An econometric analysis of money demand function in Sudan, 1960 to 2010

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1 Journal of Economics and Inernaional Finance Vol. 3(16), pp , 22 December, 2011 Available online a hp:// DOI: /JEIF ISSN Academic Journals Full Lengh Research aper An economeric analysis of money demand funcion in Sudan, 1960 o 2010 Suliman Zakaria Suliman* and Hala Ahmed Dafaalla 1 Deparmen of Quaniaive Analysis, College of Business Adminisraion, King Saud Universiy, (Riyadh), Kingdom of Saudi Arabia. 2 Deparmen of Economerics and Social Saisics, Faculy of Economics and Adminisraive Sciences, Universiy of Bakh Al Ruda, (El Dueim), Sudan. Acceped 12 November, 2011 This sudy is an aemp o es he exisence of a sable money demand funcion in Sudan during he period, 1960 o The money demand funcion includes real money balances, real GD (as scale variable), he rae of inflaion and exchange rae (as opporuniy cos of holding money balances variables). The sudy applies coinegraion and error correcion models o examine he behavior of money demand during he period of analysis, all included variables have been expressed in logarihmic form (wih he excepion of inflaion rae). Based on ime series daa (annually observaions), coinegraion resuls reveal ha here is a long-run relaionship beween real money balances and he explanaory variables. In his long-run relaionship, he esimaed coefficiens are consisen wih he economic heory behind he demand for money. Error correcion model (ECM) has been used o esimae he shor-run money demand funcion, in which he esimaed coefficiens are also consisen wih he economic heory and generally weaker in magniude han hose relaed o he long-run equilibrium. In his sudy, afer incorporaing he sabiliy ess, he empirical resuls show ha he money demand funcion is sable beween 1960 and The sudy concludes ha i is possible o use he narrow money aggregae as arge of moneary policy in Sudan. Key words: Money demand, coinegraion, error correcion, sabiliy, Sudan. INTRODUCTION Over he las few decades, modeling, esimaing and examining he sabiliy of money demand funcion in an economy has become a ferile area for research ha have araced mos aenion of economiss, researchers and policy makers in boh developed and developing counries [for he cases of developed counries, Arango and Nadiri (1981), McNown and Wallace (1992), Hoffman e al. (1995), Bohl (2000) and Gerlach and Svensson (2004). For developing counries, for examples includes, Weliwia and Ekanayake (1998), Arize e al. (1999), and Bahmani-Oskooee and Tanku (2006)], his is simply because empirical esimaion of his funcion is of crucial imporance, paricularly o he policy makers, in ensuring ha moneary policies can be conduced effecively. *Corresponding auhor. Sulimanzakaria9@yahoo.com. Tel: Fax: According o Friedman (1956), money demand funcion assumes ha here is a saionary long-run equilibrium relaionship beween money balances, real income, and he opporuniy cos of holding real balances ha formulaed he demand for money funcion. Since he inroducion of coinegraion analysis by Engle and Granger (1987), his relaionship has received a renewal aenion, paricularly he sabiliy issue of economiss who have warred abou changes in he demand for money, since demand shocks can affec oupu variabiliy and have implicaions for moneary policy; for example, Konolemis (2002) expresses, sabiliy of long run money demand funcion is an imporan facor of long run growh raes of moneary variables. There has always been an exensive lieraure examining he sabiliy of money demand funcions in he conex of developing and developed counries, neverheless, unil recenly, here was very lile research on money demand esimaion in he conex of Sudan

2 794 J. Econ. In. Finance economy. Two earlier works were done by Domowiz and Elbadawi (1987) and Abdel-Rahman (1993), and o he bes of our knowledge, since ha ime, he sabiliy issue has no been probed in he Sudanese conex, his paper aims o address his shorcoming and conribue o he lieraure on he sabiliy/insabiliy of he demand for money in developing counries for he period 1960 o The main purpose of his paper is o reconsider he demand for money in Sudan and es no only is coinegraion properies bu also for is sabiliy over ime. More specifically, he paper ries o answers he quesion: Is here a sable demand funcion for money in Sudan during he period 1960 o 2010? The money demand is consruced by means of coinegraion using annually daa, followed by an error correcion model. LITERATURE REVIEW There has been a vas number of empirical sudies ha has invesigaed he demand for money in boh developed and developing counries. Bahmani-Oskooee and Malixi (1991) esimae he demand for money funcion in 13 developing counries as a funcion of inflaion, real income and he real effecive exchange rae. They conclude ha, ceeris paribus, depreciaion in real