Empirical Verification of Milton Friedman s Theory of Demand for Real Money Balancesin Nigeria: Generalized Linear Model Analysis

Transcription

1 Journal of Emprcal Economcs Vol. 5, No. 1, 2016, Emprcal Verfcaton of Mlton Fredman s Theory of Demand for Real Money Balancesn Ngera: Generalzed Lnear Model Analyss Ernest Smeon O. Odor 1, Raymond Os Alenoghena 2 Abstract Ths study emprcally nvestgates the relatonshp between real money balances (demand for money) usng the Mlton Fredman s money demand functon and real ncome, bonds, equtes, stocks, nterest rates, and nflaton rate n Ngera. The study used annual tme seres spannng 32 years, a sample perod from Methodcally, ths study models a standard money demand functon and employed the use of ADF - Fsher Ch-square and Phllps-Perron test statstc to test for the unt root, the Engle-Granger sngle-equaton to test for the contegraton and usng the Generalzed Lnear Model (GLM) (IRLS - Fsher Scorng) method to dlate the mpacts of the explanatory varables on the explaned varable and usng the Ramsey Reset Testtodagnostcs for functonal form msspecfcaton. Partally consstent wth theoretcal postulates, ths study fnds that money demand functon s partally stable n Ngera for the sample perod and that ncome; nflaton and lag of real money demand are the most sgnfcant determnants of the demand for money. The study shows that real money demand postvely responds to an ncrease n real ncome, nflaton and past real money demand and negatvely to a rse n the nterest rates spreads. It was also gathered that stock market varables can mprove the performance of money demand functon n Ngera.The study recommended polces amed at mprovng stock market actvtes and also monetary targetng as a tool for nflaton control. Keywords: Mlton Fredman, Money Demand, Generalzed Lnear Model 1. Introducton The demand for money concept has attracted a lot of attenton from several economsts over the years. People and busnesses always keep money close as they requre t to carry out transactons on a regular bass. Economc agents requre money not just for exchange n the regular commodty market but also for transactons n Money market, captal market and foregn exchange market. Ths s why the use of money has a drect bearng on monetary polcy and also relevant to the study of macroeconomcs. The focus on the demand for money s attrbuted to the fact that monetary polcy wll only be effectve f the demand for money functon s stable. Stablty of the demand for money s crucal n understandng the behavour of crtcal macro-economc varables (Essen et al, 1996). The relaton between the demand for money and ts man determnants s an mportant buldng block n macroeconomc theores and s a crucal component n the conduct of monetary polcy (Gold feld, 1994). As a result, the demand for money s one of the topcal ssues that have attracted the most attenton n the lterature both n developed and developng countres. In the context of developed countres t s argued that dsequlbrum n the demand for money (defned as the dfference between the real money stock and the long-term equlbrum real money stock) may affect the effcacy of nterest rate polcy n the long run va ts mpact on output gap and/or nflaton. 1 PhD, Department of Economcs, Faculty of Socal Scences Unversty of Lagos, Akoka, Lagos, Ngera 2 Department of Economcs, Faculty of Socal Scences Unversty of Lagos, Akoka Lagos, Ngera 2016 Research Academy of Socal Scences 35

2 E. S. O. Odor & R. O. Alenoghena Theoretcally, the demand for real money balances could be dvded nto transactons demand component, whch s postvely related to the ncome and nversely related to nterest rates, precautonary demand component, postvely related to ncome and speculatve demand component, nversely related to nterest rates. In addton, the paper ncludes the cost of credt as a determnant of demand for money. Followng the prevous studes and real world experence, the cost of credt does matter n developng countres. Snce, n developng countres the transacton usng broad money (M2) very often takes place. The government, the busness and nvestors are usng credt or lendng to ensure the smooth runnng of ther development actvtes. The bankng system and other fnancal nsttutons create money by gvng loans. However, t s a practce that durng economc boom and the returns on nvestment s hgh and t encourages an ncrease n borrowng and lendng actvtes wth a relatvely lower cost of credt. By contrast, durng economc crss ether t s nflaton or deflaton, the banks and other fnancal nsttutons ncrease the cost of borrowng n order to dscourage the clents from borrowng. So an ncrease n the cost of borrowng s lkely to decrease the demand for money. Many advanced economes swtch between nstruments of monetary polcy by movng away from polces that nfluence the money supply towards those whch nfluence the bank rate (McPhal, 1991; Haug, 1999). In developng countres, polcymakers are concerned wth the stablty of money demand. Central banks n many developng economes have followed sut and swtch towards monetary polces drected at the bank rate.however, recent studes have rased doubts about the valdty and strength of central bank nterest rate targetng n developng economes (Bahman-Oskooee and Rehman, 2005; Raoet al., 2009; Rao and Kumar, 2009a and 2009b) Durng the 90s the growng mportance of stock markets has agan fed the dea that the prmary source of nstablty s related to monetary aggregates. Moreover, the preference for lqudty n tself mght be hghly unstable. Ths could be because of wealth effects whch nfluence non-monotoncally the demand for money. It follows that the degree of nstablty wll strongly depend not only on the fluctuatons of the ndvdual components of money demand, but also on the degree of correlaton of these components wth one another. Therefore, these components can sgnfcantly determne the dynamcs and the stablty of money demand. Our case study focuses on the Ngeran economy, whch enjoyed huge economc benefts from the ol boom of snce the 1970s but suffered varous poltcal coups n the 1980s. Snce the effort to stablze n a democratc dspensaton, varous economc programmes have been desgned and mplemented by successve admnstratons and have made sgnfcant mpact on the range of exstng economc relatonshps that determne the demand for real money balances by the average Ngeran. In ths study, we draw attenton to the nfluence of wealth on money demand n Ngeran, an area whch has been scarcely nvestgated emprcally by researchers. The man objectve of ths study s to emprcally nvestgate f demand for real money balances functon n Ngeran economy s consstent wth the Mlton Fredman s theory of demand for real money Balances for any economy. The study examnes the role of real ncome, bonds, equty, stock, nterest rates,nflaton and past level of real money demand n the money demand functon as the approprate measure of opportuntes cost of holdng money. The approprate research queston for ths study s, does the components n Mlton Fredman s money demand functon actually explans the opportuntes cost of holdng real money balances n Ngera? In the effort to justfy the underlyng the objectves and for ths study, the hypotheses to be tested may be summarzed that no sgnfcant relatonshp exsts between money balances and the components of Mlton Fredman s money demand functon (nclude; ncome, wealth, returns on other assets and expected nflaton).the justfcaton for ths study stems from the fact that despte the avalanche of lterature on the money demand functon n Ngera, very few studes have focused on the mpact of wealth n the demand for money functon. The other short comng n earler studes on ths subject matter s n part related to methodology. Most of the studes adopted the tradtonal Ordnary Least Squares (OLS) method of analyss Ths study flls that gap by estmatng a money demand functon for Ngera and by assessng the relatonshp 36

