On the nature of the nancial system in the Euro Area: a Bayesian DSGE approach∗ †

Stefania Villa June 2, 2011

Abstract This paper estimates two versions of a DSGE model with nancial intermediaries, Gertler and Karadi (2011), with Euro Area data using Bayesian techniques. The rst version of the model uses a measure of the spread which is bank based; while in the second version the measure of the spread is market based. The two models are compared on the basis of: (i) the estimated parameters and the marginal data density ; (ii) business cycle moments; and (iii) the forecasting performance. The estimated model which performs better is also used to quantitatively assess the eects of non-standard monetary policy on a simulated recession caused by nancial shocks. The main results are as follows. First, the data clearly favour the model consistent with a bank-based nancial system in the Euro Area. Second, the proposed non-standard monetary policy moderates the simulated contraction. Keywords

: banking sector, Bayesian estimation, non-standard monetary policy : C11, E44, E5

JEL codes

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Introduction

After the 2007-2009 nancial turmoil, the structure of the nancial system has received an increasing attention in the macroeconomic literature. The debate about non-standard monetary policy and macroprudential policy, e.g. Lenza et al. (2010) and Bank of England (2009), takes the characteristics of external nancing and the relative importance of nancing instruments as the starting point of the analysis.1 The features of external nancing are particularly important because of the substantial eects of lending on the real activity. Since the onset of the crisis total nancing to households and to non-nancial corporations have sharply declined both in the Euro Area and in US. In the Euro Area loans of nancial institutions to I am grateful to ... and seminar participants at the European Central Bank (ECB) for useful comments and suggestions. Part of this work was written whilst I was visiting the ECB which I thank for the hospitality. Needless to say, the views expressed in this paper do not necessarily reect those of the ECB or the Eurosystem. All remaining errors are my own. † Birkbeck College, University of London, Malet Street, London WC1E 7HX, UK and University of Foggia, Largo Papa Giovanni Paolo II, 71100 Foggia, Italy. Email : [email protected]. 1 A nancial system is bank-based if the majority of loans originate and are held by banks. While a nancial system is market-based if non-bank lenders, such as government sponsored enterprises and private issuers of asset-backed securities, and market-based nancing, such as securitisation, are more important for external nancing (ECB (2009)). ∗

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non-nancial corporations (index of notional stock) decreased by more than 10 % between 2008Q4 and 2010Q4. It is important to disentangle the relative importance of credit demand versus credit supply in explaining the credit crunch. Ciccarelli et al. (2010) found that in the Euro Area the contraction in the supply of credit to rms contributed signicantly to the decline in the GDP growth during the nancial crisis. This evidence naturally poses the question about which institutions provide external nancing to the private sector. The Euro Area (EA) has been described as a bank-based nancial system, opposed to the market-based nancial system in the United States, e.g. Trichet (2009). The main source of nancing for non-nancial corporations (NFCs) is bank nancing, accounting for an average of 63% of total nancing between 2004 and 2007Q2. By contrast, in US in the same period bank nancing accounted for an average of 18% (ECB (2009)). The rst objective of this paper is to provide additional evidence on this topic from a Bayesian DSGE perspective. This paper estimates two versions of a DSGE model with nancial intermediaries, Gertler and Karadi (2011) (GK henceforth), by using as observables real GDP, real investment, seasonally adjusted GDP deator ination, loans to non-nancial corporations (PNFCs) and the spread. Two measures of the spreads are considered: a bank-based measure of the spread and a market-based measure. The model is estimated with euro data for the period 1996Q1-2008Q3. The comparison between the two models is made mainly by: (i) examining the estimated parameters and the marginal data density; (ii) comparing business cycle moments, such as relative standard deviations and correlations, of the observed data along with the corresponding model-implied moments; and (iii) looking at their respective forecasting performance using the Kalman ltered one-sided estimates of the observed variables along with the actual variables. The estimation results are also used to assess the overall t of the model. The second objective of this paper is to quantitatively assess non-standard monetary policy in the estimated model. The paper presents a non-standard measure which aims at reducing the spread between relevant interest rates. And it analyses the qualitative and quantitative impact of this non-standard credit policy to stimulate the economy hit by nancial shocks. The results of the DSGE model estimated for the EA are compared to those for the US, in the calibrated version of Gertler and Karadi (2011); and to the results for the UK in Villa and Yang (2011). The main ndings are: the data unambiguously support the bank-based nature of the nancial system for the Euro Area. And the credit policy attenuates the nancial accelerator mechanism in the model and, therefore, makes the simulated recession less severe. The paper is organised as follows. Section 2 sketches the DSGE model. Section 3 compares the two estimated versions of model. Section 4 discusses the estimation results; in particular, the transmission mechanism of the shocks via impulse response functions (IRFs); the contribution of structural shocks to the observed uctuations in the variables used in the estimation; and, following Smets and Wouters (2007) (SW, henceforth), the contribution of each of the frictions to the marginal likelihood of the DSGE model. Section 5 presents the eect of non-standard monetary policy in the estimated model. Section 6 briey concludes.

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The model

The baseline DSGE model, based on Gertler and Karadi (2011), introduces nancial intermediaries and non-standard monetary policy in an otherwise standard DSGE model, with the SW features: sticky prices, variable capital utilization, habit formation in consumption and investment adjustment costs, except sticky wages. The agents in the model are: households, intermediate goods rms, capital producers, monopolistically competitive retailers, nancial intermediaries (FIs), and the central bank. Households consume, supply labour, save by choosing deposits, and lend to FIs. There is asymmetric information between depositors and nancial intermediaries. Households consists of two types of members: the fraction f of the household members are workers and the fraction (1 − f ) are bankers. Bankers have a nite horizon: every banker stays banker next period with a probability θ, which is independent of history. Similarly, a number of workers becomes bankers, keeping the relative proportion of each type constant. The family provides its new banker with a start-up transfer, which is a small fraction of total assets, χ. Intermediate goods rms borrow from FIs to produce a homogeneous output sold in a perfectly competitive market. There is perfect information between nancial intermediaries and intermediate goods rms, which maximise prots by choosing the quantity of factors for production. Competitive capital producing rms maximise prots, i.e. the dierence between the revenue from selling the capital and the costs of buying capital from intermediate rms and the investment needed to build new capital. Retailers set prices in a staggered fashion, according to the rule proposed by Calvo (1983). The system of all equilibrium conditions is shown in the Appendix. The remainder of the section discusses the set-up of nancial intermediaries and nonstandard monetary policy. Financial intermediaries obtain funds from the household at the real rate Rt and they lend them to rms at the market lending rate Rtk . At the beginning of the period the nancial intermediary can divert a fraction λ of total assets and transfer them to her family. The cost of doing so is that the FI goes into bankruptcy. The objective of each nancial intermediary is to maximise expected terminal wealth, Vt . The presence of the moral hazard problem implies that lenders are willing to deposit money in the FI as long as the following incentive compatibility constraint holds:

