Volume 29, Issue 2 An Empirical Analysis of he Money Demand Funcion in India Takeshi Inoue Insiue of Developing Economies Shigeyuki Hamori obe Universiy Absrac This paper empirically analyzes India's money demand funcion during he period of 1980 o 2007 using monhly daa and he period of 1976 o 2007 using annual daa. Coinegraion es resuls indicaed ha when money supply is represened by M1 and M2, a coinegraing vecor is deeced among real money balances, ineres raes, and oupu. In conras, i was found ha when money supply is represened by M3, here is no long-run equilibrium relaionship in he money demand funcion. Moreover, when he money demand funcion was esimaed using dynamic OLS, he sign condiions of he coefficiens of oupu and ineres raes were found o be consisen wih heoreical raionale, and saisical significance was confirmed when money supply was represened by eiher M1 or M2. Consequenly, hough India's cenral bank presenly uses M3 as an indicaor of fuure price movemens, i is hough appropriae o focus on M1 or M2, raher han M3, in managing moneary policy. We are graeful o an anonymous referee for helpful commens and suggesions. An earlier version of his paper was presened as an IDE Discussion Paper no.166. Ciaion: Takeshi Inoue and Shigeyuki Hamori, (2009) ''An Empirical Analysis of he Money Demand Funcion in India'', Economics Bullein, Vol. 29 no.2 pp. 1224-1245. Submied: Sep 18 2008. Published: June 03, 2009.
1. Inroducion In India, financial secor deregulaion was underaken beginning in he mid-1980s, when seps like he inroducion of 182-day Treasury bills, lifing of he call money ineres-rae ceiling, and he inroducion of cerificaes of deposi and commercial paper were aken in a bid o make he governmen securiies marke and he money marke more efficien (Sen and Vaidya, 1997). Furhermore, wih he balance of paymens crisis in 1991, here began an inermien series of more sysemaic financial secor reforms ha coninues even oday. For example, he reform of he Indian ineres-rae srucure, which had been sricly managed by he eserve Bank of India (BI), began wih he April 1992 deregulaion of deposi raes and has progressed o he poin where commercial banks are now permied o freely se erm deposi raes and lending raes for loans above s.2 lakh. 1 Moreover, he BI, which had long been consrained by he Indian governmen's fiscal managemen, enered ino an agreemen wih he governmen in Sepember 1994 o limi he issuance of 91-day ad hoc Treasury bills, which were used o finance fiscal deficis, and evenually eliminaed hese securiies alogeher in April 1997, grealy reining in he cenral bank's auomaic moneizaion of fiscal deficis. 2 The above are jus a few examples of how ineres-rae srucure deregulaion and he inroducion of new financial producs have progressed in India over he pas 20 years. Theoreical research and empirical analyses, using primarily daa on developed counries, have shown ha he money demand funcion can become unsable as a resul of such financial innovaions and financial secor reforms. Parly because of insabiliy in he money demand funcion, many cenral banks have in recen years swiched from money supply argeing focused on moneary aggregaes as he inermediae arge, o inflaion argeing, which seeks o sabilize prices by adjusing ineres raes based on inflaion forecass. The BI abandoned he flexible moneary argeing approach in favor of he muliple indicaor approach in April 1998, puing an end o he use of money supply as he inermediae arge, bu reaining i as an imporan indicaor of fuure prices. Consequenly, examining he characerisics of he money demand funcion of India's financial secor, which has undergone significan change since he 1980s, should bear significan meaning for presen and fuure consideraions of he BI s moneary policy. This paper, herefore, uses annual daa for he period of 1976 o 2007 and monhly daa for he period of January 1980 o December 2007 o esimae India's money demand funcion, which is derived from