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An analysis of the determinants of financial distress in Italy: A competingrisks approach

Alessandra Amendola, Marialuisa Restaino, Luca Sensini

PII: S1059-0560(14)00174-9DOI: doi: 10.1016/j.iref.2014.10.012Reference: REVECO 990

To appear in: International Review of Economics and Finance

Received date: 8 May 2012Revised date: 29 March 2014Accepted date: 31 October 2014

Please cite this article as: Amendola, A., Restaino, M. & Sensini, L., An analysis ofthe determinants of financial distress in Italy: A competing risks approach, InternationalReview of Economics and Finance (2014), doi: 10.1016/j.iref.2014.10.012

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An analysis of the determinants of financial distress in

Italy: a competing risks approach

Alessandra Amendolaa, Marialuisa Restainob,∗, Luca Sensinic

aDepartment of Economics and Statistics, University of Salerno, Via Giovanni Paolo II,132 84084 Fisciano (SA), Italy

bDepartment of Economics and Statistics, University of Salerno, Via Giovanni Paolo II,132 84084 Fisciano (SA), Italy

cDepartment of Management and Information Technology, University of Salerno, ViaGiovanni Paolo II, 132 84084 Fisciano (SA), Italy

Abstract

This paper investigates the influence and the effect of micro-economic indica-tors and firm-specific factors on different states of financial distress. In par-ticular, a competing risks model is estimated taking into account the differ-ences among variables leading firms to exit the market through bankruptcy,liquidation and inactivity. The determinants of financial distress for anyexit route are identified on the basis of the influence on the hazard ratios ofthe significant variables selected for each state. Furthermore, the predictiveperformance of the competing-risks model over the single-risk framework isevaluated, with respect to different time windows, by means of some accuracymeasures. The results reached on a sample of Italian firms provide supportfor the hypothesis that the factors influencing firms’ way out strongly dependon the exit routes and highlighting the need to distinguish among them bymeans of a multiple-state approach.

Keywords: Financial distress, Firm’s exit, Competing risks model,Forecasting

JEL Classification: C34, C40, G33, G34

∗Corresponding authorEmail addresses: alamendola@unisa.it (Alessandra Amendola),

mlrestaino@unisa.it (Marialuisa Restaino), lsensini@unisa.it (Luca Sensini)

Preprint submitted to International Review of Economics and Finance November 7, 2014

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1. Introduction

Modeling firm survival and studying the effect of factors that determinefirm’s exit are drawing an increasing attention from both academics andpractitioners over the last years. Most of the existing literature treats exitfrom the market as a homogeneous event or focuses on only one form of exit,separately investigating any decision to leave the market. Starting from theseminal paper of Altman (1968), researchers have essentially focused on thefailing and non-failing dichotomous variable, examining the companies thatactually went bankrupt by means of some models (logit, probit, discriminantanalysis, survival analysis and so on) (Ohlson, 1980; Zmijewski, 1984; Lennox,1999; Shumway, 2001; Brabazon and Keenan, 2004; Figlewski et al., 2012,among the others).

However, there are different exit options that may force a potentiallydistressed company to leave the business. Besides entering in involuntaryexit procedure (such as bankruptcy), a firm could choose for a merger oracquisition or decide for a voluntary liquidation. Each type of exit is likelyto be driven by different factors and can determine important implicationsfor the stakeholders and, in general, for the whole economy (Schary, 1991;Harhoff et al., 1998). Investigating the determinants leading to the dif-ferent forms of distressed firm’s exit can, therefore, be particularly rele-vant. In order to examine the effects of explanatory variables across thestates of financial distress, a multi-state approach can be used (Headd, 2003;Jones and Hensher, 2004; Rommer, 2005; Hensher and Jones, 2007; Jones and Hensher,2007). Some studies analyze the different types of exit, whereas not much issaid about the similarities or dissimilarities among factors determining them(Chancharat et al., 2010; Esteve-Perez et al., 2010).

