Modeling Guarantees, Over-Indebtedness and Financial Crises in an Open Economy

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  • ABSTRACT

    This work develops a simple framework to analyse how financial intermediaries’ balance sheet problems combined with financial guarantees make an economy more vulnerable to financial crises. A ‘double default’ problem – that is, the default of financial intermediaries on their debt repayments and of the government on its guarantees to bailout intermediaries’ losses – is modelled in this study.The possibility ofmultiple equilibria, including a crisis equilibrium where the government is not able or willing to honor its guarantees towards the domestic financial sector, arises from the interplay of all the above elements: financial intermediaries’ level of indebtedness, government implicit guarantees and high-risk creditors’ lending. This work also produces predictions concerning the vulnerability to a financial crisis: multiple equilibria are possible only in certain ranges of the fundamentals.


  • KEYWORD

    Financial guarantees , risk premium , multiple equilibria

  • 1. Introduction

    Third-generation models have been introduced to detect the origins of the financial crises that spread throughout emerging economies over the last decade. As it is well-known the canonical first-generation models, exemplified by Krugman (1979) and by Flood and Garber (1984), explain the crises as the product of budget deficits. Flood and Garber (1984) show that the abandonment of a currency peg will be typically enforced by a speculative attack of rationally acting market participants who try to sell the currency to avoid losses. The second-generation models, exemplified by Obstfeld (1994), explain the crises as the result of a conflict between a fixed exchange rate commitment and the desire to pursue a more expansionary monetary policy. A government decides whether it can defend a pegged exchange rate according to a trade-off between short-run macroeconomic flexibility and long-term credibility. However, the 1990s Asian meltdown suggested that the crisis might be not a problem of unsustainable budget deficits policies carried out by local governments, as in the first-generation models, nor is it a problem arising from ‘macroeconomic temptation’ as in second-generation models, but it is a problem of financial excess and then financial collapse (see Krugman, 1998, 1999; Salvatore, 1999).

    Third-generation type models of financial crisis have focused on problems of panic and collapse, resulting from a shift from a good equilibrium to a bad one (Morris & Shin, 1998). As Irwin and Vines (1999, 2003) suggest this collapse is underpinned by what in the financial system made a bad equilibrium possible. In a third-generation model the source of the crisis should lie primarily in the interaction between financial intermediaries’ overborrowing and financial system fragility. For example, Krugman (1998) suggests that what went wrong in the Asian financial system contained an important element of moral hazard; he points out that the presence of guarantees provided by the government to a bank-based financial system was responsible for what has been defined Asian ‘crony capitalism’. This strand of literature argues that moral-hazard-driven lending might provide a hidden subsidy to investment, which collapses when governments are not able (or not willing) to honour the guarantees (see McKinnon & Pill, 1996; Dooley, 2000)

    Irwin and Vines’ (2003) work presents a story of financial collapse by putting together Krugman’s idea of government financial guarantees with Dooley’s (2000) idea of a government-limited ability to bail out the domestic financial institutions whose liabilities were covered by such guarantees (either implicit or explicit). Aghion et al. (2000, 2001) analyse a similar story in a dynamic setting, although they focus on the changing value of firm collateral.

    The financial sector has played a central role in explaining the last decade’s crises as well as the current global crisis. The first 21st-century world-scale financial crisis has been caused by a poorly supervised bank-based financial system where the moral hazard behavior of the main market players (i.e. financial intermediaries, investment banks and also insurance companies) was in part caused by implicit financial guarantees. The global crisis had its origins in an asset-price bubble, which burst in the summer of 2007, in the US residential mortgage market where a large number of government interventions and distortions have been responsible for moral hazard behavior and excessive risk-taking by agents. In fact, many banking and financial intermediaries did not keep the mortgages on their  books and repackaged them into asset-backed securities. Domestic and foreign investors considered these securities not risky because the underlying mortgagebased products benefited from either explicit or implicit guarantees from the government (Freixas & Parigi, 2010; Freixas et al., 2004).

    The paper attempts to evaluate how the evolution of the solvency of bankbased financial systems to which the government provides guarantees might explain the origin of recent financial crises. Starting from Irwin and Vines’ (2003) model, we have developed a simple framework to study how financial intermediaries’ balance sheet problems combined with bailout policies make an economy more vulnerable to financial crises. The possibility of multiple equilibria, including a ‘bad’ equilibrium where the government is not able to honour its  guarantees, arises fromthe interplay of all the above elements: financial intermediaries’ balance-sheet currency mismatches, government guarantees and high-risk creditors’ lending. Our study, along the lines of the multiple equilibria models (Morris & Shin, 1998; Sachs et al., 1996; Jeanne, 1997; Jeanne & Masson, 2000) produces predictions concerning the vulnerability to crisis: multiple equilibria are possible only in certain ranges of the fundamentals and for certain parameter values.

    The building blocks of our model are the following: (i) due to the presence of government guarantees, financial intermediaries willingly expose themselves to exchange rate risk by borrowing both in domestic and foreign currency and lending in domestic currency without hedging the resulting risk; (ii) because of the currency mismatch in their balance sheets, financial intermediaries might find it optimal to renege on their debt and declare bankruptcywhen a devaluation occurs; and (iii) the government might be either unable or unwilling to fully afford the costs associated with financial guarantees and bank rescues.

    The paper is organised as follows. Section 2 presents the basic model. Section 3 examines the effects that follow the introduction of government guarantees on financial intermediaries’ debt. Section 4 analyses both the short-run and longrun equilibrium solutions of the model. Section 5 presents a numerical exercise. Section 6 comments on the results and highlights the policy implications of the model. Section 7 concludes.

