in Proposition 1, this means that 0 ≥ x¯ i ≥ ˘(r ). Focusing on interior solutions narrows the analysis to outcomes where changes in the parameters have an effect. The proofs are in Appendix B. Corollary 1. When the size of the multinational bank remains unchanged, but a relatively larger share of its operations takes place in country A (country B), its share of the recapitalization bill rises whether or not the liquidation option of country A is binding. Intuitively, the outcomes of burden-sharing negotiations depend on the relative size of the MNB, which is a determinant of its importance in the financial system of the country and the economic externalities of a bank failure. The larger the relative size

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of the MNB in a country, the more severe the negative effects from liquidation or a panic are. This makes the country disadvantaged in the negotiations, and it has to pay more. The implications of the deposit insurance scheme on the bargaining equilibrium are as follows. Corollary 2. Suppose that the deposit insurance coverage is extended. Whether or not the liquidation option is binding, country A’s share of the recapitalization bill increases. Suppose first that the regulator A’s liquidation option is binding. When deposit insurance coverage is extended, the reimbursements that country A must pay when it liquidates the MNB increase. Yet, higher coverage obviously alleviates the losses for uninsured depositors (national banks) in country A. Comparison of these effects shows that the first effect dominates: An extension of the coverage increases the costs of country A. When the option to liquidate is not binding, the outcomes are also affected by the implications of changes in country B. Higher coverage mitigates the losses of uninsured depositors in country B, which weakens country A’s position in the negotiations. 3.3. Policy negotiations under blanket guarantee or subordinated deposits The previous subsection illustrated that the deposit insurance scheme run by the home country determines – at least to some extent – how the countries share the fiscal burden when a systemically important MNB requires restructuring. There is plenty of anecdotal evidence on banking crises suggesting that the adjustments made by policy-makers when they observe the potential for a crisis to emerge are equally important. In practice, ex-ante agreements on deposit insurance coverage are usually revised ex-post to mitigate panic and sustain confidence. These adjustments usually involve a blanket guarantee that raises deposit insurance to 100%, thereby insulating the bank against runs. In the present model we allow the regulators to declare a blanket guarantee at the start of period 0. For simplification we assume that, if the regulators declare a blanket guarantee, the decision is definitive. A blanket guarantee or subordinated deposits cannot be removed at the start of period 1.12 The effect of a blanket guarantee on the outcomes in the ex-post negotiations are as follows. Proposition 2. If a blanket guarantee is declared at the start of period 0 and the bank later becomes insolvent, it will be recapitalized with certainty. If country A declares a blanket guarantee alone, it must always pay the entire recapitalization bill alone. Proof. Suppose a blanket guarantee is declared for the deposits of the MNB at the start of period 0 and the MNB later becomes insolvent. If the MNB is recapitalized at the start of period 1, it can keep on operating. The losses of interbank deposits in the national banking sector as well as other negative externalities are avoided. The costs of recapitalization amount to D − R. Suppose now that the MNB is liquidated. The payments to depositors entail costs D − L. Since D − L > D − R > 0, the costs are higher than under recapitalization with certainty. Thus, it is optimal to recapitalize the MNB if a blanket guarantee has been declared. Suppose that country A alone declares a blanket guarantee. When regulator A suggests in period 1 negotiations regarding

12 A solution in which the regulators remove the blanket guarantee at the start of the period 1 is a bit eccentric. At the start of the period the regulators learn if the MNB is insolvent. They could immediately first remove the blanket guarantee and then liquidate the bank. This type of solution might be illegal, as it would cause severe losses for uninsured depositors. Alternatively, uninsured depositors might panic at the end of period 0 just prior to the maturity of blanket guarantee.

