Improving bankruptcy prediction in micro-entities by using nonlinear effects and non-financial variables

144 Finance a ú ě -Czech Jou nal o Economics and Finance, 65, 2015, no. 2 JEL classi ica ion: C45, G33, G21, D81 Keywo ds: bank up cy models, mic o-en i ies, c edi isk, non- inancial in o ma ion, a i icial neu al ne wo k, logis ic eg ession Imp o ing Bank up cy P edic ion in Mic o-En i ies by Using Nonlinea E ec s and Non-Financial Va iables An onio BLANCO-OLIVER—Uni e si y o Se ille, Spain ([email protected]), co esponding au ho Ana IRIMIA-DIEGUEZ—Uni e si y o Se ille, Spain (anai [email protected]) Ma ía OLIVER-ALFONSO—Uni e si y o Se ille, Spain ([email p o ec ed]) Nicholas WILSON—Leeds Uni e si y Business School, UK ([email p o ec ed]s.ac.uk) Abs ac The use o non-pa ame ic me hodologies, he in oduc ion o non- inancial a iables, and he de elopmen o models gea ed owa ds he homogeneous cha ac e is ics o co po a e sub-popula ions ha e ecen ly expe ienced a su ge o in e es in he bank up cy li e a u e. Howe e , no esea ch on de aul p edic ion has ye ocused on mic o-en i ies (MEs), despi e such i ms’ impo ance in he global economy. This pape builds he i s bank up cy model especially designed o MEs by using a wide se o accoun s om 1999 o 2008 and applying a i icial neu al ne wo ks (ANNs). Ou indings show ha ANNs ou pe o m he adi ional logis ic eg ession (LR) models. In addi ion, we also epo ha , hanks o he in oduc ion o non- inancial p edic o s ela ed o age, he delay in iling accoun s, legal ac ion by c edi o s o eco e unpaid deb s, and he owne ship ea u es o he company, he imp o emen wi h espec o he use o solely inancial in o ma ion is 3.6%, which is e en highe han he imp o emen ha in ol es he use o he bes ANN (2.6%). 1. In oduc ion In he wake o he inancial c isis i is clea ha lende isk models and a ing sys ems ailed o adequa ely p esen he isks in he co po a e sec o . Fo his eason, bo h academics and p ac i ione s a e opening new lines o esea ch ha s i e o imp o e he pe o mance o exis ing bank up cy models. One o he mos ui ul lines o esea ch is he de elopmen o bank up cy models speci ically designed o each company ea u e, such as size (e.g. Al man and Saba o, 2007), indus y (e.g. Cha a and Ja ow, 2004) and age (e.g. Wilson and Al anla , 2014). Along hese lines, Tascon and Cas ano (2012) sugges ha he mo e homogeneous he cha ac e is ics o he companies used o he cons uc ion o a p e- dic ion model a e, he be e hei p edic i e capaci y will be. In he same line, In e nal Ra ings Based (IRB) sys ems, unde Basel ecommenda ions, also sugges o he lende o build isk models gea ed owa ds he speci ic cha ac e is ics o co - po a e sub-popula ions (e.g. la ge co po a ions, p i a e companies, lis ed companies, indus y-speci ic models), uned o changes in he mac o en i onmen and, o cou se, ailo ed o he a ailable da a. Based on his amewo k, his pape p oposes a bank up cy model speci ically designed o a new, ne e -be o e-s udied and la gely ele an company segmen : mic o-en i ies (MEs). Mic o-en i ies ha e ecen ly been de ined by he Compe i i eness Council o he Eu opean Union as hose companies wi h an annual u no e o less Finance a ú ě -Czech Jou nal o Economics and Finance, 65, 2015, no. 2 145 han EUR 700,000, o al asse s o less han EUR 350,000, and a e age numbe o employees du ing he inancial yea o no mo e han en (O icial Jou nal o he Eu opean Union, 2012). Mic o-en i ies (and all small businesses in gene al) ha e g ea quan i a i e impo ance since hey ep esen he as majo i y o all i ms in de eloped economies and hey cons i u e a segmen o i ms wi h homogenous cha ac e is ics and p oblems. The mos ele an in insic cha ac e is ics and p oblems o MEs a e (a) hei excessi e di icul ies when a emp ing o access bank unding sou ces (Ciampi and Go dini, 2013) and (b) hei limi ed inancial in o ma ion due o he ac ha MEs ile ab idged accoun s (Be ge and F ame, 2007). The e o e, we examine a la ge se o mic o-en i y da a on he p esump ion ha exis ing pa ame ic bank up cy models de eloped o small and medium-sized en e p ises (SMEs) migh no explain mic o-en i y de aul s wi h he same s a is ical e ec i eness o e iciency as models es ima ed using da a d awn s ic ly om he mic o-en i y popula ion. To build his speci ic de aul p edic ion model o MEs, we also inco po a e wo o he no el ends in his ield by (a) in oducing non- inancial and mac o- economic in o ma ion as p edic o a iables (e.g. G une e al., 2005; Al man e al., 2010; Moon and Sohn, 2010), and (b) implemen ing non-pa ame ic s a is ical echniques (mul ilaye pe cep on neu al ne wo ks) due o hei nonlinea and non- pa ame ic adap i e-lea ning p ope ies (e.g. Angelini e al., 2008). In gene al, he s ic assump ions (linea i y, no mali y and independence among p edic o a i- ables) o he pa ame ic s a is ical echniques (e.g. logis ic eg ession and dis- c iminan analysis), oge he wi h he p e-exis ing unc ional o m ela ing esponse a iables o p edic o a iables, limi hei applica ion in he eal wo ld. The e o e, he main goal o his pape is o make a pa simonious mul ilaye pe cep on (MLP) bank up cy model speci ically designed o a sub-sample o bank- unded mic o-en i ies by employing inancial and non- inancial a iables, and o compa e i s accu acy pe o mance wi h ha ob ained o a gene al bank up cy model de eloped o all SMEs (model o Al man, 2010 1 ). Mo