Vt ≥ λQt St

(1)

where St is the quantity of nancial claims on non-nancial rms and Qt is the relative price of each claim. The LHS of equation (1) represents the loss for the FI from diverting funds, and the RHS represents the gain from doing so. When the incentive compatibility constraint is binding, equation (1) can be written as:

Qt St = ξt Nt

(2)

where ξt stands for FI leverage and Nt is FI capital or net worth. According to equation (2) the assets the FI can acquire depend positively on its equity capital. Therefore, the assets side of the FI's balance sheet is endogenously constrained. These assets corresponds to the loans to intermediate goods rms, which need to fully nance their acquisition of capital. Equation (2) makes it clear that the supply of credit by nancial intermediaries depends on overall economic conditions. Each shock, that directly or indirectly aects FI capital or more generally FI's conditions, has real eects through the changes in the provision of external nancing. 3

The shocks in the model are: monetary policy, FI capital, technology, capital quality, and government shock. The last three shocks follow an AR(1) process. A second important feature of the DSGE model is non-standard monetary policy, an additional tool for central bank intermediation.2 The Central Bank conducts both standard and non-standard monetary policy, i.e. it follows a standard Taylor rule: ρ
1−ρi i exp(εit ) (3) it = iρt−1 πtρπ yt y where it is the nominal interest rate, ρi is the interest rate smoothing parameter, ρπ and ρy are the standard Taylor rule parameters, and εit is the monetary policy shock. The central bank also follows the non-standard feedback rule for credit policy:

cpt = cp + ν[(Rtk − Rt ) − (Rk − R)]

(4)

with Qt Sct = cpt Qt St where Qt Sct is the value of assets intermediated via the central bank, which is a fraction, cpt , of total assets. This fraction cpt is set according to equation (4): when the spread, Rtk − Rt , deviates from its steady state value, the central bank injects assets in the economy and the magnitude of this non-standard intervention depends on the parameter ν . The non-standard measure works as follows: after obtaining funds from households at the rate R, the central bank lends the funds to the non-nancial rms at the market lending rate Rk . Therefore, the FIs balance sheet is not aected by this policy. 3

Model comparison

The model is estimated with quarterly data for the period 1996Q1-2008Q3 using as observables real GDP, real investment, seasonally adjusted GDP deator ination, loans to non-nancial corporations (PNFCs) and the spread. A discussion about the data and their transformation is presented in the appendix. The starting date is dictated by the availability of the data. And the nal quarter corresponds to the pre-crisis period: the collapse of the Lehman Brothers in September 2008 has been used as characterizing the crisis period, e.g. Lenza et al. (2010) and Giannone et al. (2011). Before comparing the estimation results, this section presents the calibrations for 'Model 1-bank spread ', where the series on the spread used as observable is bank-based, and for 'Model 2-market spread ', where the series on the spread is market based. The comparison between the two models is made rst by looking at the estimated parameters and marginal data densities for each model. Then, business cycle moments of each model are compared to "real facts". Finally, relative forecasting performance is presented.

Calibrated parameters In the model there are 27 parameters. The parameters, mainly pertaining to the nominal and real frictions in the model as well as the exogenous shock processes, are estimated and 2

In the 2007-2009 crisis, the deterioration in the balance sheets of many nancial intermediaries has strongly contracted lending and borrowing in a way that raised credit costs. In this environment, monetary policy could not have been implemented only along the standard line because of the zero lower bound on interest rates. Therefore, new strategies and tools have been designed to protect price stability.

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the results are shown in Table 3. The remaining parameters are calibrated, because they reproduce key great ratios in the data, such as consumption over GDP and investment over GDP. The calibrated parameters also reproduce steady state values of the data, such as steady state hours of work and steady state interest rate spread. The main references for DSGE models estimated for the Euro Area are: Christiano et al. (2010)(henceforth, CMR) and Christoel et al. (2008)(henceforth, CCW). Table 1 shows the calibration for both models. The main dierences between the two models lie in the calibration of the nancial parameters, because the respective steady state spread is dierent. In the dataset the annual steady state bank-spread is 80 basis points, while the annual steady state market-spread is equal to 60 bps. Parameter

Model 1-

Model 2-

bank spread

market spread

α, capital income share β , discount factor δ , depreciation rate µ, price mark-up φ, inverse of Frisch elasticity of labour supply ω , relative utility weight of labour h, habit persistence parameter θ, survival rate χ, fraction of assets given to the new bankers λ, fraction of divertable assets ν , the feedback parameter for credit policy

0.36 0.99 0.025 1.20 0.33 4.07 0.565 0.964 0.0004 0.2207 0

0.36 0.99 0.025 1.20 0.33 4.07 0.565 0.958 0.002 0.1545 0

Table 1: Calibrated parameters variable Hours of labour C Y I Y G Y

spread (basis points)

Model 1-

Model 2-

bank spread

market spread

0.33 0.57 0.21 0.22 80

0.33 0.57 0.21 0.22 60

Data: 1996-2008

0.33 0.57 0.21 0.22 80 - bank spread 60 - market spread

Table 2: Steady state values The capital-income share in the production function, α, is set at 0.36 as in CMR and in CCW. The discount factor is set equal to 0.99, implying a steady-state interest rate of about 4 percent per year. Quarterly depreciation rate is set equal to 0.025, implying an annual depreciation rate of 10 per cent. The steady state price mark-up is 1.2, following CMR. The inverse elasticity of labour supply, the relative utility weight of labour and the habit persistence parameter are calibrated so that agents allocate, on the average, one third of their available time to work.3 The value of the habit persistence parameter is 0.565, close to the one used by CMR and the estimated value found by CCN. 3

These parameters are calibrated because of the absence of observables related to the labour market.

