ESTIMATING AVERAGE VALUE OF NIGERIA GDP USING DUMMY VARIABLES REGRESSION MODEL

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1 European Journal of Saisics and Probabiliy Published by European Cenre for Research Training and Developmen UK ( ESTIMATING AVERAGE VALUE OF NIGERIA GDP USING DUMMY VARIABLES REGRESSION MODEL Alabi Oluwapelumi*, Olarewaju kayode Joseph Deparmen of Mahemaics and Saisics, Rufus Giwa Polyechnic, Owo, Ondo Sae ABSTRACT: Dummy variables assign he numbers 0 and 1 o indicae membership in any muually exclusive andexhausive caegory. The number of dummy variables necessary o represen a single aribue variable is equal o he number of caegories in ha variable minus one. In his sudy, dummy variables regression analysis was applied o esimae he average GDP a various quarers; he GDP daa was described and graphically presened. A regression model was esimaed o deermine he average value for each quarer, he seasonal componen, and average GDP confidence inerval. The sudy provides he seasonal predicion and revealed ha he average GDP in he second, hird and fourh quarers are no saisically difference excep he firs quarer. The resul of he sudies showed ha Nigeria realised he highes income generaed by producions and services in he counry in he fourh quarer of every year. KEYWORDS: Dummy Variables, Average GDP, Seasonal Componen and Time Series INTRODUCTION Time Series A ime series is defined as a se of daa colleced sequenially in ime. Many economic ime series based on monhly or quarerly daa exhibi seasonal paern. Ofen i is desirable o remove he seasonal componen, from a ime series so ha one can concenrae on he oher componens, such as he rend. The process of removing he seasonal componen from a ime series is known as seasonal adjusmen, and he ime series hus obained is called he seasonally adjused, ime series. Imporan economic ime series, such as GDP, are usually published in seasonally adjused form. There are several mehods of deseasonalizing a ime series, bu in his sudy, based on he ime series daa of Nigeria GDP from 2010 o 2015, we consider he dummy variable regression model o firs esimae he average value of Nigeria GDP of various quarers (from firs quarer of 2010 o fourh quarer of 2015). On he oher hand, his average values are used o esimae he seasonally adjused value of he GDP. The dummy variables echniques is only appropriae for a ime series presened in addiive model of he form Y s c u (1) 13

2 European Journal of Saisics and Probabiliy Published by European Cenre for Research Training and Developmen UK ( where Y is he observed values, s represens he seasonal, he rend, c he cyclical, and u he random componen. However, if he model is muliplicaive of he form Y s )( c )( )( u ) (2) ( he echnique of dummy variables is inappropriae (Gujarai, 2004 p. 315). Gross Domesic Produc The Gross Domesic Produc is one way o measure he well being of a sae s ciizen. Economic growh refers o GDP; which measure he oal final oupu of goods and services produced by an economy, ha is, wihin a counry s erriory by residens and non-residens, regardless of is allocaion o domesic and foreign claims. I s calculaed wihou making deducion for depreciaion. The World Bank repored ha he GDP in Nigeria was worh billion US dollars in 2015, represens 0.78% of he world economy. The Nigeria GDP averaged billion US dollar from he period gained independen o In he firs hree monhs of 2016, he Nigeria GDP conraced by 0.36% year on year compared o 2. 11% expansion in previous period and below forecas of 1.7% growh. I is he firs conracion since he second quarer of 2004 as he non-oil secor conraced, mainly as a resul of slowdown in he service secors due o weakening naira and lower oil prices keep dragging he oil secor down and Governmen revenue. Dummy Variables In saisics and economerics, paricularly in regression analysis, a dummy variable is an arificial variable creaed o represen an aribue wih wo or more disinc caegories. I akes he value 0 or 1 o indicae he absence or presence of some caegorical effec ha may be expeced o shif he oucome. Dummy variables are used as devices o sor daa ino muually exclusive caegories. In a regression model, a dummy variable wih a value of 0 will cause is coefficien o disappear from he equaion. Conversely, he value of 1 causes he coefficien o funcion as a supplemenal inercep, because of he ideniy propery of muliplicaion by 1. This ype of specificaion in a linear regression model is useful o define subses of observaions ha have differen inerceps and/or slopes wihou he creaion of separae models. Charles (1970) considered five separae models o demonsrae, using numerical examples, he implicaions and inerrelaionships among various models which incorporae dummy variables. The oucome of his sudy reveals ha The independen esimaion of each qualiaive or cross secional group will give he bes possible esimaes of he parameers. The R 2 will probably be lower han wih oher proper mehods and degree of freedom may be a problem. 14

