MONEY AND INTEREST RATES IN UGANDA

Transcription

1 MONEY AND INTEEST ATES IN UGANDA JIMMY ALANI Absrac The paper analyses he influence of money on ineres raes in Uganda wihin he 98 o 007 period. Theoreical analysis is conduced wih he inenion of invesigaing he influence of money on boh he nominal and real ineres raes. The heoreical analysis involves he idea ha he lenders of money make heir decisions based on real ineres rae, he nominal money supply and he fuure value of he money supply because heir aim is o make profis in real erms. The oher idea saes ha he borrowers of money make heir decisions based on he real money balance i.e. demand for money), nominal ineres rae and he fuure value of he real money balance because heir aim is o use he borrowed money o spend on he goods and services hey demand for invesmen or execuing heir planned aciviies. To he borrowers he nominal ineres rae is he price of money, whereas o he lenders he real ineres rae is he price of money. Boh he lenders and borrowers desire o earn income using he money supplied or borrowed and he fuure value of eiher he real money balance or money supply is direcly proporional o aggregae income. Based on resuls from he relevan regressions conduced he paper finds ha a) money supply has a posiive influence on he nominal ineres rae, bu a negaive effec on real ineres rae b) he demand for money has a posiive influence on real ineres rae, bu a negaive effec on he nominal ineres rae and c) real income has a posiive influence on eiher nominal or real ineres rae. JEL Classificaion: E4 Key Words: eal Ineres ae, Nominal Ineres ae, eal Money Balance, Money Supply, eal Income.. INTODUCTION The paper examines he influence of money on ineres raes in Uganda wihin he 98 o 007 period. In an economy nearly all aggregae sock of money passes hrough he financial markes in erms of lending and borrowing. We argue ha he borrowers make heir decisions based on he real money balance and nominal ineres rae; while he lenders make heir decisions based on he real ineres rae and he nominal money supply. The value of aggregae money demanded wihin a given period of ime is aken o be proporional o he value of aggregae money supply issued by he financial insiuions. Deparmen of Economics and Business Educaion, Faculy of Educaion and Humaniies, Gulu Universiy, P. O. Box 66, Gulu Uganda; Tel: ; E mail: j.alani@gu.ac.ug

2 Empirical evidence go suppor he following proposiions: a) growh in nominal money supply has a posiive influence on nominal ineres rae, bu a negaive influence on real ineres rae and b) growh in real money balance has a negaive influence on nominal ineres rae, bu a posiive influence on real ineres rae. The research sudy is moivaed by Fisher s 907) definiion of ineres rae as an index of preference for a dollar of presen over a dollar of fuure income. In he paper, Fisher s definiion is resaed as an index of fuure value of money over he presen value of money. Thus eiher he presen value of money is in erms of demand for money or supply of money and is proporional o he real income. eal income is considered because money plays an indirec role of oher mighier facors. In oher words, he fundamenal causes a work in a money marke are economic, no moneary a all. Thus he holders of money deermine he way i is spen, such as for buying goods and services or invesmen. Therefore, he amoun of available funds for loan purposes is merely a sign of more fundamenal causes operaing upon he rae of ineres. The paper akes advanage of Lucas 990) mehodology ha capures liquidiy and loanable funds effecs. The mehodology allows us o aggregae he sock of money while avoiding he wealh effec problems. In he paper we aemp o reconcile he liquidiy preference heory of ineres wih he loanable funds heory. The economeric models esed were developed from he heoreical models based on he equilibrium condiions exising beween he presen value of aggregae money supply and presen value of aggregae demand for money.. LITEATUE EVIEW Irving Fisher 896) disinguished beween nominal and real ineres raes and empirically examined he influence of inflaionary expecaions ha had no been known. Ye, before 966,

3 mos people srongly believed in he Keynesian liquidiy preference approach ha faser moneary growh mean declining ineres raes. The rising ineres raes made i impossible o coninue acceping he sable Keynesian liquidiy preference funcion relaing he nominal quaniy of money o be inversely relaed o nominal ineres raes as an adequae ool for analyzing he effec of money changes on ineres raes Friedman, 968). Friedman 98) found an inverse relaionship beween nominal ineres rae n) and real money balance M Mn / P) or Mn /Y. He herefore, showed ha he inverse relaion beween nominal ineres rae n) and nominal money supply Mn) was wrong. Keynes failed o disinguish he nominal from he real money supply because he assumed prices o be rigid and ha any effec on income would influence real income Friedman, 98, pp ). In he paper we argue ha Keynes could have been righ if he had aken he relaion beween nominal ineres rae and money supply o be posiive. Tha is because increase in money supply or increase in aggregae supply of loans) causes he nominal ineres rae o fall say from n 0 o n ) wihin a brief period of ime o a new equilibrium level. I is his fall in nominal ineres rae ha causes he demand for money o rise in he long run i.e. wihin a given period or year). Consequenly, persisen increase in demand for money drives up he nominal ineres rae o a final equilibrium level in he money marke so ha he final ineres rae say n ) is less han he original one n 0). In he paper we also argue ha Friedman 98) was righ in wo ways. One, he quaniy demanded of money rises as nominal ineres rae falls since he demand curve is downward sloping. Two, he rise in demand for money i.e. a shif in he demand curve ouwards) is accompanied by a rise in ineres rae in a brief period of ime and o he new marke equilibrium.

