SPECIFICS OF THE APPLICATIONS OF MULTIPLE REGRESSION MODEL IN THE ANALYSES OF THE EFFECTS OF GLOBAL FINANCIAL CRISES

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1 Croatian Operational Research Review (CRORR), Vol., SPECIFICS OF THE APPLICATIONS OF MULTIPLE REGRESSION MODEL IN THE ANALYSES OF THE EFFECTS OF GLOBAL FINANCIAL CRISES Željko V. Račić Facult of Economics Banja Luka Majke Jugovića 4, 78 Banjaluka, Bosnia an Herzegovina Phone: ; Biljana T. Baraković Universit for usiness stu Banja Luka Jovana Dučića a, 78 Banjaluka, Bosnia an Herzegovina Phone: ; Astract This paper aims to present the specifics of the application of multiple linear regression moel. The economic (financial) crisis is analze in terms of gross omestic prouct which is in a function of the foreign trae alance (on one han) an the creit cars, i.e. ineteness of the population on this asis (on the other han), in the USA (from 999. to 8). We use the extene application moel which shows how the analst shoul run the whole evelopment process of regression moel. This process egan with simple statistical features an the application of regression proceures, an ene with resiual analsis, intene for the stu of compatiilit of ata an moel settings. This paper also analzes the values of some stanar statistics use in the selection of appropriate regression moel. Testing of the moel is carrie out with the use of the Statistics PASW 7 program. Ke wors: Multiple linear regression moel, statistical tests, coefficient of etermination, F scheule.. THE SEPARATION OF THE REAL SECTOR AND THE FINANCIAL SECTOR.. IDENTIFY AND ANALYZE CAUSES OF THE LAST ECONOMIC CRISIS ON A GLOBAL LEVEL The starting point of our analsis is the assertion that the great economic crisis is cause the separation of the real sector an the financial sector. First, we analze ata from BEA agencies for the perio from 99 to 8. These ata show us that the U.S. international trae in goos recore a negative sign from ear to ear, et the international trae in services recore a positive sign. This figure shows a ecline in the real sector, on the other han the growth of the service sector, in which we inclue the anking sector. 7

2 Croatian Operational Research Review (CRORR), Vol., These ata show us that at one point there was separation of real sector an the financial sector, which ultimatel resulte in the emergence of the gloal crisis. In further analsis we come to the conclusion that the main culprits of the last crisis are American consumers who on average have 9 creit cars, so the repai the loan from the first creit car with loan from another car, there making a vicious financial circle that eventuall collapses like a house of cars. The collapse comes at a time when funs remain full capture in the financial sector. In fact, consumers at one moment are not using the mone from creit cars to purchase goos, the are using them to cover the et on creit cars. Reuction of purchasing goos causes reuction in eman of those goos (proucts). Decline in eman for proucts from the real sector has the causal effect on the reuction of prouction an therefore the emergence of high unemploment an reuce of the gross omestic prouct. Article conclues with what extent the reuction of export proucts from the real sector an alance on creit cars affect the movement of gross omestic prouct. Possile evelopment irections are relate to making efficient management of the finance sector an limiting the numers an opportunities of using creit on creit cars. These irections lea us to the appearance of state intervention.. THE APPLICATION OF MULTIPLE REGRESSION PROCEDURES.. ANALYSES OF THE EFFECTS OF GLOBAL FINANCIAL CRISES Our application is ase on analses of the economic (financial) crisis in terms of gross omestic prouct as epenent variale, which is in a function of the foreign trae alance (on one han) an the creit cars, i.e. ineteness of the population on this asis (on the other han), as inepenent variales, in the USA for the perio from 999 to 8. First, we analze BEA ata for U. S. International Trae in Goos an Services for perio from 999 to 8. Here we can conclue that trae in goos has negative sign, which means that import of goos is igger than exports of goos, an trae in services has positive sign, which means that export of services is igger than import of services. This le us to conclusion that there was a isturance in the real sector. The real sector is the asis for economic evelopment, so earing this in min, we continue with further analsis. The aim of further analsis is to etermine wh there was a growth of trae in services an ecline of trae in goos. In further analses we use ata aout consumer creit in the perio from999 to 8. 8

