EVALUATING FORECASTING MODELS FOR UNEMPLOYMENT RATES BY GENDER IN SELECTED EUROPEAN COUNTRIES

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1 Inerdisciplinary Descripion of Complex Sysems 15(1), 16-35, 217 EVALUATING FORECASTING MODELS FOR UNEMPLOYMENT RATES BY GENDER IN SELECTED EUROPEAN COUNTRIES Ksenija Dumičić*, Berislav Žmuk and Ania Čeh Časni Universiy of Zagreb Faculy of Economics and Business Zagreb, Croaia DOI: 1,796/indecs Regular aricle Received: 23 January 217. Acceped: 23 February 217. ABSTRACT The unemploymen can be considered as one of he main economic problems. The aim of his aricle is o examine he differences in male and female unemploymen raes in seleced European counries and o predic heir fuure rends by using differen saisical forecasing models. Furhermore, he impac of adding a new daa poin on he selecion of he mos appropriae saisical forecasing model and on he overall forecasing errors values is also evaluaed. Male and female unemploymen raes are observed for welve European counries in he period from 1991 o 214. Four saisical forecasing models have been seleced and applied and he mos appropriae model is considered o be he one wih he lowes overall forecasing errors values. The analysis has shown ha in he period from 1991 o 214 he decreasing rend of unemploymen raes in he shor-run is forecased for more Easern Balkan han he EU-28 counries. An addiional daa poin for male and female unemploymen raes in 214 led o somewha smaller forecasing errors in more han half of he observed counries. However, he addiional daa poin does no necessarily improve forecasing performances of he used saisical forecasing models. KEY WORDS Balkan counries, forecasing error crieria, unemploymen raes by gender, saisical forecasing mehods, unemploymen CLASSIFICATION JEL: C53, E27, J29 *Corresponding auhor, : kdumicic@efzg.hr; ; *Faculy of Economics and Business, J. F. Kennedy Sq. 6, HR 1 Zagreb, Croaia

2 Evaluaing forecasing models for unemploymen raes by gender in seleced European counries INTRODUCTION The aim of his aricle is o emphasize he differences beween male and female unemploymen raes and o forecas heir fuure rends in seleced European counries. Namely, wo research quesions arise. The firs research quesion is if he decreasing rend of male and female unemploymen raes expeced o be more pronounced in he European Union member saes or in he Easern Balkan counries. The second research quesion is if adding a new daa poin resul in smaller overall forecasing errors. Thus, male and female unemploymen raes are examined for welve European counries in he period from 1991 o 214. Also, he analysed counries were divided ino wo groups: Ausria, Croaia, Greece, Porugal, Slovenia and Spain were grouped in he EU-28 member saes group, whereas Albania, Bosnia and Herzegovina, he Former Yugoslav Republic of Macedonia, Monenegro, Serbia and Turkey were classified as he Easern Balkan counries. In he empirical analysis, he average unemploymen rae concerning all he EU-28 member saes was used as a benchmark for comparison of male and female unemploymen raes. Afer a basic descripive saisical analysis of male and female unemploymen raes, forecasing mehods and models were employed. The selecion of he mos appropriae forecasing mehod and he model was based on he smalles overall forecasing error crieria, more precisely: mean squared error (MSE), mean absolue deviaion (MSD) and mean absolue percenage error (MAPE). The empirical analysis has shown ha he linear rend model was he bes forecasing model when forecasing male and female unemploymen raes for a vas majoriy of counries in he sample. The forecased unemploymen raes from previous relevan research have been used in his aricle for comparison of forecased and acual unemploymen raes in he sampled counries in 214. Furhermore, he impac of an addiional real daa poin on he forecasing error was also examined. The reminder of his aricle is as follows. Afer he shor inroducion, he secion wo presens he lieraure review. The secion hree describes daa and mehods while he secion four presens he resuls of he empirical analysis. Finally, he secion five concludes. LITERATURE REVIEW The forecass consrucion is an imporan elemen for developing macroeconomic aciviies and for economic analysis in general. However, he predicion should be followed by an evaluaion of is accuracy. There is a rich empirical lieraure relaed o he predicion mehods, bu only a few sudies are dedicaed o he accuracy assessmen and ways o improve i. Since in our sudy we aim o es he accuracy of conduced forecass of female and male unemploymen raes in seleced European counries, his secion provides a brief lieraure review relaed o forecasing accuracy assessmen. In he recen aricle of [1], a valuaion of alernaive unemploymen rae predicions for he Romanian economy is given and he bes sraegy o improve he forecass accuracy is o combine forecass of forecasers predicions. In heir iniial sudy [2] presen he mos suiable model for forecasing he unemploymen rae in Malaysia and make comparisons in order o see how well he hisorical and forecased daa mach and correlae. According o heir analysis he Hol s mehod is he mos suiable model for forecasing quarerly unemploymen raes in Malaysia. Furhermore, according o anoher sudy by [3], he evaluaion and he improvemen of forecass accuracy generae growh in he qualiy of decisional process. Therefore, he Mone Carlo mehod is no used o simulae he forecased unemploymen rae in Romania, which proved o be he bes way o increase he predicion 17

