Predicting Money Multiplier in Pakistan

Transcription

1 The Pakisan Developmen Review 39 : (Spring 2000) pp Predicing Money Muliplier in Pakisan MUHAMMAD FAROOQ ARBY The paper has developed ime-series models for he monhly money muliplier and is componens, viz., currency-deposi raio, reserve-deposi raio, ec. A comparison is made beween he predicive performance of he aggregae muliplier and he componen models. I is found ha he projeced values of he muliplier on he basis of he aggregae model are closer o acual values as compared o hose worked ou on he basis of he componen models. Thus, for he purposes of projecing he money muliplier, i may be preferable o focus on he aggregae money muliplier model. Sabiliy ess, applied o he idenified models for each componen and he overall muliplier, sugges ha all he models are sable.. INTRODUCTION The recen liberalisaion and resrucuring of he financial sysem in Pakisan has necessiaed designing a new se of insrumens o conduc moneary policy. Of hese insrumens he mos imporan is he Open Marke Operaions (OMO). Through Open Marke Operaions, he Sae Bank brings abou changes in he moneary base in accordance wih he money supply arge and he expeced money muliplier. The success of he OMO in keeping he money supply wihin arges depends o a grea exen on he accuracy of he esimaed money muliplier. The objecive of his paper is o develop a forecasing model of money muliplier for Pakisan following he Box-Jenkins (976) ime-series mehodology. Money muliplier can be prediced by using wo approaches, viz., (a) modelling he overall money muliplier, and (b) firs modelling componens of he muliplier and hen esimaing he overall money muliplier on he basis of prediced componens. In he paper, boh approaches have been adoped and compared wih respec o heir forecas abiliies. I is found ha he model for he overall muliplier performs beer han he componens models. The paper has been organised as follows. Secion 2 conains a brief review of he exising lieraure on he subjec. Secion 3 defines he money muliplier and Muhammad Farooq Arby is Assisan Direcor, General Economic Research Deparmen, Sae Bank of Pakisan, Karachi. Auhor s Noe: The views expressed in his paper are he auhor s personal opinion of he usual disclaimer applies.

2 24 Muhammad Farooq Arby is componens in he conex of Pakisan, and applies ess of saionariy o he series. Secion 4 explores appropriae ARMA models for he monhly money muliplier and is componens. In Secion 5, diagnosic checking of he models has been underaken. Sabiliy and forecas abiliies of he aggregae and componen models have been examined in Secion 6. The las secion conains he concluding remarks. 2. REVIEW OF LITERATURE One of he firs sudies using ime-series models o analyse he money muliplier was underaken by Bomhoff (977). He used he ime-series echnique for he Unied Saes and he Neherlands. Büler e al. (979) and Fraianni and Nabli (979) also used his echnique o forecas he money muliplier in Swizerland and in seven EEC counries respecively. Johannes and Rasche (979) furher exended he ime-series approach o he componens of money muliplier. They claimed ha he predicive performance of his dis-aggregaed model was superior o he aggregae model. When Hafer and Hein (984) esed his claim, hey found ha he gain in erms of forecas accuracy from he componen procedure was no significan. In he conex of Pakisan, Hamdani (976) used he money muliplier as a deerminan of money supply. Mangla and Ladenson (978) and Siddique and Ahmad (994) developed differen models for he projecion of he money muliplier. However, boh hese sudies used M-muliplier ha was lile relevan for he Sae Bank of Pakisan from he policy poin of view because moneary policy in Pakisan focused on broad money (M2). The presen paper models he money muliplier (boh aggregae- and componen-wise) based on M2 for forecasing purposes by using he laes available daa. 3. DEFINING MONEY MULTIPLIER Money muliplier is defined as a raio of moneary aggregaes (M2 in Pakisan) o reserve money, i.e., m = M2 /RM () where m is he money muliplier, M2 is moneary aggregae, and RM is he reserve money or he moneary base. Money muliplier can also be defined in erms of componens of M2 and RM all expressed as raios o deposis as given below; + c + o m = c + k + r + o (2) In Pakisan, M2 includes currency in circulaion, deposis (demand, ime, and foreign currency) wih he scheduled banks, and oher deposis wih he SBP. Reserve Money is he sum of currency in circulaion, cash in he ills, reserves of he scheduled banks wih he SBP, and oher deposis wih he SBP.

