Sovereign debt and bank fragility in Spain : a calibrated DSGE model

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Sovereign Debt and Bank Fragility in Spain:

A Calibrated DSGE Model

Matthijs Knijnenburg, BA

∗

Supervisor:

Prof. dr. S.J.G. van Wijnbergen

†

August 22, 2014

Abstract

This paper studies the negative feedback loop between the financial sector and the sovereign, with a focus on the failed recapitalisation of the Spanish banks in 2012. A dynamic stochas-tic general equilibrium modelled with a leverage constrained financial sector is calibrated on the Spanish economy and utilised to simulate a financial crisis. The study finds that the calibrated macroeconomic model provides a satisfactory approximation to the develop-ments in Spain and sheds light on the mechanisms that cause a fall in asset prices after the announcement of a recapitalisation. The dynamics that are present in the model can be discovered in high frequency data of Spain. The results also show that a fiscal stimu-lus, even when completely reversed in subsequent years, does not add to economic recovery and can even prolong a recession. In contrast, a recapitalisation of the financial sector can have negative initial effects on the balance sheets of banks, but unambiguously improves the long-term macroeconomic situation. When a recapitalisation is performed directly by an external entity, the negative effect on credit risk and asset prices is mitigated, leaving more net worth intact for banks and providing more room on balance sheets for private credit. This accelerates economic recovery, providing quantitative support to the call for granting the European Stability Mechanism the power of performing direct recapitalisations of Eurozone banks.

∗_{student number: 10615938; matthijs.knijnenburg@student.uva.nl}

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1 Introduction

The occurrence of a negative feedback loop between sovereign debt and the health of the financial sector has been receiving a growing amount of attention in the literature over the previous years. The ways in which financial and debt crises can be mutually enforcing have been highlighted to great extent by the recent global financial crisis and sovereign debt crises in Europe. Since the onset of the financial crisis in 2008, European banks have suffered large losses on their assets after financial distress spilled over from the United States. Simultaneously, yields on the government bonds of European countries started to diverge, marking the end of the converging trend that was experienced in the years before. The result was a spread in bond yields in subsequent years that was unprecedented in the European Monetary Union: the yield on Greek 10-year bonds surpassed 36 per cent, while German bonds were pushed to a historic low as the result of a flight to safety by investors (Bloomberg).

Recent studies suggest that distress in financial markets can spillover to the sovereign debt market and vice versa (Laeven and Valencia, 2013; Haidar, 2012; De Bruyckere et al., 2013; Alter

and Sch¨uler, 2012). This transmission of stress on both sectors forms a negative feedback loop in

which downward pressures are reinforcing between banks and the sovereign. Three transmission channels have been identified that are at the basis of this feedback loop: the collateral, recapitali-sation and liquidity channels (Merler and Pisani-Ferry, 2012). The collateral channel refers to the effect of bank exposure to domestic sovereign debt. Increased risk of sovereign debt often leads to falling prices of government bonds. Since banks often hold a significant amount of domestic sovereign debt on their balance sheets, a fall in the price of bonds can have dramatic effects on bank capital. Conversely, a government can respond to banks’ financial distress, whether or not caused by a sovereign debt crisis, by directly transferring capital to banks in an attempt to restore their balance sheets. This is dubbed the recapitalisation channel. However, in order to perform the recapitalisation, the sovereign is forced to take on more debt and increase its credit risk. The resulting rise in the sovereign risk premium further erodes bank capital by discounting existing sovereign debt holdings. The two channels mentioned above close a loop that causes a downward spiral in the financial and sovereign sectors. A third, amplifying channel finds its origin in the fact that a shrinking balance sheet of the financial sector reduces the extension of credit to the private sector and therefore limits economic activity. Consequently, the tax base that can be used to service the increasing sovereign debt is diminished, creating a fall in liquidity. A lack of liquidity worsens the debt position of the sovereign and again pushes bond premiums up in face of a higher perceived credit risk. The subsequent losses on bank capital worsen the credit crunch as banks become more leverage constrained, further amplifying the feedback loop.

Empirical evidence for this feedback loop has been found across Europe by Alter and Sch¨uler

(2012) and the interdependence of banks and sovereigns has been shown to have grown over time (Alter and Beyer, 2012). However, even without a comprehensive statistical examination of data the workings of the negative feedback loop can become apparent. A striking example of how distress in the financial sector and sovereign credit risk are transmitted to one another and are

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reinforced is the failed attempt at an independent recapitalisation of its banks by the Spanish government at the beginning of this decade. In the wake of the burst of the housing bubble, Spanish banks experienced large losses and saw the lion’s share of their net worth disappear in a short period of time. The resulting contraction in the extension of credit to the private sector helped to aggravate the recession started by the financial crisis. The widespread recession also caused large government deficits, more than doubling Spanish sovereign debt to over 80 per cent of GDP (Eurostat).

As was expected through the collateral channel, research shows that the feedback loop is intensified when banks have a higher exposure to domestic sovereign debt (De Bruyckere et al., 2013). Spanish banks, like those in many of Europe’s periphery countries, were highly exposed to domestic sovereign debt (European Banking Authority, 2011). Indeed, pressures on the financial sector and government debt set off a mutually reinforcing cycle in Spain, rendering the Spanish government incapable of financing an independent recapitalisation by issuing debt and forcing Spain to apply for a bailout by the European Financial Stability Facility (EFSF).

This thesis aims to analyse the situation in Spain between 2010 and 2013, and the described phenomenon of mutually reinforcing market pressures more generally, by capturing the mechanics of the negative amplification cycle through the scope of a dynamic stochastic general equilibrium model based on the monetary model built by Van der Kwaak and Van Wijnbergen (2014). The model contains a financial sector that borrows to the private sector and the government. Financial intermediaries are balance sheet constrained in order to introduce financial frictions. Also, the model includes long-term government debt to realistically capture bond price effects. This model will be calibrated to Spain to realistically approximate the effects of the model dynamics on the Spanish economy. The calibrated model is then used to simulate the effects of a financial crisis, either with or without additional government policies. Policy experiments are carried out to assess the effectiveness of a delayed recapitalisation of the financial sector and a delayed fiscal stimulus. In addition to a pure fiscal stimulus, this study will also introduce a fiscal stimulus that is subsequently perfectly reversed and assess the macroeconomic effects of such a government policy.

In section 6, a shock will be introduced to the model calibrated on Spain that approximates the financial crisis in 2008 as closely as possible and a delayed recapitalisation will be employed that matches the bank rescue plan that was employed in 2012. This experiment will be used to make a comparison between the dynamics described by the model and the data around the Spanish recapitalisation. This will allow me to discover to what extent the negative feedback mechanism can explain the failure to recapitalise the Spanish banks. Finally, I will modify the model to allow for a direct recapitalisation by an external party, allowing for a capital injection that does not add to accumulating public debt. This experiment can deliver predictions of the effectiveness of a direct recapitalisation, for example by the European Stability Mechanism, vis a vis a debt financed recapitalisation.

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2 Review of Technical Literature

There exists a vast body of contemporary literature on quantitative monetary business cycle models, starting with Christiano et al. (2005) and Smets and Wouters (2007), among others. These models, however, lack the financial frictions that can explain stress in the financial mar-ket. These frictions were first captured by Bernanke et al. (1999), although this study was not placed in the context of a monetary model. The innovation in Gertler and Karadi (2011) was the introduction of financial frictions by including a balance sheet constraint for financial inter-mediaries. This constraint arises from an agency problem between bankers and deposit holders, becoming more binding when a bank’s net worth decreases. A drop in asset prices can there-fore force banks to cut bank on lending. Kirchner and Van Wijnbergen (2012) complement this mechanism with financial intermediaries that hold short term government bonds in addition to private sector loans.