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The three nancial parameters, θ, χ and λ have been calibrated so that the steady state banks leverage ratio is 11, similarly to Gerali et al. (2010), and the annual steady state interest rate spread is 80 basis points, the value in our dataset in Model 1, while it is 60 bps in Model 2.4 The feedback parameter for credit policy is clearly set equal to zero given the absence of such a policy through the sample period; consequently, the parameter measuring the persistence in credit policy is also set to zero. Section 5 discusses the eects of switching nonstandard monetary policy on. The steady state great ratios implied by the model match their empirical counterpart over the sample period, as shown in Table 2. In particular, the share of private consumption, total investment and government to GDP are equal, respectively, to 0.57, 0.21 and 0.22.

3.1 Estimated parameters and marginal data densities Table 3 shows the assumptions for the prior distributions of the estimated parameters for both models. The locations of the prior mean correspond to a large extent to those in CMR and CCW where applicable. The inverse gamma (IG) distribution is used for the standard deviation of the shocks with a loose prior with 2 degrees of freedom. The beta distribution is used for all parameters bounded between 0 and 1 and the gamma distribution for the parameters measuring elasticities. Similarly to Villa and Yang (2011), the normal distribution is used for the unbounded parameters. However, a lower bound is set for the parameter measuring the response to ination in the Taylor rule so that the Taylor principle is satised. The last two columns of Table 3 reports the mean of the estimated parameters for each model, computed with the Metropolis-Hastings algorithm. As long as the estimates concern the nominal and real frictions in the model, the dierence between the two models is not substantial. The estimated Calvo parameter, σ , implies in both models that rms reoptimise on average every 5 quarters. This value is consistent with the evidence reported in Altissimo et al. (2006) on the degree of price stickiness in the Euro Area. The degree of price indexation, σp , is lower than its prior. For this parameter, the posterior mean of Model 2 is considerably low. The elasticity of the cost of changing investment is estimated to be lower to that assumed a priori, suggesting a higher response of investment to changes in the value of capital in both models, with a higher value in Model 1. The estimates of the elasticity of marginal depreciation with respect to capital utilization are not dierent from its prior. However, Model 1 suggests a higher variation in capital utilization, while Model 2 implies a lower response of capital utilization. As far as the monetary policy reaction function parameters are concerned, in Model 1 the mean of the reaction coecient to ination is estimated to be lower than its prior mean and lower to the value found by CMR in a larger dataset. This value is even lower in Model 2. Monetary policy appears to react to the output gap and its mean value is higher than assumed a priori. This value is consistent with the ndings of CMR, who obtained a value of 0.25. The degree of interest rate smoothing is considerably low compared to the similar studies for the Euro Area, since its mean is equal to 0.453 in Model 1, 0.14 in Model 2 versus 0.867 in CCW and 0.871 in CMR. This result is in line with Consolo and Favero (2009), who examined the problem of weak instruments to identify the degree of monetary policy inertia. According to 4

The inclusion of the post-Lehman period would have considerably increased the average annual spread.

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Consolo and Favero (2009) and Rudebusch (2002), a high degree of interest rate smoothing hardly reconciles with the low predictability of monetary policy rates. These authors found that serially correlated or persistent shocks could explain monetary policy inertia. The main dierences between the two models arise with the estimates of the exogenous shock processes. The persistence of technology shock is 0.94 in Model 1 versus 0.76 in Model 2. The estimate of the model which uses the measure of the spread bank-based is in line with existing estimates for the Euro Area, namely CMR and CCW, who obtained a value of ρa equal to 0.97 and 0.89 respectively. The same rationale applies to the persistence of the government shock. The estimated persistence of the shock to the quality of capital is similar between the two models. As long as standard deviations are concerned, Model 1 implies signicantly lower standard deviations of structural innovations, but for the standard deviation of government shock, the value of which is higher in Model 1, 0.024 versus 0.022 in Model 2. The most volatile shock is the shock to FI capital, with a standard deviation of 0.22 in Model 1 and of 0.33 in Model 2. Overall, Model 1 requires smaller shocks to describe the data. Parameters

σ , Calvo parameter σp , price indexation S 00 , Inv. adj. costs ζ , elasticity of capital util ρπ , Taylor rule ρy , Taylor rule ρi , Taylor rule ρa , persist of tech shock ρk , persist of capital shock ρg , persistence of gov shock σa , std of tech shock σk , std of capital quality shock σi , std of monetary shock σn , std of FI capital shock σg , std of gov shock

Prior distr Posterior mean Distr Mean St. Dev. Model 1 Model 2 /df bank spread market spread Beta 0.72 0.05 0.790 0.786 Beta 0.375 0.2 0.075 0.034 Gamma 5.5 0.5 4.854 4.756 Gamma 1 0.5 0.911 1.177 Normal 1.75 0.05 1.725 1.715 Normal 0.125 0.05 0.223 0.212 Normal 0.87 0.05 0.453 0.142 Beta 0.9 0.1 0.939 0.760 Beta 0.5 0.1 0.265 0.253 Beta 0.9 0.1 0.877 0.696 IG 0.01 2 0.016 0.018 IG 0.01 2 0.019 0.019 IG 0.01 2 0.018 0.026 IG 0.01 2 0.222 0.327 IG 0.01 2 0.024 0.022

Table 3: Prior and posterior distributions of structural parameters Another dimension along which the two estimated models are compared is the Bayes factor, as in Levine et al. (2010) and Rabanal and Rubio-Ramírez (2005), among many others. Such a comparison is based on the marginal likelihood of alternative models. Let mi be a given model, with mi ∈ M , θ the parameter vector and pi (θ|mi ) the prior density for model mi . The marginal likelihood for a given model mi and common dataset Y is: Z L(Y |mi ) = L(Y |θ, mi )pi (θ|mi )dθ θ

where L(Y |θ, mi ) is the likelihood function for the observed data Y conditional on the parameter vector and on the model; and L(Y |mi ) is the marginal data density.

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The Bayes Factor between model i and model j is calculated as follows:

BFij =

L(Y |mi ) exp(LL(Y |mi )) = L(Y |mj ) exp(LL(Y |mj ))

(5)

where LL stands for log-likelihood. Comparisons based on equation 5 are important in the assessment of rival models. The log data density of the two models is based via the Laplace approximation; and the Bayes factor is: exp(LL(Y |m1 )) exp(770.7) BF12 = = = 5.7 × 1020 (6) exp(LL(Y |m2 )) exp(722.9) The analysis of the marginal data densities provides clear evidence in favour of the model estimated with the measure of bank-based spread over the model estimated with the measure of market-based spread.