    2. The Baseline Model

    There is an infinite-horizon, small open-economywhere many Financial Intermediaries (FIs) operate; they own all the productive capital stock,which they borrow from domestic and foreign lenders and invest in the production of a single output sold in the domestic competitive market. Output price is determined at the beginning of each period t and it remains fixed for the entire period. Therefore, due to nominal price stickiness, the Purchasing Power Parity (PPP) holds only in expectations:

    image

    where Pt denotes the domestic price level,

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    is the expected nominal exchange rate at time , which we define as the price of one unit of foreign currency in terms of domestic currency, and the foreign price level is assumed to be constant and equal to one. We assume that during periods 1 and 2 there might be an ex-post deviation from the PPP, implying P11S1 and P2S2 due to an unexpected real shock (i.e. a fall in FIs’ productivity) that occurs after prices have been set;1 while after period 3 there are no shocks. In sum, as a result of a real shock not being accommodated by domestic price-setting, the only ex-post deviations2 from the PPP occur in periods 1 and 2.

    Arbitrage by investors between domestic and foreign assets in a world with full capital mobility is captured by the Uncovered Interest Parity (UIP) condition:3

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    where it is the domestic nominal short-terminterest rate at time t, i is the foreign interest ratewhich is assumed to be constant over time, St is the nominal exchange rate at time t and

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    is the expected exchange rate in the next period, t + 1, conditional on the information available in period t. A floating exchange rate regime has been adopted and this implies that the central bank determines the level of domestic prices.We also assume that a credible inflation target is in place:

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    where

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    is the (gross) domestic inflation rate, and the parameter z denotes the constant rate of growth of money supply. Equation (3) holds for all periods without shocks, that is from period 3 onwards. In periods 1 and 2 the nominal interest rate aswell as the exchange rate,which is assumed to be perfectly flexible, adjust in response to a real shock to clear the money market while prices remain fixed until the end of the period, when they adjust.

    With no shocks, the inflation rate targeting rule, equation (3), and the PPP, equation (1), imply that the nominal exchange rate evolves as follows:

    image

    Relationship (4) holds from period 3 onwards, and it follows from the assumption of absence of real shocks after period 2.

       2.1 Bank Indebtedness and Capital Investments

    FIs’ capital investment in each period t is financed by issuing a fraction, λ, of debt in domestic currency,

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    which pays a nominal interest rate, i, and a fraction (1 − λ) of debt in foreign currency,

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    which is risk-free and pays a world interest rate i. The composition of the FI’s debt and thus the share of domestic over foreign currency borrowing is assumed to be exogenous. The total amount of debt in real terms, dt, issued by each financial intermediary is:

    image

    where

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    is the real amount of debt in domestic currency and

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    is the real amount of debt denominated in foreign currency, with 0 ≤ λ ≤ 1.

    Following Irwin and Vines (2003), we assume that FIs produce according to a Cobb-Douglas production function:

    image

    where u is the productivity parameter, with uU[0, 1], k and n denote respectively capital and labor inputs, and α is the relative share of capital in the total product, with 0 < α < 1.

    For the sake of simplicity we assume that labor is supplied inelastically at the real wage ω; with a labor supply, n, normalized to 1, the production function (6) can be rewritten as follows:

    image

    If capital fully depreciates within one period and it is entirely financed by borrowing from domestic and foreign creditors, then FI’s capital stock at the beginning of each period is equal to:

    image

    Under equation (8), output becomes a function of the FI’s external borrowing capacity (leverage) as well as of the currency composition of its own debt:

    image

    Since we allow FI’s productivity, u, to vary in periods 1 and 2, while no further unexpected shocks occur after period 2, then productivity is constant for all t ≥ 3, that is utu. In each period after the output has been realised, FIs pay a share (1 − α) of wages4 to individuals, they service the outstanding debt and the resulting profits are distributed to FIs’ owners.

       2.2 The Sequence of Events

    As shownin Figure 1, at the beginning of period 1 FIs invest all the capital they own in the production of a single good whose price has been preset at the beginning of the period. During periods 1 and 2 an unexpected productivity shock occurs. This causes a change in the nominal exchange rate – which is assumed to be floating – and an adjustment of the domestic interest rate. Prices are fixed and they cannot change during periods 1 and 2. At the end of each period the output is realised, FIs’ earnings are determined and debt is repaid.We allow for a negative productivity shock (i.e. a fall in the productivity) to occur only in periods 1 and 2, while in all the subsequent periods no further shocks occur and FIs’ productivity is constant and sufficiently high to allow the economy to converge to its steady state.

    The FI’s end-of-period nominal net profits are equal to the difference between net output sales5 and debt repayments of principal plus interest to creditors:

    image

    where the term αy denotes FI’s net output sales. The domestic nominal interest rate, i, to be paid on the debt at the end of each period t is set one period ahead. Since we have assumed that a fraction (1 − λ) of the FI’s overall real debt, dt, is denominated in foreign currency this makes the FI’s balance sheet vulnerable to external shocks; that is, to unexpected exchange rate movements,

    image

    as clearly shownin equation (10).The above relationship also shows that if there is a positive productivity shock, that is if ut is sufficiently high, then each FI can afford to repay in full its debt, while, if a bad productivity shock occurs, FI may be not able to repay in full the debt.

