An Analysis of Italian Bad Loans: Determinants, Forecasts

and Transmission to the Real Economy

Alessandro Carboni and Andrea Carboni

This Draft: November 2014

Abstract

Since 2009 conditions in Italian credit market have been experiencing a dramaticworsening, reflecting the two most severe recessions since the Great Depression. Prob-ability of default for non financial firms has reached unexpected values, while deteri-oration in credit portfolios has spread. This paper studies bad loans for Italian nonfinancial firms during the last twenty years. We propose different linear and non-linearmethodologies focusing on short and long-term determinants, forecasting propertiesand dynamic responses. Our empirical results suggest that macroeconomic and finan-cial, but also, specified lenders and borrowers variables affect bad loans. Linear andnon-linear models augmented with financial variables and asset prices produce betterout-of-sample forecasts. A dynamic response analysis shows that default rates movewith a cyclical pattern, falling after a positive shock in macroeconomic and financialvariables. Moreover, a positive shock in bank credit or in default rate does not producea clear feedback effect from credit to the real economy. In a non-linear framework,this happens only when the default rate is above a critical value, suggesting a possiblebreakdown in the transmission of credit to the real economy when credit quality isweak.

JEL Classification: C22, C32, E44, G21.Keywords: Bad loans, credit risk, determinants, feedback effects, threshold models.

University of Siena, Master in Economics and Banking. Comments are welcome. Alessandro Carboni:alecarbo@msn.com. Andrea Carboni: andreacarbo@tiscalinet.it. Errors and omissions remain our ownresponsibility.

1 Introduction, Literature and Motivation

Since 2009 conditions in Italian credit market have been experiencing a dramatic wors-ening, reflecting the two most severe recessions since the Great Depression. Probabilityof default for non financial firms has reached unexpected values, while deterioration incredit portfolios has occurred. This phenomenon was analyzed in many financial stabilityreports produced regularly since 2010 by the Italian central bank and in various ECB banklending surveys about current and future credit conditions.1 Credit risk has received theattention of policy makers and academics interested in its determinants, business cycleeffects, stress testing, and more recently macroprudential policies.

There is a widespread consensus about bad loans determinants which can be divided inmacroeconomic factors, borrowers and lenders conditions.2 Berger and DeYoung (1998)and Salas and Saurina (2002) describe theoretically the relations between determinantsand bad loans. In the first paper, the authors define four hypothesis linking bad loans tocost efficiency in commercial banks: i) bad luck, by which external events are driversfor an increase in bad loans; ii) bad management, relating low cost efficiency, in theform of difficult monitoring and poor skills, to a growth in bad loans; iii) skimping, bywhich, lower investments in monitoring could affect both loan quality and cost efficiency;iv) moral hazard, with low capitalized banks responding to moral hazard incentives byassuming more risk taking in the form of future bad loans. In the second paper, Salas andSaurina (2002) study how the ratio of Spanish problem loans (the amount of problem loansto total loans) relates with: real GDP growth, households and firms liabilities over GDPand equity, and the growth rate of loans. Moreover, they add different banking specificvariables (lender determinants), like operating costs to operating margin, the ratio of noncollateralized loans to total loans, lagged values for net interest margin, the size, bankssolvency problems, a measure for the market power, and finally the lagged risk premiumcharged by banks. They study both commercial and savings banks and find that: i) higherpast values of real GDP and lower borrowers indebtedness are negative drivers of problemloans; ii) an increase in loan growth and managerial incentives determine future loan losses;iii) they also find different impacts of lenders specific variables for commercial and savingbanks. There are other interesting related papers. Murto (1994) uses macroeconomic andbanking specific determinants, together with contractual dummies, to study the pricingfor bank loans in Finland. Shockley (1995) analyzes the relation between bank lendingand corporate leverage, while Booth and Booth (2006) demonstrate that moral hazardcould explain why secure lending increases with default risk. Keeton (1999) offers ananalysis of how loan growth can or can not lead to higher loan losses. The author definesthree possible shifts: i) positive supply shifts, represented by a reduction in lending ratecharged on new loans and lower minimum standards, generate the following channel: lowercredit standards, higher loan growth and higher loan losses; ii) a positive demand shift:

1Bank of Italy (2013) focuses on the asset quality review on non-performing loans.2The literature on bad loans for countries all over the world is enormous. Here we referenced papers

studying advanced banking systems.

2

an increase in demand for credit unrelated to borrowers ability to pay will increase loangrowth, lending rates and tighten credit standards, raising the average credit worthinesswith a corresponding reduction in future loan losses; iii) a positive productivity shiftboosts loan growth and reduces future loan losses. Jimenez and Saurina (2006) confirm therelationship between rapid lagged credit growth and loan losses, especially during boomsin credit cycles. Ghosh (2005) considers a simultaneous equation model for non-performingloans in India, using real GDP growth, inflation, M3 growth, real cost of capital and realeffective exchange rate as macro determinants, while corporate sector leverage and theratio of capital to risk-weighted assets, for the others.3 The author finds negative signs forcurrent and lagged values of real GDP, as well as for current inflation. Lagged capital torisk-weighted assets enters with a negative impact, while higher leverage and interest ratesraise non-performing loans.4 Rinaldi and Sanchis-Arellano (2006) and Louzis et al. (2010)demonstrate unit root properties in non-performing loans for a panel of European countriesand for the Greek banking sector, respectively. Among the others, their empirical resultsbroadly confirm the signs of the determinants previously described. Louzis et al. (2010)also study the role of lagged bank ratios, adding and confirming the bad management IIhypothesis, by which worse banking performance is positively associated to an increase infuture bad loans. With a panel analysis, Klein (2013) adds lagged values of banks returnon equity to the other banks determinants, obtaining a negative response, while Beck etal. (2013) consider current and past asset prices, in the form of nominal effective exchangerates and share prices, and obtain a negative reaction of bad loans. The role of collateralwas studied by Jimenez and Saurina (2004) and Jimenez et al. (2004), who analyzedmicro data characteristics at single loan level, extracted from the Spanish banking creditregister. They find that collateralised loans have a higher probability of default, and thatthe use of collateral is high for low credit quality loans. Moreover, they also confirm thata longer lender-borrower relationship reduces the required collateral.5

Stress testing exercises allow both regulators to understand the resilience of the entirebanking system against adverse scenarios, and managers to have an idea about their in-stitution, especially for the credit risk side.6 Among the others, we refer to Hoggart et al.(2005) for an application of stress test to UK banks, Jakubk and Schmeider (2008) forspecific application of credit risk stress testing for Czech republic and Germany. More-over, Gasha and Morales (2004) study a self extracting threshold autoregressive (SETAR)model to identify threshold effects for credit risk stress testing, while in the last years,Serwa (2011) and (2013) deals with multiple regimes in a model with credit to householdsand with non-performing loans during booms and busts in credit cycle, finding different

3Non-performing loans, capital to risk-weighted assets, corporate leverage and real cost of capital areendogenous variables. See Ghosh (2005) for further information.

4Similar determinants were used by Athanasoglou et al. (2008) in a study of banking profitability.5We remember, among others, the paper of Beck et al. (2014) for a study of relationship banking over

the business cycle.6See Quagliariello (2009) for an overview of the stress testing methodology.

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responses for different regimes.7 Another stream of literature deals with the feedbackeffects of credit risk to the macroeconomy. We remember the studies of Gambera (2000)and more recently Nkusu (2011) and Klein (2013). The first paper uses bivariate vectorautoregression (VAR) linking the quality of bank loans to the business cycle, while Nkusu(2011) and Klein (2013) study dynamic responses of non-performing loans in a panel VARmodel with bad loans and macroeconomic determinants. They find that non-performingloans are affected by macro determinants, and also demonstrate that there is a feedbackeffect from the banking sector to the entire economy.