3.2 Business cycle moments In this subsection the moments generated by the two models are compared with those in the data. Table 4 reports some selected moments of the data and of the simulated models. The statistical properties of the data reveals that the volatility of investment is higher than that of output. The relative standard deviation of ination is 0.5. These results are in line with those of CCW, who used a dierent ltering technique over the period 1985-2006. Loans to PNFCs is more volatile than output. Both measures of the spread are less volatile than output: the relative standard deviation of the bank-based spread is 0.36 while the relative standard deviation of the market-based spread is equal to 0.17. As far as correlations are concerned, the data reects that output and investment are positively correlated. Loans to non-nancial corporations are also pro-cyclical. GDP deator ination is counter-cyclical, in line with Stock and Watson (1999) and Kydland and Prescott (1998). Both measures of the spread are counter-cyclical, in line with Gertler and Lown (1999). Looking at the simulated moments, Model 1-bank spread approximately reproduces the relative standard deviation of investment (3 times more volatile than output) slightly less volatile in the model than in the data. In Model 1 the relative standard deviation of ination is lower than that in the data, 0.28 versus 0.5; a similar result is found for loans, 2.98 in the model versus 3.14 in the data. The relative standard deviation of the spread is smaller in the model than in the data, 0.23 versus 0.36. Model 2-market spread overpredicts the relative standard deviation of investment, which is more than ve times more volatile than output. It overpredicts the relative standard deviation of loans, which are almost four times more volatile than output, 3.80 versus 3.14 in the data. And it also overpredicts the volatility of the market-based spread, which is more volatile than output 1.68, contrary to its value of 0.17 in the data. Both models reproduce the sign of the rst-order correlations with output, preserving the pro-cyclical/counter-cyclical properties of the observables. However, Model 1 is preferable in terms of all the value of the contemporaneous correlation with output. The correlation of investment is 0.73 in the data versus 0.70 in Model 1 and 0.80 in Model 2. Concerning ination, its correlation is −0.45 in the data, −0.44 in Model 1 and −0.95 in Model 2, with ination moving approximately opposite to the cycle. Loans are pro-cyclical, with a value of 0.23 in the data, 0.39 in Model 1 and 0.59 in Model 2, which suggests a higher degree of positive correlation between loans and the cyclical component of GDP. Spreads are counter-cyclical in 8

both models; in Model 2 the simulated coecient more than doubles the actual value, −0.71 versus −0.31 in the data; in Model 1 the simulated moment is −0.35 versus −0.49 in the data. Therefore, the model estimated with the series of the spread bank-based provides better results in terms of simulated moments. Variable investment ination loans bank spread market spread Variable investment ination loans bank spread market spread

relative standard deviation Model 1-bank spread Model 2-market 2.71 5.60 0.28 0.18 2.98 3.80 0.23   1.68 correlation with GDPt data Model 1-bank spread Model 2-market 0.73 0.70 0.80 -0.45 -0.44 -0.95 0.23 0.39 0.59 -0.49 -0.35  -0.30  -0.71 data 2.97 0.50 3.14 0.36 0.17

spread

spread

Table 4: Simulated moments

3.3 Forecasting performance The forecasting performance of each model is assessed by computing the mean forecast error between the one-step ahead forecast and the actual data. Following Kirchner and Rieth (2010), Table 5 reports the root mean squared error (RMSE) computed with one-sided Kalman ltered estimates of the observed variables, at the posterior mode of the estimated parameters in each model.5 For both models, the MFEs are positive, suggesting that both models tend to underpredict the ve observables. In terms of magnitude of the MFE, According to the values of the RMSE Model 1, which uses a bank-based measure of the spread, provides the smaller forecast error for all the observables. While the dierence between the value of the RMSE for each model is small for GDP and loans, the RMSEs for investment, ination and the spread are signicantly larger in Model 2 compared to Model 1. In both models'specications, the RMSEs for GDP and investment are larger than those for ination, loans and the spreads. Therefore two main results emerge: (i) the overall predictive performance of Model 1 is better than that of Model 2 for all variables; (ii) GDP and investment are the variables for which the forecast error is greater. Forecast errors are close to zero for the two nancial variables, loans and spreads. This result is particularly interesting since the introduction of nancial frictions, in the form of asymmetric information between nancial intermediaries and depositors, and the consequent microfoundation of the nancial sector show reasonable empirical properties. The relatively inferior forecasting performance for GDP and investment is not surprising, since the class of 5

The formula is respectively: RMSE = is the one-step ahead forecast.

q

T −1

PT

t=1 (yt

9

− yˆt f )2 , where yt stands for the observable and yˆt f

model a la Gertler and Karadi (2011) does not include factors such as the labour market and the external sector, which might contribute to provide a better forecast for these variables. In sum, the model with the measure of the bank-based spread performs better in terms of forecasting some selected variables of the Euro Area. Variable GDP investment ination loans spread

Root mean squared forecast error Model 1-bank spread Model 2-market 0.0062 0.0065 0.0206 0.0258 0.0014 0.0020 0.0032 0.0033 0.0013 0.0015

spread

Table 5: Forecasting performance In sum, all the dimensions along which the performance of two models has been compared strongly support the result that a DSGE model with nancial intermediaries estimated with the measure of bank-based spread is preferable. 4

Estimation results

This section discusses the main estimation results of Model 1-bank spread, which performs better than Model 2-market spread. It analyses the IRFs to the monetary policy, technology and nancial shocks and discusses the transmission mechanism, with particular attention to the nancial accelerator eect originating from the credit market. It also presents variance decomposition of the GDP, ination and spread at dierent time horizons. And it discusses the empirical importance of dierence frictions, by examining the value of the marginal data density.