    By using the relationship (10), net profits at the end of periods 1 and 2 expressed in real terms read as:6

    image

    where the real net profits,

    image

    at time t are equal to the difference between the net real output and the overall amount of real debt both domestic and foreign currency denominated to be repaid to creditors. Note that in equation (11) StPt due to the (unanticipated) productivity shocks that occur in periods 1 and 2 and which cause a deviation from the PPP, equation (1). The ex-post deviations from the PPP have a crucial role in this analysis as we show below.

    In all periods after period 2, the following equality holds:

    image

    Given equation (12) and using the UIP, equation (2), and the inflation targeting rule, equation (3), real net profits from period 3 onwards read as:

    image

    where

    image

    In equation (14), (1 + rt−1) denotes the (gross) real interest rate, which is equal to

    image

    Expression (13) shows that starting from time t = 3 the domestic and foreign currency denominated debt become fully equivalent; so profits do not depend on the nominal exchange rate as there is no deviation from the PPP throughout these periods. Therefore, for all periods t ≥ 3 net real profits are simply defined by equation (13).

    Relationships (1) and (4) also imply that, in the absence of shocks, the domestic and foreign real interest rates will be equal:

    image

    The above relationship follows from the UIP and the PPP conditions, since, in the absence of shocks the following relationships hold:

    image

    and St = Pt for t ≥ 3.

       2.3 The Optimal Level of Debt

    We have assumed that the economy converges to its long-run equilibrium after period 3; hence, we define the long-run as any period t ≥ 3, and the short-run as periods 1 and 2. From equations (7)–(9) the short-run and long-run real profits are respectively:

    image
    image

    where superscripts s and l denote respectively the short-term (i.e. periods 1 and 2), and the long-term(i.e. from period 3 onwards). Equation (17) follows from the UIP condition (2) under the assumption that spot and expected nominal exchange rates coincide after period 2; that is,

    image

    for t ≥ 3.

    This model also assumes that FIs have limited liability7 and no capital requirements, which implies that FIs can default without costs.Therefore, FIs can exploit all the sources of potential profit, even if the expected profits are negative. In economic models we normally think of investors as responding to expected values of the relevant variables. But if the owners of FIs do not need to put up any capital, and can simply walk away if their institutions fail, they will instead focus on the values that variables would take if it turns out that we live in what is the best of all possible worlds. This will generate a problem of overinvestment that lowers expectedwelfare, because the increased return in the favorable state will not offset the increased losses in the unfavorable state (Krugman, 1998).

    By using equation (16) under the condition of zero net profits and the assumption that there is a large number of FIs that act competitively in the domestic financial market, the FI’s short-run level of indebtedness is equal to:

    image

    where ds is the short-run level of debt and the term M denotes repayment (principal plus interest) in nominal terms on each unit debt issued by the FI, which reads as follows:

    image

    Relationship (18) highlights two important issues: (i) higher productivity, u, leads to higher indebtedness and, given the assumption on capital depreciation, to higher investments and this might resemble the so-called ‘Pangloss effect’ stylized by Krugman (1999); and (ii) a larger depreciation of the current exchange rate, by increasing the cost of foreign denominated debt, should lead FIs to reduce the total borrowing in the following periods.

    From equation (17), under the zero net profit condition and the assumption made over the distribution of the productivity parameter, u, we derive the FI’s long-run debt:

    image

    where dl denotes the long-run level of debt,8 with μtμ ≡ 1.

    In the following section,we will analyse the role played by (implicit) government guarantees on FIs’ debt; such guarantees pose a serious problem of moral hazard since they affect the interest rate at which lenders are willing to lend and this, in turn, indirectly influences the FIs’ investment decisions. This story resembles the proposition that over-guaranteed and poorly regulated intermediaries can lead to excessive investment by the economy as a whole (on this point see McKinnon & Pill, 1996).

    Therefore, in the following sections we will define both the long-run and the short-run equilibrium level of the nominal interest rate inclusive of the implicit government guarantees on the FIs’ debt. The government guarantees the loans (principal and interest) made to the domestic FIs and it commits itself to raise sufficient funds to repay the debt. Lenders formulate some conjecture on the possibility that the guarantee will be fulfilled by the government in the case of FIs’ insolvency, and this will affect the interest rate at which they are willing to lend. In fact, such guarantees, by artificially lowering the credit risk, influence the level of the lending rates atwhich FIs can borrowfunds. If interest rates are pushed down, a moral-hazard-driven overlending may be generated and the demand for credit goes beyond the level that is economically efficient. This will be further analysed in the following sections.

    1As is commonly assumed by the existing models of open monetary macroeconomics (Obstfeld & Rogoff, 1996), the shock that occurs in periods 1 and 2 is wholly unanticipated and thus it is not taken into account by the domestic market when setting prices.   2The shock causes a deviation from the PPP in periods 1 and 2 since prices are set at the beginning of each period and remain fixed; while nominal exchange rate and domestic interest rates have to adjust to absorb the shock.   3The UIP applies with risk neutrality as it is the outcome of arbitrage fromfully diversified investors.   4This share of wages is directly determined from the Cobb-Douglas production function: yt =   5Since FIs’ produce y and pay a share of wage equal to (1 − α)y, which is determined from the assumed Cobb-Douglas production function, the resulting sales net of wage payments will be equal to αy.   6Both prices and exchange rate at time 0 have been normalized to 1.   7The assumption of FIs’ limited liability, implies that if FIs’ owners have insufficient funds to make debt repayments, they can default losing their equity investment without additional costs.   8By using equation (15), relationship (20) can be also written as a function of the exogenous and constant world interest rate:

