Asymmetric effects of the business cycle on bank credit risk

Asymmetric effects of the business cycle on bank credit risk

Journal of Banking & Finance 33 (2009) 1624–1635 Contents lists available at ScienceDirect Journal of Banking & Finance journal homepage: www.elsevi...

735KB Sizes 2 Downloads 61 Views

Journal of Banking & Finance 33 (2009) 1624–1635

Contents lists available at ScienceDirect

Journal of Banking & Finance journal homepage: www.elsevier.com/locate/jbf

Asymmetric effects of the business cycle on bank credit risk Juri Marcucci a,*, Mario Quagliariello b a b

Bank of Italy, Economic Research Department, Via Nazionale, 91-00184 Rome, Italy Bank of Italy, Regulation and Supervisory Policies Department, Via Milano, 53-00184 Rome, Italy

a r t i c l e

i n f o

Article history: Received 22 April 2008 Accepted 19 March 2009 Available online 26 March 2009 JEL classification: C22 C23 G21 G28

a b s t r a c t Prior empirical research on the relation between credit risk and the business cycle has failed to properly investigate the presence of asymmetric effects. To fill this gap, we examine this relation both at the aggregate and the bank level exploiting a unique dataset on Italian banks’ borrowers’ default rates. We employ threshold regression models that allow to endogenously establish different regimes identified by the thresholds over/below which credit risk is more/less cyclical. We find that not only are the effects of the business cycle on credit risk more pronounced during downturns but cyclicality is also higher for those banks with riskier portfolios. Ó 2009 Elsevier B.V. All rights reserved.

Keywords: Credit risk Panel threshold regression models Regime-switching Default rate Business cycle Cyclicality Basel 2

1. Introduction In the recent banking literature, the relation between credit risk and the business cycle (so-called cyclicality of credit risk) has been analyzed for both macro financial stability and micro risk management purposes. Indeed, the potential impact of economic developments on banks’ portfolios is relevant for both policy makers, interested in forecasting and preventing banks’ instability due to unfavorable economic conditions, and risk managers, who pay attention to the robustness of their capital allocation plans under alternative scenarios. These different perspectives are not mutually exclusive. In fact, the reform of the Basel Accord on banks’ capital requirements made it clear the need to match the micro and macro dimensions. Focusing on the latter, this paper analyzes the relation between credit risk and the business cycle allowing explicitly for asymmetries, which have been almost always neglected so far. In fact, we seek empirical evidence for the asymmetric behavior of credit risk

* Corresponding author. Tel.: +39 06 4792 4069; fax: +39 06 4792 2601. E-mail addresses: [email protected] (J. Marcucci), [email protected] (M. Quagliariello). 0378-4266/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jbankfin.2009.03.010

cyclicality not only through the business cycle but also across different credit risk regimes, a completely unexplored issue so far. Previous work on this topic has focused on the macro prudential perspective trying to quantify the effects of macroeconomic conditions on banks’ asset quality in some countries. For example, Pesola (2001) shows that shortfalls of GDP growth below forecast contributed to the banking crises in the Nordic countries, while Salas and Saurina (2002) demonstrate that macroeconomic shocks are quickly transmitted to Spanish banks’ portfolio riskiness. Similarly, Meyer and Yeager (2001) and Gambera (2000) argue that a small number of macroeconomic variables are good predictors for the share of non-performing loans in the US, while Marcucci and Quagliariello (2008b) find that Italian banks’ borrowers’ default rates increase in downturns. Likewise, Hoggarth et al. (2005) provide evidence for the UK of a direct link between the state of the business cycle and banks’ write-offs. Analogous evidence is provided in cross-country comparisons by Bikker and Hu (2002), Laeven and Majoni (2003) and Valckx (2003). However, researchers have not explored the possibility of asymmetric effects, for which the impact of macroeconomic conditions on banks’ portfolio riskiness is dissimilar in different phases of the business cycle. This is very important since bank supervisors are inherently more concerned about downturns rather than

J. Marcucci, M. Quagliariello / Journal of Banking & Finance 33 (2009) 1624–1635

expansions. Also, assuming linear relationships may hinder some important characteristics of banks’ riskiness. To the best of our knowledge, the only exception is the paper by Gasha and Morales (2004) who apply a self-exciting threshold autoregressive (SETAR) model to country-level data showing that GDP growth affects nonperforming loans only below a certain threshold in a group of Latin American countries. Asymmetries are somehow taken into account in a related strand of literature on credit risk management and structural credit risk models. In particular, some studies on the properties of credit rating transition matrices over the cycle have analyzed whether transition probabilities are affected to a larger (smaller) extent by recessionary (expansionary) conditions. Quite often regimeswitching models are used for this kind of investigations. For example, on the basis of GDP growth, Nickell et al. (2000) divide the business cycle into three categories (peaks, normal times and troughs) finding that in peaks low-rated bonds are less prone to downgrades. The impact of the business cycle appears therefore to be asymmetric and dependent on borrowers’ creditworthiness. Likewise, in their analysis of the linkage between macroeconomic conditions and migration matrices, Bangia et al. (2002) find that downgrading probabilities, particularly in the extreme classes, increase significantly in recessions. Pederzoli and Torricelli (2005) adopt a similar framework to assess the impact of the business cycle on capital requirements under Basel 2. However, in this line of research the identification of expansions/recessions is based on some external sources. Most studies in this field employ the NBER business cycle classifications, but some authors like Lucas and Klaassen (2006) cast serious doubts on their use. A further shortcoming of this approach is that it completely ignores the possibility that asymmetries might also depend on the severity of the recession, rather than on the dichotomy expansion/recession. Finally, another gap in this literature is that it does not test the hypothesis that the effects of the business cycle on credit risk are different depending on banks’ portfolios riskiness. In this paper, we address all these issues of asymmetries in credit risk cyclicality. Using threshold regression models and both aggregate and bank level data, we test whether banks which are more exposed to credit risk are affected by the business cycle to a greater extent than those with less-risky portfolios (i.e., whether riskier banks are more cyclical than those less-risky). We also test whether the cyclicality of credit risk is stronger in severe recessions rather than in mild recessions or, a fortiori, during expansionary phases. We start with a standard threshold regression approach at the aggregate level on the time series of the Italian default rates. We then move ahead adopting panel threshold regression models with one threshold variable, which exploit data on borrowers’ default rates at the bank level. These models can be interpreted as regime-switching panel data models where each regime is determined endogenously through one observable threshold variable. We also add to the previous literature suggesting an innovative four-regime panel approach with two threshold variables which allows us to provide a more comprehensive picture of the behavior of default rates over changing economic and credit risk conditions. Our results show that for those banks with lower asset quality, the increase in default rates due to one percentage point decrease in the output gap (our measure of the business cycle) is almost four times higher than the effect for those banks with better portfolios. Furthermore, for models with two or more regimes with one threshold variable, we find that the impact of the business cycle on credit risk is stronger the lower banks’ asset quality. In the four-regime model, where we combine credit risk and the business cycle regimes, we find that (i) during economic slowdowns, the impact of the business cycle on portfolio riskiness for banks with lower asset quality (the a priori riskier ones) is more

1625

than three times higher than that for less-risky banks. Also, (ii) the impact of the business cycle on credit risk for banks with lower asset quality during recessions is more than four times higher than what we have during booms. In addition, (iii) during slowdowns the impact of the business cycle on credit risk for banks with better asset quality is almost the double of that during expansions. Finally, (iv) for riskier banks the impact of the business cycle on their riskiness during expansionary phases is about 50% more than that for less-risky banks. In sum, we conclude that riskier banks’ portfolios are more cyclical (i.e., more sensitive to the business cycle) than less-risky ones and cyclicality is more pronounced in bad economic times. Under the Basel 2 new Capital Accord, which introduces risk sensitive capital requirements, this evidence may provide some guidance to banks and supervisors in the choice of adequate capital buffers over different phases of the business cycle. Indeed, the identification of those banks that are more likely to be affected by recessionary conditions – and that therefore should build higher capital buffers in expansion – may help smooth the fluctuations of capital requirements, thus reducing Basel 2 cyclicality (Jokipii and Milne, 2008). For example, using either macroeconomic forecasts or judgmental future scenarios, supervisors may carry out stress tests in order to assess the evolution of banks’ portfolio riskiness should the scenario actually materialize. The reminder of the paper proceeds as follows. Section 2 describes the data on Italian banks’ portfolios. Section 3 presents the single threshold model at the aggregate level with two regimes. In Section 4 we describe the panel data model with single threshold variable and multiple regimes (both credit risk and business cycle regimes). Section 5 delineates the panel data model with two different threshold variables and four regimes. Finally, Section 6 draws some concluding remarks and directions for further research. 2. Data Our data set comprises both microdata on Italian banks and macroeconomic time series on a quarterly basis. Accounting ratios for the individual institutions are built up using the statistics that intermediaries are required to report to the Bank of Italy and the Central Credit Register, while the macroeconomic variables are drawn from the OECD statistics. Since we want to analyze the evolution of banks’ portfolio riskiness over the business cycle, the starting point for building up our dataset is the choice of an adequate measure of credit risk. In Italy, banks must value loans in their portfolios at their likely realizable value. In particular, the exposures to insolvent borrowers are classified as bad loans. We compute our riskiness indicator as the ratio of the flow of loans classified as bad debts in the reference quarter to the stock of outstanding performing loans at the end of the previous one. In order to improve the reliability and timeliness of our indicator of the riskiness of banks’ debtors, we use the ‘‘adjusted” bad loans as signaled by the Central Credit Register.1 The ratio can be interpreted as the default rate of Italian banks’ borrowers. With respect to other riskiness indicators, based on stock measures, such as the non-performing loan ratio, the 1 Adjusted bad loans are those outstanding when a borrower is reported to the Central Credit Register: (a) as a bad debt by the only bank that disbursed credit; (b) as a bad debt by one bank and as having an overdraft by the only other bank exposed; (c) as a bad debt by one bank and the amount of the bad debt is at least 70% of its exposure towards the banking system or as having overdrafts equal to or more than 10% of its total loans outstanding; and (d) as a bad debt by at least two banks for amounts equal to or more than 10% of its total loans outstanding. The use of this variable ensures that there are no differences across banks due to discretionary valuations. Results provided in this paper are based on seasonally adjusted data, but we obtained similar results with the unadjusted series of the default rate.