eo e , his s udy also s i es o achie e wo sub-goals. Fi s , he MLP pe o mance is benchma ked agains adi- ional logis ic eg ession 2 (LR) analysis in he de aul p edic ion models made he e. To compa e bo h s a is ical echniques, a hyb id MLP-based model is buil , in o- ducing only hose p edic o s conside ed signi ican in he LR analysis. Second, we es whe he he combined use o inancial and non- inancial a iables in es ima ed bank up cy models leads o a highe pe cen age o co ec ly classi ied mic o-en i ies. The la ge size o he sample (almos 40,000 se s o accoun s o MEs) is an impo an s eng h o he eliabili y o ou indings. Mo eo e , he use o e y ew inancial a ios (only i e) cons i u es a no ewo hy imp o emen o he applicabili y and adap a ion o ou esul ing ailu e models o he in insic cha ac e is ics o small busi- nesses (wi h limi ed inancial in o ma ion acco ding o Be ge and F ame, 2007). 3 1 The model o Al man (2010) is one o he mos ele an bank up cy models made o da e o small and medium-sized en e p ises in which bo h inancial and non- inancial a iables a e conside ed. 2 The main eason o con inuing o use logis ic eg ession o e o he pa ame ic s a is ical me hods o es ima ion is ha i p o ides a sui able balance o accu acy, e iciency and in e p e abili y o he esul s (C one and Finlay, 2012). 3 Due o he la ge da ase used he e, bo h in he numbe o yea s ( om 1999 o 2008) and in he numbe o en e p ises (almos 40,000 se s o accoun s o small i ms), we conside ha he esul s o his pape a e ele an and use ul o any de eloped economy in which mic o- en i ies o en ep esen a la ge pe cen age o he o al numbe o i ms. 146 Finance a ú ě -Czech Jou nal o Economics and Finance, 65, 2015, no. 2 Thus, he con ibu ion o his pape is o demons a e ha he de elopmen o bank up cy models buil using a sample o mic o-en i ies p o ide be e esul s han hose models buil gene ically o he o e all company popula ion (SMEs). Mo e- o e , i is shown ha an MLP ou pe o ms classic LR in he de ec ion o company ailu e, and ha he non- inancial and mac oeconomic a iables g ea ly imp o e he accu acy pe o mance o he p oposed bank up cy models. The emainde o ou pape is o ganized as ollows: Sec ion 2 con ains a b ie o e iew o he li e a u e on ailu e p edic ion. Sec ion 3 p o ides de ails o he da a- se and a iables used. Sec ion 4 con ains a desc ip ion o he applied MLP me hod- ology. In Sec ion 5, we show and discuss he esul s o he es ima ed bank up cy models. Finally, Sec ion 6 p o ides he conclusions and sugges s u u e lines o esea ch. 2. Li e a u e Re iew The de aul p edic ion li e a u e o co po a es is well known and builds on Al man’s 1968 mul iple disc iminan analysis (MDA), hough he i s bank up cy model was de eloped by Bea e (1966). The la es con ibu ions in his ield sugges he de elopmen o bank up cy models speci ically designed o each company cha ac- e is ic such as size (e.g. Al man and Saba o, 2007), indus y (e.g. Cha a and Ja ow, 2004) and age (e.g. Wilson and Al anla , 2014). Disc imina ing by using he ac o company-size ac o , Al man and Saba o (2007) de eloped one o he mos ele an models speci ically made o SMEs. Thei s udy compa ed he adi ional Z-sco e model wi h wo new models ha conside o he inancial a iables and use adi ional logis ic eg ession. On a panel o da a o o e 2,000 US SMEs in he pe iod 1994– –2002, hese au ho s ound ha he new models ou pe o m he adi ional Z-sco e model by almos 30% in e ms o p edic ion powe . Based on he abo e-men ioned esea ch, Al man e al. (2010) explo e he e ec o he in oduc ion o non- inancial in o ma ion as p edic o a iables in o he models de eloped by Al man and Saba o (2007). Employing a la ge sample (5.8 million) o se s o accoun s o unlis ed i ms om he UK in he pe iod 2000–2007, hey ound ha non- inancial in o ma ion makes a la ge con ibu ion owa ds inc easing he de aul p edic ion powe o isk models. Ne e heless, he i s s udy o model he ailu e o small i ms was ca ied ou by Edmis e (1972). His s udy examined a sample o 42 small en e p ises o e he pe iod 1954–1969 and conside ed 19 inancial a ios. Employing mul i a ia e disc iminan analysis, his s udy ob ained an R-squa ed coe icien o 74% by using only he nine ele an inancial a ios. Keasey and Wa son (1987) also de eloped a de aul p edic ion model o B i ish small i ms by employing LR. In his case, a sample wi h 146 small i ms was used, o which 50% we e ailed companies, in he pe iod 1970–1983. Wi h espec o he conside a ion o non- inancial in o ma ion as p edic o a iables, p e ious li e a u e highligh ed he u ili y o hei in oduc ion as inde- penden a iables (e.g. Peel e al., 1986; G une e al., 2005; Al man e al., 2010) as a way o adding alue o he pe o mance o he bank up cy models. This is he case especially o small companies ha a e only equi ed o ile limi ed inancial in o - ma ion in he UK (i.e. ab idged accoun s). G une e al. (2005) c ea e se e al bank- up cy models using bo h inancial and non- inancial a iables (age and ype o business, sec o , e c.). They conclude ha he combina ion o inancial and non- Finance a ú ě -Czech Jou nal o Economics and Finance, 65, 2015, no. 2 147 inancial a iables imp o es he accu acy pe o mance o he de eloped models. Peel e al. (1986) and Whi ed and Zimme (1984) show, using a sample o SMEs om he UK, ha he iming o he submission o annual accoun s is an indica o o inancial ailu e. O he s udies