    3. Introducing Government Guarantees: Bank Over-indebtedness and the Bailout Cost

    Let us introduce a financial implicit guarantee on FIs’ debt by assuming that the government may intervene to repay lenders when FIs have not enough funds to honour their debt.9 In each period the bailing out cost, Cb,t, is given by the aggregate level of funds the governmentmust raise by taxation,10 which is equal to the difference between the value of FIs’ debt and as share ζ of the output realised at the end of each period:

    image

    whereCb,t can be thought of as the cost that the government faces in each period to raise funds through taxation in order to fulfil the guarantee. Since the government is not able to recover in full the insolvent FIs’ revenues, only a fraction ζ of the net output can be used by the government to repay creditors, with 0 < ζ < 1. As we note from equation (21) the cost of the financial guarantee offered by the government increases with the level of the nominal interest rate on borrowing, since a higher interest rate makes the debt service more costly; the cost of fulfilling the financial guarantee also increases with a negative productivity shock (i.e. ut goes down) and additionally when the exchange rate depreciates, other things being equal. Actually, if the government intervenes in the current period, then (21) should include the present discounted value of the expected future cost of bailing out in the next periods, δEtCb,t+1; in this case the total cost faced by the government should be equal to Cb,t + δEtCb,t+1. We simplify the analysis by assuming the discount factor is equal to zero, δ = 0, which means that the government does not care about the future, and so in each period we simply have to compare current bailout cost, Cb, with the no-bailout cost, Cnb.

    Using equation (21) and the PPP and UIP conditions, the long-run cost of bailout reads as:

    image

    where the term

    image

    is the long-run cost of bailout faced by the government with subscript b denoting bailout and the superscript l the long-run. Relationship (22) holds in absence of shocks, that is from period 3 onwards in our model.

    Similarly we can use equation (21) to define the short-run cost of bailout faced by the government:

    image

    where the term

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    is the short-run cost of bailout faced by the government with subscript b denoting bailout and superscript s the short-run; the term M, which denotes debt repayment has been defined in (19).

    In each period, the government can choose not to bail out insolvent FIs when the cost of debt service, Cb, is sufficiently high and the commitment to bailout the insolvent FI might turn out to be very costly. In the event the government reneges on the guarantee, it will have to pay a cost:

    image

    where the overall cost of reneging on the guarantee, Cnb, is related to the level of FIs’ borrowing, d, according to a simple quadratic function with coefficients φ,β > 0. According to equation (24), the cost of reneging is positively related to the amount of FIs’ borrowing and such cost raises at a decreasing rate with respect to the outstanding FI’s debt. In fact, the underlying assumption is that for very high levels of debt it might turn out to be less costly for the government to renege on its guarantees and leave the FI to default.

    The no-bailout cost might be thought of as the cost of losing credibility faced by the government when it fails to fulfil the guarantee. In fact, once the government reneges on the guarantee it is not able to credibly offer this guarantee in subsequent periods. However, as pointed above, we assume that the government is myopic and it does not care about the future so that the no-bailout cost, Cnb, will not discount the future costs of reneging on the guarantee on FIs’ debt repayment.

    In absence of shocks, the PPP and the UIP conditions allow us to rewrite equation (24) as:

    image

    where

    image

    denotes the long-run cost of reneging on the guarantee, with the subscript nb denoting no-bailout and the superscript l the long-run; and φ´, β´> 0.

    The short-run cost of reneging on the guarantee is simply given by relationship (24) which holds in periods 1 and 2, that is:

    image

    where the term

    image

    is the short-run cost of reneging on the guarantee with the subscript nb denoting no-bailout and the superscript s the short-run.

    When the FI is insolvent and defaults, the government will intervene to fulfil the guarantee and to repay the debt only if the following condition holds in each period t:

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    Therefore, given equations (21) and (27), we can compute the threshold level of the productivity shock above which the government will fulfil the guarantee and lenders will be repaid in full. In fact, the threshold level of the productivity shock can be computed by simply comparing the cost of bailing out Cb with the cost of reneging on the guarantee Cnb. So substituting Cnb into equations (27) and using (21), we get the trigger level of the productivity shock,

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    above which the government will fulfil the guarantee:

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    where terms Cb(0) and Cb(1) denote respectively the cost of bailout faced by the government when the productivity shock is respectively low and equal to 0 and high and equal to 1 and they represent the interval for the one-off cost of nobailout, that is the cost of reneging on its guarantees, Cnb. When the no-bailout cost is greater than Cb(0), then the guarantee will be honoured for sure. While when the cost of no-bailout is less than Cb(1), then the government will not intervene to rescue the FI. There is a range of intermediate values for Cnb where the authorities may or may not intervene. As shown in equation (28), the trigger level of the productivity shock for government intervention is positively correlated to the nominal interest rate and to the FI’s level of indebtedness. As the interest rate raises, the FI’s debt service repayment raises and the cost of honouring the guarantees increases, implying that the likelihood that the FI will be bailed out is decreasing because the government will intervene in a smaller proportion of cases.

    For sake of clarity, we will label relationship (28) as the Government Guarantee (GG) relationship, which describes how the trigger level of the productivity shock should vary in response to changes both in the nominal interest rate and in the FIs’ total level of debt.

       3.1 Risk Premium and Interest Rates

    We consider investors who have rational expectations and know that the government has a limited capacity or willingness to honour its guarantees on the FIs’ debt if things go wrong; therefore, they build up a premium into the interest rate they demand to lend to domestic FIs (Krugman, 1999; Dooley, 2000).