The aim of this paper is to give a contribution in this direction studyingthe determinants of the probability of alternative exit routes, with particularattention to the differences in the factors driving firms out of the market. Theeffects of micro-economic indicators and firm-specific variables on differentstates are examined by a competing risks hazard model. This model is usedfor determining the probability and hazard ratio of three mutually exclusiveways of exit, namely bankruptcy, liquidation and inactivity. The first cate-gory includes those firms that involuntary exit the market; the second refersto firms that opt for a liquidation encouraged by several possible reasons(avoid involuntary exit, restructuring, etc.). The last category includes thosefirms that exit the market for reasons different from the previous ones. The

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active firms are selected as reference group. Unlike discrete outcome models(logit, probit), hazard models allow to account for both whether and when anevent occurs, by tracking the evolution of the risk over time. Moreover, thecompeting risks model provides information regarding whether the effects ofeach variable change across the multiple states of financial distress.

Here we develop a four-state Cox proportional hazards competing risksmodel, in which the states are considered to be independent. In order to high-light the diverse role played by the explanatory factors, a single-risk modelis also estimated in which all financial distress states are pooled together.The results obtained by the two model specifications are compared not onlyin terms of the significance and sign of the selected variables, but also onthe basis of hazard ratio and financial meaning. A further comparison ismade on the forecasting accuracy evaluating the capability of the models topredict firms’ exits by means of some accuracy measures. The analysis havebeen carried out on a sample of Italian firms. In particular we refer to thebuilding sector underlining its relevance not only in terms of relative weightof GNP, but also with respect to its role in the various objectives behindnational development planning in many European countries.

To perform these approaches and provide empirical evidence, a set of ex-planatory variables is considered from which selecting the best-set of possiblecandidate indicators to be included in the estimated models. To this purpose,few considerations pointed out in the literature have been taken into account.Some companies characteristics, such as age and size, affect the probability offailure. In particular, the likelihood of a firm to go bankrupt decreases withsize and age (Bhattacharjee et al., 2009; Esteve-Perez et al., 2010). Corpo-rate governance, specifically the structure of the firm’s board of directors andownership and the interaction among them, may also affect the probability offailure. The agency problem between the owners of a firm (its shareholders)and the management lead to inefficiency in case of ownership concentration(Zeitun, 2009). The legal form can be also considered as a potential indica-tor for risk measures. Private limited liability companies would face higherrisk, as they would have less share capital to lose compared with publiclimited liability companies (Esteve-Perez et al., 2010). From what concernthe indicators of firm’s financial performance, we consider the most rele-vant and effective indicators in highlighting current and prospective condi-tions of financial distress that refer to the different methodological proposals,from the pioneer works on the topic (Smith and Winakor, 1930; Fitzpatrick,1931, 1932) since the more recent contributions (Altman and Hochkiss, 2006;

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Balcaen and Ooghe, 2006; Ravi Kumar and Ravi, 2007; Xie et al., 2008; Amendola et al.,2011; Laitinen and Suvas, 2013).

To anticipate the results, our findings reveal several differences in thefactors determining firms’ way out with respect to the exit routes. In par-ticular, we find out that some firm-specific characteristics, such as age, legalform and size, have influence on the probability of being liquidated, inactiveand bankrupted, thus confirming the empirical results available in litera-ture. The profitability ratios also play a relevant role on the likelihood ofgoing bankrupt. Then, for the single-risk model the variables selected showsome similarities to those characterized by the inactive state and liquidation,whereas they are different for bankruptcy. Thus, our results corroborate theneed to separately investigate the different forms of exit, and allow to betterunderstand the effects of diverse explanatory factors. The method developedin this paper can be easily applied to data collected from other industries orcountries.

The paper is structured as follows. In the next section, the statisticalmethod is briefly reported. The predictors’ dataset is introduced in Sect. 3.The results are discussed in Sect. 4, while Sect. 5 concludes.

2. Methodology

The Competing risks model is one of the most popular settings of theMulti-State Models (for details, see Andersen et al., 1993; Hougaard, 2000;Andersen et al., 2002). It extends the simple mortality model for survivaldata and is based on one transient state (alive state) and a certain numberof absorbing states, corresponding to death from different causes. Thus, alltransitions are from the state alive.

