Annals of he Universiy of Peroşani, Economics, 10(4), 010, 337-346 337 THE ECONOMETRIC ANALYSIS OF THE DEPENDENCE BETWEEN THE CONSUMER, GDP AND THE INTEREST RATE USING THE EVIEWS PROGRAM NADIA ELENA STOICUŢA, ANA PETRINA STANCIU * ABSTRACT: In his paper is performed an economeric analysis of he dependence beween of consumpion, GDP and ineres raes of 15 European Union counries over a period of hree years. The main purpose of his paper is o show how his can be done using he Eviews program, he seps ha we mus go hrough his program and o forecas achievemens of he phenomenon sudied. KEY WORDS: Gross Domesic Produc (GDP); Mehod of Leas Squares (MLS); Ordinary Leas Squares (OLS); Eviews Program JEL CLASSIFICATION: C4, E0, E43 1. INTRODUCTION The subjec refers o he dependency analysis a European level beween he consumpion per capia, GDP per capia and he ineres rae, from he Keynesian heory of consumpion funcion, inerpreed as a linear dependence beween privae consumpion and disposable income. Theoreically, his dependence is posiive and can be measured by he marginal propensiy o consumpion which shows how much of each addiional moneary uni perquisie will be spen on consumpion. Typically, he economies of developed counries are characerized by lower values of BMI. For his economeric analysis were used as daa sources 15 Member Saes of he European Union for a period of hree years and has as endogenous variable he consumpion per capia and as exogenous variables he GDP and ineres rae. * Assis.Prof., Ph.D. Suden, Universiy of Peroşani, Romania, andnadia@yahoo.com Assis.Prof., Ph.D. Suden, Universiy of Peroşani, Romania, sanciu.anaperina@yahoo.com
338 Soicuţa, N.E.; Sanciu, A.P. The measuring uni used for all he daa is Euro per capia made a curren prices. For his reason, daa have been resaed wih he Consumer Price Index o provide comparable prices in 000 and o ensure comparabiliy of daa. The daa o be processed are given in Table 1. Table 1. The daa o be processed 000 001 GDP / CONSUM/ INTR./ RATE GPD / CONSUM/ INTR./ RATE Bulgaria 1700,00 1500,00 0,00 1780,69 1593,5 0,00 Czech Republic 6000,00 4400,00 7,50 648,36 4671,1 5,75 Denmark 3500,00 3700,00 5,40 368,93 3804,88 3,60 Esonia 4500,00 3400,00 0,00 4843,30 3608,74 0,00 Cyprus 14500,00 11700,00 7,00 14893,6 1088,97 5,50 Lavia 3600,00 3000,00 5,50 3933,14 344,84 5,50 Lihuania 3500,00 3100,00 10,38 3915,66 3413,65 5,50 Hungary 5000,00 3700,00 13,75 57,73 4000,00 11,5 Mala 10800,00 9100,00 5,30 10551,79 9196,5 4,80 Poland 4900,00 4000,00 3,00 5410,63 4444,44 15,50 Romania 1800,00 1600,00 35,00 1451,38 133,67 35,00 Slovenia 10800,00 800,00 11,00 10487,58 8003,68 1,00 Slovakia 4100,00 3100,00 9,5 4190,48 338,10 9,00 Sweden 30000,00 700,00 4,75 7663,73 081,11 4,50 Unied Kingdom 700,00 900,00 6,00 78,1 3114,59 4,00 00 GDP / CONSUM/ INTEREST RATE Bulgaria 1885,19 1705,65 0,00 Czech Republic 733,13 5378,48 3,75 Denmark 3806,43 417,98,95 Esonia 540,18 3953,1 0,00 Cyprus 15003,71 143,45 5,00 Lavia 3986,9 331,91 5,00 Lihuania 4308,65 3707,44 10,00 Hungary 5897,7 4465,41 9,50 Mala 10599,8 8817,55 4,30 Poland 5199,6 4443,31 8,75 Romania 1301,15 113,7 0,40 Slovenia 10506,54 7858,55 10,50 Slovakia 4399,84 3483,0 8,00 Sweden 8478,84 1743,98 4,50 Unied Kingdom 7359,50 3464,57 4,00 Daa Source: Eurosa
The Economeric Analysis of he Dependence beween he Consumer 339 Nex is presened he mahemaical model of hese applicaions wha s nex o being solved using Eviews 7.0 sofware package.. THE MATHEMATICAL MODEL In his economeric model he following noaions are used for he variables ha ener ino is composiion: - C is he oal consumpion per capia; - GDP is Gross Domesic Produc per capia; - RATA. is he ineres rae. Using he variables above, we define he following economeric model: C = b + a GDP + c RATA +ε (1) where a,b and c are he parameers o be deermined afer applying he mehod of leas squares. Nex we analyze descripively he daa ses used in his model. Therefore, afer processing he wo daa ses, we obain informaion on he saisical indicaors ha are