The model utilised in this study is based on the model without government default risk by Van der Kwaak and Van Wijnbergen (2014), which again finds its roots in Gertler and Karadi (2011) and Kirchner and Van Wijnbergen (2012), who first included short-term government bonds to the assets held on the balance sheets of financial intermediaries. Van der Kwaak and Van Wijnbergen extend this model by introducing long-term government debt, using an approach first proposed by Woodford (2001). Woodford’s approach entails assuming that government bonds have infinite maturity, and deliver a stream of payments to the holder that decreases by a fixed factor each period. The bond therefore has an effective duration that depends on the fixed factor, resembling a bond that has a maturity that is finite.

An innovation in the present study is the introduction of a third asset type on the balance sheets financial intermediaries. This third, external, asset represents capital that is injected by an external party, such as the European Stability Mechanism. The inclusion of this asset allows for a capital injection that does not appear in the government budget constraint and therefore does not add to public debt.

The private sector is modelled using a typical profit-maximizing approach, encompassing mul-tiple levels of production and applying a mechanism for introducing price rigidities as described by Calvo (1983).

This study includes a policy experiment in which a fiscal stimulus is administered and subse-quently completely reversed. The modelling of this fiscal stimulus reversal is based on Corsetti et al. (2010) and added to the base model.

Although falling outside the scope of this study, this paper will also add a sovereign default

mechanism to the model, as derived by Van der Kwaak and Van Wijnbergen (2014). This

mechanism is based on the concept of a maximum level of taxation that can politically be attained. This maximum tax level results in a maximum level of public debt. When the level of government debt (assuming intertemporal solvency) exceeds the maximum level of debt, a partial default takes place and government debt is brought back to the maximum level. This will affect the price of bonds, causing market discounting of sovereign debt.

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3 Model Description

This section will describe the macroeconomic model that is used for this study. The monetary model is composed of a private and a public sector and includes financial intermediation, price rigidities, investment adjustment costs and long term government debt.

The private sector consists of households, and financial and non-financial firms that are owned by the households. The households are utility maximising entities that are bounded by a budget constraint. Their income consists of labour income, return on deposits and profits from both the financial and non-financial sectors. Part of the household members works as banker at a financial intermediary. Financial intermediaries hold deposits from households and use these to supply loans to the non-financial sector and buy government bonds. In their operations they are bounded by a leverage constraint that arises due to the fact that bankers can divert a fraction of their assets to their households. Banks are therefore constrained in the collection of funds from households. It is also possible for banks to hold assets from a third class: the external assets. Banks receive these assets once they receive capital injections from an external source.

The non-financial sector is concerned with the creation of capital and production of goods.

Capital producers buys leftover capital and final goods to create a new capital stock. The

capital producers face convex adjustment costs of their level of investment. The capital is sold to intermediary goods producers, which finance this purchase by taking loans at the financial intermediaries with a state-contingent return. The capital is used as input together with labour to produce intermediate goods. After production, intermediate goods producers sell the capital that is left after depreciation back to the capital producers and sell their products to retail firms. These retail firms repackage the differentiated intermediate goods before selling its products to final goods producers with a mark-up. Every period only a fraction of retail firms can adjust their price, creating price stickiness. Finally, the final goods producers combine retail products into final output that is sold to households for consumption, to the government for government purchases and to capital producers for investment.

The public sector consists of a government and a Central Bank. The government purchases final goods and can provide financial aid to financial intermediaries by means of a capital injec-tion. The government finances its expenditures by issuing long-term bonds and ultimately by levying lump-sum taxes to the households. The Central Bank is concerned with determining the nominal interest rate on deposits, taking into account deviations in inflation and fluctuations in output.

The model is a closed economy. This means that the financial sector only has domestic assets on its balance sheets. Although this is an abstraction from reality, it is a suitable approximation in the context of this study. Spanish banks have been shown to have an exceptionally high exposure to domestic sovereign debt, justifying this closed economy approach.

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3.1 Households

The household sector is modelled as a continuum of identical, infinitely lived entities. Households provide labour and engage in consumption and saving. Saving takes place by providing funds to financial intermediaries. Each household consists of both labour workers and bankers. From the household, a fraction 1 − f is labour worker and earns wages that are transferred to the household. A fraction f is banker, managing a financial intermediary from which the earnings are also transferred to the household. Each period a banker has a probability of θ to stay banker in the next period. In the case that the banker has to exit the financial sector (with probability 1 − θ), he will transfer the net worth of his financial intermediary to the household and become a labour worker. There is thus a portion of (1 − θ)f of the household members that switch from being banker to labour worker each period. Also, every period a similar number of labour workers become banker. Within the household all earnings are, together with profits from producing firms owned by the household, pooled. Consumption is equal between all members, guaranteeing a representative agent framework.

The households derive utility from consumption and disutility from providing labour. In ad-dition, to more realistically approximate consumption dynamics, habit formation in consumption is assumed. Therefore, household face the following maximisation problem:

max {ct+s,ht+s,dt+s}∞s=0 Et "∞ X s=0 βslog (ct+s− υct−1+s) − Ψ h1+ϕ_t+s 1 + ϕ # s.t. ct+ dt+ τt = wtht+ (1 + rdt)dt−1+ Πt,

where ct is household consumption, ht are hours of supplied labour, wt is the wage for labour,

d1−1 are household deposits from previous period over which interest rate rtd is received, τtis a

lump sum tax that is paid to the government and Πt are profits from goods producing firms.

The Lagrangian L = Et "∞ X s=0 βs ( log (ct+s− υct−1+s) − Ψh 1+ϕ t+s 1 + ϕ − λt ct+s+ dt+s+ τt+s− wt+sht+s− (1 + rt+sd )dt−1+s− Πt+s )# ,

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house-hold’s maximisation problem: ∂L ∂ct = 0 : λt= (ct− υct−1)−1− υβEt(ct+1− υct)−1 , ∂L ∂ht = 0 : Ψhϕt = λtwt, ∂L ∂dt = 0 : 1 = βEtΛt,t+1(1 + rdt+1) ,

with Λt,t+i as the stochastic discount factor λt+i/λtfor i ≥ 0.

3.2 Financial Intermediaries

Financial intermediaries lend funds obtained from households to intermediate goods producers

and the government. They hold assets in the form of claims issued by intermediate goods

producers, government bonds and external bonds. The balance sheet of the financial intermediary is given by

pj,t= nj,t+ dj,t,

where nj,t represents the intermediary’s net worth, dj,t funds deposited by households and pj,t

the assets held by the intermediary. The assets that are held are represented by

pj,t= qtks k j,t+ q b ts b j,t+ s e j,t, with qk

t and qtb for respectively the price of claims on intermediate goods producers and

gov-ernment bonds; and sk

j,t and sbj,t for respectively the amount of claims and bonds held. sej,t

represents both the value and the number of external assets held, as these assets are not traded in a secondary market and therefore are not priced.

At t+1, households obtain a non-contingent real return of rd

t+1from the financial intermediary

on funds deposited in period t. In turn, the intermediary receive a state-contingent net real return

of rk

t+1 on their loans to goods producers and rt+1b on government bonds and external assets.

Incentives for financial intermediaries to engage in banking follow from the possibility that rk

t+1

and rb

t+1are greater than rt+1d , meaning there is potential for growth in net worth. In addition,

net worth can be altered by government support to the financial sector ng_j,t+1 and repayment of

support from previous periods ˜ng_j,t+1. The law of motion for the intermediary’s net worth is thus

as follows: nj,t+1= (1 + rkt+1)q k ts k j,t+ (1 + r b t+1)(q b ts b j,t+ s e j,t) − (1 + r d t+1)dj,t+ n g j,t+1− ˜n g j,t+1,

which, using nj,t= pj,t− dj,t and n

g j,t+1= τ n t+1nj,t, can be rewritten as nj,t+1= (rt+1k − r d t+1)q k ts k j,t+ (r b t+1− r d t+1)(q b ts b j,t+ s e j,t) + (1 + r d t+1)nj,t+ τt+1n n g j,t− ˜τ n t+1n˜ g j,t+1.