3 K. Dumičić, B. Žmuk and A. Čeh Časni accuracy. In addiion, [4] presened a research in which differen forecass for he unemploymen rae in he USA are analysed by four diverse insiuions. The muli-crieria ranking is applied and five significan measures of accuracy are simulaneously used. Even hough he recommended sraegies o improve he precision of forecass did no solve he problem of biasness, i is concluded ha he valuaion and enhancemen of forecass accuracy have an essenial impac on improving he qualiy of he decision making process. According o he research by [5], he key phase in forecasing is he selecion of a predicion mehod wih he maximum exen of precision. In ha sense in heir aricle hey made shor-erm forecass for macroeconomic variables such as he inflaion rae, he unemploymen rae and he ineres rae for Romania using various echniques. Wih he aim of improving he accuracy of forecass he auhors combined wo empirical approaches. Namely, hey made a joined predicion and consruced he forecass founded on hisorical indicaors of accuracy. Accordingly, he highes degree of accuracy was found in he case of predicions consruced on he basis of he echnique. Furhermore, [6] applied quarerly daa on unemploymen raes in Nigeria. The sudy evaluaed he forecasing performance of four compeing models using various forecas accuracy crieria. Accordingly, he resuls have shown ha he mixed ARIMA/ARCH model could be used o forecas unemploymen raes in Nigeria in he shor-run. In [7] auhors emphasize he need for high-qualiy saisics for labour policy. Namely, heir sudy is aimed a presening he mehod used for repeaedly creaing he esimaion of monhly unemploymen direcly from he Labour Force Survey (LFS) resuls. Accordingly, he improved Hol s model has shown o be he mos appropriae for predicing he monhly unemploymen rae in Romania. Finally, he recen sudy by [8] proposes he bes forecasing model for unemploymen raes for each gender in seleced European counries using yearly official ime series daa. The sudy shows a cross-counry comparison of he forecasing models efficiency for shor-erm forecass for boh genders. Accordingly, he linear rend forecasing model has shown o be he mos accurae for some counries, while for oher counries he double forecasing appeared o be he mos precise. Our sudy conribues o he exising empirical lieraure by using he mos recen daa se on male and female unemploymen raes in seleced European counries and by comparing he rend of male and female unemploymen raes in he EU-28 member saes and in he Easern Balkan counries which has no been explored ye. Also, our sudy reveals wheher adding a new daa poin resuls in smaller overall forecasing errors. DATA AND METHODS In order o collec he daa for he analysis, he World Developmen Indicaors daabase provided by [9] was used. For he purpose of his aricle only daa for wo variables were colleced. The firs variable is he male unemploymen rae (% of male labour force, modelled ILO esimae) whereas he second one is he female unemploymen rae (% of female labour force, modelled ILO esimae) [9]. Male unemploymen raes are calculaed by dividing he oal number of males who are wihou work bu available for and seeking employmen wih he oal number of male labour force. Similarly, female unemploymen raes are calculaed by aking ino accoun he oal number of females who are wihou work bu available for and seeking employmen and he oal number of female labour force. Male and female unemploymen raes are going o be analysed for a cerain number of European counries. Namely, in he Easern Balkan counries, male and female unemploymen raes are going o be compared o he corresponding unemploymen raes in some of he EU-28 member saes. The counries seleced among he Easern Balkan 18

4 Evaluaing forecasing models for unemploymen raes by gender in seleced European counries counries include Albania, Bosnia and Herzegovina, he Former Yugoslav Republic of Macedonia, Monenegro, Serbia and Turkey. By selecing hese counries he vas majoriy of Easern Balkan counries were included in he analysis. On he oher side, among he EU-28 member saes he following counries were seleced: Ausria, Croaia, Greece, Porugal, Slovenia and Spain. These counries were seleced eiher because hey have really low unemploymen raes, i.e. Ausria, or high unemploymen raes wih cerain problems wih unemploymen, i.e. Greece, Porugal and Spain. Croaia and Slovenia can be considered as he Wesern Balkan counries bu here hey are placed in he group of he EU-28 member saes. So, in he analysis, welve European counries are observed. The male and female unemploymen raes are observed for he seleced European counries in he period from 1991 o 214. Only yearly daa were considered in he analysis. The daa before 1991 were missing for some counries and because of ha previous periods were no analysed. On he oher hand, he newes daa is available for 214. Consequenly, he period of 24 years is observed. Descripive saisics mehods were used o compare male and female unemploymen raes among he observed European counries. Furhermore, male and female unemploymen raes of all he EU-28 member saes ogeher were used as a benchmark o ge a beer insigh ino he posiion of unemploymen in he observed counries. Afer descripive saisical analyses, forecasing models were used o forecas male and female unemploymen raes in he seleced counries. I is assumed ha unemploymen raes are no sable and ha hey have some rend movemens depending on he leading pary in a counry, economic crisis, invesmen cycle, and similar. Consequenly, i is assumed ha all observed ime series of male and female unemploymen raes have he rend componen. Furhermore, his assumpion will be checked by analysing line chars of acual values. Since yearly daa are observed, he seasonal componen canno be idenified. So, he following four saisical forecasing models were seleced: rend polynomial of he firs degree (linear rend) model, rend polynomial of he second degree (quadraic rend) model, rend polynomial of he firs degree ( rend) model and Hol s wo-parameer model of linear (double ). The esimaed linear rend model is given by he following expression: F ˆ ˆ 1x, 1,2,..., n, (1) F ˆ ˆ x, 1,2,3,..., (2) n 1 n where F is he esimaed (forecased) value of he ime series a ime, ˆ is he esimaed consan erm, ˆ 1 is he esimaed slope coefficien, x is he value of he ime variable a ime, F n is he esimaed (forecased) value of he ime series a ime n, x n is he value of he ime variable a ime n, n is he oal number of values in he ime series, and is he ime horizon (forecas horizon). The consan erm and he slope coefficien are esimaed by using he ordinary leas squares (OLS) approach. The equaion (1) is used o calculae forecass for periods in which acual values are known whereas he equaion (2) is used o calculae forecass for periods in which acual values are unknown. The rend polynomial of he second degree model or quadraic rend is given by: F ˆ ˆ x ˆ x, 1,2,..., n, (3) ˆ ˆ ˆ 2 F x x, 1,2,3,..., (4) n 1 n 2 n 19