3 European Journal of Saisics and Probabiliy Published by European Cenre for Research Training and Developmen UK ( The (0,1) dummy variable o allow for inercep changes is proper only if some a priori knowledge exiss o jusify he asserion ha funcion are parallel. When daa are ime series as well as eiher qualiaive or cross secional in naure, he saisical procedure should ake accoun of boh aspecs Gujarai (2004 p.305) discussed ANOVA models of he ype relaed o dummy, alhough common in fields such as sociology, psychology, educaion, and marke research, are no ha common in economics. Typically, in mos economic research a regression model conains some explanaory variables ha are quaniaive and some ha are qualiaive. Regression models conaining an admixure of quaniaive and qualiaive variables are called analysis of covariance (ANCOVA) models. ANCOVA models are an exension of he ANOVA models in ha hey provide a mehod of saisically conrolling he effecs of quaniaive regressors, called covariaes or conrol variables, in a model ha includes boh quaniaive and qualiaive, or dummy, regressors. Sraegy researchers ofen make use of dummy variables o sudy sraegic responses or orienaions. McGahan and Michell (2003) discuss how firms change in he face of consrains o change. They argue ha insead of examining he differen ways in which firms respond o consrains, i is worhwhile invesigaing wheher responses are pah-independen or pah-dependen. Each of hese wo ypes of responses can be represened by a dummy variable. The Makino e al. (2004) sudy of foreign affiliaes of Japanese firms indicaes ha counry effecs are as srong as indusry effecs as predicors of business uni performance. Similarly, culural influences have been found o affec performance (Barkema e al., 1996). These resuls sugges ha counry dummies or culural block dummies may have o be included in empirical sudies. Paul and Eric (2007) discuss wo approaches of enering dummy variables ino a regression and heir associaed inerpreaions and some common misakes of inerpreaion and hypohesis esing found in wo recenly published sraegy papers, and highligh he advanages of heir recommended approach over he approach usually adoped by managemen researchers. Their argumen show ha he pariion approach will become he preferred way of enering dummy variables ino a regression Alabi (2014) incorporaing dummy variables in regression model o sudy he average inernally generaed revenue and wage bill of he six geopoliical zones in Nigeria, caegorized hem ino six using five dummy variables. From heir resul, i was found ha only souhwes and souhsouh are fairly srong o revenue base while ha of oher four geopoliical zones are relaive low o he wage bill of heir workers. MATERIALS AND METHODS Quarerly values of Nigeria GDP in billion naira, was obained from he Bureau of saisics of Nigeria s 2016 Saisical bullein. In addiion, dummy variables were creaed o caegorize 15

4 European Journal of Saisics and Probabiliy Published by European Cenre for Research Training and Developmen UK ( he GDP o quarerly seasonal variables (i.e Q1, Q2, Q3, Q4). The sample period was from he firs quarer 2010 o fourh quarer Dummy Variable Regression Model The basic mehodological approach was o deermine he seasonal paern in he Nigeria GDP daa associaed wih various quarers and develop dummy variable regression model of he form. GDP D D D u (3) where GDP is he observed value Nigeria GDP, and he D i ' s are he dummies, aking a value of 1 in he relevan quarer and 0 oherwise. The firs quarer Q1 is reaed as reference quarer and assigns dummies o second Q2, hird Q3 and fourh Q3 quarers in order no o suppress he inercep 1. From he model (4), he average value of variable GDP a various quarer can be deermine as follows GDP Q1 1 GDP (4) Q2 1 2 GDP Q3 1 3 where GDP Q GDPQi is he average of GDP from each quarer, 1 is he inercep from he dummy variable regression model, 2, 3, 4 are he slope coefficiens of he dummy variables which ell how mush average GDP in each quarer differ from he reference quarer (i.e firs quarer). The 95% confidence inerval of he average GDP also can be esimaed using CI i z( 1 ) where is he average GDP value a various quarers, z ( 1 ) probabiliy value a 95% i confidence inerval and se is he sandard error of he coefficiens and he saisical significance of he models coefficiens can be deermine base on below hypohesis saemen 16

5 European Journal of Saisics and Probabiliy Published by European Cenre for Research Training and Developmen UK ( 2.2 Hypohesis saemen H 0 i.e no significan difference 0 : H : 0 i.e a leas one coefficien is difference 1 i Decision Rule: Rejec H 0 if P-value < 0.05 Jarque Bera (JB) Tes of Normaliy The JB es of normaliy based on he OLS residuals. This es firs compues he skewness and kurosis measures of he OLS residuals and uses he following es saisic (20) S JB n 6 2 ( k 3) 24 2 where n = sample size, S = skewness coefficien, and K = kurosis coefficien. For a normally disribued variable, S = 0 and K = 3. Therefore, he JB es of normaliy is a es of he join hypohesis ha S and K are 0 and 3, respecively. In ha case he value of he JB saisic is expeced o be 0. Under he null hypohesis ha he residuals are normally disribued. If he compued p value of he JB saisic in an applicaion is sufficienly low, which will happen if he value of he saisic is very differen from 0, one can rejec he hypohesis ha he residuals are normally disribued. Bu if he p value is reasonably high, which will happen if he value of he saisic is close o zero, we do no rejec he normaliy assumpion. RESULT AND DISCUSSION The analysis is carried ou using R saisical package and he resuls are summarized as follows: Descripive Saisics 17