effecive exchange rae resuls in a fall in he demand for domesic currency. Kallon (1992) invesigae he sabiliy of Ghanaian demand for real money balances during 1966 o 1986 period. The resuls failed o rejec he null hypohesis of srucural sabiliy. The sudy also finds evidence of he nominal adjusmen specificaion as he appropriae shor-run adjusmen mechanism for he demand for real M1 balances. Furher suggesion of foreign ineres raes no having any significan effec on he demand for money in Ghana was evidenced. Simmons (1992) invesigaed he demand for narrow money for five African counries (Democraic Republic of he Congo, Coe d Ivoire, Mauriius, Morocco and Tunisia) wihin an ECM framework. This sudy emphasizes he role of opporuniy cos variables including he domesic ineres rae and expeced exchange- rae depreciaion. His empirical resuls indicae ha he domesic ineres rae is an imporan deerminan of he demand for money funcions for hree of he five counries, whereas exernal opporuniy cos variables are significan for only one of he ohers. He also finds ha in four ou of five cases inflaion plays an exremely imporan role in deermining he demand for money. radhan and Subramanian (1997) suggesed ha money demand funcion is sable no only wih M1 bu also wih M3 and he error correcion erm for boh M1 and M3 money supply definiions was found ou o be negaive and significan. Nachega (2001) applies a coinegraion analysis and error correcion modeling o invesigae he behavior of broad money demand in Cameroon over 1963/64 o 1993/1994. The coinegraed VAR analysis idenified a sable money demand funcion and an excess aggregae demand relaionship for Cameroon. Furher empirical esimaes provided suppor for boh purchasing power pariy () and an inernaionall Fisher pariy beween Cameroon and France. Mohsen and Charikleia (2005) examined he sabiliy of he demand for moneary aggregaes M1 and M2 in Greece using quarerly daa for he period 1975I o 2002IV. The esimaion mehodology employed he coinegraion analysis approach and he cumulaive sum (CUSUM) and cumulaive sum of squares (CUSUMSQ) ess for he sabiliy of he money demand funcion. The economeric model included a vecor of ineres raes and he real income as he deerminan facors. The esimaion resuls showed ha boh moneary aggregaes are coinegraed wih income and ineres rae. The income elasiciy is posiive while he ineres rae elasiciy is negaive. However, he sabiliy ess revealed ha only M1 is a sable funcion bu no M2. Qayyum (2005) esimaed he dynamic demand for money (M2) funcion in akisan by employing coinegraion analysis and error correcion mechanism. The parameers of preferred model were found o be super-exogenous for he relevan class of inervenions. I was also found ha he rae of inflaion is significan deerminan of money demand in akisan. The analysis reveals ha he raes of ineres, marke rae, and bond yield are imporan for he long-run money demand performance. Ranani (2007) esimaed he demand for money in Iran using he auoregressive disribued lag (ARDL) approach o coinegraion analysis. The empirical resuls showed ha here is a unique coinegraed and sable long-run relaionship among M1 moneary aggregae, income, inflaion and exchange rae. The sudy also found ha he income elasiciy and exchange rae coefficien are posiive, while he inflaion elasiciy is negaive. Afer incorporaing he cumulaive sum (CUSUM) and CUSUMSQ ess, resuls reveal ha he M1 money demand funcion is sable beween 1985 o Recenly, empirical resuls of Inoue and Shigeyuki (2008) indicae ha an equilibrium relaion in money demand exiss only when money supply was defined as M1 and M2, no for M3. Coinegraion es resul indicaes ha a co-inegraing vecor is deeced among real money balance, ineres raes, and oupu when money supply is represened by M1 and M2 bu no long-run equilibrium relaionship is found for M3. Shigeyuki (2008) analyzed he money demand funcion in Sub-Saharan African, his empirical resuls revealed ha here exiss a coinegraing relaionship of he money demand funcion in he Sub-Saharan African region. In oher words, here is a close relaionship beween he money supply and he real economy over he long erm, and monioring money supply promises o play an imporan role in sabilizing he level of prices in his region. Han and ei-tha (2009) indicaed ha ECM