conained in he graphs below: 4 0 16 1 8 4 0 0 5000 10000 15000 0000 5000 Series: CONS_L Sample 1 45 Observaions 45 Mean 850.131 Median 4443.310 Maximum 417.98 Minimum 113.74 Sd. Dev. 7819.53 Skewness 1.114377 Kurosis.657091 Jarque-Bera 9.53447 Probabiliy 0.008505 Figure 1. The descripive saisics for Consumpion per capia 14 1 10 8 6 4 0 0 10000 0000 30000 Series: PIB_L Sample 1 45 Observaions 45 Mean 10797.66 Median 5410.68 Maximum 3806.43 Minimum 1301.155 Sd. Dev. 10141.09 Skewness 1.168514 Kurosis.843494 Jarque-Bera 10.8661 Probabiliy 0.005838 Figure. The descripive saisics for GDP per capia 1 10 Series: RATA_D Sample 1 45 Observaions 45 8 6 4 0 0 5 10 15 0 5 30 35 Mean 8.05889 Median 5.500000 Maximum 35.00000 Minimum 0.000000 Sd. Dev. 7.669418 Skewness.096554 Kurosis 7.798606 Jarque-Bera 76.14144 Probabiliy 0.000000 Figure 3. The descripive saisics for he benchmark ineres rae
340 Soicuţa, N.E.; Sanciu, A.P. To es he normal disribuion of he hree daa ses, we presen he hisogram of he hree series in which is observed he mean, median, minimum and maximum values, sandard deviaion, coefficien of asymmery, kurorica, and Jarque-Bera es. In he hisograms presened above, we see ha he disribuions of consumpion, GDP and ineres raes are plaikuroic (kuroica <3). In a lepokuroic disribuion, he probabiliy of occurrence of an exreme even is higher han he probabiliy of occurrence of ha even, implied by a normal disribuion. Therefore, he evaluaion models can cause errors assuming a normal disribuion of GDP. The Jarque-Bera coefficien, is esing if a disribuion is normally disribued. The es measures he difference beween he coefficien of asymmery and he kuroica of disribuion analyzed wih he normal disribuion. The es has he null hypohesis: he series is normally disribued. Thus, if he probabiliy associaed o he es is superior o he relevan level (1%, 5% or 10%), hen he null hypohesis is acceped. In he example above, as he probabiliy value is less han 10%, we can say wih cerainy ha he null hypohesis is rejeced. From he analysis of he corelograms i is seen ha beween he wo variables (consumpion and GDP) is a direc link and ype of link is one linear, his can be seen in he graphic represenaion of he cloud daa. Figure 4. Graphical represenaion of he cloud daa for he wo variables Afer descripive analysis of daa series, in wha follows we will acually solve he economeric model given by (1). To deermine hose hree parameers, we use he mehod of leas squares and we use he following command in EViews: ls cons_l c pib_l raa_d. The values of he parameers a, b and c are deermined using he mehod of leas squares using he Eviews, and are given in Figure 5. Wihin his, we see ha he sraigh regression given by he equaion (1) can be wrien as following: C = 46.0538 + 0.767030 GDP - 3,34870 RATA ()
The Economeric Analysis of he Dependence beween he Consumer 341 Also, for each independen and consan variable, EViews repors he sandard error of he coefficien (Sd. Error), he - Saisic es and probabiliy associaed wih i. Figure 5. Eviews window o deermine he parameer values of he mahemaical model Eviews, (also repors R value) (R-Squared) ha shows wha percenage of he oal variance of he dependen variable is due o he independen variable. This coefficien is aking values beween 0 and 1 and if i s closer o 1, he regression is well deermined. As in his case, R has a value of 0.991448 herefore he above condiion is saisfied. For like he model o be valid, in he following we check he assumpions he model linear regression. 3. THE CHECKING OF THE ASSUMPTIONS OF THE MODEL OF LINEAR REGRESSION Tesing he validiy of assumpions made in he linear regression model is similar o auocorrelaion analysis, he normaliy and heeroskedasiciy. 31. The average error is zero To es his hypohesis we perform hisogram of errors, highlighing he average of he errors. In he hisogram of errors we noice ha he average is 1,87 10 1, which means ha errors are normally disribued, ie normaliy is checked, so he Mean of he errors is approximaely zero.