3 Journal of Emprcal Economcs between real money demand (RM1 and RM2) and ts determnants n accordance wth Mlton Fredman s demand for money theory. The study s dvded nto sx sectons; the frst secton gves a background to the theory of Mlton Fredman s hypothess of money demand statng the problems and objectves of the study.secton 2 looks nto the revew of exstng and related lterature on the topc, whle secton 3 presents the theoretcal framework and outlnes the model specfcaton. Secton 4 explans the analytcal and estmaton technque. Secton 5 dscusses the emprcal results of the study and secton 6 presents the recommendatons and concluson. 2. Revew of Lterature Despte the lmted number of emprcal studes on the relaton between money demand and wealth, ths ssue has been the focus of many theoretcal studes n the last century. The concept of money demand has over the years attracted the nterest of great economsts. Unlke the demand for goods t s not restrcted to one market but also nvolves other markets (Money market, captal market commodty market and foregn exchange market), hence t has a drect bearng on monetary polcy and so relevant to the study of macroeconomcs. The focus on the demand for money s attrbuted to the fact that monetary polcy wll only be effectve f the demand for money functon s stable. Stablty of the demand for money s crucal n understandng the behavour of crtcal macro-economc varables (Essenet al., 1996). Why do ndvduals hold money? Answerng ths queston has attracted the nterest of great economsts, from Irvng Fsher n the early 1900s, to John Maynard Keynes n the early 1920s and 1930s, to Wllam Baumol, James Tobn and Mlton Fredman from the 1950s and on. Money generally refers to cons or paper notes and n a techncal perspectve ncludes a persons wealth ncludng ther property. In economcs, the lqudty approach to the defnton of money sees money n two ways. Frstly, ts narrow sense as the sum of depost and currency. Snce the demand for money s the desre to hold cash, money demand s the sum of depost demand (D d ) and currency demand (Curd), Md= D d + C urd, hence factors affectng money demand are the same as factors affectng deposts demand plus any factors affectng currency demand. Secondly, the lqudty approach sees money n a broader sense to nclude M2 and M3, but due to the low degree of lqudty of assets classfed under M3, t becomes almost mpossble to nclude any components of M3, hence moneyness, accordng to them, s a matter of degree. Accordng to Carpenter and Lange (2002), money s an asset wth a partcular set of characterstcs, most notably ts lqudty. Lke other fnancal assets, demand for money s part of a portfolo allocaton decson, n whch an agent s wealth s dstrbuted among competng assets based on each asset s relatve benefts (Tobn, 1969). To a certan extent, agents are wllng to gve up the hgher return of alternatve assets n order to receve the beneft of lqudty that money provdes. Carpenter and Lange (2002) further explaned that, standard money demand equatons nclude an nterest rate or nterest rate spread to measure the opportunty cost of holdng non-nterest earnng money. Ths s true n the sense that snce opportunty cost s the cost of alternatve foregone, a hgher return on alternatve assets depletes lqudty (cash holdng). The theoretcal foundatons on demand for money theores are well establshed n the economc lterature wth great consensus that the demand for money s n the frst place determned by real cash balances (Lungu et al., 2012). Accordng to Telyukova (2008), three domnant vews can be dstngushed, namely the classcal, the Keynesan and the post-keynesan vew. The classcal school kcked of the debate on the demand for money functon and approaches the subject of money from the quantty theory whch s based on the equaton of exchange. Popularly referred to as the Fsher s equaton of exchange t expresses the relatonshp between the nomnal supply of money (M) and the total nomnal expendture on fnal goods and servces produced n an economy(py), ndcatng Prces (P) multpled by Real Output (Y). The varable lnkng M and PY s the velocty of money (V). The precursor of ths vew wthn the classcal school s Irvng Fsher, who suggested that nsttutons n the economy 37