During the last years, macroprudential analysis has become essential in central bank-ing, together with price-stability oriented monetary policy, in order to deal with financialstability. The literature on macroprudential policies is immense. Among others, we men-tion the paper of Borio et al. (2001), the overview provided by Banque de France (2014),Smets (2013) and the final report of the Macro-prudential research network (MaRs).8

Jimenez et al. (2014) study the effect of monetary policy on credit risk taking using loan-level micro data from the Spanish credit register. They find that lower overnight ratesare related to a prolonged increase in credit issued by low capitalized banks to riskierborrowers. Moreover, lower long-term rate has no influence on credit. In a related pa-per, Jimenez et al. (2013) find that dynamic countercyclical loan loss provisions in Spainhelps restoring credit market stability during credit cycles.9 Finally, Behn et al. (2014)study model-based regulation applied to Germany and show that: internal risk models sys-tematically underestimate default probabilities; loans originated within the model-basedregulation have higher default rates and therefore higher interest rates charged. Theyconclude that model-based capital regulation adversely affect financial stability (Behn etal, 2014).

The Italian experience has a separated treatment in our overview of the literature.Bank of Italys economists accurately study the evolution and the implications of theItalian banking system. Quagliariello (2004) analyzes the reaction of Italian banks per-formance to the evolution of the business cycle describing, theoretically, the transmissionmechanism from the macroeconomy to the banking sector and, empirically, the procyclical-ity of banks balance sheet. Marcucci and Quagliariello (2006) and (2008) further reinforcethe procyclicality of banks portfolio riskiness through a VAR, while they also documentdifferent credit behaviors over different regimes performing threshold regression analysis.Fiori and Iannotti (2010) study the interaction between market and credit risk using afactor augmented VAR (FAVAR) approach on a large data set and provide evidence offeedback effects from the financial sector to the real economy. Bofondi and Ropele (2011)offer an analysis of macroeconomic determinants of bad loans for both non financial firmsand households. They also produce forecasts of bad loans. They find that a small numberof macroeconomic variables helps predicting bad loans, even in turbulent times. De Mitri

7See Mendoza and Terrones (2012) for a description of the anatomy of the credit boom.8See European System of Central Banks (2014)9They confirm the study of Jimenez and Saurina (2006) about the usefulness of this countercyclical tool

for the Spanish banking system.

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et al. (2010) use micro data from Centrale dei Rischi (the Italian credit register) and fromCentrale dei bilanci (company accounts data service) matching bank data with balancesheet information of the borrower. In a panel analysis, they show that relationship lend-ing changes after a financial turmoil, and particularly that firms that borrow from a smallnumber of banks are more insulated from supply shock in credit markets (De Mitri et al.,2010). More recently, Gambacorta and Mistrulli (2014) find that borrowers with closerand long-lasting bank relationship have lower interest rate spreads and that borrowingfrom banks with large capital and liquidity buffers, but also mainly involved in traditionallending, assure protection against the effects of the financial crisis. Finally, Albertazzi etal. (2014) present evidence of the impact of the sovereign crisis (measured by the 10 yearBTP - Bund spread) on different banking indicators, especially for term deposit, newlyissued bonds and loans growth. This impact is amplified for larger banks.

In this paper we study Italian bad loans for non financial firms over the last twentyyears presenting different methodologies. We analyze determinants of bad loans, focusingon macroeconomic, financial and specific lenders and borrowers variables, following thelines of the literature. Balaid (2014) is the closest paper to ours, even if the author usesdifferent methods. We produce evidence with linear and non-linear models, similar toMarcucci and Quagliariello (2008). Moreover, unconditional and conditional forecasts arepresented, in line of the exercises of Bofondi and Ropele (2011) and the credit risk stresstesting literature. Finally we offer different linear and non-linear models to understandfeedback effects, in general, and specifically the impact on bad loans, as in Quagliarielloand Marcucci (2006) and Klein (2013), among the others. Our empirical results suggestthat macroeconomic and financial, but also, lenders and borrowers variables determinebad loans. Linear and non-linear models augmented with financial variables and assetprices produce better out-of-sample forecasts. A dynamic response analysis shows thatdefault rates move with a cyclical pattern, falling as a consequence of a positive shockin macroeconomic and financial variables. Moreover a positive shock in bank credit or indefault rate does not produce a clear feedback effect from credit to the real economy. Ina non-linear framework, this happens only when the default rate is above a critical value,suggesting that when credit quality is weak, a possible breakdown in the transmissionof credit to the real economy can occur. The paper is organized as follows: Section (2)presents definitions of bad loans and time series properties. Section (3) treats linear modelfor determinants, while Section (4) non-linear models. Unconditional and conditionalforecasting is offered in Section (5), dynamic analysis in Section (6), while Section (7)summarizes the main conclusions. An Appendix at the end describes tables, figures anddata.

2 Data

According to Bank of Italy (2011), bad loans are defined as the total exposure to insol-vent borrowers, those globally unable to cover financial obligations and not expected to

5

recover, even if it does not necessarily result in legally ascertained bankruptcy. Financialintermediaries evaluates creditworthiness and decide to classify borrowers as defaulted byregistering through Centrale dei Rischi (the Italian Credit Register) an amount equal totheir exposure, regardless of any collateral received. We concentrate on two different def-initions of Italian bad loans: 1) the ratio between the flows of bad loans for non financialfirms at year t, over the stock of performing loans at year t 1 and 2) the ratio betweenthe stock of bad loans and total loans, both at time t.10 The first one can be interpretedas the default rate over the banking system, while the second reflects credit quality withinbanks balance sheets. In this way, we can compare a more timely measure of credit risk,similar to the probability of default in Duffie and Singleton (2003), with a point-in-timeindicator, based on stocks, rather than flows, more familiar with accounting and corporatefinance.

We look for determinants of our target variable by inspecting a large dataset, dividedin macroeconomic, financial, asset prices, bank specific and industrial variables. Bad loansare from the Bank of Italy Statistical Database for non financial corporations and microfirms.11 Table (1) presents summary statistics. An Appendix at the end describes thevariables employed, the method adopted for their computation, the sample availabilityand their source. Figure (1) inspects credit riskiness for Italian firms, while Figure (2)looks at the evolution of selected economic indicators. In Figure (1) both graphs showthat credit riskiness follows recessions, depicted in shaded areas according to EconomicCycle Research Institute (ECRI). This feature is stronger for the first period (EMS crisis,1992Q1-1993Q3) and after the beginning of the financial crisis (2007Q3-2009Q1), wherethe default rate (credit quality) started to increase dramatically after four quarters. Theresponse to the last recession (2011Q2-) is instead more rapid, with a reaction after onlytwo quarters. This could suggest a change in the lending cycle, due to jumps in badloans, but also to the breakdown of the traditional intermediation activity for banks.Hence, at least from a first sight, both supply and demand for credit are affected. SeeFreixas and Rochet (2008), Asea and Blomberg (1997), and Delis et al. (2014), amongothers.12 In Figure (2) business cycles paths are captured by real GDP and economicsentiment indicators. The plots of interest rates confirm the severity of EMS crisis, withan inverted yield curve, while, in the last part, the sovereign debt crisis causes an upturnin both the spread between Italian Treasury bonds (BTP) and German Treasury bonds(Bund) and between long and short rates. Residential property prices and bank credit tonon financial firms exhibit a similar pattern, which is less closer in 2003 - with a peak inproperty prices - and in years 2008 and 2010. The recession started in 2011Q2 producesa sharp decrease in bank credit, which goes into negative territory since 2012Q2.

10According to Bank of Italy (2014), total loans is the sum of repurchase agreements, performing andnon-performing loans.

11Specifically, non financial corporations and micro firms are named respectively as Societa` non fi-nanziarie and Famiglie Produttrici.

