Money Demand Funcion for Pakisan Nisar Ahmad, Amber Naz, Amjad Naveed and Abdul Jalil 1 Absrac The main objecive of his sudy is o empirically esimae he long run money demand funcion for Pakisan using ime series daa. For his purpose we used annual daa from 1953 o 23. The resuls of uni roo analysis have suggesed ha boh log of nominal GDP and log price are possibly I (2) variables. The resuls of uni roo wih srucural break for real M 1 and M 2 have suggesed ha log of real M 1 is fracionally inegraed where as log of real M 2 is rend saionary. Resuls of I(2) co-inegraion analysis have suggesed ha here are some I(2) rends in he model wih nominal variables hence in order o avoid complicaions involved in he analysis of I(2) rends we ransformed our model in real variables. We found one co-inegraion relaion for boh M 1 and M 2. The sign of he esimaed coefficiens for GDP and ineres rae in M 1 money demand funcion are according o heory bu coefficien of ineres rae has wrong sign for M 2 money demand relaion bu i is saisically insignifican. We acceped he hypohesis ha boh real GDP and ineres rae are weakly exogenous in long run money demand relaion for boh M 1 and M 2. Demand for money for boh M 1 and M 2 are found o be inelasic wih respec o ineres rae which is quie obvious for an underdeveloped counry like Pakisan where financial markes are underdeveloped, infrasrucure is poor and informaion sysem is sill very slow. I. Inroducion The main objecive of his sudy is o esimae long run sable money demand funcion for Pakisan. Some research has already been done for Pakisan on his issue bu differen sudies have arrived a differen conclusions. This is due o he fac ha differen sudies have used differen daa ses and differen 1. The auhors are, respecively, PhD. scholar a Universiy of Arhus Denmark, Research Fellow a Universiy of Arhus Denmark, Assisan Prof. a Deparmen of Economics, FC College (Universiy), Lahore and PhD. scholar a Universiy of Wuhan China.
mehodologies. In his sudy we would like o esimae money demand funcion for longer ime series and by using recen advances in ime series analysis. We have used 51 annual observaions from 1953 o 23 for esimaion. Firs we did univariae analysis of he single series o know he order of inegraion for boh nominal and real variables. We have applied ADF and KPSS uni roo es by allowing srucural break in he rend funcion for real series as here is quie visible srucural break due o oil price shock of he hisory (see Perron (1989), Busei e al (21). We have esimaed long run demand funcion for narrow money (M 1 ) and broad money (M 2 ) in dynamic vecor auo regressive (VAR) models by using Johansen coinegraion framework (Johansen (1988)). Oher variables in he model are GDP, price and ineres rae. We will do I (2) coinegraion analysis in order o make sure ha here are no I (2) rends in our model. The resuls of ADF uni roo es have shown ha log of price and log of nominal GDP are I (2) variables where as KPSS es has no suppored his evidence. The resuls of uni roo analysis for real variables have suggesed ha M 1 is difference saionary when we have no allowed srucural break where as i is fracionally inegraed when we allowed srucural break in he ess. M 2 is found o be rend saionary even when we have no allowed for srucural break bu he resuls wih srucural break srongly confirmed ha his series is rend saionary. Resuls of I (2) analysis for modelling boh nominal M 1 and M 2 have shown ha here are some I (2) rends in he model. In order o avoid he difficulies involved in I (2) analysis we hen ransformed our nominal variables ino real. The resul of I (2) analysis hen confirmed ha here are no I (2) rends in model wih real variables. We found one coinegraion relaion in modelling boh M 1 and M 2. The sign of he coefficiens in M 1 money demand relaion are according o heory where as for M 2 money demand relaion ineres rae has he wrong sign bu i is found o be saisically insignifican. The es of hypohesis for adjusmen marix have shown ha boh GDP and ineres rae are weakly exogenous in he long run money demand relaion. We also acceped he hypohesis ha boh M 1 and M 2 inelasic wih respec o ineres rae. This resul is qui obvious for an underdeveloped counry like Pakisan where mos of he people are living on subsisence level and financial marke is imperfec. Res of he sudy is organized as follows. Secion II, provides review of relevan sudies on his issue peraining o Pakisan. We discussed heoreical background on money demand in secion III. Besides, daa and differen variables included in our model are also discussed in his secion. Secion IV consiss of Uni roo analysis. Coinegraion ess are discussed in secion V. Moreover, mulivariae dynamic analysis for esimaing 33
long run money demand is also analyzed in his secion. The conclusion of he sudy is given in secion VI. II. Lieraure Review A lo of empirical research has been done for esimaing money demand funcion for differen counries. In his secion we would like o menion some of he earlier sudies and heir main findings abou he esimaion of money demand funcion for Pakisan. The firs imporan sudy for Pakisan was done by Manga (1979). This sudy only used 14 annual observaions and resuls he obained were no according o heory and were no reliable due o such a small sample. Khan (198) did his sudy on larger sample saring from 196 o 1978. The sudy ried o see he effec of inflaion and moneizaion on money demand. I was found ha inflaion has no effec on money demand before 1971 bu i has significan effec afer ha period due o higher inflaion. Khan (1981) esimaed money demand funcion for differen definiions of money by using he same daa bu he arrived a he same resuls. Cornelisse (1989) esimaed he money demand