    If lenders are rational, risk neutral and act competitively, then the domestic nominal interest rate asked on FI’s borrowing simply equals the risk-free world interest rate augmented by a risk premium that is computed as a percentage of expected default of FIs on the debt service repayments. Thus, the (gross) nominal interest rate set by creditors is a mark-up over the risk-free foreign interest rate:

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    where τ is the expected percentage of default on loan repayment, and the term

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    is the risk premium asked by lenders on FIs’ debt issued in domestic currency. Relationship (29) can be interpreted as a modified interest parity condition augmented by a risk premium. The term τ is defined as follows:

    image

    where

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    is the creditors’ expected threshold level of the shock above which they believe that the government will intervene to bail out insolvent FIs. In equation (30) the rate of default, τ , depends both on the amount of FIs’ earnings, debt and on the probability that the government will intervene to bail out the distressed FIs. In fact, lenders knowthat the government might renege on its guaranteewhen the productivity shock is sufficiently adverse and the cost of the bail out is too high. But we assume that the government will always intervene to honour the guarantee when the productivity shock is above a trigger level

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    where the term

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    denotes some arbitrary conjecture within the range

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    Under the UIP condition and equation (19), equation (30) can be rewritten as follows:

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    According to equation (31), the risk premium depends on the productivity shock, the level of FIs’ debt and the interest rate set in the previous period. As the expected trigger level rises,

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    the interval

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    within which the government is supposed to honour its guarantees will shrink so the risk premium and the interest rate on FI’s borrowing will rise.

    By plugging equation (31) into equation (29) and solving for the domestic interest rate, we can rewrite the risk premium adjusted interest parity condition as follows:

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    Relationship (32) shows that the domestic nominal interest rate set by the creditors is a function of the threshold level of the productivity shock,

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    above which creditors expect that the government will intervene to bailout the FIs,while the trigger value,

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    defined in equation (28), is the actual productivity shock above which the government will honour the guarantee. In order to find a closed form solution to the model wemust solve the system formed by equations (28) and (32) by imposing the condition that in equilibrium

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    We denote the above relationship as the Modified Interest Parity (MIP) condition since it resembles the (actual) UIP augmented by a risk premium that accounts for the FIs’ default on debt repayments. The percentage of default depends both on the expected net revenues of the FIs and on the probability that the government will not renege on its guarantees. In fact, as shown in equation (32) the threshold level of the productivity shock,

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    above which creditors expect that the government will bailout the distressed FIs, influences the interest rate set by lenders on FIs’ borrowing. Note that as

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    rises, the range of the productivity parameter values where the promises of a bailout will be honoured shrinks, this is captured by the denominator of equation (32). This implies that the probability of FIs’ default increases and thus the nominal interest rate on lending will be  higher since the risk premium increases. But this effect is dampened because, as productivity raises, profits are positive and the expected percentage of FI’s default decreases as captured by the quadratic term in the numerator of equations (31) and (32).This ‘double default’ problem, that is the FI’s default on debt repayments and the possibility that government might renege on its guarantees of bailing out the distressed FI, is crucial in our analysis. In fact, rational investors do know government’s limited capacity or willingness to pay up on its guarantees in case of FI’s default and they build up a risk premium into the price at which they are willing to lend. This implies that lenders will set an interest rate over and above the world interest rate, thus reducing the long-run equilibrium level of FIs’ capital stock. The endogeneity of the risk premium poses, in our model, a multiple equilibrium problem, as shown in sections 4 and 5. In fact, the risk premium enters nonlinearly into the model, giving rise to multiple equilibria. A financial crisis might occur when a real shock shifts the economy to a bad (i.e. a ‘crisis’) equilibrium.

    The model is now fully laid out and we can determine the short-run and longrun equilibrium levels of the nominal interest rate and of the trigger value of the productivity shock for government intervention establishing whether and when multiple equilibria exist.

    99The assumption is that government guarantees cover both principal and interest repayments.   10This can be thought as one way of financing lending of last resort operations. There are several  ways of carrying out lending of last resort facilities and, for the purpose of the model, the easiest  alternative is a lump-sum tax, including the issue of new public debt to distribute this tax over a  longer period. The injection of domestic currency by the Central Bank is not considered in this  analysis since such an injection of liquidity by driving up prices might have feedback effects on the  exchange rate.

    4. Short-run and Long-run Equilibrium

       4.1 The Short-run

    In order to compute the short-run level of the (gross) nominal interest rate and the trigger value of the productivity shock for government intervention,we restate equations (28) and (32) using the relationship for the FIs’ level of debt as defined in equation (18).

    Substituting the short-run level of FI’s borrowing, equation (18), into equation (23) and using condition (27), the short-run trigger value of the productivity shock,

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    reads as:

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    where the superscript s indicates the short-term that refers to periods 1 and 2. Relationship (33) is defined as the short-termGovernment Guarantee curve,GGs.

    Substituting the short-run level of FI’s borrowing, equation (18), into the risk premium adjusted interest parity condition (32), we get the short-term (gross) domestic nominal interest rate:11

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    Relationship (34) is a continuous function in the domain

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    when λ ≠ 0, i.e. when a fraction of the FIs’ debt is denominated in domestic currency. The equation (34) is denoted as the short-termmodified interest parity function, MIPs.

    The first and second derivatives of theGGs function, with respect to the nominal gross interest rate, are respectively positive and negative. Thus, the GGs curve is positively sloped and concave. Note that the GGs curve includes two upward segments: one on the vertical axis at

    image

    and another at

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    The fact that in the short-run the trigger level of the productivity is not decreasing with respect to the domestic nominal interest rate, can be explained by the existence of arbitrage opportunities for the FIs when they issue both domestic and foreign currency denominated debt. In fact, as the domestic interest rates rise, the FIs can issue higher levels of (less costly) foreign currency denominated debt.While, the first and second derivatives of the MIPs function with respect to the productivity shock are both positive. The MIPs curve is then positively sloped and convex.