real money balances, ineres raes, and oupu, and shed ligh on is characerisics. The nex secion of his paper consiss of a review of relevan prior research and a discussion of he unique conribuions of his paper. In he hird secion, he models are presened and in he fourh secion, variables are defined, sources are provided, and daa characerisics are explained. Moving ino he fifh secion, coinegraion ess are performed using boh monhly and annual daa, he long-erm sabiliy of he money demand funcion is examined, and dynamic OLS (DOLS) is used o examine he sign condiions and significance of oupu and ineres-rae coefficiens. Lasly, analysis resuls are used o discuss he characerisics of India's money demand funcion and he implicaions for India's moneary policy. 1 Excep for bank savings deposis, non-residen deposis, loans for less han 200,000 rupees, and expor credi, ineres raes have been grealy deregulaed. 2 Financial deregulaion beginning in he 1990s also loosened requiremens, like hose requiring commercial banks o keep cenral bank balances equal o a cerain percenage of heir own deposis and purchase governmen bonds and governmen-specified bonds, and he deregulaion relaxed barriers o enering he banking secor and opened sock markes o foreign paricipans. 1
2. Lieraure eview India's money demand funcion has been he subjec of numerous quaniaive research effors. Among hese was he firs sudy o explicily consider he saionariy of, and coinegraion relaionships among, he variables of he money demand funcion. Moosa (1992) used hree ypes of money supply cash, M1, and M2 o perform coinegraion ess on real money balances, shor-erm ineres raes, and indusrial producion over he period beginning wih he firs quarer of 1972 and exending hrough he fourh quarer of 1990. esuls indicaed ha for all hree ypes of money supply, he money balance had a coinegraing relaionship wih oupu and ineres raes. However, greaer numbers of coinegraing vecors were deeced for cash and M1 han for M2, so Moosa (1992) saes ha narrower definiions of money supply are beer for pursuing moneary policy. Bhaacharya (1995), like Moosa (1992), considered hree ypes of money supply M1, M2, and M3 and used annual daa for he period of 1950 o 1980 o analyze India's money demand funcion. Bhaacharya (1995) performed coinegraion ess for real money balances, real GNP, and long-erm and shor-erm ineres raes, deeced a coinegraing relaionship among variables only when money supply was defined as M1, and clearly showed ha long-erm ineres raes are more sensiive o money demand han are shor-erm ineres raes. In addiion, Bhaacharya (1995), afer esimaing an error correcion model based on coinegraion es resuls, found ha, in he case of M1, he error correcion erm is significan and negaive, and held ha moneary policy is sable over he long erm when money supply is narrowly defined. Bahmani-Oskooee and ehman (2005) analyzed he money demand funcions for India and six oher Asian counries during he period beginning wih he firs quarer of 1972 and ending wih he fourh quarer of 2000. Using he ADL approach described in Pesaran e al. (2001), hey performed coinegraion ess on real money supplies, indusrial producion, inflaion raes, and exchange raes (in erms of US dollar). For India, coinegraing relaionships were deeced when money supply was defined as M1, bu no M2, so hey concluded ha M1 is he appropriae money supply definiion o use in seing moneary policy. Conrasing wih he above, here is also prior research ha uses money supply defined broadly in holding ha India's money demand funcion is sable. In one example, Pradhan and Subramanian (1997) employed coinegraion ess, an error correcion model, and annual daa for he period of 1960 o 1994 o deec relaionships among real money balances, real GDP, and nominal ineres raes. They esimaed an error correcion model using M1 and M3 as money supply definiions and found he error correcion erm o be significan and negaive. Their posiion, herefore, was