funcion for Pakisan by using monhly daa from 1975 o 1989. The daa on GDP on monhly basis was no available hence he divided he annual GDP o 12 pars o accoun for his problem. The sudy also used broad and narrow definiion of money o esimae disaggregaed money demand funcion. The auhor found beer resuls for broader definiion of money as compared o narrow money. Using he daa from 1951 o 1991 Hossain (1994) performed coinegraion analysis o find sable money demand funcion. The resuls showed ha sable money demand funcion do no exis for broad definiion of money. Khan (1994) found a sable relaionship beween broad money, real income and medium erm ineres rae by using quarerly daa from 1971.3 o 1993.2. The sudy also found ha money demand is no coinegraed wih shor run ineres rae and inflaion rae. M1 money was found o be coinegraed wih real income, real ineres rae and inflaion rae. The review of above lieraure suggess ha here exis huge differences in he resuls for money demand funcion in Pakisan. The reason could be ha hese differen sudies have used differen daa se and differen mehodology. In his sudy we would raher like o use advance economeric echniques o search for sable money demand funcion. 34
III. Theoreical Background There exiss huge and diverse lieraure on heories of money demand. These differen heories direcly or indirecly sugges ha real money demand depends on real ransacions volume and nominal ineres rae. Nominal ineres rae represens opporuniy cos of holding money. The basic money demand funcion can be summarised in he following funcional from 2 : M Y = f, i P P Where M is he aggregae demand of money, Y is Gross domesic produc, P is he price index which is used o find he real money demand and Real GDP and i is he ineres rae. The long run sable relaionship in linear form can be wrien as follows: = β + β y + i m 1 2 β 3 where: m = Log of Real money balances y = Log of Real GDP i = Ineres Rae Theoreically we expec β 2 > and β 3 < for meaningful money demand relaion (for more deail see for example Ericsson and Sharma (1996)). β 2 = 1 is consisen wih quaniy heory of money and β 3 = will exclude he role of ineres rae in he deerminaion of money demand. Some sudies have also used expeced inflaion as an explanaory variable for explaining money demand. This is ypically done for he counries where financial marke is no well developed or here is very high inflaion rae (see Choudhry(1995a) and Choudhry (1995b)). Aresis e al (1991) have argued ha in developing counries which do no have alernaive financial asses o money, nominal ineres raes can be viewed as own-rae of money and expeced inflaion rae is he reurn on real asses. 3.1. Daa and Variables We used M 1 and M 2 definiion of he money. M 1 is he narrow definiion of money which is defined as he money sock which is readily available in everyday ransacions and i consiss of sum of currency ouside deposi money banks and demand deposis oher han hose of he cenral governmens. M 2 is he broad definiion of money sock wih less liquid asses and componens of his 2. For deail survey of lieraure on money demand see for example Sriram (1999). 35
sock of money are M 1 plus ime, saving and foreign currency deposis of residen secors oher han cenral governmen 3. Gross domesic produc (GDP) represens he ransacions volume. In he lieraure long run ineres rae has been used o capure he effec of opporuniy cos of holding money bu in under develop counry like Pakisan where inflaion is very high, financial markes are imperfec and real ineres rae is someimes close o zero or even negaive hence we would raher like o use shor run ineres rae which is also known as iner bank call money rae. For prices we used GDP deflaor because daa of CPI was no available for some saring years. The daa on differen definiions of money is available on monhly and quarerly basis bu i is no available for GDP series. Insead of GDP some sudies have used index of indusrial producion as an approximaion. For our sudy we would raher like o use annual daa which is available from 1953 o 23 for Pakisan. By using annual daa we can avoid a lo of seasonal variaions bu we will have fewer observaions as compared o quarerly daa. M 1, M 2 and and GDP are deflaed by GDP deflaor o find he real variables. The daa are been downloaded from he websie of Inernaional Financial Saisics 4. The graphs of he nominal and real series are shown in figure A1 and A2 in he Appendix respecively. IV. Uni Roo Analysis We would like o use he Panula principle (Panula (1989)) in order o know he inegraion order o he single series. According o his principle firs we will difference he series unil he uni roo is rejeced by using differen es. Then we will apply uni roo ess on he series wih one less difference han in he previous es. This procedure will coninue unil uni roo is rejeced. A series is saionary if he roos of he characerisic equaion lie inside he uni roo circle or roos of lag polynomial lie ou side he uni circle. There are differen es proposed by he heory and each es has is own pros and cons. These ess include Dicky Fuller es (Fuller (1976), Dickey & Fuller (1979)), Augmened Dicky-Fuller (Dicky & Fuller (1981)), Phillips Perron es (Phillips (1987), Perron (1988), Perron (1989)), KPSS es (Kwiakowski, e al (1992)). 3. These definiions have been used in he lieraure and we have aken from Inernaional Financial Saisics. 4. Link o Inernaional Financial Saisics can be found on he homepage of IMF official websie www.imf.org 36