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We assume that financial intermediaries aim to maximise profit. Each period, the fraction of bankers that continue to operate the next period equals θ and the fraction of bankers that exits the industry is 1 − θ. On exiting the industry, a banker transfers the final net worth of the intermediary to its household. Therefore, each banker maximises its expected net worth on exiting the industry, which can be given by

Vj,t= max Et

"_∞

X

i=0

βi+1Λt,t+1+iθi(1 − θ) (nj,t+1+i) #

,

or recursively:

Vj,t= max Et[βΛt,t+1{(1 − θ)nj,t+1+ θVj,t+1}] ,

where βΛt,t+1is the stochastic discount factor of the household.

If there is a positive risk premium on bonds and/or loans, the intermediary will want to expand its holdings of assets infinitely by borrowing funds from households at a rate lower than the rate of return on its assets. However, the extent to which the intermediary can leverage its equity is limited by the fact that each period a banker can divert a portion of λ of the intermediary’s assets to its household. This diversion of assets entails losing 1−λ of the assets to depositors who force the intermediary into bankruptcy. Since depositors have rational expectations, they will not provide bankers with funds if the gains of diverting assets is higher than the expected gains from continuing operations of the financial intermediaries. Therefore, the financial intermediary faces a constraint: Vj,t≥ λpj,t= λ(qtks k j,t+ q b ts b j,t+ s e j,t).

Using this leverage constraint, the maximisation problem of the financial intermediary be-comes max {qk tskj,t,qtbsbj,t,sej,t} Vj,t s.t. Vj,t≥ λ(qkts k j,t+ q b ts b j,t+ s e j,t).

To solve this problem, the assumption is made that the solution of the expected terminal net

worth of the intermediary takes the form of Vj,t = νktqtkskj,t + νbtqtbsbj,t+ νtesej,t + ηtnj,t. By

entering this conjectured solution into the maximisation problem, it can easily be deduced that

to maximise profits it must hold that νtk = νtb = νte. The intuition behind this lies in the fact

that νk

t, νtb and νte represent the shadow value of holding an additional unit of either asset. If

these were not equal, additional profit could be made by rearranging the portfolio of assets. The leverage constraint can now be rewritten as.

ν_tk(qk_tsk_j,t+ q_tbsb_j,t+ se_j,t) + ηtnj,t≥ λ(qkts k j,t+ q b ts b j,t+ s e j,t) q_tksk_j,t+ qb_tsb_j,t+ se_j,t≤ ηt λ − νk t nj,t= φtnj,t,

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where φt= _λ−νηtk t

is the maximum leverage ratio (ratio of assets to net worth) the intermediary can attain whilst remaining able to borrow from depositors. Intuitively, a higher fraction of assets that can be diverted by the banker decreases the amount of funds households will be willing to deposit and therefore lowers the maximum leverage ratio. Conversely, a higher shadow value of assets or net worth increases the expected profits from continuation and therefore relaxes the constraint placed by depositors on the level of leverage.

The above can be combined with the recursively defined maximand, resulting in Vj,t= EtβΛt,t+1(1 − θ)nj,t+1+ θ(νt+1k q k t+1s k j,t+1+ ν b t+1q b t+1s b j,t+1+ ν e t+1s e j,t+1+ ηt+1nj,t+1) = EtβΛt,t+1(1 − θ)nj,t+1+ θ(νt+1k φt+1nj,t+1+ ηt+1nj,t+1 = Et[Ωt+1nj,t+1] with Ωt+1= βΛt,t+1(1 − θ) + θ(νt+1k φt+1+ ηt+1) ,

which can be expanded to

Vj,t= EtΩt+1(rt+1k − rdt+1)qktskj,t+ (rbt+1− rt+1d )(qtbsbj,t+ sj,te ) + (1 + rdt+1)nj,t+ ngj,t+1− ˜n g j,t+1 = EtΩt+1(rt+1k − r d t+1)q k ts k j,t+ (r b t+1− r d t+1)(q b ts b j,t+ s e j,t) + (1 + r d t+1+ τ n t+1− ˜τ n t+1)nj,t .

This solution resembles the conjectured solution, which can be solved for νtk, νtb, νte and ηt,

giving the first order conditions to the intermediary’s maximisation problem:

ν_tk= νb_t = ν_te= EtΩt+1(rkt+1− r d t+1) ηt= EtΩt+1(1 + rdt+1+ τ n t+1− ˜τ n t+1)

To aggregate across the financial sector, the balance sheets of the continuum of intermediaries

can be summed up to pt= dt+ nt with pt= qktskt + qtbsbt+ set = φtnt, as the leverage ratio φt

is not firm specific. The portion of assets that are loans to the private sector is represented by

ωt= qtkskt/pt.

As described in section 3.1, each period a number of bankers the size of a fraction (1 − θ)f of the households will become a worker and vice versa. The other bankers continue operating their financial intermediary. The aggregate net worth of these continuing intermediaries, abstracted from government aid and repayment, can therefore be given by

ne,t= θ(rkt − r d t)q k t−1s k j,t−1+ (r b t− r d t)(q b t−1s b j,t−1+ s e j,t−1) + (1 + r d t)nj,t−1

Exiting bankers take the net worth of their intermediaries, (1 − θ) of aggregate net worth, to the household, of which a share is provided as starting capital to entering bankers. This share is χ/(1 − θ) of the assets held by the indermediaries of exiting bankers. The aggregate net worth

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of starting bankers is therefore

nn,t =

χ

1 − θ(1 − θ)pt−1= χpt−1.

Adding financial sector support by the government and repayment of support, the total net worth of the financial sector is

nt= θ(rkt − r d t)q k t−1s k j,t−1+ (r b t− r d t)(q b t−1s b j,t−1+ s e j,t−1) + (1 + r d t)nj,t−1 + χpt−1+ ngt− ˜n g t. Finally, he number (and value) of the external bonds is determined by the size of externally financed capital injections to banks:

se_t = se_t−1+ (1 − κe)(n

g t− ˜n

g t).

Section 3.4 will elaborate on the government support of the financial sector.

3.3 Goods Producing Firms

3.3.1 Intermediate Goods Producers

Intermediate goods are produced by a continuum of competitive non-financial firms. Intermediate

goods producers acquire capital kt from capital producers at the end of each period for a price

qkt per unit of capital. This purchase of capital is financed by issuing skt claims, equal to the

number of capital purchased, to the financial intermediaries at price qk

t. Intermediate goods

producers pay a state-contingent net real return rk

t+1over their issued claims in the next period.

No frictions arise in the financing of intermediate firms, although the required rate of return is dependent on the supply of deposits to the intermediaries. At the begin of the next period, after the firm has decided on the amount of capital that is employed, shocks occur in both the quality

of capital ξtand total factor productivity at. After these shocks are revealed, the producer hires

labour hi,t at a wage wtto produce output with the production function

yi,t = at(ξtki,t−1)αh1−αi,t−1.

Quality of capital ξt and total factor productivity atare driven by AR(1) processes

log ξt= ρξlog ξt−1+ εξ,t and

log at= ρalog at−1+ εa,t,

where εξ,t ∼ N (0, σ2ξ) and εa,t ∼ N (0, σa2) are random i.d.d. shocks. Note that the effective

capital stock is influenced by the size of the capital quality shock and cannot be fully determined by the intermediate goods producer at the end of the period before production.

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relative price of the intermediate goods to that of the final goods. Once the goods have been sold, the firms sell whatever is left of the effective capital stock after depreciation back to the

capital producers for qk

t and pay back their loans and a net return to the financial intermediaries.

This leads to the profit function

Πi,t= mtat(ξtki,t−1)αh1−αi,t + q k

t(1 − δ)ξtki,t−1− (1 + rkt)q

k

t−1ki,t−1− wthi,t.