6 European Journal of Saisics and Probabiliy Published by European Cenre for Research Training and Developmen UK ( Descripion of he Daa N Mean Median SD Skewness Kurosis Figure 1 conains graphical presenaions of Nigeria GDP. The variable exhibis srong upward movemen wih seasonal spikes. Also he descripive saisics look symmeric, as indicaed by he skewness which is closer o zero (0.06), he kurosis is -1.15, while he Jarque-Bera saisics suggess ha he null hypohesis of normaliy has no sufficien reason o be rejeced wih p-value of The GDP series is cenred on a mean, median and sandard deviaion of 19088, 18978, and respecively. 18

7 European Journal of Saisics and Probabiliy Published by European Cenre for Research Training and Developmen UK ( Regression model GDP D D3 3300D 4 (5) valu (11.04) (0.54) (1.04) (1.48) p value (0.00) (0.59) (0.31) (0.15) Table 1: Average value of GDP in Nigeria a various quarers Quarers Year 2015 GDP (in billion naira) Average GDP (in billion naira) Average GDP Confidence Inerval (in billion naira) Q , , Q , Q , Q , Table 2: GDP, Seasonal Componen and Remainder Qr Seasonal Qr Seasonal Year GDP variaion Remainder Year GDP variaion Remainder 2010 I I II II III III IV IV I I II II III III IV IV I I II II III III IV IV

8 European Journal of Saisics and Probabiliy Published by European Cenre for Research Training and Developmen UK ( DISCUSSION From he above resuls, he esimaed consan value of he regression model is he average GDP value (17383) for he firs quarer, since he firs quarer is he reference or benchmark quarer, he coefficiens of he dummies i.e 1205, 2314 and 3300 are he differences beween he firs quarer and second, hird, fourh quarer respecively. The probabiliy value from he analysis show ha he coefficiens of he dummies are saisically significan a 5% significan level, as heir p-values are 59%, 31% and 15% respecively. Therefore, he values of GDP a various quarers are no saisically difference excep he firs quarer ha is significan bu numerically, i can be seen ha he GDP from fourh seasonal quarer has he highes value follow by hird, second and firs quarers respecively. Therefore, he Nigeria GDP normally increases oward he end of every seasons (years) i.e Ocober, November and December. Comparing he esimaed average GDP confidence inerval value o he observed 2015 GDP a various quarers, i can be found ha he observed GDP value which is published by he Naional Bureau of Saisics of Nigeria were fall in he 95% GDP confidence inerval excep he firs quarer value ha is higher han he maximum GDP value in he firs quarer confidence inerval, so i is a successful average value. Table 2 presens he seasonal variaion of he GDP which esimaed from model (5) and seasonally adjused GDP which are simply residuals (remainder) from he regression model (5). This residual is he one refer o he remaining componens of he Nigeria GDP ime series, known as, rend, cycle and random componen. While figure 2 display heir movemen paerns. 20

9 European Journal of Saisics and Probabiliy Published by European Cenre for Research Training and Developmen UK ( GDP. Fied Residual CONCLUSION This sudy esimaing he average Nigeria GDP a various seasonal quarers. The GDP daa from 2010 o 2015 were caegorized ino four quarers (Q1, Q2, Q3 and Q4) using dummy variables. The regression analysis carried ou wih he dummy variables show ha he average GDP in he second, hird and fourh quarers are no saisically difference. Assessing he average GDP value numerically, he fourh quarer provides he highes average GDP. Therefore, Nigeria governmen use o realise highes income generaed by producion in he counry in he fourh quarer of every year. CONTRIBUTION TO KNOWLEDGE This sudy provides informaion on average Nigeria GDP a various quarers. I is exremely useful in formulaion of policies regarding o Nigeria economy. 21

10 European Journal of Saisics and Probabiliy Published by European Cenre for Research Training and Developmen UK ( REFERENCE [1] Alabi Oluwapelumi Incorporaing Dummy Variables in Regression model o Deermine Average Inernally Generaed Revenue and Wage Bills of he Six Geopoliical Zones in Nigeria [2] Barkema, H. G., Bell, J. H. and Pennings, J. M. Foreign Enry, Culural Barriers, and Learning, Sraegic Managemen Journal, : [3] Charles Sappingon A Numerical Example of he Pracical Use of Dummy Variables. Souhern Journal of Agriculural Economics, [4] Makino, S., Isobe, T. and Chan, C. M. Does Counry Maer Sraegic Managemen Journal, : [5] McGahan, A. M. and Michell, W How Do Firms Change in he Face of Consrains o Change Toward an Agenda for Research on Sraegic Organizaion, Sraegic Organizaion, : [6] Paul S. L. Yip and Eric W. K. Tsang Inerpreing Dummy Variables and heir Ineracion effecs in Sraegy Research, Sraegic Organizaion, 2007 Vol 5(l) 22