1626

J. Marcucci, M. Quagliariello / Journal of Banking & Finance 33 (2009) 1624–1635

Fig. 1. Italian business cycle indicators. This figure depicts the Italian business cycle as measured by three different indicators. GAPHP is the real GDP minus the HP-filtered GDP series. GAPT is the real GDP minus the potential output proxied by a fitted linear trend. GDPG is the series of the real GDP annual growth rate. Shaded areas indicate the recessions according to the ISAE chronology.

default rate is a more precise and timely proxy for banks’ portfolio riskiness. Actually a stock measure such as the non-performing loans can be misleading because it can be biased downward. In fact, charge-offs, loan sales (with recourse) and securitizations can reduce the total amount of bad loans, regardless the cyclical conditions. Since default rates are available at the bank level, we can exploit the cross-sectional dimension and work at different levels of aggregation, from the whole banking system to each single bank’s portfolio. The initial dataset on individual banks goes from 1989Q2 to 2005Q2 with a total of 44,293 bank-quarter observations. We have also excluded those banks with incomplete (or missing) information and those characterized by extreme observations for the variables of interest. We have then balanced the panel so that the resulting final dataset includes 212 banks spanning from 1990Q1 to 2005Q2 for a total of 13,144 observations. Regarding the proxy for the Italian business cycle, we focus on the output gap, defined as the difference between the actual and the potential gross domestic product (GDP).2 We compute a first measure of the output gap as the difference between the actual output and an estimate of the potential given by a linear trend (GAPT). For robustness, as alternative proxies, we employ also the deviations of the GDP series from the Hodrick–Prescott filtered series (GAPHP) and the usual GDP growth rate (GDPG).3 Fig. 1 depicts all the three macroeconomic time series. The shaded areas show the recessions in the Italian economy according to the Istituto di Studi e Analisi Economica (ISAE) as suggested by Altissimo et al. (2000). Within our sample period, the ISAE identifies three recessions: 1992Q2–1993Q2, 1995Q4–1996Q3 and 2001Q1–2004Q4. While the two measures of output gap correctly signal all the three recessions, the GDP growth is more ambiguous for the last one. This is due to the fact that the 2001–2004 recession is in reality a period of prolonged stagnation, as suggested by the ISAE, which refers to this period as an anomalous cycle.

Table 1 reports the summary statistics of the final sample for both the bank level data and the time series of the default rate and alternative indicators of the Italian business cycle. The disaggregated default rate is related to the final sample of 212 banks, while the aggregate one gives the characteristics of the time series. The second micro variable is the logarithm of banks’ total assets (in million of euros), which is used as a proxy for banks’ size. The last micro variable is the difference between the loan growth rate of each bank i at time t and the average loan growth rate for each quarter. This variable is added to control for more active banks in lending activities, which may relax credit standards and have riskier portfolios, ceteris paribus. 3. Single threshold model at the aggregate level with two regimes 3.1. The model Our starting hypothesis is that the default rate is affected by the business cycle and that such impact is subject to one or more regime-switches that characterize the asymmetries. Denoting the observed data on the dependent variable (default rate) as drt, the simplest model that relates the latter time series with macroeconomic conditions (proxied by a measure of the output gap,) under the hypothesis of one regime only (i.e. with no threshold) can be written as

drt ¼ b01 þ b11 GAPt1 þ et ;

ð1Þ

where et is assumed to be a martingale difference sequence with respect to the sigma algebra generated by the past history of the variables. This model can be simply estimated by OLS. A more general model allows for the presence of two regimes defined by an observable threshold variable qt that can be either the default rate or the business cycle indicator.4 In the former case, the model becomes

drt ¼ ðb01 þ b11 GAP t1 ÞIðdr t1 6 cÞ 2

Some studies (Meyer and Yeager, 2001; Yeager, 2004), mainly focusing on US banks, show that banks’ performance is more affected by state level macroeconomic drivers rather than by local (county) level variables. However, the distinction between local and more aggregated economic conditions is not very sensible for smaller countries such as Italy. On the other hand, one may wish to analyze the impact of European business cycle on Italian banks. However, in 2007, for the top five banking groups, foreign units accounted for 35.3% of total assets and the figures are much smaller for the entire banking system. Thus, since most banks remain prevalently domestic, we prefer focusing on national-level indicators and leave this issue for future research. 3 The use of regional breakdowns for GDP may provide valuable insights on possible differences across different geographical areas. Unfortunately, these data are not available on a quarterly basis.

þ ðb02 þ b12 GAPt1 ÞIðdr t1 > cÞ þ et ;

ð2Þ 5

where I() is the indicator function and c is the threshold. In this case we are distinguishing the two regimes with respect to the 4 Threshold regression models are regime-switching models where each regime is determined by the value of a particular observable threshold variable. These models differ from the regime-switching models à la Hamilton (Hamilton, 1989) where each regime is governed by an unobserved state variable which is usually modeled as a first-order Markov chain. For details see Hamilton (1994) or Franses and Van Dijk (2000). 5 For convenience, throughout the paper we use c or cj to indicate the threshold independently of the threshold variable.

1627

J. Marcucci, M. Quagliariello / Journal of Banking & Finance 33 (2009) 1624–1635 Table 1 Summary statistics. Description

Min

25% Percentile

Median

75% Percentile

Max

Mean

Std. Dev.

Skewness

Kurtosis

Micro variables Individual default rate drit Total assets in logs ln(TAit) Loan growth rate lgrit

0.000 1.792 0.295

0.000 5.011 0.028

0.257 5.964 0.011

0.453 7.279 0.006

1.495 12.304 0.272

0.299 6.252 0.010

0.281 1.738 0.036

1.048 0.697 0.599

4.066 3.320 10.193

Macro variables drt Aggregate default rate GDP growth rate GDPGt GAPHPt Output gap from HP-filtered GDP Output gap from linear trend GAPTt

0.309 1.840 2.126 3.001

0.379 0.402 0.513 0.734

0.539 1.169 0.116 0.168

0.671 2.528 0.639 0.920

0.972 3.818 1.779 2.539

0.554 1.363 0.017 0.037

0.179 1.338 0.829 1.298

0.498 0.115 0.313 0.222

2.361 2.368 2.588 2.316

This table provides the summary statistics for the default rate dr, both at the bank (drit) and aggregate level (drt), the total assets in logs, ln(TA), the individual loan growth rate, lgrit, the quarterly growth rate of GDP, GDPGt, the output gap computed as the difference between the GDP and the Hodrick–Prescott (HP) filtered series, GAPHPt, and the output gap computed as the difference between the GDP and a linear trend, GAPTt. All data are quarterly from 1990:Q1 to 2005:Q2 for a total of 13,144 bank-quarters (212 banks and 62 quarters, balanced panel). The default rate is computed as the flow of new bad debts in each quarter over the outstanding performing loans in the previous quarter. Both the aggregate and individual default rates are seasonally adjusted. The aggregate default rate is computed aggregating all banks’ default rates by quarter using their loans as weights. Total assets are in million of euros. The loan growth rate is the difference between the loan growth rate of each bank i at time t and the average loan growth rate for each quarter.

overall credit risk conditions. The model gives an estimate of c which ^ that characterizes good credit risk can be viewed as the threshold c ^Þ, from bad credit risk conditions, i.e. conditions, i.e. Iðdr t1 6 c ^Þ. Iðdr t1 > c When the threshold variable is the independent variable, the model becomes

dr t ¼ ðb01 þ b11 GAPt1 ÞIðGAPt1 6 cÞ þ ðb02 þ b12 GAP t1 ÞIðGAP t1 > cÞ þ et :

ð3Þ

Here, we characterize each regime depending on the general macroeconomic conditions, distinguishing between slowdowns ^Þ and expansionary phases IðGAPt1 > c ^Þ. The models IðGAPt1 6 c can be more compactly represented as

dr t ¼ GAPt1 ðcÞ0 h þ et ;

ð4Þ

  where GAP t1 ðcÞ ¼ GAP 0t1 Iðqt 6 cÞ; GAP 0t1 Iðqt > cÞ ; GAP0t1 ¼ ð1; 0 GAP t1 Þ and h = (b01, b02, b11, b12). The parameters of interest are the coefficients h and the threshold c. Even though the regression Eq. (4) is non linear in the parameters, it can be estimated through least squares (LS). Under the additional assumption that et  N(0,r2), LS is equivalent to maximum likelihood estimation. These models can be estimated by sequential conditional LS. For any given value of c, the LS estimate of h is