4.1. Dickey Fuller and Augmened Dicky Fuller Tes Dicky Fuller es is proposed o es for uni roo in firs order auo regressive model i.e AR (1) wih he assumpion ha errors are whie noise. The basic regression of his es can be wrien as follows: Y m +α + ε (1) = Y 1 In he above regression if α < 1, where α is acually he characerisic roo of he above difference equaion or reciprocal of he roo of lag polynomial, hen Y series will be saionary. The null hypohesis is ha roo is one and agains he alernaive ha i is less han one, so we are esing non-saionariy in he null hypohesis agains he alernaive of saionariy. Hence under he null hypohesis he series is random walk and is disribuion of disurbances is non sandard. The usual sandard procedure can no be applied insead Dicky-Fuller disribuion can be used and his disribuion depends upon he deerminisic pars of he model. Above analysis requires ha he disurbances are whie noise and if i is no he case hen we will have o use oher ess. One possibiliy could be o use Augmened Dicky-Fuller es. Augmened Dicky-Fuller es (Dicky & Fuller (1981)) is jus he exension of he simple Dicky-Fuller es o make he disurbances whie noise by including more lags of he dependen variable. There is anoher advanage of using ADF es over simple DF es ha i can be used o es uni roo in higher order auo regressive scheme. General ADF regression can be wrien as follows: Y = m + γ Y + β Y + β Y +... + β Y + ε 1 1 1 2 2 p p In his formaion esing for uni roo means ha we are esing for γ = agains he alernaive ha i is less hen zero. The decision abou how many lag differences o be included in he regression can be based on he model selecion crierion, for example AIC crierion or a sequenial esing procedure in which insignifican lags can be eliminaed. 4.2. ADF Tes for Series wih Srucural Breaks Perron (1989) has proposed a uni roo es for he series wih srucural break. He showed ha sandard uni roo es failed o rejec he null hypohesis of difference saionariy agains he alernaive of rend saionariy if here are srucural breaks in he series wih known ime of he breaks. He suggesed hree differen models o incorporae he changes in he rend funcion. Model (1) allows for he shif in inercep of he rend funcion and he referred i as he crash model. Model (2) allows for he change in he slope of he rend funcion and he referred his model as he changing growh. Model (3) allows for he (2) 37
change in boh inercep and slope of he rend funcion which is referred as sudden change and followed by a differen growh pah. The funcional forms of he hree models are as follows: Model (1) y = α + δt + ψd + u and u = β 1 u 1 + β 2u 2 +... + β pu p + ε Y = m + ψ D+ δt + γ Y β Y β Y... 1 1 1 1 1 1 1 2 2 β Y + ε...(3) p p+ 1 Model (2) y = φ + α + δt + D u and u = β 1 u 1 + β 2u 2 +... + β pu p + ε Y = m + φ D + δ T + γ Y β Y β Y... 2 2 2 2 1 1 1 2 2 β Y + ε...(4) p p+ 1 Model (3) y = φ + α + δt + ψd + D u and u = β 1 u 1 + β 2u 2 +... + β pu p + ε Y = m + δ D+ θ T + φ D + γ Y β Y β Y... 3 3 3 3 3 1 1 1 2 2 β Y + ε p p+ 1...(5) Where D = for T < T B and D = 1 for T T B D = for T < T B and D = T- T B for T T B Where T B is he ime when break occurred. The es of uni roo in all he above models corresponds o es he hypohesis ha coefficien of Y -1 is zero. The disribuion of es saisic depends on deerminisic of he models as in he case of ess wihou he break bu now in his case i also depends upon he ime of he break. Perron (1989) defined a parameer λ know as break fracion o capure he iming of he break and i is defined as he raio beween pre break sample size wih oal sample size. 38
4.3. KPSS es All he ess described above es for uni roo agains he alernaive of level or rend saionariy. Kwiakowski e al (1992) proposed an LM es in which we es for saionariy agains he alernaive of uni roo. This es uses he following model o es for uni roo: y = α + δ + + ε...(6) r Where + 1 r = 2 r u u is iid (, ) 2 Ho: σ = (y is saionary afer derending, demeaning or boh) u H1: σ 2 ( y is non saionary) u KPSS es saisics = T Where and S s 2 ( l) = i= 1 ε 2 = 1 S 2 σ u 2 s ( l) is he long run variance i = 1,2,..., T Normally his es is used ogeher wih oher ess o ge conclusive resul abou he saionariy of he series. Baillie e al (1996) summarized four possible oucomes if KPSS es is used ogeher wih ADF and PP es which are described as follows: Rejecion of he hypohesis by ADF and PP es and failure o rejec he hypohesis by KPSS es is viewed as srong evidence of covariance saionary process. Failure o rejec hypohesis by ADF and PP es and rejecion by KPSS es is viewed as srong evidence of uni roo process. Failure o rejec he hypohesis by ADF, PP and KPSS es is viewed as insufficiency of informaion from he daa. Rejecion of hypohesis by ADF, PP and KPSS es indicaes he possibiliy of fracional inegraion. 4.4. KPSS es wih srucural breaks Busei e al (21) modified KPSS es for presence of random walk componen in a saionary or rend saionary ime series by allowing for srucural break in he series. They also simulaed he disribuion of he modified 39
es saisic. Tes saisic is exacly he same as in he above KPSS es bu now we have o use residuals from model ha allows for srucural break by using appropriae dummy variables for shif in level or shif in he slope of he rend funcion. The general model can be wrien as follows: y = α + δ + r + α D + δ D + ε...(7) d d where D = D = before break and D = 1 and D = T - T B afer he break The choice of dummy variable D and D depends upon he naure of he break as we already discussed in secion 4.2. 