Let T and C be the failure time and the censoring time, respectively.Let T = min(T , C) be the observed time and let δ = I(T ≤ C) be anindicator function, which is equal to 1 if the cause of failure is known, andzero otherwise. Thus, the observed data are given by (T, δ).

Let D be the cause of failure (event-causing failure). Assume that thepossible causes are numbered from 1 to K. The main feature of competingrisks model is that from a given set of k causes, one and only one cause can beassigned to every failure. Analyzing competing risks data means to get insightthe joint distribution of T and D. The fundamental concept in competingrisks model is the cause-specific hazard function, i.e. the probability of failing

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due to a given cause k, after one has reached the time point t:

λk(t) = lim∆t→0

P [T ≤ t+∆t,D = k|T ≥ t]

∆t, k = 1, . . . , K. (1)

Then, the cumulative cause-specific hazard function is:

Λk(t) =

∫ t

0

λk(s)ds, (2)

and the cause-specific survival function is:

Sk(t) = exp(−Λk(t)). (3)

Finally, the overall hazard function can be written as:

λ(t) =K∑

k=1

λk(t), (4)

Since we are sometimes interested in the probability to fail from cause kup to time point t, the probabilities as functions of t, called the cause-specificcumulative incidence functions, can be considered:

Ik(t) = P (T ≤ t,D = k). (5)

Cause-specific hazard function and cumulative incidence function pointto a single cause. If we are interested in the relative contribution of thedifferent causes to the overall failure, we can transform these quantities torelative measures of the contribution. Thus, the probability to have failedbecause of a given cause k and before time t is given by:

φIk(t) = P (D = k|T ≤ t) =

Ik(t)∑k Ik(t)

. (6)

Then, we can consider the probability to fail from cause k, given one willfail within a short time interval after reaching the time point t, leading to:

φλk =

λk(t)∑k λk(t)

, k = 1, . . . , K. (7)

Let’s assume that 0 < t1 < t2 < · · · < tu are ordered distinct time pointsat which failures of any causes occur. Let dkr (r = 1, . . . , u) denote the num-ber of firms failing from cause k at tr and let dr =

∑K

k=1 dkr denote the total

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number of failures (from any cause) at tr. In the absence of ties, only one ofthe dkr equals 1 for a given r and dr = 1. Let nr be the number of firms atrisk (i.e. firms that are still in follow-up and have not failed from any cause)at time tr.

Consider a discretized version of the cause-specific hazard, i.e. the pro-portion of subjects at risk that fail from cause k:

λk(tr) = P (T = tr, D = k|T > tr−1). (8)

It would be estimated by:

λk(tr) =dkrnr

, (9)

for k = 1, . . . , K and for r = 1, . . . , u.Since the cause-specific hazards are identifiable, a regression on them is

possible. In Proportional Hazards Regression, the cause-specific hazard ofcause k for a subject i with covariate vector Zi is given by:

λik(t|Zik) = λk,0(t) exp{βTkZik(t)}, (10)

where λk,0(t) is the baseline cause-specific hazard of cause k which does notneed to be explicitly specified, Zik(t) is a vector of covariates for firm i specificto k-type hazard at time t, and the vector βk represents the covariate effectson cause k to be estimated. Since the same variables could have differenteffects on the different risks, it is reasonable to assume that, for each k, βk

is independent of each other.In order to have an estimate of the coefficients’ vector, we build the partial

likelihood function for each specific hazard k using the results available inunivariate Cox Proportional Hazard model:

Lk(βk) =

nk∏

i=1

exp{βTkZik(t)}∑

l∈R(tik)βT

kZlk(t)(11)

where nk is the number of firms in specific hazard k, and R(tik) = {l|tlk ≥ tik}is the set of individuals at risk at time tik.

