The Differentiation of Firm Survival Models in the Poviats of the Zachodniopomorskie Voivodeship

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1 Fola Oeconomca Aca Unversas Lodzenss ISSN e-issn (330) 2017 DOI: hp://dx.do.org/ / Iwona Markowcz Unversy of Szczecn, Faculy of Economcs and Managemen, Insue of Economercs and Sascs, The Dfferenaon of Frm Survval Models n he Povas of he Zachodnopomorske Vovodeshp Absrac: The am of he sudy was o consruc models of frms survval duraon for ndvdual povas n he Zachodnopomorske Vovodeshp. The frs sage was he calculaon of he Kaplan Meer esmaor and he use of a es for he verfcaon of smlares n he survval funcon for he analysed povas. As a resul, groups of povas were creaed. The nex sage of research was he consrucon of duraon ables of he suded frms and an analyss of he nensy funcon of frms lqudaon for he povas. The percenage of frms lqudaed afer wo years of acvy n dfferen povas (sage III) was presened. An analyss of correlaon beween he percenage of frms lqudaed n he analysed perod and he number of enes regsered per 10 housand of populaon n he povas (sage IV) was also conduced. Ths sudy used daa from he regsry of REGON relaed o companes esablshed n he Zachodnopomorske Vovodeshp n These enes were observed ll he end of The sudy resuls reveal he dfferenaon of frm survval models n he povas of he Zachodnopomorske Vovodeshp. Fve groups of povas were dsngushed and characersed. Keywords: models of frms duraon, nensy funcon of frms lqudaon, povas of he Zachodnopomorske Vovodeshp JEL: C10, C14, C41 [7]

2 8 Iwona Markowcz 1. Inroducon For he purpose of he survval analyss, paramerc, sem paramerc, and non paramerc models are used. The consrucon of paramerc models requres he adopon of a heorecal dsrbuon of he examned varable (Gazńska, 2003; Frączak e al., 2005), whch s dffcul n he case of sudes on he duraon of frms (Markowcz, 2012; Markowcz, 2014). Therefore, n hs sudy, connuous me non paramerc models were used: he Kaplan Meer esmaor, he duraon able (nensy lqudaon), and he Gehan es. Those mehods were employed o model he survval me and fnd dfferences n he survval of frms n he povas of he Zachodnopomorske Vovodeshp. The purpose of he presen sudy was o buld company survval models for ndvdual povas n Zachodnopomorske. In he frs sage, he Kaplan Meer esmaor was calculaed and a es o verfy he smlary of he survval funcon for he povas was conduced. The povas were classfed no groups. Nex, ables of company survval were bul and he company lqudaon nensy was analysed n ndvdual groups of povas. In he subsequen sage, he percenage of companes lqudaed n he frs and he second year of operaon was deermned n ndvdual povas and groups (sage III). Addonally, an analyss was performed of he correlaon beween he percenage of frms lqudaed durng he observaon perod and he number of regsered enes per 10 housand of populaon n he povas (sage IV). Ths sudy used daa from he regsry of REGON relaed o companes esablshed n he Zachodnopomorske Vovodeshp n (21 povas). The enes were observed ll he end of Sascal daa The arcle presens he resuls of he cohor analyss. The cohors comprse he enerprses se up n he povas of Zachodnopomorske n ha were observed ll he end of The nformaon abou he number of esablshed and closed down busnesses s shown n Table 1, whle Fgure 1 shows he number of lqudaed and censored (no lqudaed ll he end of he observaon perod) frms. Throughou , n Zachodnopomorske, 59,587 frms were esablshed. By he end of 2013, he number of lqudaed frms reached 22,234 (37%). Table 1. The number of frms esablshed n and lqudaed by he end of 2013 n he povas of he Zachodnopomorske Vovodeshp NTS4 Pova Number of frms esablshed lqudaed 01 bałogardzk choszczeńsk FOE 4(330)