^hðcÞ ¼

T X

!1 GAP t1 ðcÞGAP 0t1 ðcÞ

t¼1

T X

! GAPt1 ðcÞdr t ;

ð5Þ

t¼1

with residuals ^et ðcÞ ¼ dr t  GAP0t1 ðcÞ^ hðcÞ and residual variance r^ 2T ðcÞ ¼ T 1 RTt¼1 ^et ðcÞ2 . The LS estimate of c is the value that minimizes the residual variance, i.e.

c^ ¼ arg min r^ 2T ðcÞ;

ð6Þ

c2C

. The minimization problem in (6) can be solved by where C ¼ ½c; c ^ 2T ðcÞ takes on at most T distinct direct search. The residual variance r values as c varies. Thus, to obtain the LS estimates of (6) we can run OLS regression of (4) for c 2 C, where the elements of C are slightly less than T because we have to take a certain percentage (g%) of observations out to ensure a minimum number of them in each regime. Then the value of c that minimizes the residual variance is the LS estimate of the threshold parameter. The LS estimates of the ^Þ. Similarly, the LS residuals coefficients h are then found as ^ h¼^ hðc ^ Þ0 ^ ^Þ. ^ 2T ¼ r ^ 2T ðc h, with sample variance r are ^e ¼ dr t  GAPt1 ðc An important question is whether it is statistically sensible to move from the linear specification in (1) to the model in (2). The relevant null hypothesis that there are no asymmetries in the relation between credit risk and the business cycle is H0:bj1 = bj2,

j = 0,1. From an econometric point of view this is a non-standard testing problem because under the null there are some parameters that are not identified (the so-called ‘Davies’ problem’). Based on the theories of Davies (1977, 1987) and Andrews and Ploberger (1994), Hansen (1996) shows that if the errors are iid, a test with near-optimal power against local to the null alternatives is the standard F-statistic

 FT ¼ T



r~ 2T  r^ 2T ; r^ 2T

ð7Þ

P 0 ~ ~ 2T ¼ T 1 Tt¼1 ðdrt  GAPt1 hÞ2 is the residual variance under where r ~ the null hypothesis and h is the OLS estimate under the null of no threshold, i.e.

~h ¼

T X

!1 GAPt1 GAP0t1

t¼1

T X

! GAPt1 dr t :

ð8Þ

t¼1

^2 Since FT is a monotonic function  2of rT2 , it has2 been shown that ~ ^ T ðcÞ =r ^ T ðcÞ is the pointFT = supc2CFT(c) where F T ðcÞ ¼ T rT  r wise F-statistic against the alternative H1:bj1 – bj2 when c is known. Since c is not identified, the asymptotic distribution of FT is not a v2. Hansen (1996) shows that the asymptotic distribution of FT can be approximated by a bootstrap procedure. Letting  ut ; t ¼ 1; . . . ; T, be iid N(0, 1) and setting dr t ¼ ut , we can regress  ~ 2 and on GAPt1(c) dr t on the observations GAPt1 to obtain r T ^ 2 . Thus we can form the statistic F T ðcÞ ¼ to obtain r T  2   2 ^ ^ ~ 2  r ð c Þ = r ð c Þ and F ¼ sup F ð c Þ. Hansen (1996) shows T r c2C T T T T T that the distribution of F T converges weakly in probability to the null distribution of F T under local alternatives for h. Therefore, repeated bootstrap draws from F T can be used to approximate the asymptotic null distribution of FT. The bootstrap approximation to the asymptotic p-value of the test is constructed by counting the percentage of bootstrap samples for which F T exceeds the observed value of FT. If the errors are conditionally heteroskedastic, it is necessary to replace the F-statistic FT(c) with a heteroskedasticity consistent Wald or Lagrange multiplier test. For further details see Marcucci and Quagliariello (2008a). 3.2. Empirical results Table 2 reports the results for the two-regime threshold model estimated using aggregate data. Given the short time span of our time series, in our preferred parsimonious model, the default rate dr only depends on one-quarter lag of the business cycle indicator, GAPT. The results for model 1 confirm the well-known negative relation between default rates and business cycle, when there is

1628

J. Marcucci, M. Quagliariello / Journal of Banking & Finance 33 (2009) 1624–1635

Table 2 Estimates for 2-regime threshold model at the aggregate level. Model b01 b02 b11 b12

c R2 N1 N2 LR Test p-Value No. bootstrap Trimming %

(1)

(2) ***

0.5536 (0.0226) – – 0.0752** (0.0303) – – – 0.1171 58 – _ – – –

(3) ***

0.4074 (0.0151) 0.7020*** (0.0166) 1.50E05 (0.0277) 0.0747*** (0.0203) 0.5793** 0.7638 30 28 40.00*** 0.000 1000 0.15

(4) ***

0.3828 (0.0100) 0.6892*** (0.0175) –0.0223 (0.0169) 0.0725*** (0.0209) 0.5443** 0.8031 26 32 43.64*** 0.000 1000 0.15

0.4449*** (0.0259) 0.5559*** (0.0653) 0.2183*** (0.0356) 0.0084 (0.0776) 0.3005** 0.3200 36 22 13.02*** 0.001 1000 0.15

This table presents the conditional LS estimates for the following threshold models with 2 regimes:

Model ð1Þ : dr t ¼ b01 þ b11 GAP t1 þ et Model ð2Þ : dr t ¼ ðb01 þ b11 GAPt1 ÞIfdrt1 6 cg þ ðb02 þ b12 GAP t1 ÞIfdrt1 > cg þ et Model ð3Þ : dr t ¼ ðb01 þ b11 GAPt1 ÞIfht 6 cg þ ðb02 þ b12 GAP t1 ÞIfht > cg þ et Model ð4Þ : dr t ¼ ðb01 þ b11 GAPt1 ÞIfGAP t1 6 cg þ ðb02 þ b12 GAP t1 ÞIfGAP t1 > cg þ et P where drt is the aggregate default rate, GAPt1 is GAPTt1 and ht ¼ 4j¼1 drtj =4 is the four-quarter moving average and Ifg is the indicator function. c is the estimated threshold, N1 and N2 are the number of observations that lie in the first and second regime, respectively. LR is the likelihood ratio test for the null of no threshold whose p-value is computed through the bootstrap as suggested by Hansen (1996). N. bootstrap is the number of bootstrap replications used to compute the p-value. The trimming % is the percentage of observations that are excluded from the sample so that a minimal percentage of observations lies in each regime. Standard errors are in parenthesis. * Indicates significance at 10%. ** Indicate significance at 5%. *** Indicate significance at 1%.

only one regime. In fact, a negative coefficient on the output gap means that during recessionary conditions (i.e. when the output gap is negative) banks’ riskiness increases. Our second set of results shows that the cyclicality of credit risk depends on the overall level of banks’ riskiness, proxied by either lagged default rate (drt1) or the previous four-quarter moving average, respectively models 2 and 3. We note that there is a regime switch when the lagged default rate is above a threshold of 0.58%, which is very close to both its mean and median.6 In particular, the statistical significance and magnitude of the slope coefficient b12 suggest that when asset quality is lower, economic conditions have a statistically significant impact on banks’ riskiness. By contrast, in less-risky periods (i.e. when dr is below the threshold) the impact of the business cycle on default rates is almost nil and not significant. The LR test for the null of no regime switch is significant at any conventional level, suggesting that the model is appropriate. To check the robustness of our results we estimated the same models with different proxies of the business cycle and more lags for the threshold variable. Our results (not reported for the sake of brevity) are not affected by the choice of a longer lag for the threshold variable and are robust to the use of different proxies for the business cycle (GAPHP and GDP growth). These results also hold when we estimate this model for different institutional categories (limited companies, cooperative and mutual banks). As we mentioned above, an advantage of our methodology is that it allows to obtain an endogenous estimate of the threshold.

6 Using quantiles as the thresholds might be an alternative to our approach. However, our methodology has the significant advantage of determining the threshold endogenously, without imposing any a priori assumption on its value.