ha he money demand funcion is sable no only wih M1 bu also wih M3. Das and Mandal (2000) considered only he M3 money supply in saing ha India's money demand funcion is sable. They used monhly daa for he period of April 1981 o March 1998 o perform coinegraion ess and deeced coinegraing vecors among money balance, indusrial producion, shor-erm ineres raes, wholesale prices, share prices, and real effecive exchange raes. Their posiion, herefore, was ha long-erm money demand relevan o M3 is sable. Similarly, amachandran (2004), oo, considered only he M3 money supply in using annual daa for he period of 1951/52 o 2000/01 o perform coinegraion ess on nominal money supply, oupu, and price levels. Because sable relaionships were discovered among hese hree variables, amachandran (2004) saes ha, over he long erm, i is possible o use an increase in M3 as a laen indicaor of fuure price movemens. 2
As is he case wih he sudies referred o above, prior research in general saes ha India's money demand funcion is sable. 3 Furhermore, sudies performed using muliple money supply definiions have ended o draw he conclusion ha because India's money demand funcion is more sable when money supply is defined narrowly, he cenral bank should adop cash or M1 as he narrow definiion of money supply when deermining moneary policy. Conrasing wih ha posiion, however, oher sudies have concluded ha he money demand funcion is sable when money supply is broadly defined. Views on wha definiion of money supply o use for moneary policy, herefore, differ. This paper uses boh monhly and annual daa, considers hree ypes of money supply M1, M2, and M3, and comprehensively esimaes India's money demand funcions for each case. I also discusses he implicaions of empirical resuls for he BI s moneary policy formaion. In conras wih prior sudies, his paper, afer performing coinegraion ess on money supply, oupu, and ineres raes as money demand funcion variables, applies DOLS and sheds ligh on he characerisics of India's money demand funcion hrough examinaions of he sign condiions and saisical significance of variable coefficiens. 3. Models There are various heories concerning he money demand funcion. For example, imbrough (1986a, 1986b) and Faig (1988) came up wih he following money demand funcion as a resul of explicily considering ransacion coss. M LY (, ) P = L 0 Y >, L < 0 (1) In his formula, M represens nominal money supply for period ; P represens he price index for period ; Y represens oupu for period ; and represens he nominal ineres rae for period. Increases in oupu bring increases in money demand, and increases in ineres raes bring decreases in money demand. We use wo models corresponding o equaion (1) in order o conduc an empirical analysis. Model 1: ln( M) ln( P) = β0 + β1 ln( Y) + β2 + u, β1 > 0, β2 < 0 (2) Model 2: ln( M) ln( P) = β0 + β1ln( Y) + β2 ln( ) + u, β1 > 0, β2 < 0 (3) Boh Models (2) and (3) are log linear models, bu Model (2) uses he level of ineres raes and Model (3) uses he logarihm value of ineres raes. 4. Daa This paper uses boh monhly daa and annual daa for empirical analysis. For monhly daa, we use daa over he period of January 1980 o December 2007. The daa source for he indusrial producion index (seasonally adjused by X12) and he wholesale price index is 3 Nag and Upadhyay (1993), Parikh (1994), ao and Shalabh (1995), ao and Singh (2006), and ohers as well have also performed quaniaive analyses of India s money demand funcion. 3