5 K. Dumičić, B. Žmuk and A. Čeh Časni where F is he esimaed (forecased) value of he ime series a ime, ˆ is he esimaed consan erm, ˆ 1 and ˆ 2 are esimaed coefficiens, x is he value of he ime uni variable 2 a ime, x is he squared value of he ime variable a ime, F n is he esimaed (forecased) value of he ime series a ime n, x n is he value of he ime variable a ime n, n is he oal number of values in he ime series, and is he ime horizon (forecas horizon). The parameers here are also esimaed by he OLS approach and he difference beween performing forecass in periods where acual values are known equaion (3)) and are no known (equaion (4)) is presened also. In order o use he OLS approach, in he rend polynomial of he firs degree or rend, firs he model mus be ransformed using logarihms. The model is given by: x F ˆ ˆ, 1,2,..., n, (5) 1 ˆ ˆ x F n, 1,2,3,..., (6) n 1 where F is he esimaed (forecased) value of he ime series a ime, ˆ is he esimaed consan erm, ˆ 1 is he esimaed slope coefficien, x is he value of he ime variable a ime, F n is he esimaed (forecased) value of he ime series a ime n, x n is he value of he ime variable a ime n, n is he oal number of values in he ime series, and is he ime horizon (forecas horizon). In order o calculae forecass for periods in which acual values are known, he equaion (5) is used, whereas he equaion (6) is used o calculae forecass when acual values are unknown. The las saisical forecasing model which is going o be used in he analysis is he Hol s wo-parameer model of linear or double. The double is given by: F yˆ T, 1, 1, 1,2,..., n, (7) 1 F yˆ T, 1,2,3, (8) n n n where F 1 is he forecas a ime +1, ŷ is he esimaed value of he ime series a ime and is calculaed as yˆ 1 ˆ y y 1 T 1, T is he esimaed value of he rend a ime T yˆ yˆ T, is he level consan, is and is calculaed as 1 he rend consan, 1 1 y is he value of he ime series a ime, n is he oal number of values in he ime series, F n is he forecas a ime n, ŷ n is he esimaed value of he ime series a ime n, T n is he esimaed value of he rend a ime n, and is he ime horizon (forecas horizon). Equaions (7) and (8) are used o calculae forecass in periods in which acual values are known and in which acual values are no known, respecively. The four saisical forecasing models are used o calculae forecass for male and female unemploymen raes a each of he observed counries. The selecion of he bes forecasing model was conduced by looking a overall forecasing error values. The analysis ook ino consideraion mean absolue percenage error (MAPE), mean absolue deviaion (MAD) and mean squared error (MSE). These overall forecasing errors are calculaed as follows: 2

6 Evaluaing forecasing models for unemploymen raes by gender in seleced European counries T y F 1 1 y MAPE, y, (9) T T y F 1 MAD T, (1) T 2 y F 1 MSE T, (11) where MAPE is he mean absolue percenage error, y is he value of he ime series a ime, F is he forecas a ime, T is he number of pairs of acual values and forecass, MAD is he mean absolue deviaion, MSE is he mean squared error. According o equaions (9-11), i can be concluded ha each of he observed overall forecasing errors has cerain unique properies and characerisics in comparison o he ohers. Consequenly, i is possible ha according o one overall forecasing error, one forecasing model is beer han he oher one because i has a lower value of ha overall forecasing error. However, i could happen ha according o anoher forecasing error he second forecasing model is beer han he firs one. In ha case, a forecasing model which has more overall forecasing errors wih lower values is considered o be he bes one and i is chosen for furher analysis. According o he seleced forecasing models, furher rends in male and female unemploymen raes are forecased in he observed European counries. I has been decided ha he wo-period forecas horizon is going o be analysed. In oher words, only wo periods afer he period for which he las acual value exiss will be forecased. Forecasing in he long-run is no recommended because many facors which can have an impac on unemploymen can change in he long-run. Consequenly, he forecasing errors end o be very high in he long-run. Thus only shor-run forecass are performed. However, forecasing in he shor-run can also provide misleading forecass. In order o illusrae ha and o emphasize ha researchers should be careful abou heir conclusion when forecasing in he shor-run, he recen research by [8] has been used wih he aim of comparing he resuls wih acual values and wih resuls gained in his aricle. ANALYSIS OF MALE AND FEMALE UNEMPLOYMENT RATES DESCRIPTIVE STATISTICS ANALYSIS OF MALE AND FEMALE UNEMPLOYMENT RATES In his aricle male and female unemploymen raes of welve seleced European counries are observed. In his chaper, firs male and hen female unemploymen raes are examined. A he end of his secion, he differences beween male and female unemploymen raes are sudied. 21

7 K. Dumičić, B. Žmuk and A. Čeh Časni % Albania Bosnia and Herzegovina Macedonia, FYR Monenegro Serbia Turkey EU-28 5 Year Figure 1. Male unemploymen raes in seleced Easern Balkan counries, in he period from 1991 o 214, in % [9]. In Figure 1 male unemploymen raes in he seleced Easern Balkan counries in he period from 1991 o 214 are presened. In order o make comparisons and o ge an insigh ino wheher male unemploymen raes are low or high, he average male unemploymen rae for he whole EU-28 area is used as a benchmark in Figure 1. I can be concluded ha almos all he observed Easern Balkan counries, excep Turkey, have higher male unemploymen raes han he EU-28 counries in he whole observed period. Only male unemploymen raes in Turkey are close o he (average) EU-28 levels. The wors siuaion is in he Former Yugoslav Republic of Macedonia. In he whole observed period, he male unemploymen rae in he Former Yugoslav Republic of Macedonia was no lower han 27,7 % which was achieved in 214. Afer he Former Yugoslav Republic of Macedonia he nex counry wih very high male unemploymen raes is Bosnia and Herzegovina. Considering male unemploymen raes, he bes siuaion in Bosnia and Herzegovina was in 1991 (21,6 %) and in 28 (21,8 %). The oher hree Easern Balkan counries, Albania, Monenegro and Serbia, had male unemploymen raes beween 1 % and 2 % in he analysed period. Figure 2 presens male unemploymen raes for he seleced six EU-28 member saes in he period from 1991 o 214. Again, he average male unemploymen rae for EU-28 is included in Figure 2, in he same way as in Figure 1. 22