Firms are ultimately owned by the households and aim to maximise their stream of profits, discounted by the household’s stochastic discount factor. In addition, intermediate goods pro-ducers take all prices in the industry as given. Since the intermediate goods producer does not face adjustment costs (these can be found with the capital producers) its maximisation problem is static. The resulting maximisation problem is as follows:

max {kt+s,ht+s}∞ s=0 Et "∞ X s=0 βsΛt,t+sΠi,t+s # . The first order conditions of this problem are

kt : EtβΛt,t+1 αmt+1yi,t+1/ki,t+ qkt+1(1 − δ)ξt+1− (1 + rkt+1)q k t = 0 ht : (1 − α)mtyi,t/hi,t = wt

which intuitively state that the discounted marginal return on capital (through production and resale) must be equal to discounted marginal cost of capital; and that the marginal productivity of a unit labour must be equal to the wage in order to maximise profits.

However, in equilibrium it is given that profits are zero. Combining this with the first order condition of labour gives

Πi,t = mtyt+ qtk(1 − δ)ξtki,t−1− (1 + rkt)q

k

t−1ki,t−1− (1 − α)mtyi,t= 0,

which can be rewritten as an expression for the real net return on capital paid to the financial intermediaries: rtk = αmtyi,t+ qtk(1 − δ)ki,t−1ξt qk t−1ki,t−1 − 1.

This expression can be used to find the factor demands of the production sector: ki,t−1 = αmtyi,t qk t−1(1 + rkt) − qtk(1 − δ)ξt , hi,t = (1 − α)mtyi,t wt .

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these factor demands in the production function: yi,t = atξtα _αm tyi,t qk t−1(1 + rkt) − qkt(1 − δ)ξt α_{(1 − α)m} tyi,t wt 1−α ⇒ mt = qk t−1(1 + rkt)/ξt− qkt(1 − δ) α w1−α_t atαα(1 − α)1−α . 3.3.2 Capital Producers

As described in section 3.3.1, capital producers purchase the effective capital stock that is left

after depreciation, (1 − δ)ξtkt−1, from the intermediate goods producers at the end of the period.

This capital is converted to the next period’s capital stock by combining it with goods that are purchased from final goods producers (see section 3.3.4). The amount of units of final goods

used for creating the new capital stock can be seen as investment it. This capital stock is

subsequently sold to the intermediate goods producers at the same price q_tk that was paid for

the leftover capital from the period. Profits are then represented by

Πc_t = qk_tkt− qkt(1 − δ)ξtkt−1− it

The capital producer faces convex costs of adjusting the level of investment, so that for every

unit it only 1 − Ψ(ιt) units of capital are produced, with ιt = it/it−1 representing change in

investment level. The expression for the capital stock after the capital producers have produced (or output of capital producers) is then:

kt = (1 − δ)ξtkt−1+ (1 − Ψ(ιt)) it, with Ψ(ιt) =

γ

2(ιt− 1)

2

This leaves the profit function as

Πc_t = q_tk(1 − Ψ(ιt))it− it.

The capital producers are owned by the households who seek to maximise current and future profits, discounted by their stochastic discount factor. The maximisation problem for the capital producers is: max {it+s}∞ s=0 Et "∞ X s=0 βsΛt,t+sqt+sk (1 − Ψ(ιt+s))it+s− it+s #

The first order condition of the capital producers with respect to itis

q_tk(1 − Ψ _i t it−1 ) − q_tk it it−1 Ψ0 _i t it−1 + Et βΛt,t+1qt+1k i2t+1 i2 t Ψ0 it+1 it = 1

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From this first order condition an expression can be derived for the price of a unit of capital by

entering Ψ(ιt) =γ₂(ιt− 1)2 and Ψ0(ιt) = γ(ιt− 1), and dividing by qtk:

1 qk t = 1 −γ 2 _i t it−1 − 1 2 − γ it it−1 _i t it−1 − 1 + βEt " Λt,t+1 qk t+1 qk t γ it+1 it 2_i t+1 it − 1 # . 3.3.3 Retail Firms

The retail industry consists of a continuum of differentiated retail firms that repackage goods

purchased from the intermediate goods producers. For every unit of intermediate goods yi,t

bought for a nominal price Pm

t , the retail firms produces one retail good yf,t which it sells for

a nominal price Pf,t. Since retail goods are differentiated, firms can charge a mark-up over the

price of input so that Pf,t ≥ Ptm and earn profits (Pf,t− Ptm)yf,t. As derived in section 3.3.4,

retail firms face the demand function yf,t= (Pf,t/Pt)−yt.

Each period, only a random portion (1 − ψ) of retail firms are allowed to reset their prices, while the other firms must keep their prices fixed. Therefore, in maximising current and future profits, the retail firms must take into account the possibility that a price that is set in period

t still holds in period t + s with a probability of ψs_{. To accommodate for nominal prices, a}

factor Pt/Pt+s is added in addition to the usual stochastic discount factor of the household. The

maximisation problem of the retail firm is thus:

max Pf,t Et "∞ X s=0 ψsβsΛt,t+s(Pt/Pt+s)Pf,t− Pt+sm yf,t+s # .

Substituting the demand function, applying symmetry between firms so that all Pf,t = Pt∗ and

using Pm t /Pt= mt results in: max Pf,t Et "∞ X s=0 ψsβsΛt,t+sPt " P_t∗ Pt+s 1− − mt+s _P∗ t Pt+s −# yt+s # .

Taking the first order condition with respect to the retail price gives the solution to the optimal pricing problem: Pt P_t∗ 1 λt Et "∞ X s=0 ψsβsλt+s " (1 − ) _P∗ t Pt+s 1− + mt+s _P∗ t Pt+s −# yt+s # = 0 ( − 1)Pt∗Et "∞ X s=0 ψsβsλt+sPt+s−1yt+s # = Et "∞ X s=0 ψsβsλt+smt+sPt+s yt+s #

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results in: P_t∗ Pt = − 1 Et h P∞ s=0ψ s_βs_λ t+smt+s _P t+s Pt yt+s i Et h P∞ s=0ψsβsλt+s _P t+s Pt −1 yt+s i

By using πt∗= Pt∗/Ptand πt= Pt/Pt−1, this solution can be written recursively as:

π_t∗ = − 1 Ξ1,t Ξ2,t , with Ξ1,t = λtmtyt+ ψβEtπt+1Ξ1,t+1 , Ξ2,t = λtyt+ ψβEtπt+1−1Ξ2,t+1 .

3.3.4 Final Goods Producers

Final goods producers purchase the differentiated retail goods to produce final goods. They face the following technology constraint:

y(−1)/_t =

Z 1

0

y_f,t(−1)/df,

where represents the elasticity of substitution between goods bought from the retail firms. Final good producers operate in a perfectly competitive market and therefore sell their goods

for the same price Pt. The decision variable of final goods producers is therefore the amount of

input yf,t. Final goods are sold to households and government for consumption, and to capital

producers as input for investment. Final goods producers aim to maximise profits, but, since today’s decisions have no influence on next periods, do not have to take into account future periods. The maximisation problem is thus:

max yf,t Ptyt− Z 1 0 Pf,tyf,tdf

. Substituting the technology restraint and taking the first order condition results in the demand function for retail products:

Pt − 1 y −1/ f,t − 1 Z 1 0 y_f,t(−1)/df 1/−1 − Z 1 0 Pf,tdf = 0 ⇒ Pty−1/_f,t y 1/ t − Pf,t = 0 ⇒ yf,t = Pf,t Pt − yt = ∆tyt, where ∆t = _Pf,t Pt −

represents the dispersion resulting from the introduced price rigidities.

This dispersion can also be written recursively as ∆t= (1 − ψ)(π∗t)−+ ψπ

t∆t−1.

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Combining the demand function with the technology constraint gives an expression for the overall price level:

y_t−1/ = Z 1 0 Pf,t Pt 1− y(−1)/_t df ⇒ Pt = Z 1 0 P_f,t1−df 1−1 .