IMF (2008). We obained M1, M2, and M3 from various issues of he BI Bullein. We deflae hese moneary aggregaes by he wholesale price index, and we use he call rae as he ineres rae. The call rae was obained from BI (2006) over he period of January 1980 o December 2005, BI (2007a) and BI (2008) over he period of January 2006 o December 2007. For annual daa, we use daa over he period of 1976 o 2007. eal GDP and he GDP deflaor were aken from IMF (2008). We obained M1, M2, and M3 from various issues of he BI Bullein. We deflae hese moneary aggregaes by he GDP deflaor, and we use he call rae as he ineres rae. The call rae was obained from BI (2007b) and BI (2008). Logarihm values are used for money supply, price levels, and oupu (indusrial producion and GDP). Ineres raes are analyzed in wo ways, aking a logarihm in one case and no in he oher. As a preliminary analysis, we carried ou he augmened Dickey-Fuller ess for he logs of real money balances, oupu, and ineres raes (Dickey and Fuller, 1979). As a resul, he level of each variable was found o have a uni roo, whereas he firs difference of each variable was found no o have a uni roo. Thus, we can say ha each variable is a nonsaionary variable wih a uni roo. 5. Empirical esuls 5.1 Monhly Daa Firs, we analyzed he money demand funcion in relaion o he use of M1 using he monhly daa over he period of January 1980 o December 2007. For ha analysis, we conduced Johansen coinegraion ess for he money demand funcion (Johansen, 1991). There are wo kinds of Johansen-ype ess: he race es and he maximum eigen-value es. Table 1 shows he resuls of coinegraion ess for Model 1 and Model 2. Model 1 includes he logs of real money balances, he logs of indusrial producion, and he ineres rae; whereas Model 2 includes he logs of real money balances, he logs of indusrial producion, and he logs of ineres raes. As is eviden from Table 1, he null hypohesis of no coinegraing relaion is rejeced a he 5% significance level for boh models. As he exisence of he coinegraing relaion was suppored, we esimaed he money demand funcion using dynamic OLS (DOLS). 4 Table 2 shows he esimaion resuls wih respec o Model 1. As is eviden from his able, he oupu coefficien is significanly esimaed o be a posiive values (1.1484 for =1, 1.1498 for =2, and 1.1556 for =6). The ineres rae coefficien is significanly esimaed o be a negaive values (-0.0043 for =1, -0.0049 for =2, and -0.0050 for =6). Thus, he sign condiion of he money demand funcion holds for all cases. Table 3 shows he esimaion resuls wih respec o Model 2. As is eviden from his able, he sign condiion of he money demand funcion holds for all cases. The oupu coefficien was significanly esimaed a posiive values (1.1432 for =1, 1.1437 for =2, and 1.1478 for =6), while he ineres rae coefficien was significanly esimaed a negaive values (-0.0480 for =1, -0.0548 for =2, and -0.0595 for =6). As is eviden from he above resuls, i became clear ha a coinegraing relaion was suppored and ha he exisence of a money demand funcion wih respec o M1 was saisically suppored. Nex, we considered he money demand funcion when using M2 for he money supply componen. Table 4 indicaes he resuls of coinegraion ess for Model 1 and Model 2. As is eviden from he able, he null hypohesis of no coinegraion is rejeced a he 5% significance level for boh models. As he exisence of he coinegraing relaion was 4 Sandard errors are calculaed using he mehod of Newey and Wes (1987). 4
suppored, we esimaed he money demand funcion using DOLS. Table 5 shows he esimaion resuls wih respec o Model 1. As is eviden from his able, he sign condiion of he money demand funcion holds. The oupu coefficien was significanly esimaed a posiive values of 1.0966 for =1, 1.0977 for =2, and 1.1023 for =6, while he ineres rae coefficien was significanly esimaed a negaive values of -0.0049 for =1, -0.0055 for =2, and -0.0059 for =6. Table 6 shows he esimaion resuls wih respec o Model 2. As is eviden from his able, he sign condiion of he money demand funcion holds. The oupu coefficien was significanly esimaed a posiive values of 1.0907 for =1, 1.0908 for =2, and 1.0934 for =6, while he ineres rae coefficien was significanly esimaed a negaive values of -0.0543 for =1, -0.0617 for =2, and -0.0685 for =6. As is eviden from he above resuls, i became clear ha a coinegraing relaion was suppored and ha he exisence of a money demand funcion wih respec o M2 was saisically suppored. Finally, we considered he money demand funcion when using M3 for he money supply componen. Table 7 indicaes he resuls of coinegraion ess for Model 1 and Model 2. As is eviden from his able, he null hypohesis (in which here is no coinegraing relaion) is no rejeced a he 5% significance level for eiher of he models. I became clear ha a coinegraing relaion was no suppored and hus ha he exisence of a money demand funcion wih respec o M3 was no saisically suppored. 