4.1 Impulse response function Figures 1-4 show the impulse response functions to four shocks: monetary, technology, bank capital and the shock to the quality of capital. The solid lines represent the estimated median and the dotted lines represent the 90% highest posterior density (HPD) condence intervals. All the shocks are set to produce a downturn. Figure 1 shows the eects on key macroeconomic variables and the link with the banking sector of the sole demand shock of the model. Contractionary monetary policy reduces investment and, therefore, output. Demand downward pressures feed through changes in the output gap to ination. This is illustrated by the downward shift in aggregate demand, which reduces ination on impact. Therefore this shock has a negative impact both on output and ination. This is the standard interest rate channel of monetary policy transmission. In the model, the transmission mechanism of the policy shock is enhanced through its impact on the nancial market. Due to the retrenchment in investment, the demand for loans decreases as well. As a result, bank prots fall and net worth decreases. At this point, the FI balance sheet constraint comes into play: nancial intermediaries cannot be over-leveraged because of the incentive compatibility constraint arising from the presence of asymmetric information. Therefore, FIs increase the lending rate more than the increase in the policy rate. As a result, 10

the spread increases; this causes a further decline in loans and investment as shown in Figure 1. Figures 2-4 show the responses to the three supply shocks of the model. A contractionary technology shock, of size 1.6% of its steady state, implies an immediate decline in output. The upward shift in aggregate supply determines an increase in marginal costs and, therefore, since rms are price setters and set prices as a mark up over the marginal cost, rms react by rising prices so that ination rises. Since the Taylor rule is operating, the policy rate increases. The nancial accelerator mechanism works through a second round eect originating from the reduction of investment, which implies a reduction of both the demand for loans and asset prices. This implies a deterioration in the balance sheet of nancial intermediaries. Due to the presence of asymmetric information, depositors require nancial intermediaries not to be over-leveraged; as a consequence, the lending rate increases by more than the increase in the policy rate and the spread rises as evident in the Figure 2. The shock to the quality of capital can be interpreted as a modelling device for capturing the broad dynamics of the sub-prime crises. Such a shock is also present in the model by Gertler and Kiyotaki (2009), where it is meant to capture economic obsolescence. If capital is good-specic, when the shock hits the economy, a random fraction of goods become obsolete and the capital used to produce the obsolete goods becomes worthless. Therefore, given a standard production function in capital and labour, this shock implies a contraction in output with eects similar to the technology shock. The increase in marginal costs implies an upward pressure on ination. However, this is only part of the whole story. The shock to the quality of capital directly translates into a shock to the bank balance sheet because of the identity between capital and assets: the loans provided by the nancial intermediaries to rms are used by the latter to fully nance their acquisition of capital. Therefore, this shock implies a reduction in what GK call the "quality of intermediary assets". As explained in Villa and Yang (2011) three factors aect the prots of nancial intermediaries: the amount of loans, the lending rate and the leverage. The reduction in total assets leads to a fall in banks prots. Therefore, in order to restore prots, nancial intermediaries increase the lending rate more than the increase in the policy rate. The rise in the spread is shown in Figure 3. The increase in nancing costs makes lending more expensive and rms reduce the demand for loans, further squeezing investment. The lower prot requires a further increase in the lending rate. The shock to bank capital shown in Figure 4 implies an immediate increase in the leverage, as evident from equation (2). This endogenous balance sheet constraint is always binding; therefore, nancial intermediaries are obliged to curtail their lending. The credit crunch is therefore originated by a contraction in the supply of credit by nancial intermediaries. As a result, investment is falling as well as output. The reduction in loans causes a fall in bank prots; and the same mechanism is at work. Financial intermediaries increase the lending rate to increase prots and this causes a further decline in lending and investment. On the nominal side, the contraction in output implies higher marginal costs and, therefore, ination rises. In the GK model the two nancial shocks behave like demand shocks, while these shocks behave as supply shocks also in the DSGE model estimated for the UK by Villa and Yang (2011), with a larger dataset including the crisis period, 1979Q1-2010Q1. Aikman and Paustian (2006) also found that a shock to the bank capital behaves as a supply shock in a DSGE model calibrated for the US economy. The shock to the quality of capital directly aects the production function, aecting the supply side of the economy. Therefore, not surprisingly, it

11

behaves as a supply shock. Another possible explanation6 for the behaviour of ination is that the lower potential growth rate for the Euro Area, and therefore the smaller output gap, implies less disinationary pressure. After discussing the qualitative features of the IRFs, the quantitative implications of the model are now presented. The quantitative eect of the technology shock on the nancial variables, such as net worth and asset price, is of minor impact compared to the other shocks because this shock aects the nancial variables in a second round eect originating from the reduction in investment. The other three shocks, instead, have a more direct impact on nancial variables. The interest rate shock is a 1.8 per cent increase in the policy rate. Financial intermediaries react to the simulated recession by increasing the lending rate by more; and this justies its relatively high value in terms of percentage deviations from steady state. The magnitude of the shock to the quality of capital is higher than the shock to bank capital. This justies the higher reaction of net worth, asset price and the spread in the latter case. The eects on output, investment and lending derive from the fact that the shock to the quality of capital aects on impact both the production function and the nancial variables, while the shock to bank capital aects on impact only the nancial variables. For all the three shocks, due to the consistent reduction of asset prices, the reduction of bank capital is prominent. This, in turn, aects the amount of loans because of the nancial accelerator mechanism at work through the endogenous balance sheet constraint. Financial frictions, therefore, exacerbates the simulated crisis.

4.2 Variance decomposition Movements in GDP, ination and spread are now decomposed into parts caused by each of the shocks at dierent time horizon, based on the mean of the model's posterior distribution. The model economy is driven by ve shocks: productivity, monetary policy, government spending, bank capital, and a shock to the quality of capital. In Figure 5 the two nancial shocks have been merged and are represented by the black bar. In the short run uctuations in real GDP are mainly driven by "demand shocks", in this model interest rate (white bar) and government shock (the white bar with black lines). As the time horizon increases, the supply shock, i.e. the productivity shock (the grey bar), accounts for the majority of variations in output, more than 80 per cent. The second panel of Figure 5 shows the variance decomposition for ination: interest rate shock accounts for a very small fractions of movements in ination, less than 5 per cent. And the supply shock accounts for an average of almost 95 per cent. These results are in line with those of SW. The nal panel shows the variance decomposition for the spread. In this case the contribution of each shock is not substantially dierent between the short run and medium- and long run. Not surprisingly nancial shocks and interest rate shock are the main drivers of this variable. The two nancial shocks contribute to more than 50 per cent of uctuations in the spread. Interest rate shock is a major contributor in the variations of spread, which is dened as the dierence between lending rate and risk free rate. Therefore, the latter component is mainly explained by interest rate shocks, while the two nancial shocks contribute in the explanations in the movements of the lending rate, which originates within the banking sector. 6

See Goldman Sachs (2010).

