The Domestic and the International E¤ects of Financial Disturbances Fabio Canova, Leonor Coutinho, Caterina Mendicino, Evi Pappa, Maria Teresa Punzi and Domink Supera European University Institute February 11, 2015

Abstract We construct a two country dynamic stochastic general equilibrium model to analyze the domestic and international propagation of disturbances that a¤ect the lending/borrowing capabilities of agents. One country represents the periphery of the Euro area; the other the rest of the Euro area. We show that all disturbances generate important …nancial cycles and deep global recessions, accompanied by a fall in‡ation, in the policy rate, and in house prices. All disturbances signi…cantly a¤ect the balance sheet of the banking system, worsen the external position of the domestic country, and greatly increase domestic government debt. We examine whether prudential regulations may help to reduce the …nancial volatility, the negative real e¤ects and improve welfare.

February 11, 2015 JEL Classi…cation: E32, F41, G21. Key words: Financial shocks, international transmission, prudential policies, welfare analysis.

This research is funded by the European Commission, DG EcFin (tender reference: ECFIN 2013 008/E - OJEU 2013/S112-190350). Comments and suggestions by sta¤ members of DG EcFin are gratefully acknowledged

1

Introduction

The 2008-2009 …nancial crisis and the ensuing European debt crisis have highlighted the importance of accounting for the links between the …nancial sector, the macroeconomy and government debt. Policymakers were unable to understand the factors that led to the twin crises and their consequences because macroeconomic models paid little attention to …nancial variables as originators of shocks. Recent empirical evidence indicates that ignoring …nancial disturbances may induce important distortions in the interpretation of economic ‡uctuations. For example, according to Hubrich et. al., 2013, shocks to Euro area …nancial variables (which include disturbances to real stock prices, to real house prices, to the term spread, to loans, and to banks’ loans-to-deposit ratio) account for about 33% of the forecast error variance decomposition of output at the three year horizon, on average over the last twenty years. In comparison, monetary policy shocks account for about 10% of the forecast error variance decomposition of output at the same horizon and …scal shocks for about 15%. Similarly, Gilchrist, Yankov and Zakrasjek (2009) show that ”…nancial factors” shocks explain about 30 percent of US output and in‡ation ‡uctuations at the two years horizon; while Gilchrist and Zakasjek (2012) show that, consistent with the theories put forward by Bernanke, Gertler and Gilchrist (1999), Gertler and Karadi (2011) and Gertler and Kiyotaki (2010), widening credit spreads are causally associated with a worsening of private agents balance sheets and a drop in real activity. On the other hand, Mian and Su… (2014) show that the so-called ”household net worth channel” is largely responsible for the fall in aggregate employment in the US during the 2007 -2009 period. Thus, abstracting from the …nancial disturbances may overestimate the contribution of, say, productivity or terms of trade shocks, and incorrectly representation of the transmission mechanism of economic ‡uctuations. In addition, closed economy models are likely to give an incomplete view of …nancial shocks, since second round cross-country e¤ects are disregarded.

1.1

The content of this paper

This paper constructs a two-country, large scale, dynamic stochastic general equilibrium (DSGE) model, with interactions between the …nancial sector and the macroeconomy, and cross country linkages via trade and …nancial ‡ows. We examine the domestic and interna2

tional transmission of …nancial disturbances that a¤ect the borrowing and lending abilities of domestic agents and the role that …nancial constraints play in propagating these shocks. We focus attention on four separate issues. First, we want to examine whether …nancial shocks originating in di¤erent sectors of the economy generate di¤erences in terms of depth of the recessions, the persistence of the real e¤ects, and the domestic transmission properties. Second, we wish to highlight the channels through which …nancial disturbances a¤ect foreign real economic activity. Third, we are interested in identifying the structural parameters that may be crucial in determining the dynamics of the endogenous variables. Fourth, we want to study whether prudential policies can reduce the amplitude and the persistence of the …nancial cycle, limit real consequences, and improve welfare.

1.2

A stylized description of the model

In the model there are borrowing and lending households; borrowing entrepreneurs; a vertically integrated sector producing …nal non-durable goods; house producers; retail and investment banks; a …scal authority in each country and a common monetary authority. Domestic lending households deposit their savings in domestic retail banks which use them to lend to domestic borrowing households and to the global interbank market. Domestic investment banks borrow from the interbank market to …nance the activities of domestic borrowing entrepreneurs and to purchase a portfolio of government bonds. House producers augment the stock of houses that households hold; houses provide a service ‡ow and a store of value, and are non-traded across countries. The vertically integrated production sector takes goods produced by entrepreneurs and transform them into bundles of …nal goods, consumed by the household, the government, or used for investment. There is international trade of intermediate goods; …nal goods are non-tradable. The …scal authority …nances a budget de…cit by issuing one period bonds; the monetary authority sets the nominal interest rate as a feedback rule of area wide variables.

1.3

A summary of the results

When calibrated to produce a domestic credit contraction, all shocks produce deep output recessions, accompanied by a signi…cant contraction of private demand; by a fall in house

3

prices and housing demand; by a signi…cant and persistent decline in in‡ation and in banks’ intermediation activities. Furthermore,

the e¤ects are global. Some shocks redistribute

resources between borrowers and lenders; others, redistribute resources across countries leading, after a few periods to an export-led domestic recovery. The sector where the disturbances occur is irrelevant because all shocks contract the lending market. All shocks we analyze are transmitted, domestically, via loans and deposits markets and, internationally, via trade and the interbank market. The changes in loans and deposits rates and houses prices contract the time pro…le of income of households either within a country or across countries and lead to important output adjustments.

All shocks worsen the

short run domestic external position and expands domestic government debt, as the cost of …nancing greatly increases. Furthermore, since sovereign spreads increase, these shocks have implications for public debt management. The qualitative features of the transmission are generally robust. The parameters regulating the …nancial constraints a¤ect …nancial and real cycles di¤erently, but the e¤ects on real ‡uctuations are small. For disturbances originating in the banking sector, the e¤ects of altering crucial parameters are larger but the direction of the changes for real variables depends on the type and the branch of the banking sector where the shock originates. Prudential actions by the monetary authority are as good as cyclical capital bu¤ers in smoothing out the …nancial cycle and in reducing the real e¤ects. However, to understand the consequences that prudential policies have, one needs to know the type of the shock and the sector in which the shock occurs. Prudential policies generally produce a redistribution of the losses across agents within a country or across countries and may lead to interesting political economy trade-o¤s. Given that prudential policies are not generally designed with welfare purposes in mind, our analysis suggests that they should be used in conjunction with redistributive …scal policies (see e.g. Jeanne and Korinek, 2013), if they are to produce Pareto improving allocations along the adjustment path.

1.4

Related literature

Four di¤erent strands of recent literature relate to the work we do. The …rst tries to understand the supply side of the credit market, see e.g. van der Heuvel (2008), Curdia

4

and Woodford (2009), Angeloni and Faia (2009), Brunnermaier and Sannikov (2010), Kiley and Sim (2011), Meh and Moran (2010), Gertler and Karadi (2011), Gertler and Kiyotaki (2010), Jerman and Quadrini (2012), or Williamson (2012). The second explicitly incorporates a banking sector in standard macroeconomic models, see e.g. Gerali et al. (2010) , Dib (2010) and Kollmann et al. (2013). In these models, the presence of balance sheet constraints establishes a link between credit supply and the business cycle. Business cycle ‡uctuations a¤ect banks’ pro…ts and therefore bank capital. In turn, because of capital constraints, changes in bank capital alter the supply and the cost of loans, therefore reinforcing the e¤ects of the original shocks. Within this literature, the paper closest in spirit to what we do is Iacovello (2013).

He studies the e¤ect that shocks

disrupting the ‡ow of funds between di¤erent agents have on the domestic business cycles. A third strand of literature modelled demand for housing to capture the need for longterm …nancing on the part of households, via collateral and value-to-loan constraints, see, among others, Iacoviello and Neri (2010), and Lambertini, Mendicino, and Punzi (2013). The presence of housing markets allows researchers to model waves of optimism regarding house price appreciation, which can lead to excessive leveraging on the part of households (see e.g. Gelain, Lansing, and Mendicino, 2012).Within the literature, Adam, Kuang, and Marcet, (2011); Ferrero, (2012) highlighted the connections between house price appreciation and current account de…cits; and Cao and Le Hullier (2013) that the news-noise confusion about future fundamentals can exacerbate leveraging e¤ects. Most of the models take a closed economy perspective. Those papers who have explicitly modelled credit supply and their disruptions in an international dimension, e.g. Devereux and Yetman (2010) , Mendoza and Quadrini (2010), Kollman, et al. (2011) Guerrieri et al. (2012), Ueda (2013) have borrowing constraints in only one sector of the economy and are not rich enough to study channels of international propagation of shocks. The …nal line of research linked to our papers examines macro-prudential policies. These have been analyzed in models where moral hazard may incentivate banks to engage in investments which are too risky from a social point of view, see e.g. Begenau (2013), Rios Rull, Takamura and Terajima (2013) , Nguyen (2013), Jeanne and Korinek (2013) or where there are pecuniary externalities, see Gersbach and Rochet (2013). Some papers have also

5

addressed the issue of designing capital/ liquidity requirements under …re sales, see e.g. Kara and Ozsoy (2014), and show that the pre -Basel III regulatory framework is inferior in terms of allocations of the joint regulation of capital and liquidity. Our model combine aspects of existing models to study the propagation of …nancial shocks occurring in di¤erent sectors of the domestic economy using general equilibrium and open economy perspective. Contrary to the existing literature we construct a rich setup with trade in goods and …nancial assets, which can be used to answer a number of interesting policy questions. Moreover, we explicitly evaluate the usefulness of prudential policies in stabilizing the economy and improving welfare.

2

The model economy

The model has two countries: the domestic country captures an economy belonging to the Euro area periphery; the foreign country the rest of the Euro area. The two economies di¤er in size (0 < n < 1 is the size of the domestic economy), but they are symmetric in terms of preferences and technologies. Foreign variables are denoted by the superscript . Each country is populated by patient and impatient households, by non-…nancial …rms, and by banks. The government consumes goods and …nances expenditures with taxes and debt. A single central bank setting the policy rate as a feedback rule of the average CPI in‡ation and of the average output in the two economies. We describe the building blocks of the model for the domestic country. Because of symmetry, the foreign block is obtained by adding the superscript

2.1

to the variables.

Households

Households work, consume, buy real estate, and decide on their …nancial position. Patient households, indexed by s 2 [0; ! s n], 0< ! s < 1; have a higher discount rate than impatient households, indexed by b 2 (! s n; n];

s

>

b:

Because of the di¤erent propensity to save,

in the equilibrium we consider, the former save while the latter borrow. Housing is a durable good, non traded internationally, which depreciates over time and its demand depends on both the ‡ow of services it provides and its asset value. Impatient households, which will

6

be credit constrained in equilibrium, collateralize the value of their houses. Household takes prices, the interest rate on deposits and loans, and the nominal wage parametrically. 2.1.1

Patient Households

The representative patient household chooses Cs;t ; consumption, Hs;t ; housing, Ns;t , hours worked, and Ds;t , bank deposits, to maximize her expected lifetime utility: # " 1 1+' 1 1 X H N (C hC ) s;t s;t s;t s;t 1 t n ; max E0 + "ht hs s s 1 1 1+' fCs;t ;Hs;t ;Ns;t ;Ds;t g

(1)

t=0

where "ht is a housing preference shock,

h s

> 0 and

services and hours worked, respectively, 0 < supply;

s

< 1, '

n s

> 0 govern the utility of housing

1

> 0 is the Frish elasticity of labor

> 0 is the coe¢ cient of relative risk aversion and 0

h

1 controls habits in

consumption. The maximization is subject to the sequence of budget constraints: Pt (Cs;t +Ts;t +ACHs ;t )+PtH [Hs;t (1

H ) Hs;t 1 ]+Ds;t

= Rs;t

1 Ds;t 1 +Wt Ns;t +DIVs;t

(2)

where Pt is the price of consumption, Ts;t are real lump-sum taxes, PtH is the price of housing,

H

is the housing depreciation rate, Rs;t

1

is the gross nominal rate on deposits, Wt

is the nominal wage, DIVs;t are nominal dividends from …rms and banks, owned by patient households; and ACHs ;t are real external adjustment costs of changing the housing stock: ACHs ;t =

Hs;t Hs

sHs 2

2

1

Hs

(3)

where Hs is the steady state stock of housing of patient households, and sHs 2.1.2

0.

Impatient Households

The representative impatient household chooses cb;t consumption, Hb;t housing, Nb;t hours worked, Lb;t bank loans to maximize her expected lifetime utility: " 1 X H1 hCb;t 1 )1 t (Cb;t h h b;t max E0 + "t b b 1 1 fCb;t ;Hb;t ;Nb;t ;Lb;t g t=0

N 1+' n b;t b

1+'

#

;

(4)

subject to the sequence of budget constraints: Pt (Cb;t + Tb;t + ACHb ;t ) + PtH (Hb;t

(1

H ) Hb;t 1 ) + Rb;t 1 Lb;t 1

7

Pt "bt = Lb;t + Wt Nb;t (5)

where Rb;t

1

h b

> 0 and

L b

> 0 govern the utility of housing services and hours worked, 0
0 an elasticity parameter. The demand for

composite domestic and foreign output is determined by the minimization of the expenditure needed to produce a given amount of …nal good, subject to (20). The price of the …nal good Pt is given by: Pt 2.3.4

(1

! F ) PtY

1

+ ! F PtY

1

1=(1

)

(21)

International Trade

International trade occurs because retail …rms import composite goods from foreign wholesalers. The demand for imports is given by 11

PtY Pt

YM;i;t = ! F

Zit

Similarly, the demand for domestic products by the foreign retailer i is: YM where Zi

;t

;i ;t

PtY Pt

= !F

Zi

(22)

t

is the output of the foreign …nal goods producer i , 0

! F < 1 and

> 0,

are, respectively, the share of imports and the elasticity of substitution abroad and Pt is the price of the …nal good abroad.

2.4

Production of Houses

Construction …rms, indexed by h 2 [0; n], purchase housing investment goods Ih;t at a price Pt from the domestic retailers and transform them into new housing units,

t

sold at a nominal

price PtH . House production is subject to adjustment costs. Since the representative house producing …rm is owned by patient households, it maximizes the expected discounted value of pro…ts,

h;t

maxE0 fIht g

taking patient household preferences into account

1 X

t s s;t [ h;t ]

(23)

t=0

where: h;t

= PtH

t

Pt Ih;t

(24)

and: t

with

Ht

(1

h )Ht 1

= "It h

S h (Ih;t ; Ih;t

1)

Il;t

(25)

< 1; where "It h is an investment speci…c housing shock. The function S h (Ih;t =Ih;t

1)

represents housing investment adjustment costs and it is given by S h (Ih;t ; Ih;t where sh

1)

=

sh 2

2

Ih;t Ih;t

1

(26)

1

0. Since the production technology features decreasing returns to scale, the

speci…cation we use is equivalent to assuming that the production of houses requires a factor of production, such as land, which is in …xed supply (see Davis and Heathcote, 2005).