The overall partial likelihood function is given by:

L(β1, . . . ,βk) =K∏

k=1

nk∏

i=1

exp{βTkZik(t)}∑

l∈R(tik)βT

kZlk(t)(12)

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3. The data

The data refer to the population of Italian firms that operate in the build-ing sector1 in the period 2004-2009. The information on individual firmsand their financial characteristics have been obtained from the Amadeusdatabase, provided by Bureau van Dijk. Our main interest is in investigatingthe determinants of firms that end up in financial distress and compare thesedeterminants for each different form of exit. The focus is on three mutuallyexclusive states of exit from the market: bankruptcy, liquidation and inactiv-ity. The bankrupt status includes those firms that have been legally declarednot to be able to pay its creditors and are under a Court supervision. Thesecond status includes those companies that no longer exists because theyhave ceased their activities and are in the process of liquidation. The laststate includes those firms that exit the database, but it is unknown the rea-son of the exit. The reference group is given by active firms. From the overallpopulation of active and non-active firms, we select a cluster random sampleof n = 1462 firms based on the geographical distribution of the industrialfirms across the regions. The distribution of the final sample consists of 221companies that went bankrupt, 129 that had entered voluntary liquidation,and 228 that were inactive. The companies in the active state are 884.

The predictors data-base for the years of interest (2004-2009) is elabo-rated starting from the financial statements of each firm included in the sam-ple, for a total of 8030 balance sheets. In particular, we compute nv = 24 in-dicators selected as potential predictors among the most relevant in highlight-ing current and prospective conditions of financial distress (Dimitras et al.,1996; Altman and Hochkiss, 2006). The selected indicators reflect the mainaspects of the firms’ structure such as profitability, solvency and liquidity.The specifications of the financial indicators included in the analysis areare shown in Table 1. Non-financial information on the corporate gover-nance such as region, legal form, number of shareholders, presence of auditorsboard, firm size and firm age, are also considered.

A pre-processing procedure is performed on the original data set. Theresults of exploratory data analysis indicate that there are some account-ing data observations which are severe outliers. These observations would

1Following part of the literature, the analysis is focused on a specific economic sectorand, as state in the Introduction, we refer to the building sector given its relevance not onlyin terms of relative weight of GNP but also in terms of socio-economic policy implications.

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Table 1: Specification of financial predictors.

Area nv Indicators

Profitability 8

PM = (PBT/OR)∗100EBITDA = R − E(EITDA)EBIT= R - E - DACF/ORROE = EA / SEROCE = RBIT /CE.ROA = NI/TAROTA= (NI + IE + T) / TNA

Operational 5NAT = OR/(SF + NCL)IC = OP / IPST = OR / STOCOP = (D/OR)*360CRP = (C/OR)*360

Structure 5CR = CA/CLLR = (CA - STO)/CLSLR = SF/NCLSR = (SF/TA)*100GE = ((NCL+LO)/SF)*100

Firm-specific variables 6Region, Legal Form, Number ofshareholders, Auditors Board,Firm Size and Firm Age.

C=Creditors; CA=Current assets; CE=Capital Employed; CF=Cash flow; CL=Current liabilities;COP=Collection period; CR=Current ratio; CRP=Credit period; D=Debtors; DA=Depreciation &Amortization; E=Expense; EA=Earnings; EBIT=Earnings Before Interest and Tax; EBITDA=EarningsBefore Interest, Taxes, Depreciation and Amortization; EITDA= excluding interest, taxes, depreciationand amortization; GE=Gearing; IC=Interest cover; IE=Interest Expense; IP= Interest paid; LO=Loans;LR=Liquidity ratio; NAT=Net assets turnover; NCL=Non current liabilities; NI=Net Income; OP =Operating profit; OR=Operating revenue; PBT=Profit before tax; PM=Profit margin; R=Revenue;RBIT=Return (before Interest and Tax); ROA=Return on Assets; ROCE=Return on Capital employed;ROE=Return on Equity; ROTA=Return on Total Assets; SE=Shareholders Equity; SF=Shareholdersfunds; SLR = Shareholders liquidity ratio; SR = Solvency ratio; ST=Stock turnover; STO=Stock;T=Taxes; TA=Total Assets; TNA=Total Net Asset.