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recapitalization, regulator B declines in the knowledge that regulator A will capitalize the MNB with certainty even without the participation of regulator B.13  4. Effect of deposit insurance coverage: a numeric example To show that the outcomes illustrated in the previous section are indeed feasible, we give a numeric example of how deposit insurance coverage and the distribution of the deposits between countries affect the partition of the recapitalization costs. We consider an economy with parameter values DA = 10, DB = 200, R = 200, L = 160, rud = 0.05. The relationship between bargaining outcomes and deposit insurance can then be illustrated in the following manner: The horizontal axis portrays deposit insurance coverage, ˛. The vertical axis shows restructuring costs. They consist of the recapitalization costs and are equal to 10. The figure illustrates how the recapitalization costs are shared between the countries with each level of deposit insurance. Cost sharing is feasible at deposit insurance levels between 2.81% and 17.21%. The figure can be interpreted using four relevant deposit insurance ranges. First, when the insurance coverage is below 2.81%, the outside option of country B is binding: it recapitalizes the MNB on its own and incurs a cost equal to 10. Second, when the coverage exceeds 2.81%, bargaining outcomes dominate outside options because it allocates lower cost of recapitalization to country A than liquidation. Triangle D1 thus illustrates how much less country A ends up paying compared to country B in outcomes described in Proposition 1 (ii). Third once the deposit insurance exceeds 6.98%, where country A is indifferent between liquidation or acceptance of the bargaining outcome, the outside option involving liquidation becomes binding. Proposition 1 (iii) is an analytical illustration of this case. In Fig. 1, region D2 illustrates how much more country A pays in relation to country B’s share of the cost. Finally, country A recapitalizes the MNB alone, if the coverage is higher than 17.21%. In this case, country B rejects any costs related to the restructuring of the bank, and the cost of liquidation is higher than the cost of recapitalization. 5. Blanket guarantee or subordinated deposits in period 0 In this section we focus on the ex-ante policies that regulators can agree upon to mitigate panic or reduce the costs of restructuring. At the start of period 0 financial distress extends over countries A and B, but the MNB is legally solvent. This may make uninsured depositors nervous so that they panic and aim to withdraw their deposits from the MNB during period 0. Since the MNB is solvent, a panic represents a pure panic. Given the illiquidity of bank assets, the panic drives even the solvent MNB to bankruptcy by exhausting its assets to zero. When the regulators at the start of period 0 become aware of the threat of insolvency and panic they have two options.14 They

13 Alternatively, the regulators can inject subordinated deposits (capital) into the MNB at the beginning of period 0. When the amount of subordinated deposits is D − L, uninsured depositors cannot lose anything in a bank run, because the liquidation value of bank assets, L, is equal to the value of their deposits. Consequently, the depositors know that their deposits are perfectly safe and have no reason to panic. A bank run is therefore avoided. The result is similar to Proposition 2. Thus, the effects of a blanket guarantee and subordinated deposits are identical. Importantly, the first method is achievable only to regulator A whereas the latter method is achievable to both regulators. 14 Regulators must have precise hard evidence on insolvency before than they can begin the liquidation process. Closing a solvent bank destroys the value of bank assets due to the costs of liquidation. Additionally, and more importantly, regulators

can extend the deposit insurance coverage by declaring a blanket guarantee so that the deposits of the MNB are protected, which prevents panic. Alternatively, one of the countries (or both) can inject subordinated deposits into the MNB so that panic is avoided. We have noticed that a blanket guarantee and injection of subordinated deposits generate the very same costs and benefits. First, panic is avoided. Second, if the MNB proves to be insolvent it is recapitalized. Third, if the MNB proves to be solvent, neither the blanket guarantee nor the subordinated debt entails costs. Regulators are indifferent between these methods. For simplification, only a blanket guarantee is explored below. Although only regulator A can declare a blanket guarantee, regulators optimally negotiate the solution together (this is shown below) and decide jointly on the share of costs, and regulator A finally declares a blanket guarantee. Next we examine the optimal choice at the start of period 0. Is it optimal to a declare blanket guarantee? First, let us suppose that it is. Since a blanket guarantee leads to the recapitalization of insolvent banks, regulators must concurrently negotiate about the division of the recapitalization payments even the MNB is still solvent. If country A declares a blanket guarantee alone, country B will not pay anything later (Proposition 2). Second, suppose that a blanket guarantee is not optimal. Then, it is not used and the negotiations are postponed to the start of period 1. If the MNB is then solvent, no negotiations are needed. If it is insolvent, regulators negotiate regarding the optimal restructuring policy. These negations are detailed above in Sections 2–4. In Section 5.1, we study whether or not it is optimal to declare a blanket guarantee. In Section 5.2 we show how this optimal solution is achieved in the Nash bargaining process. 5.1. Optimal blanket guarantee The probability that a panic occurs during period 0 is t. Furthermore, the probability that the MNB turns out to be solvent at the end of period 0 is s. It is insolvent with probability 1 − s.15 The expected payoff with a blanket guarantee is (1 − s)˘(r ).