12See also Cure (2012) about the freezing of the monetary transmission mechanism in period of crisisand for a clear interpretation of what happened to the bank lending channel.

6

Table (2) presents comovements among default rates and our selected variables, sum-marizing macroeconomic and financial environments, but also banks and firms specificcharacteristics. Macroeconomic variables anticipate default rates, confirming the empiri-cal evidence found in the literature. However, as in Bofondi and Ropele (2011), real GDPgrowth, unemployment rate and current account to GDP move slower than our targetvariable for the sample considered. Financial variables and asset prices exhibit their pre-dictive content for default rates. This is stronger for short and long rate, but also for thespread between BTP and Bund. Banks and firms indicators are also good predictors ofdefault rates, suggesting that a profitable, efficient and capitalized banking system is aprecondition for a sound credit portfolio (supply side). On the demand side, instead, aprofitable, efficient and adequately balanced firm is a precondition for debt servicing.13

Table (3) replicates the same analysis on the definition based on the stock of bad loans.Without loss of generality, we can confirm previous results and implications, even if co-movements with macroeconomic and financial variables are more persistent, while thoseon banks and firms specific indicators show lower cross-correlations.14 In order to furtheranalyze the statistical properties of the variables, different unit root tests are presentedin Table (4), focusing on linearities and non-linearities, in the form of one and two breaksin the series. In particular, we perform the augmented Dickey and Fuller (1979) test, theKPSS test of Kwiatkowski et al. (1992), the DF-GLS test of Elliot et al. (1996), butalso the Zivot and Andrews (1992) test, the LS test of Lee and Strazicich (2003), and thetest of Perron (2006) for a one or two breaks in the unit root properties of a time series.Perron (1990) distinguishes between innovational outliers (IO), with a shift in the errorprocess and additive outliers (AO), with a change in the level of the process. Looking atFigure (2) we decided to move in favor of an AO model.15 The left block of the Table dealswith test for unit root without breaks. We can broadly confirm that the majority of ourlisted variables contains a unit root during the period analyzed. This is also supported forour two credit riskiness indicators. The right block instead describes unit root tests withbreaks. Results suggest that the null hypothesis of unit root with one or two breaks is notrejected, and the proposed dates, corresponding to minimum t-statistics on the coefficientfor one lagged riskiness indicator in the different models, seem replicate breaks from Figure(1).16

13Specifically, we use the expressions profitable, efficient and capitalized or adequately balancedto be in line with indicators used: profitable is concerned with ROE, efficient, with ROA and inverselywith operating costs to income and capitalized or adequately balanced with capital and financialstructure. See the Appendix for more details.

14In the spirit of business cycle literature, i.e. Stock and Watson (1999), we conducted an alternativeanalysis by using the same determinants expressed in their cyclical component (i.e. the difference betweenthe level and the filtered variable, calculated with an Hodrick-Prescott filter with tuning parameter =1600) with similar evidence for both credit quality indicators. Results are available from the authors uponrequest.

15See also Table (3) for additional information about the null hypothesis for these tests.16Results for the entire dataset, not shown, are available from the authors upon request.

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3 Determinants

Macroeconomic, financial, banks and firms specific variables are main determinants ofbad loans. See for example Beck et al. (2013) and Bofondi and Ropele (2011), Louziset al. (2010), Salas and Saurina (2002) and Klein (2013), and Ghosh (2005), for eachgroup, respectively. Giving previous results, we decided to analyze differenced variablesto avoid the problem of spurious regressions with misspecified fitting and residuals auto-correlation.17 Hence, our study could be interpreted, at least for these experiments, witha short-run perspective. Equations (1) and (2) describe our models of interest:

Risk Indicator = +

pi=1

iRisk Indicatorti +q

i=0/1

iDeterminantsti + t (1)

and

Risk Indicator = +

pi=1

iRisk Indicatorti +q

i=0/1

iDeterminantsti +

+ (Anxious Dummies)t + t,

(2)

where Risk Indicator reflects our proposed definitions and Determinants are our pre-dictors. Graphical inspection, cross-correlations evidence, literature on lending cycles andtheir stylized facts, suggest to concentrate on current and lagged values of determinants.18

Similar to Bofondi and Ropele (2011) and Ghosh (2005), we select the number of lags pand q for Equations (1) and (2) in stepwise regressions, by checking the statistical signifi-cance of the estimated coefficients. Our models also include different dummies to take careof anxious episodes, recently studied by Delies et al. (2014) and Fostel and Geanakolpos(2008) for leverage cycles. As in the first paper, anxious dummies correspond to thosequarters with a consecutive two quarters decline in agents (firms and bankers) confidence,measured by surveys, when the economy is not in a recession.19

Tables (6) to (9) present our estimates based on models in Table (5). Specifically, weuse pre-specified set of variables in models (a) to (d), while in models (e) - (e) the firstthree factors from a principal component analysis.20 Column (f) presents the Bofondi and

17Ghosh (2005) implicitly bypasses this problem with a linear trend in his model equation for levelsof credit quality indicators. Louzis et al. (2010) and Rinaldi and Sanchis-Arellano (2006) confirm thepresence of non-stationarity in non-performing loans.

18See once again Asea and Blomberg (1997), Berger and DeYoung (1997), Keeton (1999), and morerecently Puri et al. (2011), Claessens and Kose (2014), DellAriccia et al. (2014), and ESRB (2014b). Seealso Albertazzi et al. (2014) and Gambacorta and Mistrulli (2014) for the Italian experience.

19Specifically, we use business surveys from Eurostat, Economic Sentiment Indicator from EuropeanCommission and Bank Lending Survey from European Central Bank. See Table (5) and the notes ofTables (6) and (8) for further information.

20Following Stock and Watson (2002), we extract three principal components explaining more than 50%

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Ropele (2011) model, while the estimation of the Ghosh (2005) model with instrumentalvariables is shown in column (g). Moreover, columns (h) to (l) describe results from Louziset al. (2010), and column (m) repeats the same analysis with loan loss provisions overloans, as alternative bank determinant.

As in Louzis et al. (2010), selected lagged values of default rate show a negative per-sistence over three periods across models analyzed. Evidence on macroeconomic variablesconfirms expected signs, in line with empirical literature. More specifically, past values ofreal GDP growth, investments and current account over GDP help predict a reduction infuture default rates for Italian firms. On the other hand, unemployment rate is positivelycorrelated with credit riskiness. The evidence on CPI is uncertain, while both the threemonth rate and real lending rate have expected sign for shorter horizons. Results for assetprices and bank credit support their role in determining future values of default rates, asexpected. Banking variables confirm that higher ROA, liquidity and capital decrease de-fault rates. However, lower efficiency measured by the cost income ratio reinforce defaultrates. This evidence is in line with bad management, skimping and moral hazardhypothesis in Berger and DeYoung (1997), and with bad management II hypothesis sug-gested by Louzis et al. (2014). Estimates do not suggest a clear interpretation for leverageand loan loss provisions over loans: for the first, a risky bank, highly levered, is not nec-essarily a bank with a mediocre credit portfolio, while for the second, the managementof loan loss provisions depends on expectations of future bad loans (positive coefficient),as well as on balance sheet issues (negative coefficient). Firm specific determinants enterin model with expected sign, except for leverage in model (d). A riskier, more financiallyconstrained and low capitalized firm is expected to default and therefore to increase badloans over the banking system. Determinants from principal component analysis denotesa significant role only for the third factor, suggesting that liquidity and expectations arepredictors of bad loans. In Table (7), we re-estimate the same models by adding anxietydummies as in Delis et al. (2014). Results are in line with our expectations only forthe Bank Lending Survey dummy, which confirms procyclicality of bank credit, especiallyduring anxious periods. The negative sign of the ESI dummy, derived from both demandand supply effects, could instead reflect anxiety in flows of bad loans.