Recalling the staggered Calvo pricing (see section 3.3.3), this can be expressed as

Pt1− = (1 − ψ)(Pt∗)

1−_{+ ψP}1− t−1,

which can be divided by P_t1− to find

1 = (1 − ψ)(π∗_t)1−+ ψπ−1_t .

3.3.5 Aggregating the Goods Sector

Now that we have described the complete goods sector, we can aggregate over all firms using

yi,t= yf,t= ∆tyt. Aggregate demand for capital and labour is thus:

kt−1 = αmt∆tyt qk t−1(1 + rkt) − qtk(1 − δ)ξt , ht = (1 − α)mt∆tyt wt ,

for which the aggregate ratio kt−1/htis equal to the individual ratio ki,t−1/hi,t.

We can now find aggregate supply by taking

Z 1 0 at(ξtki,t−1)αh1−αi,t di = Z 1 0 atξt ki,t−1 hi,t α hi,tdi ⇒ atξtα kt−1 ht αZ 1 0 hi,tdi = at(ξtkt−1)αh1−αt−1

and knowing thatR1

0 yi,tdi =

R1

0 ∆tytdi = ∆tyt, resulting in aggregate supply:

yt = ∆−1at(ξtkt−1)αh1−αt−1

.

3.4 Government

To finance its expenditures in period t, the government issues bt bonds at price qtb and levies a

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past financial aid. These funds are used for gt government purchases, injecting ngt capital into

financial intermediaries and repay debt from period t − 1 plus a real return rtb. The government’s

budget constraint is therefore:

qb_tbt+ τt+ κen˜gt = gt+ κengt+ (1 + r

b t)q

k t−1bt−1.

κe determines the share of the capital injection that is financed by the government. κe = 1

implies that the government pays for the full recapitalisation, while κe= 0 represents a situation

in which the capital injection is completely done by an external party (e.g. the ESM). Government purchases are determined by the following rule:

gt = ¯g + ζ(ξt−o− ¯ξ) + κg(bt−v− ¯b); ζ ≤ 0, κg≥ 0, o ≥ 0, v ≥ 1.

ζ indicates the size of the fiscal impulse in response to a capital quality shock and κgthe feedback

of government debt on government purchases. The delay in the government response to a capital quality shock is o quarters, whereas the lag in the response of government expenditure to the size of government debt is v quarters.

The lump sump tax depends on the level of outstanding debt and capital injections and is given by the following tax rule:

τt = ¯τ + κb(bt−1− ¯b) + κnngt; 0 < κb ≤ 1, 0 ≤ κn ≤ 1,

where ¯τ is the steady state tax level and ¯b is the steady state level of debt. The feedback

parameter of debt on taxes κbmust be larger than zero to obtain debt sustainability. The value

of κn determines whether aid to the financial sector is financed by tax increases, debt issuance

or a combination.

The amount of injected capital in period t depends on the quality of capital and is given by:

ngt = κ(ξt−l− ¯ξ)nt−1; κ ≤ 0, l ≥ 0.

κ controls the amount of funds the government inject into the financial sector given a certain capital quality shock, whereas l determines the lag with which the recapitalisation takes place. A fraction ϑ of these funds must be paid back by the financial intermediaries after e periods:

˜

ngt = ϑn

g

t−e; ϑ ≥ 0, e ≥ 1.

Note that the government can even penalise financial intermediaries with an interest rate over received financial aid by setting ϑ > 1.

The real return on government bonds rtbdepends on the maturity structure of the government

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that decreases each period by a factor 1 − ρ. The duration of public debt is then 1/(1 − βρ)1_.

Consequently, each bond that is issued at price qt−1b pays out a fixed return of rc in period t,

ρrc in period t + 1, ρ2rc in period t + 2 and so on. This can be represented as a return of rc

plus ρ times a new bond in period t: rc+ ρqbt. The government debt service then adds up to

(rc+ ρqtb)bt−1 in period t, which must be equivalent to (1 − rbt)q

b t−1bt−1, implying that: rb_t = rc+ ρq b t qb t−1 − 1.

3.5 Central Bank

The Central Bank sets the nominal interest rate on deposits for each period. It uses a standard Taylor rule to determine the policy rate:

r_tn = (1 − ρr)(¯rn+ κπ(πt− ¯π) + κylog (yt/yt−1)) + ρrrt−1n ; κπ> 0, κy> 0,

where ¯rn _{is the nominal interest rate in steady state and ¯}_{π the target level of inflation. ρ}

r represents a smoothing parameter of the nominal interest rate. The aim of the Central Bank is thus to keep inflation at its target level and to minimize fluctuations in output.

The real return on deposits is given by:

r_td = (1 + rn_t−1)/πt− 1.

3.6 Equilibrium

In equilibrium, there is clearance in all markets. For the goods markets this entails that aggregate supply equals aggregate demand:

yt = ct+ it+ gt.

In the asset markets, the number of loans to the intermediate goods producers must equal the size of the capital stock and the number of bonds owned by financial intermediaries must equal the number of bonds issued by the government:

sk_t = kt,

sb_t = bt.

These equations close the description of the macroeconomic model in this section. 1_{Duration is defined as}

P∞

j=1jβj(ρj−1rc)

P∞

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4 Calibration

The model described above is calibrated to match the Spanish economy as closely as possible. The calibration as in Van der Kwaak and Van Wijnbergen (2014) is taken as the starting point for the adaptation to Spain, which in its turn is based on the calibration by Gertler and Karadi (2011). Subsequently, country specific parameter values that are common in the literature are taken from both micro data and Bayesian estimation of parameters as performed by Burriel et al. (2010).

The subjective discount factor β, share of effective capital in production α and the

coeffi-cients of the Taylor rule κπ and κy can be derived from data and are found in Burriel et al.

(2010). The smoothing parameter of the nominal interest rate ρris set to zero, which reflects an

aggressive monetary policy typical to crisis periods. Parameters that have been approximated using Bayesian estimation include habit formation υ, labour supply coefficient Ψ, inverted Frisch elasticity of labour supply ϕ, elasticity of substitution between intermediate goods , Calvo probability ψ and the investment adjustment parameter γ. Burriel et al. find a value for Calvo probability ψ of 0.898. This, however, leaves the model without a solution as it causes indeter-minacy. Therefore, the Calvo probability is slightly reduced to 0.85, for which the model has a solution. A robustness test will be provided in Annex I to assess whether this slight alteration significantly distorts the results of the model. As can be seen in table 2, especially the values of the household parameters derived from Bayesian estimation differ significantly from those in our starting calibration. At 28.954, the parameter of the adjustment costs of investments especially deviates greatly from its original value. The large value of the adjustment cost parameter distorts the solution of the model to such an extent that a decision is made to retain the original value. A reason for this is that the model on which Burriel et al. performed their estimation slightly differs from the model employed in this study. In addition, there can be found no reason in the literature as to why Spain would face extremely high adjustment costs of investment.

Now that the parameters common in the literature are accounted for, some less common parameter values are left to calibrate. The average lifetime of bankers cannot be derived from data and must therefore be determined by assumption. The assumption is made that bankers survive for an average of 24 quarters, resulting in a survival rate θ of 0.9583. The maturity structure parameter ρ is calibrated to reflect the weighted average maturity of government bonds in Spain between 1998 and 2008, which is 6,1 years according to the OECD Stats database. ρ is therefore set to 0.97 (duration in quarters = 1/(1 − βρ)). The annual fixed real payment on long-term government bonds is set to 0.041, which is the 1998-2008 average of the interest rate on Spanish government bonds with a maturity of 10 years found in the Statistical Data Warehouse of the ECB. Although this is not a precise proxy for the fixed real payment on bonds, it is a

good approximation for rc in this model.