3 Croatian Operational Research Review (CRORR), Vol., Tale : U.S. International Trae in Goos an Services for perio from 999 to 8. (in millions of ollars) Source: The Bureau of Economic Analsis BEA Tale : Consumer Creit: ( in illions of ollars) * Authors ajustments of ata for 999 an 8 (ajustments are for analses; other ata are from Feeral Reserve Sstem) Source: Boar of Governors of the Feeral Reserve Sstem, 6 th March 8. We use ata from Eurostat, the Statistical Office of the European Commission, which give us percentatage change of GDP volume for the Unite States in perio from 999 to 8. Business an economic analsis has certain unique characteristics in comparison with the analsis that is one in other isciplines. Multiple regression is a ver important tool for economists. We egin with the implementation which illustrates an important task of regression moel specifications. Moel specification inclues selection of exogenous variales an functional forms of moels. The economic crisis is analze in terms of GDP (epenent variale, Y ) which is in a function of the foreign trae alance (inepenent variale, ) an creit ineteness of people in the U.S. (inepenent variale, ) for the perio from 999. to 8. 9

4 Croatian Operational Research Review (CRORR), Vol., Tale 3: Growth rate of GDP volume percentage of change on previous ear Percentage change of USA GDP on previous ear 999 4,8 4,,,8 3,5 4 3,6 5 3, 6,7 7, 8,4 Source: Eurostat, 9. From these ata we can see ecrease of GDP from ear to ear. The analsis of efine prolem an selection of variales efine the specification of the moel in general form: () The moel specification strateg was conitione the goals we want to achieve. One goal was to preict the epenent or output variale, GDP. Another ojective was to assess the marginal effect of each inepenent variale. Marginal change is more ifficult to assess ecause the inepenent variales are associate not onl with the epenent variale ut also with each other. If two or more inepenent variales change in mutual irect linear relationship, it is ifficult to etermine the iniviual effect of each inepenent variale on epenent variale. Now we will consier a multiple regression moel in more etail. The coefficients j represent the evaluation of the unknown parameters an the are erive ase on the expressions elow. The meaning of these coefficients is analogous to the meaning of the coefficients in the simple linear moel. For example, coefficient inicates the expecte values of epenant variale in the case where oth inepenent values are equal zero, while coefficients an show average change of epenent variale (occurrence of Y) with the unit shift of one of the epenent variales, respectivel. Therefore, we have Yˆ () (3) (4) 3 x x ( ( ) )

5 Croatian Operational Research Review (CRORR), Vol., (5) (6) (7) Y Y Solving this moel, we have:, ,7775., We otain the following moel Yˆ,945,8, 775. Since coefficient inicates the expecte value of the epenent variale in the case where oth inepenent values are equal to zero, the value,945 inicates that the value of the epenent variale can e expecte at this level with zero-level inepenent variales. Value, 7775 inicates the average change (increase) in GDP when the foreign trae alance increases the unit, provie that creit ineteness remains unchange (this is a irect relation etween the epenent an inepenent variales). B analog,, inicates the average change of GDP when creit ineteness increases the unit an the foreign trae alance remains constant (this is the inverse relation etween the epenent an inepenent variales ecause the regression coefficient has a negative sign). Since the regression coefficients are asolute inicators, the phenomena inclue in the moel are commonl reporte in ifferent measurement units, an it oes not make sense to use them to compare their mutual influence of inepenent variales on the epenent variale. In the analsis we introuce the coefficient of multiple etermination to explain the variation percentage of GDP, explaine the mutual influence of inepenent variales inclue in the moel: (8) R Y /,68. The coefficient of multiple etermination inicates that 68% of the variance of GDP is explaine the mutual influence of the foreign trae alance an creit ineteness. What remains, i.e. 3 %, is the share of unexplaine variailit an shows the influence of those factors not inclue in the moel. To use a previousl shown regression equation for assessing an preicting the value of GDP, first we must test the significance of overall moel. To test the valiit of the moel, we use the F scheule. As realize value F 7, 34 is greater than tale value 3, 74 (with a 5% risk, f: an 4), we conclue that we shoul 3