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seriously distort the estimation results if they were included in the defaultrisk model. Therefore, those firms showing values of the financial predictorsoutside the 3th and 97th percentiles are excluded from the analysis. In orderto achieve stability, we apply a modified logarithmic transformation, definedfor non-positive argument.

Finally, the sample is divided into two parts: in-sample set, used for theclassification ability, in order to determine how accurately a model classifiedbusinesses, and out-of-sample, used for prediction ability, in order to deter-mine how accurately a model classified new businesses. Two predictions’windows are considered: 1-year ahead and 2-years ahead.

4. Empirical findings

4.1. The determinants of different exit routes

This section provides the empirical results obtained from the estimatedsingle-risk and competing risks models. The effect of some strategic factorson the likelihood of exiting the market for different reasons are investigatedand the determinants of various exit routes are compared.

To better understand the effects of the explanatory variables used in ouranalysis, we consider a non-parametric test, the Log-rank test (Kalbfleisch and Prentice,2002), for testing the equality of hazard functions across groups of firms, ac-cording to some explanatory variables. This test is considered as a startingpoint in order to check which variables have an effect on each exit routeand whether some differences arise not only between the single-risk (whereall states of financial distress are pooled together) and the competing risksmodels, but also among the different exit routes.

Table 2 shows the p-values of the log-rank test, for single-risk model (col-umn 5) and for the three competing events (columns 2-4) for 1-year aheadpredictions2.

Regarding the risk of exiting the market, the test results show that thereare significant differences in the hazard rates between groups for most of thevariables, looking at both the competing risks and the single-risk models.

Considering the different competing events, some variables are significantfor all the three status. Namely, the legal form, the firm size, the first and

2Although the test is performed for both time-windows (1-year ahead and 2-year ahead),here we only report the results of the first period considered.

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Table 2: Log-Rank Test for the equality of hazard functions of different exit routes, byexplanatory variables, for 1 year ahead.

Bankruptcy Inactive Liquidation Single-risk

Limited Company ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗One Shareholder ∗ ∗ ∗∗ ∗∗Micro Firmsa ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗Small Firms ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗Medium Firms ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗Large Firms . ∗Age1b ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗ ∗ ∗ ∗ ∗∗Age2 ∗ ∗∗Age3Age4 ∗∗ ∗Age5 ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗North ∗∗CenterSouth . ∗∗Return on total assets ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗Profit margin ∗ ∗ ∗∗ . ∗ ∗ ∗∗ ∗ ∗ ∗∗EBITDA ∗ ∗ ∗∗ ∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗EBIT ∗ ∗ ∗∗ ∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗Cash flow/Operating revenue ∗ ∗ ∗∗ ∗∗ ∗ ∗ ∗∗ROE ∗∗ ∗ ∗ ∗∗ROA ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗ROCE ∗ ∗ ∗ ∗ ∗ ∗ ∗∗Net assets turnover ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗Interest cover ∗ ∗ ∗∗ . ∗ ∗ ∗∗ ∗ ∗ ∗∗Stock turnover ∗ ∗ ∗ ∗ ∗ ∗Collection period ∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗Credit period ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗∗ ∗ ∗ ∗∗Current ratio ∗ ∗ ∗∗ . ∗∗ ∗ ∗ ∗∗Liquidity ratio ∗ ∗ ∗∗ ∗Shareholders liquidity ratio ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗Solvency ratio ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗Gearing ∗ ∗ ∗∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗∗

The levels of significance are: ∗ ∗ ∗∗ 0.0001, ∗ ∗ ∗ 0.001, ∗∗ 0.01, ∗ 0.05, . 0.10, 1.00.

a For the firms’ size, the European classification is used. Micro firms are those having a number of workersless than 10 and sales less than 2 milions; small firms are those having a number of workers between 11and 50 and sales between 2 and 10 milions; medium firms are those having a number of workers between51 and 250 and sales between 10 and 50 millions; large firms are those having a number of workers greaterthan 350 and sales greater than 50 millions.b The age of firms is classified into 5 classes: 1) up to 7 years; 2) from 8 to 13 years; 3) from 14 to 21years; 4) from 22 to 30 years; 5) more than 30 years.