also sugges ha un a o able audi epo s (Peel and Peel, 1989) and he exis ence o paymen p oblems (Wilson and Al anla , 2014) a e ele an a iables o p edic ing he ailu e o a i m. Simila indings a e ound when c edi -sco ing models a e buil in he mic o inance indus y (e.g. Rayo e al., 2010; Blanco e al., 2013). Howe e , whe eas he impo ance o inancial ac o s is widely accep ed because hei impac is measu able, he ele ance o non- inancial a iables is mainly conside ed in a holis ic manne . Addi ionally, in ecen yea s he mos widely used pa ame ic echniques (MDA and LR) ha e been eplaced wi h a ious non-pa ame ic me hods allied o he ields o a i icial in elligence and s a is ical lea ning algo i hms (such as neu al ne wo ks, suppo ec o machines, and classi ica ion and eg ession ees) in an e o o inc ease he p edic ion capaci y o ailu e models. Due o hei nonlinea and non-pa ame ic adap i e-lea ning p ope ies, hese non-pa ame ic models o en ou pe o m he classic me hods (Angelini e al., 2008). In gene al, he s ic assump ions (linea i y, no mali y and independence among p edic o a iables) o he pa ame ic s a is ical echniques (e.g. LR and MDA), oge he wi h he p e-exis ing unc ional o m ela ing esponse a iables o p edic o a iables, limi hei applica ion in he eal wo ld. Ne es and Viei a (2006) based hei s udy on F ench indus ial i ms o e he pe iod 1998– –2000 and ind ha neu al ne wo ks (hyb id model encompassing Lea ning Vec o Quan iza ion and Mul ilaye Pe cep on) clea ly ou pe o m LDA. By using a da ase om he Slo enian banking sec o , Jag ic e al. (2011) also show he supe io i y o he Lea ning Vec o Quan iza ion neu al ne wo k o e classic logis ic eg ession. Ciampi and Go dini (2013) use a da ase o 7,000 I alian small en e p ises o demon- s a e ha he neu al ne wo k ob ains highe accu acy pe o mance han classic logis ic eg ession and disc iminan analysis. Thei esul s also sugges ha he di i- sion o he sample o i ms in e ms o business sec o , size and geog aphical a ea inc eases he powe o hei ailu e models. The indings ob ained by Gepp e al. (2009) and Ince and Ak an (2009) also sugges he highe p edic ion accu acy o non- pa ame ic me hods in compa ison wi h linea s a is ical echniques. Fle che and Goss (1993) compa e an MLP-based model o he classic LR app oach o he p edic- ion o company bank up cy. Based on a small da abase o 36 i ms (50% ailed i ms) and employing only h ee inancial a ios (cu en a io, quick a io and income a io), hese au ho s show ha he MLP ou pe o ms he pa ame ic LR model. Coa s and Fan (1993) compa e he MLP o LDA using a sample ob ained om Compus a du ing he pe iod 1970–1989. They also sugges ha he MLP is mo e accu a e han LDA. Lache e al. (1995) u ilize he same sample as Coa s and Fan (1993) and compa e he capaci y o p edic inancial dis ess be ween Al man’s Z-sco e algo i hm and a neu al ne wo k wi h cascade-co ela ion a chi ec u e. They demons a e ha his non-pa ame ic model p edic s he inancial heal h o a i m mo e accu a ely han he adi ional Z-sco e me hod. Zhang e al. (1998) compa e he accu acy o ANN agains ha o LR o p edic co po a e bank up cy. The inpu s o bo h models we e o med by six a ios comp ising he i e a ios used by Al man (1968) and he a io o cu en asse s/cu en liabili ies. The da ase consis ed o 110 ma ched pai s o bank up and non-bank up US manu ac u ing companies o 148 Finance a ú ě -Czech Jou nal o Economics and Finance, 65, 2015, no. 2 he pe iod 1980–1991. The wo subse s we e ma ched on indus y classi ica ion and size, concluding o bo h es se s (small and la ge) ha ANN ou pe o ms LR. A iya (2001) sugges s ha , in gene al, ANN ou pe o ms s a is ical echniques in p edic ing bank up cy and consequen ly he esea ch communi y should hence o h y o imp o e he p edic i e abili y o ANN. In con as , ce ain au ho s epo di e en expe iences on he issue o he supe- io i y o ANNs o e adi ional s a is ical me hods. Bo i z and Kennedy (1995) compa e se e al ANNs agains LDA, LR and he p obi model. Thei indings sug- ges ha he pe o mance o ANN models is no supe io o ha o adi ional models. Al man e al. (1994) compa es he MLP wi h LDA o diagnose co po a e inancial dis ess o 1,000 I alian i ms. His indings s a e ha he MLP is no a clea ly dominan ma hema ical echnique compa ed o adi ional LDA. 3. Da a and Va iables 3.1 The Da ase This s udy uses a da ase p o ided by a U.K. c edi agency ha con ains 4,813,391 (98.32% non- ailed and 1.68% ailed) se s o accoun s o unlis ed SMEs in he UK o he pe iod 1999–2008. 4 In line wi h o he s udies, we de ine co po a e ailu e as en y in o liquida ion, adminis a ion o ecei e ship be ween 1999 and 2008, since wo- hi ds o businesses closed unde ci cums ances o he han hose o inancial p oblems (Headd, 2003). The accoun s analyzed o ailed companies a e he las se o accoun s iled in he yea p eceding insol ency. To ob ain a sample exclusi ely comp ising mic o-en i ies, all i ms ha ailed o sa is y he equi emen s o he de ini ions o a mic o-en i y we e elimina ed. A e selec ing all he mic o-en i ies and elimina ing missing cases, 5 2,089,140 cases e- mained. Among hese, 20,228 (0.97%) we e de aul ed cases and 2,068,912 (99.03%) we e no . Gene ally, inancial a ios a e con amina ed by some deg ee o e o and i hese i ems o da a a e no elimina ed, hen he es ablished model may be uns able. The e o e, o build a mo e accu a e model, he abno mal