3 The Dfferenaon of Frm Survval Models n he Povas of he Zachodnopomorske Vovodeshp 9 Śwnouśce (cy) Szczecn (cy) Koszaln (cy) łobesk wałeck śwdwńsk szczecneck sargardzk sławeńsk pyrzyck polck myślborsk koszalńsk kołobrzesk kameńsk gryfńsk gryfck golenowsk drawsk choszczeńsk bałogardzk NTS4 Pova Number of frms esablshed lqudaed 03 drawsk golenowsk gryfck gryfńsk kameńsk kołobrzesk koszalńsk myślborsk polck pyrzyck sławeńsk sargardzk szczecneck śwdwńsk wałeck łobesk Koszaln (cy) Szczecn (cy) Śwnouśce (cy) Vovodeshp Source: own sudy (REGON daa) lqudaed by he end of 2013 cenzored NUMBERS Fgure 1. The number of frms esablshed n , lqudaed and censored n he povas of he Zachodnopomorske Vovodeshp Source: own sudy FOE 4(330) 2017

4 10 Iwona Markowcz 3. Groups of povas wh smlar survval funcons A non paramerc frm survval model n he povas of Zachodnopomorske can be bul by means of he Kaplan Meer mehod (Produc Lm Esmaon), provded ha we assume he presence of censored observaons. In conras o he survval ables, hs mehod does no requre groupng he observaon mes no class nervals. The frms survval me s he realsaon of he random varable (T; δ): Tz for δ = 1 T =, (1) Tc for δ = 0 where: T z he survval me of a lqudaed frm; T c he survval me of a censored frm; δ he random varable adopng 1 for a complee observaon and 0 for a censored observaon. The Kaplan Meer esmaor can be calculaed as (Kaplan, Meer, 1958; Markowcz, 2012): Sˆ ( ) = 1 for 1,.., k, = z n where: he momen n whch here was a leas one even (frm lqudaon), z he number of evens a me (complee observaons), n he number of uns of observaon a me. The Kaplan Meer esmaor s a funcon ha s non ncreasng, perodcally consan, wh leaps a random me pons deermned by complee observaons (lqudaon of a leas one enerprse). The esmaor adops he values: ( ) 1 z 1 = n 0 undefned for for ˆ 1 S 0 for > for > k k k when δ = 1 n when δ = 0 The nal value of he survval funcon s 1 and decreases a subsequen pons of me a whch a leas one analysed even has occurred. Accordng o he leraure, he sascal properes of he Kaplan Meer esmaor are regarded as good when he sample s large 1. When usng he Kaplan Meer esmaor, he n (2) (3) 1 The modfcaon of he Kaplan Meer esmaor for small samples was proposed by Rossa, FOE 4(330)

5 The Dfferenaon of Frm Survval Models n he Povas of he Zachodnopomorske Vovodeshp 11 probably of survval can be esmaed a any me. The sascal relevance of he dfferences n survval models bul for groups can be measured wh an adequae non paramerc sascal es, akng no consderaon he presence of censored daa. The hypohess ha he survval funcons for groups are equal (Gehan, 1965; Klanbaum, Klen, 2005) s verfed by means of he Gehan es, whose sascs are wren (Namboodr, Suchndran, 1987) as follows: where (Domańsk, Pruska, 2000; Domańsk e al., 2014): W G =, (4) V n n U W, (5) U for for for or or or or or (6) where: complee observaons of he frs group, complee observaons + + of he second group, censored observaons of he frs group, censored observaons of he second group. In order o dsngush he groups of Zachodnopomorske povas wh smlar frm survval mes, he relevance of dfferences n he survval mes of frms esablshed n n 21 povas was examned. Kaplan Meer esmaors were calculaed for each pova and compared par wse. The groups were separaed n such a way as o ensure ha each of hem conans povas where he dfferences among survval me models were no sascally sgnfcan. For each par of povas, he hypohess H 0 : S 1 () = S 2 () for each was esed. The dfferences were consdered sgnfcan when p Therefore, each group conaned only he povas wh smlar survval funcons. The funcons n he povas of one group can be sgnfcanly or rrelevanly dfferen from he povas n oher groups. Moreover, he groups were ordered accordng o he decreasng probably of he analysed frms survval over me. On he oher hand, he povas whn he groups were ordered dependng on he ncreasng number of smlares o he povas n oher groups. The groups are shown n Table 2. In keepng wh he above scheme, fve groups of povas wh smlar frm survval me models were dsngushed. The frs group conssed of he followng povas: Koszaln (cy), Szczecn (cy) and polck (adacen o Szczecn), where he probably of he analysed frms survval n he successve monhs was he hghes. Anoher group comprsed a sngle FOE 4(330) 2017