8 Evaluaing forecasing models for unemploymen raes by gender in seleced European counries % Ausria Croaia Greece Porugal Slovenia Spain EU-28 Year Figure 2. Male unemploymen raes in he seleced EU-28 member saes in he period from 1991 o 214, in % [9]. By far he bes counry wih he lowes male unemploymen raes in he observed periods is Ausria. Namely, Ausria did no have he lowes male unemploymen raes in each observed period bu i had male unemploymen raes undoubedly lower han he EU-28 benchmark. Afer Ausria, Slovenia seems o have he lowes male unemploymen raes. However, male unemploymen raes are much closer o he EU-28 benchmark values. The male unemploymen raes in oher four counries had a srong increase from 27 or 28. Tha increase sopped in 214. I is obvious ha hese Croaia, Greece, Porugal and Spain are above he EU-28 benchmark, especially since 28. According o he recen male unemploymen raes, Spain and Greece seem o have he same male unemploymen rae levels whereas Croaia and Porugal also have similar male unemploymen rae levels. The mos recen analysed year was 214. According o Figure 3, in 214 he Former Yugoslav Republic of Macedonia and Bosnia and Herzegovina had he highes male unemploymen raes, boh wih he value above 25 %. These Easern Balkan counries are followed by wo EU-28 member saes Spain and Greece. Boh counries had male unemploymen raes above 2 %. The nex five counries, Serbia (19,4 %), Monenegro (18,3 %), Albania (16,9 %), Croaia (16,8 %) and Porugal (14.1 %) had male unemploymen raes around 5,3 %. Figure 3 reveals ha 9 counries had heir male unemploymen raes above he EU-28 benchmark whereas only 3 counries had male unemploymen raes under he benchmark value of 1.1 %. Ou of hese hree counries wo of hem, Slovenia (9, %) and Ausria (4,9 %), are he EU-28 member saes. Turkey (8,6 %) is he only Easern Balkan counry wih is male unemploymen rae lower han he EU-28 benchmark. 23

9 Macedonia, FYR Bosnia and Herzegovina Spain Greece Serbia Monenegro Albania Croaia Porugal EU-28 Slovenia Turkey Ausria K. Dumičić, B. Žmuk and A. Čeh Časni % Counry Figure 3. Male unemploymen raes in he seleced European counries in 214, in % [9]. Figure 4 shows female unemploymen raes in seleced Easern Balkan counries in he period from 1991 o 214. The conclusions are almos he same as in he case of male unemploymen raes in he seleced Easern Balkan counries in he same period. The Former Yugoslav Republic of Macedonia and Bosnia and Herzegovina have he highes female unemploymen raes in he analysed period. On he oher side, Turkey has he lowes female unemploymen raes in he same period in comparison o he oher seleced Easern Balkan counries. The female unemploymen raes in Turkey end o be very close o he average female unemploymen raes in he EU-28. I has o be emphasized ha Monenegro seems o have a very low variabiliy level of female unemploymen raes in comparison o he oher counries whose variabiliy levels are much higher. According o Figure 5, Ausria has he lowes female unemploymen raes in comparison o he oher observed EU-28 member saes. Slovenia is found o be under he EU-28 benchmark values as well. However, he values of female unemploymen raes of he observed EU-28 counries, excep Ausria, have shown a srong increase in values since 28. Consequenly, Slovenia came very close o he average EU-28 level. The female unemploymen raes in Greece were almos a he EU-28 level bu since 28 he difference has been becoming greaer and greaer. Consequenly, Greece has become he EU-28 member sae wih he highes female unemploymen rae in he mos recen period (214). Considering female unemploymen raes in recen years, Spain is very close o Greece. Croaia and Porugal also end o have similar female unemploymen raes in he recen years. 24

10 Evaluaing forecasing models for unemploymen raes by gender in seleced European counries % Albania Bosnia and Herzegovina Macedonia, FYR Monenegro Serbia Turkey EU-28 5 Year Figure 4. Female unemploymen raes in he seleced Easern Balkan counries in he period from 1991 o 214, in % [9]. % Ausria Croaia Greece Porugal Slovenia Spain EU-28 Year Figure 5. Female unemploymen raes in he seleced EU-28 member saes in he period from 1991 o 214, in % [9]. 25

11 Greece Serbia Bosnia and Herzegovina Spain Turkey Monenegro Slovenia Macedonia, FYR Porugal EU-28 Ausria Croaia Albania Greece Bosnia and Herzegovina Macedonia, FYR Spain Serbia Monenegro Croaia Albania Porugal Turkey EU-28 Slovenia Ausria K. Dumičić, B. Žmuk and A. Čeh Časni % Counry Figure 6. Female unemploymen raes in he seleced European counries in 214, in % [8]. Figure 6 shows female unemploymen raes for seleced European counries in he year 214. Surprisingly, Figure 6 reveals ha Greece (31,4 %) had he highes female unemploymen rae among all he observed European counries in 214. However, Bosnia and Herzegovina and he Former Yugoslav Republic of Macedonia wih female unemploymen raes of 29,8 % and 28.1 %, respecively, are following Greece closely. Spain (26, %) and Serbia (25,9 %) had almos he same female unemploymen raes in 214. Croaia having he female unemploymen rae of 16,6 % follows afer Monenegro wih he female unemploymen rae of 2,1 %. Albania (14,8 %) had a slighly higher female unemploymen rae han Porugal (14,4 %) in 214. Turkey wih he female unemploymen rae of 1,7 % is slighly above he EU-28 benchmark level (1,4 %). The only wo counries which had female unemploymen raes in 214 below he EU-28 benchmark level are Slovenia (1, %) and Ausria (5, %). Difference in unemploymen raes, % Counry Figure 7. Absolue differences beween female and male unemploymen raes in he seleced European counries in 214, in % [9]. The absolue differences beween female and male unemploymen raes in 214 are calculaed and presened in Figure 7. I has o be emphasized ha he differences were calculaed by subracing female and male unemploymen raes for each observed European counry and he differences are given in percenages. 26