The calibration targets to which the model is set to hit include a set of steady state ratios and levels. The ratio of investments, government consumption and government debt over GDP are derived from Eurostat data. The 15-year average percentage of GDP that can be ascribed to

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Target Definition Starting value

Calibrated

value Reason

¯i/¯y Investment ratio 0.2 0.226 1994-2008 average

¯

g/¯y Government spending ratio 0.2 0.178 1994-2008 average

¯

b/¯y Government debt ratio 2.4 2.128 1995-2008 average

Γ Credit spread 0.0025 0.0054 1994-2008 average

φ Leverage ratio 4 5.1 2001-2008 average

Table 1: List of steady state calibration targets and source of calibration

private investments and government consumption is taken between 1994 and 2008. This results in steady state ratios of 22.6 per cent for investments over GDP and 17.8 per cent for government consumption over GDP. This pins down the depreciation rate δ at a quarterly 3.74 per cent. The steady state ratio of government debt to output is set to 53.2 per cent, which is the 1995-2008 average of Spanish government debt to GDP ratio. For the steady state credit spread Γ, the 9-year average interest rate spread (lending rate minus deposit rate) between 1994 and 2002 is taken from the Worldbank database. For this period the average credit spread in Spain was 216 basis points, which amounts to a steady state quarterly spread of 0.0054. The target value of

inflation ¯π is set to 1.

The steady state leverage ratio of the financial sector is more difficult to calibrate. In this model, all returns to loans to the private sector are outcome-dependent. In reality banks often hold loans that represent liabilities to firms rather than equity. Furthermore, there exist large differences between leverage ratios across the financial sector. In Spain, leverage ratios go as high as 34 for Banco Santander, whereas other financial institutions clearly have lower leverage ratios. To attempt to average across these different segments of the financial sectors, the average ratio of consolidated equity to consolidated financial assets of the Spanish financial sector is taken between 2001 and 2008 from the OECD Stats database. This results in a steady state leverage ratio of 5.1, which resembles the leverage ratio chosen by Gertler and Karadi (2011) of 4.

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Parameter Definition Starting value

Calibrated

value Reason

Households

β Subjective discount factor 0.990 0.990

-υ Degree of habit formation 0.815 0.847 Bayesian estimation

Ψ Disutility weight of labour 3.409 6.772 Bayesian estimation

ϕ Inverse Frisch elasticity 0.276 1.835 Bayesian estimation

Financial sector

θ Survival rate of bankers 0.9722 0.9583 Assumption

λ Divertable fraction of assets 0.3863 0.5401 By definition

χ Transfer share to new bankers 0.0021 0.0011 By definition

Producing firms

α Effective capital share 0.330 0.362 Micro data

Elasticity of substit. (goods) 4.176 8.577 Bayesian estimation

ψ Calvo prob. (price stickiness) 0.779 0.850 Bayesian estimation2

γ Investment adjustment cost par. 1.728 1.728 Retained

δ Depreciation rate 0.0494 0.0374 By definition

Policy parameters

ρ Government debt maturity par. 0.96 0.97 1998-2008 average

rc Real payment to bondholder 4.0 4.1 1998-2008 average

ρr Interst rate smoothing par. 0 0 Crisis policy

κb Gov. debt feedback on taxes 0.05 0.05 Stability

κπ Inflation feedback on rn 1.500 1.700 Taylor rule EMU

κy Output feedback on rn 0.125 0.125 Taylor rule EMU

¯

π Inflation rate target 1 1 Retained

Table 2: List of calibrated parameter values and source of calibration.

5 Results

5.1 Financial Crisis

A financial crisis is modelled by introducing a negative capital quality shock of 5 per cent with

respect to steady state with the autoregressive component ρξ set to 0.66. The financial crisis

deteriorates capital quality and therefore forms a negative shock in the production function of intermediate good producers. The lower productivity of capital pushes down wages, since the marginal product of labour decreases. The household’s consumption decreases as a result of a tightening of its budget constraint, pushing down output. Meanwhile the nominal interest rate decreases sharply as a result of the drop in output.

As capital becomes less productive, the price of capital goes down. Since the securities

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issued by intermediate good producers are state-contingent, a negative capital quality shock also decreases ex-post returns on capita. As their assets decrease in value and their profits fall, the net worth of financial intermediaries shrinks. The lower net worth tightens the balance sheet constraint and forces the intermediaries to reduce their loans to the intermediate goods producers. This limits investment by the private sector, driving down the price of capital and output even further. The fall in investment causes a decrease in the capital stock and therefore an additional decrease in labour demand and wages. Intermediaries will want to sell government bonds, since the decrease in the price for capital drives up the expected return on capital. Due to arbitrage, bonds will be sold and will be expected to have an increasingly higher return. Further deterioration in the balance sheet of the intermediary, caused by the sale of government bonds and the associated fall in bond prices, prolong this effect up to the point where the expected return on bonds has increased enough for intermediaries to hold all government bonds.

5.1.1 Calibration Differences

There are notable differences between the effects of the financial crisis on the model with standard calibration and those on the model with Spanish calibration, as can be seen from figure 1. In general, the recession that follows the financial crisis is more pronounced and persistent if the Spanish calibration is used. The added persistence is partly caused by a higher Calvo probality and an inelastic labour supply (see section 7). Since the Spanish calibration contains larger price rigidities resulting from a higher Calvo probability, the recession is more stretched out and recovery is slower. Firms are less able to quickly adapt to the capital quality shock and its effects on the economy. The share of firms that is able to maximise its prices is smaller each period, driving a wedge between supply and demand and hampering economic recovery. In addition, the supply of labour is less responsive to wage signals, creating larger persistence in the recession. For more information on the effects of price rigidity and labour supply elasticity, refer to Annex I.

Another cause of the heavier effect of the capital quality shock on the economy is the fact that the Spanish calibration includes a higher value for the effective capital share. In case of a higher capital share, relatively more capital will be utilized in production. This results in a higher supply of funds from financial intermediaries to intermediate goods producers. However, when the economy is hit with a negative capital shock, this hurts a larger portion of their balance sheets and therefore intermediary net worth will decrease more in case of a larger capital share. This results in a more severe tightening of the leverage constraint and consequently a higher credit spread. Thus, if the share of capital in output is larger, a shock to capital quality will have a larger negative effect to productivity and therefore to wages, consumption and output. This is reflected in the nominal interest rate, which (because of the very aggressive Taylor rule) shoots down significantly more. Also, a larger loss in productivity of capital causes investment to drop more dramatically and creates a larger decrease in capital stock compared to the initial calibration.

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Finally, due to the higher steady state leverage ratio and the higher steady state credit spread, the banks are hit harder by the financial crisis. This is reflected in the larger drop in intermediary net worth and the sharper increase in leverage. This deepens the negative effect on investment and therefore worsens the recession.

0 20 40 60 −6 −5 −4 −3 −2 −1 0 Quality of Capital Rel. ∆ from s.s. in percent 0 20 40 60 −6 −5 −4 −3 −2 −1 0 Output Rel. ∆ from s.s. in percent 0 20 40 60 −8 −6 −4 −2 0 Consumption Rel. ∆ from s.s. in percent 0 20 40 60 −20 −15 −10 −5 0 5 10 Investment Rel. ∆ from s.s. in percent 0 20 40 60 −15 −10 −5 0 Capital Rel. ∆ from s.s. in percent 0 20 40 60 −10 −8 −6 −4 −2 0 2 Price of Capital Rel. ∆ from s.s. in percent 0 20 40 60 −60 −40 −20 0 20

Intermediary Net Worth

Rel. ∆ from s.s. in percent Quarters 0 20 40 60 −10 0 10 20 30 40 50 Intermediary Leverage Rel. ∆ from s.s. in percent Quarters 0 20 40 60 0 50 100 150

Credit Spread E[rk−rd]

Abs.

∆

from s.s.

in basis pts.