cases, which lie wi hin he op 1% and he bo om 1% o each inancial a io, we e also elimina ed, and 2,020,492 cases emained (0.98% o which we e de aul ed cases and 99.01% we e no ). Simila o p e ious bank up cy s udies ( o an example, see Fle che and Goss, 1993), his pape also adop s a ma ched-pai app oach. The e o e, a inal andom sampling was pe o med: 19,855 (50%) ailu e cases and 19,855 (50%) non- ailu e cases. A supe ised lea ning p oblem is o mula ed clea ly. Ou wo k conside s wo s a is ical lea ning models: logis ic eg ession (LR) and mul ilaye pe cep on (MLP). Usually, he con igu a ion o machine lea ning models equi es ca e ul selec ion o he alues o one o mo e pa ame e s, o example he size o he hidden laye in MLP models. The e o e, di e en con igu a ions mus be app op ia ely compa ed, choosing he bes se o pa ame e s. This p ocess is known as model selec ion. When he model has been de eloped in his way, i is necessa y o es ima e he p edic ion 4 The da ase used in he p esen s udy was suppl ied unde a license ag eemen and canno be made publicly a ailable. 5 In his s udy, missing cases a e hose ha ha e a leas one ins ance o missing da a o any indep enden a iable. Finance a ú ě -Czech Jou nal o Economics and Finance, 65, 2015, no. 2 149 e o (gene aliza ion e o ) o he inal model on new da a; his is known as model assessmen . Following Has ie e al. (2009), a sugges ed app oach o sol e bo h p oblems is he andom di ision o he da ase in o h ee pa s (sub-se s): a aining se , a alida ion se and a es se . The aining se is used o build he model o each pa ame e con igu a ion; he alida ion se is used o es ima e he p edic ion e o o model selec ion; and he es se is used o assessmen o he gene aliza ion e o o he inal chosen model. Consequen ly, in o de o un bo h app oaches (LR and MLP) ou inal da ase was andomly spli in o h ee sub-se s: a aining se o 60%, a alida ion se 6 o 20% and a es da ase o 20%. 7 3.2 Desc ip ion o Inpu Va iables 3.2.1 Financial In o ma ion No accep ed inancial heo y o bank up cy exis s (Pea , 2007). In spi e o he abundan li e a u e, he e is an absence o a amewo k ha clea ly explains he ela ionships be ween he inancial beha io o companies, measu ed h ough inancial a ios and non- inancial in o ma ion, and he de aul o companies. Ac oss coun ies, a a ie y o accoun ing sys ems, economic condi ions, unding s uc u es and ax codes may a ec he p edic i e powe o he same inancial a ios. Fo hese easons, he e a e a la ge numbe o possible inancial a ios iden i ied in he li e a- u e as use ul in he p edic ion o a company’s de aul . All he inancial a ios used in his s udy ha e been employed in p io esea ch, such as Al man (1968), Al man e al. (2010), Ohlson (1980), Ta le (1984) and Zmijewski (1984). Mo eo e , since he majo i y o he a iables used in his s udy we e employed by Al man e al. (2010) in hei SME model, i is possible o make a compa ison o he esul s ob ained. 8 In o al, 14 inancial a ios a e con- side ed in his pape . These a ios a e ca ego ized in o i e ca ego ies acco ding o he inancial aspec s o he business ha he a iables measu e: le e age, liquidi y, p o i abili y, ac i i y and size o he gi en i m. Table 1 desc ibes hese a ios and how hey a e calcula ed. 9 In p e ious s udies, le e age and deb se ice a ios ha e appea ed o be s ong p edic o s ela ed o bank up cy and a e a key componen o inancial isk. Mo eo e , in acco dance wi h co po a e inance heo y, hose i ms wi h highe olumes o liabili ies wi h espec o he le el o equi y will ha e subs an ial p obabili ies o expe iencing inancial p oblems. In his s udy, ou le e age a ios a e employed: capi al employed/ o al liabili ies, sho - e m liabili ies/ o al asse s, o al liabili ies/cu en asse s and ne wo h/ o al asse s. These ou le e age a iables should play an impo an ole in he p edic ion o bank up cy in mic o-en i ies due o hei impo ance in ela ion o he u u e commi men s o he i ms. 6 In he case o logis ic eg ession, he op imal cu -o poin is ob ained h ough he alida ion sub- sample. In he case o neu al ne wo ks, wi h he alida ion sub-sample we ob ain he numbe o hidden uni s minimizing he alida ion sum o he squa ed e o (SSE). 7 Since he same sample is used o aining, alida ion and es ing o bo h logis ic eg ession and neu al ne wo ks, he esul s ob ained o bo h me hodologies can be compa ed. 8 Fo an exhaus i e desc ip ion o he a iables used in his s udy, see Al man e al. (2010). 9 Tables A1 and A2 o he Appendix summa ize he desc ip i e s a is ics o all a iables o bo h he ailed and non- ailed samples. 150 Finance a ú ě -Czech Jou nal o Economics and Finance, 65, 2015, no. 2 Table 1 Financial Ra ios Va iable Abb e ia ion Accoun ing a io ca ego y Theo e ical ela ionship o bank up cy Capi al employed / To al liabili ies Cel Le e age - Sho - e m liabili ies / To al asse s S l a Le e age + To al liabili ies / Cu en asse s Tlca Le e age + Ne wo h / To al asse s Nw a Le e age - Quick asse s / Cu en asse s Qaca Liquidi y - Cash / Ne wo h Cashn Liquidi y - Cu en asse s / Cu en liabili ies Cacl Liquidi y - Cash / To al asse s Cash a Liquidi y - Re ained p o i / To al asse s Rp a P o i abili y - T ade c edi o s / T ade deb o s Tc d Ac i i y + T ade c edi o s / To al liabili ies Tc l Ac i i y + T ade deb o s / To al asse s Td a Ac i i y + Napie ian loga i hm o al asse s Ln_asse Size +/- To al asse s T_asse Size +/- Liquidi