4 I is his rise in ineres rae say from n 0 o n ) ha causes he supply curve of money o shif o he righ o he new marke equilibrium. As a resul, in he long run i.e. wihin he course of a year), he persisen increase in money supply causes he ineres rae o fall say o n ) below he original ineres rae n 0). Pinna 00) defines ineres rae as he profi overime due o financial insrumens. In a loan srucure, he ineres rae is he deference in percenage beween money paid back and money go earlier, aking ino accoun he duraion of ime ha has elapsed. All over he world, banks esablish ineres rae o he public by making reference o he percenage hey charge more han he cenral bank base lending Pinna, 00). Ineres rae is defined as he amoun a borrower pays in addiion o he principal of loan o compensae, he lender for use of he money. Ineres rae herefore, is he expression of ineres as a percenage of he principal, while lending is he principal business aciviy for mos commercial banks. Banks execue one of heir mos imporan funcions by acceping deposis for he purpose of lending. Whenever deposis are acceped, he banks agree o repay he amoun of deposis wih ineres o he deposior on mauriy. Banks recover loan amouns and advances and use hem o repay deposi amouns o he cusomers on mauriy Nakayizi, 0, pp.-7). Branson 00, pp.58-6), conend ha he speculaive and ransacions demand for money canno be separaed. To avoid puing ogeher he speculaive and ransacions demand for money in one equaion, we spli our marke ino one depicing he borrowers and lenders markes. Fisher 907, p.) defines he rae of ineres o be an index of preference for a dollar of presen over a dollar of fuure income.

5 In he paper our heories of ineres rae have been direcly moivaed by Fisher s definiion of ineres rae in erms of fuure value of money. We hen modify his Fisher s definiion and redefine ineres rae o be an index of preference for a dollar of fuure income over he presen dollar i.e. fuure value of money, FV ) over he presen value of money Mn, where is he real ineres rae. The revised definiion is more accurae because from he lender s poin of view, he ineres rae is he fuure value of money, FV Mn ) over he presen value of money Mn) and can be expressed as Mn )/ Mn. In oher words, he ineres rae is defined as fuure aggregae income Y or FV Y of lenders over he presen value of he aggregae sock of money supply Mn) wihin he banking sysem, i.e. Y / Mn. Likewise, from he borrower s poin of view, he ineres rae is defined as a fuure income, FV M n) over he presen value of demand for money M, i.e. n Y / M. When he expecaions of borrowers and lenders are a par hen Mn ) Y M n), implying a) he inverse relaionship beween nominal ineres rae n) and real money balance M), b) posiive relaionship beween nominal n) ineres rae and money supply Mn), c) inverse relaion beween real ineres rae ) and Money supply and Mn), and d) posiive relaion beween real ineres rae ) and real money balance M ). I is a well known fac ha moneary injecions occur hrough he financial insiuions. These financial insiuions inermediae beween borrowers and savers and hey ac as he channel hrough which he cenral bank injecions occur. The moneary injecions make he borrowers relaively cash rich and i simulaes heir demand for goods and services hey purchase, consequenly pushing up he nominal ineres raes Fuers, 990). Oherwise, he moneary injecions i.e. growh in money supply), lower he real ineres rae and increases nex

6 period s capial sock and level of oupu. These analyses focus mainly on wealh effecs where borrowers bid up asse prices and decrease real ineres raes Grossman and Weiss, 99; oenberg, 984; Weiss, 986; Kehoe, Levine and Woodford, 988). The common problem in earlier approaches is he small se of moneary policies ha can be analyzed. In he paper we make generalizaions o eliminae enirely problems associaed wih wealh effecs, by employing a mehodology suggesed by Lucas 990). The mehod involves aggregaing all he secors of he economy ino one giganic household. In each secor cash is used o carry ou ransacions in separae markes and is subjec o wihin period liquidiy resuling from moneary injecions. The advanage of he Lucas 990) mehodology is ha cash injecions can be modeled, while capuring he liquidiy and loanable funds effecs. The mehodology enables us o isolae he liquidiy and loanable funds effecs so ha he paper is absoluely free from he wealh effec problems Fuers, 990). Ineres rae i.e. he price of loans) is deermined by supply and demand for loans, or by supply and demand for money where loans are given and aken Tsiang, 980). Tobin believes ha he demand for money is sensiive o ineres raes and found an inverse relaionship beween ineres raes and idle balances. Addiional empirical evidence confirm he inverse relaionship beween demand for money and nominal ineres raes Laider, 96, 966, 99; Friedman, 959; Brunner and Melzer, 96). Tsiang 956), calls for reconciliaion of liquidiy preference heory of ineres wih he loanable funds heory. Tha is because no only Keynesians and Neo- Keynesians, bu also he Chicago moneariss coninue o formulae he demand for money as a funcion of income and ineres rae. Furhermore, if aggregae planned expendiure is subsiued for money demand funcion, i makes he liquidiy preference heory of ineres come

7 o he same hing as he loanable funds heory. I is herefore, he oal planned expendiure ha should be regarded as he primary deerminan of ransacions demand for money Tsiang, 980). Moneary policy is very close o realiy and ha i is less absrac han mos economic heory Hicks, p.56). In he real world, money comes ino exisence along wih debs occurring ypically as conracs for differed paymen Friedman, 97, p.). The exisence of financial insiuions, normally operae under he sae conrol. I is he sae ha provides he assurances of coninuiy beween he presen and fuure ha is imporan for holding money as a sore of value. Wha gives money is purchasing power is is inimae relaionship o provide conracs in general and conracs involving labor offers specifically Davison, 97). In economics, ineres rae heory is composed of loanable funds heory, liquidiy heory, he IS-LM model deerminaion of ineres rae and he more recen general equilibrium-based models of ineres rae deerminaion. Each of hese heories are based on facors ha deermine ineres raes. The disadvanage of dealing wih he heories individually is ha each of he heories emphasizes a paricular deerminan, hus causing i o misrepresen oher causes of ineres raes, resuling in confusing hose rying o undersand hem. Loanable funds heory is a heory of choice for characerizaion of how ineres raes depend on savings. Liquidiy preference heory refers o changes in money demand linked o ineres raes and how money demand affecs he bonds marke and oher deb securiies. In liquidiy heory, he asse modeled is money. The general equilibrium-based ineres heories deermine ineres raes ogeher wih he equilibrium aggregae level of oupu in an economy Elwood, 007). The new dimension of ineres rae heory was inroduced in form of he IS-LM model advanced by Grossman and Weiss 98) and oernberg 984). ecen conribuions by Lucas 990), Fuers 99), Chrisiano and Eichenbaum 995) have clearly shown ha he new sandard ineres rae heory