4.5. Resuls of Uni Roo Tess The resuls of uni roo ess described above are repored and discussed in his secion. Table: 1. Resul of Uni Roo for Nominal Variables Variable Level Firs Difference Second Difference Saus ADF es KPSS es ADF es KPSS es ADF es KPSS es saisic Saisic saisic Saisic Saisic saisic Nominal -3.8 (3) -5.91 () -8.27 (1).368.49 Money M 1 C, T C C.34 I (1) Nominal -2.59 (1) -5.15 () -6.59 (2).336.332 Money M 2 C, T C C.24 I(1) Nominal -2.27 (1) -2.51 (3) -8.68 ().335.378 GDP C, T C C.69 I(2) Price -2.56 (1) -2.79 (3) -6.54 (1).27.288 C, T C C.55 I(2) Ineres -1.87 () Rae C 1.161-7.18 ().371-9.52 (1).113 I(1) Criical Value 5% 3.5 (C, T).146 (C, T) 2.92 (C).463 (C) 2.92 (C ).463 (C) Number in he parenhesis represens number of lags included in he ADF regression o make he error whie noise In KPSS es auomaic lag selecion crierion is used for selecing opimal lags for calculaing long run variance C and T represen consan and rend respecively as deerminisic of he model. 4.5.1 Uni Roo Analysis of Nominal Variables The graphs of he nominal series are shown in he appendix A.1. The resuls of he uni roo analysis for nominal variables are repored in able (1). Following he Panula principle firs we applied uni roo ess on he second differences for all he series and resuls have shown ha second differences of all 4
he series are saionary. In second sep we applied uni roo ess on firs differences. For M 1 series boh ADF and KPSS es rejeced heir respecive hypohesis hence here is possibiliy of fracional inegraion in firs difference of he series. Firs difference of M 2 is urned ou o be saionary by boh ADF and KPSS es. The uni roo es resuls on he firs differences of Log of nominal GDP and log price have shown ha here is insufficiency of informaion from he daa since boh ADF and KPSS es have acceped heir respecive hypohesis. Firs difference of ineres rae is found o be saionary. Then we proceed o es for uni roo on level of he differen series. We included rend in he regression for all he series excep for ineres rae. All he series excep ineres rae are found o difference saionary in level where as ineres rae is found o be nonsaionary. The above discussion suggess ha excep nominal GDP and price all he series are inegraed of order one where as hese wo series could possible be I (2). 4.5.1 Uni Roo Analysis of Real Variables In order o avoid he complicaions involved in analysis of I (2) variables we hen ransformed nominal variables ino real variables by dividing nominal variables wih price. The analysis of real variable is more ineresing and imporan so we will discuss he uni roo analysis of individual series separaely and in more deail. Following he Panula principle firs we applied uni roo on firs differences and firs differences of all he series are found o be saionary hence we proceeded by applying uni roo es on level of each series. 4.5.2 Log of Real Money M 1 and M 2 If we see he graph of real money M 1 and M 2 in figure 2, here is clearly a srucural break a he year 1974. This break is well known due o he oil price shock 5 of he hisory ha affeced almos all he counries. I can be seen ha he level of M 1 series is shifed downward where as slope of i is increased by his srucural change. For M 2 only level is shifed downwards bu he slope of he series is consan. Hence in M 1 series we allowed wo dummies, one for he change in he inercep and one for he change in he slope of he rend funcion where as in M 2 series only inercep dummy is allowed o capure level shif. Model (3) is esimaed for uni roo es on M 1 and Model (1) is esimaed for M 2. The criical values of he es saisic depend on he value λ which is equal o.4 in our sudy. The series are difference saionary under he null and rend 5 The srucural break could also be due o he separaion of he Pakisan ino Eas Pakisan (Bangladesh) and Wes Pakisan (Pakisan) in 1971. 41
saionary agains he alernaive hypohesis. If D and D is no included hen his is usual Augmened Dicky Fuller regression. The resuls of uni roo (wih and wihou srucural break) are repored in able 2. For M 1 series ADF es failed o rejec uni roo es and KPSS es has rejeced he hypohesis of saionariy hence here is srong evidence of difference saionariy. For M 2 series he null hypohesis of he ADF es is rejeced a 5% level (bu acceped a 1% level) where KPSS es fails o rejec he null hypohesis even a 1% level of significance hence here is srong evidence of rend saionariy in M 2 a 5% level (bu no a 1% level of significance). 9.5 9.25 Log of Real M1 Fied 9. 8.75 8.5 8.25 8. 7.75 7.5 7.25 1955 196 1965 197 1975 198 1985 199 1995 2 25 1. Log of Real M2 Fied 9.5 9. 8.5 8. 7.5 1955 196 1965 197 1975 198 1985 199 1995 2 25 Figure 2. Graph of he acual series wih deerminisic fied rend When we allowed srucural break in M 1 series hen his series urned ou o be fracionally inegraed since boh ADF and KPSS es have rejeced heir respecive hypohesis. Resuls wih srucural break in M 2 confirmed ha i is rend saionary and now boh ADF and KPSS ess have rejeced and failed o rejec he null hypohesis respecively a 1% level of significance. This resul is opposie o he earlier findings where boh M 1 and M 2 definiion of money were found o be difference saionary (Hossain (1994)). This difference could be due 42
o differen reasons bu resuls of his sudy are more reliable since we have used longer ime series and applied beer echnique since ADF wihou srucural break has less power because i akes known srucural break as a noise ino he process Perron (1989). Wihou Srucural Break Wih Srucural Break Table: 2. Resul of Uni Roo Tes for Real Money Supply Series ADF KPSS Saus L= L= 4 L= 8 Auo 6 L = 4 Fail o rejec by ADF es and rejeced by M 1 -.296 (-2.91).492.184.146.184 KPSS hence here is srong evidence of M 2 -.434 ( -3.76).244.14.16.14 Criical -3.5.146 Value a 5% M 1 -.499 (-4.25).25.17.98.17 Criical Value a 5% -4.22.66 M 2 -.674 (-5.64).23.95.16.95 Criical Value a 5% -3.74.123 () -saisic is repored in parenhesis for ADF es difference saionary. Rejecion by ADF and Failure o rejec by KPSS. Hence Srong Evidence of Trend Saionariy Rejecion by ADF and rejecion by KPSS is he evidence of Fracional Inegraion Same resul as above bu now ADF is rejeced even a 1 % level. Trend Saionariy 4.5.3 Uni Roo Tes on Log Prices The graph of he series in figure (3) shows ha afer 1974 boh inercep and slope of he rend funcion has been changed due o srucural break. Resuls 6. Auo means auomaic bandwidh selecion procedure proposed by Newey and Wes (1994) as described by Hobijn e al. (1998, p.7) is used o deermine maximum lags. In ha case, a single value of he es saisic is produced, a he opimal bandwidh. Saa 7 used ha procedure by defaul o selec lag auomaically. 43