12

2.5

Financial Intermediation

The intermediary sector is composed of retail and investment banks. Retail banks lend to borrowing households and provide funds to the global interbank market. Investment banks lend to entrepreneurs and to the government. Retail banks obtain funds from depositors; investment banks borrow funds from the global interbank market. 2.5.1

Retail Banks

Retail banks, indexed by m 2 [0; n], are owned by patient households but run by managers who discount the future more than their stockholders - managers prefer pro…ts today more than the patient household as they do not know if they will continue to manage the bank in the future; for a similar assumption see Rios Rull, Takamura and Terajima (2014). The problem of the representative retail bank is to choose deposits, Dm;t , loans to domestic impatient households, Lm;t , and funds to be lent in the interbank market, IBm;t ;to maximize max

fDm;t ;IBm;t ;Lm;t g m


0. Retail banks incur default

losses because domestic households default or because domestic or foreign investment banks default. "t is a shock a¤ecting …nancial integration -

t

measures the amount of loans

that investment banks obtain from foreign retail banks, see below. Equations (28) and (31) imply that bank capital accumulates as: B B Km;t = Km;t m;t

where 1

1

+ 1

m;t

N Im;t

N Im;t

(32)

N Im;t are retained earnings.

N Im;t

Retail banks face a capital adequacy constraint linking the value of their assets and their net worth, see also Guerrieri, Iacoviello and Minetti (2012), and Iacoviello (2013): B Km;t

where 0

t

B Km;t

1

+ (1

m)

IB t IBm;t

+

Lb t Lm;t

Pt " m t

1 measure the riskiness of various assets in the bank portfolio.

Capital adequacy requirements depend on the risk weight coe¢ cients j t

(33)

1 allows for inertia in the adjustment over time of the capital constraint and

m

IB ; Lb t t

0

m

= 0 asset j is riskless and the higher is

j t,

IB t

and

Lb t .

If

the riskier that asset is for the purposes of

capital adequacy. We allow the valuation coe¢ cients to re‡ect economic conditions:

where

Lb 0

> 0,

Lb 0

Lb t

=

IB t

=

Lb 0

"tm +

IB 0

"tm +

Lb 1 IB 1

Lm;t =GDPt 1 Lm =GDP IBm;t =GDPt 1 IBm =GDP

> 0; "tm is a capital requirement shock; and

(34) (35) Lm and IBm are the

steady-state equilibrium values for household and interbank loans. Thus, the speci…cation we use comprises two important features of the Basel III regulatory system: the risk-weighted assessment of assets, and the cyclicality of capital requirements 1 . 2.5.2

Investment Banks

Investment banks, indexed by f 2 [0; n] ; are also owned by patient households. The manager of the investment banks are also assumed to discount the future more than patient house1

The 2010 Basel III rule requires banks to hold 4.5% of common equity and 6% of Tier I capital of "risk-

weighted assets". The 2011 revision introduces "additional capital bu¤ers": (i) a "mandatory capital conservation bu¤er" of 2.5% and (ii) a "discretionary counter-cyclical bu¤er", which would allow national regulators to require up to another 2.5% of capital during periods of high credit growth (BIS, 2011).

14

holds,

f


1,

EA

(49)

is the (quarterly)

target for gross CPI in‡ation, Y EA is the steady state output and f inEA is the steady state aggregate credit to GDP of the non-…nancial sector. The area-wide variables are de…ned as: EA t

= n

t

+ (1

YtEA = nYt + (1 f inEA = n t

2.8

(1

n)

(50)

t

n) Yt

(51)

! s ) Lb;t + Le;t + (1 Pt GDPt

n)

(1

! s ) Lb;t + Le;t Pt GDPt

(52)

The resource constraints and market clearing conditions

Since agents of the same type choose identical allocations in equilibrium, the aggregate quantity, expressed in domestic per-capita terms, of any home variable @i;t is: 1 @t = n

Zn

@i;t di

(53)

0

The aggregate quantity, expressed in foreign per-capita terms, of any foreign variable @i @t =

1 1

n

1 Z n

@i ;t di

;t

is:

(54)

0

Cross-border variables will be expressed either in home or foreign per-capita terms, as convenient. Per-capita domestic GDP is given by Yt = YD;t +

1

17

n n

YM

;t

(55)

where YM

;t

is measured in foreign per-capita terms. Per-capita domestic demand is: Zt = Ct + Ie;t + Ih;t + Gt

Letting

e;t

be entrepreneurs pro…ts,

(non-retained) pro…ts of retail banks, IBf

;t

be aggregate pro…ts of branding …rms,

z;t

pro…ts from …nal goods producing …rms, f;t

(56)

h;t

be pro…ts of house producing …rms,

i;t

be

m;t

be

be (non-retained) pro…ts of banks and expressing

and Bf;;t in foreign per-capita terms, the market clearing conditions are: Ct = ! s Cs;t + (1

! s ) Cb;t

(57)

Ht = ! s Hs;t + (1

! s ) Hb;t

(58)

Nt = ! s Ns;t + (1

! s ) Nb;t

(59)

It = Ie;t + Ih;t

(60)

Dm;t = ! s Ds;t

(61)

Lm;t = (1

(62)

! s )Lb;t

Lf;t = Le;t

(63)

IBt = IBf;t +

1

n n

IBf

(64)

;t

Bt = Bf;t + Bf ;t 1 n BPt = Bf;t + Bf ;t n DIVt = e;t + z;t + i;t +

(65) (66) h;t

+

m;t

+

f;t

+ Pt ACt = ! s DIVs;t

(67)

Aggregating the economy’s budget constraints and using equation (55) determines the balance of payments identity: T Bt =

1

n Bf;t Rt 1 Bf;t 1 + IBf ;t RtEA1 IBf ;t 1 + t Pt "f n Rt 1 Bf ;t 1 + IBf;t RtEA1 IBf;t 1 + t Pt "f;t Bf

;t

(68)

where the trade balance de…ned as: T Bt

2.9

1

n n

PtY YM

;t

PtY YM;t

(69)

Sources of Fluctuations

The model features many sources of traditional demand and supply shocks (productivity, "z , housing demand, "h , government expenditure, "g , tax shock, 18

;two investment speci…c,

"Ik , "Ih ; and monetary policy,

R ;disturbances)

which can be ampli…ed via the …nancial

constraints in the standard way and will not be considered here. Instead, we focus attention on three default shocks (one for impatient households, "b , one for entrepreneurs, "e , and one for investment banks, "f ), on three valuation shocks (one for impatient households, "ib , one for entrepreneurs, "ie ; and one for investment banks, "if ), on the capital requirement shock "im and the …nancial integration shock " : The process for these seven shocks is assumed to be an AR(1) with either common or independent disturbances, see below. The optimality conditions of the model and the strategy adopted to solve the model are in appendix A.

2.10

Discussion

A number features of our model economy deserve some discussion. First, the vertically integrated production structure, which transforms investment goods into …nal good in various layers, is chosen to separate the pricing problem from the trade and aggregation problem, see Dib, 2008, Bouakez, Cardia, and Ruge-Murcia, 2009, Resende, Dib and Kichian, 2010, and Dib, Mendicino and Zhang, 2013 for similar setups. Second, while loans are not a direct argument of the production functions, the volume of loans is an important determinant of production in our model. Since output is demand driven and since impatient household and entrepreneurs face binding borrowing constraints, the volume of banks loans indirectly a¤ects aggregate demand and output. Third, while the model features default shocks, there is no default, in the sense that borrowers renege on their obligations in certain states of nature. Banks su¤er ”haircuts’ when default shocks occur and take this possibility into account in their lending strategies. Thus, while the model does not capture a scenario where a series of negative income shocks make borrowers unable to repay their debt, it can mimic a situation where lenders are forced to accept less than what is contractually agreed, possibly, to avoid a disorderly default process. Notice that default shocks enter the collateral constraints since banks observe default shocks and form expectations. If banks do not foresee these shocks, loans will be instantaneously contracted only to the extent that default shocks indirectly a¤ect the value of the collateral through interest rates and prices .

19

Fourth, the model features an interbank market between (lending) retail banks and (borrowing) investment banks. This market exists not because di¤erent types of banks have di¤erent investment opportunities (see e.g. Zhang, 2014) , there are maturity mismatch between assets and liabilities, or liquidity issues in the balance sheet of banks, but because the lending market is segmented - di¤erent banks specialize in di¤erent types of loans. Notice that the interbank market resembles a repo market: at the beginning of each period retail banks lend part of the deposits to investment banks and they receive collateral assets that the investment banks purchase with the funds (Government bonds or entrepreneurs loans). Thus, investment banks in the model behave like real world shadow banks: they do not collect deposits but purchase funds from other banks and then lend to the private sector. Note that the interbank market is global, competitive, clears at the area wide interest rate and never shuts down: shocks a¤ect the amount of funds intermediated, but they will never cause the market to stop functioning. Fifth, the capital adequacy constraint on retail banks is equivalent to a borrowing constraint. In fact, using the de…nition of bank capital, the capital constraint can be equivalently written as a constraint on deposits: Dm;t

t Dm;t 1

m m

+ (IBm;t + Lm;t )

t (IBm;t 1

+ Lm;t

(1

m)

IB t IBm;t

+

Lb t Lm;t

1)

Pt "m;t (70)

The model features two types of domestic …nancial-real linkages:

one endogenous

and one exogenous. The endogenous mechanism is due to the fact that traditional demand and supply shocks a¤ect the …nancial constraints by changing the value of the collateral pledged by borrowers - this is the standard …nancial accelerator mechanism of Bernanke, Gertler and Gilchrist (1999). For example, a contractionary monetary policy shock, increases in the nominal interest rate and makes production fall. However, since it reduces the value of the collateral, the amount of loans to the private sector falls, and this further contracts economic activity amplifying the initial e¤ect the shock. Exogenous sources of linkages instead come from …nancial shocks. Default and valuation disturbances alter the willingness of banks to grant loans, for a given value of the collateral they receive. These shocks may have real consequences because, when the assets of the banking sector decrease, it becomes more di¢ cult to produce or buy 20

houses - the …nancial frictions becomes tighter - and since aggregate demand contracts, the real economy shrinks as well. Capital requirement shocks, on the other hand, change the supply of loans for a given value of bank assets. Finally, integration shocks change the composition of interbank loans, alter the amount of loans entrepreneurs of both countries receive and thus a¤ect demand and production. Because the …nancial shocks we consider redistribute wealth either between lenders and borrowers or across countries, they may a¤ect the composition of demand and produce additional real adjustments. Since the two economies are open, one should expect …nancial shocks to generate international repercussions. Given that our economy features both trade and …nancial ‡ows, idiosyncratic domestic disturbances may be

transmitted via demand for goods and via

interbank transactions. One interesting question is which channel is more important and whether foreign quantities or prices respond most to the disturbances.

3

Parameter selection

The parameter values used in the exercises are in table 1. Most of the values are standard, see e.g.

the capital depreciation rates, the risk aversion coe¢ cient, the external habit

parameter, the adjustment cost parameters, etc.. Some of the parameters are selected to give realistic starting values for the dynamic exercises: thus, for example, we chose the steady state government debt to output ratio to be 0.9, the size of the periphery to be 0.2, and the steady state nominal interest rate to be 2 per cent. Parameters speci…c to the class of models featuring patient and impatient households are set in line with what the previous literature has used (see e.g. Lambertini, Mendicino and Punzi, 2013) or estimated (see e.g. Iacoviello and Neri, 2010). The parameters regulating the …nancial constraints of di¤erent agents are selected using two criteria: the speed of adjustment is chosen to produce duration of responses that match what other work has assumed (see In’t Veld et al., 2011, or Kollman, Enders and Mueller, 2011); the valuation parameters re‡ect perceptions of the relatively riskiness of various assets. Since several …nancial parameters are not pinned down by these two criteria, we use our judgment to select them and present sensitivity analysis to robustify the conclusions. Finally, the parameters of the law of motion of the shocks, the adjustment costs parameters for deposits and 21

loans, and the price stickiness parameter are selected to obtain particular response path of certain variables - see the next section for details. To make sure that the model produces a realistic setup, we have computed the steady states of the endogenous variables. A sample of the value obtained for the domestic variables is in Table 2. On average, the domestic consumption is about 79 percent, investment in equipment is about 10 percent, loans are about 66 percent and imports are about 50 percent of output. In comparison, in the periphery of the Euro area (Portugal, Ireland, Italy, Spain and Cyprus) over the period 1980-2013, the average consumption to output ratio is between 70 and 84 percent; the (total) investment to output ratio is between 9 and 17 percent; the loans to GDP ratio is between 0.62 and 0.80 percent; the average import to GDP ratio is between 25 and 51 per cent. The capital-output ratio is close to the average capital-output ratio in the Euro area (4.5). Patient households own, on average, almost twice as much housing as impatient households - housing is an investment good for patient households. In the model, corporate loans are about half of mortgage loans as a percentage of GDP. In the data this ratio varies a lot: in Portugal, Spain and Ireland it is between 50 and 80 percent; in Italy about 130 percent. Since deposits are roughly as large as output in the steady states, the steady state loans to deposits ratio is two-thirds, which is close to the average in the Euro area periphery in the 1980s but considerably below the value in the 2000’s - in this period, the ratio is 0.9 in Portugal and 1.4 in Italy. To check that our calibration also produces reasonable cyclical ‡uctuations, we set the persistence of all autoregressive shocks to 0.9 and all the standard deviations to 1.0 and compute second moments of the endogenous variables. Table 3 present the results when the economy is simultaneously hit by the three default shocks ("b , "e ,"f ), the three valuation shocks ("ib , "ie , "if ), the capital requirement shock "im , the …nancial integration shock " ; the productivity "z shocks and the …ve demand shocks ("h , "g , "Ik , "Ih ;

m ).

In the model, consumption and house holdings have low relative standard deviations, while investments, mortgage and commercial loans ‡uctuate more than output.

In the

cross section of peripheral Euro area countries, house holdings is less volatile than output (around 0.5), consumption is roughly as volatile as output (the range is 0.8-1.1), investment is more volatile than output (the range 4.0- 11.5) as are mortgage and commercial loans

22

(range 1.8-4.9). Two features of the model ‡uctuations are somewhat inconsistent with the data: in‡ation is less volatile than output in the model, but roughly as volatile as output in the data (range 0.8-1.3); hours are less volatile than output in the model; in the data, this relative volatility varies (range 0.65,- 1.8). Reporting and to measurement errors may account for the di¤erences. Hours and in‡ation are the variables with the lowest persistence, followed by investment and output; all other variables have a …rst order autoregressive coe¢ cient of at least 0.9. Notice that house holdings of patient and impatient households have di¤erent persistences, because the latter type of households face a borrowing constraint. In the cross section of peripheral Euro area countries we …nd that hours is indeed not very persistent (range 0.1-0.6) but that in‡ation is somewhat more persistent than in the model (range 0.75-0.85). The persistence of investment and output are country speci…c and range from 0.5-0.8. Finally, in accordance with the predictions of the model, the persistence of …nancial variables and house prices is high and generally larger than 0.9. The model also predicts that domestic output is positively correlated with the amount of housing held by patient households, with lending to the entrepreneurs, and with in‡ation. In turn, (CPI) in‡ation is positively correlated with the amount of housing held by patient households. The nominal interest rate is also positively correlated with the amount of housing held by both households, with output and in‡ation. Finally, lending to entrepreneurs is positively correlated with lending to the households. These patterns are also found in peripheral Euro area countries.