Tables (8) and (9) do the same exercise for the ratio between the stock of bad loans overtotal loans. The evidence broadly confirms previous findings, but with minor differences:we can see a lower persistence for lagged values of the target variable, but also a morepronounced negative impact of liquidity ratio. Moreover, anxiety dummies from businessand banking sector present different signs reflecting opposite views for both borrowers andlenders during turbulent times.

of variance, and define them as: macroeconomic factor, liquidity factor and expectations factor. TheAppendix on factor model contains R-squared plotted as bar charts for each variable and the graphicalevolution of the three extracted factors. See also Fiori and Iannotti (2010) for a similar analysis.

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4 Threshold and Switching Models

Since the financial crisis erupted, bad loans experienced an unprecedented growth as aresult of a deterioration among main macroeconomic and financial indicators, as reportedin Figures (1) and (2). This represents a huge breakdown with respect to the historicalpath, also confirmed by previous statistical tests for the presence of breaks. Given this ev-idence, this Section is therefore dedicated to non-linearities in bad loans. We present twoclasses of models, i) threshold models, in which the threshold is observed as an estimatedvalue of the bad loans and ii) regime-switching models, where each regime is determinedby the value of an unobserved state variable, usually modeled as a first order Markovchain. See Hamilton (1989) and (1994), for an econometric analysis of switching models,Terasvirta (1994) and (2006) for threshold models, and more recently Gasha and Morales(2006), Serwa (2011), Franta (2013) and Marcucci and Quagliariello (2008) for an appli-cation of threshold effects in credit risk stress testing, multiple regimes in credit marketsfor OECD countries, non-linearities between credit conditions and economic activity, andfor an application to Italian adjusted default rate, respectively.

4.1 Smooth Transition Regression (STR): LSTR and ESTR for BadLoans

The STR model can be stated as follows:

yt = Xt + XtG (Ztd, , c) + t, (3)

where = (1, 2, ..., m) and = (1, 2, ..., m) are parameter vectors, while t

i.i.d.(0, 2

). The transition function G (Ztd, , c) is bounded between zero and one and

is continuous everywhere in the parameter space for any value of Ztd. G (Ztd, , c)depends upon a scale or slope parameter and a location parameter c, but also on thethreshold variable Ztd which is a lagged value of the dependent variable. We use twotransition functions, the logistic LSTR and the exponential ESTR:

G (Ztd, , c) =

{1 [1 + exp ( (Ztd c))]1 for LSTR1 exp

( (Ztd c)2

)for ESTR

(4)

In Equation (3), yt is alternatively one of our indicators, while Xt contains selected ex-planatory variables. As LSTR converges to a threshold model with break at c;as 0, it converges to least squares.21 We adopted the following procedure: first, wetest for non-linearities, then we decide the shape of the transition function and finally wespecify and estimate the model. For the first point, we select the delay d as the optimallag from information criteria, after testing for linearity versus LSTR or ESTR, with aLagrange multiplier (LM) test. Finally we estimate the model by non-linear least squares.

21For computational purposes, we replace with / for the LSTR model, while /2 for the ESTRmodel, where is the standard deviation of Z. The mean of Z is the guessed initial value of c.

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Results from the LM test point to an LSTR for default rate but ESTR for the ratio be-tween the stock of bad loans and total loans. In both two cases, the threshold variable isthe indicator with eight lags. Our estimation strategy is based on the same set of determi-nants presented in Section (3). We therefore proceed as follows: separate estimation of thestandard and the transition equation with same variables; choice of statistically significantdeterminants; re-estimation of both standard and transition equation; final estimation ofEquation (3).

Table (10) presents results for the LSTR model, while Table (11) those for the ESTRmodel. Once the target variable goes above the threshold value c, the model depicts amore pronounced reaction to past movements in different determinants. This is moreclear in the LSTR model, where variables have higher coefficients (in absolute value) inthe transition equation, while the ESTR model does not offer an obvious interpretation.Looking at the values of the two unobserved coefficients and c, both models exhibita change in regime when the target indicator is approximately above its mean. Morespecifically, we find that c ranges from 0.764 to 0.839 for default rates, while from 5.574to 7.249 for the other definition. During the last two recessions, credit risk indicatorsgoes above c in 2011Q3 for default rate, and in 2010Q3 for the ratio between the stock ofbad loans and total loans: remembering Figure (1), a jump occurs around these specifieddates.

4.2 Hamilton Switching Model for Bad Loans

Switching models allow us to extract the probability of migration from a regime to anotherin a simple univariate framework for bad loans. We apply the Hamilton switching model,Hamilton (1989), to bad loans which are assumed to follow different time series processesover two different regimes:

yt = st+1

(yt1 st1

)+2

(yt2 st2

)+3

(yt3 st3

)+4

(yt4 st4

)+t,

(5)where yt is the growth rate of the target variable, std is the average growth rate withlags d = 0, ..., 4, while s follows a two-state Markov chain with transition probabilitypij .

22 Table (12) shows results from the maximum likelihood estimation of the Hamiltonswitching model: states 1 and 2 are the contractionary and expansionary regimes, i.e. animprovement in credit quality conditions and a deterioration of credit worthiness. P(1,1)is the probability that contraction will be followed by another quarter of contraction, sothat this regime will persist for 1/ (1 P (1, 1)), whilst P(1,2) = 1 - P(2,2), where P(2,2)is the probability that an expansion will be followed by another quarter of expansion, withduration 1/ (1 P (2, 2)). Looking at default rates, the average growth in expansions ishigher than in contractions and s indicate upward persistence. Each regime has a longmemory, and if we look at SBL / Loans we can see that the duration of an expansionaryregime is about 7 quarters. Figure (3) provides estimated transition probabilities from

22See Chapter 22 of Hamilton (1994) for a theoretical background.

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an expansionary regime followed by another expansionary quarter for both credit riskdefinitions, together with the time series of the growth rates. The evolution of default ratesis adequately followed by the transition probability of being in an expansionary regime:since the financial crisis and after the sovereign debt crisis, the transition probability isclose to 1, indicating that the deterioration of credit riskiness persists. Moreover, it startsgoing up since 2006Q4, approximately one year before the beginning of the recession, andtwo years before the visible spike in bad loans.

5 Forecasting and Scenario-Based Analysis

Concluded the analysis of determinants in linear and non-linear models, it is time topoint towards multivariate frameworks, to deeply understand the relationship betweenthe previously selected macroeconomic, financial and specific microeconomic (bankingand firms) variables and credit riskiness indicators.23 This Section deals with this issueby using different vector autoregressions (VARs) to forecast bad loans. More precisely, wefocus on the impact of determinants on credit riskiness.24 Moreover, following the lines ofESRB (2014) and ECB (2014), we also conduct a stress testing exercise, conditioning ourmodels to produce scenario-based forecasts. Before going on, however, it is important toremark that the estimation strategy adopted in Section (3) was conducted on differencedvariables, with a short-term focus. Therefore, the first task of this Section is describinglong-term properties of credit quality indicators and determinants, as a background forthe next level, forecasting.

5.1 Long-Term Analysis

Generally, long-term analysis of economic and financial variables develops on a theoreticalbasis, the starting point for any robust assessment and interpretation of the long-termbehavior of the phenomenon analyzed. The purchasing power parity (PPP), in economics,and the credit default swap basis, in finance are two good examples. In our specifiedcase, among the others, Rinaldi and Sanchis-Arellano (2006) and Klein (2013) study non-performing loans in a panel environment and perform unit root and cointegration analysis,extracting a unique long-term cointegrating vector relating households non-performingloans to macroeconomic variables.25 Time series analysis also requires both unit roottests, performed in Section (2) and cointegration tests, like Johansen (1988) and (1991) trace and max, together with an estimation of the cointegrating vector.26 Results

23We remember the studies of Gambera (2000), Marcucci and Quagliariello (2006), and Klein (2013)for vector autoregression models, while, Fiori and Iannotti (2010) and more recently Bessler and Kurman(2014) for the use of a factor augmented vector autoregression model. IMF (2010) Global Financial StabilityReport studies impulse response function from a VAR for emerging markets.