3 Predicing Money Muliplier 25 where c = Currency/ Deposi. 2 o = Oher deposis wih he Sae Bank/Deposi. k = Cash in he ills of scheduled banks/deposi. r = Reserves of he scheduled banks wih he Sae Bank/Deposi. Monhly series of money muliplier and componens raios from July 989 o June 999 are presened in Figure. Daa for all hese variables have been exraced from various issues of he Sae Bank s Annual Repor. The overall money muliplier shows volailiy, wih some upward jumps over he sample period. The firs upward jump by he money muliplier may be noed in 992, soon afer he inroducion of residens foreign currency deposis. Residens foreign currency deposis no only discouraged currency holdings on he par of he public bu also acceleraed he process of deposi creaion on he par of commercial banks, as banks ofen used hese deposis as collaeral o give advances o heir deposiors. This wo-fold impac of RFCDs reduced he currency-o-deposi raio significanly and hus increased he money muliplier. The oher conribuory facor for a jump in he money muliplier was a reducion in he required reserve raio back o 5 percen from 3 percen by he Sae Bank in January 992. The nex significan jump in he money muliplier and a coinciding reducion in he currency/deposi raio may be observed in 996. In fac, mid-990s is he period when Pak rupee was devalued frequenly, hereby increasing he opporuniy cos of currency holding. Paricularly, during 996, devaluaion of more han percen was underaken wihin a monh or so (Sepember 0 Ocober 22). Associaed wih devaluaion, inflaion during his period was abou 2 percen, which fuelled dollarisaion of he economy. As a resul, he currency/deposi raio declined and he money muliplier increased. Again he reducion of he reserve requiremen on Is July, 996 also conribued o he upward jump in he money muliplier. During 990s, he reserve requiremen was changed quie frequenly, which also caused flucuaion in he money muliplier. Since 968, he reserve requiremen had been 5 percen of he demand and ime liabiliies of commercial banks. In Ocober 99, i was raised from 5 o 3 percen (5 percen wihou ineres, and 7 percen remunerable a he rae of 0 percen). As menioned above, in January 992, i was again fixed a 5 percen. During 995, i was changed hree imes, in he range of 5 o 8.5 percen. Effecive June 998, i was fixed a 3.75 percen for rupee liabiliies and 5 percen for FCDs of he banks. The reserve raio as depiced in Figure gives a combined impac of required reserves and excess reserves of banks. If he impac of required reserves is filred ou, he excess reserves-o-deposi raio has a declining rend over ime (no shown 2 Deposis include demand deposis, ime deposis, and residens foreign currency deposis wih he scheduled banks. These deposis are he base of he Sauory Reserve Requiremen.