6 Croatian Operational Research Review (CRORR), Vol., reject the null hpothesis (that the foreign trae alance an creit ineteness o not affect the GDP), i.e. that the moel is aequate. The secon part of the paper is evote to the analsis of the economic crisis in terms of GDP (the epenent variale, Y ) which is in a function of the foreign trae alance (the inepenent variale, ) an the ineteness of population of the Unite States on creit cars (as the most important part of the creit ineteness of people from the first part of the analsis, the inepenent variale, ) for the perio from 999. to 8. 3 Tale 4: Foreign Trae alance an Creit Cars et outstaing Years GDP (%) Foreign Trae alance (importexport) in mil. $ Ineteness of the population on creit cars in illions $ 999 4, , , , , , , , , , Total 6, Source: Eurostat 9, The Bureau of Economic Analsis BEA, The Nilson Report, Carpinteria, CA, Twice-monthl newsletter We otain the following moel Yˆ 5,76,, 39 Now we can interpret the meaning of the coefficients. The coefficient shows that with zero-level inepenent variales the value of the epenent variale can e expecte on the level of 5,76. The value,8 inicates the average change (increase) in GDP when the foreign trae alance increases the unit, provie that ineteness of the population on creit cars remains unchange (this is a irect relation etween the epenent an inepenent variales). B analog,, inicates the average change of GDP when ineteness of the population on creit cars increases the unit an the foreign trae alance remains constant (it is the inverse relation etween the epenent an inepenent variales ecause the regression coefficient has a negative sign). In this case the coefficient of multiple etermination is otaine in this wa:.

7 Croatian Operational Research Review (CRORR), Vol., The coefficient of multiple etermination inicates that 58 % of the variance of GDP is explaine the mutual influence of the foreign trae alance an ineteness of the population on creit cars. What remains, i.e. 4 %, is the share of unexplaine variailit an shows the influence of those factors that are not inclue in the moel. To test the valiit of the moel, we use the F scheule. As realize value F 4, 93 is greater than the tale value 4, 74 (with a 5% risk, f: an 7), we conclue that we shoul reject the null hpothesis (that the foreign trae alance an ineteness of the population on creit cars o not affect the GDP), i.e. that the moel is aequate. CONCLUSION In this paper we have presente the necessar founations for the application of multiple regression proceures. The aim is to ientif an analze causes of the last economic crisis on a gloal level, ase on theoretical an methoological research, as well as their impact on the reuction of economic activities of moern economies. The practical contriution of the paper is reflecte in the creation of new empirical evience which prove that the ecrease of exports an excessive creit orrowing are the ke riving factors causing last gloal crisis. Polic makers are to use our results to focus their activities in this irection. REFERENCES R Y Anerson, D. (3). An introuction to management science Quantitative approaches to ecision making, th eit., Thomson, South Western, Ohio. Everitt, B.S. (6). The Camrige Dictionar of Statistic, Camrige Universit Press, The Einurgh Builing, Camrige c ru, UK Hiller, F.S. an Lieerman, G.J. (5). Introuction to operations research, Seventh Eition, McGraw-Hill, New York. Hwang, CH-L. an Yoon, K. P. (6). Multiple attriute ecision making, Methos an applications, Springer-Verlag, Berlin Heielerg New York. Kollo, R., an Rosen, von D. (5). Avance Multivariate Statistics with Matrices. Dorrecht, The Netherlans. Komić, J., Lovrić. M, Stević, S. (5). Statistička analiza. Ekonomski fakultet, Banja Luka Newol, P., Carlson, W. an Thorne, B. (7), Statistics for usiness an economics, Prentice Hall, New Jerse. /,

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