5.2 Annual Daa We also analyzed he money demand funcion in relaion o he use of M1 using he annual daa over he period from 1976 o 2007. Since indusrial producion does no necessarily reflec he oal level of oupu in he Indian economy, i is worhwhile o analyze he money demand funcion using annual daa, which enables us o use he GDP daa. Table 8 shows he resuls of coinegraion ess for Model 1 and Model 2. As is eviden from Table 8, he null hypohesis of no coinegraing relaion is rejeced a he 5% significance level for boh models. As he exisence of he coinegraing relaion was suppored, we esimaed he money demand funcion using DOLS. Table 9 shows he esimaion resuls wih respec o Model 1. As is eviden from his able, he oupu coefficien is significanly esimaed o be posiive (1.0037 for =1, 0.9812 for =2, and 0.9769 for =3). The ineres rae coefficien is significanly esimaed o be negaive (-0.0366 for =1, -0.0260 for =2, and -0.0242 for =3). Thus, he sign condiion of he money demand funcion holds for all cases. Table 10 shows he esimaion resuls wih respec o Model 2. As is eviden from his able, he sign condiion of he money demand funcion holds for all cases. The oupu coefficien was significanly esimaed o be posiive (1.0020 for =1, 1.0011 for =2, and 1.0624 for =3), while he ineres rae coefficien was significanly esimaed o be negaive (-0.3399 for =1, -0.2321 for =2, and -0.2378 for =3). As is eviden from he above resuls, i became clear ha a coinegraing relaion was suppored and ha he exisence of a money demand funcion wih respec o M1 was saisically suppored. Nex, we considered he money demand funcion when using M2 for he money supply componen. Table 11 indicaes he resuls of coinegraion ess for Model 1 and Model 2. As is eviden from he able, he null hypohesis of no coinegraion is rejeced a he 5% significance level for boh models. As he exisence of he coinegraing relaion was suppored, we esimaed he money demand funcion using DOLS. Table 12 shows he esimaion resuls wih respec o Model 1. As is eviden from his able, he sign condiion of he money demand funcion holds. The oupu coefficien was significanly esimaed a posiive values of 0.9402 for =1, 0.9173 for =2, and 0.9132 for =3, while he ineres rae coefficien was significanly esimaed a negaive values of -0.0397 for =1, -0.0295 for 5
=2, and -0.0278 for =3. Table 13 shows he esimaion resuls wih respec o Model 2. As is eviden from his able, he sign condiion of he money demand funcion holds. The oupu coefficien was significanly esimaed a posiive values of 0.9381 for =1, 0.9374 for =2, and 0.9988 for =3, while he ineres rae coefficien was significanly esimaed a negaive values of -0.3669 for =1, -0.2648 for =2, and -0.2715 for =3. As is eviden from he above resuls, i became clear ha a coinegraing relaion was suppored and ha he exisence of a money demand funcion wih respec o M2 was saisically suppored. Finally, we considered he money demand funcion when using M3 for he money supply componen. Table 14 indicaes he resuls of coinegraion ess for Model 1 and Model 2. As is eviden from his able, he null hypohesis (in which here is no coinegraing relaion) is no rejeced a he 5% significance level in hree ou of four cases. I became clear ha a coinegraing relaion may no be suppored and hus ha he exisence of a money demand funcion wih respec o M3 may no be saisically suppored. Our empirical resuls using annual daa are consisen wih hose using monhly daa. Thus, he coinegraing relaion for he money demand