12 Evaluaing forecasing models for unemploymen raes by gender in seleced European counries Figure 7 shows ha he highes difference beween female and male unemploymen raes in 214 was in Greece. Namely, in Greece he female unemploymen rae was 8,8 %, which is higher han he male unemploymen rae in 214. In Serbia, he female unemploymen rae was 6,5 % higher han he male unemploymen rae in 214. Serbia is following counries wih moderaely high female unemploymen raes: Bosnia and Herzegovina (3,1 %), Spain (2,3 %), Turkey (2,1 %), Monenegro (1,8 %) and Slovenia (1, %). The Former Yugoslav Republic of Macedonia (,4 %), Porugal (,3 %) and Ausria (,1 %) had slighly higher female unemploymen raes han male unemploymen raes in 214. If all he EU-28 member saes are aken ino accoun, i can be concluded ha he female unemploymen rae in he EU-28 member saes was,3 % higher han he male unemploymen rae in 214. Only in Croaia and Albania he male unemploymen rae was higher han he female unemploymen rae in 214. So, in Croaia he male unemploymen rae was.2 % higher han he female unemploymen rae whereas he difference in Albania was 2,1 % in favour of he higher male unemploymen rae. FORECASTING MALE AND FEMALE UNEMPLOYMENT RATES In furher analysis male and female unemploymen raes in welve observed European counries are forecased by using four seleced saisical rend forecasing models. In order o selec he mos precise and he bes forecasing saisical model he overall forecasing error approach is used. The forecasing models wih he smalles MAPE, MAD and MSE are chosen. However, in some cases here was no forecasing model which was he bes according o all he hree overall forecasing errors. In ha case, a model which was he bes a leas for wo overall forecasing errors was chosen. The seleced forecasing models for male unemploymen raes based on daa for he period are shown in Table 1 whereas he seleced forecasing models for female unemploymen raes are shown in Table 2. Table 1. Forecasing male unemploymen raes: Seleced saisical forecasing models for 12 European counries wih overall forecasing errors, based on daa for he period Counry Forecasing model Equaion / Smoohing Overall forecasing errors consans MAPE MAD MSE Albania Quadraic rend F =13,43,1 +,8 2 9,88 1,35 3,31 Ausria Linear rend F =3,3+,6 8,51,34,16 Bosnia and Herzegovina Linear rend F =23,47+,12 4,71 1,16 2,65 Croaia α=1,1611; β=, ,47 4,78 Greece α=,474; β=59,61 1,4,81 1,35 Macedonia, FYR α=1.2187; β=, ,39 3,56 Monenegro Exponenial rend F =19,6 (,9973 ) 4,93, Porugal α=1,3484; β=,965 14,94,92 1,39 Serbia Quadraic rend F =13,78,35 +, , Slovenia α=,997; β=,1 15,81 1,8 2,74 Spain α=1,6284; β=,781 14,88 1,94 5,14 Turkey α=1.2189; β=,372 8,7,83 1,55 According o resuls from Table 1, he linear rend and he quadraic rend were he bes forecasing models for forecasing male unemploymen raes in wo counries, he rend in jus one counry, and he double was he bes forecasing model for forecasing male unemploymen raes in seven counries. In case of forecasing female unemploymen raes only wo forecasing models seem o be he bes choice. So, according o he resuls from Table 2, he quadraic rend was he bes forecasing model for forecasing female unemploymen raes in five counries whereas he double 27

13 K. Dumičić, B. Žmuk and A. Čeh Časni was he bes forecasing models for forecasing female unemploymen raes in seven counries. Table 2. Forecasing female unemploymen raes: Seleced saisical forecasing models for 12 European counries wih overall forecasing errors, based on daa for he period Counry Forecasing model Equaion / Smoohing Overall forecasing errors consans MAPE MAD MSE Albania Quadraic rend F =2,38,32 +,1 2 14,98 2,48 11,42 Ausria α=,9699; β=,1 8,4,35.21 Bosnia and Herzegovina Quadraic rend F =26,2+,43, ,55 4,45 Croaia α=1.266; β=,698 7,98 1,17 3, Greece α=1,5745; β=,1229 9,42 1, Macedonia, FYR Quadraic rend F =28, ,53 2 3,92 1,34 3,11 Monenegro Quadraic rend F =2,8+,9,6 2 2,86,58,62 Porugal α=1,5546; β=, ,9 1,52 Serbia Quadraic rend F =18,87,51 +, ,51 2,48 1,9 Slovenia α=1.2896; β=,72 9,73,69,77 Spain α=1,519; β=,5419 9,12 1,78 4,95 Turkey α=,9924; β=,442 11,31,98 1,4 Table 3. Forecased male unemploymen raes in 12 European counries in 215 and 216 (ime horizon τ=2). Counry Acual values Forecased values Recen forecas endency Albania 17,6 16,9 15,34 15,61 Increase Ausria 4,9 4,9 4,75 4,81 Increase Bosnia and Herzegovina 26,3 26,7 26,47 26,59 Increase Croaia 17,7 16,8 16,98 17,43 Increase Greece 24,3 22,6 15, Decrease Macedonia, FYR 29, 27, , Decrease Monenegro 18,7 18,3 18, Decrease Porugal 16,4 14,1 13,61 14,15 Increase Serbia ,4 21,39 22,37 Increase Slovenia 9,4 9, 9,5 9,1 Increase Spain 25,8 23,7 22,93 23,65 Increase Turkey 8, 8,6 8,66 8,54 Decrease I has o be emphasized ha overall forecasing errors are no direcly comparable neiher among differen counries, nor male and female unemploymen raes overall errors in a counry because differen forecasing models and/or differen parameers in forecasing models were used. Thus, rends in male and female unemploymen raes in he observed European counries are analysed. The las acual male and female unemploymen raes are officially available for 214. Because of ha, forecass for 215 and 216, developed using he models from Table 1 and Table 2 and he forecas ime horizon τ=2, are observed o deermine he shor-run endencies in male and female unemploymen raes. I has been decided o forecas only wo periods in he fuure because unemploymen raes are influenced by differen facors. In Table 3, he forecass and deermined rends in male unemploymen raes are shown, whereas in Table 4, he forecass and deermined rends in female unemploymen raes are presened. Unforunaely, he resuls from Table 3 and Table 4 are no as posiive as one migh expec because Gross Domesic Produc per capia is rising on he World level since 21 [1]. Namely, only in four counries (Greece, he Former Yugoslav Republic of Macedonia, 28