4

Dynamic analysis

In this section we describe the dynamics induced by …nancial disturbances, examine di¤erences that shocks to di¤erent sectors produce, and provide some evidence on how crucial parameters a¤ect the responses of key macroeconomic variables.

4.1

Default shocks

The dynamics induced by the three default shocks in …gures 1-4. Recall that a household default shock unexpectedly transfers resources from the retail bank sector (and thus from 23

the patient households who own them) to impatient households; an entrepreneur default shock transfers resources from the investment bank sector to the entrepreneur sector, both of which are owned by patient households; and a investment bank default shock redistribute resources within the banking sector. Household (entrepreneur) default shocks are calibrated to produce a large and persistent fall in domestic household (commercial) loans to GDP ratio - 10 percent from the steady state after one year and around 5 percent of the steady state value up to 5 years. The investment bank default shock is instead calibrated so that, on impact, retail bank capital falls by 5 percent from the steady state value - its dynamic path is left unrestricted. Default shocks are globally recessionary: they contract aggregate demand, production and in‡ation in both countries; a signi…cant reduction in the intermediation activities of banks; and a decline in house prices and house constructions. Moreover, the central bank interest rate persistently declines. Default shocks a¤ect the pro…ts of the banking sector, which responds by contracting loans. Since pro…ts fall, patient households income also falls. Thus, to limit the reduction in the current level of consumption and housing, they reduce deposits, leading to a contraction of the domestic intermediation activities. As mentioned, with household default shock, there is a redistribution of wealth from patient and impatient households which is absent when the default shock occurs in the other two sectors. However, the unexpected income windfall is more than compensated by the increase in the borrowing rate and by the fall in the value of their housing assets. Thus, in all cases, impatient households demand falls. Since the demand for goods by both types of households fall, and since investment demand also falls, aggregate demand declines. Output, which is demand determined, falls as well, leading to a fall in hours worked and real wages. Furthermore, since the marginal cost of production falls, in‡ation declines as well.

The policy rate then fall because both area wide output and area

wide in‡ation fall and the decrease is more pronounced with bank default shocks. International transmission occurs via trade and the interbank market. With household default shocks, domestic retail banks have extra funds (deposits fall less than household loans) and they channel them to the interbank market. However, foreign investment banks do not take immediate advantage of the increase volume of interbank transactions

24

because the fall in domestic imports induces a fall in foreign production of intermediate goods. This leads to a reduction in the loans demanded by foreign entrepreneurs, in foreign aggregate demand, and output. With the other two default shocks the volume of transactions in the interbank markets falls. Thus, foreign investment banks contract loans to foreign entrepreneurs. This contraction further reduces foreign aggregate demand, leading to lower output and in‡ation. In response to default shocks domestic and foreign real asset rates increase on impact. The exception are foreign rates when household default shocks occur since the volume of transactions in the interbank market increases. Four additional features of the simulations are worth discussing. First, while default shocks induce persistent adjustments in …nancial variables, they produce short lived recessions and only consumption is persistently a¤ected. Real adjustments are short lived because the …nancial accelerator is relatively weak. In fact, the price of assets used as collateral do not respond strongly and persistently to the shocks. Second, the magnitude of the adjustments in the real exchange rate (RER) is small. Responses are negligible because the RER is determined by technological conditions which are una¤ected by the shocks. Intuitively, the aggregate demand in the two countries moves in the same way. Thus, the prices of domestic and foreign consumption, which move one to one with the price of aggregate demand, are similarly a¤ected. Third, in response to household default shocks, domestic investment and import increase after a few periods. This occurs because our simulations produce a small medium term increase in foreign output, which is accompanied by an increase in foreign hours worked, foreign investment and foreign demand for domestically produced goods which is accommodated by increasing domestic investments and production. Thus, after an initial contraction, an export led recovery materializes in the domestic economy. Fourth, the dynamics of loans and deposits deserves some attention. All domestic default shocks imply a substantial and persistent contraction of lending activities abroad making the credit crunch global. The dynamics of deposits are instead shock speci…c: they instantaneously decline with household and entrepreneurs default disturbances, because the income of patient households is negatively a¤ected.

They instead increase, both

domestically and abroad, after bank default shocks because the volume transacted in the

25

interbank market falls substantially. Thus, foreign banks adjust their balance sheet by o¤ering higher rates on deposits. Because the return on comparable assets move together, the domestic deposit rate also increases, leading patient households to save more. Default shocks produce important sectorial changes. Consumption of both types of households in both countries falls and household default shocks produce the most persistent consumption responses because patient households ’ income is more strongly a¤ected. However, the dynamics house holdings of patient and impatient households di¤er. Recall that impatient households are on a corner solution. Thus, whenever the constraint is relaxed, as in the case of household default shocks, they will buy more houses. The housing demand by patient households instead depends on their income. Thus, when income falls, their demand for houses also falls.

4.2

Private valuation shocks

We calibrate valuation shocks to generate a 10 percent decline in household (commercial) loans to GDP ratios from its steady state after one year and to remain persistently below the steady state by 5 percent up to …ve years. Since we interpret valuation shocks as re‡ecting lenders’perceptions about the value of the collateral, we report simulations when household and entrepreneurs valuation shocks are perfectly correlated and name them in …gures 5–8 ”risk perception” shocks. Risk perception shocks also produce a global recession, a fall in aggregate demand, hours worked and real wages, both in the domestic and in the foreign economy; a signi…cant decline in house prices and house demand, a fall in the area wide in‡ation and in the central bank policy rate. The adjustments produced by risk perception shocks are similar to those induced by impatient households and entrepreneurs’default shocks. Since these disturbances alter the perceived value of the collateral posted by borrowers, domestic loans will be reduced. The contraction of credit makes entrepreneurs and banks pro…t decline. Hence patient households have less pro…t income and shift resources away from deposits and housing in order to smooth the e¤ects of the disturbances on consumption. Impatient households, who face a credit crunch, …nd themselves with lower income. Thus, domestic aggregate

26

demand output, hours worked, real wage and in‡ation all fall. The international transmission occurs, also in this case, via goods and interbank markets: since the volume of the interbank market increases, more funds are available to foreign banks. However, since domestic imports fall a lot, foreign production instantaneous contracts. With a lag foreign commercial loans and foreign deposits increase - the latter following an increase in the deposit rate - and the increase in credit produces a positive a small expansion in foreign activity which increases foreign demand for domestic goods and thus domestic investment and output. Hence, the model predicts that risk perception shocks will also generate a medium term export-led domestic recovery. The recovery will be weaker because the contraction of domestic credit is smaller. The positive foreign e¤ects are driven by the fact that …nancial resources are shifted from the domestic to the foreign economy, as retail banks alter the composition of their portfolio of loans. A shift of …nancial resources from the periphery and to the core of the Euro area did occur during the recent credit crunch, but a global credit crunch also impaired the functioning of the interbank market. Because the interbank market can not be exogenously shut down in the model, we can only conjecture that the foreign expansion will be made weaker in this situation. Note that there are two reasons for why, after the initial fall, domestic investments quickly recover. On one hand, global demand channel produces an export-led increase. On the other, the return to domestic capital declines on impact but then immediately increases and converges to the steady state from above. This capital e¤ect reinforces the export-led demand push on domestic investments. With risk perception shocks domestic and foreign asset rates have di¤erent adjustments: domestic rates all increase, while foreign rates all fall, at least instantaneously, as …nancial resources move to the foreign economy. The central bank real rate instantaneously falls, as both area wide output and in‡ation fall, and persistently stays below the steady state because of the persistent fall in area wide in‡ation. Risk perception shocks redistribute resources across domestic households. Consumption of both patient and impatient households falls, both at home and abroad, since the income of both types of households contracts. However, while patient households reduce their holdings of houses and their hours worked, borrowers increase their holdings of houses and

27

their labor supply. The di¤erence is due to the fact that both the deposit and the loan rate increase. Thus, patient households increase their deposits and their leisure. Impatient household which are constrained in equilibrium, smooth utility variations by increasing their labor supply and buying housing, which has both a ‡ow and a stock value.

4.3

Capital requirement shocks

Valuation shocks may also a¤ect the banking sector. Given the equivalence between a borrowing and a capital requirement constraint, we chose to make banks valuation shocks perfectly correlated and call them capital requirement shocks. To mimic a real world scenario, we calibrated them so that, in both cases, the retail bank capital increases by 5 percent instantaneously and by about 30 percent after …ve years. Since capital requirement shocks tighten …nancial constraints, one should expect them to produce dynamics which are similar to those produced by risk perception shocks: risk perception shocks negatively a¤ect the value of the collateral; capital requirement shocks a¤ect the willingness of banks to lend, given a level of riskiness of collateralized assets. Indeed, the responses in …gures 5-8 con…rm this intuition. A domestic capital requirement shock generates

a global recession, a fall of aggregate demand, in‡ation, hours worked and

real wages in both countries and, in agreement with the evidence Wieladek (2014) has collected in the UK, a contraction in private sector credit. The recession, as with the other …nancial shocks, is relatively short lived. Relatively speaking domestic credit and real wages fall less than with risk perception shocks, but the e¤ects on output, investment, imports, exports, hours worked, lending and policy rates are larger, at least on impact because the cost of production is larger along the adjustment path following capital requirement shocks - real wages fall less and borrowing costs are higher. Thus, hire less labor making the fall in aggregate demand larger. After the initial negative impact, the foreign country experiences a small expansion and, as with risk perception shocks, the domestic economy recovers because foreign demand for domestically produced goods increases. Relatively speaking the expansionary e¤ect are smaller than with risk perception shocks. One variable reacts di¤erently from the case of risk perception shocks and thus may

28

allow us to empirically distinguish the two types of shocks.

Since

banks do not

raise new equities, capital requirement shocks have to be accommodated by changing the assets or the liabilities side of banks’ balance sheet. Figures 5-8 suggests that to obtain more funds, retail bank increase the domestic deposit rate and patient households respond by increasing deposits, rather than decreasing them as with risk perception shocks. The increase in expected future wealth makes patient households better o¤ and the fall in the consumption along the adjustment path is smaller than with risk perception shocks. Since domestic retail banks lend less to the private sector and have more deposits, volume of interbank transaction increases. However, because foreign loan rates increase and the demand for foreign goods fall, foreign credit and output decrease. The dynamics of house holdings by di¤erent types of consumers changes relative to risk perception shocks.

Since the deposit rate increases, patient household temporarily

increase their holdings of houses. Impatient households have to bear higher borrowing costs. This negative wealth e¤ect makes them persistently cut their house holdings. 4.3.1

Sensitivity to parameters

One should expect the magnitude of the …nancial ‡uctuations and of the real transmission to depend on some structural parameters we have judgementally chosen. In this subsection, we examine how the dynamics of domestic mortgage and commercial loans, output, consumption, investment, export and in‡ation in response to the shocks change when i) we increase the size of the domestic country (n moves from 0.2 to 0.4); ii) we decrease the level of …nancial integration ( moves from 0.35 to 0.05); iii) we lower asset valuation in the LTV constraints by half (

b 0

moves from 0.7 to 0.35 and

e 0

from 0.37 to 0.175); iv) we decrease the speed of

adjustment in the LTV and capital constraints by half ( to 0.375;

B

from 0.75 to 0.375,

banks 50 percent tighter (

L 0

e

m

goes from 0.9 to 0.45;

f

from 0.75

from 0.6 to 0.3); v) we make capital requirements for retail

goes from 0.1 to 0.015 and

IB 0

from 0.01 to 0.015) and the LTV

constraint of investment banks 50 percent looser (decreasing

e 0

from 0.5 to 0.25) - the latter

implies a 50 percent increase in the capital requirement of investment banks; vi) we change the share of borrowing households (1 ! goes from 0.3 to 0.5); vii) the decrease the import share (! F goes from 0.5 to 0.3). Intuitively, the size of the country and the level of

29

…nancial integration could a¤ect the transmission across countries and the cross country distribution of the costs. Changes in the parameters regulating the …nancial frictions may a¤ect the magnitude and, to some extent, the persistence of the real responses. Changes in the speed of adjustment, on the other hand, may alter the time pro…le of default costs. Finally, the size and the connection of the two economies may also matter. When the domestic economy is larger or more connected, output, exports and in‡ation should fall much less, while risk sharing opportunities and consumption could be more a¤ected. Figures B1-B8 in the appendix report the original responses and the responses obtained with the new parameter values. Overall, the responses our simulations produce are robust and changing, for example, the LTV parameters for households and entrepreneurs or the capital requirements of banks have minor real e¤ects with default shocks. The sign of the responses changes at times with bank default shocks: mortgage loans, consumption and investments increase when the domestic economy is larger; mortgages and commercial loans and in‡ation increase when the speed of adjustment is low. The change in sign is due to the fact that the foreign economy is more negatively a¤ected by the shocks when the domestic economy is larger.

On the other hand, faster deleveraging implies larger negative real changes but

smaller e¤ects on the balance sheet of the intermediaries. Finally, changes in the persistence of the LTV constraints of households and entrepreneurs, on the other hand, have negligible e¤ects on the dynamics of real variables and in‡ation. The magnitude of responses to risk perception shocks is also very robust and only consumption is a¤ected. This occurs, for example, when the size of the country and the level of …nancial integration change because the amount of international risk sharing available to households changes and domestic consumption is less negatively a¤ected by the shocks when the size of the country and …nancial integration are higher. The speed of deleveraging seems matter for the responses to risk perception shocks: faster deleveraging of retail banks produces a bene…cial e¤ect on domestic consumption, investments and output;

faster deleveraging for households and entrepreneurs makes

domestic consumption, investments and output decrease more. The reason is that in the latter case the volume of intermediation of the economy is negatively a¤ected and lower domestic loans lead to lower domestic output,

30

consumption and investments.

The dynamics following capital requirement shocks are more a¤ected by the choice of parameters regulating …nancial frictions. For example, a lower LTV for households and entrepreneurs makes the economy contract less in response to the capital requirement shock and, with higher capital requirement parameters, capital requirements shocks induce larger …nancial cycles and deeper recessions.

A faster speed of deleveraging, on the

other, does not a¤ect output or in‡ation; but mortgage and commercial loans fall more instantaneously. Finally, the faster is the deleveraging speed in the banking sector, the more negative are the dynamics of consumption in response to capital requirement shocks. The share of borrowing households has little in‡uence on the shape and the persistence of the responses to the …ve shocks. The only variables a¤ected are aggregate consumption , which falls more on impact with household default, risk perception and capital requirement shocks; and commercial loans, which fall more on impact with household default and capital requirement shocks. When the share of borrowing households is larger the e¤ects of household default and capital requirement shocks on total loans and bank pro…ts are larger and this penalizes lending households, which have to share larger losses over a reduced number of units. With risk perception shocks total loans are hardly a¤ected but output falls slightly more on impact, making aggregate consumption fall more. The import share, on the other hand, a¤ects the magnitude but not the direction of the adjustments of loans in response to the shocks and, for most disturbances, the lower the import share is, the larger is the e¤ect. Real variables are a¤ected but it is primarily the magnitude of the consumption responses which is altered because a lower import share makes the economy more autharkic.

4.4

What happens to the current account and to government debt?