funcion is saisically suppored for M1 and M2, bu no for M3 for boh monhly and annual daa. 6. Some Concluding emarks If an equilibrium relaionship is observed in he money demand funcion, financial auhoriies can employ appropriae money supply conrols o mainain a reasonable inflaion rae. This paper empirically analyzed India's money demand funcion over he period of 1980 o 2007 using monhly daa and he period of 1976 o 2007 using annual daa. esuls suppored he exisence of an equilibrium relaion in money demand when money supply was defined as M1 or M2, bu no such relaion was deeced when money supply was defined as M3. These resuls were obained for boh monhly and annual daa, so hey were no affeced by daa inervals and were robus in his sense. Wha are he implicaions of hese resuls for India's moneary policy? In he mid-1980s, he BI adoped moneary argeing focused on he medium-erm growh rae of he M3 money supply. Moneary argeing was used as a flexible policy framework o be adjused in accordance wih changes in producion and prices, raher han as a sric policy rule. However, amid ongoing financial innovaions and financial secor reforms, he BI announced in April 1998 ha i would swich o he muliple indicaor approach in order o be able o consider a wider array of facors in seing policy. Under his new policy framework, he M3 growh rae is used as one reference indicaor. In general, a reference indicaor, as an indicaor of fuure economic condiions, is used as somehing beween an operaing insrumen and a final objecive, and no arge levels are se, as is he case, for example, wih inermediae arges. However, in India, where i is used as a reference indicaor, he forecas growh rae for he M3 money supply is publicly announced on an annual basis, and i is focused on as a measure of fuure price movemens. Consequenly, Indian financial auhoriies, despie he fac ha hey have changed heir policy framework, coninue o pay significan aenion o M3 movemens. The empirical resuls of his paper, hough, sugges ha he BI would be able o more appropriaely conrol price levels if i would refer o he M1 and M2, raher han he M3, money supplies in managing moneary policy. 6
eferences Bahmani-Oskooee, M. and H. ehman (2005) Sabiliy of he Money Demand Funcion in Asian Developing Counries Applied Economics 37, no.7: 773-792. Bhaacharya,. (1995) Coinegraing elaionships in he Demand for Money in India The Indian Economic Journal 43, no.1: 69-75. Das, S. and. Mandal (2000) Modeling Money Demand in India: Tesing Weak, Srong & Super Exogeneiy Indian Economic eview 35, no.1: 1-19. Dickey, D.A. and W.A. Fuller (1979) Disribuion of he Esimaors for Auoregressive Time Series wih a Uni oo Journal of he American Saisical Associaion 74, no.366: 427-431. Faig, M. (1988) Characerizaion of he Opimal Tax on Money when i Funcions as a Medium of Exchange Journal of Moneary Economics 22, no.1: 137-148. Inernaional Moneary Fund (2008) Inernaional Financial Saisics, Washingon, D.C.: IMF, April. Johansen, S. (1991) Esimaion and Hypohesis Tesing of Coinegraion Vecors in Gaussian Vecor Auoregressive Models Economerica 59, no.6: 1551-1580. imbrough,.p. (1986a) Inflaion, Employmen, and Welfare in he Presence of Transacions Coss Journal of Money, Credi, and Banking 18, no.2: 127-140. imbrough,.p. (1986b) The Opimum Quaniy of Money ule in he Theory of Public Finance Journal of Moneary Economics 18, no.3: 277-284. Moosa, I. (1992) The Demand for Money in India: A Coinegraion Approach The Indian Economic Journal 40, no.1: 101-115. Nag, A.. and G. Upadhyay (1993) Esimaing Money Demand Funcion: A Coinegraion Approach eserve Bank of India Occasional Papers 14, no.1: 47-66. Newey, W and. Wes (1987) A Simple Posiive Semi-Definie, Heeroskedasiciy and Auocorrelaion Consisen Covariance Marix Economerica 55, no.3: 703-708. Parikh, A. (1994) An Approach o Moneary Targeing in India eserve Bank of India Developmen esearch Group Sudy, no.9. Pesaran, M.H., Y. Shin, and.j. Smih (2001) Bounds Tesing Approaches o he Analysis of Level elaionships Journal of Applied Economerics 16, no.3: 289-326. Pradhan, B.. and A. Subramanian (1997) On he Sabiliy of he Demand for Money in India The Indian Economic Journal 45, no.1: 106-117. amachandran, M. (2004) Do Broad Money, Oupu, and Prices Sand for a Sable elaionship in India? Journal of Policy Modeling 26, nos.8-9: 983-1001. ao, B.B. and Shalabh (1995) Uni oos Coinegraion and he Demand for Money in India Applied Economics Leers 2, no.10: 397-399. ao, B.B. and. Singh (2006) Demand for Money in India: 1953-2003 Applied Economics 38, no.11: 1319-1326. eserve Bank of India (2006) Handbook of Moneary Saisics of India, Mumbai: BI. eserve Bank of India (2007a) Macroeconomic and Moneary Developmens Firs Quarer eview 2007-08, Mumbai: BI. eserve Bank of India (2007b) Handbook of Saisics on Indian Economy, Mumbai: BI. eserve Bank of India (2008) Macroeconomic and Moneary Developmens in 2007-08, Mumbai: BI. eserve Bank of India (various issues) BI Bullein, Mumbai: BI. Sen,. and.. Vaidya (1997) The Process of Financial Liberalizaion, Delhi: Oxford Universiy Press. 7
Table 1 Coinegraion Tess (M1, Monhly daa) Hypohesized Model Number of Coinegraion Maximum Eigen- Value Tes Trace Tes Equaions Model 1 0 60.8885* 75.5725* A mos 1 13.9371 14.6841 A mos 2 0.7470 0.7470 Model 2 0 62.6358* 77.4240* A mos 1 14.0725 14.7883 A mos 2 0.7157 0.7157 * indicaes ha he null hypohesis is rejeced a he 5% significance level. 8
Table 2 Dynamic OLS (M1, Monhly daa, Model 1) 0 1 2 i= yi i i= ri i log( M1 ) log( P) = β + β log( Y) + β + γ Δ log( Y ) + γ Δ + u Lead and Lag 2 Variable Coefficien SE -Saisic p-value = 1 Consan 2.9533 0.0741 39.8611 0.0000 0.9911 ) 1.1484 0.0158 72.4935 0.0000-0.0043 0.0012-3.5416 0.0005 = 2 Consan 2.9478 0.0626 47.0700 0.0000 0.9923 ) 1.1498 0.0135 85.2199 0.0000-0.0049 0.0012-4.0843 0.0001 = 6 Consan 2.9130 0.0539 54.0741 0.0000 0.9947 ) 1.1556 0.0107 108.2575 0.0000-0.0050 0.0015-3.3923 0.0008 Noe: SE is he Newey-Wes HAC Sandard Error (lag runcaion=5). 9
Table 3 Dynamic OLS (M1, Monhly daa, Model 2) log( M1 ) log( P) = β + β log( Y) + β log( ) + γ Δ log( Y ) + γ Δ log( ) + u 0 1 2 i= yi i i= ri i Lead and Lag 2 Variable Coefficien SE -Saisic p-value = 1 Consan 3.0363 0.0894 33.9515 0.0000 0.9911 ) 1.1432 0.0164 69.6620 0.0000 log( ) -0.0480 0.0134-3.5715 0.0004 = 2 Consan 3.0445 0.0755 40.3038 0.0000 0.9924 ) 1.1437 0.0138 82.8285 0.0000 log( ) -0.0548 0.0127-4.3211 0.0000 = 6 Consan 3.0247 0.0655 46.2015 0.0000 0.9950 ) 1.1478 0.0104 109.8776 0.0000 log( ) -0.0595 0.0144-4.1434 0.0000 Noe: SE is he Newey-Wes HAC Sandard Error (lag runcaion=5). 10
Table 4 Coinegraion Tess (M2, Monhly daa) Hypohesized Model Number of Coinegraion Maximum Eigen- Value Tes Trace Tes Equaions Model 1 0 25.3333* 39.3050* A mos 1 11.8306 13.9716 A mos 2 2.1411 2.1411 Model 2 0 26.2955* 39.6353* A mos 1 11.0450 13.3398 A mos 2 2.2948 2.2948 * indicaes ha he null hypohesis is rejeced a he 5% significance level. 11
Table 5 Dynamic OLS (M2, Monhly daa, Model 1) 0 1 2 i= yi i i= ri i log( M 2 ) log( P) = β + β log( Y) + β + γ Δ log( Y ) + γ Δ + u Lead and Lag 2 Variable Coefficien SE -Saisic p-value = 1 Consan 3.2129 0.0760 42.2970 0.0000 0.9899 ) 1.0966 0.0165 66.5934 0.0000-0.0049 0.0012-3.9508 0.0001 = 2 Consan 3.2096 0.0655 49.0098 0.0000 0.9913 ) 1.0977 0.0143 76.7408 0.0000-0.0055 0.0012-4.5206 0.0000 = 6 Consan 3.1817 0.0583 54.5536 0.0000 0.9938 ) 1.1023 0.0117 94.5821 0.0000-0.0059 0.0015-3.8277 0.0002 Noe: SE is he Newey-Wes HAC Sandard Error (lag runcaion=5). 12
Table 6 Dynamic OLS (M2, Monhly daa, Model 2) log( M 2 ) log( P) = β + β log( Y) + β log( ) + γ Δ log( Y ) + γ Δ log( ) + u 0 1 2 i= yi i i= ri i Lead and Lag 2 Variable Coefficien SE -Saisic p-value = 1 Consan 3.3066 0.0914 36.1578 0.0000 0.9900 ) 1.0907 0.0170 64.2289 0.0000 log( ) -0.0543 0.0139-3.8990 0.0001 = 2 Consan 3.3180 0.0787 42.1394 0.0000 0.9914 ) 1.0908 0.0146 74.9043 0.0000 log( ) -0.0617 0.0133-4.6363 0.0000 = 6 Consan 3.3084 0.0700 47.2392 0.0000 0.9941 ) 1.0934 0.0114 96.2653 0.0000 log( ) -0.0685 0.0149-4.6022 0.0000 Noe: SE is he Newey-Wes HAC Sandard Error (lag runcaion=5). 13