4 E. S. O. Odor & R. O. Alenoghena determne the velocty of money by affectng the way n whch economc agents conduct transactons (Mshkn, 2009). He argued that because of slow advances n transactons technology, the velocty of money wll reman constant n the short run. Underlyng the theory s the belef that agents hold money only for transactons purposes, therefore gnorng the senstvty of nterest rate to money demand. The Cambrdge Equaton (wth Marshall and Pgou) represents what has been called the cash-balance approach to the value of money. It smply says that the value of money depends on demand for cash-balance and the supply thereof, at any gven tme. Here we need draw attenton to one pont on the demand sde. The demand for money does not merely depend on the physcal quantty of resources or of the goods and servces, whch are sought to be exchanged, but t largely depends on the perod of tme whch the transactons are ntended to cover. Thus, only a fracton of the whole ncome s kept n cash, the rest s nvested. The amount of cash held should not be too much, because to keep cash locked up dly means a loss besdes beng a danger. Therefore, The Cambrdge School asserts that people demand money as a medum of exchange and as store of wealth. The latter lnks the level of people s wealth to money demand and, as a result, wealth can be consdered as a proporton of nomnal ncome. In ths way, wealth s a component of money demand. Patnkn (1956), followng Pgou, argues that ndvduals hold part of ther wealth n lqud form. The fundamental dfference wth respect to the Pgou s theory s that Patnkn beleves that the amount of money holdngs does not depend only on real varables, but also on what he called real-balances effects. Keynes (1936) developed the lqudty preference theory whch explctly hghlghts the transacton, precautonary and speculatve motves for holdng money. The most mportant nnovaton n Keynes analyss s hs speculatve demand for money. The prmary result of the Keynesan speculatve theory s that there s a negatve relatonshp between money demand and the rate of nterest. Keynes defned the rate of nterest as the reward for partng wth lqudty for a specfed perod of tme. Accordng to hm, the rate of nterest s determned by the demand for and supply of money. Therefore, the hgher the rate of nterest, the lower the speculatve demand for money, and lower the rate of nterest, the hgher the speculatve demand for money. To facltate hs analyss, Keynes used the assets theory, ndcatng that f the expected return of holdng bonds s greater than the return on holdng money, ndvduals wll hold bonds as a store of wealth rather than money (Mankw, 2010). Profound developments of the Keynesan approach were conducted by Baumol and Tobn n order to understand the role of nterest rates n the money demand. The three basc propostons of Keynes for holdng money were mantaned as a bass, but only precse theores were developed to explan the money demand motves (Mshkn, 2009). Accordng to the domnant Keynesan orthodoxy t was beleved that ths nstablty was manly related to money markets. Therefore, the man dea was that monetary authortes should control the nterest rates. The 70s were characterzed by the frst ol crss; so many economsts began to gve greater weght to real shocks and to the nablty of monetary authortes to correctly predct the expected rate of nflaton. In a world where prces growth was hghly volatle, they suggested the opportunty to control the money supply. A key role for the evoluton of fnancal markets was brought by the lberalzaton process and the subsequent reacton of fnancal ntermedares. In the late 70s and durng the 80s most ndustralzed countres experenced a process of lberalzaton of fnancal markets and credt. As a consequence, wealth was consdered to be a factor that can greatly nfluence money demand. As a matter of fact, when wealth s omtted, the elastcty of money demand wth respect to ncome changes, and ths s probably enough to justfy ts ncluson. Fredman (1988) asserts that the ncrease n wealth, caused by the expanson of asset prces, may be related to the ncrease n the demand for other lqud assets, such as money, drven by portfolo choces. Mlton Fredman made very crucal contrbutons to the demand for money theory. Fredman reled on assets demand determnants whch s almost n conformty wth Keynes analyss. In hs post-keynesan vew, money s consdered as a type of asset mplyng ts demand must also be nfluenced by the same factors affectng the demand of any other assets. Hence, he arranged bonds, equty and goods as types of assets to form hs wealth concept. The assessment of an ndvdual to hold an asset rather than money depends on the 38

5 Journal of Emprcal Economcs expected return of the asset wth respect to that of money. However, snce the ncentve to hold money does not change very much, the mpact of nterest on the demand for money s, accordng to Fredman's theory, very poor. Ths s n contradcton wth the explanaton of Keynes concernng the role of nterest wthn the money demand functon. The Fredman equaton ndcates that the money demand functon s determned by the expected return on money and permanent ncome of whch the permanent ncome s postve correlated wth the demand for money whle all other varables are negatvely correlated (Mshkn, 2009).The permanent ncome whch s the present value of all expected future ncome has short run fluctuatons because many movements of the ncome are short-lved. Income wll ncrease n tmes of economc growth, but because much of ths ncrease s temporary, permanent ncome wll not change much (Mankw, 2010). Ths ensures that the demand for money does not fluctuate much wth the cyclcalty of the economy, whch s usually also temporary. Money demand n part reflects a portfolo decson. As equtes have become a sgnfcant store of wealth, t seems plausble that varatons n equty markets could affect the money demand. Through tme, the stock market has become a more mportant store of wealth for households. Growth and nnovatons n mutual fund ndustry and the emergence of nternet tradng have reduced transacton costs and thus ncreased the substtutablty between equtes and money. In macroeconomc lterature, an enormous research has been conducted to estmate the money demand functon. The advancement n the tme seres econometrcs has been a major contrbuton to the estmaton of money demand functon n the last few decades. Such advancement has motvated researchers to queston the credtablty and the sgnfcant fndngs of the prevous emprcal models. Ths secton provdes a bref survey of the emprcal modelng and estmaton technques used n the appled money demand functon. James Tobn (1947) conducted one of the earlest studes on the lnk between nterest rates and money demand usng U.S. data.tobn separated out transactons balances from other money balances, whch he called dle balances, assumng that transactons balances were proportonal to ncome only, and dle balances were related to nterest rates only. He then looked at whether hs measure of dle balances was nversely related to nterest rates n the perod by plottng the average level of dle balances each year aganst the average nterest rate on commercal paper that year. When he found a clear-cut nverse relatonshp between nterest rates and dle balances, Tobn concluded that the demand for money s senstve to nterest rates. For developng countres, Arze (1989) estmates the demand for money n four Asan economes: Pakstan, the Phlppnes, South Korea, and Thaland. He argues that foregn nterest rates, exchange rate deprecaton and technologcal change are mportant determnants of the Asan money demand functons. Bahman-Oskooee and Malx (1991) estmate the demand for money functon n 13 developng countres as a functon of nflaton, real ncome and the real effectve exchange rate. They conclude that, ceters parbus, deprecaton n real effectve exchange rate results n a fall n the demand for domestc currency. However, they dd not nclude the nterest rate spread to capture the general process of fnancal asset substtuton. Recently, Bahman-Oskooee and Rehman (2005) analyzed the money demand functons for Inda and sx other Asan countres durng the perod begnnng wth the frst quarter of 1972 and endng wth the fourth quarter of Usng the ARDL approach descred n Pesaran et al. (2001), they performed contegraton tests on real money supples, ndustral producton, nflaton rate, and exchange rates (n terms of US dollar). For Inda, contegraton relatonshps were detected when money supply was as M1, but not M2, so they concluded that M1 s the approprate money supply defnton to use n settng monetary polcy. Attempts to demonstrate the determnants and stablty of the demand for money functon n Ngera dates back to the early 1970s. Ths debate started n the early 1970s amongst a group of scholars n Ngera n what s popularly referred to as the Tattoo Debate. Tomor (1972) generated a lot of debate (n what s now known as the Tattoo Debate ) on the subject matter and consequently led to further emprcal nvestgatons of the ssue. Tomor (1972) found ncome, nterest rate and real ncome to be the major 39