14 Evaluaing forecasing models for unemploymen raes by gender in seleced European counries Monenegro and Turkey) here is a decrease of male unemploymen raes. So, according o Table 3, only in four counries he decrease in male unemploymen raes is expeced. I is ineresing ha ou of hese four counries, hree are he Easern Balkan counries whereas jus one is he EU-28 member sae. The resuls from Table 4 show ha he female unemploymen rae decrease is forecased in only four counries. All counries in which a decrease of he female unemploymen rae is expeced are he Easern Balkan counries (Albania, Bosnia and Herzegovina, he Former Yugoslav Republic of Macedonia, Monenegro and Turkey). The only wo counries in which a decrease in boh, male and female, unemploymen raes is forecased are he Former Yugoslav Republic of Macedonia and Monenegro. Consequenly, i is expeced ha in hese wo counries he overall unemploymen rae will also decrease in he fuure periods. Table 4. Forecased female unemploymen raes in 12 European counries in 215 and 216 (ime horizon τ=2). Counry Acual values Forecased values Recen forecas endency Albania 13,8 14,8 13,6 12,8 Decrease Ausria 4,9 5, 5,3 5,7 Increase Bosnia and Herzegovina ,8 29,34 29,17 Decrease Croaia 16,9 16,6 16,75 17,1 Increase Greece 31,3 31,4 31,98 33,43 Increase Macedonia, FYR 29, 28,1 26,8 25,34 Decrease Monenegro 2,5 2,1 19, Decrease Porugal 16,6 14,4 13,4 13,76 Increase Serbia 25,9 25,9 28,83 3,17 Increase Slovenia , 9,64 9,85 Increase Spain 27, 26, 26,16 26,48 Increase Turkey 1,4 1,7 1,77 1,84 Increase DISCUSSION AND COMPARISONS OF MALE AND FEMALE UNEMPLOYMENT RATES As i was menioned earlier, forecasing is easy o perform bu i is hard o rely on forecass. As a consequence, conducing forecass in a long-run should be avoided because he fuure is very unpredicable, especially when economy is observed. Furhermore, ofen forecass in he long-run do no have meaningful inerpreaion. Therefore, i is highly recommended o conduc only shor-erm forecass. In his aricle only wo periods in he fuure were forecased. Tha was he minimal number of forecass o deermine fuure rends in male and female unemploymen raes developmens in he observed counries. I has o be emphasized ha lile or no care was given o he exac forecass values. The reason for ha is very simple. Namely, wih a high reliabiliy level i can be concluded ha he calculaed poin forecass are going o be differen from he real values in he fuure. In oher words, i can be concluded ha no maer which saisical forecasing approach is used, here would always be a cerain forecasing error. However, by using he mos appropriae saisical forecasing model hese forecasing errors in he fuure should be minimal. In order o selec he mos appropriae saisical forecasing model i is necessary ha enough daa poins are available. If here are no enough daa poins available, he developmen of he observed variable canno be described very well by any saisical forecasing model. Consequenly very high values of overall forecasing errors are presen. Of course, in case of a small number of available daa poins here is a danger of choosing he wrong saisical forecasing model which seems o be he bes by observing only a small number of daa poins. However, he quesion is wheher an addiional daa poin necessarily leads o smaller overall forecasing errors or he impac of an addiional daa poin can be negleced. 29