(5.1)

When the bank is insolvent, it is recapitalized. It is optimal to declare a blanket guarantee if t[CA (0S ) + CB (0S )] + (1 − t)(1 − s)[A (∗) + B (∗)] ≤ (1 − s)˘(r ).

(5.2)

The left-hand side (LHS) reveals the expected payoff without a blanket guarantee. The second term represents a case in which the MNB avoids a panic during period 0 but becomes insolvent in period 1. Negotiations regarding the optimal restructuring policy then begin. The negotiations are illustrated in Sections 2–4. The results from the negotiations are denoted by A ( * ), B ( * ). If country A, for example, recapitalizes the MNB alone, then A ( *)= ˘( r ), but if country B alone pays the recapitalization bill, then A ( *)= 0. The first term on the LHS shows a new term, Ci ( 0S ), i ∈{A, B}, which

cannot use illegal methods. The following example is from Argentina (BIS, 1999. p. 62): ‘In Argentina, judges forced the central bank to compensate the shareholders on the grounds that a bank was solvent at the time of intervention, and that the insolvency actually resulted from mismanagement during the intervention.’ 15 It is possible to assume that the regulators receive at the start of period 0 a signal that MNB is insolvent. The signal is true and the bank is insolvent with probability 1 − s (here s is relatively small). The depositors learn about the signal with probability t and panic. The regulators cannot close the bank, because the bank is not insolvent with certainty. The closure decision needs to be based on hard, verifiable information.

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Fig. 1. The effect of deposit insurance on cost allocation.

denotes the costs when a solvent MNB fails due to a panic in period 0. It is equal to the costs when an insolvent bank fails due to a panic, Ci ( 0 ). Thus, we use symbol Ci ( 0 ) below. It is easy to observe from the LHS that the solution in which only one country alone takes the decision on a blanket guarantee (or subordinated debt) cannot be optimal because the said country pays attention only to its own costs and benefits. Thus, the countries need to take the decision together. If the optimal restructuring policy in (5.2) is recapitalization, we have A ( *)+ B ( *)= ˘( r ), but if it is liquidation, we have A ( *)= A ( l ) and B ( *)= B ( l ). When the optimal restructuring policy is recapitalization, the result is as follows. Proposition 3. When the MNB is in such a state that the optimal restructuring policy is to recapitalize it, it is optimal to declare a blanket guarantee once the financial distress is observed. Proof.

Inserting A ( *)+ B ( *)= ˘( r ) into (5.2) provides

t[CA (0 ) + CB (0 ) − (1 − s)˘(r )] ≤ 0.

(5.3)

The LHS is negative because CA ( 0 ) + CB ( 0 ) < A ( l ) + B ( l ) < ˘( r ).  Intuitively, if a panic is avoided and if the MNB proves to be insolvent, a blanket guarantee entails no extra costs, because the MNB will be recapitalized even without it. If the MNB proves to be solvent, the guarantee also entails no cost, because no recapitalization is needed. Yet, since a guarantee can eliminate the threat of a panic, it is optimal to declare a blanket guarantee. Suppose now that the optimal restructuring policy is liquidation. Restating (5.2), we observe that a blanket guarantee is optimal if t[CA (0 ) + CB (0 ) − (1 − s)A (l ) − (1 − s)B (l )] ≤ (1 − s)[˘(r ) − A (l ) − B (l )].