8 should be wihin a dynamic, general equilibrium framework. The liquidiy preference heory and loanable funds heory canno be easily inegraed Keynes, 96; Tsiang, 980; Foley, 975; Buier, 980, Davison, 978; Mayer, 996; Hicks, 99; Bilow, 000; Leijonhafvud, 98). Mos ex books having boh heories, presen hem separaely Bernanke, 007; Lieberman, 006 and Mankiw, 00 as sighed in Elwood, 007). Elwood 007), observes ha he IS curve and is represenaion of goods marke equilibrium involves real ineres rae, while he LM curve and is represenaion of financial marke equilibrium depends on he nominal ineres rae. The mos common exbook approach o addressing he conroversy is o force he wo raes o be equivalen by assuming ha inflaion is zero. The IS-LM model also suffers he loanable funds problem of being unable o represen he impac of pre-exising deb securiies a he beginning of he period being modeled. Ye he LM curve ha incorporaes liquidiy preference heory in he IS-LM model, offers no beer accouns for he prevailing sock of deb securiies han he liquidiy preference heory does. More recen ineres rae heory has no aemped o discover a beer equilibrium approach in he model of loanable funds or liquidiy preference heory. Insead he recen ineres rae heory has concenraed on models ha improve upon he join deerminaion of oupu and ineres raes as found in he IS-LM model. eal business cycle heory has effecively esablished he supremacy of dynamic models of oupu over saic models. As a resul, for more han wo decades now, journals have examined oupu using dynamic models. Many of hese models are concerned wih how moneary shocks i.e. change in liquidiy) influence oupu as well as ineres raes Lucas, 990; Fuers, 99; Chrisiano and Eichenbaum, 995).

9 . THEOETICAL ANALYSIS If wihin a year he aggregae demand for money i.e. real money balance) in he economy is M and he prevailing nominal ineres is n, hen he fuure value of he demand for money FV is given by M n ) FV... ) In our analysis we herefore define nominal ineres rae n ) in erms of fuure value of demand for money as a raio of demand for money. n FV / M.... ) In our ineres rae heory analysis we reason ha he aggregae fuure value of demand for money i.e. money held by he invesors and needed for purchasing goods and services) is proporional o he aggregae demand for goods and services or aggregae income). FV Y.. ) Subsiuing Equaion 7) in Equaion 6) provides n Y / M.... 4) If wihin a year he aggregae money supply i.e. real money balance) in he economy is Mn and he prevailing real ineres is, hen he fuure value of he money supply FV is given by Mn ) FV... 5) In our analysis we herefore define real ineres rae ) in erms of fuure value of money supply as a raio of money supply. FV / Mn.. 6)

10 In he ineres rae heory analysis being advanced we reason ha he aggregae fuure value of money supply i.e. money issued by he financial insiuion o he invesors and consumers required for purchasing goods and services) is proporional o he aggregae level of income. FV Y. 7) Subsiuing Equaion 7) in Equaion 6) provides Y / Mn ) Wihin he economy of a counry, he nominal ineres rae, aggregae money supply, real ineres rae and aggregae demand for money are conneced by he real income. Mn n )/ Y M )/.... 9) Equaion 0) provides he equilibrium relaionship beween money and ineres raes. Mn n ) M ).... 0) Equaion ) implies ha in he long run, real money balance has a posiive influence on real ineres rae, bu money supply has negaive influence on he real ineres rae. ln ) ln / ) ln n ) ln M) ln Mn)..... ) Equaion ) implies ha in he long run, real money balance has a negaive influence on real nominal rae, bu money supply has posiive influence on he nominal ineres rae. ln n ) ln / ) ln ) ln Mn) ln M) ) We combine Equaions 4) and 8) o consiue an equilibrium condiion given by n ) Y / M ) Y / Mn )

11 Equaion 4) shows ha he nominal ineres rae is posiively relaed o he aggregae income of financial insiuions Y / Mn) ha lend money, bu negaively relaed o he aggregae income Y / M) of he borrowers of money from he financial insiuions. n ) Y / M) Y / Mn) ) We ransform Equaion 4) o enable us deermine he relaionships beween nominal ineres rae and money, i.e. money in erms of money supply as a raio of real income and money in erms of demand for money as a raio of real income. n ) M / Y) Mn / Y) ) Afer ransformaion of Equaion 5) ino logarihm i becomes clear he nominal ineres rae is posiively relaed o money supply, bu negaively relaed o demand for money. ln n ) ln ) ln M / Y) ln Mn / Y) ) Equaion 7) shows ha he real ineres rae is posiively relaed o he aggregae income of borrowers from he financial insiuions Y / M) ha lend money, bu negaively relaed o he aggregae income Y / Mn) of he financial insiuions involved in lending money. n ) Y / M) Y / Mn) ) We ransform Equaion 7) o enable us deermine he relaionships beween real ineres rae and money, i.e. money in erms of money supply as a raio of real income and money in erms of demand for money as a raio of real income. n ) M / Y) Mn / Y) ) Afer ransformaion of Equaion 7) ino logarihm i becomes clear he real ineres rae is negaively relaed o money supply, bu posiively relaed o demand for money.

12 ln ) ln n ) ln M / Y) ln Mn / Y) ) Furhermore, we spli he variable real money balance as a raio of income ino demand for money and real income o enable us deermine he influence of real income and demand for money on nominal ineres rae. As can be discerned from Equaion 0), he relaionship beween income and nominal ineres is posiive. ln n ) ln ) ln M) ln Y) Mn / Y).... 0) Similarly, we spli he variable money supply as a raio of income ino money supply and real income o enable us deermine he influence of real income and money supply on nominal ineres rae. As can be discerned from Equaion ), he relaionship beween income and real ineres is posiive. ln ) ln n ) ln M / Y) ln Mn) ln Y).... ) Alernaively, we may ake he influence of money on nominal ineres rae o be purely a phenomenon of moneary growh. To do ha we express he fuure value of demand for moneyfv in he previous year in erms of he previous year s demand for money M and nominal ineres rae n. M n ) FV.. ) We ake he fuure value of demand for money held a year ago o be direcly proporional he level of demand for money in he curren year. FV M.. ) Subsiuing Equaion ) in Equaion ) give rise o Equaion 4) n M / M )