are repored in able 3. Hence we allowed wo dummies one for change in he inercep and one for change in he slope of he rend funcion. Hence model (3) is esimaed o es for uni roo. ADF es has failed o rejec he null hypohesis where KPSS es rejeced he hypohesis a 5% hence here is srong evidence ha series is difference saionary. We hen allowed for srucural break in inercep and slope bu sill ADF es failed o rejec he uni roo hypohesis bu now KPSS es also failed o rejec he hypohesis hence his resul is viewed as insufficiency of informaion from he daa. 4.5 Log Price Fied 4. 3.5 3. 2.5 2. 1.5 1955 196 1965 197 1975 198 1985 199 1995 2 25 Figure 3. Graph of he acual values along wih fied rend Table: 3. Resul of Uni Roo Tes for Log Price (wih and wihou Srucural Break) ADF KPSS Saus Wihou Srucural Break Criical Value a 5% Wih Srucural Break Criical Value a 5%.116 ( -2.56) L= L= 4 L= 8 Auo L= 4.663.164.121.164-3.5.146 -.316 (-4.3).23.93.124.88-4.22.66 Failure o rejec by ADF and Rejecion by KPSS. Hence Srong Evidence of Difference Saionariy Fail o rejec by ADF and Rejecion by KPSS is viewed as Difference Saionariy 4.5.4 Uni Roo Tes on Log of Real GDP The graph of GDP in figure (4) also shows ha inercep of he rend funcion is shifed lile bi down afer 1974; hence we applied he uni roo es 44
wih srucural break ha allows for shif in he inercep of he rend funcion where as slope is almos consan afer he break. The crash model (1) is esimaed for his series as i was used in he case of uni roo es on log of real money supply. The resuls are repored in able 4. ADF es is failed o rejec he null hypohesis and KPSS has rejeced he null hypohesis hence here is srong evidence of difference saionary. The resuls wih srucural break have given he same resuls. 1.5 Log of Real GDP Fied 1.25 1. 9.75 9.5 9.25 9. 8.75 8.5 8.25 1955 196 1965 197 1975 198 1985 199 1995 2 25 Figure 4. Graph of he acual values along wih fied rend Table: 4. Resul of Uni Roo Tes for Log of Real GDP (wih and wihou Srucural Break) ADF KPSS Saus Wihou Srucural Break -.123 L = L = 4 L = 8 Auo L = 4 ( -2.14).678.165.115.165 Criical Value a 5% Wih Srucural Break Criical Value a 5% -3.5.146 -..88 (-1.49).614.184.124.184-3.74.123 Failure o rejec by ADF and Rejecion by KPSS. Hence Srong Evidence of Difference Saionariy Same resul as above Difference Saionariy Uni roo analysis above has suggesed ha real GDP and log price are difference saionary and ineres rae is non saionary around level where as M 1 is difference saionary bu wih srucural break i is fracionally inegraed and M 2 is rend saionary. 45
V. Coinegraion Analysis The basic objecive of he coinegraion analysis is o look for sable long run relaionship among variables. There are wo mehods o look for sable relaion, firs, Engle and Granger single equaion saic analysis proposed by Engle and Granger (1987), second, muliple equaion dynamic analysis suggesed by Johansen (1988). 5.1 Coinegraion Analysis in Engle-Granger s Framework. In his procedure coinegraion exiss if he linear combinaion of differen I (1) variables is I (). The mehodology of his procedure is o regress variables in level and hen apply uni roo es on residuals obained from he regression. If he residuals urn ou o be saionary hen he variables are said o be coinegraed and his linear combinaion could be inerpreed as sable long run relaionship. We have no used his procedure because i is based on very resricive assumpions ha all explanaory variables are exogenous. 5.2 Coinegraion Analysis in Johansen s Framework. Johansen coinegraion analysis is based on dynamic VAR model (see Johansen (1988)). The unresriced VAR model wih lag order of k can be wrien as follows: y = m k + π i y j + ε i= 1 Where y is he vecor of variables o be included in he model wih dimension p x 1 and y -j is he marix of coefficiens for vecors of lag variables. π i is he marix of coefficiens for lag variables. ε is p x 1 vecor of sochasic random erm disribued independenly and idenically. The vecor error correcion formulaion of he model can be wrien as follow o represen shor run and long run componens of he model. y = m + Πy 1 + Γ1 y 1 +... + Γk 1 y k + 1 Where Π = 1 π 1... π k Π 1 + ε y explains he sable long run relaionship beween he level of he variables and he remaining erms explains he shor run changes. The dynamic properies of he model depend upon he properies of he Π marix. In order o deermine he number of coinegraion relaion we need o deermine he rank of his marix Π. If his marix has full rank i.e. p hen all variables in he model 46