6 E. S. O. Odor & R. O. Alenoghena determnants of demand for money n Ngera. Owng to perceved shortcomngs of Tomor s work, Ajay (1974), Terba (1974), Ojo (1974) and Odama(1974) reacted to the fndngs. The debate centered around the sgnfcance of ncome n money demand functon for Ngera, the stablty of the functon, and the choce of approprate defnton of money demand functon n Ngera. The Central Bank of Ngera used the monetary aggregate M2, whch consstng of cash held by the publc, demand deposts, all short-term labltes held by the publc at bankng nsttutons etc for monetary polcy and analytcal purposes. On the approprate defnton of money demand n Ngera, Tomor concludes that M1 performs better than M2. In contrast, Ajay asserts that M2 performs better than M1. In an attempt to medate between Tomorand Ajay, contends that both M1 and M2 can be used as the defnton of money n Ngera. As lvely as the debate was, the ssue stll remans nconclusve. One major ssue that has nfluenced money demand n Ngera s the ntroducton of economc reforms. Snce the economc reform measures started, several studes have been carred out on the demand for money n Ngera, though not all made explct attempts at nvestgatng the stablty of money demand functon. Asogu and Mord (1987) examned the monetary sector n general to dscover some major determnants of money demand functon. Ikhde (1998) also examned nterest rate deregulaton n Ngera to see whether t s of major sgnfcance n the money demand functon n Ngera. Essen, Onwoduokt and Osho (1996), n ther work on the demand for money n a debt-constrant economy observed that ndebtedness could sgnal to prvate economc agents the drecton of government fscal and monetary polcy whch n turn nfluences the demand for money n the domestc economy. Audu (1988) n a research on selected West Afrcan countres observed that for Ngera, a stable money demand relatonshp exsts. Nwaob (2002) has also made efforts to examne the stablty of the Ngera s money demand functon and found t to be stable. Nwaob then suggests that monetary polcy could be effectve and that ncome s an approprate determnant n the estmaton of money demand n Ngera. Anoruo (2002) explores the stablty of M2 money demand functon n Ngera durng the Structural Adjustment Programme (SAP) perod. He observed that M2 money demand functon n Ngera s stable for the study perod. Agan, lke Nwaob, he asserts usng M2 money demand functon, that t s a vable monetary polcy tool that could be used to stmulate economc actvty n Ngera. Ths study concurs wth Nwaob that ncome s an mportant varable n the demand for money n Ngera and that nterest rate s nsgnfcant n the functon makng t stable. 3. Theoretcal Framework and Specfcaton of Model Theores of money demand based on portfolo choces emphasze the role of money as a store of value. These theores pont out that ndvduals hold money n ther portfolos because t provdes a low rsk nomnal return. Mlton Fredman s theory consders money demand lke the demand for any other asset (Fredman, 1956). Therefore, t should be a functon of wealth and the returns of other assets relatve to money. Accordng to the author, money demand depends on three major sets of factors: (1) Total wealth, (2) the prce and return on wealth, and (3) preferences. Accordng to Fredman there s nothng specal about money per se snce t s one of several exstng assets, and t s just one form n whch a consumer can hold hs wealth as a productve enterprse holds hs captal good. If the demand for money s not dfferent from the demand for any other commodty, we can smply specfy the varous factors whch wll nfluence the amount of t that s held. Ths, accordng to Fredman are the budget constrant of the ndvdual whch may be hs ncome or hs wealth, the prces of the varous assets (ths n the case of money demand should be the rate of return of the varous assets whch are or could be held as alternatves to money); and lastly, the tastes of preferences of the ndvdual. Aganst the background of the precedng dscusson Fredman postulates and contends that, money demand, lke the demand for any other asset, should be a functon of wealth and the returns of other assets relatve to money. In other words accordng to In Fredman, there are fve dfferent forms n whch wealth could be held: money, bonds, equtes, physcal goods, and human captal. The allocaton of total wealth between the varous forms of assets s dependent on the relatve rates of return on the varous assets. In a 40