24For a two-way relationship, i.e. feedback effects, the reader is referred to Section (6).25See Section (5) of Rinaldi and Sanchis-Arellano (2006).26See Hamilton (1994) for a general treatment and Juselius (2006) for cointegration analysis in the VAR

model.

12

for cointegration analysis performed on different models are illustrated in Table (13). Itis obvious that both Johansens tests confirm that the cointegrating vector is not uniquefor different credit quality indicators.To be more precise, when the cointegration rank is larger than one, or when the numberof cointegrating vectors is greater than one, there is an identification problem. Therefore,the interpretation of long-run equilibria is not straightforward. Without a strong androbust long-term theory for the selected variables in hand, we decided to follow anotherstrand of the literature on cointegration by focusing on bivariate vectors27, with thresholds,breaks and asymmetric behaviors. The referenced papers are: Balke and Fomby (1997),Tsay (1998), Enders and Granger (1998), Enders and Siklos (2001) and Hansen and Seo(2002), among the others, while Tong (1983) provides an excellent textbook treatment onthreshold autoregressive (TAR) models.

Once cointegration tests confirm the presence of a long-run relationship, bivariatevectors are formed using the difference between the default risk indicator and selecteddeterminants, taken at different lags, to understand the interactions of micro and macroe-conomic variables with default rate. Cointegrating vectors are evaluated alternatively withStock and Watson (1993) dynamic OLS and with the Engle and Granger (1987) procedure.We start with the TAR process described as:

yt = It1 [yt1 a0] + (1 It) 2 [yt1 a0] +p1i=1

iyti + t, (6)

where the Heaviside indicator function assumes the following form:

It =

{1 if yt1 a00 if yt1 < a0.

(7)

In Equation (6), we assume that the cointegrating vector yt has an equilibrium pointaround a0, the attractor, which can be interpreted as the long-run distance between defaultrate and the other variable. Then, we test how the model coefficients 1 and 2 changethrough different regimes, denoting an asymmetric reaction. According to Enders andGranger (1998), 2 < (1, 2) < 0 is required for stationarity of the series, while both 1and 2 should be negative to have a convergent process, as suggested by Enders and Siklos(2001). Following the lines of Enders and Granger (1998), we inspect the behavior of thedefault rate indicator with:

Def. Ratet = + 1 (Def. Ratet1) + 2 (Def. Ratet2) + 1 (Determinantt1) +2 (Determinantt2) + m (z plust1) + m (z minust1) + t,

(8)

where (z plust1) = It (Def. Ratet1 dolsDeterminantt1 attractor) and (z minust1) =(1 It) (Def. Ratet1 dolsDeterminantt1 attractor).

27This is the same to apply zero restrictions on all beta coefficients, except for the variable consideredin the bivariate cointegrating relation.

13

Tests for the significance and for the equality of the coefficients, the estimations of theattractor and asymmetric coefficients z are depicted in Table (14). dols coefficients arein line with the theory proposed in the Introduction and empirically confirmed in Section(3): interest rates have a positive correlation with default rates while for macroeconomicvariables and asset prices the opposite is true. However, we do not obtain a clear responsefrom micro banking and firms variables. Results from columns Above and Belowpoint toward an asymmetric long-term adjustment, such that the attractor is strongerfor positive changes in the relationship between default rate and alternatively, real GDP,investments, CPI, stock returns and lending spreads. On the other hand, we have anasymmetric long-term adjustment, such that the attractor is stronger for negative changesin the relationship between default rate and, alternatively, long rate, debt to GDP, res-idential property prices and bank credit. An accurate analysis of z plus and z minusin Equation (8) reveals two interesting points. First, an intense long-term response to apositive discrepancy between the default rate and, alternatively, real GDP, investments,CPI, stock returns and lending spreads, denotes a faster reaction during periods of reces-sion, lower consumer prices, stock returns and interest rate spreads, respectively. Second,we observe a deep long-term response to a negative discrepancy between the default rateand, alternatively long rate, debt to GDP, as well as residential property prices and bankcredit. In this last case, when the growth rate of residential property prices goes down,reduction in the value of collateral occurs and, therefore, a strong response in default ratesis registered. Moreover, results for capital to loans and loan loss provisions to loans seemto be affected by the two-way relationship between bad loans and credit risk management.

For robustness we conduct an analysis in the spirit of Enders and Siklos (2001) on thesame set of variables, using this equation:

t = It1t1 + (1 It) 2t1 +p1i=1

iti + t, (9)

where the Heaviside indicator function now has the following form:

It =

{1 if Determinantt1 0 if Determinantt1 < ,

(10)

where is the estimated threshold for the determinant. When is unknown, we needto search for a value that minimizes the sum of squared residuals for a superconsistentestimation, as in Chan (1993). Applying a trimming of 15%, each of the remaining valuesare taken as possible thresholds. Residuals are instead derived from the Engle and Granger(1987) procedure. Results in Table (15) substantially confirm those in Table (14), but alsoadd more information: as example, thresholds for unemployment rate range from 6.50%to 7.40%, while those for spread from 125 to 460 basis points, that could correspond tofigures at the beginning of the financial and the sovereign crisis.

Finally, to further reinforce long-term analysis, we propose the Hansen and Seo (2002)test of linear versus threshold cointegration, together with the estimation of the bivariate

14

VECM. The following model is estimated:

xt =

{A1Xt1 () if wt1 () A2Xt1 () if wt1 () > ,

(11)

where Xt1 () = (1, wt1 () ,xt1,xt2), and the notation () means that we areevaluated at generic value of , while is the threshold.

In Table (16), when the results are significant, macroeconomic variables indicate amore incisive reaction in the above regime: this is true for CPI, debt to GDP, the slopeand the first factor from the principal component analysis. The opposite holds for loan lossprovisions, while interest expenses show a huge reaction in the below regime.28 This couldbe in line with the selected break dates, coinciding, for example, with the introductionof Basel regulatory frameworks in late nineties, or with the adoption of near-zero interestrate policies by the ECB.

To sum up, all the results illustrated in this Section allow us to confirm the long-term relationship between the default rate of Italian non financial firms and selecteddeterminants in a bivariate environment. The behavior of this linkage is clearly differentfor the two regimes considered and denotes a more pronounced, and therefore, fast reactionof our variables in the above regime.

5.2 Vector Autoregressions

Now time has come to analyze multivariate frameworks for forecasting purposes. Webuild models with non differenced variables, against what we have done in Section (3).Despite their flexibility and ability to fit the data, unrestricted VARs suffer from therisks of overparameterization and imprecise inference, causing large uncertainty about thefuture paths projected by the model. See, among others, the survey by Karlsson (2013).Sims et al. (1990) confirm that the stationarity of the series is unnecessary in BayesianVAR (BVAR) models, while Hamilton (1994) demonstrates that a VAR model built withvariables in levels is the same as the VECM model, expect for the study of the cointegratingvector. Given these theoretical features and based on what we have found from non-linearanalysis, we decided to produce forecasting with the following different models: i) BVARmodel with Minnesota prior, in the spirit of Doan et al. (1984) and Litterman (1986); ii)a factor augmented VAR (FAVAR), as in Bernanke et al. (2004); iii) a threshold VAR(TVAR) following the study of Balke (2000); iv) the threshold bivariate VECM of Balkeand Fomby (1997).

The BVAR we present is based on Minnesota priors, where the standard priors havethe following characteristics: the priors on the deterministic variables, in each equation,are flat; the prior distributions on the lags of the endogenous variables are independentGaussian; the means of the prior distributions for all coefficients are zero, except for the

28Given the problems of discontinuity in the likelihood function, we add four variables for which theestimated p-value is near the non rejection region.