3 Suliman and Dafaalla 795 clearly showed ha here is a long-run relaionship beween real money balances and is deerminans. For he case of Sudan, he sabiliy of money demand was firsly invesigaed by Domowiz and Elbadawi (1987) and Abdel-Rahman (1993). Domowiz and Elbadawi implemen an error-correcion approach o check he sabiliy of money demand funcion over he period 1956 o 1982 using wo merics based on ou of sample forecasing performance. The sabiliy ess of he model proved ha sable demand for money in Sudan exiss. While Abdel-Rahman sudied he demand for narrow money balances o invesigae he effecs of high inflaion on he formulaion of adjusmen and error correcion mechanisms governing basic money demand funcion; he empirical resuls showed ha sources of insabiliy in money demand sem from he occurrence of a high and rapidly acceleraing inflaion. SECIFICATION OF MONEY DEMAND MODEL IN SUDAN While invesigaing he money demand funcion, a criical poin o consider is he idenificaion problem. By his noion, we mean he non-observabiliy of he money demand. We can only measure he quaniy of money supplied. And in his poin, we have o make an imporan supposiion ha he quaniy of money supplied and demanded equal each oher, hus assuming equilibrium in he money marke (Laidler, 1973). Demand for money refers o he funcional relaionship beween he quaniy of money demanded and is deermining facors. There is an exensive lieraure on he heory of his relaionship, he general agreemen in he lieraure is ha a money demand funcion should conain a scale variable relaing o he level of ransacions in he economy and a variable represening he opporuniy cos of holding money. The principal issues in consrucing a demand for money funcion, herefore, relae o he definiion of he money sock (moneary variable) and he appropriae specificaion of scale income and opporuniy cos variables, besides some oher variables ha migh sysemaically affec he demand for money funcion. Moneary variable The definiion of money which will be aken o deal wih in he esimaion of money demand funcion in Sudan is a narrow one, M 1, including currency in circulaion plus demand deposis, as defined by he Cenral Bank of Sudan. The reason is ha he analyical work on M 1 was more amenable o conrol by he moneary auhoriies, also sudies on a number of developing counries indicae ha he models using narrow definiion of money beer han hose employing broad money reflecing he weak banking sysem and low level of financial secor developmen (Moosa, 1992; Hossain, 1994). Scale variable The firs deerminan of he money demand funcion is he scale variable measuring he level of economic aciviy. The holding of money and hus he demand for money are relaed o he volume of he ransacions, using he fac ha he amoun of he ransacions is proporional o he level of income. Eiher a wealh variable or an income variable can be used as a scale variable. Generally, when wealh daa is no available, an income variable like he Gross Naional roduc (GN) or Gross Domesic roduc (GD) can be aken ino consideraion. In our case, he scale variable which will be used in he esimaion process is he Sudanese Gross Domesic roduc (GD), which is based on he naional income accoun. Opporuniy cos variable An opporuniy cos variable in a demand for money funcion is inended o measure he yield on money agains oher asses ha migh be held. In financially developed economies, his variable is usually an ineres rae. However, when dealing wih he case of developing counry like Sudan, where ineres raes were abolished wihin Islamizaion package for he economy effeced in 1984, i would be useful o make use of inflaion rae as he proxy for he ineres rae variable (Many researchers ofen use he inflaion rae as he proxy for he ineres rae variable for example, Bahmani- Oskooee and Tanku (2006) and Budina e al. (2006). The relaionship beween inflaion and he demand for money has been sudied widely. If here are high flucuaions in prices, he rae of inflaion becomes an imporan deerminan of he money demand funcion. Money demand (in real erms) is inversely relaed o expeced inflaion rae, since an increase in inflaion increases he cos of holding money. Because he Sudanese economy is subjec o no only a high degree of price level bu also a high variabiliy in he prices, he price level has a considerable impac on he reurn of financial asses; as money holders will have difficulies in predicing he prices, he risk in saving money will raise and consequenly he holding of money will end o decrease. Oher variables Moreover, aking he currency subsiuion phenomenon ino accoun, many sudies on he demand for money in developing counries ofen include exchange rae variable in money demand funcion. This inclusion of exchange rae variable in he sandard funcion of money demand is firs suggesed by Mundell (1963). Accordingly, he general specificaion of money demand funcion is assumed o ake he following funcional form: M = f ( y, INF, Exch where M is he demand for real money balances founded by dividing nominal money balances (M1) o price index (); y is he real income level which represens he scale variable. INF and Exch are respecively he inflaion and real exchange raes. The exchange rae, here, is defined as he amoun of domesic currency per uni of foreign currency. Therefore, he increase (decrease) of Exch is inerpreed as he depreciaion (appreciaion) of domesic currency agains foreign currency. The long-run money demand funcion, when log ransformed, reads as follows: M = β 0 + β1( y ) + β 2( INF ) + β3( Exch ) + ε where ε represens an error erm which is assumed o be a whie )