the last categories of firm age, EBITDA, EBIT, credit period and gearing aresignificant for all exit routes with a p-value less than 0.05. The remainingvariables have a different effect in bankruptcy, inactivity and liquidation. For

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example, the number of shareholder and the ROCE are only significant forthe inactive state; the stock turnover and the liquidity ratio are importantonly for the bankruptcy; the second and the fourth groups of the age andthe firms being in Northern Italy are relevant only for the liquidation state.Therefore, it came up there are some differences in variables influencing eachexit and we cannot neglect them when predicting the probability of droppingout. Moreover, as expected, these results suggest that bankruptcy, inactivestate and liquidation are three rather different events.

Looking at the results for the risk of pooled exits, it can be noted thatthe variables relevant for some states in the competing risks model are alsosignificant for the single-risk model. In particular, the results are in line withthose regarding the risk of being inactive and liquidated, but they divergefor the risk of being bankrupted.

The variables which are significant by the log-rank test are considered asthe initial set of explanatory variables in the model, in order to assess theireffect on the hazard rate of each exit route. The final set of variables to beincluded in each state is further selected by stepwise procedure3. The resultsfor the estimated competing-risks and single-risk models are shown in Tables3 and 4. They respectively display the sign of the coefficients’ estimates andthe hazard ratios , obtained by computing the exponential of coefficients β.The hazard ratios attest the effect of the covariates on the hazard. A hazardratio equal to one means that the variable has no effect on survival, whereasa hazard ratio greater (less) than one indicates that the effect of the covariateis to increase (decrease) the hazard rate.

In Table 3, columns 3-5 report the results for the three risks consideredand the last column displays the results for the pooled model. The regres-sion results show some remarkable differences supporting the need to use thecompeting risk model over the single risk one. Moreover, the variables aredifferent in the determinants of the three exit routes and in their sign, notonly between the competing risks and single-risk models, but also among thestates. In particular, looking at the different exit routes, we notice that thelegal form has a positive effect on being bankrupted and liquidated. Themedium size and the last category of age (more than 30 years) have a nega-tive effect on being inactive and liquidated. The first category of age (up to7 years) has a positive coefficient for bankruptcy and inactive states. Finally,

3For a discussion on the variable selection problem, see Amendola et al. (2011).

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gearing has a different sign for inactivity and bankruptcy. In fact, it has anegative impact on the probability of being inactive, while it has a positiveimpact on the probability of going bankrupt.

Some of the variables are selected as potential predictors of exit for onlyone state. Actually, the geographical division, the number of shareholders,the profit margin and the collection period are relevant for being inactive.Then the size, the profitability ratios, the interest cover and the current ratioare selected as potential predictors of going bankrupt. Significant variablesfor being liquidated are the third group of age (from 22 to 30 years), returnon total assets, net assets turnover, credit period and solvency ratio.

To sum up, the main difference among the competing risks is related tothe role of the profitability ratios, which are only selected as predictors ofbankruptcy. The reason may be related to their nature of assessing the firm’sability of generating earnings as compared to its expenses and other relevantcosts incurred during a specific period of time. In other words, they mea-sure the company’s use of its assets and control of its expenses to generatean acceptable rate of return. Consequently, since the inactive state includesfirms for which the cause of exit is unknown, we do not have any informationabout their activity.

The effect of the financial ratios and the firm-specific variables can befurther explored by examining the hazard ratios (Table 4).

It can be noted that the limited companies have a greater probabilityof being liquidated and going bankrupt. In fact, there is an increase in therisk of liquidation and bankruptcy, as compared to the firms having otherlegal forms. Regarding the dimension of firms and controlling for other firms’characteristics, we note that the risk of being bankrupted is higher for smallfirms, while the risk of being liquidated and inactive is lower for medium sizedfirms. Moreover, young firms have a higher probability of going bankrupt orbecoming inactive. On the contrary, old firms have a lower probability ofbeing liquidated and becoming inactive. Then, the effect of the number ofshareholder is to increase the hazard rate of being inactive.