All the shocks we have considered induce considerable …nancial market volatility and important adjustments in real variables. One may guess that these disturbances also have implications for the external position of the domestic country and that they may alter the ability of the governments to …nance their debt. Indeed, all shocks instantaneously worsen the external position of the domestic country the current account to GDP ratio falls, and in some cases by quite a lot. However, the medium

31

term consequences for the external position depend on the type of shock and the sector where the disturbance occurs. For instance, household and entrepreneur default shocks lead to medium term current account surpluses; with bank default or capital requirements shocks the adjustments are insu¢ cient to close the current account gap. All disturbances increase domestic government debt, both instantaneously and in the medium run, as the cost of …nancing greatly increases. The yield on government bonds increases because there are arbitrage conditions among di¤erent assets that must hold in equilibrium. Thus, the dynamics of government yields must follow the dynamics of domestic loans rates, regardless of who holds government bonds in the model. The foreign government is also negatively a¤ected, as the cost of …nancing increases with four of the …ve shocks - the model does not feature ”safe-heavens” e¤ects that could counteract the increase in foreign bond yields. Thus, while all …nancial disturbances widen sovereign spreads, impatient household default shocks can generate both large spreads and large imbalances in the government debt position, which may require strong public deleveraging, either through a stronger feedbacks from government debt to taxes or through exogenous changes in the …scal rule, to make the debt sustainable. In both cases, second round adjustments may make the real consequences of …nancial shocks more severe. Because in the baseline scenario, taxes respond to debt to GDP ratio with a small elasticity (t1 = 0:01), we have also studied what happens if the …scal authority is more aggressive in bringing the debt to GDP back to its steady state (t1 = 0.15). Qualitatively speaking, the di¤erences with the baseline simulations are small. Quantitatively, the e¤ects are larger on impact since higher taxes means lower output.

4.5

Summary

Our simulations show that all …nancial shocks can produce a deep output recession, a signi…cant contraction of private demand, drops in house prices and housing demand, a large fall in in‡ation, and a considerable reduction of the amount of intermediation activities of domestic banks.

Gilchrist,

Yankov and Zakrasjek (2009) showed that these dynamics

occurred in the US in response to what they call ”credit spread” disturbance - a shock which makes the banking sector less willing to lend because its balance sheet situation

32

deteriorates. However, the model does produce enough persistence in real adjustments: the dynamics of the price of capital, which weaken the …nancial accelerator mechanism, and the international redistribution of resources which lead to an export-led recovery with some shocks, drive the result. Financial shocks spread internationally generating global recessions and both the goods and the interbank markets are responsible for transmitting the shocks to the foreign economy.

All shocks also lead to deterioration of the external

position of the domestic economy, of domestic government …nances and spreads. Household default, risk perception and capital requirement shocks have domestic distributional e¤ects because the alter the relative income of patient and impatient households. Furthermore, these shocks also lead to an international redistribution of resources. In general, the goods and the interbank markets are responsible for the international transmission and both prices and quantities adjust to absorb the shocks. The qualitative features of the transmission that …nancial shocks generate are robust. Quantitatively, the value of parameters regulating the …nancial frictions, the size of the economy and the …nancial integration, the import share and the share of borrowing households have some important repercussions only with capital requirement shocks.

5

Prudential policies

The …nancial shocks we consider produce persistent adjustments in …nancial markets and important e¤ects on production, demand and in‡ation. Furthermore, they force households to adjust their house holdings and, in the case of patient households, their deposits holdings with important contractionary e¤ects on house prices and the volume of banking intermediation. In this section we examine to what extent prudential policies alter the dynamics in response to shocks. We are interested in whether they can help to dampen …nancial ‡uctuations and reduce their persistence (see Lambertini et. al, 2013); and whether they can shield real variables from the negative e¤ects of …nancial shocks. The model features a number of prudential tools: we focus on two which have received attention in the literature. The …rst policy we consider is a direct targeting of credit aggregates in the monetary rule. Such a policy has been advocated, for example by Borio (2003), as a tool to lean against credit and house price bubbles; see also Repullo and Saurina (2011) and Gersbach and 33

Rochet (2013). Credit may enter the monetary rule when the monetary authority wishes to minimize the variability of output, of in‡ation, and of credit to GDP ratio. Figure 28 presents the dynamics of a selected number of …nancial and macroeconomic variables in response to the …ve shocks when the central bank (i) only targets output and in‡ation ‡uctuations; and (ii) when the aggregate credit to GDP ratio in deviation from its steady state value enters the rule with the coe¢ cient

f in

= 0:5:

The second policy we consider is a countercyclical capital requirement on banks (see Galati and Moessner, 2011). As discussed in section 3, the coe¢ cients regulating the capital adequacy requirement and the borrowing constraints of banks may depend on cyclical conditions. The policy we consider takes into account that excessive credit expansion may lead to higher risks. Thus, in equations(34)-(42)- we set

Le 1

= 1 and

Lb 1

= 2 so that a

one percent expansion in the loans to GDP from its steady state leads to a 100 (or 200) basis point increase in the riskiness valuation of private loans. Figures 29 and 30 report the dynamics of selected real and …nancial variables induced by the …ve shocks in the baseline scenario and when either

Le 1

or

Lb 1 are

di¤erent from zero.

Targeting credit aggregates matters for …nancial volatility in the case of entrepreneurs default shocks and of risk perception shocks. Since, the fall in private loans is somewhat reduced. Also, while the magnitude of the instantaneous output fall is broadly unchanged, the length of the recession is reduced by half and this makes consumption responses fall by much less than in the baseline case. The output loss is uniformly smaller than in the baseline case because domestic investments and exports quickly pick up after the initial fall. In turn, the superior performance of investments is due to the fact that the nominal interest rate falls substantially more than in the baseline scenario. Notice also that with these two shocks in‡ation persistently declines up to 10 years. Thus, our model predicts that de‡ation dynamics may prevail when entrepreneurs default and risk perception shocks hit the domestic economy and the central bank aggressively adjusts the policy rate to the credit to GDP ratio. With the other shocks, targeting credit aggregates has minor e¤ects on both output and in‡ation, some smoothing e¤ect on commercial loans and, depending on the shocks, either favorable or unfavorable e¤ects on domestic consumption. Hence, the stabilizing properties of the policy crucially depend on the type

34

of shock driving the dynamics of the credit to GDP ratio away from its steady state. Absent such an information, targeting credit aggregates may help to stabilize the …nancial cycle, but may not reduce the negative real consequences of …nancial shocks. Prudential capital bu¤ers have relatively limited stabilization e¤ects. For example, capital bu¤ers on retail banks reduce somewhat …nancial ‡uctuations but, quantitatively speaking, the e¤ect is small. As a consequence, the deepness and the persistence of the output recession, and the dynamics of in‡ation are almost unchanged, except perhaps in the case of risk perception shocks. Cyclical capital bu¤er policies are bene…cial in this case because the negative consequences these disturbances have on the risk valuation coe¢ cients are reduced making the initial negative response of investments and exports smaller. However, because redistribution e¤ects are magni…ed, the negative response of aggregate consumption becomes larger. Cyclical requirements on investment banks help to attenuate the …nancial cycle and the output recession in the case of entrepreneur default shocks and of risk perception shocks because domestic investments and exports fall less. Thus, the adjustment path of consumption is above the one obtained when no policy is implemented and, instantaneously, in‡ation falls less than in the baseline scenario. However, the policy leaves the dynamics of real variables and in‡ation unchanged with the other shocks.

6

Welfare analysis

The …nancial shocks we consider do not only have aggregate real consequences; they generally produce a redistribution of wealth between households either within one or across countries and this redistribution may have important welfare implications. In this section we ask (i) which shock induces the largest (smallest) welfare losses and which type of household or which country is most a¤ected; (ii) whether prudential policies help to contain welfare losses; and, if this is the case, which policy is preferable. We calculate the welfare e¤ects of shocks as follows. For each type of household we compute the conditional expectation of lifetime utility: "1 # X t Vjt max Et j U (Cj;t ; Hj;t ; Nj;t j"t ) t=0

35

(71)

where Vjt = fVst ; Vbt g is the welfare of patient and impatient households and "t is a generic shock. Welfare for each country is: W elft

[! s Vst + (1

! s )Vbt ] ;

(72)

n)W elft ] ;

(73)

where ! s is the share of savers. Global welfare is: W elftg

[nW elft + (1

where n is the size of the domestic economy. Table 4 presents the welfare measures we construct, conditional on each of the …ve shocks. In the …rst panel we report the welfare level in the baseline case with no prudential policies; in the second and the third panels welfare changes when the monetary authority targets credit aggregates or when cyclical capital bu¤ers are imposed on both retail and investment banks. Household default shocks produce the worst and bank default shocks the best global welfare outcomes. However, the distribution of welfare losses is not homogenous across countries: for the domestic economy, losses are minimized with household default shocks; for the foreign economy losses are minimal with bank default shocks. This happens because a large portion of the credit contraction costs are passed to the foreign economy with the …rst disturbance but not with the second. In particular,

domestic household default

shocks a¤ect foreign savers a lot; domestic bank default shocks leave them less a¤ected. Welfare losses for borrowers are similar across shocks:

the worst possible outcome

obtains with capital requirement shocks since borrowers of both countries experiences falls in consumption and housing and increases in hours worked. Overall, household default, bank default, and capital requirement shocks produce redistribution of wealth either between savers across countries or between borrowers and savers within a country, and the losses they produce are large compared to other shocks. Prudential policies generally improve global welfare. This always true for cyclical capital requirement; for targeting credit aggregates it is true, except with bank default shocks. Welfare falls in this case because foreign savers losses are large compared with bene…ts the policy produces. Quantitatively speaking, the gains obtained targeting credit aggregates are larger than those obtained with cyclical capital requirement because both countries bene…t. Within a country, savers are better o¤ when the fall in the central bank 36

rate is large, while borrowers losses are more insensitive to the fall in the central bank rate. An exception is with household default shocks: here targeting credit aggregates redistributes resources across countries, making domestic agents worse o¤. While targeting monetary aggregates produce a redistribution of wealth between borrowers and lenders in each country, capital requirement policies produce a redistribution of wealth across countries bene…ting the foreign economy for all shocks - welfare of both foreign lenders and borrowers improves. Capital requirements reduce the transmission of shocks via the interbank market, limit the foreign costs and force the domestic economy to bear the adjustment costs. An exception occurs with household default shocks: here cyclical capital requirement shocks make domestic savers much worse o¤, while domestic borrowers, foreign savers and foreign borrowers welfare improves. Overall, while no policy alters allocations in such a way to improve utility of all agents in both countries, targeting monetary aggregates lead to the largest global gains. Thus, if the policy is employed in conjunction with say, redistributive …scal policies, improvements for all agents could be achieved. Our analysis shows that prudential policies have important political economy implications: while foreign households always prefer capital requirements relative to inaction, domestic households are generally worse o¤ with such a policy. Similarly, the gains from prudential policies are not distributed between patient and impatient households. In general, the share of borrowing households and the size of the country experiencing the shocks are going to be important to determine whether area wide prudential policies will receive popular support or not.

7

Conclusions and extensions

We use a two-country dynamic model with international trade and international …nancial ‡ows, to examine how shocks a¤ecting the borrowing and lending capabilities of agents are transmitted within and across countries. We also study how relevant parameters a¤ect the propagating of these shocks and evaluate whether prudential policies reduce the magnitude and the persistence of the …nancial cycle, limit the real consequences, and improve welfare. We …nd that all …nancial shocks produce a deep output recession; a signi…cant contraction of private demand; drops in house prices and housing demand; a signi…cant and persistent fall 37

in in‡ation; and a considerable reduction of the intermediation activities. Furthermore, the e¤ects these shocks produce are global. Some shocks redistribute resources between borrowers and lenders; others redistribute resources across countries and, after a few periods, they lead to an export-led domestic recovery. The sector where the disturbances occur does not matter because all shocks contract the lending market. All the shocks are transmitted, domestically, via loans and deposits markets and, internationally, via trade and the interbank market. Furthermore, all shocks worsen the external position of the domestic country, at least in short run, and make domestic government debt expand, as the cost of …nancing greatly increases. Because sovereign spreads also increase, these shocks have important implications for the management of public debt. The qualitative features of the transmission are generally robust. The parameters regulating …nancial constraints a¤ect the dynamics of …nancial and real cycles di¤erently, but the e¤ects on real ‡uctuations are small in the case of private sector default shocks and risk perception shocks. For disturbances originating in the banking sector, the e¤ects of changing crucial parameters are larger. The direction of real changes depends on the type of shock and, to some extent, the branch of the banking sector where the shock originates. Prudential actions by the monetary authority are as good as countercyclical capital bu¤ers in smoothing out the …nancial cycle and in reducing the real e¤ects of the …nancial shocks. However, to understand the consequences that prudential policies have, it is important to know the type of the shock hitting the economy and the sector in which the shock occurs. Prudential policies generally produce a redistribution of the losses across agents within a country or across countries and may lead to interesting political economy tradeo¤s. Given that prudential actions are not generally designed with welfare purposes in mind, our analysis suggests that they should be used in conjunction with, e.g., redistributive …scal policies, if they are to produce Pareto improving allocations along the adjustment path. The model is rich and can be used to analyze other questions such as public sector deleveraging or the consequences of sovereign shocks we do not address in the paper. In addition, while we focus on monetary and capital prudential tools, the model also features …scal and supervisory instruments, which can be used for stabilization purposes. An analysis of this kind may carry important policy insights.

38

The model can be re…ned in many dimensions. For example, the di¤erences between the retail and the investment banking sector can be made sharper by adding deposit insurance or di¤erential prudential controls. Certain parameters can be made endogenous. For example, there is some empirical evidence that banks take more risks when the interest rate is low. Making valuation coe¢ cients function of the nominal interest rate may boost the real transmission of …nancial shocks. The investment process in physical capital, can be enhanced by directly linking it to the state of the loans market. One could consider adding …re sales when default shocks are large and study policies that mitigate their real e¤ects. Finally, the entrepreneurial sector has no net worth - entrepreneurial pro…ts are transferred on a period-by-period basis back to patient households. If entrepreneurs retaining part of the pro…ts (see e.g. Bernanke, Gentler and Gilchrist, 1999), collateral constraints become richer and may allow researchers to examine complex …rm …nancing issues. The international features of the model can also be improved. For example, the model features no direct lending by foreign banks to domestic agents and banks retain national characteristics in their asset side. One could also alter the way the government …nances its de…cit to re‡ect the fact that in some countries a large portion of government debt is held domestically. We leave all these extensions to future work.