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5 Predicing Money Muliplier 27 separaely). The raio of cash in he ills remained fairly sable, excep a few ouliers during early 995. The Oher deposis wih he SBP includes he Sae Bank employees G.P. Fund, Saff Welfare Fund, sundry deposis accoun, ec. Therefore, any behavioural aribues canno be associaed wih his variable. A quaniaive evaluaion of he properies of hese series may be made by using he Augmened Dicky-Fuller (ADF) es. In fac, he firs sep in modelling ime-series is o es he saionariy of he series by applying he ADF es and o find some saionary ransformaions if he original series are non-saionary. We have applied he following Augmened Dicky-Fuller es o each series. z = α + βz n + γi z i + ε (3) where indicaes he firs difference, z is any series of m or is componens. A rend variable may also be included in he above equaion o es rend-saionariy of a series. The null hypohesis for he ADF es is he following; H 0 : β = 0 The series z is non-saionary if H 0 is acceped. We have used 5 percen Mckinnon criical values for esing he hypohesis. If a series is found non-saionary in is level form, he same es is applied a is firs or higher-order difference o examine is difference-saionariy. The resuls of he ADF ess are given in Table, which shows ha he money muliplier and currency raios are non-saionary in heir level forms. They become saionary in he firs differences. Thus he ARMA models for heir firs differences have been developed. 3 The models of Oher Deposi Raio, Cash in he Tills Raio, and Reserves Raio are consruced on heir level forms because hey are level saionary series. Table Resuls of he ADF Tes on Level and Firs Difference of he Series (Sample Size: 989:07 999:06) Series Name Level Saionary Trend Saionary Difference Saionary m No No Yes c No Yes Yes o Yes No Yes k Yes Yes Yes r Yes Yes Yes Noes: (i) In case of k six ouliers (from 994:2 o 995:05) have been excluded from he sample. (ii) Compuer sofware Economeric Views 3. has been used for he applicaion of ess. 3 Though currency raio is also rend-saionary, is firs-difference ransformaion is used because ha is more useful for shor-run forecasing. However, if he objecive is long-run forecas, hen he series may be used in level-form, including rend, or i may be derended by a suiable polynomial rend.

6 28 Muhammad Farooq Arby 4. IDENTIFICATION OF ARMA MODELS To deermine he order of Auoregressive (AR) and/or Moving average (MA), use is made of auocorrelaion funcion (AC) and parial auocorrelaion funcion (PAC) of he series. Boh hese funcions for he firs differences of m, and c, and level forms of o, k and r are given in he Annexure. The resuls show ha for all variables, boh AC and PAC are significan (on he basis of Q- Saisic) a almos all lags included in he funcions. An appropriae ARMA model should have o include all ACs/PACs ha are significan. We have applied various-order mix of AR and MA erms on each series and seleced relaively beer ARMA model in erms of Akaike Informaion Crierion (AIC). In order o ensure he principle of parsimony we have considered only hose parameers which are significanly differen from zero a leas 95 percen confidence level. However, in some models, insignifican inerceps have been allowed. We have found ha he following ARMA models are good approximaions of rue daageneraing processes; (i) ( α L α 2 L 8 α 3 L 36 )( L) m = α 0 + ( + β L 3 )ε (ii) ( δ L 2 )( L)c = δ 0 + ( + η L + η 2 L 5 + η 3 L 9 + η 4 L 2 )ε (iii) ( φ L) o = φ 0 + ( + π L) ε (iv) ( θ L) k = θ 0 + ( + ω L + ω 2 L 3 ) ε (v) ( ρ L ρ 2 L 2 ρ 3 L 3 ) r = ρ 0 + ( + σ L + σ 2 L 2 ) ε (4) where L is lag operaor, such ha L i z = z. The esimaes of parameers are given in Table 2. Oher characerisics of he equaions are given below: (i) R 2 =0.59, DW=.9, Akaike Informaion Crierion = 2.40, F-saisic = 27.5 (ii) R 2 =0.63, DW=2.0, Akaike Informaion Crierion = 5.9, F-saisic = 39.4 (iii) R 2 =0.74, DW=.9, Akaike Informaion Crierion = 9.27, F-saisic = 69.5 (iv) R 2 =0.65, DW=.9, Akaike Informaion Crierion = 9.60, F-saisic = 68.5 (v) R 2 =0.55, DW=2.0, Akaike Informaion Crierion = 5.56, F-saisic = 27.8 I may be noed ha he selecion of models has been made on he basis of he Akaike Informaion Crierion by keeping i as small as possible. Any aemp o include more lags as regressors in order o improve R 2 will increase he AIC, making he model less aracive. In fac, in he case of he ARMA models, he mos appropriae measure of he overall goodness of fi is he Akaike Informaion Crierion or he Schwarz Bayesian Crierion insead of R 2.