As concerns the financial indicators of profitability area selected as poten-tial predictors of bankruptcy state, they have a negative effect on the hazardrate, except for the ROCE. The different sign may be related to the fact thatthe ROCE includes debt funds like loans and preference capital.

Finally, it results that the variables in single-risk framework are substan-tially different from those in competing risks model. In particular, very smallcompanies have a faster hazard timing of exit the market, as opposite to big

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Table 3: Sign of Coefficients’ Estimates for the competing risks and the single risk models,for 1 year ahead.

Variables Areaa Bankruptcy Inactive Liquidation Single-Risk

Limited Company 4 Positive Positive PositiveSouth Italy 4 NegativeMicro Firms 4 Positive PositiveSmall Firms 4 PositiveMedium Firms 4 Negative Negative NegativeLarge Firms 4 NegativeOne Shareholder 4 Positive PositiveAge1 4 Positive Positive PositiveAge4 4 NegativeAge5 4 Negative Negative NegativeReturn on total assets 1 NegativeProfit margin 1 PositiveEBIT 1 NegativeCash flow/Operating revenue 1 NegativeROE 1 NegativeROCE 1 PositiveNet assets turnover 2 Positive PositiveInterest cover 2 Negative NegativeCollection period 2 NegativeCredit period 2 Negative NegativeCurrent ratio 3 NegativeShareholders liquidity ratio 3 NegativeSolvency ratio 3 Negative NegativeGearing 3 Positive Negative Negative

a: The numbers from 1 to 4 refer to the Profitability ratios, Operational ratios, Structure ratios andfirm-specific variables, respectively.

ones. Moreover, the young firms have a higher probability of leaving the mar-ket, compared to the older ones. Then, other important characteristics thatdetermine an increase of the hazard rate are the legal form and the numberof shareholders. Furthermore, it is important to notice that the profitabilityratios are not selected as potential predictors in single-risk, as shown before.The results confirm most of the main theoretical hypothesis set up in thedefault risk models and are mainly in line with those found in the empiricalliterature (Rommer, 2005; Belovary et al., 2007; Esteve-Perez et al., 2010).

4.2. Predictive performance

After selecting the most relevant variables for the competing events andthe single risk, we evaluate the predictive performance of the developed mod-els by means of some accuracy measures. Firstly, we compute the type I error,i.e. a failing firm is misclassified as a non-failing firm, and the type II error,i.e. a non-failing firm is wrongly assigned to the failing group. Then, as total

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Table 4: Hazard Ratios for the competing risks and the single risk model, for 1 year ahead.

Variables Area Bankruptcy Inactive Liquidation Single-Risk

Limited Company 4 2.0158 3.5913 2.0340South Italy 4 0.5328Micro Firms 4 71.8679 2.8020Small Firms 4 7.0732Medium Firms 4 0.1030 0.2193 0.1421Large Firms 4 0.2677One Shareholder 4 2.2712 1.5049Age1 4 1.6327 1.4888 1.4769Age4 4 0.3312Age5 4 0.4576 0.3862 0.5702Return on total assets 1 0.8643Profit margin 1 1.0795EBIT 1 0.8752Cash flow/Operating revenue 1 0.7466ROE 1 0.9164ROCE 1 1.1457Net assets turnover 2 1.2245 1.1535Interest cover 2 0.8187 0.8942Collection period 2 0.8036Credit period 2 0.8632 0.9475Current ratio 3 0.4602Shareholders liquidity ratio 3 0.8986Solvency ratio 3 0.7292 0.8871Gearing 3 1.2187 0.9013 0.8994

misclassification error, we consider the Miss-Classification errors (type I andII), the Area under the ROC curve (AUC) and the Accuracy Ratio (AR)(Engelmann et al., 2003). These measures are displayed in Tables 5 and 6for in-sample and out-of-sample sets with respect to the two time-windows(1-year ahead and 2-years ahead). Looking at the in-sample set, used fortesting the classification ability of the models, it can be noted that the cor-rect classification rate is slightly higher for bankruptcy and liquidation thanthe single-risk and it does not increase at approaching the year of exit, whilethe inactive state’s rate is lower than the one of both the other two statesand pooled model. Moreover, the AUC, which considers the impact of theI and II type errors, has a very discriminative power for bankruptcy andliquidation, compared to the single-risk framework, and its power increasesas the failure time is approaching.