Table 7 Coinegraion Tess (M3, Monhly daa) Hypohesized Model Number of Coinegraion Maximum Eigen- Value Tes Trace Tes Equaions Model 1 0 20.4033 27.3507 A mos 1 5.2173 6.9474 A mos 2 1.7301 1.7301 Model 2 0 19.4088 25.9354 A mos 1 5.0979 6.5266 A mos 2 1.4287 1.4287 * indicaes ha he null hypohesis is rejeced a he 5% significance level. 14
Table 8 Coinegraion Tess (M1, Annual daa) Hypohesized Model Number of Coinegraion Maximum Eigen- Value Tes Trace Tes Equaions Model 1 0 29.0382* 40.3709* A mos 1 8.8912 11.3327 A mos 2 2.4415 2.4415 Model 2 0 31.2939* 42.7403* A mos 1 8.9359 11.4464 A mos 2 2.5105 2.5105 * indicaes ha he null hypohesis is rejeced a he 5% significance level. 15
Table 9 Dynamic OLS (M1, Annual daa, Model 1) 0 1 2 i= yi i i= ri i log( M1 ) log( P) = β + β log( Y) + β + γ Δ log( Y ) + γ Δ + u Lead and Lag 2 Variable Coefficien SE -Saisic p-value = 1 Consan 4.0407 0.2939 13.7502 0.0000 0.9716 ) 1.0037 0.0768 13.0640 0.0000-0.0366 0.0099-3.7002 0.0014 = 2 Consan 3.8224 0.1669 22.9069 0.0000 0.9944 ) 0.9812 0.0448 21.9224 0.0000-0.0260 0.0058-4.4821 0.0005 = 3 Consan 3.7578 0.1312 28.6378 0.0000 0.9952 ) 0.9769 0.0470 20.7860 0.0000-0.0242 0.0048-5.0189 0.0010 Noe: SE is he Newey-Wes HAC Sandard Error (lag runcaion=5). 16
Table 10 Dynamic OLS (M1, Annual daa, Model 2) log( M1 ) log( P) = β + β log( Y) + β log( ) + γ Δ log( Y ) + γ Δ log( ) + u 0 1 2 i= yi i i= ri i Lead and Lag 2 Variable Coefficien SE -Saisic p-value = 1 Consan 4.4896 0.3875 11.5861 0.0000 0.9738 ) 1.0020 0.0772 12.9872 0.0000 log( ) -0.3399 0.0873-3.8949 0.0009 = 2 Consan 4.0882 0.2591 15.7774 0.0000 0.9942 ) 1.0011 0.0524 19.1028 0.0000 log( ) -0.2321 0.0615-3.7765 0.0020 = 3 Consan 3.8970 0.1522 25.6072 0.0000 0.9944 ) 1.0624 0.0446 23.8410 0.0000 log( ) -0.2378 0.0532-4.4676 0.0021 Noe: SE is he Newey-Wes HAC Sandard Error (lag runcaion=5). 17
Table 11 Coinegraion Tess (M2, Annual daa) Hypohesized Model Number of Coinegraion Maximum Eigen- Value Tes Trace Tes Equaions Model 1 0 29.4465* 40.2924* A mos 1 8.9430 10.8459 A mos 2 1.9029 1.9029 Model 2 0 31.8685* 42.6966* A mos 1 8.9294 10.8281 A mos 2 1.8988 1.8988 * indicaes ha he null hypohesis is rejeced a he 5% significance level. 18
Table 12 Dynamic OLS (M2, Annual daa, Model 1) 0 1 2 i= yi i i= ri i log( M 2 ) log( P) = β + β log( Y) + β + γ Δ log( Y ) + γ Δ + u Lead and Lag 2 Variable Coefficien SE -Saisic p-value = 1 Consan 4.3669 0.2886 15.1317 0.0000 0.9676 ) 0.9402 0.0760 12.3674 0.0000-0.0397 0.0098-4.0638 0.0006 = 2 Consan 4.1610 0.1650 25.2232 0.0000 0.9936 ) 0.9173 0.0443 20.7286 0.0000-0.0295 0.0057-5.1387 0.0002 = 3 Consan 4.1007 0.1311 31.2843 0.0000 0.9948 ) 0.9132 0.0478 19.1190 0.0000-0.0278 0.0049-5.7213 0.0004 Noe: SE is he Newey-Wes HAC Sandard Error (lag runcaion=5). 19
Table 13 Dynamic OLS (M2, Annual daa, Model 2) log( M 2 ) log( P) = β + β log( Y) + β log( ) + γ Δ log( Y ) + γ Δ log( ) + u 0 1 2 i= yi i i= ri i Lead and Lag 2 Variable Coefficien SE -Saisic p-value = 1 Consan 4.8505 0.3788 12.8058 0.0000 0.9702 ) 0.9381 0.0757 12.3845 0.0000 log( ) -0.3669 0.0857-4.2806 0.0004 = 2 Consan 4.4693 0.2556 17.4837 0.0000 0.9935 ) 0.9374 0.0511 18.3566 0.0000 log( ) -0.2648 0.0613-4.31665 0.0007 = 3 Consan 4.2862 0.1556 27.5495 0.0000 0.9938 ) 0.9988 0.0463 21.5558 0.0000 log( ) -0.2715 0.0541-5.0207 0.0010 Noe: SE is he Newey-Wes HAC Sandard Error (lag runcaion=5). 20
Table 14 Coinegraion Tess (M3, Annual daa) Hypohesized Model Number of Coinegraion Maximum Eigen- Value Tes Trace Tes Equaions Model 1 0 20.7221 31.4139* A mos 1 6.7122 10.6918 A mos 2 3.9796 3.9796 Model 2 0 18.0444 28.3185 A mos 1 6.5157 10.2741 A mos 2 3.7584 3.7584 * indicaes ha he null hypohesis is rejeced a he 5% significance level. 21