are saionary and here is no problem. If i has reduced rank r han here are some non-saionary variables in he model and here are r coinegraion relaions and n-r non saionary variables. Π wih reduce rank can hen be decomposed in he marix of coefficiens for explaining long run relaion and he adjusmen marix i.e. Π = α β. Where α = Adjusmen marix meaning how quickly he variables respond o correc for disequilibrium errors. β = marix of long run relaionship or marix of coinegraion relaion. Johansen (1988) has provided wo procedures o es he rank of marix Π. The null hypohesis of r coinegraion relaion (rank = r) is esed agains he alernaive hypohesis of greaer number of relaion using race saisic which is given by he following formula. p i= r+ 1 ( 1 λ ) κ = T ln λ = ih eigen value i i In second procedure null hypohesis of rank r is esed agains he alernaive hypohesis of rank r +1 by using max saisics which is give as follows: ( 1 ˆ λ ) κ = T ln r+ 1 Where λ s are esimaed eigen values from esimaed marix Π. 5.3 Coinegraion I (2) Analysis for Nominal Variables Firs of all we did I(2) analysis in order o see if here are some I(2) rend in he nominal variables. The resuls are repored in able A.1 and A.2 in he appendix. Resuls show ha here is possibiliy of I(2) rends hence we ransformed our variables in real in order o avoid complicaions involved in he analysis of I(2) rends. 5.4 Modelling Demand for Narrow Money (M 1 ) We esimaed unresriced VAR model wih hree variables real M 1, real GDP, and ineres rae. The order of he VAR is fixed a 2 by using AIC crierion and LM es (AR-1) for deecing serial correlaion. Alhough we are using real variables and we are no expecing I (2) rend bu we will do I (2) analysis in real variables jus o make sure ha here is no I (2) rend in he daa. The resuls of unresriced I (2) analysis are repored in he appendix able A3 and resuls confirmed ha here are no I (2) rends in he daa. 47
Resuls for he I (1) coinegraion analysis for esing rank using race saisic are repored in able (5). The resuls show ha here could be one coinegraion relaion a 1% level meaning one long run relaionship beween variables ha can be inerpreed as money demand relaion. Error correcion model is hen esimaed wih he resricion of one coinegraion relaion. We have esed o resric he consan in o he coinegraion relaion bu LR es rejeced he hypohesis of resriced consan hence consan can no be resriced o coinegraion space. This is due o he fac ha here is rend in he level of he series. Table: 5 Coinegraion analysis; Demand for Narrow Money M 1 H: Rank Trace es p-value 28.484 [.71] 1 4.6619 [.84] 2.1429 [.747] The resuls of he sable long run relaionship β and adjusmen vecorα are repored in able (6). The signs of he coefficiens are as expeced. GDP is posiively relaed wih money demand where as ineres rae has negaive relaion wih money demand. We have also ried o include inflaion in he model o es wheher i is playing any role in he deerminaion of long run relaionship bu is coefficien urned ou o be posiive which is no according o heory so we have no included i in he model. The magniude of he coefficiens is showing ha money demand is more sensiive o changes in GDP and less sensiive (less elasic) o he changes in ineres rae. We esed he hypohesis o see he Table: 6. Sable Long Run Money Demand Funcion for M 1 Money Demand M 1 Log of Real GDP Ineres Rae β 1. 1.45 (.34) α -.588.29 (.123) (.59) Sandard errors of he esimaes are repored in he parenhesis -.122 (.8) 5.276 (2.761) significance of ineres rae for money demand in he long run and we acceped he hypohesis ha ineres is no affecing M 1. This resul is quie obvious as we 48
have esimaed he money demand funcion for narrow definiion of money which consis of mos liquid form of money hence ineres rae is no affecing demand for his money. People only demand he money for heir daily ransacions. Adjusmen coefficien for money demand M 1 is negaive meaning ha his variable responds o correc he disequilibrium errors of he pervious period. The adjusmen coefficien for GDP and ineres rae is posiive meaning ha hese variables respond in opposie direcion o correc for he disequilibrium errors bu hey seem o be insignifican. We esed he significance of adjusmen coefficiens for GDP and ineres rae individually and simulaneously by using likelihood raio es and boh hypohesis are acceped. We can conclude ha hese wo variables are found o exogenous in his long run relaionship. We esed earlier ha ineres rae is no affecing money demand in he long run bu again we es is join significance wih oher acceped resricion and he resuls are repored in able 7. LR saisic has acceped his join hypohesis a 5% level hence he resuling is more efficien long run relaionship beween money demand and GDP. Table: 7. Tesing he Join Hypohesis for Exogeniy of GDP and Ineres Rae And Ineres Inelasiciy of Money Demand for M 1 Money Demand M 1 Log of Real GDP Ineres Rae β 1..985 (.27) () α -.426 (.94) () () LR es of resricions: Chi^2(3) = 6.315 [.973] We can es one more ineresing hypohesis ha he coefficien of GDP equal o one. The inerpreaion of his hypohesis is ha price will be cancelled in his relaionship and here will be no difference beween he model wih nominal variables and model wih real variables. This hypohesis also corresponds o radiional quaniy heory of money. The resuls of he join es wih oher acceped resricion are repored in able 8 and LR es rejeced he hypohesis. 49
Table: 8. Tesing he hypohesis for coefficien of GDP equal o one Money Demand M 1 Log of Real GDP Ineres Rae β 1. 1. () () α -.46 (.94) () () LR es of resricions: Chi^2(4) = 23.372 [.1] 5.6 Modelling demand for Broad Money M 2 We already menioned ha in modelling nominal variables ha here is evidence of I (2) rends hence we ransformed our variables in real o avoid complicaions. In order o make sure ha here are no I (2) rends in real variables we did I (2) coinegraion analysis wih real variables. The resuls of he analysis are repored in appendix A2. These resuls sugges ha here is no evidence of I (2) rends in real variables. The lags of he unresriced VAR model are fixed a 2 using AIC and LM es (AR-1) for deecing serial correlaion. The resuls of I (1) coinegraion analysis are repored in able (9) using race saisics. The resuls show ha here is one coinegraion relaion beween hese variables ha can be inerpreed as money demand relaion. We hen esimaed he error correcion model o