(5.4)

Both sides are negative. The inequality is satisfied if the risk of a panic is sufficiently high and the probability of insolvency, 1 − s, is sufficiently low. On the contrary, if 1 − s is large in comparison with t, the inequality is not satisfied and no blanket guarantee is declared. A conclusion follows. Proposition 4. Suppose that the optimal restructuring policy is liquidation. The parameter values will then determine whether it is optimal to declare a blanket guarantee. The probability that a blanket guarantee is declared increases with the panic risk and decreases with the risk of bank insolvency. If the probability of a panic is high and the probability of insolvency is sufficiently low, it is optimal to declare a blanket guarantee.

Now the risk that a panic will destroy a solvent MNB is severe. To prevent this, a blanket guarantee is needed. In addition, since the probability of bank insolvency is low, the probability that regulators will need to recapitalize an insolvent bank is also low. Hence, the expected recapitalization costs owing to a blanket guarantee are small. Suppose that a blanket guarantee is declared. If the MNB proves to be solvent at the start of period 1, it can keep on operating. If insolvent, it is recapitalized, because it is always optimal to recapitalize the MNB under a blanket guarantee (Proposition 2). Note that the blanket guarantee changes the restructuring policy. If the restructuring process began at the start of period 1, it would be optimal to liquidate the MNB. Yet, when the threat of a panic during period 0 is recognized, it is optimal to declare a blanket guarantee at the start of period 0 and in this way make recapitalization the optimal restructuring policy. When the risk of a panic is small and the probability of insolvency is high, it is not optimal to declare a blanket guarantee, as this would raise the costs of bank restructuring, because the recapitalization would then be applied to the insolvent MNB instead of the optimal liquidation. This ‘mistake’ is likely, because 1 − s is high. On the other hand, the risk that a panic will destroy a solvent MNB is small. Under the policy choice of no blanket guarantee, a panic may drive the MNB to failure. If a panic is avoided, the financial condition of the MNB becomes apparent at the start of period 1. If the MNB is solvent, it can keep on operating. If it proves to be insolvent, it is liquidated. Given Propositions 3 and 4, if the regulators do not declare a blanket guarantee, this signals that they will later liquidate the MNB if it proves to be insolvent. We have now solved the optimal policy. We will see that the Nash bargaining process generates this optimal solution. 5.2. Nash bargaining in period 0 At the start of period 0 regulators analyze whether it is optimal to declare a blanket guarantee.16 Since a blanket guarantee will make recapitalization the optimal policy at a later stage, the regulators need to bargain at the same time over the costs of recapitalization. As above, a disagreement point in Nash bargaining is the same as a breakdown point. If negotiations break down and the regulators

16 The fact that only country A can declare a blanket guarantee has no effect on the bargaining process, because the very same allocation can be achieved by employing subordinated debt and both regulators have the same opportunities to invest subordinated debt in the MNB.

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cannot reach an agreement, the bargaining process stops at the start of period 0. If the MNB later proves to be insolvent, a new bargaining process begins in period 1 (Sections 2–4). The disagreement point of country A is dˆ A = tCA (0 ) + (1 − t)(1 − s)A (∗).

(5.5)

The first term on the RHS expresses the expected costs from a panic during period 0. The risk of a panic is present because no blanket guarantee is declared. The second term reveals the expected costs to regulator A from the optimal restructuring policy in period 1. These costs are realized only if the bank is not liquidated in a panic during period 0 and if it proves to be insolvent in period 1. Note that (5.5) also represents the outside option to postpone the negotiations: regulator A can opt out from the negotiations in period 0, wait for a period and then restart the negotiations in period 1 if the MNB then proves to be insolvent. The disagreement point and outside option of country B is dˆ B = tCB (0 ) + (1 − t)(1 − s)B (∗).

(5.6)

The outside options thus appear in the disagreement point. In addition, both regulators have an outside option to commit to recapitalizing the MNB on their own if it proves to be insolvent in period 1. Besides, the recapitalization payoffs of countries A and B, XA , XB , must cover the total recapitalization payoff XA + XB = ˘(r ).