13 Once more we may ake he influence of money on real ineres rae o be purely a phenomenon of moneary growh. To do ha we express he fuure value of money supply FV4 in he previous year in erms of he previous year s money supply Mn and real ineres rae. Mn ) FV ) Similarly, we ake he fuure value of money supply issued a year ago o be direcly proporional he level of money supply in he curren year. FV4 Mn ) Subsiuing Equaion 5) in Equaion 4) give rise o Equaion 6) Mn / Mn ) We hen combine Equaions 4) and 7) o provide an equilibrium condiion exising in he money marke expressed by Equaion 8). n M / M ) Mn / Mn ) Equaion 8) can be rewrien in erms nominal ineres rae as a funcion of real ineres rae, money supply growh and growh in demand for money. n ) M / M Mn / Mn.... 9) Therefore, growh in demand for money raise nominal ineres rae, bu money supply growh causes reducion in nominal ineres rae. n ) ) M M )/ M Mn Mn )/ Mn... 0) Also Equaion 8) can be rewrien in erms real ineres rae as a funcion of nominal ineres rae, money supply growh and growh in demand for money.

14 n ) M / M Mn / Mn.... ) Hence, growh in demand for money raise nominal ineres rae, bu money supply growh causes reducion in nominal ineres rae. ) n ) M M )/ M Mn Mn )/ Mn... ) 4. METHODOLOGY Under he mehodology secion we develop he economeric models o be esed from he heoreical models ha have been buil for heoreical analyses. The models ha appear below come o be esablished as a resul of a) developing hem and b) evenually modifying hem afer having successfully conduced reliable empirical ess. The Economeric model i.e. Equaion ) was developed from Equaion ). ln n ) ln ) d ln M) 4d ln Mn ).... ) Where 4 0. The Economeric model i.e. Equaion 4) was developed from Equaion ). ln ) ln n ) d ln M) 4d ln Mn ) ) Where 4 0. The Economeric model i.e. Equaion 5) was developed from Equaion 6). ln n ) ln ) d ln M / Y ) 4d ln Mn / Y ) ) Where 4 0. The Economeric model i.e. Equaion 6) was developed from Equaion 9).

15 ln ) ln n ) d ln M / Y ) 4d ln Mn / Y ).... 6) Where 4 0. The Economeric model i.e. Equaion 7) was developed from Equaion 0). ln n ) ln ) d ln M) 4d ln Y ) 5d Mn / Y ).. 7) Where The Economeric model i.e. Equaion 8) was developed from Equaion ). ln ) ln n ) d ln M / Y ) 4d ln Mn ) 5d ln Y )... 8) Where The Economeric model i.e. Equaion 9) was developed from Equaion 0). n ) M M )/ M 4 Mn Mn )/ Mn. 9) Where 4 0. The Economeric model i.e. Equaion 40) was developed from Equaion ). n ) M M )/ M 4 Mn Mn )/ Mn. 40) Where 4 0. The Economeric model i.e. Equaion 4) was developed from Equaion 7). ln ) d ln Mn ).... 4) Where 0. The Economeric model i.e. Equaion 4) was developed from Equaion 8). ln ) d log Y ) d ln Mn ) ) Where 0.

16 The Economeric model i.e. Equaion 4) was developed from Equaions 0) and 4). ln n ) d ln Mn ) d ln M) ) Where 0. The Economeric model i.e. Equaion 44) was developed from Equaion 9). ln ) ln n ) d ln Y / Mn ) 4d ln Y / M) ) Where 0. The Economeric model i.e. Equaion 45) was developed from Equaion 0). ln n ) ln ) d ln Y / Mn ) 4d ln Y / M) ) Where 4 0. The Economeric model i.e. Equaion 46) was developed from Equaions 8). n d ln Mn ) d ln M) ) Where 0. The Economeric model i.e. Equaion 47) was developed from Equaions 4). n d ln Y / Mn ) d ln Y / M) ) Where 0. Having go he economeric models hey are confroned wih money daa on money supply, ineres raes real GDP for Uganda for he period. Wih respec for esing he adequacy of he models presened we firs of all express he model as a k-variable regression model in he form given by Y i X X... XK )

17 Wih respec o esing he significance of he parameers, we sae he hypohesis ha he rue value of he parameer in quesion is equal o zero i.e. H : 0 K,,..., K). 0 K The hypohesis is esed agains a wo sided alernaive and he saisic o be used is given by 0 / Var K ) ~ /, nk,,..., K) K 49) When K, i implies ha he inercep is equal o zero, meaning ha he regression line passes hrough he origin. When K,,..., K; he hypohesis ha 0 means ha he K variable X has no influence on he mean of Y. If he compued value exceeds he criical K value a a given level of significance say ), he null hypohesis H0) is rejeced, oherwise i is acceped. Alernaively, if he compued p value of obained is low, we rejec he H 0. The esimaed P value of is he probabiliy of obaining a given compued value or greaer. The F-disribuion provides a more exensive saemen of he null hypohesis in ha none of he explanaory variables has an influence on he mean of Y, and i is saed as H 0 : K... 0 K,,..., K) agains he alernaive hypohesis ha he null hypohesis is unrue i.e. H0 : No all slope coefficiens are simulaneously zero. If null hypohesis H0) is rue, hen he variaion of Y from observaion o observaion is no affeced changes in any of he explanaory variables, bu is purely random. If ha is correc, hen he observed value of explained sum of squares ESS) differs from zero only because of sampling. If he null hypohesis is rue hen