Looking at Table 2, we observe that the value of the threshold is very similar across models and specifications, ranging between 0.54% and 0.58%. Taken at its face value, this means that when the aggregate default rate is above these figures, the banking system tends to be more sensitive to macroeconomic turbulences. In a macro prudential perspective, this advises supervisory authorities to reinforce monitoring activities in these periods. With model 4, we try to assess whether the impact of the business cycle on Italian banks’ riskiness is also subject to a second kind of regime switch, which depends on the phase of the business cycle itself. Our results suggest that, while in recessions the impact of the business cycle on credit risk is sizeable, in expansionary phases it is not statistically significant. Again, these results are generally robust to different specifications. The results presented so far are very supportive of the hypothesis that credit risk is cyclical. However, they also seem to suggest that the issue of cyclicality, as described hitherto by the empirical literature, has been somehow misinterpreted. Indeed, according to our evidence, the negative relation between banks’ portfolio riskiness and the business cycle holds only in either unfavorable economic conditions or when average credit quality is already unsatisfactory. By contrast, it does not seem to be statistically significant in good times (i.e., when either economic conditions improve or loan riskiness is low). However, the small sample size leads us to interpret these preliminary results at the aggregate level with some caution and to deepen our analysis, exploiting the cross-sectional dimension of our rich dataset. 4. Panel data model with a single threshold variable and multiple regimes Using the information on borrowers’ default rates available on a bank-by-bank basis and panel data techniques, we can analyze whether the impact of the business cycle on riskier and less-risky banks is asymmetric. At a first glance, we expect riskier banks to have more cyclical portfolios than less-risky ones. 4.1. The model As in Hansen (1999) we start assuming that the observed data are from a balanced panel {drit,xit,qit} with 1 6 i 6 N and 1 6 t 6 T. The scalar drit is the dependent variable, the k  1 vector xit contains the exogenous (and/or predetermined variables), while qit is an s  1 vector (sP1) containing the threshold variables. The subscript i indicates the individual bank, while t designates the time period (in our case the quarter). The simplest version of the model is a static panel data model with two regimes

drit ¼ li þ a1 lnðTAit Þ þ a2 lnðTAit Þ2 þ a3 lnðTAit Þ3 þ a4 lgrit 2

3

þ a5 lgrit þ a6 lgrit þ a7 lnðTAit Þlgrit þ b11 GAPt1 Iðdr it1 6 c1 Þ þ b12 GAP t1 Iðdrit1 > c1 Þ þ eit ;

ð9Þ

where li are individual fixed effects, ln(TAit) and lgrit are the log of total assets and the loan growth rate of bank i at time t minus the quarterly average, respectively, while I() is the indicator function. The logarithm of total assets is included to control for banks’ size, while loan growth rate controls for different lending policies. Following Hansen (1999), the non-linear terms are included to reduce the possibility of spurious correlations due to omitted variable bias.7 In model (9) the observations are divided into two regimes depending on whether the default rate of bank i at time t  1 is 7 Lack of bank data at higher frequencies does not allow the estimation of models with a richer set of bank-specific variables.

J. Marcucci, M. Quagliariello / Journal of Banking & Finance 33 (2009) 1624–1635

smaller or larger than the threshold c1. This threshold is endogenously determined by the model and separates banks with less and more cyclical portfolios. Each regime is characterized by different regression slopes b1j, j = 1,2 and to identify them it is required that both the regressors and the threshold variables are not time invariant. The errors eit are assumed to be iid with zero mean and finite variance r2. The asymptotic analysis is performed with fixed T and N ? 1. Model (9) can be generalized in two ways. Firstly, as we did in Eq. (3), we can identify different business cycle regimes by using a measure of output gap as the threshold variable, i.e.

dr it ¼ li þ a1 lnðTAit Þ þ a2 lnðTAit Þ2 þ a3 lnðTAit Þ3 þ a4 lgrit 2

3

þ a5 lgrit þ a6 lgrit þ a7 lnðTAit Þlgrit þ b11 GAPt1 IðGAP t1 6 c1 Þ þ b12 GAPt1 IðGAPt1 > c1 Þ þ eit :

ð10Þ

In this way, the first regime is characterized by recessionary conditions, while in the second one we have booming conditions (the output gap is greater than a certain threshold, c1). Secondly, we can generalize model (9) by considering the possibility of more than two regimes over the same threshold variable. For example we can consider three regimes over the banks’ riskiness indicator (that is less-risky, fairly risky and riskier banks) with the following model

dr it ¼ li þ a1 lnðTAit Þ þ a2 lnðTAit Þ2 þ a3 lnðTAit Þ3 þ a4 lgrit 2

3

þ a5 lgrit þ a6 lgrit þ a7 lnðTAit Þlgrit þ b11 GAPt1 Iðdr it1 6 c1 Þ þ b12 GAPt1 Iðc1 < dr it1 6 c2 Þ þ b13 GAP t1 Iðdr it1 > c2 Þ þ eit ; ð11Þ where c1 < c2. We can further generalize the model by including a third threshold, so that we can characterize four credit risk regimes. The same strategy can be adopted for model (10) with different business cycle regimes. A more compact way to represent models (9) and (10) and their generalizations is

dr it ¼ li þ h0 xit ðcÞ þ eit ;

ð12Þ

where h = (a1, . . . , a7, b11, b12 , . . .) and

 2 3 xit ðcÞ ¼ lnðTAit Þ; lnðTAit Þ2 ; lnðTAit Þ3 ; lgrit ; lgrit ; lgrit ; lgrit  lnðTAit Þ; 0

GAP t  Iðdr it1 6 c1 Þ; GAP t  Iðdr it1 > c1 ÞÞ ;

ð13Þ

in case of model (9). To estimate this class of models we employ a fixed effects transformation by removing the individual effects. We take the averages over time of (12) getting

dr i ¼ li þ h0 xi ðcÞ þ ei ; 1

ð14Þ 1

where dri ¼ T Rt drit ; ei ¼ T Rt eit and  xi ðcÞ ¼ T the differences between (12) and (14) yields

1



dr it ¼ h0 xit ðcÞ þ eit ;  drit

Rt xit ðcÞ. Taking ð15Þ

where ¼ drit  cÞ ¼ xit ðcÞ  xi ðcÞ and ¼ eit  ei . Stacking data and errors for each individual i with the first time period deleted and then stacking what results over individuals we get the vector of the dependent variable Y*, the independent variables X*(c) and that of the errors e*. With this notation, (12) is equivalent to dr i ; xit ð

Y  ¼ X  ðcÞh þ e ;

eit

ð16Þ

and for any given value of the threshold c this model can be estimated by OLS, i.e.

^hðcÞ ¼ ½X  ðcÞ0 X  ðcÞ1 X  ðcÞ0 Y  ;

ð17Þ

1629

with regression residuals ^e ðcÞ ¼ Y   X  ðcÞ^ hðcÞ and sum of squared errors (SSE)

h i  1 SðcÞ ¼ ^e ðcÞ0 ^e ðcÞ ¼ Y 0 I  X  ðcÞ X  ðcÞ0 X  ðcÞ X  ðcÞ0 Y  :

ð18Þ

Chan (1993) and Hansen (1999) recommend estimating c by LS minimizing the concentrated SSE in (18). Thus the LS estimator of c becomes

c^ ¼ arg min SðcÞ:

ð19Þ

c¼½c;c

^ to be selected when it Since, it is undesirable for a threshold c sorts too few observations in one regime, we can exclude this by restricting the minimization in (19) to values of c such that a minimal percentage of observations (e.g. 1% or 5%) lie in each regime. ^Þ, the resid^ is obtained the slope estimate becomes ^ h¼^ hðc Once c ^Þ and the residual variance is e ðc ual vector is ^ e ¼ ^ r^ 2 ¼ ½nðT  1Þ1 ^e0 ^e ¼ ½nðT  1Þ1 Sðc^Þ. Since the SSE S(c) depends on the threshold only through the indicator functions, the SSE is a step function with at most NT steps. The minimization in (19) can thus be reduced to a search over at most NT different values of the threshold variable. This is achieved by sorting the threshold eliminating the smallest and the largest d% to ensure a minimum number of observations in each regime. However, since this procedure might be numerically intensive with long time spans and large panels, Hansen (1999) suggests using 393 quantiles, reducing the grid search over {1.00%, 1.25%, 1.50%, . . . , 98.75%, 99.00%}. As in the aggregate case, it is important to test whether the models in (9) and (10) are statistically significant relative to their linear specifications in which there are no thresholds c’s. The relevant null hypothesis of no threshold (or one regime) can be represented as H0:b11 = b12. As before, under the null the thresholds c’s are not identified (‘Davies’ problem’), implying that classical tests have non-standard distributions. We again adopt the bootstrap procedure suggested by Hansen (1996, 1999) to simulate the asymptotic distribution of the test under the null hypothesis of no threshold and compute the bootstrap p-value of the test. For further details on the implementation of the bootstrap for this case, see Marcucci and Quagliariello (2008a). 4.2. Empirical results with the default rate as the threshold variable: Credit risk regimes The results of the estimated panel threshold regression models with two or more regimes over the same threshold variable are provided in Table 3. We start with model 1, which includes only a single threshold, and move on to models 2 and 3, which include two and three thresholds, respectively. The use of multiple thresholds over the same variable makes it possible to identify up to four regimes (from the least to the most cyclical), in which we classify banks depending on their portfolios’ riskiness. For simplicity, from the lowest to the highest threshold, we refer to them as less-risky, slightly risky, fairly risky and riskier banks. When a single threshold is introduced, we find that both less-risky and riskier banks are significantly affected by the business cycle, but the magnitude of the coefficient on the business cycle indicator is larger for those banks with a lower asset quality (i.e., riskier banks are also more cyclical). In particular, the increase of dr as the result of one percentage point decrease of GAP is almost four times higher for riskier banks than for less-risky ones. Models 2 and 3 provide further support to the application of regime-switching models for analyzing credit risk cyclicality. We find that the magnitude of the coefficients on the output gap monotonically increases as we move from lower-risk to higher-risk intermediaries. In particular, looking at the results for model 3, we

1630

J. Marcucci, M. Quagliariello / Journal of Banking & Finance 33 (2009) 1624–1635

Table 3 Estimates for panel threshold regression models with 2 or more regimes over the same threshold variable. Model

a1

(1)