15

first lag of the dependent variable in each equation which has a prior mean of one. In thiscase, coefficients have variances as functions of a small number of hyperparameters. Thestandard deviation of the prior distribution for lag l of variable j in equation i assumesthe form:

S (i, j, l) ={g(l)f(i, j)} si

sj; f(i, i) = g(l) = 1.0,

where si is the standard error of a univariate autoregression on equation i, is the standarddeviation on the first own lag, g(l) is the tightness on lag l relative to lag 1, and f(i, j)is the tightness on variable j in equation i relative to variable i. We use = .1, g(l) = 1and f(i, j) = .5.

The FAVAR consists of two steps: unobservable factors are extracted from a largedataset, as in Stock and Watson (2002) and common latent factors are put in a VAR.The assumption is that the dynamics can be represented by the following VAR (transitionequation): (

FtYt

)= (L)

(Ft1Yt1

)+ t, t N (0,) . (12)

Equation (12) is a VAR in (Ft, Yt) which cannot be estimated directly because factorsFt are unobservable. The inference is possible through a set of observable variables, ourdataset Xt, which we assume to be related with unobservable factors Ft and with theobserved variables Yt by an observation equation of the form:

Xt = fFt +

yYt + et, (13)

where f is a matrix of factor loadings and et is a vector of idiosyncratic errors thatmust vanish at infinity. The main idea is that both observed variables Yt and the unob-servable factors Ft represent common forces driving the dynamics of Xt.

The TVAR model of Balke (2000) is expressed as:

Yt = A1Yt +B

1 (L)Yt1 +(A2Yt +B

2 (L)Yt1)I (ctd > ) + Ut, (14)

where Yt is the vector of endogenous variables, B1 (L) and B2 (L) are lag polynomial

matrices, while Ut is a vector of disturbances. Moreover, ctd is the threshold variable,that determines which regime the system is in, and I (ctd > ) = 1 when ctd > andzero otherwise. We fix d = 1, as in the original paper and in Marcucci and Quagliariello(2008), while c is the target credit quality indicator.29

Finally, following Balke and Fomby (1997) we propose a threshold biviariate VECMbetween the credit risk indicator and unemployment rate, chosen among different macroe-conomic variables from the analysis in Table (15). The model is the following:

Xt = (i)x + C

(i) (L) Xt + (i)1 Itzt1 + +

(i)2 (1 It) zt1(i)t , (15)

29The threshold value is not known a priori and is estimated by least squares with a value of 0.742for default rate and 5.556 for the stock of bad loans over total loans. The difference between regimes arestrongly confirmed by a likelihood ratio test. The estimated thresholds are very close to the ones estimatedin Section (4.1) from the STR models.

16

where

It =

{1 if ztd 0 if ztd < .

(16)

The threshold delay d is estimated with the Tsay (1998) test for threshold autoregressivemodels. Both models for the two definitions indicate 4 lags for the delay. A completelist of models and variables used is presented in Table (17), where we also add an ARMAmodel for comparison.

We estimate each model through 2010Q1, leaving 2010Q2-2014Q2 for examining theaccuracy of out-of-sample forecasts at horizons one to eight quarters ahead. More specifi-cally, the models are estimated through 2010Q1 and a set of out-of-sample forecasts oneto eight steps ahead are computed, spanning the period 2010Q2-2012Q2. Next, a newobservation is added to the estimation sample and a new set of forecasts are computed,spanning the period 2010Q3-2012Q3. This process is repeated until the last sample dateis reached. Updating the forecasting window is possible through a Kalman filter.30 Theforecasting properties of the model are assessed using the resulting collection of one toeight steps ahead forecasting errors. We compute the Theils U statistic, the ratio of theroot mean squared error (RMSE) of our model and the RMSE of a random walk (naive)model, as a forecasting performance measure.31

Tables (18) and (19) present forecasting performance. For default rate, models (a) to(d) with macroeconomic variables have valid forecasting performance only for few quartersahead, except for model (a) where the inclusion of the spread between lending rate andshort rate improves forecasting capacity.32 On the other hand, model (e), the BVARwith only financial variables have a good forecasting ability, especially at longer horizons.Models (f) and (g) built with micro variables should only be interpreted with caution, giventhe nature of interpolated data, obtained using splines and filtered to remove measurementerrors.33 Among the FAVAR models, (h) and (i), only the first one expresses sufficientproperties at all horizons, supporting the view of Corradi and Swanson (2014) about factorloadings instability in presence of breaks. The TVAR model of Balke (2000) has the bestforecasting performance among the models, but only for the lower regime for the defaultrate. Finally, the TVECM model has a short-term predictive capacity. For the ratiobetween the stock of bad loans and total loans, the model (d) with macro and financialvariables, is comparable with the FAVAR models, that, especially for (h), exhibit adequateforecasting performance. Except for model (j), both the TVECM and the ARMA (2,0)models present good forecasting properties for the entire horizon.

Tables (18) and (19) present different models forecasting performance. Although our

30ARMA models are updated through recursive regressions. See Table (17).31In this paper, we only concentrate on point forecasts and not on predictive density forecasts, as in

Amisano and Geweke (2013) and Clark and McCracken (2013), among others.32See, for example Sanjani (2014) on the properties of banking spreads in a DSGE model for US business

cycle.33Alternatively, mixed-frequency models could mitigate this drawback. See for example Foroni and

Marcellino (2013).

17

aim is not to find a theory for a small set of predictors for bad loans, we demonstrate that,in a forecasting window characterizing recession, central banks should consider differentkinds of variables and models. Results suggest more emphasis on financial variables andasset prices, and also a modeling strategy based on threshold models. Moreover, we thinkthat forecasting exercises like model combination, as in Amisano and Geweke (2013) couldbe helpful. Finally, Figure (4) shows fan charts for selected models.

5.3 Conditional Forecasting

The analysis in the previous Section can be enhanced by conditioning upon future values ofendogenous variables through a scenario-based analysis. We adopt model (a), the BVARwith Minnesota priors, with two lags, for: the spread between the lending rate for loanswith a maturity up to five years and the 3 month rate; CPI; real GDP; bank credit to nonfinancial sector and the indicator. We produce forecasts from 2014Q1 to 2018Q1 usingthe above mentioned BVAR with Gibbs sampling from an inverse Wishart distribution byusing 60,000 draws, the first 10,000 of which were discarded.

Our model is conditioned on these adverse scenarios:

real GDP growth: reduction of .25% year over year; real GDP growth: adverse scenario EBA. See ESRB (2014a); CPI: reduction of .05% year over year; CPI: adverse scenario EBA. See ESRB (2014a); Bank credit to non financial sector: reduction of 2.00% year over year; Lending spread: increase of 100 basis points year over year.Figures (5) and (6) contain unconditional and conditional forecasts for default rate

and the ratio between the stock of bad loans over total loans. The negative scenario onreal GDP growth affects the default rate approximately after two years, with respect tounconditional forecast, while the indicator reflecting the riskiness of banks credit portfoliois more sensitive, with a reaction after one year. The negative path of inflation throughoutthe forecasting horizon influences bad loans in both designed scenarios, with a persistentimpact on the second indicator. When we consider the adverse dynamics of bank specificdrivers, prices (the mark up) and quantities (bank credit to non financial sector), weencounter a consistent upward movement of the two credit quality indicators. Price effectsboost bad loans immediately, with a peak after two years and a half for default rate(reaching 1.5%), while there is a persistent increase for the other indicator. Quantitieseffects, on the other hand, generate an increasing path after one year, reaching 1.4% at theend of 2017, for default rates. Looking at the Figures, we confirm empirical evidence aboutthe lagged response of bad loans to movements in macroeconomic variables; moreoverlending specific features, like price and quantity, affect bad loans in a timely and consistent

18

manner. This evidence should be supported by a feedback effects analysis, presented inthe next Section.