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0 20 40 60 −4

−3 −2 −1

0Portfolio weight claims

Rel. ∆ from s.s. in percent 0 20 40 60 0 0.5 1 1.5 2 2.5 Number of bonds Rel. ∆ from s.s. in percent 0 20 40 60 −8 −6 −4 −2 0 Price of bonds Rel. ∆ from s.s. in percent 0 20 40 60 −12 −10 −8 −6 −4 −2 0 Wages Rel. ∆ from s.s. in percent 0 20 40 60 −3 −2 −1 0 1 2 3 Labor Rel. ∆ from s.s. in percent 0 20 40 60 −1.5 −1 −0.5 0 0.5 1 Inflation Rel. ∆ from s.s. in percent 0 20 40 60 −300 −200 −100 0 100 200

Nominal interest rate

Abs. ∆ from s.s. in basis pts. Quarters 0 20 40 60 −20 0 20 40 60

Return on bonds E[rb]

Abs. ∆ from s.s. in basis pts. Quarters 0 20 40 60 −20 0 20 40 60

Return on capital E[rk]

Abs.

∆

from s.s.

in basis pts.

Quarters

Figure 1: Impulse response functions for the model with standard calibration (red,...) and calibration

on Spain (blue,-) after a negative capital quality shock of 5 percent relative to steady state.

5.2 Delayed Recapitalisation

One possible government response to a financial crisis is a recapitalisation of the financial inter-mediaries, alleviating the tightening of balance sheets. This section investigates the effect of a recapitalisation of 1.25 per cent of annual output in steady state. Since such a policy typically takes some political preparation, the recapitalisation is modelled to be announced directly after the financial crisis hits, but to come in effect only after four quarters. The recapitalisation is

financed completely by issuing government bonds and has no direct feedback on taxes (κg= 0).

At the moment of recapitalisation, intermediary net worth is increased and leverage is reduced. This effect is however already visible before the actual recapitalisation, as can bee seen in figure 2. Since the recapitalisation increases the continuation value for bankers and depositors are aware of the pending recapitalisation, the leverage constraint becomes less tight. The financial intermediaries have more place on their balance sheets for private loans and bonds, creating upward pressure on the prices of these assets. Bond prices still decrease in anticipation of the large issuance at the moment of the recapitalisation, but less than in the no policy case. This has a positive effect on the net worth of intermediaries as losses on their assets are reduced.

At the moment of recapitalisation, debt issuance goes up dramatically, causing bond prices to drop even further. However, the losses incurred by the price collapse do not dominate the positive effect of the recapitalisation on the banks’ balance sheets. Net worth of the intermediary is

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constantly above the no policy case, as are the prices for bonds. The effect of the recapitalisation on the real economy is obvious. The increased supply of loans to the private sector pushes up investment and therefore output, wages, labour and ultimately consumption. A delayed recapitalisation therefore helps limit the recession following a financial crisis and speeds up the recovery of the economy calibrated on Spain.

0 20 40 60 −6 −5 −4 −3 −2 −1 0 Quality of Capital Rel. ∆ from s.s. in percent 0 20 40 60 −6 −5 −4 −3 −2 −1 0 Output Rel. ∆ from s.s. in percent 0 20 40 60 −8 −6 −4 −2 0 Consumption Rel. ∆ from s.s. in percent 0 20 40 60 −20 −15 −10 −5 0 5 Investment Rel. ∆ from s.s. in percent 0 20 40 60 −15 −10 −5 0 Capital Rel. ∆ from s.s. in percent 0 20 40 60 −10 −8 −6 −4 −2 0 2 Price of Capital Rel. ∆ from s.s. in percent 0 20 40 60 −60 −40 −20 0 20

Rel. ∆ from s.s. in percent Quarters 0 20 40 60 −10 0 10 20 30 40 50 Intermediary Leverage Rel. ∆ from s.s. in percent Quarters 0 20 40 60 0 20 40 60 80 100 120

Abs.

∆

from s.s.

in basis pts.

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0 20 40 60 −4 −3 −2 −1 0

Portfolio weight claims

Rel. ∆ from s.s. in percent 0 20 40 60 0 2 4 6 8 Number of bonds Rel. ∆ from s.s. in percent 0 20 40 60 −6 −5 −4 −3 −2 −1 0 Price of bonds Rel. ∆ from s.s. in percent 0 20 40 60 −12 −10 −8 −6 −4 −2 0 Wages Rel. ∆ from s.s. in percent 0 20 40 60 −3 −2 −1 0 1 2 Labor Rel. ∆ from s.s. in percent 0 20 40 60 −1.5 −1 −0.5 0 0.5 Inflation Rel. ∆ from s.s. in percent 0 20 40 60 −300 −200 −100 0 100

Abs. ∆ from s.s. in basis pts. Quarters 0 20 40 60 −40 −20 0 20 40

Abs.

∆

from s.s.

in basis pts.

Quarters

Figure 2: Impulse response functions for the model with a delayed recapitalisation of the financial sector

(blue,-) of 1.25 per cent of annual steady state output occurring four quarters after the capital quality shock and the model without additional government policy (red,...).

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5.3 Delayed Fiscal Stimulus

The next government response to the financial crisis that will be investigated is an increase in government spending 4 quarters after the onset of the crisis. The size of the fiscal stimulus is 5 per cent of steady state annual GDP. In addition to a general fiscal stimulus without reversal, this section will also look at a fiscal stimulus that is followed by a perfect reversal. In the case of the perfect reversal, total discounted additional government spending is zero. To obtain this,

the feedback parameter of government debt on government spending κg is set to 0.066. The

government spending response functions for both cases are displayed in figure 3.

0 10 20 30 40 50 60 −1 0 1 2 3 4 5 6 Government Spending Share of s.s. output in percent Quarters

Figure 3: Government spending as share of steady state output in the case of no reversal (red,-.) and

with perfect reversal (κg = 0.66) (blue,-) after a capital quality shock of 5 per cent relative to steady

state.

5.3.1 No Reversal

The main purpose of a fiscal stimulus is to boost output in a time of recession. As can be seen from figure 4, a fiscal stimulus directly increases output at the time of the stimulus. This is paired with an immediate sharp increase in labour to accommodate the additional demand. However, it can be seen that consumption does not benefit from the stimulus. The reason for this is a negative welfare effect of the fiscal stimulus on households as their future tax burden increases. As the fiscal stimulus takes place, the government finances all extra expenditures by issuing additional bonds (the tax feedback of government spending is set to zero). As a result, government bonds will necessarily take a larger share of banks balance sheets (this happens by a decrease in bond prices), leaving less room for loans to the private sector and therefore hampers investments. This crowding out of investments in the model is caused by financial frictions: the balance sheet constraint is worsened by the drop in bond prices. Contrary to a recapitalization, the intermediary net worth of banks is not directly improved by the government policy. Other dynamics in the model are similar to that of the case of recapitalisation.

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the actual implementation of the stimulus. This is because, in anticipation of the fiscal expansion, consumption drops beyond the no policy situation. Consumers know that their tax burden is increased as a result of the fiscal expansion, and through inter-temporal substitution lower their consumption in present periods to compensate for the larger tax payments in the future.

0 20 40 60 −6 −5 −4 −3 −2 −1 0 Quality of Capital Rel. ∆ from s.s. in percent 0 20 40 60 −8 −6 −4 −2 0 Output Rel. ∆ from s.s. in percent 0 20 40 60 −8 −6 −4 −2 0 Consumption Rel. ∆ from s.s. in percent 0 20 40 60 −25 −20 −15 −10 −5 0 5 Investment Rel. ∆ from s.s. in percent 0 20 40 60 −20 −15 −10 −5 0 Capital Rel. ∆ from s.s. in percent 0 20 40 60 −10 −8 −6 −4 −2 0 2 Price of Capital Rel. ∆ from s.s. in percent 0 20 40 60 −80 −60 −40 −20 0 20

Rel. ∆ from s.s. in percent Quarters 0 20 40 60 −20 0 20 40 60 Intermediary Leverage Rel. ∆ from s.s. in percent Quarters 0 20 40 60 0 20 40 60 80 100 120

Abs.