18 ESS / dfn ESS / K ) / K ) F ~ F, K, nk.. 50) SS / df SS / n K) )/ n k) d Where ESS explained sum of squares, SS residual sum of squares, df n K degrees of freedom of numeraor, df d n K degrees of freedom of denominaor, coefficien of deerminaion, and level of significance. If he compued F Saisic is higher han he abulaed criical F, K, nk value, we rejec he null hypohesis and conclude ha all he independen variables have join effec on he dependen variable. Alernaively, if he P value of F obained is low, we rejec H 0. The esimaed P value of F is he probabiliy of obaining a given compued F value or greaer Gujarai, 004, 46; Kmena, 97, p.69). In esing for heroscedasiciy, he Koenker Basse KB) es for heeroscedasiciy is used. The KB es for heeroscedasiciy is based on squared residuals, e. The squared residuals are regressed on he esimaed values of he independen variable, Y. ˆ If he original model is Y X X... e K.... 5) The model can be esimaed by geing e he from he model and hen esimae eˆ Yˆ ) e... 5) Where Yˆ are he esimaed values from he model. Here H 0. If ha is he case we 0 : accep he null hypohesis and conclude ha here is no heeroscedasiciy. The null hypohesis is hen esed by he usual es or he F es, where F Gujarai, 004, p.45).. K K

19 In esing for he absence of auocorrelaion we use he Durbin Wason es. In his case we es he hypohesis ha here is no auocorrelaion, i.e. H 0 : agains he alernaive hypohesis ha here is posiive auocorrelaion, i.e. H 0 : 0. We apply he es by calculaing he value of a saisic d expressed as d n n ) / e e e. 5) Where he error erms e represen he ordinary leas squares residuals. If he compued d is less han he lower limi dl we rejec he H 0. If he d L is greaer han d U we accep Ho. If he d, falls wihin he range of d d, he es is inconclusive Kmena, 97, pp.94-95). L d U Lasly, adequacy of models is esed by conducing Augmened Dickey Fuller ADF) uni roos ess for saionary on, n, M, Mn and Y daa. The decision rule used in esing for saionary saes ha: If he compued ADF saisic is more negaive han he criical values a cerain levels of significance, hen rejec he null hypohesis, implying ha ha he series in quesion has no uni roo problem and he series is saionary. A uni roo problem exiss when he ADF es saisic is no more negaive han he criical values. We hen corner he uni roo problem by conducing he Johansen coinegraion ess in order o avoid producing spurious regressions. All he variables used in he 5 regression equaions here have been found o be coinegraed. The radiional mehodology is appropriae o daa involving nonsaionary ime series. A es for coinegraion can be hough of as a prees o avoid spurious regression siuaions, Granger, 989, p.6; Gujarai, 004, pp ).

20 5. ESULTS In his presen secion, fifeen resuls are presened along wih fifeen regression models. Economeric and saisical ess are conduced o esablish he adequacy of he regression models o be used in drawing conclusions involving he relaionships beween money and ineres rae variable. The ess conduced are a) es i.e. es of he individual effecs on he dependen variables, b) F es i.e. he es for he join effecs of he respecive dependen variables on he independen variables by using he Fisher s saisic, c) es for presence of auocorrelaion by using he Durbin Wason D.W.) Saisic and d) es for presence of heeroscedasiciy by using he Koenker Basse es. The square ) is very high in all he regressions and ranges from 0.8 o I herefore implies ha each of he regression lines can explain almos all he variaions in he given independen variable. Also he join effec of he independen variables on he dependen variables is exremely high because he probabiliy of he F saisic is zero for all regressions presened. Lasly, adequacy of models are esed by conducing ess for saionary on daa se of he respecive variables by conducing uni roos ess, in paricular by conducing he Augmened Dickey Fuller uni roos ess on, n, M, Mn and Y. Uni roo ess show ha and n are no saionary bu are I) and require no differencing for conducing regressions. For M, Mn and Y, heir firs differences are no saionary bu are I) and heir firs differences can be used in making adequae regressions. The n series is no saionary because he compued ADF es saisic -.07) is negaive han he criical values -.75, -.00 and -.64) a %, 5% and 0% level of significance respecively. A firs difference makes n saionary because he compued ADF es saisic -

21 4.6) becomes more negaive han he criical values -.77, -.00 and -.64) a %, 5% and 0% level of significance respecively. Also, he series is no saionary because he compued ADF es saisic -.4) is less negaive han he criical values -.75, -.00 and -.64) a %, 5% and 0% level of significance respecively. A firs difference makes saionary because he compued ADF es saisic ) becomes more negaive han he criical values -.77, -.00 and -.64) a %, 5% and 0% level of significance respecively. The Mn series is also no saionary because he compued ADF es saisic -4.) is no less negaive han he criical values -.74, -.00 and -.64) a %, 5% and 0% level of significance respecively. Differencing he Mn series once sill does no make i saionary because he compued ADF saisic.7) sill does no becomes more negaive han he criical values -.77, -00 and -.64) a %, 5% and 0% level of significance respecively. The second differencing makes Mn saionary because he compued ADF es saisic -4.58) becomes more negaive han he criical values -4.47, -.65 and -.6) a %, 5% and 0% level of significance respecively. The M series is no saionary because he compued ADF saisic.46) is no more negaive han he criical values -.75, -.00 and -.64) a % level of significance respecively. Differencing he M series once sill does no make i saionary because he compued ADF saisic -0.8) does no becomes more negaive han he criical values -.77, -.00 and -.64) a %, 5% and 0% level of significance respecively. The second differencing makes he M series saionary since he ADF es saisic -5.55) becomes more negaive han he criical values -.79, -.0 and -.65) a %, 5% and 0% level of significance respecively.