find he coefficiens of long run money demand relaion. Firs in error correcion formaion we esed wheher consan can be resriced o coinegraion space or no. The hypohesis is rejeced so we can no resric he consan o be in he coinegraion space have he inerpreaion ha here is rend in he level of he series. The resuls of sable long run relaion wih unresriced consan are repored in able (1). The sign of he coefficien for GDP is posiive as suggesed by heory. The ineres rae coefficien is also posiive which is no according o heory bu i is saisically insignifican. We applied likelihood raio es o es he significance of he coefficien of ineres and hypohesis is acceped a 5% level of significance. This resul is no surprising for an underdeveloped counry like Pakisan since mos of he people are very poor and living on he subsisence level. They demand money only o fulfil heir daily 5
ransacion and hey don have long run perspecive of holding money. There could be anoher reason ha financial markes are imperfec and here is high inflaion rae. Table: 9. I (1) Coinegraion analysis Demand for Broad money M 2 H:rank Trace es p-value 33.325 [.18] 1 4.7219 [.834] 2.55926 [.813] Table: 1. Sable Long Run Money Demand Funcion for M 2 Money Demand M 2 Log of Real GDP Ineres Rae β 1. 1.19 (.33).13 (.7) α -.539 (.98) -.27 (.53) 2.554 (2.551) Sandard errors of he esimaes are repored in he parenhesis The adjusmen coefficiens for money demand M 2 and GDP are negaive meaning ha hese variables adjus o correc for pas disequilibrium bu he coefficien for ineres is posiive. The significance of hese coefficiens is esed using likelihood raio es and resuls suggesed ha he coefficien of adjusmen for boh GDP and ineres rae urn ou o be saisically insignifican individually and simulaneously. These resuls sugges ha hese wo variables are exogenous in he long run money demand relaion. We hen esed he join hypohesis ha money demand is inelasic wih respec o ineres rae and GDP and ineres are exogenous in he long run money demand relaion. The hypohesis is acceped and he final sable money demand relaion is repored in able (11). We again esed he hypohesis for coefficien of GDP o be equal o one bu again we rejeced ha hypohesis as in he case of modelling M 1. 51
5.7. Esimaion of model in Sub Samples. We have seen in he univariae analysis ha here is srucural break in he series so i is very imporan o incorporae ha in he mulivariae analysis bu i is bi complicaed o include dummy variables in he VAR models. Insead we Table: 11. Tesing he Join Hypohesis for Exogeniy of GDP and Ineres Rae and Ineres Inelasiciy of Money Demand for M 2 Money Demand M 2 Log of Real GDP Ineres Rae β 1. 1.146 (.24) () α -.451 (.83) () () LR es of resricions: Chi^2(3) = 3.9753 [.2641] Sandard errors of he esimaes are repored in he parenhesis. have esimaed our model in he sub sample ha is sample before he break and sample afer he break o see if here is some change in he resuls. The resuls are repored in able A5 and A6 for boh M 1 and M 2 respecively. Resuls have shown ha here is no coinegraion relaion for boh M 1 and M 2 before he break (1953-1973) and here is one coinegraion relaion for sample afer he break (1974-23). For he sample afer he break we found almos same resuls as we obained for he whole sample. VI. Conclusion In his sudy we have ried o esimae sable money demand funcion for Pakisan using 51 annual observaions from 1953 o 23. The resuls of uni roo analysis have suggesed ha boh log of nominal GDP and price could possibly be inegraed of order (2). The resuls uni roo analysis for real M 1 and M 2 by allowing srucural break in he series, due o oil price shock of he hisory, have suggesed ha M 1 is fracionally inegraed where as M 2 is rend saionary by using boh ADF and KPSS es. I(2) coinegraion analysis wih nominal variables have suggesed here are some I(2) rends in he model hence in order o avoid he complicaions involved in I(2) analysis we ransformed our model in real variables. We esed again for I 52
(2) rends in he model wih real variables jus o make sure ha here are no I (2) rends in he model and we found no evidence for I (2) rends. We found one coinegraion relaion for boh definiions of money. Signs of he coefficiens are according o heory for M 1 money demand relaion. For M 2 ineres rae has wrong sign bu i is saisically insignifican. Boh GDP and ineres rae are found o be weakly exogenous in he long run money demand relaion. We also found ha demand for boh M 1 and M 2 are inelasic wih respec o ineres rae. This finding is quie obvious for an underdeveloped counry like Pakisan where mos of he people are living on subsisence level. The main conclusion from our sudy is ha demand for boh ypes of real money does no respond o he changes in he ineres rae bu hey do respond o he changes in real GDP. The implicaion of his finding could be ha he moneary auhoriies can no use ineres rae as a policy variable o adjus money demand. 53