15 K. Dumičić, B. Žmuk and A. Čeh Časni In his aricle male and female unemploymen raes were forecased for he observed European counries by using daa from 1991 o 214. Based on performed forecass and calculaed overall forecasing errors he bes saisical forecasing models were chosen and presened in Table 1 and Table 2. In order o examine he impac of addiional daa poins on he overall forecasing errors and he precision of he seleced saisical forecasing models, addiional forecasing was conduced. Again, male and female unemploymen raes will be forecased for he observed European counries bu by using daa from 1991 o 213. So, in he process of forecasing, one daa poin less will be used in comparison o he previously conduced forecasing. In order o make overall forecasing errors comparable, forecasing is conduced only by using previously seleced saisical forecasing models which had he smalles overall forecasing errors based on daa from 1991 o 214. Afer he overall forecasing errors were calculaed based on daa poins from 1991 o 213, heir values have been compared o he overall forecasing errors values which have been calculaed based on daa poins from 1991 o 214. The differences beween overall forecasing errors have been observed in an absolue and in a relaive sense. In order o calculae absolue differences beween overall forecasing errors, he simple subracion of overall forecasing errors based on daa poins from 1991 o 213 from overall forecasing errors values based on daa poins from 1991 o 214 was conduced. The relaive differences were calculaed by using he following expression: OFE OFE DIFF 1 1, (12) OFE 1 where DIFF is he relaive difference beween wo overall forecasing errors, OFE is he overall forecasing error value based on daa poins from 1991 o 214, OFE 1 is he overall forecasing error value based on daa poins from 1991 o 213. As overall forecasing errors in he analysis MAPE, MAD and MSE were used. The absolue and relaive differences are shown in Table 5 for male unemploymen raes and in Table 6 for female unemploymen raes in he analysed European counries. Opposie o he expeced, he resuls from Table 5 and Table 6 have shown ha adding a new daa poin for 214 does no necessarily lead o smaller overall forecasing errors. If he male unemploymen raes forecass are observed, i can be concluded ha an addiional daa poin resuled in smaller overall forecasing errors in 9 counries by using MAPE, in 7 counries by using MAD and in 7 counries by using MSE. So, for he majoriy of counries an addiional daa poin led o smaller overall forecasing errors. The larges decrease in overall forecasing errors by adding a new daa poin is achieved in Slovenia. In case of Slovenia, he addiional male unemploymen rae daa for 214 resuled in he 28,12 % decrease of MAPE, in he % decrease of MAD and in he 3,15 % decrease in MSE. On he oher side, in Porugal he addiional male unemploymen rae daa for 214 resuled in he 1,78 % increase of MAPE, in he 15, % increase of MAD and in he 38,6 % increase in MSE. In Albania and in he Former Yugoslav Republic of Macedonia adding an addiional daa poin resuled in an increase of all he hree observed forecasing errors, also. According o resuls from Table 6, if female unemploymen raes forecass are observed, i can be concluded ha an addiional daa poin resuled in smaller overall forecasing errors for 8 counries by using MAPE, in 7 counries by using MAD and in 7 counries by using MSE. So, again an addiional daa poin resuled in lower overall forecasing errors in he majoriy of he observed European counries. However, he improvemens of overall forecasing errors are much less expressed in he case of female unemploymen raes han in he case of male unemploymen raes. The bes improvemens of overall forecasing errors are 3

16 Evaluaing forecasing models for unemploymen raes by gender in seleced European counries presen in he case of Turkey. Namely, in Turkey, he addiional female unemploymen rae daa for 214 resuled in he 4,73 % decrease of MAPE, in he 4,76 % decrease of MAD and in he 7,12 % decrease in MSE. On he oher side, in four European counries (Croaia, Greece, Slovenia, Spain) all he hree observed overall forecasing errors increased because a new female unemploymen rae from 214 was included in he analysis. The larges increase of overall forecasing errors is presen in Slovenia where MAPE increased by 9,5 %, MAD increased by 12,89 % and MSE increased by 21,56 %. Table 5. Differences in overall forecasing errors values when male unemploymen raes in he period from 1991 o 214 and in he period from 1991 o 213 are compared in 12 considered European counries. Overall forecasing error Counry Forecasing MAPE MAD MSE model (difference) (difference) (difference) Absolue Relaive Relaive Relaive Absolue Absolue (%) (%) (%) Albania Quadraic rend,14 1,39,2 1,43,7 2,4 Ausria Linear rend -.2-2,34 -,1-2,1 -, -2,85 Bosnia and Herzegovina Croaia Greece Macedonia, FYR Monenegro Porugal Linear rend -, , ,11-3,95 Exponenial rend -,11 -,86,1,59 -,8-1,56-1,15-9,97 -,12-12,39,,18,5 1,18,1, ,19-3,65 -,4-3,64 -,6-4,11 1,45 1,78,12 15,,38 38,6 Serbia Quadraic rend ,73 -, ,16-2,92 Slovenia -6,19-28, ,18-3,15 Spain Turkey ,93,3 1,45,17 3,47 -,18-2,8 -,2-2,33 -,1-5,95 The main reason why in some counries all he hree overall forecasing errors have increased by adding a new daa poin could be in saisical forecasing model misspecificaion. In oher words, i could happen ha if daa from 1991 o 213 are observed, one saisical forecasing model is he mos appropriae bu if daa from 1991 o 214 are observed, anoher saisical forecasing model should be chosen because of lower overall forecasing errors. In order o ake his fac ino accoun, he lis of seleced saisical forecasing models from recen research by [8] was aken and presened in Table 7. In [8] he auhor also forecased male and female unemploymen raes, bu by using daa from 1991 o 213. Table 7 summarizes saisical forecasing models which appeared o be he 31

17 K. Dumičić, B. Žmuk and A. Čeh Časni bes o perform forecass of male and female unemploymen raes for he observed European counries according o [8] and according o he research presened in his aricle. According o Table 7, an addiional daa poin of he male unemploymen rae in 214 led o a change of he bes saisical forecasing model in he case of 5 counries (Albania, Monenegro, Porugal, Serbia, and Spain). Similarly, an addiional daa poin of he female unemploymen rae in 214 led o a change of he mos appropriae saisical forecasing model in 5 counries also (Albania, Bosnia and Herzegovina, he Former Yugoslav Republic of Macedonia, Monenegro, Serbia). However, if hese liss of counries are compared o he liss of counries in which all he hree overall forecasing errors increased only one mach can be found. Only when male Table 6. Differences in overall forecasing errors values when female unemploymen raes in he period from 1991 o 214 and in he period from 1991 o 213 are compared in 12 observed European counries. Counry Albania Ausria Bosnia and Herzegovina Croaia Greece Macedonia, FYR Monenegr o Porugal Serbia Slovenia Spain Turkey Forecasing model Quadraic rend Quadraic rend Quadraic rend Quadraic rend Quadraic rend MAPE (difference) Absolue Relaive, % Overall forecasing error MAD (difference) Absolue Relaive, % MSE (difference) Absolue Relaive, %,4-2,62 -,7-2,66 -,36-3,3.28-3,35 -, ,1-4.22, , ,19-4,4,3,38,1,61,,14,6,62,, ,87,17 4,17,6 4,18,13 4,16,7 2.27,1 2,34,2 2,41,2,15,7 8, ,94,17 1,33,2, ,54,84 9,5,8 12,89,14 21,56,1,14,4 2.27,18 3,67,56 4,73,5 4,76,11 7,12 32