39

8

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45

Tables and …gures Table 1a: Parameter values Description

Symbol

Value

Steady state government expenditure to output ratio

g

0:18

Steady state government debt to output ratio

b

0:9

Share of imports

!F

0:5

Elasticity of substitution for imports

1:2

Elasticity of substitution for intermediate varieties

6

Share of capital

0:3

Depreciation rate:houses

H

0:025

Depreciation rate:capital

k

0:02

Returns to scale in house production

0:4

Share of patient households

!s

0:7

Housing preference parameter

vsh ; vbh

0:1

Housing adjustment cost, borrowers

sHb

2

Housing adjustment cost, savers

sHs

0:1

Risk aversion coe¢ cient

1

External habit parameter

h n; n s b

Labour preference parameter Inverse of the Frish elasticity

'

Price rigidity (probability to keep prices …xed)

0:8 1 0:01 0:3

Investment adjustment costs, physical capital

sk

0:1

Investment adjustment costs, housing

sh

0:1

Size of the periphery

n

0:2

Steady state policy rate

REA

1:005

46

Table 1b: Parameter values Description

Symbol R

Monetary policy, interest rate inertia

Value 0:75

Monetary policy, in‡ation targeting parameter

0:5

Monetary policy, output targeting parameter

Y

0:5

Monetary policy, …nancial targeting parameter

F in

0

Fiscal rule, debt targeting parameter

t1

0:01

Fiscal rule, countercyclical parameter

t2

0:0

Discount rate, patient households

s

0:996

Discount rate, impatient households

b

0:95

Discount rate, banks

m;

Discount rate, entrepreneurs

e

0:96

Speed of adjustment capital requirement, retail banks

m

0:9

Speed of deleveraging, investment banks

f

0:75

Speed of deleveraging, impatient households

b

0:75

Speed of deleveraging, entrepreneurs

e

0:6

Collateral valuation parameter, impatient households

b 0

0:7

Collateral valuation parameter, entrepreneurs

e 0

0:35

Risk-adjusted valuation parameter, households loans

Lb 0

0:1

Risk-adjusted valuation parameter, interbank loans

IB 0

0:01

Risk-adjusted valuation parameter, entrepreneur loans

Le 0

0:5

Risk-adjusted valuation parameter, government loans

BP 0

1

Countercyclical bu¤er parameter for banks

IB ; BP 1 1

0:00

f

0:98

Share of the periphery bonds in its portfolio

!p

0:8

Share of the periphery bonds in core portfolio

!p

0:2

Financial integration

0:35

Adjustment cost parameter, deposits

as

0:75

Adjustment costs parameter, household and entrepreneur loans

ab ; ae

0:1

47

Table 2: Steady-States Variable name (in per-capita)

Ratio to Output

Consumption

0:79

Housing (patient households)

0:81

Housing (impatient households)

0:49

Capital stock

4:91

Capital investment

0:10

Household loans

0:44

Corporate loans

0:22

Deposits

1:07

Loans/Deposit ratio

0.66

Domestic bond holdings

0:48

Foreign bond holdings

0:12

Interbank loans to domestic banks

0:67

Interbank loans to foreign banks

0:74

Net taxes/transfer

0:18

Imports

0:50

48

Table 3: Theoretical volatilities and persistences Variable name (in per-capita)

Symbol

Relative Standard Deviation

AR(1) Coe¢ cient

House prices

pH

0.62

0.89

Housing - patient households

Hs

0.21

0.99

Housing - impatient households

Hb

0.04

0.97

Consumption - patient households

Cs

0.42

0.99

Consumption - impatient households

Cb

0.42

0.99

Corporate loans

Le

1.33

0.98

Household loans

Lb

1.34

0.98

0.75

0.55

In‡ation Output

Y

1.00

0.78

Labor

N

0.64

0.41

Investment

I

4.46

0.68

Nominal interest rate

REA

0.54

0.90

49

Table 4: Welfare Household Firm Default

Bank

Risk

Capital

Default Default Perception Requirement

Baseline simulations Domestic Savers

-632,44

-692,70 -692,75 -688,42

-676,52

Domestic Borrowers -94,09

-93,76

-96,12

Foreign Savers

-1370,83 -1363,12 -1372,45

-1376,05

Foreign Borrowers -162,95

-159,73 -159,94 -159,88

-164,62

Home country

-470,94

-513,02 -513,07 -510,22

-502,40

Foreign country

-1036,22

-1007,50 -1002,16 -1008,68

-1012,62

Global

-923,16

-908,60 -904,35 -908,99

-910,58

-1410,48

-93,83

-94,43

Changes with prudential monetary policy Domestic savers

-2,89

5,00

-0,08

32,13

0,55

Domestic borrowers -0,09

-0,20

0,03

-1,06

-0,03

Foreign savers

5,80

9,23

-1,10

54,24

-1,72

Foreign borrowers

0,06

-0,04

-0,04

-0,73

-0,03

Home country

-2,04

3,44

-0,07

22,14

0,38

Foreign country

5,22

7,51

-0,85

27,97

0,80

Global

3,41

7,31

-0,64

34,86

0,96

Changes with prudential capital requirement Domestic savers

-14,43

-1,13

-0,04

-0,10

-0,19

Domestic borrowers 0,20

-0,01

0

-0,12

0,03

Foreign savers

8,75

0,83

0,10

1,29

0,24

Foreign borrowers

0,72

0,07

0

0,09

0,03

Home country

-10,04

-0,79

-0,03

-0,81

-0,12

Foreign country

6,34

0,56

0,08

0,83

0,18

Global

3,06

0,18

0,05

0,59

0,12

50

Appendix A: The optimality conditions of the model In this appendix we summarize the optimality conditions for the domestic economy in real terms. The conditions for the foreign economy are analogous and omitted. The equations we present are obtained using the market clearing conditions (61)-(62)-(63)-(66); the expression for the …x cost in production that makes branding …rm pro…ts equal to zero, and de‡ating the expressions with the consumer price de‡ator Pt . In addition, …scal variables are Ds;t expressed as a ratio to output. In this appendix, the following de…nitions hold, ds;t ; Pt IBf;t IBf ;t Lb;t IBf;t IBf ;t Lm;t Le;t lb;t ; lm;t ;le;t ; ibf;t ; ibf;t ;ibf ;t ;ibf ;t ; Pt Pt Pt Pt Pt Pt Pt Bf;t Bf ;t Bf ;t Bf;t Pt Gt Tt Bt =Pt ;bf ;t ;bf;t ;bf ;t ; rert ; gt ; tt ; bt ; bf;t Pt Pt Pt Pt Pt Yt Yt Yt Wt H PtH Pt s;t ; b;t Pt b;t ; wt ;pt s;t Pt Pt The optimality conditions for the patient households are: s;t = (Cs;t h "t hs Hs;t

hCs;t

+ Et

s;t

wt =

1)

s (1

(74) H)

s;t+1 H pt+1 s;t

nN ' s s;t

= pH t + sHs

Hs;t Hs

1

(75) (76)

s;t s Et

s;t+1

rs;t = 1

(77)

s;t

The trade-o¤ between the marginal utility of consumption and the marginal utility of housing in equation (75) is regulated by the relative price of the two goods, adjusted for the fact that housing is durable and yields utility services also in the next period. The trade-o¤ between the marginal utility of consumption and leisure in equation (76), instead, depends on the real wage. Conditions (74) and (77) imply that the ratio of the marginal utility of consumption between two subsequent periods is related to the real rate on deposits.

51

The optimality conditions for the impatient households are: b;t

= (Cb;t

pH t + sHb (1

hCb;t Hb;t Hb

1)

1

=

(78) "ht hb Hb;t b;t

b ib b )( 0 t ) b;t Et

H ) (1

"

+ #

pH t+1 + rb;t

b (1

H ) Et

b;t+1 H pt+1 b;t

nN ' b b;t

wt =

(79) (80)

b;t

1

b;t

=

b Et

b;t+1

rb;t

(81)

b b;t+1

b;t

H

lb;t =

b lb;t 1

+ (1

b)

(

pt+1 (1 H )Hb;t b ib 0 t )Et rb;t

Cb;t + tt Yt + ACHb ;t + pH t (Hb;t

(1

H ) Hb;t 1 )

"bt + rb;t lb;t

(82) 1

"bt = lb;t + wt Nb;t (83)

The intratemporal and intertermporal trade-o¤s for the patient and the impatient households are similar. The main di¤erence is that now the consumption housing trade-o¤ also includes a term re‡ecting the collateral constraint that impatient households face. Note that when the collateral constraint is not binding, b;t = 0, and (79) is the same as (75) apart from a di¤erent discount factor. Notice also that (78) and (81) indicate that when the borrowing constraint is binding, the ratio of the marginal utility of consumption in two subsequent periods is related not only to the real borrowing rate but also to the shadow price of the borrowing constraint in those two periods. This is due to the persistence present in the borrowing constraints. Once again, if b;t = 0 for all t; (81) is similar to (77). Finally, equations (82) and (83) represent, respectively, the borrowing and the budget constraints of the impatient household.

52

The optimality conditions for the entrepreneurial sector are: 1 = qe;t + qe;t = + wt = 1

e;t

=

e Et

s;t+1

e ie e ) ( 0 t )Et

s;t

Ie;t

( pX t+1 Yt+1 + e;t X pt+1

re;t

1 1 2

Ie;t+1 Ie;t

1 1 1

Ie;t

#

Ie;t

1

(84)

Ke;t1 + qe;t+1 (1

Y

Yt+1 +

1 1

!

k ))

Ke;t1

Y

(85)

Yt + 1 1 Y ) Nt

(1

s;t+1

e Et

"

sk

Ie;t+1 Ie;t

s;t

(1 pX t

1

Ie;t

1

sk

s;t+1

re;t

1 1

Kt

Ie;t 1 0

+ (1 Y ) px t 1

2

Ie;t

sk 2

"It k

e)

@(

+ qe;t (1

qe;t

(86) (87)

e e;t+1

s;t

e le;t 1 (Yt +

rt =

qe;t+1

Ie;t

e Et

Kt = Ie;t

le;t =

"

2

Ie;t

sk 2

"It k

1

#

e ie 0 t )Et

+ (1

k )Kt 1

pX t+1 Yt+1 +

1

(88) 1Y

re;t

k)

wt+1 Nt+1

1

"et A (89) (90)

1

The …rst two equations describe the intertermporal trade-o¤s the entrepreneurs face in selecting investment and capital via the Tobin’s Q. Note that in equation (85) the Tobin’Q, qe;t ,depends on the lagrange multiplier on the borrowing constraint. Thus, the …nancial friction that the borrowing constraint implies will have real repercussions via the capital decision of entrepreneurs. The next equation is the optimal labor demand by the sector. As with impatient households, the ratio of marginal utility of dividends between two subsequent periods is related to the real borrowing costs and to the shadow price of the borrowing constraints in those two periods. When e;t = 0; for all t, equation (87) collapses to the standard conditions linking the ratio of marginal utility of dividends in two subsequent periods to the real borrowing rate. Finally, note that equation (88) gives the law of motion of capital and equation (89) the borrowing constraint faced by entrepreneurs. (90) de…nes the returns to capital. The condition for intermediate goods production is: Yt +

1 1

Y = "zt (Kt

53

1)

(Nt )1

(91)

where the …xed costs are taken into account. The optimal pricing conditions are: $t

s(

)

t

s(

)1

pYt

=

"

(1

Et

t+1 $ t+1 1 t+1

Et

1

+(

X s;t ) pt

pYt

pYt

s;t )

Yt

(92)

Yt

(93)

1

+

(

t)

1

pYt

(1

)

1

t

1

! F ) pYt

1 = (1

t+1

$t

)

+(

#

1 1

(94)

1

+ ! F rert pYt

(95)

Equation (94) is a standard Philips’ curve and (95) describes the composition of the price de‡ator. The optimality conditions for the housing sector are: Ht pH t

Ih;t

h )Ht 1 2

Ih;t

sh 2

Ih t

(1 1

1

!

s Et

=

Ih;t 1

"

Ih t

Ih;t

Sh

Ih;t

Ih;t

pH t sh

Ih;t

1 1

Ih;t+1 Ih;t

s;t+1 H pt+1 sh s;t

1

Ih;t

1

Ih;t Ih;t

(96)

+ 1

+1 Ih;t+1 2 Ih;t

#

= 1

(97)

Equation (96) is the production function for new housing while equation (97) is the optimality condition for housing investment weighting the gains of producing new houses against the cost of producing one extra unit of housing and adjusting the existing stock. The optimality conditions for the retail banking sector are: i h i h dm;t s;t+1 s;t+1 a 1 = E r (98) 1 + E s s;t m;t+1 m t m;t m m t dm s;t s;t i h lm;t Lb (99) 1 1 = m Et s;t+1 rb;t m;t (1 + (1 m ) t ) + ab m m;t+1 lm s;t h i s;t+1 IB 1 (1 (100) rtEA m;t (1 m ) t ) = m Et m m;t+1 s;t ! s dt (1 IB t Lb t

m ! s dt 1

IB t ibt

m) IB 0

Lb 0

= ibt + (1

"t +

"tm +

+

IB 1 Lb 1

Lb t

! s ) lb;t

(1

m (ibt 1

! s ) ltb

(1

ibf;t + 1 nn ibf ibf + 1 nn ibf lm;t =Yt lm =Y

;t

1

=Yt =Y

0 "t

+ (1

) "ft !!

1

! s ) lb;t

0 "t

1)

rert "ft

(1

! s ) "bt (101) (102) (103)

Equations (98)-(100) provide arbitrage relationships for rs;t ; rb;t and rtEA . For example, absent adjustment costs, (99) and (100) state that impatient household real borrowing rate may be di¤erent from the real area wide real policy rate only to the extent that the valuation IB di¤er. Note also from (98) that deposits have an additional function b coe¢ cients L t and t for retail banks because they in‡uence the leverage constraint in di¤erent periods. Note that 54

equation (101) is the LTV constraint for retail banks, while (102)-(103) describe structure of the valuation parameters. The optimality conditions for the investment banking sector are: h i h i s;t+1 s;t+1 EA 1 + E = E r t t f;t f f f;t+1 f t s;t s;t h i h i s;t+1 s;t+1 EA t+1 1 + E = E r t t f f f t f;t s;t s;t t+1 f;t+1 h i l Le s;t+1 f;t 1 = E r 1 1 (1 " ) + " + a e t e;t f 0 f;t 0 f t t t f;t lf s;t 1

1

Le t

Le 0

0

BP t

1

n n

ibft

@

(1

BP 0

)

f;t

+

0 "t f;t

=

s;t+1

f Et

s;t

! p;t rt + (1

! p;t )

"tf 1

! p;t ! p;t

+ 1

bf;t

+ 1

f

f

(1

0 "t

0 "t

)

(105) (106)

(108) 11

1AA

(109) (110)

e ltf L t + rert

BP t

bft 1 n f b + rert n t

Le f t lt

BP t

bft +

+

(104)

rert+1 r rert t (107)

Le 1

f f (ibt 1 ) f f ibt 1

0 "t

!! ltf =pYt Yt 1 lf =pY Y 0 f bt + 1 nn rert bft =pYt Yt BP @ 1 bf + 1 nn rerbf =pY Y

"tf

rerbf;t =

=

ibft =

BP t

f

the

1

n n

!

rert bft

("e;t "f;t ) rert

!