    In the following section we will plot both the GGs and the MIPs relationships in a

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    space. The first and second derivatives of the GGs with respect to the productivity shock are both positive (see Appendix A). Therefore, the GGs and the MIPs functions plotted in a

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    diagram are both positive sloping and convex curves (see Figures 24).

       4.2 The Long-run

    To compute the long-run values of the interest rate and of the trigger level of the productivity shock, we use equation (20) to substitute the long-run level of debt, dl, into equations (28) and (32). The long-term trigger value of the productivity shock,

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    reads as:

    image

    where the superscript l indicates the long-term, that is from period 3 onwards. Relationship (35) is defined as the long-run Government Guarantee curve, GGl.

    The relationship for the long-run gross nominal interest rate is:

    image

    In equations (35) and (36) the term

    image

    denotes the long-run level of the productivity shock

    image

    while the term il denotes the long-run level of the interest rate i. The function (36) is defined as the long-term MIP curve, MIPl.

    TheGGl curve is negatively sloped and convex (seeAppendix B). In the long-run the trigger level of the productivity shock is decreasing in the domestic interest rate since domestic and foreign currency denominated debts become fully equivalent. In fact, both the PPP and the UIP conditions hold in the long-run, implying that no arbitrage opportunities exist for the FIs, so it is not profitable to switch from domestic to foreign currency denominated debt. Therefore, an increase in the domestic interest rate induces the FIs to reduce their debt exposure, lowering the cost of the guarantee (i.e. the threshold level of the productivity shock for government intervention is reduced), thus making the fulfillment of the guarantee more likely. As we want to plot the GGl and MIPl curves in the same

    image

    diagram, we express the GGl function with respect to the (gross) nominal interest rate, whose first and second derivatives with respect to the productivity shock are respectively negative and positive. The first derivative of the MIPl function is always positive, while the sign of the second derivative depends on the value of

    image

    (seeAppendix B). As shownin the following section, a unique interior equilibrium exists; a condition for this to happen is that the MIPl curve intersects the (1 + i)- axis below the GGl curve (see Figure 5). This follows because the (gross) interest rate,

    image

    is increasing in the trigger level of the productivity shock for government intervention,

    image

    whilst

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    is decreasing in

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    This is sufficient to ensure a unique point of intersection.

    Proposition 1 A sufficient condition for a unique interior long-run equilibrium is that

    image

    11As recalled in the previous section both prices and the nominal exchange rate at time 0 have been set equal to 1.

    5. Plotting the ‘Government Guarantee’ and the ‘Modified Interest Parity’ Curves

    In this sectionwe provide additional insight into the analytical results by performing a numerical exercise of the basic model. Starting with the short-run period and setting the parameters with the values reported in Table 1, we graphically report both the MIPs and the GGs curves for the two following cases: (i) the more general case with FIs’ debt denominated both in foreign and domestic currency, and (ii) the special case with the FIs’ debt entirely denominated in foreign currency. The outcomes for each of the two cases are represented in Figures 2 and 3, and in Figure 4, respectively.

    The short-term equilibrium solutions for the interest rates and the trigger level of the productivity shock are simply determined by the intersection of the GGs and MIPs curves. Figure 2 depicts a case where short-run multiple equilibria may arise. As shown in case 1 with λ = 0.1 there may be up to three equilibria. There are two interior solutions at points E1 and E2, and a boundary solution at point E3 and we refer to the latter as the ‘crisis’ or ‘collapse’ equilibrium since at point E3 the interest rates are very high and the trigger level of the productivity shock for government intervention is equal to 1; that is, government guarantee is not credible. And the collapse equilibrium is self-fulfilling; in fact, if lenders expect that the government will renege on its guarantees12 they will ask a higher risk premium, this leads to a rise in the interest rates, and for sufficiently high levels of interest rates the government is likely to renege on its guarantees; that is,

    image

    tends to 1, thus confirming creditors’ expectations.Therefore, in the configuration with multiple equilibria the switch from the higher interest rate interior solution equilibrium at point E2, to the boundary solution, or ‘collapse’ equilibrium, at point E3 can be explained either (i) by the investors’ behaviour: if they perceive that the government guarantee is not fully credible they will demand higher interest rates thus forcing the government to renege on its guarantees, which in turn will tend to move the MIPs curve upwards, or (ii) by a bad shock to the fundamentals, which leads to a crisis. For example, in our analysis a negative productivity shock that occurs in periods 1 and 2, shifts both theGGs curve downwards and the MIPs upwards, switching the economy to the scenario depicted in the the collapse equilibrium, E3, where there is no possibility that the government can afford to honour its guarantees. The likelihood that the economy flips to the ‘crisis’ equilibrium increases in the presence of a risk premium-adjusted interest parity condition. In fact, an increase in the expected probability of FIs’ default does reflect into a higher risk premium which raises the lending interest rate, and this in turn reinforces the upwards shift of the MIPs curve.

    Figure 3 shows that with a cost of reneging on the guarantee, Cnb, sufficiently large and greater than zero, a unique interior equilibrium solution exists at point E1 with low nominal (gross) interest rates and a low value for the trigger level of the productivity shock, that is, the government guarantee is credible. Notice that for higher levels of the foreign debt, that is for λ = 0.5, with all other parameters being equal, we expect that the MIPs curve becomes steeper due to the fact that as the fraction of FIs’ debt issued in foreign currency rises, the risk premium asked by (foreign) investors increases and this in turn affects interest rates, which increase more proportionally as the share of FIs’ foreign debt increases. The MIPs curve is positive sloping and increasing with the trigger level of the productivity shock  for government intervention,

    image

    But as depicted in Figure 3, the MIPs curve is less steep than the GGs curve and this rules out multiple equilibria.