For evaluating the predictive power of the models, we also compute theabove-mentioned measures on the out-of-sample set. Looking at the resultsdisplayed in Table 6, we notice that even though the correct classification

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rate is higher for the single-risk model than for the other three states, thecompeting risks model has a better performance than the single-risk frame-work in terms of AUC. Therefore, we can conclude that the competing-risksmodel produce an improvement for predicting the failure of firm.

Table 5: Accuracy measures for in-sample.

Bankruptcy Inactive Liquidation Single-Risk

2004-2008

MissClassification 0.38683 0.42363 0.39823 0.39864Error II 0.39492 0.42881 0.40173 0.41319Error I 0.02484 0.16552 0.09524 0.13846AUC 0.91090 0.76163 0.84261 0.80605AR 0.82180 0.52326 0.68522 0.61211

2004-2007

MissClassification 0.33213 0.40703 0.37943 0.40719Error II 0.33596 0.40885 0.38130 0.41835Error I 0.14634 0.26316 0.05714 0.12821AUC 0.84980 0.74844 0.81609 0.81837AR 0.69961 0.49689 0.63217 0.63674

Table 6: Accuracy measures for out-of-sample.

Bankruptcy Inactive Liquidation Single-Risk

2009

MissClassification 0.25113 0.29624 0.21955 0.22105Error II 0.25227 0.29892 0.21782 0.22147Error I 0.00000 0.18750 0.23729 0.21795AUC 0.89930 0.79488 0.86435 0.83672AR 0.79859 0.58975 0.72870 0.67344

2008-2009

MissClassification 0.27970 0.25564 0.20000 0.21053Error II 0.27795 0.25116 0.19142 0.19761Error I 0.66667 0.43750 0.28814 0.30769AUC 0.58258 0.76714 0.83812 0.82606AR 0.16516 0.53428 0.67623 0.65212

5. Conclusions

In this study the competing risks model was estimated for investigat-ing the differences and the effects of potential predictors on the probabilityof firms’ exit the market for different reasons and it was compared to the

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single-risk model, in which all financial distress states are pooled together.A dataset of financial statements of a sample of Italian firms was analyzedand three different exit routes were considered: bankruptcy, liquidation andinactivity. The starting point was to test the significance level of the micro-economic and firm-specific variables on all the three states by means of thelog-rank test. Then, the variables influencing the exit route were selected bythe stepwise procedure. After that, we analyzed the sign and the influenceof the estimated coefficients on each exit route and evaluated the predictiveperformance of the competing-risks model over the single-risk framework, attwo time horizons, by considering some accuracy measures.

The results discovered some differences in firm-specific variables and micro-economic factors determining firm exit with respect to the different routes.In particular, we found out that some firm-specific characteristics, such asage, legal form and size influence the probability of being liquidated, inac-tive and bankrupted, confirming the empirical results available in literature.Moreover, it can be noted the important role of the profitability ratios onthe likelihood of going bankrupt. Then, for the single-risk model the vari-ables selected are quite similar to those characterizing the inactive state andliquidation, while they are different for bankruptcy. Therefore, our resultsgave evidence in favor of distinguishing among bankruptcy, inactivity andliquidation as three different forms of exit and give ground for the use ofmultiple-state models. Further research could include the development ofmore appropriate procedure of selecting the variables in the competing risksframework.

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• We investigate the effects of some variables on different states of financial distress.

• We estimate a competing risks model on a sample of Italian firms in the period 2004-2009.

• Some differences in variables influencing firms’ exit have been found.

• The performance of the competing-risks model is higher than that of the single-risk framework.

Research Highlights