(111)

"e;t + "f;t (112)

(104)-(107) provide another set of arbitrage conditions linking re;t ; rp;t rtEA and rtBP : Note that the …rst two conditions imply investment banks should be indi¤erent between borrowing from domestic or from foreign retail banks as long as the shadow price of the foreign leverage constraints (111) re‡ects the shadow price of the domestic leverage constraint (112) and the in‡ation di¤erentials. The optimality conditions for the problem of the government are : gt + r t

1 bt 1

Yt Yt 1

1

= bt + tt

(113)

gt = g"gt bt Yt = bf;t + bf tt ln = t1 ln t

(114) (115)

;t

bt 1 b

+ t2 ln

Yt Y

+ "t

(116)

Equation (113) is the budget constraint and (116) the …scal rule. (114) de…nes what government expenditure is and (115) is the supply of domestic bonds. 55

The market clearing conditions are: Ct = ! s Cs;t + (1

! s ) Cb;t

(117)

Ht = ! s Hs;t + (1

! s ) Hb;t

(118)

Nt = ! s Ns;t + (1

! s ) Nb;t

(119)

It = Ie;t + Ih;t

(120)

pYt Yt = Ct + It + gt Yt +

1

YM;t = ! F rert pYt

(Ct + It + gt Yt )

(122)

(Ct + It + gt Yt )

(123)

YM

= !F

;t

pYt rert

n n

pYt YM

;t

rert pYt YM;t

(121)

Equation (121) is the national account identity, while equations (122) and (123) de…ne what imports and exports are. Balance of payments equilibrium requires:

=

1

n

1

hn (bf n

n

rert bf;t ;t

rt

pYt YM

;t

rert rt

1 bf ;t 1 )

1 bf;t 1

+ ibf

;t

rtEA1 ibf

rert rtEA; 1 ibf;t

+ rert ibf;t

;t 1 1

+

rert pYt YM;t

+

0 "t

rert "f i

;t

0 "t "f;t

(124)

Imports, exports and the CA balance are de…ned as Impt = pYt YM;t 1 n Expt = pYt YM ;t n Expt Impt CAt = Yt

(125) (126) (127)

The following Fisher equations de…ne real rates for various assets: rs;t =

t

rb;t =

t

re;t = rt EA rt EA; rt

1

Rs;t

(128)

1

Rb;t

(129)

1

Re;t

(130)

1

Rt

(131)

t

=

t 1

= = (

56

EA t Rt 1 EA t ) Rt

(132) (133)

The central bank policy rule is: ln

RtEA REA

= ln

"

RtEA1 REA

EA t YtEA

n

! t

R

EA t EA

[

+ (1

n)

nYt + (1

f inEA t

n

(1

YtEA Y EA

f inEA t f inEA

Y

f in

#1

R

+ "R t (134) (135)

t

n) Yt

(136)

! s ) lb;t + le;t + (1 Yt

n)

(1

! s ) lb;t + le;t Yt

(137)

Finally, the processes for the exogenous shocks hitting the economy are: "bt = "et = "ft

=

b b "t 1 + ub;t e e "t 1 + ue;t f f "t 1 + uf;t

(139)

(138) (140)

ln "ib t

=

ib

ln "ib t 1 + uib;t

(141)

ln "ie t

=

ie

ln "ie t 1 + uie;t

(142)

"if t 1

"if t

=

if

ln "im t

=

im

=

z

ln

ln "ht

=

h

ln "ht

ln "It k

=

Ik

ln "It k 1 + uIk ;t

(147)

ln "It h

=

Ih

ln "It h 1 + uIh ;t

(148)

ln

ln ("zt )

ln ("gt ) = "R = t ln ("t ) = "t

=

g

+ uif;t

(143)

ln "im t 1 + uim;t

(144)

ln

"zt 1

ln "gt

R R "t 1

1

1

+ uh;t

+ ug;t

+ uR;t

ln "t "t

1

+ uz;t

1

+u

+u ;t

(145) (146)

(149) (150)

;t

(151) (152)

Overall, there are 55 structural equations for each country, plus 4 (common) monetary policy equations, a (common) balance of payments equation, and 29 autoregressive equations describing the behavior of exogenous disturbances. Thus, there are 144 equations in the model which determine 144 endogenous variables as a function of the 29 exogenous shocks. To …nd a solution to the model, we use perturbation methods. That is, given that the optimality conditions are of the form Ef (xt+1 ; xt ; xt 1 ; t+1 ; t ; ) = 0; where xt are the endogenous variables, t the exogenous shocks, the structural parameters and f is a generic non-linear function, we seek for a solution of the form xt = g(xt 1 ; t ; ). Since g is unknown we take a …rst order Taylor expansion of g and of f and match the coe¢ cients.

57

RtBf,t   PtGt  

 

 

Goods  Distributors   PYtYD,t  

 

PYtYM*,t  

Branding  Firms  &     Wholesalers  

RtBf*,t   Bf*,t  

PHtΔHs,t  ,  PHtΔHb,t   Tt   Rs,tDs,t   Saving               Households  

PtCs,t  ,PtCb,t  

Ds,t   Borrowing   Households  

Lb,t   Rb,tLb,t  

WtNt  

 

House  Producing   Firms   PtIh,t  

 

Bf,t  

Government  

PtIe,t  

  Investment   Banks  

Le,t  

Entrepreneurs  

QXtXt  

Retail  Banks  

Re,tLe,t  

IBf,t   EA

R tIBft   IB*f,t  

Common  M onetary  Authority:  REAt   IBf*,t   EA

Entrepreneurs*  

QX*tX*t  

Investment   Banks*  

R*e,tL*e*,t  

R tIBf*t   IB*f*,t   REAtIB*f*t  

P*tI*e*,t  

Goods  Distributors*  

House  Producing   Firms*  

L*e*,t  

W*tN*t  

PY*tY*D,t  

Branding  Firms  &     Wholesalers*  

P*tI*h*,t  

PY*tY*M,t  

REAtIB*ft  

P*tC*s*,t  ,  P*tC*b*,t  

L*b*,t   R*b,tL*b*,t  

Borrowing   Households*  

Saving               Households*  

D*s*,t   R*s,tD*s*, t  

*

T t  

PH*tΔH*s*,t  ,  PH*t ΔH*b*,t  

B*f*,t   Government*  

R*tB*f*,t  

P*tG*t  

Figure

1: The

Retail  Banks*  

structure

of

the

model

B*f,t   R*tB*f,t  

Commercial Loans D

Commercial Loans F

Mortgages D

Mortgages F

0

0

0

0

-0.1 -0.1

-5

-5

-0.2 -0.3

-0.2 -10 5

10

15

5

Deposits D

-0.4

-10

-0.3 10

15

5

Deposits F

10

15

Consumption D

-0.1

Consumption F

-0.2

-0.1

-0.2

15

5

Output D

10

15

5

Output F

0

-0.4

-0.2

-0.3 10

15

0

0

5

10

0

0.1 0 -0.2 -0.4 -0.6 -0.8

5

10

15

5

Labor D

15

10

15

10

15

Labor F 1

0

0

10

0

-2 -1

-4 -6

-2

-8

-3 5

10

-2 -3 -10

15

5

Investment D

10

15

0

-20

15

5

10

Default Shock for Households

Figure

2: Responses

Import D

1

0

0

-2 -4 -6

-3

-60 10

5

-2

-40

-30

15

-1

-10 -20

10

Export D

0

5

5

Investment F

10

-1

-5

to

15

5

10

Default Shock for Entrepreneurs

financial disturbances

15

5

Default Shock for Banks

Inflation D

Inflation F

0

2

-5

0

Net Interbank loans

-2

-10

Capital Return D 0.2

20

0

0

-0.2 -0.4

-20

-4 -15

-0.6

-40 5

10

15

5

Capital Return F

10

15

5

Real Wage D

10

15

-0.8

Real Wage F

0.5

-0.5

-0.6

-0.3

-1

-0.8

-0.4 15

5

Deposit Rate D

15

-0.4

-0.2

10

10

-0.2

-0.1

5

15

Policy Rate

0

-0.5

10

0

0

0

5

10

15

5

Deposit Rate F

10

15

5

Mortgage Rate D

Mortgage Rate F

15

15 4 10

4 10

2

2

5

0

5

0

0

-2

0

-2

5

10

15

5

Commercial Loan Rate D

10

15

5

Commercial Loan Rate F

10

15

5

Bond Rate D

10

15

Bond Rate F

15

15

4

4 10

10

2

5

5

0 -2

0 5

10

15

2 0 -2

0 5

10

Default Shock for Households

15

5

10

Default Shock for Entrepreneurs

Figure 3: Responses

to financial

15

5

Default Shock for Banks

disturbances

10

15

Output EA

Inflation EA

Policy Rate

0

0

0

-1

-1

-0.2

-2

-2

-0.4

-3

-3

-0.6

-4

-0.8

-4 5

10

15

5

House Prices F

10

15

0 -0.1 -0.2 5

Capital Price D

House Prices D

10

15

0

5

10

15

Consumption Savers D

-1

-0.2 5

10

15

-2 5

Consumption Borrowers D

10

15

Consumption Savers F

0 -0.05 -0.1 -0.15 -0.2

-0.1 -0.2 5

10

15

5

Labor Savers D

10

-0.2

-0.2

-0.4

-0.4

15

5

Labor Borrowers D 0

-5

-1

-2

-10

-2 -3 10

15

15

5

10

15

Labor Borrowers F 0.6

0

5

10

Labor Savers F

0

-15

5

Consumption Borrowers F 0

0 0

15

0

-0.1

-0.1

10

1

0

-0.5

15

2

0.1

0.1

10

-13 x 10RER

Capital Price F

0

-1

5

5

10

15

Default Shock for Households

Figure 4: Responses

0.4 0.2

-4

0

-6

-0.2 5

10

Default Shock for Entrepreneurs

to

financial disturbances

15

5

Default Shock for Banks

10

15

Housing Borrowers D

Housing Savers D

Housing Savers F

Housing Borrowers F

0

0 0.2

-0.05

0.02

-0.1

0.01

-0.15

0

-0.05 0.1 -0.1 0 5

10

15

-0.2 5

Retail Bank Capital D

10

15

Retail Bank Capital F

200

200

100

100

0 10

15

15

10

3

2

2

1

1

15

10

15

5

10

-0.2

50

-0.3

0 10

15

4

20

2

-50 -100 10

15

4

20

2

10

0

5

10

15

5

Default Shock for Households

10

15

5

10

Default Shock for Entrepreneurs

Figure 5: Responses

to

15

-2

0

-4

10

Investment Bank Liabilities F

30

-2 0

5

Investment Bank Liabilities D

0

10

50

5

Investment Bank Assets F

30

15

0

5

Investment Bank Assets D

10

100

150 100

15

5

Investment Bank Capital F

0.1 -0.1

15

0 5

Investment Bank Capital D

0

10

Retail Bank Assets F

3

Retail Bank Liabilities F

0 -0.2 -0.4 -0.6 -0.8

5

0 5

Retail Bank Liabilities D

10

Retail Bank Assets D

0 5

-0.01 5

financial

15

5

Default Shock for Banks

disturbances

10

15

Commercial Loans D

Commercial Loans F

0

Mortgages D

0

-5

-5

-10

-10 5

10

15

5

Deposits D

10

-2

-2

-4

-4

-6

-6

-8

-8

15

5

-0.02

-0.05

-0.04

-0.1

-0.06

-0.15

-0.08 10

15

5

Output D

10

-0.5

-2

-1

-0.02

-0.05

-0.04

-0.1

-0.06

-0.15

-0.08

-0.2 5

10

15

5

10

15

Investment D

5

10

5

10

15

0

0

-0.5

-1

15

-2

-1.5 5

to

5 Import D

-1

Risk Perception Shock

Figure 6: Responses

10

-1.5

Export D

-20 15

15

-1

15

-15 10

10

-0.5

-10

5

15

0

-5

-10

10

Labor F

-1

0

-5

15

0

Investment F

0

5

Labor D

-3 -1.5

10

Consumption F

-2

-3

5

0

15

0

-1

15

0

Output F

0

10

Consumption D

0

5

0

Deposits F

0

Mortgages F

0

10

15

Capital Requirement Shock

financial

disturbances

5

10

15

5

Risk Perception Shock (both countries)

Inflation D

Inflation F

0

0.2

-1

0

-2

-0.2

-3

-0.4

-4

-0.6 5

10

15

0

0

1

-0.1

0

5

10

15

5

-0.05

-0.1

-0.1

-0.2

-0.2

-0.2 10

15

10

15

10

15

-0.1 -0.2 -0.3

15

5

Deposit Rate F

10

0

-0.4 5

5 Policy Rate

-0.3

15

Deposit Rate D

10

Real Wage F 0

-0.15

-0.2

-1

0

-0.1 5

2

Real Wage D

0.1

Capital Return D

3

-0.8

Capital Return F

Net Interbank loans

10

15

5

Mortgage Rate D

Mortgage Rate F

0.8 4

0.6

3

0.4

2

0.2

1

0

0

4

0.5

2

0 -0.5

0

-0.2 5

10

15

5

Commercial Loan Rate D

10

15

5

Commercial Loan Rate F

10

15

5

Bond Rate D

10

15

Bond Rate F 0.8

4

0.5

4

0.6

2

0

3

0.4

2

0.2

1

0

-0.5 0 -1 5

10

15

-0.2

0 5

Risk Perception Shock

Figure 7: Responses

10

15

Capital Requirement Shock

to

financial

5

10

15

5

Risk Perception Shock (both countries)

disturbances

10

15

Output EA

Inflation EA

0

Policy Rate

0

-0.5 -0.5

-1 -1.5 10

0

-0.1

-0.05 -0.1

-0.3

15

5

House Prices F

0

-0.2

-1 5

House Prices D

10

15

5

Capital Price D

10

15

5

10

15

10

15

-14 x 10RER

Capital Price F

0.05

0

-0.15

2

0.05

1

-0.1 0

0

-0.2 -0.3

0

-0.05

-1

-0.05 5

10

15

Consumption Savers D

5

10

15

Consumption Borrowers D 0

0

5

10

15

Consumption Savers F

5

Consumption Borrowers F 0

0

-0.02

-0.02

-0.05

-0.05

-0.04

-0.04

-0.1

-0.1

-0.06

-0.06

-0.15

-0.15

-0.08

-0.08

-0.2

-0.2

5

10

15

5

Labor Savers D

10

15

5

Labor Borrowers D

10

15

5

Labor Savers F

10

15

Labor Borrowers F

1.5

0

0

0.6

1

-2

0.4

-1 0.5

-4

0.2 -2

0

-6

0 -0.2

5

10

15 Risk Perception Shock

5

10

15

Capital Requirement Shock

Figure 8: Responses

to

financial

5

10

15

5

Risk Perception Shock (both countries)

disturbances

10

15

Housing Savers D

Housing Borrowers D

Housing Savers F

0.1

0

Housing Borrowers F

0 0.04

-0.02 0.05

-0.02

-0.04

0

-0.04

0.02

-0.06 0

-0.08 5

10

15

5

Retail Bank Capital D

10

15

5

Retail Bank Capital F

10

15

5

Retail Bank Assets D

10

15

Retail Bank Assets F

0.6 10

30 20

0.1

0.4 0.2

5

10

0

0 0

0 5

10

-0.2

15

5

Retail Bank Liabilities D

10

15

5

Retail Bank Liabilities F

10

15

-0.1

Investment Bank Capital D

5

10

15

Investment Bank Capital F

60 0

0 -0.05 -0.1

-0.02

40

0

-0.04

20

-5

-0.06

-0.15

0

-0.08 5

10

-10

15

5

Investment Bank Assets D

10

15

5

Investment Bank Assets F 3

0 5

15

10

15 Risk Perception Shock

15

Investment Bank Liabilities F

0.1 0 -0.1

1

-0.2

-0.4 5

10

0.2

2

-0.2

0

5

Investment Bank Liabilities D

0.2

10

10

5

10

15

0

5

Capital Requirement Shock

Figure 9: Responses

to

financial

10

15

5

Risk Perception Shock (both countries)