(2) ***

(3) ***

b13

0.1633 (0.0186) 0.0219*** (0.0014) 0.6089*** (0.1862) 0.1238*** (0.0463) 0.2072*** (0.0299) 0.0648*** (0.0271) 0.0241*** (0.0017) 0.0878*** (0.0058) –

b14



0.1654 (0.0186) 0.0221*** (0.0014) 0.6003*** (0.1860) 0.1183** (0.0461) 0.2038*** (0.0297) 0.0650** (0.0270) 0.0181*** (0.0021) 0.0340*** (0.0028) 0.0878*** (0.0058) –

c1 c2 c3

0.743** – – 212 61 393 0.01 561.93** 0.022 1000

0.317** 0.743** – 212 61 393 0.01 21.55** 0.008 1000

a2 a3 a4 a5 a6 b11 b12

No. of banks No. of quarters No. of quantiles Trimming % LR Test p-Value No. bootstrap

(4) ***

0.1651 (0.0186) 0.0220*** (0.0014) 0.6073*** (0.1861) 0.1188** (0.0462) 0.2034*** (0.0298) 0.0634* (0.0270) 0.0181*** (0.0021) 0.0289*** (0.0034) 0.0421*** (0.0047) 0.0878*** (0.0058) 0.317** 0.513** 0.743** 212 61 393 0.05 5.73 0.634 1000

(5) ***

(6) ***

(7) ***

0.1833 (0.0187) 0.0234*** (0.0014) 0.6265*** (0.1870) 0.1118*** (0.0466) 0.2115*** (0.0302) 0.0621*** (0.0273) 0.0513*** (0.0034) 0.0210*** (0.0019) –

0.1754 (0.0205) 0.0234*** (0.0015) 0.7537*** (0.1957) 0.1214*** (0.0467) 0.2084*** (0.0299) 0.0441*** (0.0281) 0.0202*** (0.0017) 0.1032*** (0.0053) –





0.1713 (0.0205) 0.0231*** (0.0015) 0.7401*** (0.1949) 0.1205*** (0.0466) 0.2088*** (0.0298) 0.0470*** (0.0279) 0.0202*** (0.0017) 0.0796*** (0.0063) 0.1453*** (0.0087) –

1.822** – – 212 61 393 0.01 474.70 0.400 1000

0.629** – – 212 58 393 0.01 629.96*** 0.000 1000

0.629** 0.815** – 212 58 393 0.01 47.81 *** 0.000 1000

0.1684*** (0.0205) 0.0228*** (0.0015) 0.7382*** (0.1946) 0.1200*** (0.0466) 0.2082*** (0.0299) 0.0466*** (0.0279) 0.0138*** (0.0022) 0.0296*** (0.0028) 0.0798*** (0.0063) 0.1451*** (0.0087) 0.290** 0.629** 0.815** 212 58 393 0.05 20.98** 0.024 1000

This table displays the conditional LS estimates for the following panel threshold regression models with 2 or more regimes over same threshold variable: 2

3

Model ð1Þ : dr it ¼ a1 lnðTAit Þ þ a2 lnðTAit Þ2 þ a3 lgrit þ a4 lgrit þ a5 lgrit þ a6 lgrit lnðTAit Þ þ b11 GAP t1 Iðdrit1 6 c1 Þ þ b12 GAP t1 Iðdr it1 > c1 Þ þ eit 2

Model ð2Þ : dr it ¼ a1 lnðTAit Þ þ a2 lnðTAit Þ þ a3 lgrit þ a 2

Model ð3Þ : dr it ¼ a1 lnðTAit Þ þ a2 lnðTAit Þ þ a3 lgrit þ a þ b14 GAP t1 Iðdr it1 > c3 Þ þ eit

2 4 lgrit 2 4 lgrit

2

3

þ a5 lgrit þ a6 lgrit lnðTAit Þ þ b11 GAP t1 Iðdrit1 6 c1 Þ þ b12 GAP t1 Iðc1 < drit1 6 c2 Þ þ b13 GAP t1 Iðdrit1 > c2 Þ þ eit 3

þ a5 lgrit þ a6 lgrit lnðTAit Þ þ b11 GAP t1 Iðdrit1 6 c1 Þ þ b12 GAP t1 Iðc1 < drit1 6 c2 Þ þ b13 GAP t1 Iðc2 < drit1 6 c3 Þ 3

Model ð4Þ : dr it ¼ a1 lnðTAit Þ þ a2 lnðTAit Þ2 þ a3 lgrit þ a4 lgrit þ a5 lgrit þ a6 lgrit lnðTAit Þ þ b11 GAP t1 IðGAP t1 6 c1 Þ þ b12 GAP t1 IðGAPt1 > c1 Þ þ eit P Model (5–7): same as (1–3), respectively, with threshold drit1 replaced by hit ¼ 4j¼1 dritj =4 where drit is the individual default rate, GAPt1 is GAPTt1 and I() is the indicator function. cj, j = 1, 2, 3 are the estimated thresholds. LR is the likelihood ratio test for: (i) the null of no threshold in models (1), (4) and (5), (ii) the null of one threshold in models (2) and (6), and (iii) the null of two thresholds for models (3) and (7). Its p-value is computed through the bootstrap as suggested by Hansen (1999) with No. bootstrap replications. The trimming % is the percentage of observations that are excluded from the sample so that a minimal percentage of observations lies in each regime. The coefficients a4 and a5 are divided by 10 and 100, respectively. Standard errors are in parenthesis. * Indicates significance at 10%. ** Indicate significance at 5%. *** Indicate significance at 1%.

note that the slope coefficient b is equal to 0.02 and 0.03 for less-risky and slightly risky banks, respectively. This coefficient jumps to 0.04 and 0.09 for fairly risky and riskier banks, respectively, which are therefore much more cyclical than the previous ones. As a matter of fact, in this model, riskier banks are affected by macroeconomic conditions five times more than the less-risky ones. In the meantime, the influence of the business cycle on the slightly risky banks is almost twice that for less-risky ones, while for fairly risky ones it is three times as much as that for those slightly risky. Finally, the effect of the business cycle on riskier banks is twice that for fairly risky ones. All the models we have analyzed share this kind of monotonicity. For example, in model 2, riskier banks are affected by the business cycle almost five times more than those less-risky. These are quite substantial differences also corroborated by a series of Wald tests which all reject the null hypothesis that the slope coefficients are equal across regimes. We note that more cyclical banks are already selected with the two-regime model (i.e., model 1) so that the last estimated threshold remains unchanged as the number of regimes increases. This suggests that the use of more than two regimes is helpful only for classifying less cyclical banks.

This evidence is confirmed when ht, i.e. the moving average of drit over the previous four quarters, is employed as an alternative threshold variable (models 5–7). This also allows us to overcome possible problems of endogeneity. Here, we can notice that more cyclical banks are selected only with the three-regime model (i.e., model 6). Hence, as we add further thresholds, we discriminate more precisely more cyclical banks, suggesting that using multiple regimes can be important to identify fragile intermediaries. As a robustness check, we also estimated these models for different institutional categories of banks (limited, cooperative and mutual banks). The results for these specifications are consistent with those presented above and are therefore not reported for the sake of brevity. For models 1 and 2 the LR test for the null of one and two regimes, respectively, is significant at any conventional level, while for model 3 the null of three regimes cannot be rejected at usual significance levels. This indicates that the model with three regimes (two thresholds) is adequate. When we use the moving average of drit in the previous four quarters as the threshold variable, the LR tests for the null of one and two regimes are significant at any conventional level, while the LR test for the null of three

J. Marcucci, M. Quagliariello / Journal of Banking & Finance 33 (2009) 1624–1635

regimes is significant at 5%. This shows that in this case the model with four regimes is suitable for distinguishing asymmetric effects in credit risk cyclicality. The endogenously determined thresholds can be used to assess the evolution of Italian banks’ riskiness over time. The three charts of panel A in Fig. 2 depict the percentages of Italian banks in the more cyclical regimes in each quarter for the models with two, three and four regimes and the lagged default rate as threshold (models 1–3 of Table 3) along with the ISAE recessions (shaded areas). We notice that banks tended to migrate towards more cyclical regimes in both the 1992Q2–1993Q2 and the 1995Q4–1996Q3 recessions. However, only a modest migration towards riskier regimes seems to happen in the 2001Q1–2004Q4 recession, notwithstanding the stagnant economic conditions. A possible explanation for this finding is that banks have improved borrower selection criteria in the last years of our sample due to the increasing importance of risk management. Furthermore, the very low level of interest rates and the limited level of indebtedness may have helped firms and households to honor their obligations even in unfavorable times. Another reason for the modest migration toward riskier regimes could be the mild nature of the 2001Q1– 2004Q4 recession. All these factors may have alleviated the cyclicality of credit risk during the last recession in our sample. We also note that the share of banks under the fourth regime is only partially affected by macroeconomic conditions. This extreme riskcategory (dr > 0.74%) is probably more affected by idiosyncratic factors than systematic ones.