y is a common ca ego y in mos c edi decisions and is especially ele an in he case o MEs due o he simplici y o hei balance shee s. Fou a ios a e conside ed in his pape : cash/ o al asse s, cu en asse s/cu en liabili ies, quick asse s/cu en asse s and cash/ne wo h. The i s a io, Cash/ o al asse , is an im- po an a iable ela ing o de aul in he p i a e da ase (Chen e al., 2011). In ou opinion, hese liquidi y a ios should be signi ican in ou model since MEs ha e ewe op ions o access o unding. A p o i abili y a io, e ained p o i / o al asse s, was conside ed in ou analysis. This measu es he abili y o i ms o accumula e ese es ou o p o i s and i he e o e p oxies long- e m p o i abili y. This a iable is widely conside ed o be ele an in he p edic ion o bank up cy o all ypes o i ms. The ade deb o s/ o al asse s, ade c edi o s/ o al liabili ies and ade c edi o s/ / ade deb o s a ios a e signi ican o small i ms ha end o ely on ade inance bo h o pay o supplies ( ade c edi ) and o a ac cus ome s ( ade deb ). Small i ms in dis ess a e likely o accumula e unpaid ade deb s and obsole e in en o y and ha e di icul y a aining sho - e m c edi om supplie s o banks. Fu he - mo e, ade c edi comp ises a la ge pe cen age o a i m’s liabili ies, and his ac is especially ele an o mic oen e p ises. The e o e, we assume ha all hese ac i i y a ios ha e a nega i e ela ionship wi h espec o bank up cy. In acco dance wi h he gene al end in he li e a u e, he napie ian loga i hm o he o al asse s (Ln_asse ) and o al asse s (T_asse ) wi hou pe o ming any ans- o ma ion a e also conside ed in his s udy. Wi h espec o company size, many p e ious s udies ound ha la ge i ms a e less likely o encoun e c edi cons ain s hanks o he e ec o a good epu a ion, and he e o e hese s udies conclude ha a i m’s small size may lead o insol ency (Die sch and Pe ey, 2004). In con as , Al man e al. (2010) ind ha he ela ionship be ween asse size and insol ency Finance a ú ě -Czech Jou nal o Economics and Finance, 65, 2015, no. 2 151 Table 2 Non-Financial In o ma ion Va iable Abb e ia ion Ca ego y Theo e ical ela ionship o bank up cy Audi ed accoun s Audi ed No (0) + Yes (1) - Posi i e judgmen audi epo Aq_clean No (0) + Yes (1) - Nega i e judgmen audi epo Aq_no_clean No (0) - Yes (1) + Change audi o Change_audi o No (0) - Yes (1) + Numbe o legal claims Numbe _LCs + Value o legal claims Value_LCs + La e iling days La e_ iling_day + Napie ian loga i hm age Ln_age - Cha ge on asse s Cha ge_asse No (0) - Yes (1) + Family i m Family_ i m No (0) - Yes (1) + Indus y sol ency Indus y_sol ency - isk appea s o be nonlinea , since i is posi i e when he i ms ha e less han GBP 350,000 in asse s and is nega i e when hei asse s a e highe han his alue. 3.2.2 Non-Financial In o ma ion In line wi h he p io li e a u e, we also conside non- inancial in o ma ion as p edic o a iables (see Table 2). 10 Th ee ypes o dummy a iables linked o audi ed accoun s a e employed he e. Fi s , we use he Audi ed accoun s a iable, which akes a alue o 1 whe e he i m has been audi ed and 0 o he wise. Usually, he inancial in o ma ion o mic o- en i ies wi h audi ed accoun s is mo e eliable han ha o i ms which do no audi hei inancial s a emen s. Second, wo dummy a iables a e used which cap u e he in o ma ion con ained in audi epo s: Posi i e judgmen audi epo (Aq_clean) akes a alue o 1 when he audi epo is a o able, i.e. he audi o did no de ec any inancial p oblems, and Nega i e judgmen audi epo (Aq_no_clean) akes a alue o 1 whe e he audi o de ec ed inancial p oblems. Audi o s can quali y accoun s acco ding o he se e i y o hei conce ns. The ypical pa e n is: (a) he audi epo is unquali ied bu e e ed; (b) he audi epo is quali ied owing o a scope limi a- ion; (c) he audi epo is quali ied owing o mild unce ain ies/disag eemen s; (d) he audi epo has an ongoing-conce n quali ica ion; and (e) he audi epo is quali ied owing o a se e e ad e se opinion o disclaime o opinion. Thi d, we employ he Change_audi o a iable which akes a alue o 1 whe e he i m has 1 0 The non- inancial in o ma ion is limi ed o he a iables a ailable. In his case, he same a iables as in Al man e al. (2010) U.K. SME model we e used. 152 Finance a ú ě -Czech Jou nal o Economics and Finance, 65, 2015, no. 2 changed i s audi o and 0 o he wise. F equen ly, a change o audi o is linked o disc epancies o c i e ia be ween he audi o and he i m wi h espec o he con en s o he audi epo . These disc epancies o en happen when he audi o highligh s p oblems which ad e sely a ec he inancial heal h o he company. In spi e o he signi icance o hese a iables o all ypes o companies, in he ME segmen he weigh in model pe o mance is no expec ed o be high due o he sca ce numbe o audi ed mic o-en i ies. One o he i s e en s ha occu in companies in inancial dis ess is delay in paymen s o supplie s. I such a delay is p olonged in ime, sup- plie s o en b ing a legal claim o collec he money owed o hem. The e o e, he accumula ion o legal claims (LCs) agains a company is indica i e ha he gi en i m is inancially oubled, which can lead o he ailu e o he company. The e o e, wo a iables ela ed o LCs agains a company a e conside ed as p edic o s o co po- a e insol ency, he numbe o LCs (Numbe _LCs) agains a company and he alue, in mone a y uni s, o hese LCs (Value_LCs). Bo h a iables a e ela ed o he las wel e mon hs. A p io i, we conside