18 Evaluaing forecasing models for unemploymen raes by gender in seleced European counries unemploymen rae forecass for Albania is observed i can be concluded ha an addiional daa poin for 214 resuled in an increase of all he hree observed overall forecasing errors and resuled in he change of he mos appropriae saisical forecasing mehod. Thus, i can be concluded ha he increase of overall forecasing errors by including a new daa poin in he analysis does no have suppor in he misspecificaion and choosing he wrong saisical mehod. The reason for he increase of he overall forecasing error herefore should be in adding a new daa poin. I is possible ha a new daa poin has a srong impac on he model parameers which lead o a differen shape of he forecased model. Consequenly, he forecasing errors also change. Table 7. Comparison of he seleced saisical forecasing model for forecasing male and female unemploymen raes by using daa from 1991 o 213 (approach developed in [8]), and by using daa from 1991 o 214 (longer period approach) in he 12 observed European counries. Male unemploymen rae seleced saisical forecasing models Female unemploymen rae seleced saisical forecasing models Counry 1991 o o o o 214 based forecass based forecass based forecass based forecass Albania Linear rend Quadraic rend Linear rend Quadraic rend Ausria Linear rend Linear rend Bosnia and Herzegovina Croaia Greece Macedonia, FYR Linear rend Linear rend Linear rend Quadraic rend Monenegro Linear rend Exponenial rend Porugal Serbia Slovenia Spain Turkey Quadraic rend Linear rend Quadraic rend Quadraic rend Quadraic rend Quadraic rend 33

19 K. Dumičić, B. Žmuk and A. Čeh Časni CONCLUSIONS In his aricle shor-run forecass of male and female unemploymen raes for he seleced group of European counries using hisoric ime series daa for 1991 o 213 is performed, and o he unemploymen raes in he group of he Easern Balkan counries are compared. The accuracy of predicions by adding a new daa poin, for 214, and by comparing our esimaes wih relevan research by [8], which was developed for he period from 1991 o 213 only, is evaluaed. According o he empirical analysis and 1991 o 214 based forecass, he linear rend and he quadraic rend were he bes forecasing models for forecasing male unemploymen raes in only wo observed counries, he rend in only one counry, and he double was he bes forecasing model for forecasing male unemploymen raes in seven observed counries. In he case of forecasing female unemploymen raes, only wo forecasing models seem o be he bes choice. Namely, he quadraic rend was he bes forecasing model for forecasing female unemploymen raes in five counries whereas he double was he bes forecasing model for unemploymen raes in seven counries. Adding a new daa poin has a srong impac on he model parameers which may lead o a differen shape of he bes forecasing model and, as a resul, o he changed forecasing errors. This research raised a number of quesions ha sill have o be answered, offering a good basis for furher research. Thus, fuure research migh focus on he impac of a new daa poin on he forecasing model shape. In ha way he exac change of rend values and forecass as a consequence of adding new daa poins can be esimaed. Furhermore, in order o selec he bes saisical forecasing model o perform forecass he believabiliy crieria insead of he smalles overall forecasing error crieria should also be aken ino accoun. REFERENCES [1] Simonescu, M.: The improvemen of unemploymen rae predicions accuracy. Prague Economic Papers 24(3), , 215, hp://dx.doi.org/ /j.pep.519, [2] Nasir, M.N.M.; Hwa, K.M. and Mohammad, H.: An Iniial Sudy on he Forecas Model for Unemploymen Rae. Saisics Malaysia Journal of he Deparmen of Saisics 1(1), 27-43, 28, [3] Simonescu, M.: The Performance of Unemploymen Rae Predicions in Romania. Sraegies o Improve he Forecass Accuracy. Review of Economic Perspecives Národohospodářský Obzor 13(4), , 213, [4] Simonescu, M.: The Accuracy and Bias Evaluaion of he USA Unemploymen Rae Forecass. Mehods o Improve he Forecass Accuracy. Annals of he Universiy of Peroşani, Economics 12(4), 17-32, 212, [5] Brau, M. and Marin, E.: Shor run and alernaive macroeconomic forecass for Romania and sraegies o improve heir. Journal of Inernaional Sudies 5(2), 3-46, 212, hp://dx.doi.org/ / /5-2/4, [6] Nkwaoh, L.S.: Forecasing Unemploymen Raes in Nigeria Using Univariae Time Series Models. Inernaional Journal of Business and Commerce 1(12), 33-46, 212, [7] Voineagu, V.; Pisica, S. and Caragea, N.: Forecasing monhly unemploymen by economeric echniques. Economic compuaion and economic cyberneics sudies and research / Academy of Economic Sudies 3(3), , 212, 34

20 Evaluaing forecasing models for unemploymen raes by gender in seleced European counries [8] Dumičić, K.: Developing Forecasing Models for Unemploymen Rae by Gender: Cross Counries Comparison. Proceedings of he World Saisics Congress WSC ISI'215, Rio de Janeiro, 215, hp:// er/284/1592/pp-a1-p12-s.pdf, [9] The World Bank: World Developmen Indicaors. hp://daabank.worldbank.org/daa/repors.aspx?source=world-developmen-indicaors, [1] The World Bank: GDP per capia growh (annual %). hp://daa.worldbank.org/indicaor/ny.gdp.pcap.kd.zg?end=215&name_desc=false&sar =1961&view=char. 35