(5.7)

The bargaining problem maximizes max(XA − dˆ A )(XB − dˆ B ),

(5.8)

xa ,xb

when (5.5)–(5.7) are satisfied. In addition, the outside options to commit to the recapitalization of the MNB alone and the postponement of the negotiations for a period are present. Obviously, the Nash bargaining solution is feasible only if it is a optimal policy: dˆ A + dˆ B ≤ (1 − s)˘(r ).

(5.9)

The expected joint payoff in the breakeven point (the LHS) is smaller than the expected recapitalization costs. This is the same constraint as in (5.2). If (5.9) is not satisfied, the negotiations break down (one of the regulators chooses the outside option to postpone the negotiations), no blanket guarantee is declared and the restructuring decision is postponed to period 1. The MNB is liquidated in period 1 if it then proves to be insolvent. However, this is again optimal because (5.2) is not satisfied. Suppose that (5.9) is satisfied. It is again illuminating to express the negotiation results in two phases. First, we calculate the Nash bargaining solution without the outside options. Then, we add the outside option to recapitalize the MNB alone. Since the outside options to postpone the negotiations appear already in the breakdown point, these outside options are binding only if it is optimal to abandon a blanket guarantee. Proposition 5. tion X¯ A =

In period 0 the Nash bargaining process gives parti-

˘(r ) − dˆ B (0 ) + dˆ A (0 ) , 2

X¯ B =

˘(r ) − dˆ A (0 ) + dˆ B (0 ) . 2

When the outside options to recapitalize the MNB alone are recognized, we obtain, i = A, B



X¯ i∗ =

0 ˘(r ) Xi

if X¯ i ≥ 0 . if X¯ i < ˘(r ) if 0 ≥ X¯ i ≥ ˘(r )

The equilibrium can be described as follows. If a blanket guarantee is not optimal, then country A will not announce it and there will be

no cost sharing agreement in period 0. The bank will be liquidated in period 1 if it becomes insolvent. If a blanket guarantee is optimal, then the countries will negotiate on how to share the costs of the guarantee. Country A will announce a blanket guarantee in period 0. In this case, the countries’ equilibrium payoffs are specified above, X¯ A∗ , X¯ B∗ . Again, the regulator’s outside option to recapitalize the MNB on his own ensures that a regulator’s payoff cannot be lower than the total payoff of the recapitalization, X¯ i < ˘(r ). If his bargaining power is weak so that the negotiation process provides him a payoff which is smaller than the total payoff of the recapitalization, X¯ i < ˘(r ), he opts out and commits to recapitalize the MNB alone. The MNB may be such that the regulators declare a blanket guarantee with certainty. This generates the idea that the deposit insurance coverage could as well be 100 percent initially. Yet, the difference is important. If the deposit insurance coverage is initially 100%, regulator A must always recapitalize the MNB alone because L − D < R − D. If regulator A suggests any negotiations to regulator B, he optimally rejects the offer. He knows that regulator A will recapitalizes the MNB alone. When the deposit insurance coverage is sufficiently low, regulator A has more bargaining power. If he operates alone, he does not declare a blanket guarantee and recapitalize the MNB. This compels regulator B to negotiate. The regulators decide to declare a blanket guarantee with certainty and share the costs of recapitalization. We have assumed that a decision on a blanket guarantee is made at the start of period 0 before the regulators know whether or not a panic will occur. Alternatively, it may be possible that the regulators declare a blanket guarantee only when they observe that a panic is about to begin. To investigate this, we reconstruct the model as follows. The financial distress extends over countries A and B at the start of period 0. A panic occurs at once or is totally avoided in period 0. This is learnt immediately by the regulators. If a panic is avoided, a blanket guarantee is unnecessary. If a panic occurs, the regulators must immediately decide whether or not to declare a blanket guarantee. The reconstructed optimal decision rule (5.2) shows that a blanket guarantee is optimal if CA (0 ) + CB (0 ) ≤ (1 − s)˘(r ).