6 12 Iwona Markowcz pova,.e. he drawsk pova. The ess ndcaed he smlary of he survval funcon o some povas n groups 1 and 3. The remanng groups were characersed by ncreasngly faser declnng survval funcons. I needs o be noed ha he las group, he gryfck pova, had he lowes probables of survval n he successve monhs. The ess demonsraed he sgnfcance of he dfferences beween he frm survval model n ha pova and he remanng povas. The las column n Table 2 shows he es values for many samples desgnaed for groups of mul povas. The resuls reveal a lack of sgnfcan dfferences n he survval funcon whn he groups. Table 2. Groups of povas wh a smlar frms duraon model NTS4 Pova Numbers of smlares ousde he group Group 61 Koszaln (cy) 0 62 Szczecn (cy) polck 2 03 drawsk wałeck 1 08 kołobrzesk 2 10 myślborsk 2 15 szczecneck 2 16 śwdwńsk golenowsk 3 06 gryfńsk 3 63 Śwnouśce (cy) 3 07 kameńsk 5 13 sławeńsk 0 18 łobesk 0 14 sargardzk 1 12 pyrzyck choszczeńsk 4 01 bałogardzk 7 09 koszalńsk 8 05 gryfck 0 5 Tes (p value) (0.3760) (0.6021) (0.6051) Source: own sudy FOE 4(330)

7 The Dfferenaon of Frm Survval Models n he Povas of he Zachodnopomorske Vovodeshp Inensy of frms lqudaon The nex sage of he analyss was he consrucon of cohor ables of frms survval n ndvdual povas (21 areas). The abular model was bul for he hree monh models (Markowcz, 2015). The enerprses ha dd no go no lqudaon by he end of 2013 are consdered censored. Based on he elemens of he able, he nensy funcon of frm lqudaon (hazard funcon) was analysed. The esmaor ĥ of nensy funcon s calculaed as he rao of he probably esmaor of a frm s lqudaon n he nerval (, + 1) o he half of he sum of he esmaors of he frm s probably o oulve beyond he nervals (, + 1) and ( 1, ) (Balck, 2006): ˆ ˆ f h =. (7) / 2 ( Sˆ + Sˆ ) Many sudes have confrmed ha he nensy funcon of frms lqudaon adops he nvered U shape wh a fxed maxmum, whch s n keepng wh he heorecal learnng model (Markowcz, 2012; Markowcz, 2016). 1 Inensy of frm s lqudaon 0,10 0,08 0,06 0,04 0,02 0,00 gr 1 gr 2 gr 3 gr 4 gr Duraon me (monhs) Fgure 2. Esmaon of he nensy of frms lqudaon Source: own sudy Fgure 2 shows he nensy funcon of he analysed frms lqudaon for fve groups of povas. The funcons of ndvdual groups ake he characersc shape. The survval me s analysed n nervals (Fgure 2 he begnnng of he me nerval). Havng analysed he shape of he nensy funcon of frms lqudaon n ndvdual groups of povas bul accordng o he survval models, he followng observaons were made: 1) he nensy funcon of frms lqudaon for group 1 akes he ypcal nvered U shape wh he maxmum marked whn monhs; adops low values; FOE 4(330) 2017