∆

from s.s.

in basis pts.

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0 20 40 60 −5 −4 −3 −2 −1 0

Rel. ∆ from s.s. in percent 0 20 40 60 0 2 4 6 8 Number of bonds Rel. ∆ from s.s. in percent 0 20 40 60 −8 −6 −4 −2 0 Price of bonds Rel. ∆ from s.s. in percent 0 20 40 60 −20 −15 −10 −5 0 Wages Rel. ∆ from s.s. in percent 0 20 40 60 −5 0 5 Labor Rel. ∆ from s.s. in percent 0 20 40 60 −1.5 −1 −0.5 0 0.5 Inflation Rel. ∆ from s.s. in percent 0 20 40 60 −300 −200 −100 0 100

Abs. ∆ from s.s. in basis pts. Quarters 0 20 40 60 −50 0 50 100 150 200

Abs.

∆

from s.s.

in basis pts.

Quarters

Figure 4: Impulse response functions for the model with a delayed fiscal stimulus by the government

with no reversal (blue,-) of 1.25 per cent of annual steady state output occurring four quarters after the capital quality shock and the model without additional government policy (red,...).

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5.3.2 Perfect Reversal

A possible method to eliminate the negative welfare and substitution effect of the fiscal stimulus could be to completely reverse the additional government expenditures after a period of time. If the discounted additional government spending sum up to zero, the total tax burden on households will not increase.

Figure 5 demonstrates that the drop in consumption caused by the unreversed fiscal stimulus is indeed eliminated by the perfect reversal. However, no significant benefits are seen over the case of no additional government policy. Even with an announced reversal, there is a negative anticipation effect of the fiscal policy on investment and therefore output. This is a result of the additional tightening of the balance sheet constraint, as the financial intermediaries experience larger losses on their bonds in anticipation of the large bond issuance. As soon as the reversal reaches completion, the economy is in the same condition as it would be if the stimulus and reversal would not have taken place at all. One exception is that consumption is slightly higher at the end of the recession. An explanation for this is that, by design, the government debt returns to its steady state value more quickly as debt is paid off during the reversal. This leaves the households with a lower tax burden and relaxes their budget constraint.

Although a fiscal stimulus followed by a perfect reversal is preferred over a pure fiscal stimulus, it is not a viable method to help solve a financial crisis.

0 20 40 60 −6 −5 −4 −3 −2 −1 0 Quality of Capital Rel. ∆ from s.s. in percent 0 20 40 60 −8 −6 −4 −2 0 Output Rel. ∆ from s.s. in percent 0 20 40 60 −8 −6 −4 −2 0 Consumption Rel. ∆ from s.s. in percent 0 20 40 60 −30 −20 −10 0 10 Investment Rel. ∆ from s.s. in percent 0 20 40 60 −20 −15 −10 −5 0 Capital Rel. ∆ from s.s. in percent 0 20 40 60 −15 −10 −5 0 5 Price of Capital Rel. ∆ from s.s. in percent 0 20 40 60 −80 −60 −40 −20 0

Rel. ∆ from s.s. in percent Quarters 0 20 40 60 0 10 20 30 40 50 60 Intermediary Leverage Rel. ∆ from s.s. in percent Quarters 0 20 40 60 0 50 100 150

Abs.

∆

from s.s.

in basis pts.

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0 20 40 60 −5 −4 −3 −2 −1 0

Rel. ∆ from s.s. in percent 0 20 40 60 0 2 4 6 8 Number of bonds Rel. ∆ from s.s. in percent 0 20 40 60 −10 −8 −6 −4 −2 0 Price of bonds Rel. ∆ from s.s. in percent 0 20 40 60 −20 −15 −10 −5 0 Wages Rel. ∆ from s.s. in percent 0 20 40 60 −6 −4 −2 0 2 4 Labor Rel. ∆ from s.s. in percent 0 20 40 60 −1.5 −1 −0.5 0 0.5 Inflation Rel. ∆ from s.s. in percent 0 20 40 60 −300 −200 −100 0 100 200

Abs.

∆

from s.s.

in basis pts.

Quarters

Figure 5: Impulse response functions for the model with a delayed fiscal stimulus by the government

with perfect reversal (blue,-) of 1.25 per cent of annual steady state output occurring four quarters after the capital quality shock and the model without additional government policy (red,...).

6 Recapitalising the Spanish Banking Sector

This section will zoom in on the banking crisis that took place in Spain in recent years and will investigate the macroeconomic developments that unfolded. The resulting reform of the financial sector included a hefty recapitalisation of Spanish banks. This recapitalisation is reproduced using my macroeconomic model calibrated on the Spanish economy. An assessment is made whether the effects of a recapitalisation in my model can be recognized in the effects of the Spanish recapitalisation in 2012 and 2013. Finally, an experiment will be performed in which Spanish banks are recapitalised directly by an external entity, circumventing the government budget constraint.

6.1 Spanish Final Sector Reform

Spain adopted a reform of its financial sector in July 2012 during a severe recession and global distress on financial markets. The burst of the real estate bubble and the pressure on sovereign debt had caused a painful example of the negative link between losses on the balance sheets of banks, exploding borrowing costs, increases in public debt and a decrease in access to credit. A shrinking economy and vast unemployment were the result. An important factor in the crisis

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was the fact that a large portion of the Spanish banking system was undercapitalised, with few opportunities to find new capital at a reasonable cost.

In response to the financial crisis that had substantially hurt its national banks, in May 2012 Spain committed to provide new capital to banks if they could not raise it privately. The gov-ernment expected that an injection of public capital in the hurting Spanish banks would put the financial markets at ease and relax the leverage constraints of intermediaries, creating more room on balance sheets for loans to the Spanish private sector. However, it quickly became apparent that the expectations of the significant increase in Spanish public debt put upward pressure on the yield on Spanish bonds and drove bond prices down. This effectively prevented the Spanish government from obtaining the necessary funds for the recapitalisation on the financial markets at a acceptable borrowing costs (Reuters, 2012).

In order to address this problem, on June 25 2012 the Spanish government submitted an official request to obtain the necessary funds from the European Financial Stability Facility. This request was approved by the Eurogroup and the responsibility for the financing of the bank rescue programme was transferred to the new European Stability Mechanism in November 2012. The most important aspect of the programme was the recapitalising of banks in need. An independent stress test of the balance sheets of all Spanish banks identified ten banks that were unable to reach a CT1 capital ratio of 6 per cent by the end of 2014 under an adverse scenario. The identified capital shortfalls totalled 56 billion euros. Approximately 70 per cent of these shortfalls were filled by the Spanish government in the first quarter of 2013. The remaining capital shortfalls were addressed by bailing-in junior debt and private capital injections (International Monetary Fund, 2014).

At present day, the Spanish state is controlling owner of a large share of the financial sector

in Spain. As a result of the loans taken from the ESM, the ratio of government debt has

increased with nearly 24 per cent point to 94 per cent of GDP from 2011 to 2013. In comparison, government debt amounted to 36 per cent of GDP before the start of the crisis in 2007 (Eurostat).

6.2 Macroeconomic Developments

6.2.1 Model Predictions

To simulate the recapitalisation that took place in Spain, a capital quality shock of 5 per cent with respect to steady state is introduced to the Spanish calibrated model. As the Spanish financial sector was first hit during late 2010 and GDP took a dive after the first quarter of 2011, I take the beginning of 2010 as the starting point for my simulation. Since the actual recapitalisation of the Spanish banks mainly took place at the start of 2013, I set the recapitalisation to take place after a delay of 8 quarters. One drawback of this method is that in the model, a recap is announced immediately at the time of the capital quality shock, whereas the recapitalisation in Spain was not announced until the spring of 2012. Accounting for this fact, however, would require a significantly more complicated approach. Since 70 per cent of the total costs of the

Sovereign debt and bank fragility in Spain : a calibrated DSGE model