ha bo h a iables should ca y majo signi i- cance in he de ec ion o a company’s bank up cy (independen o i s size) since, on he majo i y o occasions, p io o decla ing hemsel es bank up , companies end o p esen de aul s in some o hei paymen s. In he UK, i ms ha e en mon hs o submi hei annual accoun s. La e submission o annual accoun s is a iola ion o business egula ions and is usually due o easons ha ad e sely a ec he company's inancial heal h. La e submission is likely o be an indica o o inancial dis ess, and he e o e we in oduce he a iable La e_ iling_day, which s a es he numbe o days ha he i m delays submi ing i s annual accoun s. The nepe ian loga i hm o he age o he i m in days (Ln_age) a he da e o he la es accoun s is used in o de o de e mine he e ec o age on he de aul o i ms. Acco ding o Hudson (1987), young i ms ha e highe de aul p obabili ies han old en e p ises. The e o e, we suppose ha you h and bank up cy a e posi i ely ela ed. In he case o bo owe s wi h highe c edi isk, lende s o en equi e inancing o be secu ed by cha ges on asse s o he company. The e o e, bo owe s who ha e cha ges on asse s will ha e a highe p obabili y o bank up cy han hose ha do no . The Cha ge on asse s a iable is a dummy a iable which akes a alue o 1 when i ms ha e gua an ees based on asse s and 0 o he wise. Family i ms o en ha e ce ain p oblems linked o hei own idiosync asies, such as amily successions, non-p o essional CEOs and low p oduc i i y. Mo en e al. (2007) ind ha ela i ely less p o i able i ms ha a e managed by amily CEOs a e mo e likely o ile o bank up cy o o be liquida ed han a e compa able i ms ha a e headed by non- amily CEOs. The e o e, we posi ha amily companies un a g ea e likelihood o de aul han non- amily i ms. We use he Family_ i m a iable in o de o include his cha ac e is ic. This a iable akes a alue o 1 when he company is a amily i m and 0 o he wise. Mic o-en i ies a e, in he majo i y o cases, i ms o a amily cha ac e and hence, in acco dance wi h he easoning ou lined abo e, he a iable Family_ i m should ca y g ea e weigh in o de o de ec company bank up cy. Finally, i is impo an o moni o he mac oeconomic condi ions aced by companies since he de aul o i ms has a close ela ionship wi h he mac oeconomic si ua ion (Moon and Sohn, 2010). To his end, he Indus y_sol ency a iable is inco po a ed which measu es he inancial heal h o he sec o wi hin which he i m ope a es; his is he in e se o he p obabili y o bank up cy o he sec o . The e o e, Finance a ú ě -Czech Jou nal o Economics and Finance, 65, 2015, no. 2 159 Figu e 1 Sensi i i y Analysis o Misclassi ica ion Cos s sugges ha , in gene al, he MLPs ained wi h second-o de algo i hms ha e highe AUC aluesand lowe misclassi ica ion cos s, and can be i ed in lowe ime han hose which use he adi ional g adien descen algo i hm. The model ha yields he highes AUC alues uses he Le enbe g-Ma qua d aining algo i hm (MLP 8), which has eigh een hidden nodes and whose sum squa ed e o (SSE) is 0.165. Howe e , conside ing he misclassi ica ion cos s, he bes model is ha which employs he esilien back-p opaga ion as i s lea ning ule (MLP 10). Finally, as p e iously men ioned, he misclassi ica ion cos s p esen ed in Table 7 we e calcula ed by conside ing a ela i e a io o 1:5 (Wes , 2000). Howe e , in he UK lending ma ke s, he ela i e a io o misclassi ica ion cos s is dependen on he di e ence be ween e ail in e es a es and LIBOR a es. This dependency is due o he ac ha Type I e o s would lead he bank o miss ou on hese lending p o i s ( e ail in e es a es minus LIBOR a es). De aul isk has d as ically changed in he pas decade due, o ins ance, o he huge economic down u n and a massi e numbe o business ailu es. In e es a es ha e changed as ly o e he pas 13 yea s and a e now a ac ion o wha hey we e a decade ago. 14 The LIBOR a es a e now abou 0.2% compa ed o abou 6% in 2000 (a he ime Wes ′s pape was published). The ela i e a io o misclassi ica ion cos s is he e o e likely o be a highe oday. To add ess his change, a sensi i i y analysis is conduc ed o a a ie y o a ios (1:1 o 1:100) in o de o illus a e he pe - o mance o each model unde hese assump ions and h eshold a which each model becomes op imal o , con e sely, sub-op imal (see Figu e 1). This will allow UK banks o make an es ima e o hei own co po a e ela i e a io o misclassi ica ion cos s, and consul his sensi i i y analysis o de e mine which model will pe o m op imally unde hei cos s uc u e. As can be obse ed in Figu e 1, he model wi h he lowes misclassi ica ion cos s is MLP 10. The esul s o misclassi ica ion cos s in Figu e 1 a e in consonance wi h he accu acy capaci y o each de aul p edic ion model. The e o e, lende s should use hose bank up cy models which ha e highe pe o mance in e ms o 1 4 See h p://www. edp ime a e.com/libo /libo _ a es_his o y.h m 160 Finance a ú ě -Czech Jou nal o Economics and Finance, 65, 2015, no. 2 Table 8 Bank up cy Models o Mic o-En i ies e sus SME 2 wi h he U.K. Weigh s Model T aining Sample Valida ion Sample Models Va iables and s a is ical echniques AUC model mic o- en i ies AUC model Al man e al . (2010) AUC model mic o- en i ies AUC model Al man e al. (2010) Model 1 (LR 1) Financial a iables / / Logis ic eg ession 0.736 0.740 0.770 0.710 Model 2 (LR 2) Financial and non- inancial a iables / / Logis ic eg ession 0.809 0.800 0.806 0.750 Model 3 (MLP 