7 Predicing Money Muliplier 29 Table 2 Esimaes of Parameers (Sample Size: 989:07 999:06) Parameer Esimae -value Equaion i: α α α α β Equaion ii: δ δ η η η η Equaion iii: φ φ π Equaion iv: θ θ ω ω Equaion v: ρ ρ ρ ρ σ σ Noes: Invered roos of AR and MA erms in all models are less han one. 5. DIAGNOSTIC CHECKING Diagnosic checking is also an imporan ingredien of he Box-Jenkins mehodology. In fac, idenificaion and diagnosic checking run parallel in he process of selecing an appropriae ARMA model. The sandard pracice is o see if he residuals esimaed from a paricular model are whie noise; if hey are, hen he model is accepable; if no, i may be re-specified and re-esimaed. In he presen case, residuals from all he models esimaed above are whie noise as deermined by he Auocorrelaion and Parial Auocorrelaion funcions. As Table 3 shows, none of he auocorrelaions and parial auocorrelaions is individually significanly differen from zero on he basis of Q-saisic. The probabiliy of Q-saisic of all he ACs/PACs (no shown) remained below 95 percen confidence level.

8 30 Muhammad Farooq Arby Table 3 Auocorrelaion and Parial Auocorrelaion Funcions of Residuals Equaion-i Equaion-ii Equaion-iii Equaion-iv Equaion-v Lags AC PAC AC PAC AC PAC AC PAC AC PAC

9 Predicing Money Muliplier 3 6. STABILITY AND FORECAST ABILITY To evaluae he forecasing abiliy, he above models were re-esimaed wih a runcaed sample size by dropping he las 2 observaions. The re-esimaed parameers are given in Table 4. Table 4 Re-esimaed Parameers (Sample Size: 989:07 998:06) Parameer Esimae -value Equaion i: α α α α β Equaion ii: δ δ η η η η Equaion iii: φ φ π Equaion iv: θ θ ω ω Equaion v: ρ ρ ρ ρ σ σ Noe: Economeric Views 3. is used for esimaion. Oher characerisics of he equaions are given below: (i) R 2 =0.58, DW=.9, Akaike Informaion Crierion = 2.30, F-saisic = 22.5 (ii) R 2 =0.63, DW=2.0, Akaike Informaion Crierion = 5.0, F-saisic = 35. (iii) R 2 =0.74, DW=.9, Akaike Informaion Crierion = 9.6, F-saisic = 46.0 (iv) R 2 =0.57, DW=.9, Akaike Informaion Crierion = 9.57, F-saisic = 42.3 (v) R 2 =0.54, DW=2.0, Akaike Informaion Crierion = 5.48, F-saisic = 23.5

10 32 Muhammad Farooq Arby A comparison of he re-esimaed parameers presened in Table 4 wih hose in Table 2 indicaes he sabiliy of he models given in (4). All parameers have he same signs and almos he same values in boh he ables. Sabiliy of he reesimaed co-efficiens has furher been checked by using he following Chow forecas es. F = T ε 2 T T Where ε ε T 2 ε 2 T k * T (5) 2 is he sum of squared residuals of he original models; ε T 2 is he sum of squared residuals of he re-esimaed model wih runcaed sample; T is he oal number of observaions in he original models; T is he observaions in reduced models; and k is he number of parameers esimaed. F-saisic has an exac finie sample F-disribuion, given he errors are independen, and idenically, normally disribued. The Null hypohesis of he es is ha he model is no unsable. The resuls of he es are given below. These show ha all he models are sable (Table 5). Table 5 Chow Forecas Tes Equaion F-Saisic Probabiliy Remarks (i) H 0 acceped, he model is sable (ii) H 0 acceped, he model is sable (iii) H 0 acceped, he model is sable (iv) H 0 acceped, he model is sable (v) H 0 acceped, he model is sable A comparison has also been made beween he projeced values from he reesimaed models and acual observaions for he period of 998:07 999:06 on he basis of (i) he roo mean squared error, (ii) mean absolue error, (iii) mean absolue percenage error, and (iv) Theil inequaliy coefficien (Table 6). As a rule, he smaller he values of hese saisics, he beer would be he forecas. The saisics of Table 6 show ha he aggregae model of money muliplier performs quie well in projecions as compared o models of componen raios in erms of he mean absolue