12

4.3 Dierent frictions The presence of many frictions poses the question of which frictions are important to account for the dynamics of the model. Similarly to Villa and Yang (2011), three types of frictions have been analysed: nominal frictions, related to the presence of price stickiness and price indexation; real frictions, related to the presence of investment adjustment cost and variable capital utilization; and nancial frictions. As in SW and Chang et al. (2002), the value of the marginal data density provides an indication of the overall likelihood of the model given the data. Table 6 shows the mode of the estimated parameters as well as the value of the marginal likelihood when each friction is drastically reduced one at a time. The rst column reproduces the baseline estimates and the marginal likelihood based on the Laplace approximation for the model. It should be noted that the DSGE model without nancial frictions collapses to a standard SW economy (without wage stickiness), where the spread between lending rates and policy rate is equal to zero and the bank capital shock is absent. In order to make an eective comparison between all model specications, the variable spread is not used as an observable and the bank capital shock has been removed. Consequently, estimates presented in Table 6 refer to a model with four structural shocks (technology, monetary policy, quality of capital and government) and estimated with four observables (GDP, investment, ination and loans), dierently from the estimates showed in Table 3. The second column of Table 6 reports the estimates of the baseline model for the purpose of comparison; the value of the marginal likelihood is equal to 623.1. The degree of price stickiness has been reduced to 0.1, implying that rms change prices every quarter, while the estimates suggest that rms reoptimise on average every 5 quarters. The marginal likelihood is signicantly reduced to the value of 573. The mode of the other parameters are substantially equivalent, but the persistence of government shock with a lower mode. Removing price indexation to past ination slightly aects marginal likelihood, and its value is 622.8. The mode of the Calvo parameter has slightly increased; overall, the parameters are substantially unaected by this change. On the side of real frictions, removing investment adjustment costs implies a considerable deterioration in terms of marginal likelihood, with a value of 560.7. The parameter most aected is the response of output gap in the Taylor rule, the mode of which increases. The presence of variable capital utilization is examined by setting the value of the elasticity of depreciation with respect to capital utilization to 5. A larger value of the elasticity implies higher marginal depreciation cost, and therefore less variation in capital utilization. Removing this friction does not imply a deterioration of the marginal likelihood; its value is even higher, equal to 630.9 versus 623.1 in the baseline model. Similarly to SW, shutting this friction comes at no cost in terms of model's performance. The last column of Table 6 presents the results for the model without nancial frictions (FF). The model without nancial intermediaries collapses to a standard SW model, without wage stickiness. The marginal likelihood is reduced to the value of 578.1. Eliminating nancial friction increases the real friction of the model in terms of variable capital utilization and aects the Taylor rule parameter on interest rate smoothing, which have a higher mode. The standard deviation of all the shocks has increased, but for the interest rate shock: its mode is robust across all specications, always equal to 0.018. This result could re-conciliate with 13

the ndings of Consolo and Favero (2009) and Rudebusch (2002), according to whom the "illusion" of monetary policy inertia can be related with the presence of persistent unobserved shocks to the process generating ination. The most volatile shock of Table 3, the shock to bank capital capital, is absent in this specication without nancial frictions. And the data clearly favour the model with nancial frictions for the Euro Area. Base

σ = 0.1

σp = 0

S 00 = 0.1

ζ = 10

no FF

623.1

573.0

622.8

560.7

630.9

578.1

0.10 0.151 5.016 1.018 1.817 0.198 0.458 0.977 0.181 0.816 0.014 0.018 0.013 0.019

0.81 0 5.019 1.07 1.767 0.186 0.481 0.896 0.212 0.904 0.015 0.018 0.013 0.019

0.818 0.133 0.10 1.026 1.765 0.275 0.446 0.86 0.192 0.887 0.015 0.018 0.012 0.017

0.801 0.159 5.014 5 1.778 0.178 0.478 0.927 0.191 0.914 0.016 0.018 0.014 0.020

0.795 0.137 4.933 0.973 1.796 0.187 0.665 0.929 0.26 0.79 0.027 0.018 0.026 0.021

Marginal likelihood

Mode of estimated parameters

σ , Calvo parameter σp , price indexation S 00 , Inv. adj.costs ζ , capital util. ρπ , Taylor rule ρy , Taylor rule ρi , Taylor rule ρa , persist of tech shock ρk , persist of capital shock ρg , persist of gov shock σa , std of tech shock σi , std of monetary shock σk , std of capital shock σg , std of gov shock

0.791 0.141 5.019 1.08 1.771 0.18 0.479 0.915 0.214 0.907 0.015 0.018 0.013 0.019

Table 6: Empirical importance of dierent frictions 5

Non-standard monetary policy

In response to the nancial crisis, the ECB has undertaken non-standard monetary policies dened "enhanced credit support" (see Trichet (2009) and Lenza et al. (2010) for detailed discussions). The non-standard measures implemented by the ECB are based on four main blocks: 1. the unlimited provision to banks of liquidity through "xed rate tenders with full allotment"; 2. the expansion in the list of eligible collateral; 3. the innovations in the number and variety of Euro-system longer-term operations, in order to lengthening of the maturities of ECB renancing operations; 4. and the outright purchase of covered bonds, in order to alleviate bank funding conditions and promoting credit creation through the banking system. In addition, the ECB has provided liquidity in foreign currencies. Such policies have been designed for the specic nancial structure of the Euro Area; the ECB has largely implemented the non-standard measures via the banking sector. 14