7 Journal of Emprcal Economcs functonal form, the demand for money n real terms s wrtten by Fredman as follows d 1 dp M f rm, re, rb,,w, y p, (1) p dt where d M on equty, denote demand for real balances, r b r m s the expected rate of return on bonds, s the expected return on money, 1 dp p dt r e s the expected return s the expected nflaton rate (proxy for rate of return on physcal assets), ws the rato of human to nonhuman wealth, y p s the permanent ncome(the expected long-run average of current and future ncome), that s the real GDP-producton as a proxy to capture transactons and precautonary demand for money and s the tastes and preferences. There are major dfferences between the Fredman formulaton and the old quantty theory of money. Frst, n the Fredman analyss, velocty s no longer constant. Rather, velocty s a functon of a lmted number of varables. In the specfcaton, k s expressed as a functon of the rates of return on the assets that are alternatves to holdng money. If there s a rse n any of the alternatves assets, k would fall mplyng the ncreased desrablty of the alternatve asset. Also, from the above dscusson, there are sgnfcant dfferences between the Keynes theory of the demand for money and that of the Fredman. Frst, Keynes s vew of the demand for money was that t was unstable shftng wth changes n the publc confdence n the economy. Second, Fredman s analyses gnore the compartmentalzaton of money nto the dfferent motves as Keynes dd. Fredman does not fnd t useful or necessary to separate the attrbutes whch make money useful nto separate demands based on the uses of money. Thrd, whle Keynes focused on the choce between money versus bonds, Fredman s analytcal framework ncludes separate yelds for varous fnancal assets and durable goods. Thus, an allowance s made n the Fredman s analyses for the possblty of substtuton between fnancal assets and also substtuton from money drectly nto commodtes (durable goods) as there are changes n the rate of return. To acheve our research objectves and analyze the margnal mpacts (short and long run) of Mlton Fredman s money demand determnants demand for real balance,t s necessary and proper to drve our model from Fredman s functonal form (equaton 1). That s we test for the effect of those Fredman s factors on demand for real balances ( ) usng the followng equaton (1). The emprcal model adopted n ths study after a mnor modfcaton of equaton (1) s formally s specfed as follows: M d where m d t m ( m - p) y RM RB RS RE p ( m - p) (2) d t t 0 1 t 2 t 3 t 4 t 5 t 6 t 7 t 1 t s the real money balances, t s tme startng from 1981 to 2013, m s nomnal money demanded, p s the prce level, y s the real GDP-producton as a proxy to capture transactons and precautonary demand for money, rm s rate of return on money(the lendng nterest rate), that s the short-run of nterest on money tself, rb s the rate of return on bonds, rs s the rate of return on stocks, re s the rate of return on equtes, pt In( pt ) In( pt 1) s the rate of nflaton, s consdered as a proxy to measure the return on holdngs of goods (ncludng foregn currences), and ts coeffcent should be negatve,.e. <0, as goods (e.g ( m- p) t s the lagged real estate and other currences) are an alternatve to holdng domestc currency and 1 value of real money balances(valadkhan and Alauddn, 2003).All varables shown n lowercase (.e. m, y, and p) are n natural logarthms whle the remanng varables (.e.rm, RB, RS, and RE ) are n levels. Ina more conventonal way we may rewrte equaton 2 as; 41

8 E. S. O. Odor & R. O. Alenoghena logrmd t 0 1 logrgdp t + γ2logrob t + γ3logroe t + γ4logros t + γ5rom t + γ6inft (3) + γ logrmd + ε 7 t-1 t The model above s desgned to measure the relatonshp that exst between the dependent varable; real money demand (RMD) and the ndependent varables; real gross domestc ncome (RGDP),return on bonds(rob), return on equtes (ROE), return on stocks (ROS), return on money (ROM) and nflaton rate (INF) and the lag value ofreal money demand (RMD t-1). Ths s to see how hat s how these ndependent varables nfluence the money balance or money demand ether postvely or negatvely. The parameter 1 and 6 denote the short-run ncome and nflaton elastctes of the demand for money, whereas 2 and 5 are short-run sem- elastctes of, ROB,ROE, ROS and ROMwth respect to money demand, respectvely. Adoptng anadaptve expectatons model, one can dvde these coeffcents by (1- correspondng long-run elastctes or sem-elastctes. The a-pror assumptons for the above model based on (equaton 3.) are: 6 0, 7 0.The parameters, 0 s 1 0, 2 0, ) to obtan the, 5 0 mples a postve relatonshp between the dependent varable and ndependent varables.ths mples that an ncrease n these ndependent varables wll lead to an ncrease n money demand. The parameters, 0 s means that there s a negatve relatonshp between the dependent varable and the ndependent varables, Ths means that an ncrease n the ndependent varables wll lead to a decrease n money demand.the expectatons of the model are qute clear from the apror sgns of the coeffcents based on economc lteratures. Money demand s postvely related to permanent ncome. However, permanent ncome, snce t s a long-run average, s more stable than current ncome, so ths wll not be the source of a lot of fluctuaton n money demand. The other terms n Fredman's money demand functon are the expected returns on bonds, stocks and goods relatve the expected return on money. These tems are negatvely related to money demand: the hgher the returns of bonds, equty and goods relatve the return on money, the lower the quantty of money demanded. Fredman dd not assume the return on money to be zero. The return on money depended on the servces provded on bank deposts (check cashng, bll payng, etc.) and the nterest on some checkable deposts. So the demand for real money balances, accordng to Fredman, ncreases when permanent ncome ncreases and declnes when the expected returns on bonds, stocks, or goods ncreases versus the expected returns on money, whch ncludes both the nterest pad on deposts and the servces banks provde to depostors. Analytcal and Estmaton Technque Generalzed lnear models are a remarkable synthess and extenson of famlar regresson models such as the lnear models. Generalzed lnear models have become so central to effectve statstcal data analyss, however, that t s worth the addtonal effort requred to acqure a basc understandng of the subject.the GLM approach s attractve because t (1) provdes a general theoretcal framework for many commonly encountered statstcal models; (2) smplfes the mplementaton of these dfferent models n statstcal software, snce essentally the same algorthm can be used for estmaton, nference and assessng model adequacy for all GLMs. GLMs offer a common framework n whch we may place all of these specfcaton, facltatng development of broadly applcable tools for estmaton and nference. In addton, the GLM framework encourages the relaxaton of dstrbutonal assumptons assocated wth these models, motvatng development of robust quas-maxmum lkelhood (QML) estmators and robust covarance estmators for use n these settngs. A wde range of famlar models may be cast n the form of a GLM by choosng an approprate dstrbuton and lnk functon. 42,