    Another case ofmultiple equilibria is depicted in Figure 4,where theGGs curve has been restated under the assumption that λ = 0, that is the entire FIs’ debt is denominated in foreign currency. Unlike the previous case, nowthe MIPs curve has a slope that sharply rises as

    image

    u increases, and tends to infinity as

    image

    approaches 1 (see Appendix C). Figure 4 shows thatmultiple equilibriamay exist, analogously to the graphical representation of Case 1 in Figure 2. As before, with a cost of reneging on the guarantee, Cnb, sufficiently large, a ‘good’ interior solution equilibrium will exist at a low interest rate. This solution ensures that the government is able to (credibly) offer the guarantee. But there is another interior solution, we refer to this interior solution as the unstable bad equilibrium with a higher interest rate and a higher value of the threshold level of the productivity shock for government intervention. Figure 4 shows that the slope of the interest rate curve sharply rises and tends to infinity as the trigger level of the productivity shock

    image

    approaches 1. If the economy flips away from point E3 there is no way the government can afford and fulfil the guarantee. In fact, beyond this equilibrium point the interest rate rises to infinity and the trigger value of the shock approaches 1, and the government’s financial guarantee is not credible at all; this case is referred to as the ‘collapse’ or ‘crisis’ equilibrium.

    Like in Morris and Shin’s (1998) analysis, there is some tripartite classification of the fundamentals that gives rise either to multiple equilibria or to a unique equilibrium scenario. In fact, by setting λ = 0.5 (or even higher), that is by reducing balance-sheet currency mismatch problems, we find that the outcome is a unique interior equilibrium without crisis (Case 1). But for lower values of the parameter λ, that is for λ close or equal to zero, multiple equilibria might arise (Case 2). We also observe that for intermediate values of the trigger value of the productivity shock and of the interest rate (i.e. the economy fundamentals), the cost of reneging the guarantee is large enough and there is an unstable equilibrium solution where a crisis might or might not happen, as depicted in point E2 of Figures 2 and 4. Therefore, when the fundamentals worsen and they are bad enough, then a collapse equilibrium is the outcome. Only with very good fundamentals is there a no-crisis equilibrium solution, as depicted in point E1 of Figures 2 and 4.

    Finally, the long-run GGl and MIPl functions are graphically depicted, setting the parameters according to the values reported in Table 2.

    Figure 5 shows that the function GGl is negatively sloped and convex, implying that the trigger level of the productivity shock for government intervention (i.e. in case of bailout) decreases as the interest rate increases, while the MIPl function is positively sloped and changes the concavity within the interval [0, 1]. With a positive and sufficiently high cost of reneging the bailout guarantee, Cnb, we find that an interior solution equilibrium exists at the point of intersection between the two curves. At this long-run equilibrium point the government may intervene to bail out the FIs since the cost of reneging the guarantee is sufficiently high. There is also a boundary solution at

    image

    where the interest rate is low13 and the financial guarantee is fully credible. Therefore, we conclude that in the longrun a unique equilibrium does exist and it can be either a boundary solution with a fully credible guarantee of bailout, or an interior solution with a partially credible guarantee of bailout. But as long as we assume that after period 2 no further productivity shock occurs, the long-run equilibrium will be a low-interest rate interior solution equilibrium with a trigger level of government intervention different from zero. In fact, after period 2, both the PPP and the UIP conditions hold, implying that no arbitrage opportunities exist for the FIs, so that they are completely indifferent to borrowing in foreign and/or in domestic currency and the parameter λ does not affect any more FIs’ investment decisions. All FIs’ debt is denominated in domestic currency since the FIs cannot exploit anymore the less costly borrowing in foreign currency. Therefore, when lending interest rates rise, the FIs will reduce their long-run level of debt.

    This lowers the cost of guarantees, so that a government can fulfil them in a larger proportion of circumstances and the ‘good’ equilibrium, with no collapse, will be the most likely outcome as illustrated in Figure 5.

    12As the threshold level of the productivity shock, above which creditors expect that the government will intervene to bailout the FIs, increases then the risk premium, τ , given by relationship (31) rises and the implied nominal interest rate on lending, equation (29), will be higher.   13At this long-run boundary solution equilibrium, the domestic interest rate is equal to (1 + i*)

    6. Model Results and Policy Implications

    In our analysis the mechanism that generates a financial crisis relies entirely upon the interplay of private sector behavior (both financial intermediaries and investors) and the public sector behavior (governments). Implicit government guarantees on FIs’ debt in the presence of an unregulated financial system in which financial intermediaries can default on loans at no cost might induce the FIs to increase their debt exposure, exploiting the low level of the interest rate. And investors are more willing to lend to the FIs since they know about the  existence of implicit government guarantees on FIs’ borrowing. The presence of guarantees means that as bank leverage and default risk increase, the true cost to the provider of the guarantee (here the government) rises, but the cost to the bank does not. Hence, banks have the option to increase leverage to very high levels without incurring higher costs of default.