22 Lasly, he Y series is no saionary because he compued ADF saisic.09) is no more negaive han he criical value -.75, -.00 and -.64) a %, 5% and 0% level of significance respecively. Differencing he Y series sill does no make makes i saionary because he compued ADF saisic -0.87) does no becomes more negaive han he criical values -.77, -.00 and -.64) a %, 5% and 0% level of significance respecively. The second differencing makes he Y series saionary because he compued ADF es saisic -4.5) becomes more negaive han he criical values -.79, -.0 and -.65) a %, 5% and 0% level of significance respecively. In Table, each of he compued saisic 4.49,.97, 6.4) is greaer han he criical saisic.8) in absolue erms, a percen level of significance. The criical 0.005, F 5.78) saisic is less han he calculaed F 54.55) saisic a percen level of 0.0,, significance. The compued Durbin Wason saisic D. W.84) is greaer han he criical upper value of he D. W..4) saisic a percen level of significance. By esing for heroscadasiciy using he Koenker Basse mehod, he compued F Saisic F 0.55) is less han he criical F saisic F 0.) a percen level of significance or F 4.) a 5 0.0,, 0.05,, percen level of significance. Therefore, based on he resuls presened in Table, he regression model presened in he able is adequae and he conclusions ha can be drawn from i are reliable. In Table, each of he compued saisic 4.59, 9.07,8.69) is greaer han he criical saisic.8) in absolue erms, a percen level of significance. The criical 0.005, F 5.78) saisic is less han he calculaed F 84.5) saisic a percen level of 0.0,,

23 significance. The compued Durbin Wason saisic D. W.08) is less han he criical upper value of he D. W..4) saisic. By esing for heroscadasiciy using he Koenker Basse mehod, he compued F Saisic F.50) is less han he criical F saisic F 0.) 0.0,, percen level of significance or F 4.) a 5 percen level of significance. Therefore, 0.05,, based on he resuls presened in Table, he regression model presened in he able is adequae and he conclusions ha can be drawn from i are reliable. a In Table, each of he compued saisic 4.96,.76, 7.) is greaer han he criical saisic.8) in absolue erms, a percen level of significance. The criical 0.005, F 5.78) saisic is less han he calculaed F 59.) saisic a percen level of 0.0,, significance. The compued Durbin Wason saisic D. W.) is greaer han he criical upper value of he D. W..4) saisic. By esing for heroscadasiciy using he Koenker Basse mehod, he compued F Saisic F.4) is less han he criical F saisic F 0.) a percen level of significance or F 4.) a 5 percen level of 0.0,, 0.05,, significance. Therefore, based on he resuls presened in Table, he regression model presened in he able is adequae and he conclusions ha can be drawn from i are reliable. In Table 4, each of he compued saisic 4.96, 9.0,7.95) is greaer han he criical saisic.8) in absolue erms, a percen level of significance. The criical 0.005, F 5.78) saisic is less han he calculaed F 8.6) saisic a percen level of 0.0,, significance. The compued Durbin Wason saisic D. W.8) is less han he criical lower value of he D. W..4) saisic. By esing for heroscadasiciy using he Koenker Basse

24 mehod, he compued F Saisic F.90) is less han he criical F saisic F 0.) 0.0,, percen level of significance or F 4.) a 5 percen level of significance. Therefore, 0.05,, based on he resuls presened in Table 4, he regression model presened in he able is adequae and he conclusions ha can be drawn from i are reliable. a In Table 5, each of he compued saisic 4.5,9., 6.76,4.6) is greaer han he criical saisic.85) in absolue erms, a percen level of significance. The criical 0.005, 0 F 4.94) saisic is less han he calculaed F 9.58) saisic a percen level of 0.0,,0 significance. The compued Durbin Wason saisic D. W.6) is less han he criical upper value of he D. W..5) saisic. By esing for heroscadasiciy using he Koenker Basse mehod, he compued F Saisic F.) is less han he criical F saisic F 0.) 0.0,, percen level of significance or F 4.) a 5 percen level of significance. Therefore, 0.05,, based on he resuls presened in Table 5, he regression model presened in he able is adequae and he conclusions ha can be drawn from i are reliable. a In Table 6, each of he compued saisic 4.5, 8.78,.6,7.) is greaer han he criical saisic.85) in absolue erms, a percen level of significance. The criical 0.005, 0 F 4.94) saisic is less han he calculaed F 9.58) saisic a percen level of 0.0,,0 significance. The compued Durbin Wason saisic D. W.) is greaer han he criical upper value of he D. W..5) saisic. By esing for heroscadasiciy using he Koenker Basse mehod, he compued F Saisic F.8) is less han he criical F saisic F 0.) a percen level of significance or F 4.) a 5 percen level of 0.0,, 0.05,,

25 significance. Therefore, based on he resuls presened in Table 6, he regression model presened in he able is adequae and he conclusions ha can be drawn from i are reliable. In Table 7, each of he compued saisic.5,.9, 6.7) is greaer han he criical saisic.8) in absolue erms, a percen level of significance. The criical 0.005, F 5.78) saisic is less han he calculaed F 50.9) saisic a percen level of 0.0,, significance. The compued Durbin Wason saisic D. W.97) is greaer han he criical lower value of he D. W..4) saisic. By esing for heroscadasiciy using he Koenker Basse mehod, he compued F Saisic F.9) is less han he criical F saisic F 0.) a percen level of significance or F 4.) a 5 percen level of 0.0,, 0.05,, significance. Therefore, based on he resuls presened in Table 7, he regression model presened in he able is adequae and he conclusions ha can be drawn from i are reliable. In Table 8, each of he compued saisic 4.5,.8, 6.7) is greaer han he criical saisic.85) in absolue erms, a percen level of significance. The criical 0.005, 0 F 4.4) saisic is less han he calculaed F 50.0) saisic a percen level of 0.0,4,0 significance. The compued Durbin Wason saisic D. W.70) is greaer han he criical upper value of he D. W..5) saisic. By esing for heroscadasiciy using he Koenker Basse mehod, he compued F Saisic F.0) is less han he criical F saisic F 0.) a percen level of significance or F 4.) a 5 percen level of 0.0,, 0.05,, significance. Therefore, based on he resuls presened in Table 8, he regression model presened in he able is adequae and he conclusions ha can be drawn from i are reliable.