The DSGE model, instead, implies direct central bank intervention in the non-nancial sector. Therefore, the non-standard monetary policy implemented by the ECB cannot be compared to the simple unconventional monetary policy introduced in the DSGE model, equation (4). Notwithstanding, similarly to the non-standard measures implemented by the ECB, the credit policy described in equation (4) aims at reducing the spreads, after their considerable increase since the onset of the crisis. At their peak following the collapse of the Lehman Brothers, the spreads skyrocketed. Lenza et al. (2010) reported that the spread between unsecured deposit rates (EURIBOR) and overnight indexed swap (OIS) rates at the threemonth maturity approached 200 basis points in the euro area. Equivalent spreads were even higher in the US and UK. The reduction of the spreads is the driver of the transmission mechanism followed by credit policy. In this counter-factual experiment, the channel of non-standard monetary policy is activated by setting the value of the response parameter of equation (4), ν , non-zero. The DSGE model is now solved by using the estimated parameters of Table 3 and two values for ν are used: ν = 10 corresponding to a moderate intervention and ν = 100 corresponding to an aggressive intervention. In setting the parameter for this experiment, it should be noted that the magnitude of the intervention of the ECB cannot be compared to that of the Bank of England or of the Fed. The total size of the balance's sheet at the Fed and Bank of England more than doubled after the collapse of the Lehman Brothers, while the Eurosystem balance sheet increased by approximately 60% (see charts 5, 7 and 8 in Lenza et al. (2010)). In Figure 6 the response of output, ination, loans and spread to the two nancial shocks are analysed, as in Villa and Yang (2011). The solid line shows the response of the variable without the credit policy; the black dotted line represents the response of the corresponding variable with a moderate credit market intervention. And the red dashed line represents aggressive credit policy. In the case of the shock to the quality of capital the rst column of Figure 6 shows the responses of the macroeconomic and nancial variables. The parameter ν = 10 corresponds to a fraction of assets intermediated via the central bank equal to 0.9% of the total assets in the economy. When ν = 100 , the fraction of assets intermediated via the central bank corresponds to 1.4% of total assets in the economy. In both cases non-standard monetary policy alleviates the crisis. Since the additional instrument aims at reducing the spread, the spread is reduced by more than 50 bps as evident in the chart. As a consequence, the contraction in loans is less pronounced and the crisis is less severe. The purpose of this non-standard rule is to attenuate the amplication eect deriving from the nancial accelerator mechanism. When non-standard monetary policy is switched on, the modest increase in the spread does not have a considerable impact in the bank's prots and on the demand for loans, dierently from the IRFs described in the previous section. In the case of the shock to bank capital the parameter ν = 10 corresponds to a relatively small fraction of assets intermediated via the central bank equal to 0.7% of the total assets in the economy. The more aggressive intervention requires a value of ν = 100, which corresponds to 1.1% of total assets in the economy. Central bank intermediation implies a reduction of the spread of the order of almost 100 bps. The non-standard measure clearly supports the ow on bank loans to the corporate sector. The tightening of loans and the contraction of output followed by the shock to the quality of capital are of negligible amount compared to the no-credit policy scenario, as evident from the second column of Figure 6.

15

Credit policy is benecial not only in terms of contraction of output, but also in terms of ination. Therefore, similarly to the results of the GK model calibrated for the US economy and of the GK model estimated for the UK economy by Villa and Yang (2011), the proposed credit policy moderates the contraction. The reduction of the spread followed by a non-standard monetary policy measure is also found by Lenza et al. (2010), who applied an empirical methodology based on a Bayes vector autoregression model of the euro area. 6

Conclusion

A DSGE model with nancial intermediaries, à la Gertler and Karadi (2011), has been estimated with Bayesian techniques for the period 1996Q1-2008Q3 with Euro area data. Two measures of the spread have been used: a measure of the spread is bank-based while the other is market-based. The model estimated with the bank-based spread provides better results according to all the following criteria: the comparison of estimated parameters and the analysis of the marginal data density; the comparison between the simulated versus actual moments; the forecasting performance. These ndings support the evidence on the bank-based nature of the nancial system for the Euro Area. The estimated model is used also to quantitatively assess non-standard monetary policy in the form of loans to the private sector. This policy does not replicate the "enhanced credit support" implemented by the ECB. In this counter-factual experiment, the intervention of the central bank aiming at reducing the spreads makes the simulated crisis less severe when the economy is hit by nancial shocks.

16

References

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Bank

Altissimo, F., Ehrmann, M., and Smets, F. (2006). Ination Persistence and Price-Setting Behaviour in the Euro Area-A Summary of the IPN Evidence. ECB Occasional Paper, (46). Bank of England (2009). The Role of macroprudential policy. Technical report, Discussion Paper. Calvo, G. (1983). Staggered prices in a utility-maximizing framework. Economics, 12(3):383398.

Journal of Monetary

Chang, Y., Gomes, J., and Schorfheide, F. (2002). Learning-by-doing as a propagation mechanism. American Economic Review, 92(5):14981520. Christiano, L., Motto, R., and Rostagno, M. (2010). Financial factors in economic uctuations. ECB Working Paper, (1192). Christoel, K., Coenen, G., and Warne, A. (2008). The new area-wide model of the euro area: a micro-founded open-economy model for forecasting and policy analysis. ECB Working Paper, (944). Ciccarelli, M., Maddaloni, A., and Peydro, J. (2010). Trusting the bankers: a new look at the credit channel of monetary policy. ECB Working Paper, (1228). Consolo, A. and Favero, C. (2009). Monetary policy inertia: More a ction than a fact? Journal of Monetary Economics, 56(6):900906. ECB (2009). The external nancing of households and non-nancial corporations: a comparison of the Euro Area and the United States. ECB Monthly Bulletin, 04:6984. Gerali, A., Neri, S., Sessa, L., and Signoretti, F. (2010). Credit and Banking in a DSGE Model of the Euro Area. Journal of Money, Credit and Banking, 42:107141. Gertler, M. and Karadi, P. (2011). A model of unconventional monetary policy. Monetary Economics, 58(1):1734.

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Gertler, M. and Kiyotaki, N. (2009). Financial Intermediation and Credit Policy in business cycle analysis. Manuscript. Gertler, M. and Lown, C. (1999). The information in the high-yield bond spread for the business cycle: evidence and some implications. Oxford Review of economic policy, 15(3):132. Giannone, D., Lenza, M., Pill, H., and Reichlin, L. (2011). Non-Standard Monetary Policy Measures and Monetary Developments. ECB Working Paper, (1290). Goldman Sachs (2010). The puzzling behaviour of core ination. 10/32.

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Kirchner, M. and Rieth, M. (2010). Sovereign risk and macroeconomic uctuations in an emerging market economy. Tinbergen Institute Discussion Papers, 10-100/2. 17

Kydland, F. and Prescott, E. (1998). Business cycles: real facts and a monetary myth. business cycles: a reader, pages 383398. Lenza, M., Pill, H., and Reichlin, L. (2010). Monetary policy in exceptional times. Policy, 25(62):295339.