10) Financial and non- inancial a iables / / Mul ilaye pe cep on 0.835 - 0.827 - he AUC es and misclassi ica ion cos s, independen ly o hei cos s associa ed wi h Type I-II e o s. The e o e, in line wi h o he au ho s (e.g. Angelini e al., 2008; Jag ic e al., 2011; Ne es and Viei a, 2006; Wilson and Sha da, 1994) we sugges ha , in gene al, no only does he MLP ha e highe AUC alues, bu i has lowe misclassi ica ion cos s han he adi ional LR app oach. These empi ical esul s con i m he heo e i- cal supe io i y (p incipally, nonlinea and non-pa ame ic adap i e-lea ning p ope ies) in he de elopmen o bank up cy models using he MLP o e he pa ame ic LR model. The e o e, we sugges ha p ac i ione s should explo e he use o MLP-based models ins ead o he adi ional pa ame ic models since e en a small imp o emen in he p edic i e accu acy o he MLP de aul p edic ion model is c i ical. In he case o banks, a 1% imp o emen in accu acy can educe losses in a la ge loan po olio and sa e millions o dolla s (Wes , 2000). Fo o he use s (in es o s, manage s and audi o s), he imp o emen an icipa es bank up cy in a imely way, acili a ing p o- ac i e managemen o loan po olios o mi iga e losses. In his sense, he esul s sugges ha he di e ence be ween he bes MLP in e ms o misclassi ica ion cos s (MLP 12) and LR (LR 2) is o e 7.7% (see Table 7). This means ha implemen a ion o he neu al ne wo k app oach educes bank losses signi ican ly (7.73% exac ly) and he e o e cons i u es a way o ob ain a compe i i e ad an age o hose banks which implemen his s a is ical echnique. Finally, we examine whe he he isk models designed speci ically o sub- popula ion i ms wi h la ge homogeneous cha ac e is ics (mic o-en i ies) ob ain highe p edic abili y han hose models buil gene ically o he o e all company popula ion (SMEs). To his end, he model called SME 2 wi h he UK weigh s o mu- la ed by Al man e al. (2010) was chosen as he benchma k. The choice o his model is due o he ac ha i is one o he ew and mos ele an s udies in ol ing he smalles SMEs. As can be obse ed in Table 8, he accu acy capaci y ob ained by he bes bank up cy model de eloped he e speci ically o mic o-en i ies is highe han ha a ained by he model buil o SMEs. Speci ically, he imp o emen ob ained by he selec ion o a mo e homogeneous company popula ion is 5.60% in e ms o he AUC o he models ha conside only inancial a ios (LR 1) and 6% o he models which in oduce bo h inancial and non- inancial a iables (LR 2). 15 Finance a ú ě -Czech Jou nal o Economics and Finance, 65, 2015, no. 2 161 Mo eo e , when he mul ilaye pe cep on echnique is applied, he accu acy pe - o mance o he esul ing model is s ill be e , by 82.70% (see model MLP 10 o Table 8). The e o e, based on his empi ical e idence, we sugges making isk models gea ed o he speci ic cha ac e is ic o he co po a e sub-popula ion, mic o-en i ies in ou case. Based on he abo e indings, we a i m ha despi e he signi ican imp o e- men p oduced by he implemen a ion o MLP-based models ins ead o use o he LR app oach, (2.1% in e ms o he AUC), he imp o emen esul ing om he in o- duc ion o non- inancial p edic o s is e en highe (3.6% in e ms o he AUC). This inding ein o ces he idea ha , in o de o inc ease he p edic i e powe o bank- up cy models, no only is he choice o s a is ical echnique o majo impo ance, bu so a e conside a ion o non- inancial a iables and selec ion o i ms wi h e y homogeneous cha ac e is ics (mic o-en i ies in ou case). In he la e case, i.e. conside a ion o mic o-en i ies, he imp o emen is app oxima ely 6% in e ms o he AUC. I is he me hod ha p o ides he mos ele an imp o emen among he h ee lines o esea ch conduc ed he e (in oduc ion o non- inancial a iables, implemen a ion o he non-pa ame ic s a is ical echnique and selec ion o i ms wi h homogeneous cha ac e is ics). 6. Concluding Rema ks and Fu u e Lines o Resea ch In his pape we in es iga e he use ulness o pa simonious bank up cy models de eloped o mic o-en i ies based on mul ilaye pe cep on neu al ne wo ks and using bo h inancial and non- inancial a iables. Ou indings show h ee ele an conclusions. Fi s , he pa simonious bank- up cy models de eloped speci ically o mic o-en i ies ob ain g ea e p edic i e powe han he mos signi ican bank up cy model buil gene ically o he o e all popula ion o SMEs ( he model called SME 2 wi h he UK weigh s c ea ed by Al man e al., 2010). Ou esul s show an imp o emen o app oxima ely 6% in e ms o he AUC when bank up cy models a e de eloped speci ically o mic o-en i ies. I is he e o e wo h sepa a ing e y small businesses om o he companies when de eloping bank up cy models since he imp o emen in he p edic i e capabili y jus i ies he po en ial di icul ies in hei implemen a ion. This imp o emen in pe o mance is pa icula ly ele an in oday’s clima e o economic c isis, which has highligh ed he ine iciency o cu en c edi isk models in a business segmen (mic o-en i ies sec o ) wi h high a es o bank up cy, excessi e di icul y in accessing ex e nal unding; and signi ican impac on he GDP o he majo i y o de eloped economies. Mo eo e , he use o e y ew inancial a ios (only i e) cons i u es a no ewo hy imp o emen o he applicabili y and adap a ion o ou esul ing ailu e models o he in insic cha ac e is ics o small businesses (wi h limi ed inan- cial in o ma ion). Second, he mul ilaye pe cep on bank up cy models can wo k o p edic he bank up cy o mic o-en i ies, ob aining highe accu acy pe o mance (in e m o he AUC, es accu acy and Type I-II e o s) and lowe misclassi ica ion cos s han he adi ional LR app oach. The e o e, bank up cy p edic ion models, especially hose de eloped unde he ANN pa adigm, cons i u e ele an ools ha enable all 15 Bo h esul s a e e e ed o he alida ion sub-sample. 