disturbances

10

15

Current Account/GDP D

Government Debt/GDP D

Government Debt/GDP F

1

30

8

0

25

6

-1

20

-2

15

4

2 -3

10 0

-4

5 -2

-5

5

10

15

0

Default Shock for Households

5

10

15

Default Shock for Entrepreneurs

5

10

15

10

15

Default Shock for Banks 1.5

9 0 8 7

1

6

-0.5

5 0.5 4 3

-1

0

2 1 -1.5

5

10

15

0

5

Risk Perception Shock

Figure

10: Responses of

the

10

15

-0.5

5

Capital Requirement Shock

current account to

GDP and

Debt

to

GDP

Mortgages D Commercial Loans D Output D -5 -10 -15 5

10

0.2 0 -0.2 -0.4 -0.6 -0.8 15

0.15 0.1 0.05 0 -0.05 10

Bank default

15

5

10

5

15

-5

-0.5

-1

-0.15

-10

-1

-2

5

15

10

-1.5 15

5

10

15

10

0.15 0.1 0.05 0 15

-2

5

15

10

15

5

-0.5

10

15

10

15

5

10

5

10

-10

-1

-0.38

-2

5

10

15

5

0

-0.06

-2

-0.08

-4 5

10

15

10

5

5

10

15

5

10

baseline calibration

Figure

0

-2

-2

15

5

10

15

5

15

0

-0.5

-1

-1

-2

10

-15

10

0

-0.5 -1 -1.5 -2 -2.5 15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

-4 5

15

-10 -0.06 15

15

0

10

-5

-0.04

-3

10

-4

-20

-0.04

15

5

0

0

-0.36

15

2

0

5

5

-0.34

15

10

-1

-1

10

5

-0.1

-10

5

15

-0.5

-8

-0.1

10

-10

-6

-0.05

15

0

-6

Risk Perception

10

0

-4

10

-40

0

-4

5

-20

0 -5 -10 -15

-0.05

15

-8

0

5

Inflation D

D

0

-0.2 10

-0.05 -0.1 -0.15 -0.2 -0.25 15

Export 0 -2 -4 -6

-5

-0.1

5

Capital requirment

10

0

0.2 0.1 0 Commercial -0.1

default

5

-15 5

Household default

0 -2 -4 -6 -8

Consumption D Investment D

5

10

15

-2 -4 5

10

15

Domestic country twice as large

11: Responses as a function

of

the

size

of

demestic

country

Mortgages D Commercial Loans D Output D -5

Household default -10 5

10

0.2 0 -0.2 -0.4 -0.6 15

0.15

5

10

15

Export D

Inflation

-0.1

0 -2 -4 -6

0

0 -20 -40 -60

-0.2 -0.3 5

10

0

-5

Commercial 0.1 default 0.05

15

5

10

15

5

-0.05

0

-0.1

-10

-0.15 15

-20

10

-0.5 -1

0 -0.05

-10 5

Bank default

0 -2 -4 -6 -8

Consumption D Investment D

10

15

10

0 -0.1 -0.2 -0.3 15

0.1 0 -0.1 -0.2 -0.3 5

5

-4

-6

Risk -6 Perception

-8

10

-1.5 15

5

10

10

-2

-0.1

-3

-0.2 15

15

5

10

0

10

15

Capital requirment

5

10

15

5

10

-0.42 15

5

10

15

5

10

15

-15 10

15

0

0

-0.5

-1

-1

-2

15

5 0

-20

-2

-40

-4 5

10

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

0 -2

10

15

baseline calibration

Figure 12: Responses as a

5

10

15

-5

-0.5

-1

-10

-1

-2

5

10

15

10

-0.5 -1 -1.5 -2 -2.5 15

-30 5

10

0

-20

-0.15

5

0

-10

-0.1

15

0

0

-3 10

10

-10 5

0

15

-0.05

-2 5

5

15

-0.1

-1

-0.4

-0.2

10

-0.5

-0.38

-0.1

5

-0.05

-10 5

15

-5

-4

-1

-8

10

0

-1

5

5

15

D

15

5

5

10

15

-2 -4 5

10

15

Lower financial integration (=0.05)

function

of

the degree

of

financial

integration

Mortgages D Commercial Loans D Output D -5 -10 Household -15 default -20 -25 5

10

0.2 0 -0.2 -0.4 -0.6 15

0 -2 -4 -6 -8 5

10

15

5

10

Commercial 0.05 default

-10

-0.1 -0.15 -0.2 -0.25 15

10 0 -10 -20 -30 5

10

15

-0.05

0

0.1

Consumption D Investment D

-0.1 -1

-20 5

10

15

5

10

0.05 0 Bank default -0.05 5

10

-0.1 15

-4

-6

Risk -6 Perception

-8

5

10

5

10

15

10

15

5

10

0 -0.5

10

-0.28 -0.3 -0.32 -0.34 -0.36 -0.38 15

-0.05

Capital requirment -0.1 5

5

10

15

5

10

5

10

15 2

-0.04

0

-0.06

-2

-0.08 15

-4 5

10

15

5

10

-0.03 15

function

of

15

-10 -15 5

10

5

5

0

-0.5

-1

-1

-2

15

5

15

5

10

15

10

-0.2 -0.4 -0.6 -0.8 -1 -1.2 15

5

10

15

5

10

15

5

10

15

-0.5

-1

-1

-2

10

-0.5 -1 -1.5 -2 -2.5 15

5

to value ratio

15

5

0

15

10

15

0

10

5

10

10

15

-2 -4 5

10

50% lower LTV for Households and firms

the loan

15

0

-4 10

-5

10

-5

-2

0

5

0

0

5

-0.02

baseline calibration

Figure 13:Responses as a

10

-10

-3 15

-0.02 15

5

Inflation D

0 -2 -4 -6 15

0 -2 -4 -6 -8

-0.02

-2 10

15

-0.01

-1

5

10

0

-10 5

5

0.02

-1

-8

15

0.04

-0.5 -1 -1.5 -2

-0.05

-0.1

15

10

0 -2 -4 -6

-0.5

0

5

Export D

15

Mortgages D Commercial Loans D Output D Consumption D Investment D Household default

-5

0 -2 -4 -6 -8

0 -0.5

-10

-1 5

10

15

0.15 0.1 Commercial 0.05 default 0 -0.05

15

-0.1 -0.15 -0.2 -0.25 5

10

15

-10 10

15

5

10

15

-0.15 15

-5

5

10

5

10

10

0

-8

-0.5

15

10

-0.02 15

10

-0.04 -0.06 -0.08 -0.1 -0.12 -0.14 15

5

10

-0.022 -0.024 -0.026 -0.028 -0.03 -0.032 15

-0.4

Capital -0.1 requirment

-1

-0.5

-2 -0.6 -3 5

10

15

5

10

15

5

baseline calibration

Figure

14:Responses as

a

10

15

function

10

5

10

5

10

15

10

-15 5

10

15

0

0

-0.5

-1

-1

-2 5

10

15

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

-0.2 -0.4 -0.6 -0.8 -1 -1.2 5

10

15

0

0

-0.5

-1

-1

-2

-1.5 5

10

15

5

10

15

-0.5 -1 -1.5 -2 -2.5

-10 15

-10

-4 10

-5

10

-5

-2

0

5

0

0

5

15

Inflation D

0 -2 -4 -6

15

2 0 -2 -4 -6 5

Export D

15

0 -2 -4 -6 -8

0

-1.5 10

5

0.02

-1 5

15

5

0 -2 -4 -6

0.04

5

-6

15

-0.05

5

15

-10

-10

15

-0.1

-0.5 -1 -1.5 -2

-0.1 10

10

-1

-0.05

5

5

-0.05

0 -0.5

0.05 0 -0.05 -0.1 -0.15

Risk Perception

10

-5

5

Bank default

5

10 0 -10 -20 -30

5

10

15

-2 -4 5

10

15

50% faster deleveraging for Households and Firms

of

the

speed

of

deleveraging in

private sector

Mortgages D Commercial Loans D Output D Consumption D Investment D -5

Household default -10 5

10

0.2 0 -0.2 -0.4 -0.6 15

0.1

5

10

15

5

10

0

-5

Commercial default 0.05

-1 -10 5

10

15

5

10

-1.5 15

0.2

0.2

0

0.1

0.1

-1

0

0

-0.1 5

10

-0.1 15

-4

-6

Risk -6 Perception

-8

5

10

15

10

0.05 0 -0.05 -0.1 -0.15 15

-2 5

10

15

5

0 -0.5 -1

-8

-10 5

10

15

5

10

15

-0.05 -0.1 -0.15 -0.2 -0.25 15

5

10

5

10

15

-0.1

-0.38

-1

-0.4

-2

5

10

15

10

15

5

10

15

5

10

5

10

-2

-0.08

-4 5

10

15

15: Responses as a function

of

15

-1

-1

-2

15

5

10

15

5

10

10

15

5

10

15

0

0

-0.5

-1

-1

-2

15

5

10

15

0 -5

-1

-10

-2

10

15

5

10

15

5

10

15

50% faster deleveraging for banks

the

speed

of

10

15

5

10

15

5

10

15

5

10

15

5

10

15

-1 -2 -3 -4 -5

-3 5

5

2 1 0 -1

-4 5

-0.06

-15 10

-0.5

-2

0

-10

0

-5

-0.04

-0.04 15

10

-5

0

0

15

Inflation D 0

5

0

2

baseline calibration

Figure

5

15

-10

-0.03

-3 5

10

0 -2 -4 -6 -8

-0.02

-0.05

Capital requirment

5

-0.02

15

Export D 0 -2 -4 -6

10 0 -10 -20 -30

-0.04 -0.06 -0.08 -0.1 -0.12

-0.5

0

Bank default

0 -2 -4 -6 -8

deleveraging

of

banks

Mortgages D Commercial Loans D Output D -5

Household default -10 5

10

15

0.1

5

10

15

5

10

0

-5

Commercial 0.05 default

Consumption D Investment D -0.1 -0.15 -0.2 -0.25 15

10 0 -10 -20 -30 5

10

15

-0.05

-0.5 -0.1

0 10

15

5

10

0.05 0

-0.05

-0.1 5

10

-0.1 15

-4

-6

Risk -6 Perception

-8

5

10

15

5

10

10

15

10

-0.4 -0.45 -0.5 -0.55 15

-0.05

Capital requirment-0.1 -0.15 5

5

10

5

10

15

5

10

-0.02 15

0

-0.04

-0.5

-0.06

5

10

10

15

-5 -10 -15 5

10

15

0

-2

-0.5

-1

-1

-2

5

15

10

15

5

15

5

15

5

10

15

10

-0.2 -0.4 -0.6 -0.8 -1 -1.2 15

5

10

15

5

10

15

5

10

15

-4 10

10

15

-2

5

5

10

0

2

0

0

-0.5

-1

-1

-2

-2

-0.08 5

0

0

0

15

Inflation D

0 -2 -4 -6 15

0 -2 -4 -6 -8

0

Export D

0

15

0.02

-10 5

15

0.04

-1

-8

10

-6

-0.5 -1 -1.5 -2

-0.05

5

-4

-1

-10 5

Bank default

0 -2 -4 -6 -8

0.2 0 -0.2 -0.4 -0.6

-4 5

10

15

5

10

15

5

10

15

0 -1 -2 -3

-0.03 -2 -4 5

10

15

5

10

-0.04

-10

-0.05

-20

15

baseline calibration

Figure 16: Responses as

a

function

5

10

15

5

10

15

-2 -4 -6 5

10

50% higher Capital Requirements

of capital requirement of

banks

15

Mortgages D Commercial Loans Output D D 0

-5 0

Household default

-5

-0.5 -10 10

-20

-10 10

15

5

10

15

-0.5

0 10

15

5

10

15

0.05 0 -0.05 -0.1 5

10

15

-4 Risk Perception -6

5

10

10

15

10

-0.05

15

5

10

10

-0.02 15

5

10

-2

-0.1

-0.39 5

10

15

15

10

10

15

5

10

baseline calibration

Figure 17:Responses as a function

-20 5

10

15

-1

-2

5

10

15

5

15

-0.03

-10 15

15

15

5

10

15

5

10

15

5

10

15

5

10

15

-1 -4 10

15

10

5

10

15

0

0

-0.5

-1

-1

-2

-1.5

-3

15

5

10

15

-0.5 -1 -1.5 -2 -2.5 5

of

10

-0.5

10

15

-1 -2 -3 -4 -5 5

10

15

Share of borrowing households (1-s=0.5)

of the share

5

0

-2

5

-5

10

0

5

-0.025

10

-10

-1

0

5

-10

-0.5

-0.02

15

-5

-2

-3 5

0

0

2 0 -2 -4 -6 5

0

0

15

-0.1

-1

-0.38

10

Inflation D

15

0 -2 -4 -6 -8 5

Export D

0

15

-0.05

-0.37

Capital requirment

10

0 5

15

5

0.02

-10 5

10

-4

0.04

0 -0.5 -1 -1.5

-8

5

-6 5

15

-6

-8

15

-0.1

-0.5 -1 -1.5 -2

-0.05

-0.1

10

-1

-10 5

5

-0.05

0

-5

0.1

Commercial 0.05 default

-40

-0.4 5

15

0

-0.2

-1 5

Bank default

Consumption D Investment D

borrowing

households

Tighter Fiscal Policy Current Account/GDP D

Government Debt/GDP D

1

Government Debt/GDP F

30

8 7

0

25

-1

20

-2

15

6 5 4 3 2

-3

1

10

0 -4

-1

5

-2 -5

5

10

15

0

5

Default Shock for Households 0

10

15

Default Shock for Entrepreneurs

8

5

10

15

Default Shock for Banks

1.2

7

-0.2

-3

1

6 0.8

-0.4 5 -0.6

0.6

4

0.4

3

-0.8 -1

5

10

15

2

0.2

1

0

0

5

Risk Perception Shock

10

15

5

10

15

Capital Requirements Shock

Figure 18: Responses of the current account to GDP and the debt to GDP with tighter fiscal policy