1631

The three charts of Panel B in Fig. 2 show the same percentages as Panel A when the four-quarter moving average of the default rate is used as the threshold (models 5–7 of Table 3). The results are quite similar to those already discussed. In principle, our analysis may be improved including more bank-specific variables in the econometric specification. For example, some indicators based on banks’ financial statement may help control the possible causes of cyclicality. Unfortunately, lack of data with a sufficient time span and above all at higher frequencies than yearly did not allow us to perform this check. To provide some further evidence of heterogeneous bank behavior we have analyzed some characteristics of more cyclical banks. In particular, we have focused on intermediaries classified in the two most cyclical regimes by model 3 of Table 3 (four-regime panel data) between 1992 and 2004. These banks are very often small banks; on average their market share on either total assets or loans represented less than 4% of the whole banking system. Their average solvency ratio, computed according to the Basel 1 rules, is about 15%, which is not only much higher than the regulatory minimum, but also of the other banks’ figures. However, we note that in Italy smaller banks are generally better capitalized than larger ones also for regulatory reasons (in particular, mutual banks are subject to specific rules concerning profit allocation). Therefore, it is difficult to argue that more cyclical banks tend – prudently – to keep higher capital buffers than less cyclical ones. Indeed, the loan-loss provision ratio, which can be considered another proxy of a cautious risk management, appears very similar in

Fig. 2. Percentage of banks in each credit risk regime by quarter (panel threshold regression models with 2 or more regimes). This figure displays the percentage of the 212 banks that fall in the more cyclical regimes within the panel threshold regression models with 2 or more regimes (see Table 3). Panel A depicts the percentage of banks in the second regime, the second and the third regimes and the second, the third and the fourth regimes, respectively from left to right, when the threshold variable is the lagged default rate. For example, in model (1) the first chart on the left of panel A shows the percentage of banks for which drit1 > c1. Panel B displays the same charts for models P where the threshold variable is the four-quarter moving average of the default rate, i.e. hit ¼ 4j¼1 dr itj =4. For example, in model (5) the first chart on the left of panel B shows the percentage of banks for which hit > c1.

1632

J. Marcucci, M. Quagliariello / Journal of Banking & Finance 33 (2009) 1624–1635

these two categories of banks. Similar results (not reported for the sake of brevity) hold for those banks classified as fairly risky and riskier by model 7 of Table 3. 4.3. Empirical results with the output gap as the threshold variable: Business cycle regimes When we use the output gap as the threshold variable (model 4 of Table 3), we find further evidence that the relation between credit risk and the business cycle is stronger in recessionary conditions rather than in booms. While the LR test fails to reject the null hypothesis of one regime (i.e., no threshold), a Wald test on the equality of the slope coefficients b11 and b12 is rejected at any usual significance level, indicating that the model still captures some of the features of the cyclicality of credit risk. Based on the estimated thresholds for GAPT, we can identify periods in which economic conditions tend to affect banks’ portfolios to a larger extent than in normal times. In unreported results, we identify four ‘‘high-impact” periods: between 1993-Q1 and 1994-Q2, in 1997-Q1/Q2, 1999-Q1 and 2005-Q2. We note that these periods do not necessarily overlap with the ISAE recessionary phases. 4.4. Robustness checks and a Monte Carlo exercise

Table 4 reports the summary results for the Monte Carlo exercises for all models estimated in this paper with 1000 iterations. For each model we present both the median and mean value of all the coefficients and thresholds along with the average values of the two measures of goodness of fit (LABS and LSQ). For all models of this section, both the average and median values of the absolute and squared deviations of the forecasted default rate from the actual value are quite small (i.e. close to zero), suggesting that these models give a good description of the relation between credit risk and the business cycle both in-sample and in particular out-ofsample. 5. Combining credit risk and business cycle: Panel data model with two threshold variables and four regimes 5.1. The model As an extension of Hansen’s (1999) model, we use a four-regime panel threshold regression model where the regimes are determined by two different threshold variables, as suggested by Marcucci and Lotti (2007). The simplest version of the model takes the form

drit ¼ li þ a1 lnðTAit Þ þ a2 lnðTAit Þ2 þ a3 lnðTAit Þ3 2

As a first step to check the robustness of our results we have estimated both panel threshold regression models with one threshold variable over different subsamples. First we have split our full sample in two subsamples: 1990Q1–1997Q4 and 1998Q1–2005Q2. In the first subsample we have almost two complete business cycles, while in the second one we have almost one complete cycle. This sample splitting allows us to control for the possible impact of geographical diversification, which increased over the last decade.8 In both subsamples the estimated thresholds (unreported) are in line with those estimated for the full sample. In addition, the previously found negative relation between credit risk and the business cycle still holds as well as the monotonic relation between coefficients in different regimes. As a further robustness check, we have estimated both models on a sequence of rolling five-year subsamples starting from 1990Q1–1994Q4 through 2001Q1–2005Q2. All the previous findings again hold. This also confirms that notwithstanding the increased ability of some Italian banks to diversify their assets across several foreign markets, they still remain sensitive to the domestic business cycle. Besides, the estimated thresholds are quite consistent across subsamples. Furthermore, we set up a Monte Carlo experiment to check the robustness of our models out of sample. We split our sample in two parts. The first one is the in-sample one where we select 160 banks (about 75% of the full sample). This in-sample part is used to estimate each model. The second part is the out-of-sample one where we leave the other 52 banks for evaluation purposes. This part is used to test the behavior of our model out-of-sample. We first estimate the model with the 160 banks in-sample, then we use them to compute the fitted values of the default rate (our dependent variable) for our 52 banks out-of-sample. Since we have the realized values of such default rates, we compute two measures of goodness of fit. The first one is the difference in absolute value between the fitted values of the default rates out-of-sample and their realized values, which is called LABS. The second one is the squared difference between the fitted values out-of-sample of the default rates and their realized values, called LSQ.

8

However, as we have already discussed, while some major players extended their activity particularly in other European countries, the majority of Italian banks is still domestic.

3

þ a4 lgrit þ a5 lgrit þ a6 lgrit þ a7 lnðTAit Þ  lgrit þ b11 GAP t1 Iðdrit1 6 c1 ÞIðGAP t1 6 c2 Þ þ b12 GAP t1 Iðdrit1 6 c1 ÞIðGAP t1 > c2 Þ þ b13 GAP t1 Iðdrit1 > c1 ÞIðGAPt1 6 c2 Þ þ b14 GAP t1 Iðdrit1 > c1 ÞIðGAPt1 > c2 Þ þ eit

ð20Þ

where li are individual fixed effects, ln(TAit) and lgrit are the log of total assets and the loan growth rate of bank i at time t minus its average in each quarter, respectively, while I() is the indicator function. In model (20) the observations are divided into four regimes depending on both the lagged default rate of each bank and the output gap. With this model we can study less-risky and riskier banks in both booming and recessionary conditions. In this way we can look at their behavior over different phases of the business cycle and across credit risk regimes. As before, each regime is characterized by different slopes (b1j, j = 1,. . . , 4) and to identify them it is required that both the regressors and threshold variables are not time invariant. The errors are assumed to be iid with zero mean and finite variance while the asymptotic analysis is again performed with fixed T and N ? 1. To estimate this model we employ the fixed effects transformation as with the two-regime panel data model discussed before. We then apply conditional LS minimizing the concentrated SSE as in (19). As before, it is fundamental to test whether model (20) is statistically significant relative to the simplest models with only one threshold. The null hypothesis in this case is that of one threshold. Thus, we again have the problem of some parameters not being identified under the null, implying a non-standard testing problem. To compute the bootstrap p-value of the test we therefore adopt the bootstrap procedure suggested by Marcucci and Lotti (2007), which is similar to that one used in the case of only one threshold variable. For further details see Marcucci and Quagliariello (2008a). 5.2. Empirical results The final set of results is obtained estimating a model with two different threshold variables: the micro variable drit1 and the business cycle indicator (GAPTt1). In this way, we try to depict a more comprehensive picture of the evolution of credit risk across

Table 4 Summary results of Monte Carlo exercises. (1) 2 regimes

(2)

(3)

(4) 3 regimes

(5)

(6) 4 regimes

(7)

(8) 4 regimes

Threshold variable

dr(t  l)

h(t)

GAPT(t  l)

dr(t  l)

h(t)

dr(t  l)

h(t)

dr(t  1),

GAPT(t  l)

h(t),

GAPT(t  l)