(5.10)

The following result can be achieved. Proposition 6. Suppose that regulators can delay a blanket guarantee decision until a panic actually occurs. If the amount of uninsured deposits does not exceed the value of the insolvent bank’s assets, (1 − ˛)D ≤ R, the regulators declare a blanket guarantee. Proof. The LHS of (5.10) is at most −˛D (the payments on insured deposits) and the RHS is larger than R − D. Hence, (5.10) is satisfied at least when −˛D ≤ R − D. This implies that if (1 − ˛)D ≤ R, it is always optimal to declare a blanket guarantee.  Recall that the regulators cannot liquidate the MNB in period 0, because it is still (legally) solvent. The obvious consequence of this blanket guarantee rule is simple: rational depositors know that all deposits will be insured when a financial crisis becomes actual. Consequently, the uninsured deposits are implicitly insulated against the default of the MNB implying that it can attract uninsured deposits without a risk premium. The liquidity of uninsured deposits is optimal to the MNB. By issuing liquid uninsured deposits it ensures that regulators will declare a blanket guarantee during an economic distress. That is, by issuing liquid uninsured deposits the MNB de facto enforces the regulators to extend the coverage of deposit insurance. This guarantees that the regulators will recapitalize the bank if it later becomes insolvent.

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6. Robustness In this section we investigate how small changes in the model setting affect the findings. 6.1. Subordination Suppose that uninsured deposits are subordinated to insured deposits. This has no effect on the costs of recapitalization or the costs of disagreement. Yet, the costs of liquidation change: Lemma 4. When uninsured deposits are subordinated to insured deposits, the total costs of liquidation are lower to regulators than without subordination. The costs from liquidation to country A (country B) are smaller (larger) with subordination. Proof. Two cases appear depending on the volume of insured deposits. If Min(˛D, L) = L, liquidation proceeds are allocated to insured depositors and uninsured depositors obtain no proceeds. In comparison to the case without subordination, (1 − ˛)L is transferred to the deposit insurance scheme by uninsured depositors. Obviously, regulator A’s costs from deposit insurance decrease by (1 − ˛)L and the losses of uninsured depositors increase by (1 − ˛)LDi /D in country i. Given (2.3), the regulators’ total costs decline. If Min(˛D, L) = ˛D, the liquidation value of the MNB’s assets covers the payments on insured deposits and the deposit insurance scheme bears no costs. In comparison to the case without the subordination, the costs of the deposit insurance scheme decline by ˛(D − L) but the losses of uninsured depositors increase by ˛(D − L)Di /D in country i. Given (2.3), the regulators’ total costs decline. The subordination rule unambiguously reduces the total costs from liquidation. We have seen above that subordination increases the total losses of uninsured depositors in country B, and thus the negative externalities in the national banking sector also increase. Insured depositors are unaffected by subordination. Neither does subordination change the magnitude of CBe . In all, subordination makes liquidation more expensive to regulator B. Since subordination reduces the total costs from liquidation, and increases the costs from liquidation to regulator B, it must diminish the costs from liquidation to regulator A.  Intuitively, subordination does not change the volume of liquidation proceeds, but transfers them from uninsured depositors to the deposit insurance scheme. In country B, the transfer reduces the income of uninsured depositors and has no other effects. The total effect in country B is thus negative. In country A, the uninsured depositors’ wealth decreases, but there is a positive welfare effect as the costs of deposit insurance decline. Here, the second effect dominates and subordination makes liquidation more profitable for country A. Lemma 4 leads to the following result: Proposition 7. Subordination of uninsured deposits to insured deposits boosts the profitability of liquidation as an optimal restructuring policy in comparison to recapitalization. It also raises the value of the country A’s liquidation option. If the liquidation option is binding in the policy bargaining, subordination thus reduces the recapitalization payment of country A. 6.2. Different objective functions Until now regulators have been cost minimizing. They focus on the costs of deposit insurance as well as the costs of bank recapitalization. In practice, regulators may have different charters. In

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the United Kingdom, for example, the charter of the Financial Services Authority (FSA) emphasizes the protection of depositors. In Germany, the regulator is also obligated to be concerned with the return of the bank investment; implying that regulators also pay attention to the shareholders’ welfare. The differences in charters pose the question of whether the model can be used to explore the alternative charters. ¯ i ) denotes the costs the regulator i bears for In the model, Cin (ˇ restructuring the national banks in country i due to the liquidation of the MNB. This implies that the regulator is concerned about the losses of uninsured depositors only if the losses drive other banks to bankruptcy. To take into account the possibility that the regulator puts a positive weight on the welfare of the uninsured depositors, it is easy to construct alternative cost terms. If the regulator, for example, stresses the losses of each uninsured depositor identically in the liquidation process, the new cost term is ¯ i, CiD = i × ˇ

(6.1)

where ␪i is the weight of uninsured depositors’ losses in the regulators’ preferences in country i. In a panic the cost term is CiD = i × ˇi .