26 In Table 9, each of he compued saisic 8.4,.4) is greaer han he criical saisic.8) in absolue erms, a percen level of significance. The criical 0.005, F 7.95) saisic is less han he calculaed F 79.8) saisic a percen level of 0.0,, significance. The compued Durbin Wason saisic D. W.97) is greaer han he criical upper value of he D. W..0) saisic. By esing for heroscadasiciy using he Koenker Basse mehod, he compued F Saisic F.0) is less han he criical F saisic F 0.) a percen level of significance or F 4.) a 5 percen level of 0.0,, 0.05,, significance. Therefore, based on he resuls presened in Table 9, he regression model presened in he able is adequae and he conclusions ha can be drawn from i are reliable. In Table 0, each of he compued saisic 7.,.4) is greaer han he criical saisic.8) in absolue erms, a percen level of significance. The criical 0.005, F 7.95) saisic is less han he calculaed F 4.8) saisic a percen level of 0.0,, significance. The compued Durbin Wason saisic D. W.8) is greaer han he criical lower value of he D. W..0) saisic. By esing for heroscadasiciy using he Koenker Basse mehod, he compued F Saisic F 4.05) is less han he criical F saisic F 0.) a percen level of significance or F 4.) a 5 percen level of 0.0,, 0.05,, significance. Therefore, based on he resuls presened in Table 0, he regression model presened in he able is adequae and he conclusions ha can be drawn from i are reliable. In Table, each of he compued saisic.97,5.87, 5.4) is greaer han he criical saisic.8) in absolue erms, a percen level of significance. The criical 0.005,

27 F 5.78) saisic is less han he calculaed F 47.) saisic a percen level of 0.0,, significance. The compued Durbin Wason saisic D. W.9) is greaer han he criical upper value of he D. W..4) saisic. By esing for heroscadasiciy using he Koenker Basse mehod, he compued F Saisic F 5.) is less han he criical F saisic F 0.) a percen level of significance or F 4.) a 5 percen level of 0.0,, 0.05,, significance. Therefore, based on he resuls presened in Table, he regression model presened in he able is adequae and he conclusions ha can be drawn from i are reliable. In Table, each of he compued saisic 4.96,9.0, 7.96) is greaer han he criical saisic.8) in absolue erms, a percen level of significance. The criical 0.005, F 5.78) saisic is less han he calculaed F 8.6) saisic a percen level of 0.0,, significance. The compued Durbin Wason saisic D. W.8) is greaer han he criical upper value of he D. W..4) saisic. By esing for heroscadasiciy using he Koenker Basse mehod, he compued F Saisic F.90) is less han he criical F saisic F 0.) a percen level of significance or F 4.) a 5 percen level of 0.0,, 0.05,, significance. Therefore, based on he resuls presened in Table, he regression model presened in he able is adequae and he conclusions ha can be drawn from i are reliable. In Table, each of he compued saisic 4.96,.76,7.) is greaer han he criical saisic.8) in absolue erms, a percen level of significance. The criical 0.005, F 5.78) saisic is less han he calculaed F 59.) saisic a percen level of 0.0,, significance. The compued Durbin Wason saisic D. W.) is greaer han he criical upper value of he D. W..4) saisic. By esing for heroscadasiciy using he Koenker

28 Basse mehod, he compued F Saisic F.5) is less han he criical F saisic F 0.) a percen level of significance or F 4.) a 5 percen level of 0.0,, 0.05,, significance. Therefore, based on he resuls presened in Table, he regression model presened in he able is adequae and he conclusions ha can be drawn from i are reliable. In Table 4, each of he compued saisic.0, 8.08) is greaer han he criical saisic.8) in absolue erms, a percen level of significance. The criical 0.005, F 7.95) saisic is less han he calculaed F 40.49) saisic a percen level of 0.0,, significance. The compued Durbin Wason saisic D. W.) is greaer han he criical upper value of he D. W..0) saisic. By esing for heroscadasiciy using he Koenker Basse mehod, he compued F Saisic F.87) is less han he criical F saisic F 0.) a percen level of significance or F 4.) a 5 percen level of 0.0,, 0.05,, significance. Therefore, based on he resuls presened in Table 4, he regression model presened in he able is adequae and he conclusions ha can be drawn from i are reliable. In Table 5, each of he compued saisic 8.8, 6.00) is greaer han he criical saisic.8) in absolue erms, a percen level of significance. The criical 0.005, F 7.95) saisic is less han he calculaed F.08) saisic a percen level of 0.0,, significance. The compued Durbin Wason saisic D. W.95) is greaer han he criical lower value of he D. W..0) saisic. By esing for heroscadasiciy using he Koenker Basse mehod, he compued F Saisic F.7) is less han he criical F saisic F 0.) a percen level of significance or F 4.) a 5 percen level of 0.0,, 0.05,,

29 significance. Therefore, based on he resuls presened in Table 5, he regression model presened in he able is adequae and he conclusions ha can be drawn from i are reliable. DISCUSSION OF ESULTS Oher hings equal a percen rise in real ineres rae migh have caused he nominal ineres rae o rise wihin he range of 0.7 and 0.77 percen see Tables,, 5, and ). On he oher hand a percen rise in he nominal ineres rae could have caused he nominal ineres rae o rise wihin he range of 0.65 o 0.7 percen see Tables, 4, 6, and ). The reverse effecs beween real and nominal ineres raes appear o be he same because he ineres raes end o move ogeher. A percen growh in nominal money supply was followed by increase in nominal ineres rae wihin he range of.08 o.5 percen see Tables,, 5, and 4). Tha is because wih he nominal ineres rae on he verical axis and demand for money i.e. real money balance) on he horizonal axis; increase in money supply causes he supply curve o shif o he lef from he firs equilibrium o he second equilibrium and he ineres rae falls. I is his fall in ineres rae ha causes he demand for money e.g. loans o rise) in he shor run. Thus causing he demand curve o shif o ouwards o a hird equilibrium, where he equilibrium ineres rae is higher han he firs equilibrium ineres rae. Therefore, in he long run, moneary nominal money supply) growh causes an increase in nominal money supply. A percen increase real money balance could have led o reducion in nominal ineres rae wihin he range of.47 o.64 percen see Tables,, 5, and 4). This empirical evidence is in line wih he argumen ha given he nominal on he verical axis and real money balance.e. demand for money) on he horizonal axis, increase in demand for money would cause he