Coefficients

Mean 0.1603 0.0215 0.7049 0.0972 0.2141 0.0500 0.0256 0.0978 – –

Median 0.1588 0.0213 0.6976 0.0961 0.2111 0.0517 0.0256 0.0985 – –

Mean 0.1769 0.0233 0.8119 0.0921 0.2130 0.0352 0.0217 0.1119 – –

Median 0.1760 0.0233 0.8175 0.0906 0.2108 0.0360 0.0216 0.1096 – –

Mean 0.1840 0.0231 0.7291 0.0814 0.2180 0.0457 0.0563 0.0221 – –

Median 0.1822 0.0230 0.7237 0.0807 0.2151 0.0484 0.0563 0.0222 – –

Mean 0.1614 0.0215 0.7089 0.0944 0.2104 0.0474 0.0209 0.0454 0.0997 –

Median 0.1597 0.0214 0.7013 0.0933 0.2072 0.0489 0.0212 0.0455 0.0992 –

Mean 0.1712 0.0228 0.8073 0.0907 0.2141 0.0366 0.0207 0.0826 0.1598 –

Median 0.1701 0.0228 0.8118 0.0889 0.2119 0.0378 0.0208 0.0834 0.1567 –

Mean 0.1610 0.0215 0.7063 0.0941 0.2108 0.0480 0.0205 0.0453 0.0756 0.1110

Median 0.1596 0.0213 0.6979 0.0933 0.2077 0.0500 0.0208 0.0444 0.0868 0.1124

Mean 0.1684 0.0226 0.8022 0.0900 0.2135 0.0369 0.0132 0.0327 0.0875 0.1610

Median 0.1672 0.0225 0.8107 0.0882 0.2113 0.0373 0.0132 0.0307 0.0849 0.1566

Mean 0.1527 0.0201 0.7431 0.0760 0.2108 0.0402 0.0249 0.0207 0.1083 0.0048

Median 0.1508 0.0199 0.7297 0.0793 0.2086 0.0426 0.0231 0.0211 0.1035 0.0063

Mean 0.1566 0.0207 0.8009 0.0747 0.2046 0.0297 0.0167 0.0215 0.1171 0.0374

Median 0.1598 0.0208 0.7769 0.0711 0.2035 0.0344 0.0153 0.0224 0.1115 0.0332

c1 c2 c3

0.739 – –

0.742 – –

0.655 – –

0.639 – –

1.688 – –

1.614 – –

0.480 0.759 –

0.512 0.743 –

0.617 0.857 –

0.634 0.819 –

0.454 0.695 0.985

0.512 0.741 1.065

0.304 0.644 0.864

0.291 0.636 0.819

0.606 0.393 –

0.545 0.219 –

0.552 0.219 –

0.505 0.219 –

Measures of fit LABS LSQ

0.192 0.064

0.192 0.064

0.198 0.067

0.197 0.066

0.165 0.051

0.165 0.051

0.193 0.065

0.192 0.064

0.233 0.089

0.231 0.088

0.203 0.071

0.200 0.069

0.233 0.089

0.231 0.087

0.164 0.050

0.162 0.049

0.162 0.049

0.162 0.050

a1 a2 a3 a4 a5 a6 b11 b12 b13 b14

(9)

Thresholds

This table reports the summary results for the Monte Carlo out-of-sample exercises for all models estimated in this paper. The models are the following: 2

3

2 4 lgrit 2 lgr 4 it

3 5 lgrit 3 lgr 5 it

Model ð1Þ : drit ¼ a1 lnðTAit Þ þ a2 lnðTAit Þ2 þ a3 lgrit þ a4 lgrit þ a5 lgrit þ a6 lgrit lnðTAit Þ þ b11 GAPt1 Iðdr it1 6 c1 Þ þ b12 GAPt1 Iðdr it1 > c1 Þ þ eit : Model ð2Þ is the same as model ð1Þ with drit1 replaced by hit ¼ 2

X4 j¼1

dr itj =4:

Model ð3Þ : drit ¼ a1 lnðTAit Þ þ a2 lnðTAit Þ þ a3 lgrit þ a

þa

þ a6 lgrit lnðTAit Þ þ b11 GAPt1 IðGAPt1 6 c1 Þ þ b12 GAPt1 IðGAPt1 > c1 Þ þ eit :

Model ð4Þ : drit ¼ a1 lnðTAit Þ þ a2 lnðTAit Þ2 þ a3 lgrit þ a X4 ¼ dr itj =4: j¼1

þa

þ a6 lgrit lnðTAit Þ þ b11 GAPt1 Iðdr it1 6 c1 Þ þ b12 GAPt1 Iðc1 < drit1 6 c2 Þ þ b13 GAPt1 Iðdr it1 > c2 Þ þ eit : Model ð5Þ is the same as model ð4Þ with drit1 replaced by hit

2

2

3

2

2

3

2

3

Model ð6Þ : drit ¼ a1 lnðTAit Þ þ a2 lnðTAit Þ þ a3 lgrit þ a4 lgrit þ a5 lgrit þ a6 lgrit lnðTAit Þ þ b11 GAPt1 Iðdr it1 6 c1 Þ þ b12 GAPt1 Iðc1 < drit1 6 c2 Þ þ b13 GAPt1 Iðc2 < dr it1 6 c3 Þ þ b14 GAPt1 Iðdr it1 > c3 Þ X4 þ eit : Model ð7Þ is the same as model ð6Þ with drit1 replaced by hit ¼ dr itj =4: j¼1

J. Marcucci, M. Quagliariello / Journal of Banking & Finance 33 (2009) 1624–1635

Model

Model ð8Þ : drit ¼ a1 lnðTAit Þ þ a2 lnðTAit Þ þ a3 lgrit þ a4 lgrit þ a5 lgrit þ a6 lgrit lnðTAit Þ þ b11 GAPt1 Iðdr it1 6 c1 ÞIðGAPt1 6 c2 Þ þ b12 GAPt1 Iðdr it1 6 c1 ÞIðGAPt1 > c2 Þ þ b13 GAPt1 Iðdr it1 > c1 ÞIðGAPt1 6 c2 Þ þ b14 GAPt1 Iðdrit1 > c1 ÞIðGAPt1 > c2 Þ þ eit Model ð9Þ : drit ¼ a1 lnðTAit Þ þ a2 lnðTAit Þ2 þ a3 lgrit þ a4 lgrit þ a5 lgrit þ a6 lgrit lnðTAit Þ þ b11 GAPt1 Iðhit 6 c1 ÞIðGAPt1 6 c2 Þ þ b12 GAPt1 Iðhit 6 c1 ÞIðGAPt1 > c2 Þ þ b13 GAPt1 Iðhit > c1 ÞIðGAPt1 6 c2 Þ þ b14 GAPt1 Iðhit > c1 ÞIðGAPt1 > c2 Þ þ eit

For each model, the Monte Carlo exercises are performed as follows. At each iteration, we randomly select an out-of-sample of 52 banks, leaving 160 banks in sample. Since in the full sample of 212 banks we have 73 limited banks (34%), 18 cooperative banks (9%) and 121 mutual banks (57%), we decided to maintain the same percentages for each category in both samples. Therefore in the out-of-sample we have 18 limited banks, 4 cooperative banks and 30 mutual banks. We then estimate all models in sample, saving the estimated coefficients and thresholds. We thus use these estimated coefficients and thresholds to compute the fitted default rates out-of-sample for the 52 banks. We then compute two measures of goodness of fit. The absolute difference between the out-of-sample real value and the fitted one (LABS) and the squared difference between the realized and the fitted value of the default rate (LSQ). This table reports for each model the means and medians of all the coefficients and thresholds along with the two measures of fit.

1633

1634

J. Marcucci, M. Quagliariello / Journal of Banking & Finance 33 (2009) 1624–1635

banks and through the business cycle. It is not straightforward to guess the impact of the business cycle conditions on banks with different portfolios. However, our a priori belief is that less-risky banks should be less affected by the overall economic conditions than riskier ones. In other words, less-risky banks should be less cyclical, while riskier banks should be more cyclical. In addition, as suggested by our previous results, for the latter intermediaries, the impact of the business cycle should be stronger during slowdowns. Table 5 shows the results for the four-regime panel threshold regression models with two different threshold variables. In model 8, where the thresholds are drit1 and GAPTt1, we notice that all the b1j, j = 1, . . . , 4 coefficients on GAPTt1 across different regimes are negative and significant. In addition, the monotonic relationships we previously found, both between less-risky and riskier banks and between recessionary and expansionary phases, are all confirmed. Riskier banks are affected by the business cycle during recessions more than four times as much as in expansion. In addition the impact of macroeconomic conditions on riskier banks in recessionary phases is more than three times that on less-risky banks. During recessions less-risky banks are affected by the business cycle almost twice as much as similar banks in booming phases. Finally during expansions, riskier banks are 40% more sensitive to the business cycle than less-risky intermediaries. We find similar results with model 9, where the four-quarter moving average of the default rate is used as the threshold. In fact, all the coefficients on GAPTt1 across different regimes are again negative and significant. In addition, the monotonicity still holds both between less-risky and riskier banks and between booms

and busts. Our results show that riskier banks are affected by the business cycle during slumps more than two times as much as in booms. Also the effect of macroeconomic conditions on riskier banks during slowdowns is more than six times that on less-risky ones. Less-risky banks are affected by the business cycle according to a similar magnitude during recessions and in booming phases. Finally during expansions, riskier banks are twice as much more sensitive to the business cycle than less-risky intermediaries. As a further robustness check, we also estimated models 8 and 9 of Table 5 for institutional categories. The results we obtained are quite similar to the previous ones for the whole sample and are unreported for the sake of brevity. In the last two columns of Table 4 we present the mean and median results of our out-of-sample Monte Carlo exercise described in Section 4 for the two four-regime models with two different threshold variables (models 8 and 9). In both cases, the average and median estimated thresholds are close to those obtained for the full sample. In addition, the regime-dependent estimates are similar to those obtained from the full sample, thus further corroborating our conclusions. We also estimated these four-regime models with two different threshold variables in two subsamples (1990Q1–1997Q4 and 1998Q1–2005Q2) obtaining results similar to the full sample. These results can be extremely helpful for supervisory authorities in monitoring credit risk during different phases of the business cycle. However, further research is needed to ameliorate and calibrate these regime-switching models based on panel data and threshold regression with multiple thresholds.