4 796 J. Econ. In. Finance Table 1. Augmened Dickey-Fuller (ADF) es for variables in levels. Variable Inercep Trend and Inercep -es saisics Lag lengh -Tes saisics Lag lengh M * 0 y INF exchange * indicaes rejecion of he null hypohesis of uni roo a 10% significan level. Table 2. Augmened Dickey-Fuller (ADF) es for variables in firs difference. Variable Inercep Trend and Inercep -es saisics Lag lengh -es saisics Lag lengh M ** y * ** 1 INF ** ** 0 exchange ** ** 0 * and ** indicaes rejecion of he null hypohesis of uni roo a 10 and 1% significan level, respecively. noise error. Based on he convenional economic heory, he income elasiciy coefficien, β 1, is expeced o be posiive; he coefficien of inflaion, β 2, is expeced o be negaive. For he elasiciy coefficien on he exchange rae variable ( β 3 ), i can be eiher posiive or negaive. If he increase in exchange rae (depreciaion) is perceived as he increase in wealh and leads o he rise of domesic money, he coefficien of exchange rae is posiive. Bu, if he increase in exchange rae leads o he decrease in domesic money demand (currency subsiuion), hen he coefficien of exchange rae is negaive. The coefficiens of variables in logarihms specify he long run elasiciies (ha is, income elasiciy and exchange rae elasiciy), where as he coefficien of he inflaion, which is no expressed in logarihm form, is he long-run semi-elasiciy. The shor-run specificaion of he demand for money in Sudan will be of he following form: M = α + α M + α ( y 1 ) + α 3 ( INF 1 ) + α 4 ( Exch 1 ) + α 5 ECM where variables are as defined earlier. ECM 1 is he error correcion erm (lagged one period). Daa issue The daa which will be used in esimaing money demand funcion in Sudan are annual observaions over he period 1960 o 2010, on real narrow money M1, real GD, exchange rae (official), and inflaion rae. These four series were obained from he Cenral Bank of Sudan (CBoS) saisical annual repors. EMIRICAL RESULTS In he firs sep, he variables are esed for saionariy using Augmened Dickey-Fuller (ADF) ess. The second sep involves esing for coinegraion among he inegraed variables. In his paper, he Johansen (1991) maximum likelihood procedure is used. rovided ha one or more coinegraing relaionships exis, he hird sep of he sandard procedure involves he esimaion of a VEC specificaion conaining he coinegraing relaionship(s), lagged firs differences of he variables in he coinegraing relaionship(s), and any saionary variables hough o influence money demand. Tesing for saionariy A he firs sep, he Augmened Dickey Fuller (ADF) (Dickey and Fuller, 1981) uni roo es is applied o all he variables o es for he saionariy of hese variables. The es is applied o boh he original series (in log form) and o he firs differences. Resuls of his es are repored in Tables 1 and 2, respecively. The resuls, repored in Table 1, indicae ha all he series are non-saionary a heir level when he model only included inercep and also when including rend and

5 Suliman and Dafaalla 797 Table 3. Johansen coinegraion es of he demand for money in Sudan for he period 1960 o Eigen value Likelihood raio 5% criical value 1% criical value Hypohesized no. of CE(s) None** A mos 1* A mos A mos 3 *(**) denoes rejecion of he hypohesis a 5% (1%) significance level. Table 4. Normalized coinegraed coefficiens. M y exchange Inflaion Consan inercep. The only excepion is ha M is saionary in he laer case. On he oher hand, when aking he firs difference of he variables, Table 2 shows ha he variables become saionary which mean ha, hese series are inegraed of order one, I(1). Coinegraion analysis of real money demand funcion in Sudan 1960 o 2010 The coinegraion resuls are presened in Table 3. According o he resuls, he hypohesis ha no coinegraing vecor exiss is rejeced in favor of a leas one coinegraing vecor exiss boh a 5 and 1% significance level, on he oher hand he exisence of a mos wo coinegraed vecors is no rejeced a 5% level. Based on his model, he coinegraing vecor represening he longrun money demand funcion for real M1 is as shown in Table 3. According o he resuls shown in Table 3, LR indicaes 2 coinegraion equaions a 5% significan level. Based on he resuls shown in Table 4, he coinegraing vecor represening he long-run money demand funcion for real M1 is as follows: M = ( y ) ( INF ) ( Exch ) + ε The esimaion resuls of log-run elasiciies of he demand for money are compaible wih economic heory behind he demand for money. The long-run money demand funcion has approximaely uni income elasicciy. The real exchange rae has also a negaive sign; as an increase in he real exchange rae implies an appreciaion of Sudanese ound, when he domesic currency appreciaes, he demand for real money balances ends o decrease. On he oher hand, money demand is negaively affeced by he