6 Impulse Response Functions

In this last Section we further investigate the dynamics of Italian bad loans focusing onan impulse response analysis from different models.34 First, we propose an overview ofthe responses from model (a), and the detailed responses of default rate from model (e),with financial variables only. Then, we study the Primiceri (2005) model with time varyingstochastic volatility, discussing different combinations of determinants for the default rate,and finally the model of Balke (2000) with changes in regimes.35 All models are estimatedup to the end of our sample and contain two lags.

Figure (7) presents feedback effects from model (a), after imposing a Choleski decom-position to get orthogonalized impulse response functions, with variables ordered fromspread to default rate. As a first step, we focus on the causal link that goes from defaultrate to the other variables in the system. The responses of the spread between lendingrate and the short rate to different shocks seem reasonable: positive macroeconomic andcredit conditions tend to reduce the riskiness of Italian firms, while an increase in thedefault rate reinforces the negative assessment of credit quality. Also the CPI shows thesame reaction to positive macroeconomic and credit conditions, while it seems unaffectedby an increase in the default rate. The real GDP growth, however, moves in a differentway: a positive shock in bank credit and in the default rate generate unexpected reactionsof real GDP growth. In our opinion, this could reflect low cross-correlations with defaultrate, as shown in Section (2). As a robustness check, we invert the order of real GDP withCPI with similar results. We also substitute real GDP with unemployment rate obtainingthe expected theoretical reaction.36 Although model (a) may suffer from focusing only onmacroeconomic and credit determinants, and hence without banking, firms specific andfinancial variables, we think that it is quite complete to describe macro-credit linkages. Itis possible to interpret the unexpected reaction of real GDP by looking at the bad perfor-mance of Italian economy since 2007: more than five years of persistent low and extremelynegative growth, during the crisis, may have weaken the dynamic link between supply sideof the credit market (quantity of credit, and, therefore, bad loans) and the gross domesticproduct (our proposed demand side). Unemployment rate seems better reflecting how

34Table (17) describes all the models. For brevity, we only present results for the default rate indicator.Results for the other indicator are available from the author upon request.

35We would like to thank Dimitris Koroblis for providing Matlab programs to perform the Primiceri(2005) model. We refer to Primiceri (2005) and Koop and Korobilis (2010), among others, for a specificand broad theoretical study on Bayesian inference and estimation for macroeconometric analysis.

36This does not invalidate our scenario-based forecasting exercise which does not require an orthogonal-ization. Moreover, that was done to explain the causal link from determinants to default rate. However,we also produce scenario-based forecasts with the same model conditioned on unemployment scenarios,confirming the upward reaction in future default rates.

19

the supply side of the credit market affects the entire economy. Finally, the response ofbanking variables to the shocks of all variables in the system goes in the expected direc-tion, especially for default rate. Figure (8) shows, in particular, the negative reaction ofdefault rate after a shock in real GDP growth. Hence, the link between a positive macroe-conomic shock and bad loans seems going in the expected direction. Figure (9), instead,focuses on model (e) from Table (17), the one with financial variables and asset pricesonly (forward looking variables): shocks to residential property prices (a possible proxyfor collateral), together with bank credit and stock returns produce a negative reactionof the default rate. On the other hand, expectations on the Italian economy, implied inthe sovereign spread BTP versus Bund and in the slope of the term structure (long versusshort), provide an upward movement in bad loans.

We re-adapt the macroeconometric model of Primiceri (2005) for robustness, dealingwith impulse response functions with stochastic volatility. Figures (10) to (14) presentresults for selected dates in our sample. The first four Figures allow us to focus on theother side of the causal relationship, the impact of determinants on the default rate, whilethe last one repeats the same study, although with short rate, real GDP and defaultrate. Shocks in real GDP growth and CPI produce, respectively, a negative and a positivereaction of default rate, confirming that better economic conditions are negatively relatedwith credit quality. Moreover, when we consider either short rate or the lending spread,together with real GDP and default rate, we have a different reaction. On the one hand, ashock in the 3-month rate produces a slight positive reaction of default rate throughout thehorizon, while, on the other, a positive shock on the lending spread generates an immediatereaction, as expected. Finally, Figure (14) confirms the upward movement of real GDPafter a shock on default rate. Again, we test the same model with the unemployment rateand obtain a positive response, as the theory suggests.

The last exercise studies the feedback effects from the Balke (2000) threshold modelwith real GDP growth, short rate, bank credit and the default rate. Given the non linearityof the model, we present generalized impulse response functions, to take care of differentdynamics in different regimes.37 Figures (15) and (16) show the responses of default ratein the two regimes, while (17) and (18) those for output. When the default rate goes abovethe specified threshold of 0.742, the model produces expected responses: for example, a twostandard deviation shock to output generates a reduction in default rate, lasting for twoyears and a half; a two standard deviation shock in bank credit moves default rate downthrough the first year. Figure (16) confirms the overall dynamics, but in the lower regimeall responses have a smaller magnitude. The responses of real GDP to different shocks,conditioning on different regimes, also exhibit this feature. However, in the two regimes,we also find the unexpected reaction of real GDP to a shock in default rate. On the otherhand, only in the lower regime a shock in bank credit generates a coherent movement ofreal GDP. We can conclude that when Italian firms credit quality is considerably weak,i.e. the default rate is above the threshold (upper regime), a possible breakdown in the

37See Koop et al. (1996) for a detailed analysis of GIRF.

20

transmission of credit to the macroeconomy occurs, with a negative procyclical effect.Hence, non-linear models could allow policy makers to extend their knowledge aboutthe link between credit and the macroeconomy, in particular, and about the monetarytransmission mechanism (bank lending channel), in general, during different regimes.

7 Concluding Remarks

Since 2009 credit conditions have been experiencing a dramatic worsening, reflecting thetwo most severe recessions since the Great Depression. This paper studies bad loans forItalian non financial firms during the last twenty years. Motivated by the existing literatureand based on exploratory statistical analysis, we propose different linear and non-linearmethodologies focusing on short and long-term determinants, forecasting properties anddynamic responses.

For the determinants, we find that credit riskiness is affected by lagged values ofmacroeconomic and financial environment, but also by specific lenders and borrowerscharacteristics. Positive (negative) macroeconomic and financial conditions generate areduction (increase) in future bad loans. For bank specific variables, our evidence pointsin the direction of bad management, skimping and moral hazard. Moreover, ariskier, more financially constrained and low capitalized firm is expected to default, and,therefore to stimulate bad loans over the banking system. Anxiety dummies from agents(bankers and firms) surveys also reinforce our findings. Furthermore, non-linear analysisconfirm that when bad loans reach their critical value, determinants have a stronger effectson future credit quality, which persist over time. Long-term non-linearities, in the form ofbreaks, asymmetries and changes in regime also corroborate these findings.

Forecasting exercises demonstrate that models with different macroeconomic variablesperform best at shorer horizons, but those based on financial variables and factors ex-tracted from a large dataset could perform better at all horizons. This could suggestgreater emphasis on linear models with financial variables and asset prices, but also non-linear models, where regimes and endogenous estimates of thresholds could be helpful in amacroprudential perspective. The stress test analysis confirms that future values of de-fault rate are affected by adverse macroeconomic and financial scenarios, especially thoserelated to lending (price and quantity effect of credit).