34 Soicuţa, N.E.; Sanciu, A.P. 3.. The series of errors is homoscedasic Figure 6. The hisogram of he erors The verificaion of he homoscedasic errors hypohesis for his model will be done using Whie es.by using Eviews program he following resuls were opained: Figure 7. The check of he hypohesis of homoscedasiciae model: The Whie es is a saisical es ha is based on he following regression 0 1 3 _ r = a + a GDP L + a GDP L + a GDP L RATA_ D + (3) + a RATA_ D + a RATA_ D 4 5
The Economeric Analysis of he Dependence beween he Consumer 343 Afer running he EViews program, parameers are esimaed using ordinary leas squares (OLS): r = -3313,5+ 10,6188 GDP _ L - 0.000111 GDP _ L - -5,349450 GDP _ L RATA _ D + 936,740 RATA _ D + 147,9055 RATA _ D (4) Analyzing he indicaors F-Saisic and Obs*R_squared and comparing hem wih he abulaed values, resuls: F S =7,57 > F 0,05;;10 = 3,3 and LM =,17 > χ 0,005; = 5,99 ha indicaes us he exisence of heeroskedasiciy, herefore we smus use oher mehods for esimaing he parameers. 3.3. Non-auocorrelaion of he error The verificaion of he hypohessis of independence of errors which implies ha cov( ε, ε -1) =0, is performed using he Durbin-Wason es, consising of calculaing he variable d and comparing i wih wo heoreical values d 1 and d,, from he Durbin Wason disribuion able, according o a significance hreshold α (α = 0.05), he number of explanaory variables k (k = ) and he number of observaions n (n 45). Observaion: he Durbin-Wason able is buil for a number of n 45 observaions; for he lower values will work wih he calculaed values for n = 45, ie d 1 = 1,430 and d = 1,615. Because he calculaed value d = 1,79076 ranges beween he d < d < 4 d =,385 resuls a nonexisen auocorrelaion of errors. 3.4. Daa series for hese feaures are no sochasic Figure 8. The Eviews window presening he covariance marix To do his we mus show ha he variables pib_l and raa_d, are uncorrelaed in oher words cov(pib_l,resid)=0 şi cov(raa_d,resid)=0. To do his we calculae he covariance marix and read he values on he secondary diagonal. We noe ha he values 1.45*10-9 şi 1.4*10-11 are approximaive 0.