8 14 Iwona Markowcz 2) passng from group 1 o group 5, we can observe a less and less dsnc shape of he nensy funcon n he form of nvered U shape, ncreasngly hgher nenses of frms lqudaon and ncreasngly sronger flucuaons of hs nensy over me. 5. Lqudaon of frms afer 2 years of economc acvy Beween 2009 and 2011, n he Zachodnopomorske Vovodeshp, 59,587 enerprses were esablshed. By he end of 2013, 37.3% of hem were closed down. In ndvdual povas, he percenage of lqudaed frms was: 33.3% (group 1; n he povas of 32.6% o 34.3%), 36.1% (group 2; one pova), 38.6% (group 3; n he povas of 36.5% o 41.4%), 41.7% (group 4; n he povas of 39.6% o 43.8%), 45.4% (group 5; one pova). Thus, from group 1 o 5, he share of lqudaed frms was growng. The above presened analyss of he nensy funcon revealed ha he crcal momen was he 24h monh of acvy. Laer, he nensy of lqudaons decreased. Therefore, he auhor deermned he ndcaor of lqudaon afer 24 monhs of enerprse acvy. The resuls are shown n Fgure 3 (he ndcaor of lqudaon afer 1 year of acvy was also calculaed). In he vovodeshp, 23.2% of frms were lqudaed afer 24 monhs of exsence. Fgure 3 shows he povas by groups. The percenage of lqudaed frms s growng; n successve groups, respecvely: % (group 1), 21.7% (group 2), % (group 3), % (group 4), and 31.1% (group 5). Vovodeshp Koszaln (cy) Szczecn (cy) polck drawsk kołobrzesk myślborsk Śwnouśce (cy) gryfńsk wałeck golenowsk szczecneck śwdwńsk kameńsk koszalńsk bałogardzk choszczeńsk sargardzk sławeńsk łobesk pyrzyck gryfck frs year second year The percenage of frms lqudaed (%) Fgure 3. The percenage of frms lqudaed afer 2 years (also afer 1 year) of economc acvy Source: own sudy FOE 4(330)

9 The Dfferenaon of Frm Survval Models n he Povas of he Zachodnopomorske Vovodeshp Lqudaed frms vs operang enerprses The las sage of he sudy conans an analyss of he correlaon beween he number of frms esablshed n ha were lqudaed by he end of 2013 and he number of busnesses exsng n 2013 per 10 housand resdens n ndvdual povas. I seems ha n he povas wh lower densy of frms, he possbly for new sar ups o emerge and survve was bgger. The relaonshp beween he examned varables s shown n Fgure 4. The Pearson correlaon coeffcen was , ( = ; p = ). Thus, urns ou ha he more operang busnesses per 10 housand resdens, he lower he percenage of lqudaed frms. I was n he povas wh hgh densy of busnesses where new enes found her marke nche. In Fgure 4, he prevously creaed groups of povas are marked. Groups 1 5 are placed along he regresson lne sarng from he lowes percenage of lqudaons (wh slgh derogaons). The percenage of frms lqudaed choszczeńsk łobesk pyrzyck śwdwńsk myślborsk sławeńsk bałogardzk sargardzk szczecneck golenowsk koszalńsk wałeck gryfńsk drawsk gryfck kameńsk Śwnouśce (cy) kołobrzesk 34 polck Szczecn (cy) Koszaln (cy) Enes per 10 housand resdens Fgure 4. The percenage of frms lqudaed and he number of enes per 10 housand resdens n he Zachodnopomorske Vovodeshp povas Source: own sudy FOE 4(330) 2017