11 Predicing Money Muliplier 33 percenage error and he Theil inequaliy coefficien. 4 Projeced m on he basis of he aggregae model is also closer o he acual values as compared o ha obained indirecly (m * ) hrough projeced componens. Thus, conrary o he findings of Johannes and Rasche (979), he model of he overall money muliplier gives a beer forecas in he case of Pakisan as compared o he componen models. The resuls are inuiive as in he case of he componen approach. The forecas errors of all componen models accumulae while working ou he money muliplier, whereas in he case of he aggregae approach, he forecas errors are already minimum. Model Aggregae Model: Roo Mean Squared Error Table 6 Forecas Evaluaion Mean Absolue Error Mean Absolue Percenage Error Theil Inequaliy Coefficien m Componen Models: c o k r m * m * = Money muliplier esimaed on he basis of projeced componens. 7. CONCLUSION The paper has developed ime-series models for he monhly money muliplier and is componen raios. A comparison is made beween he predicive performance of he aggregae muliplier and he componen models. I is found ha he projeced values of he muliplier on he basis of he aggregae model are closer o acual values as compared o hose worked ou on he basis of he componen models. Thus, for he purposes of projecing money muliplier, i may be preferable o focus on he performance and modelling of he aggregae money muliplier. 4 The roo mean squared error and he mean absolue error are very low in he case of componen raios as compared o hose for he muliplier. Bu hese saisics are no comparable because he componen raios are in fracions while he muliplier has values more han one. Thus, for he purposes of comparison in his case, he mean absolue percenage error and he Theil inequaliy coefficiens are more relevan.

12 34 Muhammad Farooq Arby Annexure Auocorrelaion and Parial Auocorrelaion Funcions m c o k r Lags AC PAC Q-Sa Prob AC PAC Q-Sa Prob AC PAC Q-Sa Prob AC PAC Q-Sa Prob AC PAC Q-Sa Prob Noe: Economeric views 3. is used o esimae correlograms. AC = Auocorrelaion funcion, PAC = Parial Auocorrelaion Funcion.

13 Predicing Money Muliplier 35 REFERENCES Bomhoff, E. J. (977) Predicing he Money Muliplier. Journal of Moneary Economics 3: Box, G. E., and G. Jenkins (976) Time-series Analysis Forecasing and Conrol. San Francisco: Holden-Day. Büler, H. J., J. F. Gorgera, H. Schilknech, and K. Schilknech (979) A Muliplier Model for Conrolling he Money Sock. Journal of Moneary Economics 5: Fraianni, M., and M. Nabli (979) Money Sock Conrol in he EEC Counries. Welwirschafliches Archiv 5: Hafer, R. W., and S. E. Hein (984) Predicing he Money Muliplier, Forecass from Componen and Aggregae Models. Journal of Moneary Economics 4: Hamdani, S. M. Mazher Hasnain (976) Money Muliplier as a Deerminan of Money Supply: The Case of Pakisan. The Pakisan Developmen Review 5: Johannes, J. M., and R. H. Rasche (979) Predicing he Money Muliplier. Journal of Moneary Economics 5: Mangla, I. U., and Mark Ladenson (978) Shor-run Forecas of he Money Sock in Pakisan. The Pakisan Developmen Review 7: Siddique, Anjum, and Waheed Ahmad (994) Tracking M via he Money Muliplier in Pakisan. (Typescrip). Applied Economics Research Cenre, Universiy of Karachi, Karachi.