References Aresis, Philip and Panicos O. Demeriades (1991), Coinegraion, Error Correcion and he Demand for Money in Cyprus, Applied Economics, Vol. 23, No. 9 (Sepember 1991), pp. 1414-24. Baillie, R. T., Chung C. F. and Tieslau M.A. (1996), Analysing Inflaion by he Fracionally Inegraed ARFIMA-GARCH Model, Journal of Applied Economerics, 11, 23-4, 1996. Busei F., and Harvey A., (21), Tesing for he Presence of a Random Walk in Series wih Srucural Breaks, Journal of Time Series Analysis Vol. 22, pp. 127-15. Choudhry, Taufiq (1995a), Long Run Money Demand Funcion Argenina During 1935-1962: Evidence from Coinegraion and Error Correcion Models. Applied Economics, Vol. 27, No. 8 (Augus 1995), pp. 661-67. Choudhry, Taufiq (1995b), High Inflaion Raes and he Long Run Money Demand Funcion: Evidence from Coinegraion Tess, Journal of Macroeconomics, Vol. 17, No.1 (Winer 1995), pp. 77-91. Cornelisse, P.A and Jan Maren. (1989), Shorrun Money Demand and Supply relaion in Pakisan. The Pakisan Developmen Review. Vol. 28, no 4 (ii), pp. 995-17. Dickey, D. A. and W. A. Fuller (1979), Disribuion of he Esimaors for Auoregressive Time Series wih Uni roo, Journal of he American Saisical Associaion, 74, 427-431. Dickey, D. A. and W. A. Fuller (1981), Likelihood Raio Saisics for Auoregressive Time Series wih a Uni roo, Economerica, 49(4). Engle, R. F., and Granger C. W. J., (1987), Coinegraion and Error Correcion: Represenaion, Esimaion, and Tesing, Economerica, Vol. 55, No. 2, pp. 251-76. Ericson, Neil R., and Sunil Sharma (1996), Broad Money Demand and Financial Liberalizaion in Greece, IMF Working paper no. WP/96/ 62 (Washingon: Inernaional Moneary Fund, June1996) Hobijn B., Philip H. F., Marius O. (1998), Generalizaions of he KPSS-es for Saionariy, Economeric Insiue Repor, no. 982/A (Erasmus Universiy, Roerdam) Hossain, A. (1994), The Search for a Sable Money Demand Funcion for Pakisan: An Applicaion of he Mehod of Co-inegraion. The Pakisan Developmen Review. Vol. 33, no. 4 (ii), pp. 969-983. Johansen, S., (1988), Saisical Analysis of Coinegraion Vecors, Journal of Economic Dynamics and Conrol, Vol. 12, No. 2/3, pp. 231-54. 54
Khan, A. H. (198), The Demand for Money in Pakisan: Some Furher Resuls. Pakisan developmen Review. Vol, 19, no. 1, pp. 25-5. Khan, A. H. (1994), Financial Liberalisaion and he Demand For Money in Pakisan. The Pakisan Developmen Review. Vol. 33, No. 4(ii), pp. 997-11. Kwiakowski, Denis, Peer C. B. Phillips, Peer Schmid, and Yongcheol Shin (1992), Tesing he Null Hypohesis of Saionary Agains he Alernaive of a Uni Roo: How Sure are we ha Economic Time Series Have a Uni Roo, Journal of Economerics, Vol. 54, No 1-3, pp. 159-78. Mangla, I.U (1979), An Annual Money Demand Funcion for Pakisan: Some Furher Resuls. The Pakisan Developmen Review. Vol.18, no.1, pp. 21-33. Newey W. K., Wes K. D., (1994), Auomaic Lag Selecion for Covariance Marix Esimaion, Review of Economic Sudies, 61 631-653. Panula, S. G. (1989), Tesing for uni roos in ime series daa, Economeric Theory 5, 256 271. Perron, P., (1989), The Grea Crash, he Oil Price Shock, and he Uni Roo Hypohesis, Economerica, Vol 57, No. 6, pp. 1361-141. Phillips, Peer C. B., and Peirre Peron (1988), Tesing for a Uni Roo in Time Series Regression, Biomerika, Vol. 75, No. 2, pp. 335-46. Sriram, Subramanian S. (1999), Survey of Lieraure on Demand for Money: Theoreical and Empirical Work wih Special Reference o Error-Correcion Models. IMF Working Paper, WP/ 99/64. 55
Appendix A.1 Graph of he Log of Nominal Series Log of Nominal M1 15. Log of Nominal M2 12.5 12.5 1. 1. 196 197 198 199 2 15. Log of Nominal GDP 12.5 1. 196 197 198 199 2 5 4 3 2 196 197 198 199 2 Price 196 197 198 199 2 1 Ineres Rae 5 196 197 198 199 2 56
Figure A2. Graph of he Log of real series. 9 Log of Narrow Money M1 1 9 Log of Broad Mone M2 8 8 196 197 198 199 2 196 197 198 199 2 1 Log of Real GDP 1 Ineres Rae 9 5 5 4 196 197 198 199 2 Log price 196 197 198 199 2 3 2 196 197 198 199 2 57
Table A.1 Tesing for I (2) Trends in Nominal Variables Modelling: Nominal M1, Log of Nominal GDP, Ineres Rae and Log Prices p= 1 2 3.4938.345.1394 61.594 28.25 7.4423.12.761.5337 n-p-s= Q_p [pval] n-p-s= p = S_p,s [pval] p = 1 S_p,s [pval] p = 2 S_p,s [pval] p = 3 S_p,s [pval] 4.6697 186.14.... 3.578 14.38..5867 123.5... 2.418 98.44.1.5441 8.189..53443 52.489.5..17.86.7689 1.25 72.86.16.241 41.692.232.1434 15.2.3952.342 2.649.6 Table A.2 Tesing for I (2) in Nominal Variables Modelling Nominal M2, Log of Nominal GDP, Ineres Rae and Log Prices p= 1 2 3 n-p-s= Q_p [pval] n-p-s= p = S_p,s [pval] p = 1 S_p,s [pval] p = 2 S_p,s [pval] p = 3 S_p,s [pval].476 59.598.22 4.594 171.91.....358 27.884.83 3.541 127.71..585 14.4....118 6.1682.679 2.355 89.475.15.394 6.92.5.421 41.615.151. 8.94e-.43.947 1.156 67.962.59.158 36.356.9.155 14.47.441.28 16.133.26 58
A. 3 I (2) Coinegraion analysis on Real Variables Modelling: Real M1, Real GDP, and Ineres Rae. p= 1 2 n-p-s=.3851.88819.2126 Q_p 28.484 4.6619.1429 [pval].713.841.7467 n-p-s= 3 2 1 p =.59846.57826.36486 S_p,s 137.74 93.3 5.725 [pval]...14 p = 1.58933.55426 S_p,s 87.864 44.255 [pval]... p = 2.53655 S_p,s 37.788 [pval]... A.4 I (2) Coinegraion analysis on Real Variables Modelling: Real M2, Real GDP, and Ineres Rae. p= 1 2 n-p-s=.44218.98.11 Q_p 33.325 4.721.559 [pval].18.834.813 n-p-s= 3 2 1 p =.58911.551.353 S_p,s 132.77 89.185 54.717 [pval]...4 p = 1.56456.412 S_p,s 71.486 3.747 [pval]...2 p = 2.51 S_p,s 34.197 [pval]... 59
Table A.5 Esimaion Resuls for Sub Samples: Long Run Relaionship before and Afer he Break for M1 Variable Resuls of Sub Esimaes of Sub Sample 1953-1973 Sample 1953-1973 Pre Break Sample Afer Break Sample Esimae of he Full Sample 1974 23 Money Demand No Long Run -.75 M1 relaionship found (.111) Log of Real GDP () Ineres Rae () Tes of Valid Resricions Imposed α β α β 1. -.426 (.94) 1.1347 (.26) () () () LR es of resricions: Chi^2(3)=3.5276 p-value [.3172] 1..985 (.27) () LR es of resricions: Chi^2(3)=6.315 P-value [.973] Table A.6 Esimaion Resuls for Sub Samples: Long Run Relaionship before and Afer he Break for M2 Variables Resuls of Sub Sample 1953-1973 Pre Break Sample Money Demand No Long Run -.858 M2 relaionship found (.157) Log of Real GDP () Ineres Rae () Tes of Valid Resricions Imposed Esimaes of Sub Sample 1953-1973 Afer Break Sample Esimae of he Full Sample 1974 23 α β α β LR es of resricions: Chi^2(2)=5.3262 p-value [.697] 1. -.451 (.83) 1.32 (.25) () -.22 (.7) () 1. 1.146 (.24) () LR es of resricions: Chi^2(3)=3.9753 p-value [.2641] 6