10 16 Iwona Markowcz 7. Conclusons The sudy resuls presened n hs arcle reveal he dfferenaon of frm survval models n he povas of he Zachodnopomorske Vovodeshp. Fve groups of povas were dsngushed. The groups (from 1 o 5) were characersed by: 1) decreasng me o frms lqudaon (decreasng survval funcons), 2) a less and less dsnc shape of he nensy funcon (nvered U shape), 3) growng nensy of frms lqudaon, 4) ncreasngly sronger flucuaons of nensy n me, 5) an ncreasngly hgher percenage of enerprses lqudaed durng wo years of acvy, 6) decreasng densy of frms accompaned by a growng percenage of lqudaons. The research has shown ha a crcal momen s he 24h monh of operaon. One of he reasons for he obaned rae of frms lqudaon may be he perod of subsdsed socal secury conrbuons (ZUS, 2014). Snce 2005 sar up owners can pay sgnfcanly lower socal secury conrbuons for he frs 24 monhs of operaon, whch defnely helps enerprses o survve. However, he falure of busnesses afer he perod of subsdsed conrbuons comes o an end suggess her weakness. References Balck A. (2006), Analza przeżyca ablce wymeralnośc, PWE, Warszawa. Domańsk Cz., Pruska K. (2000), Neklasyczne meody saysyczne, PWE, Warszawa. Domańsk Cz., Pekasewcz D., Baszczyńska A., Waszczyk A. (2014), Tesy saysyczne w procese podemowana decyz, Wydawncwo Unwersyeu Łódzkego, Łódź. Frączak E., Gach Cepela U., Babker H. (2005), Analza hsor zdarzeń. Elemeny eor, wybrane przykłady zasosowań, SGH, Warszawa. Gazńska M. (2003), Poencał demografczny w regone. Analza loścowa, Wydawncwo Naukowe Unwersyeu Szczecńskego, Szczecn. Gehan E.A. (1965), A Generalzed Two SampleWlcoxon Tes for Double Censored Daa, Bomerka, vol. 52, no. 3 4, pp Kaplan E.L., Meer P. (1958), Nonparamerc Esmaon from Incomplee Observaons, Journal of he Amercan Sascal Assocaon, vol. 53, no. 282, pp Klenbaum D.G., Klen M. (2005), Survval Analyss, Sprnger, New York. Markowcz I. (2012), Saysyczna analza żywonośc frm, Wydawncwo Naukowe Unwersyeu Szczecńskego, Szczecn. Markowcz I. (2014), Busness Demography Sascal Analyss of Frm Duraon, Transformaons n Busness & Economcs, vol. 13, no. 2B (32B), pp Markowcz I. (2015), Duraon Analyss of Frms Cohor Tables and Hazard Funcon, Inernaonal Journal of Busness and Socal Research, vol. 5, ssue 11, pp FOE 4(330)

11 The Dfferenaon of Frm Survval Models n he Povas of he Zachodnopomorske Vovodeshp 17 Markowcz I. (2016), Tablce rwana frm w woewódzwe zachodnopomorskm według rodzau dzałalnośc, [n:] K. Jauga, M. Walesak (eds.), Taksonoma, no. 26, Prace Naukowe UE we Wrocławu, no. 426, pp Namboodr K., Suchndran C.M. (1987), Lfe Table Technques and Ther Applcaons, Academc Press Inc., New York. Rossa A. (2005), Meody esymac rozkładu czasu rwana zawsk dla danych cenzurowanych oraz ch zasosowana, Wydawncwo Unwersyeu Łódzkego, Łódź. ZUS (2014), Ubezpeczena społeczne ubezpeczene zdrowone osób prowadzących pozarolnczą dzałalność osób z nm współpracuących, hp:// pdf [accessed: ]. Zróżncowane modelu rwana frm w powaach woewódzwa zachodnopomorskego Sreszczene: Celem przeprowadzonych badań była budowa modelu rwana frm dla poszczególnych powaów woewódzwa zachodnopomorskego. Perwszym eapem było oszacowane esymaora Kaplana Meera oraz zasosowane esu weryfkuącego podobeńswo funkc przeżyca dla powaów. Uworzono grupy powaów. Nasępny eap badań o budowa ablc rwana frm analza funkc nensywnośc lkwdac frm w grupach powaów. Nasępne przedsawono odseek frm zlkwdowanych po dwóch laach dzałalnośc w poszczególnych powaach (eap III). Przeprowadzono akże analzę współzależnośc mędzy odsekem zlkwdowanych w badanym okrese frm lczbą zareesrowanych podmoów na 10 ys. ludnośc w powaach (IV eap). W badanu wykorzysano dane z reesru REGON, doyczące frm powsałych w woewódzwe zachodnopomorskm w laach (21 powaów). Obserwaca rwała do końca 2013 roku. Wynk badań pozwolły wskazać na zróżncowane model rwana frm w powaach woewódzwa zachodnopomorskego. Uworzono pęć grup powaów scharakeryzowano e. Słowa kluczowe: model rwana frm, funkca nensywnośc lkwdac frm, poway woewódzwa zachodnopomorskego JEL: C10, C14, C41 by he auhor, lcensee Łódź Unversy Łódź Unversy Press, Łódź, Poland. Ths arcle s an open access arcle dsrbued under he erms and condons of he Creave Commons Arbuon lcense CC BY (hp://creavecommons.org/lcenses/by/3.0/) Receved: ; verfed: Acceped: FOE 4(330) 2017