162 Finance a ú ě -Czech Jou nal o Economics and Finance, 65, 2015, no. 2 he use s o make be e decisions by educing he unce ain y associa ed wi h decision-making and, inally, by educing he cos s associa ed wi h bad business decisions. In he case o lende s, hese indings ha e a - eaching consequences due o he added 7.7% cos sa ings ha implemen a ion o he bes MLP model (MLP 12) yields he e in compa ison wi h he bes LR model (LR 2). The MLP app oach p o ides sa ings o millions o dolla s and is he e o e a means o ob aining a compe i i e ad an age o e hose banks which implemen adi ional LR. Thi d, we ind ha he in oduc ion o non- inancial a iables as p edic o s o business ailu e signi ican ly imp o es he accu acy pe o mance o models buil speci ically o mic o-en i ies. Thanks o he in oduc ion o non- inancial p edic o s, he imp o emen , in e ms o he AUC, is 3.6%, which is e en highe han he imp o e- men ha in ol es he use o he bes MLP (2.6%). The e o e, bo h he implemen a- ion o he neu al ne wo k app oach and he in oduc ion o non- inancial a iables as p edic o s a e wo impo an means o imp o ing he accu acy pe o mance o bank up cy p edic ion models o mic o-en i ies. Thus, all s akeholde s o mic o-en i ies, pa icula ly banks, c edi o s and sha e- holde s, should ca e ully conside he esul s o his esea ch o he de ec ion o inancial dis ess in i ms o his size. In his sense, in a es ic i e en i onmen such as he one p esen ed he e, whe e iable in es men p ojec s planned by small i ms canno be ca ied ou by weak and cau ious inancial in e media ies, ou bank up cy model p o ides an inno a i e pa adigm no only o mi iga ion o he isk o a de aul occu ing in he mic o-en i y segmen , bu also o imp o emen in such i ms’ access o unding esou ces (mainly in he o m o equi y, bank deb and comme cial deb ). On he o he hand, he models de eloped he e can be use ul o manage s o mic o-en i ies in analyzing in e nal p oblems and moni o ing he pe o mance o hei companies by an icipa ing insol ency si ua ions and aking s eps o esol e hem. Due o he e y la ge da ase used he e, bo h in he numbe o yea s ( om 1999 o 2008) and in he numbe o en e p ises (almos 40,000 se s o accoun s o small i ms), he con ibu ions o his pape a e ele an and use ul o any small en e p ise in any de eloped economy in he wo ld. Howe e , his s udy can be u he imp o ed in u u e esea ch by using da ase s o mic o-en i ies om o he coun ies and compa ing hei esul s wi h hose ob ained he e. Ye ano he way o imp o e his wo k could be by collec ing non- inancial in o ma ion o a mo e ele- an na u e o mic o-en i ies, such as co po a e go e nance a iables, managemen skills and expe ience o company di ec o s, ea u es o audi o s (such as he le el o indus y specializa ion), and he inno a ion capaci y o i ms, in o de o inc ease he de aul p edic ion accu acy o ou model. Finally, he s a is ical echniques used in his s udy can be compa ed wi h o he non-pa ame ic me hods such as suppo ec o machines, classi ica ion and eg ession ees, and andom o es . Finance a ú ě -Czech Jou nal o Economics and Finance, 65, 2015, no. 2 163 APPENDIX Table A1 Desc ip i e S a is ics o he Quan i a i e P edic o Va iables Va iable Failed Non-Failed Mean S d. Des . Mean S d. Des . Capi al employed / To al liabili ies 0.45 1.32 1.77 4.95 Sho - e m liabili ies / To al asse s 0.12 0.23 0.06 0.17 To al liabili ies / Cu en asse s 3.24 5.55 2.45 5.40 Ne wo h / To al asse s -0.70 1.81 0.41 1.19 Quick asse s / Cu en asse s 0.81 0.29 0.88 0.26 Cash / Ne wo h 4.55 5.66 2.91 4.59 Cu en asse s / Cu en liabili ies 1.17 2.56 2.35 4.31 Cash / To al asse s 0.15 0.22 0.37 0.34 Re ained p o i / To al asse s -0.56 1.43 0.01 0.03 T ade c edi o s / T ade deb o s 6.67 17.25 12.66 22.84 T ade c edi o s / To al liabili ies 0.84 0.27 0.85 0.30 T ade deb o s / To al asse s 0.43 0.31 0.31 0.31 Ln o al asse s 10.36 0.55 10.08 0.61 To al asse s 36,312.26 16,952.53 28,585.85 16,637.25 Numbe o legal claims 0.31 0.85 0.03 0.09 Value o legal claims 1,519.40 4,756.56 64.76 214.70 La e iling days 32.59 82.89 18.92 69.01 Ln age 7.48 0.68 7.51 1.08 Indus y sol ency -0.07 0.24 0.18 0.52 164 Finance a ú ě -Czech Jou nal o Economics and Finance, 65, 2015, no. 2 Table A2 Desc ip i e S a is ics o he Quali a i e P edic o Va iables Va iable Ca ego y S a us F equency (%) Cha ge on asse No (0) Failed 46.75 Non-Failed 49.40 Yes (1) Failed 3.25 Non-Failed 0.60 Family i m No (0) Failed 28.30 Non-Failed 25.56 Yes (1) Failed 21.70 Non-Failed 24.44 Audi ed accoun s No (0) Failed 47.26 Non-Failed 48.14 Yes (1) Failed 2.74 Non-Failed 1.86 Posi i e judgmen audi epo No (0) Failed 48.10 Non-Failed 48.32 Yes (1) Failed 1.90 Non-Failed 1.68 Nega i e judgmen audi epo No (0) Failed 49.68 Non-Failed 49.89 Yes (1) Failed 0.32 Non-Failed 0.11 Change audi o No (0) Failed 47.40 Non-Failed 47.63 Yes (1) Failed 2.60 Non-Failed 2.37 REFERENCES Angelini E, Tollo G di, Roli A (2008): A neu al ne wo k app oach o c edi isk e alua ion. 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