9 Journal of Emprcal Economcs The Structure of Generalzed Lnear Models The canoncal treatment of GLMs s Nelder and Wedderburn (1972), and ths revew closely follows ther notaton and approach. Begn by consderng the famlar lnear regresson model, Y X, where 1,..., N ' varables or predctors,, s a k Y stochastc dsturbances. Typcally, the s a dependent varable, X s a vector of -by-1 vector of unknown parameters and the k explanatory are zero-mean are assumed to be ndependent across observatons wth constant varance, and dstrbuted normal. That s, the normal lnear regresson model s characterzed by the followng features: a) A random component or stochastc component: specfyng the condtonal dstrbuton of the response varable, Y (for the th of nndependently sampled observatons), gven the values of the 2 explanatory varables n the model. The Y wth E( ), wth constant varance 2 Y,or are usually assumed to have ndependent normal dstrbutons Y N d 2 ~ (, ) b) A lnear predctor or systematc component: the covarates coeffcents to form the lnear predctor X k k ' X. That s a lnear functon of regressors X X X (4) c) A smooth and nvertble lnearzng lnk functon response varable, EY ( ) components:the lnear predctor g(.) combne lnearly wth the, whch transforms the expectaton of the to the lnear predctor. That s thelnk between the random and systematc X s a functon of the mean parameter g( ). Note that for the normal lnear model, g s an dentty. ' g( ) X X... X (5) k k va a lnk functon, The correspondng densty functons for the normal dstrbutonfrom the exponental famly s gven by: ( y - 2yu u 2 w 2 / w f ( y, u,, w ) exp for - y Recall that the man am of ths study s to emprcally nvestgate whether ther relatonshp exsts between certan combnatons of Mlton Fredman s factors for money demand and the real money balances n relaton to Ngeran economy. As such an approprate estmaton procedure wll be adopted. Wth the formulated models n equaton 3, we carred out the model estmatons. The frst step s the unt root test whch nvolves the determnaton of the order of ntegraton, usng the ADF - Fsher Ch-square and Phllps-Perron test statstc.the second aspect s totest for contegraton, usng the Engle-Granger sngle-equaton contegraton test.the thrd aspect sthe mpact relatonshp between the dependent and the ndependent varables whch s run over the sample perod , usngthe Generalzed Lnear Model (GLM)(IRLS - Fsher Scorng)method. IRLS, whch stands for Iterated Reweghted Least Squares, s a commonly used algorthm for estmatng GLM models. IRLS s equvalent to Fsher Scorng, a Newton-method varant that employs the Fsher Informaton (negatve of the expected Hessan matrx) as the update weghtng matrx n place of the negatve of the observed Hessan matrx used n standard Newton-Raphson. The fourth and fnal test s for Specfcaton Errors whch s carred out by Ramsey Regresson Equaton Specfcaton Error Test (RESET). (6) 43

10 E. S. O. Odor & R. O. Alenoghena The data for ths study conssts of annual tme seres, they are generated n lne wth the perod covered by the study whch s , a perod of 34. Ths choce s predcated by the research method adopted for ths work and followng the purposes and objectves of the study. The data used for ths study are obtaned from the publcatons of the Central Bank of Ngera (CBN, 2010, 2013) Statstcal Bulletn and Annual Reports on major economc ndcators. 4. Emprcal Results Unt Root Test Table 1 shows Augmented Dckey-Fuller (ADF) - Fsher Ch-square and Phllps-Perron Test Statstctest of unt root conducted on all the varables to test for statonarty of the varables (Raza, 2015). From the A(ADF) - Fsher Ch-square and PP test statstcs, the results show that LOGRMD s ntegrated at order two, that s I(2) or t was statonary at second dfference, whle LOGROB, LOGROE, LOGROS, ROM and INF were all ntegrated at order one, that s I(1) or they were statonary at frst dfference. Ths poston s further renforced by the values of the varous probabltes. All the varables (except for INF that was statstcally sgnfcant at 5% and 10% crtcal values) were statstcally sgnfcant at 1%, 5% and 10% crtcal values n frst dfference. Table 1: Statonarty Test Result Null Hypothess: Unt root (ndvdual unt root process) Seres: LOGRMD, LOGRGDP, LOGROB,LOGROE, LOGROS, ROM, INF Method: ADF - Fsher Ch-square Phllps-Perron Test Statstc Order of Maxmum Order of Seres t-stat Prob. ntegraton Lag Adj. t-stat Prob. ntegraton D(LOGRMD,2) I(2) I(2) 1 D(LOGRGDP) I(1) I(1) 1 D(LOGROB) I(1) I(1) 1 D(LOGROE) I(1) I(1) 1 D(LOGROS) * I(1) * I(1) 1 D(ROM) I(1) I(1) 1 D(INF) I(1) I(1) 1 1% level % level % level % level % level % level Notes: * ndcate statstcal sgnfcance at the 5% and 10% Source: Authors Computaton Sngle-Equaton Contegraton Test Maxmum Lag The Engle-Granger tau-statstc (t-statstc) and normalzed auto-correlaton coeffcent (whch we term the z-statstc) both reject the null hypothess of no contegraton at the 5% sgnfcance level. The probablty values are derved from the MacKnnon response surface smulaton results. Gven the small sample sze of the probabltes and crtcal values there s evdence of four contegratng equaton at the 10% level of sgnfcance usng the tau-statstc (t-statstc) and evdence of fve contegratng equaton at the 10% level of sgnfcance usng the z-statstc Ths mples that the both dd not rejected the null hypothess of no contegraton among the varables at the 10 per cent level of sgnfcance. On balance, usng the tau-statstc (t-statstc) the evdence clearly suggests that LOGRGDP, LOGROB, LOGROE and ROM are contegrated, whle, LOGRMD, LOGRGDP, LOGROB, ROM and INF are contegrated usng the z-statstc. Ths mples that there exsts a long-run relatonshp or contegraton between real money demand and ts determnants. 44