344 Soicuţa, N.E.; Sanciu, A.P. 3.5. The explanaory variables are no correlaed wih residual variables To es his hypohesis, he following wo corelogrames mus be creaed: Figure 9. The Eviews window wih presening wo corelograme I is noiced ha he values are uncorrelaed because hey don exceed he confidence band, excep lag 7. 3.6. Among he explanaory variables here is no significan linear dependency Figure 10. Graphical represenaion of he daa cloud of GDP and ineres rae
The Economeric Analysis of he Dependence beween he Consumer 345 To es his hypohesis a poin cloud is made beween explanaory variables raa_d pib_l, where we can observe ha beween GDP and ineres rae here is no linear link, ie a sraigh line can' go hrough a daa cloud leaving ou a smaller number of poins, wih a smaller error. 3.7. The normaliy of errors Normaliy of errors is seen in he hisogram of errors. The Skewness indicaor isn close o 0 and kurosis is no close o 3, he resul is an error for rejecing he null hypohesis (normal disribuion of p = 0). From he assumpions above, we conclude ha he linear regression model mus be correced o mee he assumpions of a muliple linear regression model, because he admission of his model may cause errors such as: - oversaemen of he deerminaion rapor - he inefficien esimaors in esimaion; - erroneous resuls afer applying he -Suden es indicaing a higher significance of he esimaors Given he above, we sugges a model equivalen o he inerpreaion of elasiciies as: log( CONS _ L = C(1) + C() log( GDP _ L) + C(3) log( RATA_ D), (5) ) i j ij ij Esimaing he parameers using OLS we lead o he following relaion: log( CONS _ L = 0.07648345836 + 0.9685414436 log( GDP _ L) ) ij - 0.008151603069 log( RATA _ D), ij ij (6) This economeric model is beer han he previous one because of he following reasons: - errors follow a normal disribuion, by he medium 0 and he repariion σ - he hypohesis of he auocorrelaion is fulfilled, he Durbin-Wason saisic DW [d L, 4-d U], shows no auocorrelaion - he hypohesis of he homoscedasiciae is fulfilled. 4. MAKING FORECAST Applying his model on he series of known daa, ie GDP and ineres raes in 003, we can predic his year's consumpion for hree counries: Hungary, Poland and Unied Kingdom. Afer running he EViews program, he following prognoses were exraced: - For Hungary: he consumpion is 5441.164895 having an error of approx. 15% - For Poland: he consumpion is 4447.89486 having an error of approx. 8% - For Unied Kingdom: he consumpion is 379.98065 having an error of approx. 15% In making he predicions on his economeric model, we noe ha his model has o be improved o achieve a probabiliy value under 5%.
346 Soicuţa, N.E.; Sanciu, A.P. 5. CONCLUSIONS Based on he model above can be seen ha in Romania he ineres rae correlaes well wih he growh rae of GDP. This rae decreases when he oal expendiure increases, due o increased consumpion. This conclusion emerges from he annual BNR references from 000 o 003 where we can see ha beween he GDP and he ineres rae here is an inverse relaion, meaning ha as he ineres rae decrease (in 000 he average ineres rae decreased from 46.6 o 0.34 in 003) he macroeconomic variable GDP sars o increase (he GDP regarding he prices raised from 803773 billion in 000 and 1890778 billion in 003). REFERENCES: [1]. Andrei, T.; Bourbonnais, R. (008) Economerie, Ediura Economică, Bucureşi []. Greene, W.H. (000) Economeric Analysis, 5h ediion, Prenice Hall Inc, [3]. Migliarino, A. (1987) The Naional Economeric Model, A Layman s Guide Graceway Publishing [4]. Soicuţa, N.; Bilă, A.M.; Soicuţa, O. (009) Adjusing economic of he Romania s GDP using economeric model of he sysem: budge expendiure-gdp, Annals of he Universiy of Perosani, Economics, 9(), pp. 91-300 [5]. Soicuţa, N. (009) Economeric modeling of he energy sysem of he European Union, Inernaional Scienific Conference XXIII. microcad [6]. Suis, D.B. (196) Forecasing and Analisys wih an Economeric Model, American Economic Review, marh, pp. 104-13 [7]. Terisco, M.; Soica, P. (1980) Idenificarea si esimarea paramerilor sisemelor, Ediura Academiei, Bucuresi [8]. Vogelvang, B. (005) Economerics-Theory and Applicaions wih Eviews, Prenice Hall [9]. hp://epp.eurosa.ec.europa.eu