Finally, findings from dynamic response analysis reveal two interesting points. A shockin macroeconomic variables produces expected future reactions in default rates, supportingour empirical evidence for the short-term. A positive shock in either bank credit or indefault rate do not generate clear evidence of a feedback effect from banking sector tothe real economy. This only happens when we consider the entire sample and when thedefault rate is in the above regime. However, in tranquil times (lower regime for defaultrate), real GDP has the expected theoretical behavior. We can conclude that when creditquality is considerably weak, a possible breakdown in the transmission of credit to themacroeconomy occurs, with a negative procyclical effect. Hence, non-linear models could

21

allow policy makers to extend their knowledge about the functioning of the link betweencredit and the macroeconomy, in particular, and the monetary transmission mechanism(bank lending channel), in general, during turbulent times.

22

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29

Tables

Variable Min 25th %-tile Median 75th %-tile Max Mean St. Dev. Skewness Kurtosis

MacroeconomicReal GDP -6.904 -0.286 1.069 1.968 4.130 0.647 2.134 -1.211 2.206

Private Cons. -4.514 -0.277 1.028 1.854 4.890 0.578 2.045 -0.665 0.161Investments -13.618 -3.292 0.952 3.541 9.896 -0.182 5.360 -0.714 0.023

Durable Cons. -31.473 -3.745 1.170 4.776 20.996 0.240 9.052 -0.789 2.018CA to GDP -4.020 -2.050 -0.650 1.200 3.870 -0.458 1.987 0.212 -0.919

CPI 0.100 1.825 2.400 3.300 5.700 2.687 1.298 0.632 -0.119Unempl. Rate 4.800 6.400 7.100 8.300 10.500 7.311 1.392 0.369 -0.322Debt to GDP 75.143 106.475 110.631 118.272 135.827 112.224 10.999 -0.503 1.856

Deficit to GDP -15.745 -6.090 -3.060 -1.500 7.412 -3.959 3.959 -0.608 1.087ESI 77.867 94.742 100.383 106.842 119.633 100.036 10.030 -0.354 -0.367

Financial and Asset PricesStock index -64.864 -8.083 9.443 18.295 66.218 3.867 24.599 -0.466 0.412

REER -13.579 -1.840 0.700 1.956 15.608 0.525 4.050 0.419 3.457Res. Prop. Prices -7.770 -2.620 0.110 3.560 10.710 0.482 4.395 0.310 -0.360

Short Rate 0.200 2.065 3.445 6.710 16.430 4.523 3.701 1.064 0.557Long Rate 3.090 4.273 4.825 6.585 13.850 6.197 2.968 1.391 0.553

Slope -2.620 0.453 1.495 2.763 5.330 1.673 1.543 0.335 -0.106Vol. Eurexx -66.769 -17.945 -4.992 20.161 83.566 0.247 27.601 0.223 0.272

Spread ITA vs GER 0.140 0.260 0.850 3.018 6.450 1.766 1.868 0.990 -0.354Bank Credit to NFS -4.044 3.146 6.272 8.553 15.049 5.717 4.207 -0.395 -0.276

BankingLeverage 8.729 11.524 12.532 12.887 14.705 12.040 1.474 -0.664 -0.359

ROE -7.020 2.187 6.843 9.257 12.234 5.036 5.243 -0.821 -0.164ROA 1.777 2.086 3.196 3.530 3.962 2.927 0.746 -0.434 -1.383

Oper. costs / Income 0.544 0.595 0.610 0.655 0.698 0.622 0.040 0.108 -0.858LLP / Loans 0.265 0.510 0.612 0.816 1.410 0.671 0.285 0.802 0.295

Capital / Loans 11.046 11.601 12.298 12.681 18.007 12.875 1.848 1.340 0.496Int. Margin / 0.427 0.520 0.552 0.679 0.839 0.588 0.105 0.847 -0.412Gross Margin

Liquidity Ratio 2.599 5.001 5.932 6.354 7.793 5.462 1.357 -0.779 -0.133Funding Ratio 3.631 4.244 4.575 5.932 7.427 5.046 1.067 0.548 -1.075

Non Financial FirmsROE -12.957 2.939 5.759 8.941 13.949 5.111 5.796 -1.200 1.809ROA 2.714 3.797 4.398 5.169 6.197 4.414 0.908 -0.197 -0.832

Int. Costs / EBITDA 0.133 0.193 0.253 0.295 0.530 0.260 0.096 1.220 1.331Leverage 0.270 0.312 0.343 0.354 0.455 0.344 0.047 0.677 0.045Structure 0.898 0.962 1.035 1.059 1.111 1.010 0.059 -0.195 -1.284

Capitalization 0.255 0.324 0.369 0.380 0.405 0.353 0.040 -0.942 -0.256

Credit Quality IndicatorsDefault Rate 0.252 0.380 0.628 0.823 1.447 0.664 0.307 0.610 -0.489

Bad Loans / Loans 3.320 5.061 5.900 8.670 14.526 6.970 2.706 0.920 0.110

Bank Lending Rates and SpreadsLending rate < 5y 2.734 3.755 4.920 5.938 11.595 5.485 2.496 1.209 0.448Lending rate > 5y 2.686 3.522 5.033 6.082 11.738 5.518 2.596 1.096 0.255Lending rate avg. 3.071 3.979 5.370 6.534 13.064 6.020 2.767 1.321 0.796

Deposit Rate 0.601 0.939 1.462 2.255 6.447 2.039 1.604 1.629 1.587Spread < 5y 0.229 1.370 1.895 2.408 3.494 1.943 0.740 0.306 -0.480Spread > 5y 0.372 1.490 1.932 2.495 3.467 1.976 0.643 0.099 -0.298

Table 1: Descriptive statistics on selected variables. Lending rate < / > 5y is the lending rate for non financial firms on a loan witha maturity below or above five years, respectively. Spread is the spread between the lending rate for non financial firms and theshort rate. The same holds for < / > 5y definitions. Stock index and Vol. Eurexx are measured with annualized returns.

30

Cross

correla

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nD

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ult

Rate

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Serie

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Real

GD

P-0

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6-0

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-0.2

3-0

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-0.3

0-0

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5-0

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70.0

30.1

40.2

00.2

60.3

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10.3

2P

rivate

Cons.

-0.2

4-0

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-0.2

7-0

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-0.3

5-0

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-0.4

0-0

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-0.2

8-0

.15

-0.0

50.0

50.1

50.1

90.2

50.2

70.2

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ments

-0.3

1-0

.32

-0.3

4-0

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-0.4

0-0

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-0.4

3-0

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-0.3

1-0

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-0.0

90.0

20.1

00.1

90.2

50.3

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PI

0.4

30.5

00.5

20.5

40.5

40.4

90.4

50.3

90.3

20.2

80.2

50.2

50.2

60.2

90.3

10.3

50.3

7U

LC

-0.0

20.0

20.0

50.0

60.0

90.0

2-0

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-0.0

4-0

.14

-0.1

9-0

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-0.3

0-0

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0.0

00.0

30.1

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50.2

40.3

20.4

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80.5

50.5

80.6

00.5

90.5

90.5

60.5

40.5

20.5

2D

ebt

toG

DP

0.0

50.0

30.0

40.0

50.1

00.2

00.2

90.3

30.3

80.4

00.4

10.4

10.3

90.4

00.3

80.3

60.3

1D

efi

cit

toG

DP

-0.2

4-0

.23

-0.1

8-0

.31

-0.2

2-0

.34

-0.1

7-0

.26

-0.1

8-0

.32

-0.2

4-0

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-0.1

6-0

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-0.0

5-0

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-0.0

1C

Ato

GD

P0.0

00.0

20.1

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60.2

30.2

90.4

20.4

90.5

70.5

90.6

50.6

60.6

40.6

30.6

50.6

60.6

8E

SI

-0.3

4-0

.38

-0.4

2-0

.47

-0.5

2-0

.53

-0.5

3-0

.47

-0.3

9-0

.28

-0.1

6-0

.03

0.0

60.1

40.1

60.1

80.1

7Sto

ck

index

-0.0

9-0

.10

-0.1

0-0

.11

-0.0

9-0