As for the bargaining process, we simply replace Cin with CiD in the liquidation costs and in the costs of a disagreement. Thereafter the bargaining game goes on as above and the results would reflect the new cost parameters. We have investigated an alternative bargaining game in which regulators fully internalize not only the regulatory costs but also the losses of uninsured depositors so that ␪A = ␪B = 1.17 For brevity, we summarize the main results. It is always optimal to recapitalize the MNB and declare a blanket guarantee. In addition, it is optimal to negotiate. If country A alone makes the decisions, it is possible that it will not recapitalize the MNB nor declare a blanket guarantee. Again, the countries split the costs of recapitalization. It is impossible to say whether country A (or country B) pays more or less than in the model above (in which the regulators are cost minimizing). Alternatively, the regulators may have divergent preferences. Regulator A may weigh depositors’ losses using CAD , whereas the ¯ i ). When the diverregulator B minimizes the costs of his own, C n (ˇ B

gence in the preferences has been recognized, it is possible to rewrite the terms of liquidation costs and the costs of disagreement. Thereafter, the final part of the bargaining process is the same as above. Finally, suppose that both regulators are initially cost minimizing, CAn , CBn . Then, the government of country B changes the charter of regulator B. He must now weigh the losses of each depositor in the same way. This means that CBn is replaced with CBD where ␪B = 1. Obviously, we have CBD > CBn . The change generates more bargaining power for regulator A. 7. Conclusions This paper studies the restructuring policies of multinational banks and how countries affected by a crisis share the financial burden. To this end, we develop a bargaining model that includes the key elements of policy negotiations likely to emerge and crossborder externalities that shape the regulators’ decision whether to liquidate or recapitalize the MNB. The model illustrates that ex-post burden-sharing, which is an outcome of policy bargaining after the MNB is found to be insolvent (weakly) welfare-dominates unilaterally designed restructuring policies.

17

We thank the anonymous referee for this suggestion.

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The outside options available for the regulators have an influence on the burden-sharing outcomes. Since the home-country regulator has the legal right to liquidate and close the MNB, it has a stronger bargaining power when the cost of the option to liquidate is low relative to the cost the country incurs when it recapitalizes the MNB jointly with the foreign regulator. However, the fact line with the current European legislation, that the home country runs the deposit insurance scheme for the MNB increases its share of the costs. The risk of a panic and the resulting breakdown of negotiations affect both countries, and therefore, the country with a high expected cost of a panic is more likely to end up with a higher share of the total costs. In the model a panic induces negative externalities for those banks that have plenty of deposits in the MNB. The panic has also other negative externalities, e.g. to the payment system. Thus, the expected costs from a breakdown point are high in a country where a relatively large proportion of the MNB’s operations take place. The costs resulting from a panic are, however, relatively higher for the home country, because a panic among uninsured depositors destroys the value of the MNB the regulator can channel for insured depositors. To prevent a panic, regulators often declare a blanket guarantee on the deposits of the MNB or inject subordinated deposits into it. We illustrate that a blanket guarantee, which is declared before the regulators are aware of the financial status of the MNB, always induces recapitalization should the MNB become insolvent. The decision of a blanket guarantee can be made by the home country and the decision affects the ex-post policy bargaining. Countries may therefore have an incentive to cooperate on the decision regarding the blanket guarantee and the partition of the expected recapitalization costs ex-ante. In equilibrium, regulators always declare a blanket guarantee when they anticipate that the ex-post bargaining decision entails full recapitalization, because a blanket guarantee insulates the MNB against panic. The MNB fails to receive protection from a blanket guarantee when the optimal ex-post policy equilibrium involves liquidation, the risk of a panic is sufficiently low and the risk of insolvency is sufficiently high. The results of the paper help to understand how cross-border externalities and the risk of panic may affect the policies aimed at solving financial problems of large, complex and international financial institutes. The model is obviously a simplification of a complex system of country- and business-level relationships. For instance, we do not consider financial contagion of panic or the moral hazard effects related to blanket guarantees.18 Moreover, we exclude political factors from the analysis. In practice, it might be optimistic to presume that in the event of collapse of a large MNB, the home country spends domestic taxpayers’ money to repay to the foreign depositors. In addition, the relative size (political power) of the countries may influence their bargaining power.