11 Journal of Emprcal Economcs Table 2: Engle-Granger Contegraton Test Results Dependent tau-statstc Prob.* z-statstc Prob.* Long-run resdual varance LOGRMD LOGRGDP LOGROB LOGROE LOGROS ROM INF Source: Authors Computaton Long-run resdual varance s the estmate of the long-run varance of the resdual based on the estmated parametrc model. The estmator s obtaned by takng the resdual varance and dvdng t by the square of 1 mnus the sum of the lag dfference coeffcents. These resdual varance and long-run varances are used to obtan the denomnator of the z-statstc. Interpretaton of Estmated Coeffcents Table 3: Coeffcents mpacts Estmate Dependent Varable: LOGRMD Method: Generalzed Lnear Model (IRLS - Fsher Scorng) Famly: Normal Lnk: Identty Dsperson computed usng Pearson Ch-Square Coeffcent covarance computed usng expected Hessan Varable Coeffcent Std. Error z-statstc Prob. C LOGRGDP LOGROB LOGROE LOGROS ROM INF LOG(RMD(-1)) Mean dependent var S.D. dependent var Sum squared resd Log lkelhood Akake nfo crteron Schwarz crteron Hannan-Qunn crter Devance Devance statstc Restr. devance LR statstc Prob(LR statstc) Pearson SSR Pearson statstc Dsperson Source: Authors Computaton Fredman s work on the demand for money began wth The Quantty Theory of Money: A Restatement (1956) publshed as the lead essay n Studes n the Quantty Theory of Money (Fredman, Ed, 1956). These tems n our result n Table 3 that are n Fredman's money demand functon are negatvely 45

12 E. S. O. Odor & R. O. Alenoghena related to money demand: the hgher the returns of bonds, equty, stock and goods relatve the return on money, the lower the quantty of money demanded. Although, LOGROB, LOGROE, LOGROS and ROM are negatvely related to the level of money demand n Ngera, the p-values statstcs shows that they were not statstcally sgnfcant.elastcty, whch s the measure of opportunty cost of holdng money are found to be , , and respectvely. Ths not sgnfcant relatonshp provdes evdence n support of opportunty cost of holdng money n Ngera. These are consstent wth most emprcal studes on the determnants of real money balances. An ncrease n the nterest rate wll lead to a reducton n the demand for money. So, an nvestor wll decde to allocate ts portfolo between money and bonds An ncrease n the nterest rate wll lead to a reducton n the demand for money a proportonal ncrease n the nomnal demand for money: n fact, f prces of all. If bond prces decrease, then the: nterest rate decreases and transactons demand for money wll ncrease. An ncrease n the nterest rate wll lead to a reducton n the demand for money because hgher nterest rates wll lead nvestors to put less of ther portfolo n money (that has a zero nterest rate return) and more of ther portfolo n nterest rate bearng assets (Treasury blls).fredman dd not assume the return on money to be zero. The return on money depended on the servces provded on bank deposts (check cashng, bll payng, etc) and the nterest on some checkable deposts. Other mportant varables estmated n ths model are real GDP, rate of nflaton and past value of real money demand. The estmated regresson lne shows that real GDP (LOGRGDP), rate of nflaton (INF) and past value of real money demand (LOG(RMD(-1))).have postve relatonshp wthreal money demand n Ngera. The regresson coeffcent of LOGRGDP, INF and LOG(RMD(-1)) are , and , respectvely whch mples that %, 13.80% and 90.99% of the ncrease n the real money demand n the perod under revew are accounted for by a 100% ncrease n real GDP, rate of nflaton and past value of real money demand,respectvely. The p-values statstcs shows that they were statstcally sgnfcant. Ths mpact mples that these varables are the major contrbutor to money demand n Ngera. Also, we found the results consstent wth most emprcal studes except for nflaton whch most consdered to be negatvely related to money demand. Accordng to most emprcal studes, an ncrease n the ncome of the nvestor wll lead to an ncrease n the demand for money. In fact, f ncome s hgher consumer wll need to hold more cash balances to make transactons (buy goods and servces).in the case of nflaton we explaned that, an ncrease n the prce level (nflaton) wll lead to a proportonal ncrease n the nomnal demand for money: n fact, f prces of all goods double, we need twce as much money to make the same amount of real transactons. Snce the nomnal money demand s proportonal to the prce level, we can wrte the real demand for money as the rato between money demand and the prce level. Then, the real demand for money depends only on the level of transactons and the opportunty cost of money (the nomnal nterest rate): Regresson Specfcaton Error Test In ths study, we use the Ramsey s (1969) Regresson Specfcaton Error Test (RESET) as a General Test for Functonal Form Msspecfcatonfor the lnear regresson model. RESET has proven to be useful n ths regard that s detectng neglected nonlneartes n estmated models. More specfcally, t tests whether non-lnear combnatons of the ftted values help explan the response varable. The ntuton behnd the test s that f non-lnear combnatons of the explanatory varables have any power n explanng the response varable, the model s ms-specfed. Ramsey's suggeston s to nclude powers of the predcted values of the dependent varable (whch are, of course, lnear combnatons of powers and cross-product terms of the explanatory varables). In our study, we used the RESET test as a general test for the followng types of specfcaton errors: (1) Omtted varables; the explanatory varables (LOGRGDP LOGROB LOGROE LOGROS ROM INF (LOGRMD(-1)))do not ncludeall relevant varables. (2) Incorrect functonal form; some or all of the 46