Mortgages D Commercial Loans Output D D -6 Household -8 -10 default -12 -14

5

10

0.2 0 -0.2 -0.4 -0.6 15

10

-6 -8 -10 -12 -14 15

10

-0.05 -0.1 -0.15 -0.2 -0.25 15

0.1

Commercial 0.05 default 0

-0.05 5

Bank default

0.05 0 -0.05 -0.1 -0.15 5 -4

Risk

Consumption D Investment D

0 -0.1 -0.15

-5

-0.2 5

10

-10 15

5

10

-0.25 15

0

-0.05

-0.5

-0.1

5

10

20 0 -20 -40 -60 15

5

10

15

5

10

15

10

0.06 0.04 0.02 0 -0.02 15

-0.5 -1 -1.5 -2 5

10

15

5

5

10

-10 15

5

10

-0.5

10

5

10

15

-0.08 5

10

15

5

10

15

-0.34 -0.06

Capital -0.08

-0.36

-0.1 requirment

-0.38

-2

10

5

10

5

5

10

15

5

10

15

5

10

15

a

function

5

of

5

the

10

15

-2

-0.5

-4

-1

-6

-1.5

15

5

import

10

15

0

0

-0.5

-1

-1

-2 5

10

15

5

10

15

5

10

15

10

15

5

10

15

5

10

15

-1 -2 -3 -4 5

Lower import share (ωF=0.3)

baseline calibration

Figure 19: Responses as

15

5 0

-2

10

-15 15

15

-1

-0.5 -1 -1.5 -2 -2.5 15

-10

10

10

-1

15

-5

5

5

10

-3

-0.12

-15

0

0

-0.03 -0.04 -0.05 -0.06

-1

5

2 0 -2 -4 -6

-0.06

-10

-0.5

-5 -10 15

-5

0

0

0

-1 5

15

-5

-0.15

-8 -10 15

10

0

-0.04

Perception-8

5

Inflation D 0

0 -2 -4 -6 -8

-1

-6

-6

Export D

share

10

15

Commercial Loans D

Commercial Loans F

0

Mortgages D

0

0 -0.2

-0.2

-5

Mortgages F

0

-5 -0.4

-0.4 -0.6

-10

-10 5

10

15

5

Deposits D

10

15

5

Deposits F

10

15

Consumption D

-0.1 -0.2

-1

-0.2

-0.1

-0.4

-0.2

-0.6

-0.3 5

10

15

-0.8 5

Output D

10

15

-0.3

Output F

0 -5

5

10

15

0 -2

-5

15

10

15

10

15

-2 -4

-10

5

Investment D

15

0

-6 -8

-15 10

10

Labor F

-6 5

5

Labor D 0

-4 -10

15

Consumption F

0

0

-0.5

10

0

0.1 0

5

10

15

5

Investment F

10

15

5 Import D

Export D 0

0 0

0

-5

-2

-50

-20

-4 -40

-10

-100 5

10

15

5

Default Shock for Households

Figure 20: Responses

10

15

Default Shock for Entrepreneurs

to

financial shocks

5

10

15

Default Shock for Banks

5

Joint default shock

Inflation D

Inflation F

0

2

-5

0

-10

-2

-15

Net Interbank loans

Capital Return D

20

0

0

-0.5

-20

-4

-1

-40 5

10

15

5

Capital Return F

10

15

5

Real Wage D

10

15

5

Real Wage F 0

-0.2

-0.5

-0.5

0

-0.4

-1

-0.5

-0.6

-1.5

-0.8

-2

0

-1 5

10

15

5

Deposit Rate D

10

5

10

15

5

Mortgage Rate D

Mortgage Rate F

4

15

4

10

2

10

2

5

0

5

0

-2

0

-2

5

10

15

5

Commercial Loan Rate D

10

15

5

Commercial Loan Rate F

10

15

5

Bond Rate D

4

15

4

10

2

10

2

5

0

5

0

-2 5

10

15

Default Shock for Households

Figure

21: Responses

10

15

5

Default Shock for Entrepreneurs

to

financial

15

-2

0 5

10

Bond Rate F

15

0

15

-1.5

15

0

10

-1

15

Deposit Rate F

15

Policy Rate

0

0.5

10

shocks

10

15

Default Shock for Banks

5

10

15

Joint default shock

Output EA

Inflation EA

0 -2

Policy Rate

0

0

-2

-0.5

-4

House Prices D 0 -0.2

-1

-4 -6

-0.4

-1.5 -6

-8 5

10

15

5

House Prices F

10

15

5

Capital Price D

0

0.2

-0.5

0.1

-1

0

-1.5

-0.1

10

15

10

5

0

0

-5

-0.2

-10

-0.1

-0.1

-0.2

-0.2

10

15

5

10

15

Consumption Savers F

-0.3 5

10

15

5

Labor Savers D

10

Consumption Borrowers F 0 -0.2

-0.4

-0.4

-0.6

-0.6

-0.8

-0.8

15

5

10

15

5

10

15

-5 -10 5

Default Shock for Households

Figure

10

15

5

Default Shock for Entrepreneurs

22: Responses

to

financial

15

0.8 0.6 0.4 0.2 0 -0.2

-2 -3

10

Labor Borrowers F

0

-1

-20

5

Labor Savers F

0

-10

5

-0.2

Labor Borrowers D

0

15

-15

0 0

10

x 10RER

0.2

Consumption Borrowers D

0

15

5

15

Consumption Savers D

10

-14

Capital Price F

-0.4 5

5

10

15

Default Shock for Banks

shocks

5

10

15

Joint default shock

Housing Savers D

Housing Borrowers D

0

Housing Savers F

0.3

-0.05

0 -0.3

0 5

10

-0.01

15

5

Retail Bank Capital D

0.01

-0.2

0.1

-0.15

0.02

-0.1

0.2

-0.1

Housing Borrowers F

0

10

15

5

Retail Bank Capital F

10

15

5

Retail Bank Assets D

10

15

Retail Bank Assets F

6

400

3

200

300 200

4

100

2

100 0 10

15

5

Retail Bank Liabilities D

1

0

0 5

2

10

0

15

5

Retail Bank Liabilities F

10

15

Investment Bank Capital D

-0.5 -1 5

10

-0.1

100

-0.2

50

-0.3

0

50 0 -50

15

5

Investment Bank Assets D

10

-100

15

5

Investment Bank Assets F 4

20

2 0

10

5

10 15 Default Shock for Households

5

10

0

shocks

10

15

Investment Bank Liabilities F

2

10 15 Default Shock for Entrepreneurs

Figure 23: Responses to financial

5

20

-2

0

-4

15

4

-2 0

10

Investment Bank Liabilities D 30

30

15

100

150

0

10

Investment Bank Capital F

0.1 0

5

5

10 15 Default Shock for Banks

5

10 15 Joint default shock

Commercial Loans D

Commercial Loans F

Mortgages D

0

Mortgages F

0 0

-5

0

-2

-0.05

-4

-0.1

-6

-0.1 -0.2

-8

-10 5

10

15

-0.15

Deposits D

5

10

15

5

Deposits F

15

5

Consumption D

0.01 0

10

10

15

Consumption F

0

0

-0.05

-0.1

0

-0.05 -0.01

-0.1

-0.02

-0.15

-0.2

-0.1

-0.03 5

10

15

5

Output D

10

15

5

Output F

0

0

-1

-0.5

-2

-1

-3

15

5

Labor D

10

15

10

15

10

15

Labor F

0 0 -2 -1

-1.5

-4

10

-4

-2

-2 5

10

15

5

Investment D

10

15

Investment F

-10

-20

-15 15

5

10

Risk Perception Shock

Figure 24: Responses

5 Import D 0

-0.5

-1

-1

-2

-1.5

-3

-2

-30 10

15

0

-10

-5

10

Export D

0

0

5

5

to

financial

15

5

10

Capital Requirement Shock

shocks

15 Jointly

5

Inflation D

Inflation F

0

0.2

-2

0

Net Interbank loans

Capital Return D

4

0

2

-0.2

-0.2

-4

-0.4

-6

-0.6 5

10

15

5

Capital Return F

10

15

0

Real Wage D

15

-0.4 -0.6 10

15

0.1

15

6

0.2

4

0.1 -0.1

0

-0.2 10

15

5

Commercial Loan Rate D

10

15

-0.2 5

Commercial Loan Rate F

10

15

0.1 4

-0.2 5

10

15

0

2

-0.1

0

15

0.2

6

0 2

10

Bond Rate F

0.1

4

5

Bond Rate D

0.2

6

0

2

-0.1 5

5

Mortgage Rate F

0

2 0

10

Mortgage Rate D

0.2

4

-0.5 5

Deposit Rate F

6

15

-0.3

-0.4

5

Deposit Rate D

10

-0.2

-0.3 15

15

Policy Rate

-0.2

-0.2

10

10

-0.1

-0.1

5

5

0

0.2

-0.2

10

Real Wage F

0

0

-0.4 5

-0.1 -0.2

0 5

10

Risk Perception Shock

Figure 25: Responses

to

15

5

10

Capital Requirement Shock

financial

shocks

15

5 Jointly

10

15

Output EA

Inflation EA

Policy Rate

House Prices D

0

0

0 -0.1

-0.5

-1

-0.05

-0.2

-0.1

-0.3

-1

-0.15

-0.4

-2 5

10

15

House Prices F

-0.2

-0.5

-1.5

5

10

15

5

Capital Price D

10

15

0

-0.05 -0.05 10

Consumption Savers D

-0.1 10

5

10

-2

15

Consumption Borrowers D 0

-0.05

5

-0.1

15

0

5

10

15

Consumption Savers F

5

Consumption Borrowers F 0

0

-0.05

-0.1

-0.1

-0.1

-0.2

-0.2

15

5

Labor Savers D

15

2

0

0

5

10

4

0.05

-0.2

15

x 10RER

0.1 0.05

10

-14

Capital Price F

0

-0.4

5

10

15

5

Labor Borrowers D

10

15

5

Labor Savers F

10

15

Labor Borrowers F 0.3

0

-5

2

0

1.5

-1

1

-2

0.5 5

10

0.1 0

-3

0

-10

0.2

15

5

10

15

Risk Perception Shock

Figure 26: Response

to

financial

5

10

Capital Requirement Shock

shocks

15

5 Jointly

10

15

Housing Savers D

Housing Borrowers D

Housing Savers F

0.1

0 -0.02

0.05

-0.04

Housing Borrowers F

0

0

-0.05

-0.005

0

-0.06

-0.01

-0.1 5

10

15

5

Retail Bank Capital D

10

15

5

Retail Bank Capital F

10

15

5

Retail Bank Assets D

10

15

Retail Bank Assets F

0.6 30

0.15

10

0.4

20 5

10

0.1

0.2

0.05

0

0 5

10

15

0

Retail Bank Liabilities D

0

-0.2 5

10

15

5

Retail Bank Liabilities F

10

15

Investment Bank Capital D 0

0 -0.01 -0.02

-0.15 10

15

5

Investment Bank Assets D

40

-5

20

-10

0

-0.03 5

10

15

5

Investment Bank Assets F

10

15

10

15

15

Investment Bank Liabilities F

-0.2

-0.4

5

10

-0.1

4 2

-0.3

-0.6 0

5

0

-0.2

5

-15

Investment Bank Liabilities D

0 10

15

60

-0.05 -0.1

10

Investment Bank Capital F

0.01 0

5

5

10

15

Risk Perception Shock

Figure 27: Responses

to

0

5

10

Capital Requirement Shock

financial shocks

15

5 Jointly

10

15

Mortgages D Commercial Loans D Output D -5

0.2 0 -0.2 -0.4 -0.6

Household default -10 5

10

15

Commercial0.15 0.1 default

10

15

10 0 -10 -20 -30

-0.1 -0.2 5

10

15

5

10

0 0

10

15

10

-0.02 -0.04 -0.06 -0.08 -0.1 15

0.05 0 -0.05 -0.1 5

-4

5

10

15

-2 5

10

15

10

-0.05

15

5

10

5

10

-0.34

Capital requirment

-2

-0.1

-0.38 5

10

15

-3 5

10

15

15

5

10

15

baseline calibration

Figure

10

10

28: Prudential

monetary

5

10

0 -10 -15 5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

0 -1

-0.5 -1 10

15

-2 5

10

15

0

0

-5

-2

-0.5

-10

-4

-1

5

10

15

5

10

15 0

0

-1

-0.5

-2

-1 5

10

15

5

0

0

-5

-1

-10

-2

-15

-3

5

10

15

Adding credit gap in the Taylor rule

policy

-5

0

15

15

Inflation D

0 -2 -4 -6 -8 15

4 2 0 -2 -4 5

Export D

0

5

15

-0.02 -0.025 -0.03 -0.035

-1

-0.36

5

-0.05

-1 15

15

0

-0.5 10

10

0.05

0

5

5

15

0.5

-10 5

15

0.04 0.02 0 -0.02

-1

-8

-8

10

0

-6

-6

-0.1 5

10

2 0 -2 -4 -6

-0.05

-1

-10

5

15

-0.5

5

Risk Perception

5

-5

0.05 0

Bank default

Consumption D Investment D

0 -2 -4 -6 -8

10

15

-2 -4 5

10

15

Mortgages D Commercial Loans D Output D Consumption D Investment D -5

Household default

0 -2 -4 -6 -8

0.2 0 -0.2 -0.4 -0.6

-10 5

10

15

Commercial 0.1 0.05 default

5

10

15

5

10

15

5

10

15

5

10

15

0.05 0

-0.05 -0.1 5

10

15

-4

5

10

10

15

5

10

15

0 10

-0.02 15

5

10

-0.05

15

10

15

10

15

5

10

-0.38 -0.1

-1

-0.025

-2

-0.03

10

15

5

10

15

5

10

baseline calibration

15

5

10

10

15

10

15

0

0

-0.5

-1

-1

-2 5

10

15

10

15

0

0

-0.5

-1

-1

-2 5

10

15

-0.5 -1 -1.5 -2 -2.5 5

10

15

retail

10

15

5

10

15

5

10

15

5

10

15

5

10

15

-2 -4 5

10

Countercyclical buffer on retail banks

Figure 29: Countercylical capital requirement for

5

-0.2 -0.4 -0.6 -0.8 -1 -1.2 5

15

-10 5

-15 5

15

-5

-0.035

-3 5

10

0

-0.37

Capital requirment

-10

-4 5

15

-5

-2

-4 5

0

0

-2

-0.1

Inflation D

0 -2 -4 -6

15

0

-0.5

5

10

Export D

15

2

-0.05

-1 10

5

15

-10 5

10

0 -2 -4 -6 -8

0.02

5

5

0 -2 -4 -6

0.04

0

-8

-8

15

-0.1 5

15

-6

-6

10

-0.05

-0.5 -1 -1.5 -2

-0.05 -0.1

5

-1

-10

Risk Perception

-0.2

-0.5

0

Bank default

-0.1

0

-5

10 0 -10 -20 -30

banks

15

Mortgages D Commercial Loans D Output D -5

Household default -10 5

10

15

Commercial 0.1 0.05 default

10

5

15

10

-1

-10 10

15

5

10

15

-0.02 -0.04 -0.06 -0.08 -0.1

0.05 0 -0.05 -0.1 5

10

15

-4

10

15

10

5

10

-10 5

10

-0.05 Capital requirment

15

5

10

15

-0.38 5

10

-0.39 15

15

15

5

10

10

10

-2

15

5

15

10

15

-0.08 15

-4 15

5

10

15

-3

-0.035 15

5

10

baseline calibration

Figure 30: Countercylical

15

15

5

10

15

5

10

15

0

0

-0.5

-1

-1

-2

15

5

10

15

-0.5 -1 -1.5 -2 -2.5 5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

5

10

15

-0.2 -0.4 -0.6 -0.8 -1 -1.2

-4 10

-10 10

10

-2

-5

5

5 0

5

-2

-0.03

15

-1

-0.06

-2

10

-1

-0.04

-1

-15 5

-0.5

0

-0.025

-10

-2

2

10

-5

0

-0.02

5

0

0

0 -2 -4 -6 -8 5

Inflation D

0 -2 -4 -6

0

-6 10

Export D

15

-4 5

-0.02 15

5

0

-0.37

-0.1

10

0

-1

-8

5

0.02

-0.5

-8

-0.1 -0.15 -0.2 -0.25 15

10 0 -10 -20 -30

0.04

0

-6

-6

5

-0.5 -1 -1.5 -2 5

Consumption D Investment D

-0.02 -0.04 -0.06 -0.08 -0.1 -0.12

0 -0.5

5

Risk Perception

5

-5

0

Bank default

0 -2 -4 -6 -8

0.2 0 -0.2 -0.4 -0.6

-2 -4 5

10

15

Countercyclical buffer on investment banks

capital requirements for investment

banks