30 demand curve o shif ouwards in he shor run from he firs equilibrium posiion o he second one, bu a a higher equilibrium ineres rae. As a resul increase in he ineres rae would arac he financial insiuions lending money o provide more loans i.e. supply more money) o he borrowers. Consequenly, he supply curve shifs o he lef o a hird equilibrium posiion, bu a a lower ineres rae han he firs equilibrium ineres rae. Hence, in he long run growh in demand for money leads o a reducion in nominal ineres rae. A percen growh in real money balance could have brough abou a rise in real ineres rae wihin he range of.08 and.54 percen. This empirical evidence is in agreemen wih he argumen ha when we have he real ineres rae on he verical axis and he nominal money supply on he horizonal axis, any increase in demand for money in he long run would cause he demand curve o shif o he lef o a new equilibrium posiion, bu a a higher ineres rae level. Therefore, he conclusion reached is ha growh in demand for money leads o an increase in he real ineres rae. Increase in nominal money supply was accompanied by reducions in real ineres rae wihin he range of.05 o. percen see Tables, 4, 6 and 9). This empirical evidence is suppored by he argumen ha when we have he real ineres rae on he verical axis and he nominal money supply on he horizonal axis, any increase in aggregae money supply in he long run would cause he supply curve o shif o he lef o a new equilibrium posiion, bu a a lower ineres rae level. Therefore, he conclusion reached is ha growh in money supply leads o a reducion in real ineres rae. This liquidiy heory, herefore, is compaible wih he loanable funds heory ha he sudy is advancing. Thus, given an exogenous shock, he sysem mainains iself a full employmen by

31 changes in equilibrium ineres rae. Any fall in supply of money e.g. lending) would perfecly be offse by an increase in real ineres rae and vice versa. Similarly, any shif in demand for real money balance e.g. borrowing) will cause via ineres rae an offseing change in money supply e.g. lending) so as o cause full employmen. By regressing one lag of money supply on ineres rae, he moneary iming evidence reveals how he rae of money growh moves relaive o he real ineres rae. Timing evidence is based on he principle ha if one even occurs afer anoher, he firs even mus have caused he second one Mishkin, 04, p.6). Over he sudy period he money supply growh occurred before real ineres rae did. In fac a percen money supply growh in every pas one year could have caused he curren real ineres rae o fall wihin he range of 0.76 o.05 percen per annum on average see Tables 9 and 0). The conclusion ha we reached on he basis of his evidence is ha money growh caused reducions in real ineres rae wihin he 984 o 007 period, bu affeced he real ineres rae wih lag of one year. This finding proves wrong he criicism shared by many Pos Keynesians such as Lavoire 994) who rejec he liquidiy preference heory on he grounds ha i involves he assumpion of exogenous money supply. The Pos Keynesians believe ha in a modern credi economy, he money supply is caused by he demand for i, as a resul, any change in demand auomaically brings abou a change in supply Moore, 988a, p.5). Their rejecion of he idea of ineres rae as a price coordinaing he demand and supply of money is herefore found o be baseless. Aggregae income had a posiive influence on boh he real and nominal ineres raes. A percen growh in aggregae income causes nominal ineres and real ineres rae o increase by. and.4 percen respecively wihin he period see Tables 5, 6 and 0). Moreover, a percen growh in aggregae income in he pas one year could have caused he

32 curren real ineres rae o rise by.6 percen per annum see Table 0). These wo ses of evidence on aggregae income reveals ha people demand money or borrow) because hey would like o make ransacions o saisfy heir individual wans or run some projecs in order o earn some income. A percen growh in income of lenders as a percen of nominal aggregae money supply led o. and -. percen growh in nominal ineres rae and real ineres rae respecively. This finding is suppored by he argumens ha increase in he lenders income reflecs he capaciy of he financial insiuions o supply more money and ha in he financial markes he lenders make heir decisions based only on real ineres rae and he nominal money supply. Similarly, a percen increase in he borrowers income as a percen of real aggregae demand for money i.e. real money balance i.e. money held by he public) migh have raised he real ineres rae and he nominal ineres rae by -.54 and.55 respecively see Tables and ). Tha is because increase in he borrowers income reflecs increase in demand for money and he borrowers make heir decisions based only on real money balance and nominal ineres rae. Inflaion comes abou if growh in supply of money is greaer han he growh demand for money. The argumen is suppored by a percen growh in money supply and real money balance ha migh have caused.08 and -.5 percen growh respecively in inflaion see Table 4). Therefore, i is he growh in aggregae money spen no he aggregae money sock saved ha is responsible for inflaion. This conclusion is confirmed by he fac ha a percen growh in he borrowers spending and lenders savings caused. and -.47 percen rise in inflaion respecively wihin he given period see Table 5). These wo ses of empirical evidence are based on he fac ha growh in money supply causes increase in nominal ineres, and growh in

33 demand for money leads o a rise in real ineres rae. Ye, he inflaion rae is he nominal ineres rae less real ineres rae. 7. CONCLUSION The definiion of ineres rae as a raio of fuure value of money o presen value of money of fuure income helped us in developing some heoreical models and proposiions ha were economerically esed and found o be reliable. Therefore, i was worhwhile for he research o be moivaed by he Fisher s 907) definiion of ineres rae as an index of he preference for presen value of money over he fuure value of money income. Empirical evidence reveled ha: i) money supply had a posiive influence on nominal ineres rae and a negaive effec on real ineres rae. ii) demand for money had a negaive influence on nominal ineres rae, bu a posiive influence on real ineres rae and iii) income had a posiive influence on boh real and nominal ineres raes in Uganda wihin he period from 984 o 007. Money supply and real income were found o affec real ineres rae wih a lag of one year. Hence, i was righ for us o rea money supply as an independen variable and ineres rae as a dependen variable. Thus, money supply as an independen variable could be used o conrol real ineres rae. Furher, empirical evidence revealed ha increasing incomes of borrowers was inflaionary, bu increasing incomes of he financial insiuions as lenders was no. Hence, governmen could conrol inflaion by expanding he financial secor and improving upon heir capaciy o issue more long erm loans o he public. EFEENCES Bernanke, B.S. 00), Some eflecions on Keynes Finance Moive for he Demand for Money, Cambridge Journal of Economics, Vol.9, No.5, pp Bilow, J. 00), The Loanable Funds Fallacy in erospec, Hisory of Poliical Economy, Vol., pp