13 Journal of Emprcal Economcs varables n model should be transformed to logs, powers, recprocals, or n some other way. (3) Correlaton between explanatory varables and the error term, whch may be caused, among other thngs, by measurement error n explanatory varables, smultanety, or the presence of lagged RMD values and serally correlated dsturbances. Table 4: Regresson Specfcaton Error Test Result Ramsey RESET Test Specfcaton: LOGRMD C LOGRGDP LOGROB LOGROE LOGROS ROM INF (LOGRMD(- 1)) Omtted Varables: Powers of ftted values from 2 to 3 Value DF Probablty F-statstc (2, 24) Lkelhood rato F-test summary: Sum of Sq. DF Mean Squares Test Devance Restrcted Devance Unrestrcted Devance Dsperson SSR LR TEST SUMMARY: VALUE DF Restrcted Devance Unrestrcted Devance Dsperson Source: Authors Computaton The result n Table 4 shows that theramsey RESET test used the powers of the ftted values of real money demand (RMD) as we assumed that all explanatory varables are exogenous and the test are lkelhood rato based tests.the top porton of the output shows the test settngs, and the test summares. Lookng at the F-statstc, lkelhood and probablty value, the results show evdence of lnearty wth no case of omtted varables, ncorrect functonal form and correlaton between explanatory varables and the error term. 5. Recommendatons and Conclusons The purpose of ths study s to nvestgate the demand for money n the Ngera. The results obtaned were n tandem wth a pror expectaton n terms of sgns and magntude. Income and nflaton turned out to be postve and sgnfcant n affectng the demand for real money balances whle, other varables n the specfcaton such as returns on stock, return on equty and return on money were negatve and sgnfcant conformng to a pror expectatons. Ths ndcates that the demand for real money balance n Ngera possesses a predctable monetary aggregate.the stablty of money demand s crucal n assessng the longer-term relatonshp between money and prces To understand the economc mechansm that leads to ths adjustment, the nvestor must decde how much to nvest n money and how much to nvest n bonds. Snce the demand for money s a negatve functon of the nterest rate, the demand for bonds wll be a postve functon of the nterest rate: as nterest rates become hgher, the nvestor would lke to put more of her wealth n bonds and less of her wealth n cash. 47

14 E. S. O. Odor & R. O. Alenoghena Gven the fndngs above, the followng recommendatons are hereby proposed for ths research study: Frst, the monetary authortes should have the poltcal-wll to effectvely control and accurately predct aggregate monetary varables to acheve macroeconomc objectves whch transcends to economc growth n Ngera. It s encouraged that the monetary authorty should be truly ndependent or autonomous n order to effectvely and effcently dscharge her monetary polcy oblgatons to the economy. Second, the government should free the fnancal market from the shackles of her manpulatons to allow the forces of demand and supply determne what happens n the fnancal market as ths s the case n most developed countres. Ths would make t easer to acheve the objectves of monetary polcy n terms of nflaton control, compettve nterest rate, approprate exchange rate and money supply. Thrd, the nvestment habts of the Ngeran people should be mproved through carefully planned fnancal ncluson programmes that are nspred by the monetary authortes. Ths would stmulate more postve bankng habts among the people and enhance decson on the sophstcated choces between nvestment n securtes and holdng on to money balances. Fourth, the monetary authortes should take account of some mportant varables n the determnaton of money demand n Ngera; of partcular mportance s the lagged value of money demand whch played an mportant role durng the perod under revew n ths study. So far, the mpact of ths varable has not been gven much attenton n the determnaton of money demand analyss n Ngera. Fnally, monetary macroeconomc polcy nconsstency and ad-hoc responses to macroeconomc trends should be dscontnued forthwth n the management of the country s macroeconomc affars. Frequent,llconceved and reactve changes n monetary macroeconomc polces most often serve to further exacerbate a worsenng economc drecton for a country. Proper long-term plannng wth a clear strategc drecton for the country s monetary macroeconomc stuaton s more benefcal for the country s long-term growth objectve. The above recommendatons are n conformty to our stated a-pror expectaton that there exsts a postve relatonshp between the Real Gross Domestc Product and money demand and Consumer Prce Index and money demand n Ngera and also an nverse relatonshp between return on stocks, return on equty and nterest rate on money demand n Ngera. The Ngeran stuaton has shown support for the exstng relatonshp between money and prces over tme. The analyss somewhat establshes that the relatonshp could be essentally ndependent of the tme perod consdered. References Ajay S.I (1974): The Demand for Money n Ngera: Comments and Extensons NJESS, 16 (1) Pp Anoruo, E. M. (2002): Stablty of the Ngeran M2 Money Demand Functon n the SAP Perod. Economcs Bulletn. Vol. 14, No. 3, P. 179 Arze, A, 1989, An Econometrc Investgaton of Money Demand Behavour n four Asan developng countres, Internatonal Economc Journal 3(4), Asogu, J. O and C.N.O Mord (1987): An Econometrc Model of the Ngeran Monetary Sector: Outlne and Prelmnary results, Mmeo, Central Bank of Ngera. Audu, M. M. (1988): Stablty of Demand for Money Functons n Selecton West Afrcan Countres ( ), unpublshed M. Sc. Thess, Department of Economcs, Unversty of Lagos. Bahman Oskooee, M. and Rhee, H.J. (1994), Long Run Elastcty s of the Demand for Money n Korea: Evdence from Co ntegraton Analyss, Internatonal Economc Journal, 8(2). Baumol E.J. (1953), The Transactons Demand for Cash: An Inventory Theoretc Approach Quarterly Journal of Economcs,Vol