    But agents know the limited capacity or willingness of the government to fulfil the guarantees and thus they lend to the FIs at a mark-up over the risk free foreign interest rate. This is captured by a risk premium adjusted interest parity condition introduced in the model. Therefore, if investors believe there is a range of productivity shocks that will force the government to renege they will ask for a higher risk premium, raising the interest rate on lending over and above the risk-free world interest rate. And if lenders raise the interest rate sufficiently it might be that the government has no choice but to renege, thus validating the (higher) risk premium so a crisis occurs. Similar to other studies that follow a multiple equilibria approach, in our model a self-fulfilling crisis might occur given the endogeneity of the risk premium on loans. But, with credible guarantees, interest rates are kept low and the government is more likely to afford and to pay up on its obligations in case of default. Like fundamentals-based models, our analysis also predicts that balance sheet currency mismatches of highly leveraged financial institutions are crucial in explaining the outbreak of a crisis. A large enough depreciation of the current exchange rate leads to an increase in the foreign currency debt repayment obligations, and consequently to a fall in profits  that might induce FIs to default when the share of the foreign over domestic debt is high enough. Therefore, either changes in expectations on future exchange rate or an unexpected real shock (a productivity shock in our model) that reduce FI’s networthmay result in less investment and less output in the next periods and this brings a domestic currency depreciation, further amplifying the real shock. This basic story is very similar to the credit-based models of currency and financial crisis (see Aghion et al., 2001, 2004).

    In addition, the public sector might exacerbate the problems of the private sector; in fact, the presence of implicit guarantees on FIs’ debt repayment and the possibility that a government might not fulfil these obligations leaving the FIs to default are crucial in moving the economy to a crisis equilibrium. The investors are aware that the government promises are only partially credible and this credibility relies heavily on their conjecture about the threshold level of the productivity shock, above which the government is supposed to intervene and  bail out the distressed FIs. Therefore, agents’ expectations might push up the risk premium and the interest rates if they believe that the likelihood that such (public) obligations will not be honoured is low. This lack of public sector credibility is another important feature of the model.

    Previous financial crises have seen the wide use of government blanket guarantees to the financial system. While the guarantees brought stability, they limited the subsequent options for dealing with financial distress. In fact, these guarantees create complacency, delay the restructuring, while increasing the (fiscal) costs (Bank for International Settlements, 2009). The lessons from the Asian crisis suggest that blanket guarantees may have adverse consequences for financial system stability. A reason for this is that government guarantees help to stabilise sizable systemic financial crises although they do not instill market discipline. In fact, governments cannot allow banks to fail for fear that the collapse of one will cause a systemic crisis. Our work highlights that regulators should remind themselves that guarantees are a double-edged sword. On one hand, they are necessary and helpful tools in the event of a systemic crisis both for political reasons and for efficiency considerations. On the other, they might impinge on the process of reforming the financial markets in order to prevent a recurrence of global financial crises. In fact, recent theoretical literature points out that governments limit their policy options by implementing blanket guarantees that extend forbearance and increase moral hazard – a greater willingness of creditors and debtors to take the risks of such crises (Irwin & Vines, 2003). Paradoxically, government guarantees make banks and the economy less stable, not more stable. This is consistent with some empirical evidence provided by Demirgüç-Kunt and Detragia (2002) who highlight that government guarantees are detrimental to bank stability.

    7. Conclusions

    The financial sector has a central role in explaining the more recent crises. The end-of-20th-century financial crises as well as the current global financial crisis have originated in poorly supervised bank-based financial systems, where the moral hazard behavior of the main market players (i.e. financial intermediaries, investment banks and also insurance companies) was in part fuelled by implicit financial guarantees.

    A ‘double default’ problem, that is the default of FIs on their debt repayments and of government on its guarantees to bailout FIs’ losses, is modelled in thiswork by analysing how it affects the interest rates set by investors. We show how (i) financial intermediaries’ level and composition of debt, (ii) guarantees from the public sector and (iii) moral-hazard-driven creditors’ lending could make an economy more vulnerable to financial crises. In fact, the presence of guarantees means that as banks’ leverage and default risk increase, the true cost to the provider of the guarantees (here the government) rises, but the cost to the intermediaries does not. Hence, banks have a free option to increase leverage to very high levels. In addition, this analysis takes into account the increasing cost of financial intermediaries’ debt repayment, when a currency depreciation occurs by modelling a balance sheet currency-mismatch problem. The presence of guarantees on FIs’ debt repayment and the possibility that a government might not be able or willing to fulfil these obligations, leaving the FIs to default, are then crucial in moving the economy to a ‘crisis’ equilibrium.

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  • [Figure 1.] The sequence of events.
    The sequence of events.
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  • [Figure 2.] Short-run ‘government guarantee’ and ‘modified interest parity’ curves: Case 1.
    Short-run ‘government guarantee’ and ‘modified interest parity’ curves: Case 1.
  • [Figure 3.] Short-run ‘government guarantee’ and ‘modified interest parity’ curves: Case 2.
    Short-run ‘government guarantee’ and ‘modified interest parity’ curves: Case 2.
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  • [Figure 4.] Short-run ‘government guarantee’ and ‘modified interest parity’ curves: Case 3.
    Short-run ‘government guarantee’ and ‘modified interest parity’ curves: Case 3.
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  • [Figure 5.] Long-run ‘government guarantee’ and ‘modified interest parity’ curves.
    Long-run ‘government guarantee’ and ‘modified interest parity’ curves.
  • [Table 1.] Parameter values for the short-run MIP and GG functions plotted in Figures 2?4
    Parameter values for the short-run MIP and GG functions plotted in Figures 2?4
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  • [Table 2.] Parameter values for the long-run MIP and GG functions plotted in Figure 5
    Parameter values for the long-run MIP and GG functions plotted in Figure 5