Appendix A. The proof of Lemma 1 The total costs of liquidation in both countries is lower than the cost of a panic if ¯ A ) − C n (ˇ ¯ B ) + C n (ˇ ) ˘(l ) − CA (0 ) − CB (0 ) = ˛L − CAn (ˇ B A -A + CBn (ˇB ) > 0. -

(A.1)

¯A +ˇ ¯ B − ˛L the LHS denotes the losses of uninIn ˇA + ˇB = ˇ sured depositors under a panic, whereas the RHS indicates their losses under liquidation. Given this and (2.3), (A.1) is positive. In country B the cost of a liquidation is larger than the cost of a ¯ B ) − C n (ˇ ) < 0. Since the panic, because CB (l ) − CB (0 ) = −CBn (ˇ B -B total cost of a panic is larger than the cost of liquidation, but the opposite is true in country B, the cost of a panic in country A must exceed the cost of liquidation.  Appendix B. The proofs of Corollaries 1 and 2 The proof of Corollary 1: Since the size of the MNB does not change, we have dDA = − dDB ; if the size of the MNB grows in country A, its size must fall in country B and vice versa. This implies ∂D/∂DA = ∂D/∂DB = 0. From the liquidation constraint of country A, we obtain: ¯A ∂C n ∂CAe ∂A ∂ˇ =− A × − < 0, ¯ ∂DA ∂DA ∂DA ∂ˇA

(B.1)

¯ A /dDA > 0. When ¯ i = (D − LR)(1 − ˛)Di /D follows dˇ because from ˇ the liquidation constraint is not binding, we obtain ∂ˇ ∂X¯ A 1 ∂CA 1 ∂CB ∂DB 1 ∂CAn = − × =− × -A 2 ∂DA 2 ∂DB 2 ∂ˇA ∂DA ∂DA ∂DA e n e ∂ˇ 1 ∂CA 1 ∂CB 1 ∂CB − − × -B − < 0, (B.2) 2 ∂DA 2 ∂ˇB 2 ∂DB ∂DB because dˇA /dDA > 0, dˇB /dDB > 0.  The proof of Corollary 2: The liquidation constraint gives ¯A ∂CAn ∂A ∂ˇ = (L − D) − = −(D − R) × ¯A ∂˛ ∂˛ ∂ˇ



D ∂CAn 1− i ¯A D ∂ˇ



< 0. (B.3)

If the liquidation constraint is not binding, we have ∂X¯ A (∂CA (0 )/∂˛) − (∂CB (0 )/∂˛) = 2 ∂˛ =

−D + (∂CAn (ˇA )/∂ˇA )DA − (∂CBn (ˇB )/∂ˇB )DB . 2

(B.4)

In the dominator the sum of the first two terms is negative and the third term is negative. The effect is negative.  References

Acknowledgements We thank the seminar participants at Bank of Finland, Esa Jokivuolle, Klaus Kultti, Tuomas Takalo, Jouko Vilmunen, Matti Viren, Christoph Melchior, Editor Iftekhar Hasan and anonymous referees for useful comments and suggestions. Financial support from the Yrjö Jahnsson Foundation is gratefully acknowledged.

18 We investigated the moral hazard consequences of blanket guarantee but the investigation provided standard results (e.g. Merton, 1977). Therefore, we excluded the investigation from the manuscript.

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