Table 5 Estimates for panel threshold regression models with four regimes over different threshold variables. Model

a1 a2 a3 a4 a5 a6 b11(Less-risky/recession) b12 (Less-risky/expansion) b13 (Riskier/recession) b14 (Riskier/expansion)

Model

(8)

(9)

0.1656*** (0.0186) 0.0216*** (0.0014) 0.6327*** (0.1861) 0.1045** (0.0460) 0.2078*** (0.0296) 0.0590** (0.0271) 0.0333*** (0.0035) 0.0187*** (0.0020) 0.1130*** (0.0067) 0.0263*** (0.0099)

0.1585*** (0.0206) 0.0210*** (0.0015) 0.7387*** (0.1946) 0.1037** (0.0462) 0.2043*** (0.0292) 0.0416 (0.0279) 0.0170*** (0.0037) 0.0195*** (0.0031) 0.1030*** (0.0051) 0.0412*** (0.0099)

(8)

(9)

c1 c2

0.729 1.614

0.500 0.219

No. of banks No. of quarters No. of quantiles (micro) No. of quantiles (macro) Trimming %

212 61 393 60 0.01

212 58 393 57 0.01

LR Test p-Value No. bootstrap

78.54*** 0.000 500

91.71*** 0.000 500

This table presents the conditional LS estimates for the following panel threshold regression models with four regimes (different threshold variable: one micro and one macro): 2

2

3

2

3

Model ð8Þ : dr it ¼ a1 lnðTAit Þ þ a2 lnðTAit Þ þ a3 lgrit þ a4 lgrit þ a5 lgrit þ a6 lgrit lnðTAit Þ þ b11 GAP t1 Iðdrit1 6 c1 ÞIðGAP t1 6 c2 Þ þ b12 GAP t1 Iðdrit1 6 c1 ÞIðGAPt1 > c2 Þ þ b13 GAP t1 Iðdr it1 > c1 ÞIðGAPt1 6 c2 Þ þ b14 GAP t1 Iðdr it1 > c1 ÞIðGAP t1 > c2 Þ þ eit Model ð9Þ : dr it ¼ a1 lnðTAit Þ þ a2 lnðTAit Þ2 þ a3 lgrit þ a4 lgrit þ a5 lgrit þ a6 lgrit lnðTAit Þ þ b11 GAP t1 Iðhit 6 c1 ÞIðGAP t1 6 c2 Þ þ b12 GAP t1 Iðhit 6 c1 ÞIðGAP t1 > c2 Þ þ b13 GAP t1 Iðhit > c1 ÞIðGAP t1 6 c2 Þ þ b14 GAP t1 Iðhit > c1 ÞIðGAPt1 > c2 Þ þ eit where drit is the individual default rate and GAPt1 is GAPTt1, hit ¼

P4

j¼1 dr itj =4

and I() is the indicator function. c1 and c2 are the estimated micro and macro threshold, respec-

tively. LR is the likelihood ratio test for the null of one micro threshold whose p-value is computed through the bootstrap as suggested by Marcucci and Lotti (2007) with No. bootstrap replications. The trimming % is the percentage of observations that are excluded from the sample so that a minimal percentage of observations lies in each regime. Standard errors are in parenthesis. * Indicates significance at 10%. ** Indicate significance at 5%. *** Indicate significance at 1%.

J. Marcucci, M. Quagliariello / Journal of Banking & Finance 33 (2009) 1624–1635

6. Concluding remarks Prior research on the macroeconomic determinants of credit risk and its evolution over the business cycle indicates that banks’ portfolio riskiness is cyclical. However, most of these studies often neglect the presence of asymmetric behavior over different phases of the business cycle. This paper examines credit risk cyclicality allowing explicitly for asymmetries not only through the business cycle but also across credit risk regimes. We thus allow for a different degree of cyclicality across banks with dissimilar levels of riskiness. Using a threshold regression approach combined with panel data and exploiting data on Italian banks’ borrowers’ default rates, we find that the impact of the business cycle on banks’ riskiness is significantly more pronounced not only during economic slowdowns but in particular when credit risk levels are higher. In addition, we endogenously identify the risk threshold(s) over/below which such impact is different, thus providing a powerful tool for financial stability monitoring. Among the other results, in the two-regime panel threshold regression model, we find that both less-risky and riskier banks are significantly affected by the business cycle, but the impact is stronger for the latter banks. In particular, the increase in the default rate as a result of one percentage point decrease in the output gap is almost four times higher for riskier banks. This evidence is robust to the use of different proxies for the overall economic conditions and holds at various levels of aggregation. In addition, we find a certain degree of monotonicity in the impact of macroeconomic conditions on credit risk that is higher for riskier banks as well as during recessions. The evidence arising from our panel threshold regression model with two different threshold variables and four regimes is similar. Overall, our results may provide some guidance to banks and supervisors in the assessment of capital buffers in the various phases of the business cycle. Furthermore, the methodology we propose may be employed by supervisors for selecting institutions that – being more cyclical – are more prone to capital requirements fluctuations and thus should be required to build higher capital buffers in good times. Acknowledgement We would like to thank Ike Mathur, the Editor, and an anonymous referee for many extensive comments and helpful suggestions on earlier drafts, which helped to improve the paper considerably. Furthermore, we would like to thank Max Bruche, Dick van Dijk, Giuseppe Grande, Ashay Kadam, Aneel Keswani, Sebastiano Laviola, Francesca Lotti, Alistair Milne, Domenico J. Marchetti, Fabio Panetta, Anna Rendina, Andrea Resti, Til Schuermann, Timo Terasvirta, Howell Tong and Giovanni Urga for their precious comments on a previous version of the paper. We also would like to thank participants at the 2006 Workshop on nonlinear dynamical methods and time series, the 2nd Italian Congress of Econometrics and Empirical Economics, the 2007 FDIC-Basel Committee Workshop on Banking, Risk and Regulation, the 2007 North American Summer Meeting of the Econometric Society and seminar participants at the University of Rome Tor Vergata, the Cass

1635

Business School and the Federal Reserve Bank of Boston for their comments. Previous drafts circulated under the title ‘‘Credit Risk and Business Cycle Over Different Regimes”. The views expressed are those of the authors and do not necessarily reflect those of the Bank of Italy.

References Altissimo, F., Marchetti, D.J., Oneto, G.P., 2000. The Italian business cycle: Coincident and leading indicators and some stylized facts. Working Paper No. 377, Bank of Italy. Andrews, D.W.K., Ploberger, W., 1994. Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62, 1383–1414. Bangia, A., Diebold, F.X., Kronimus, A., Schagen, C., Schuermann, T., 2002. Ratings migration and the business cycle, with application to credit risk portfolio stress testing. Journal of Banking and Finance 26, 445–474. Bikker, J.A., Hu, H., 2002. Cyclical patterns in profits, provisioning and lending of banks. Banca Nazionale del Lavoro Quarterly Review 55, 143–175. Chan, K.S., 1993. Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model. The Annals of Statistics 21, 520–533. Davies, R.B., 1977. Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 64, 247–254. Davies, R.B., 1987. Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 74, 33–43. Franses, P.H., Van Dijk, D., 2000. Nonlinear Time Series Models in Empirical Finance. Cambridge University Press. Gambera, M., 2000. Simple forecasts of bank loan quality in the business cycle. Federal Reserve Bank of Chicago, Supervision and Regulation Department, Emerging Issues Series, S&R-2000-3. Gasha, J.G., Morales, R.A., 2004. Identifying threshold effects in credit risk stress testing. Working Paper 150, IMF. Hamilton, J.D., 1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57, 357–384. Hamilton, J.D., 1994. Time Series Analysis. Princeton University Press. Hansen, B.E., 1996. Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 64, 413–430. Hansen, B.E., 1999. Threshold effects in non-dynamic panels: Estimation, testing, and inference. Journal of Econometrics 93, 345–368. Hoggarth, G., Sorensen, S., Zicchino, L., 2005. Stress tests of UK banks using a VAR approach. Working Paper No. 282, Bank of England. Jokipii, T., Milne, A., 2008. The cyclical behaviour of European bank capital buffers. Journal of Banking and Finance 32 (8), 1440–1451. Laeven, L., Majoni, G., 2003. Loan loss provisioning and economic slowdowns: Too much, too late? Journal of Financial Intermediation 12, 178–197. Lucas, A., Klaassen, P., 2006. Discrete versus continuous state switching models for portfolio credit risk. Journal of Banking and Finance 30, 23–35. Marcucci, J., Lotti, F., 2007. A threshold model for firms’ investment over the business cycle. Unpublished Working Paper, Bank of Italy. Marcucci, J., Quagliariello, M., 2008a. Credit risk and business cycle over different regimes. Working Paper No. 670, Bank of Italy. Marcucci, J., Quagliariello, M., 2008b. Is bank portfolio riskiness procyclical? Evidence from Italy using a vector autoregression. Journal of International Financial Markets, Institutions and Money 18, 46–63. Meyer, A.P., Yeager, T.J., 2001. Are small rural banks vulnerable to local economic downturns? Federal Reserve Bank of St. Louis Review, 25–38. Nickell, P., Perraudin, W., Varotto, S., 2000. Stability of rating transitions. Journal of Banking and Finance 24, 203–227. Pederzoli, C., Torricelli, C., 2005. Capital requirements and business cycle regimes: Forward-looking modelling of default probabilities. Journal of Banking and Finance 29, 3121–3140. Pesola, J., 2001. The role of macroeconomic shocks in banking crises. Discussion Paper No. 6, Bank of Finland. Salas, V., Saurina, J., 2002. Credit risk in two institutional settings: Spanish commercial and saving banks. Journal of Financial Services Research 22, 203– 224. Valckx, N., 2003. What determines loan loss provisioning in the EU? Unpublished Working Paper, ECB. Yeager, T., 2004. The demise of community banks? Local economic shocks are not to blame. Journal of Banking and Finance 28, 135–153.