annual rae of inflaion since i shows he reurn on real asses. The semi-elasiciy of he inflaion rae is , which means ha he impac of he expeced inflaion on real balances is subsanially imporan in he model. Dynamic error correcion model he nex sep is o esimae he shor-run demand for broad money using an error correcion model (ECM). The shor-run model coefficiens measure he dynamics of he model, he ECM measures he speed of adjusmen o he long run equilibrium which is aking place. A one year lag was applied. The resuls of error correcion model are presened in Table 5. Based on he ECM resuls appearing in Table 5, a full model is consruced in he form of a single equaion for he analysis of he shor-run dynamics of real money balances. Being he firs difference of log real M1 on he lef hand side of he equaion, he righ hand side comprises one lagged erm of differenced log real M1, firs differences of oher variables, and one lag of he saionary error erm. Afer he deerminaion of he coinegraing relaionship, M M = ( y 1 ) ( INF 1 ) ( Exch 1 ) ECM 1

6 798 J. Econ. In. Finance Table 5. Shor-run model of he demand for money in Sudan, 1960 o Variable Coefficien S.E T. Saisic Consan M y Exch INF ECM Now, all he esimaed coefficiens of included variables are consisen wih economic heory, ha is, income elasiciy is posiive and he exchange and inflaion raes have a negaive elasiciies. Beside, he error correcion erm has he expeced sign. The negaive coefficien of he error correcion erm is significan, assuring ha he coinegraion relaionship beween he included variables is valid. Looking a he oher coefficiens, we conclude ha he income elasiciy falls o , whereas he impacs of exchange rae and he annual inflaion rae decrease considerably in he shor run. arameer consancy arameer consancy is a criical issue for money demand equaions. In paricular, o be able o inerpre he esimaed equaion as a money demand equaion, i is necessary o assure ha he parameers are sable over he esimaion period. To achieve his, he sudy implemened he mehodology based on he cumulaive sum (CUSUM) and he cumulaive sum of squares (CUSUMSQ) ess proposed by Brown e al. (1975). The advanage of such a es over some oher ess (Like Chow es) is ha he former es requires he specificaion of he break poins, while he laer es uses he cumulaive sum of recursive residuals based on he firs n observaions and is updaed recursively and ploed agains break poin (Ouaara, 2004). On he oher hand, CUSUMSQ es uses he squared recursive residuals in he same manner as CUSUM es. The decision abou he parameer sabiliy relies on he posiion of he plo relaive o he 5% criical bound. The CUSUM es is based on he cumulaive recursive sum of recursive residuals. The CUSUMSQ es, on he oher hand, is based on he cumulaive sum of squares of recursive residuals. Boh he CUSUM and CUSUMSQ es saisics are updaed recursively and ploed agains break poins in he daa. For sabiliy of he shor-run dynamics and he long-run parameers of he real money demand funcion, i is imporan ha he CUSUM and CUSUMSQ saisics say wihin he 5% criical bound (represened by wo sraigh lines whose equaions are deailed in Brown e al., 1975 aforemenioned). A graphical presenaion of hese wo ess is provided in Figures 1 and 2. As i can be seen from Figures 1 and 2, neiher he CUSUM nor CUSUMSQ plos cross he 5% criical lines, herefore, we can safely conclude ha he esimaed parameers for he shor-dynamics and long-run of he real M1 money demand funcion in Sudan are sable. In oher words, a sable real M1 demand funcion exiss over he enire sample period. SUMMARY AND CONCLUSIONS This sudy has examined boh he deerminans and he sabiliy of he demand for money funcion in Sudan over he period 1960 o The Johansen Maximum Likelihood procedure shows ha here is a long-run relaionship for real money in Sudan. In his long-run relaionship, he empirical findings sress he exisence of a posiive relaionship beween money aggregaes and he level of income, also he income elasiciy is found o be near uniy, a resul ha is consisen wih he economic heory; in addiion o ha, boh he inflaion rae and exchange rae are found o negaively affec M1. The negaive effec of inflaion rae on M1 suppors he heoreical expecaion ha as he inflaion rae rises, he demand for money falls. This indicaes ha people prefer o subsiue physical asses for money balances. The resuls of sabiliy ess reveal ha M1 money demand in Sudan is sable over he period of he sudy. These resuls sugges ha i is possible o use he narrow money aggregae as arge of moneary policy in Sudan. ACKNOWLEDGEMENTS The auhors graefully acknowledge he financial suppor provided by he German Academic Exchange Service (DAAD). The auhors are mos graeful o Dr. Khalafalla Ahmed Mohamed Arabi, Dean of he Graduae College, Universiy of Bakh Al Ruda El Dowaim, (Sudan) for his kind help and suppor.

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