Real

Economic

Levine, P., Pearlman, J., Perendia, G., and Yang, B. (2010). Endogenous Persistence in an Estimated DSGE Model under Imperfect Information. Department of Economics Discussion Papers. Rabanal, P. and Rubio-Ramírez, J. (2005). Comparing New Keynesian models of the business cycle: A Bayesian approach. Journal of Monetary Economics, 52(6):11511166. Rudebusch, G. (2002). Term structure evidence on interest rate smoothing and monetary policy inertia. Journal of monetary economics, 49(6):11611187. Smets, F. and Wouters, R. (2007). Shocks and frictions in US business cycles: A Bayesian DSGE approach. American Economic Review, 97(3):586606. Stock, J. and Watson, M. (1999). Business cycle uctuations in US macroeconomic time series. Handbook of Macroeconomics, 1:364. Trichet, J. (2009). The ECB's enhanced credit support. In Speech at

the University of Munich

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Villa, S. and Yang, J. (2011). Financial intermediaries in an estimated DSGE model for the UK. The Financial Crisis and Lessons for Monetary Policy, ed. J. Chadha and S. Holly.

18

−3

x 10

Output

Investment

0

−3

0.01

0

0

−2

−0.01 −5

x 10

Loans

−4

−0.02 −6

−0.03 −10

−0.04

−8

−0.05

−10

−0.06 −15

−12

−0.07 10

20

30

10

Marginal Cost

−3

−3

x 10

1

x 10

20

30

10

Inflation

20

30

Net worth

0

−0.1 0.5 −0.2

−5 0

−0.3 −0.4

−10

−0.5 −0.5

−15

−1

−0.6 −0.7

−1.5

−20 10

20

30

10

Asset price

−3

x 10

20

30

10

Spread

20

30

Lending Rate 0.03

0 −0.01

10

−0.02

8

0.025 0.02

−0.03 6

0.015

−0.05

4

0.01

−0.06

2

0.005

−0.04

−0.07 10

20

30

0

10

20

30

0

10

20

30

Figure 1: The estimated IRFs to a monetary shock. The standard error of the monetary policy shock is 1.8%. 19

Output

Investment

−3

0

0

−0.005

0

−2

−0.01

−4

x 10

Loans

−6

−0.02 −0.01

−8 −0.03 −10 −0.04

−0.015

−12

−0.05 −0.02

−14 −16

−0.06 10

−3

x 10

20

30

10

Marginal Cost

−3

x 10

20

30

10

Inflation

20

30

Net worth 0

16

6 −0.05

14

5

12

−0.1

10

4

8

3

−0.15 −0.2

6

2

4

−0.25 1

2 0

−0.3 0 10

20

30

10

Asset price

−3

x 10

0

20

30

10

Spread

20

30

Lending Rate

−3

7

5

x 10

6

−0.005

5

4 −0.01

4 3

−0.015 −0.02

2

−0.025

1

3 2 1 0

−0.03

0 10

20

30

−1 10

20

30

10

20

30

Figure 2: The estimated IRFs to a technology shock. The standard error of the technology shock is 1.6%. 20

−3

x 10

Output

Loans

Investment 0.03 −0.015

0 0.02 −2

0.01

−4

0

−0.02 −0.025

−0.01 −6

−0.03

−0.02 −8

−0.03

−0.035

−0.04 10

20

30

10

Marginal Cost

−3

x 10

−4

x 10

3.5

20

30

10

Inflation

20

30

Net worth

16

3

14

2.5

12

−0.1 −0.2

10

2

−0.3

8 1.5

6

−0.4

1

4

−0.5

0.5

2

0

0

−0.6 10

20

30

10

Asset price

−3

x 10

0

20

30

10

Spread

Lending Rate

7

7 6

6

−0.015

5

5

−0.02

4

4

−0.025

3

3

−0.03

2

2

1

1

−0.035

30

−3

x 10

−0.005 −0.01

20

−0.04 10

20

30

0

10

20

30

10

20

30

Figure 3: The estimated IRFs to a shock to the quality of capital. The standard error of the quality of capital shock is 1.9%. 21

−3

x 10

Investment

Output

0 −2 −4

−3

0.01

0

0

−2

−0.01

−4

−0.02

−6

−0.03

x 10

Loans

−8

−6 −0.04

−10

−0.05

−8

−12 −0.06 −10 10

20

30

10

Marginal Cost

−4

−3

x 10

x 10

20

30

10

Inflation

20

30

Net worth

5 16

−0.1

14

4

−0.2

12 3

−0.3

10 −0.4

8 2 1 0

6

−0.5

4

−0.6

2

−0.7

0 10

20

30

10

Asset price

−3

x 10

20

30

10

Spread

30

Lending Rate

−3

x 10

0

12

12

−0.01

10

10

8

8

6

6

4

4

2

2

−0.02

20

−0.03 −0.04 −0.05 10

20

30

0

0 10

20

30

10

20

30

Figure 4: The estimated IRFs to a shock to bank capital. The standard error of the bank capital shock is 22%. 22

GDP 100%

financial government

75%

technology interest rate

50%

25%

0% Q1

Q4

Q12

Q40

Q80

Inflation 100%

financial 75%

government technology

50%

interest rate

25%

0% Q1

Q4

Q12

Q40

Q80

Spread 100%

financial

75%

government technology

50%

interest rate 25%

0% Q1

Q4

Q12

Q40

Q80

Figure 5: Variance decomposition 23

Quality of capital shock

−3

−3

x 10 0

−2

−2

Output

Output

x 10 0

−4

Bank capital shock

−4 −6

−6

5

10

15

20

25

30

5

10

15

20

25

30

10

15

20

25

30

10

15

20

25

30

−3

x 10

−4

Loans

−0.025

−6 −8 −10

−0.03 5

10

15

20

25

30

5 −4

−4

x 10

12

12

10

10

Inflation

Inflation

x 10

8 6 4

8 6 4 2

2 5

10

15

20

25

30

5

100

Spread (bps)

60

Spread (bps)

Loans

−2 −0.02

50 40 30 20 10 5

10

15

20

25

30

60 40 20 0

Figure 6: Credit Policy 24

no cp ν=10 ν=100

80

5

10

15

20

25

30