Keywords: Granger causality, Frequency-domain, Money supply, Monetarist, RBI,

Transcription

1 Causaliy beween Prices, Oupu and Money in India: An Empirical Invesigaion in he Frequency Domain Ashuosh harma 1 Abodh Kumar 2 Neeraj Haekar 3 Absrac: Wheher money supply Granger causes, oupu and prices has been inensively invesigaed in he Indian conex. However, he quesion involves seling of he issue over he shor -run, business cycle as well as in he long -run, because he behavior of he Phillips curve depends upon wheher a long -run or a shor -run relaionship is being invesigaed. In his paper, we examine he issues using a bivariae mehodology developed by Lemmens e al. (2008) in order o decompose Granger causaliy beween money supply, prices and oupu in frequency-domain. We conclude ha here is evidence for money-oupu rade-off over he shor -run, bu in he long -run, money supply deermines prices, no oupu. The empirical resuls also indicae ha oupu and prices does no Granger causes money supply reflecing exogeneiy of money supply. Keywords: Granger causaliy, Frequency-domain, Money supply, Monearis, RBI, 1 Ashuosh harma, Ph.D scholar, Deparmen of Economics, Universiy of Mumbai, Mumbai. ashuofrabi@gmail.com. 2 Abodh Kumar, Ass. Prof. ymbiosis Cenre for Managemen and Human resource Developmen, Pune and Ph.D scholar, Deparmen of Economics, Universiy of Mumbai, Mumbai. abodhkumar@gmail.com 3 Prof. Neeraj Haekar, Deparmen of Economics, Universiy of Mumbai, Mumbai.neeraj.haekar@gmail.com. 1

2 Causaliy beween Prices, Oupu and Money in India: An Empirical Invesigaion in he Frequency Domain Inroducion Does money have a role in deermining real oupu and prices? This relaionship has been exensively invesigaed in previous sudies and ye he debae is unseled regarding he size and naure of he effecs of moneary policy on income and prices, in shor-run as well as in he long-run. I may be ha money supply could be independen of real income and prices, and being an exogenous variable i influences he real income and prices. On he oher hand, real income and prices may be he major deerminan of supply of money, reflecing endogeneiy of he money supply. Moreover, hese relaionships and heir srengh may vary in shor-run and in long-run. A number of hypoheses regarding he causaliy relaionship among hese variables wih plausible heoreical argumens have been formulaed in he pas. The proponens of quaniy heory model assume ha money supply is exogenous. While Cagan (1965) argues ha money supply exhibis boh endogenous and exogenous properies. For shor -run and cyclical flucuaion, Cagan (1965) proposed a relaion in which he money supply is endogenously deermined by changes in real secor. However, he assers ha in he long -run secular rend movemens in money supply are independen of real secor and are deermined exogenously. In monearis view, increase in money supply, may lead o increase in oupu in he shor -run, bu in he long -run i influence only prices. The monearis discards he exisence of long-run Phillips relaion and in heir view, money is he cause and prices are he effecs in he long-run. 2

3 Theoreical argumens and hypoheses regarding money supply, oupu and price behaviour in he macroeconomy requires empirical invesigaion in seling down he issue, in a manner in which shor-run and long-run causaliy, if any, can be disinguished. Granger Causaliy (hereafer GC) is a well esablished echnique for measuring causaliy and applying GC over he specrum may prove o be useful in measuring he srengh and direcion of he causaliy, which could vary over he frequencies. Granger (1969) was he firs o sugges ha a specral-densiy approach would give a richer and more comprehensive picure han a one-sho GC measure ha is supposed o apply across all periodiciies. Thus measuring he bivariae GC over he specrum has meri compared o he one-sho GC es. This paper aims o sudy he causaliy relaionship beween money, oupu and price in Indian conex. The plan of he paper is as follows. ecion 1 briefly reviews he exising lieraure on money, oupu and price causaliy in Indian conex. ecion 2 oulines he GC mehodology over he specrum and daa used in his sudy. ecion 3 presens he GC resuls relaed o money, oupu and prices. ecion 4 concludes he paper. 1. Lieraure review The causaliy link beween prices, oupu and money has been vigorously invesigaed in India, for differen ime period. The foundaion of his debae lies in is imporance for conducing moneary policy and is role in macroeconomic heory, bu he magniude of his debae reflecs he differences in conclusions arrived by earlier researchers. Ramachandra (1983, 1986) using annual daa for he period , found ha money causes real income and price level, price level causes real income and nominal income causes money. He ook money sock measure as annual average of monhly values as sum of coins, currency and ne demand deposis wih he commercial and co-operaive banks. harma (1984) invesigaed he causaliy beween price level and money supply 3

4 (M 1 and M 2 ) using Granger (1969) and ims (1972) saisical echnique for he period and esablished bidirecional causaliy beween M 1 and Price level as well as M 2 and Price level. Alhough he found he causaliy from M 1 o Price level was much sronger han he reverse causaliy beween Price levels o M 1. Nachane and Nadkarni (1985) found unidirecional causaliy from money sock o prices based on heir sudy on quarerly daa over he period o In heir sudy he causaliy resuls beween real income and money sock remained inconclusive. ingh (1990) se up bidirecional causaliy beween money sock (M 3 ) and prices (WPI) and revealed comparaively less significan causaliy from money supply o prices. Biswas and aunders (1990) also found bidirecional causaliy or feedback beween money supply (M 1, M 2 ) and price level (WPI) by using quarerly daa for wo periods: and They made use of Hsiao s (1981) lag selecion crieria and conradiced harma s findings of comparaively weaker reverse causaliy beween M 1 o Price level. Masih and Masih (1994) revealed ha money supply was leading and price was he lagging variable for he period During he period of heir sudy prices had a feedback effec on money supply bu no srong enough o be saisically significan a 5% probabiliy level. Ashra, Chaopadhyay and Chaudhuri (2004) esablished bidirecional causaliy beween price (GDP deflaor) and M 3. The available sudy for India provides us mixed resuls in conex of money, oupu and price causaliy direcion and srengh. Therefore our sudy is an effor o find ou money, price and oupu causaliy direcion as well as he srengh of causaliy over he specrum in order o solve he puzzle of shor-run and long-run. 2. Mehodology and Daa The dynamic behaviour of economic ime series has been widely analysed in he imedomain. However, analysing he ime series in frequency-domain i.e specral analysis could be helpful in supplemening he informaion obained by ime-domain analysis (Granger and Haanaka, 1964; Priesley, 1981; Press e al., 1986; Medio, 1992). pecral analysis lies on he remark ha mos regular behaviour of a ime series is periodic; hus, 4

5 he periodic componens embedded in he analyzed series can be deermined by compuing heir periods, ampliude, and phase (Ghil e al., 2002). pecral analysis is a powerful ool for inspecing cyclical phenomena and highlighing lead-lag relaions among series. Cross specral analysis allows a deailed sudy of he correlaion among series (Iacobucci, (2003). The purpose of his sudy is o es he direcion and srengh of GC beween money supply, oupu and prices in frequency-domain. Therefore we have applied he bivariae GC es over he specrum proposed by Lemmens e al. (2008). Pierce (1979) proposed an R-squared measure for ime series and decomposed i over each frequency of he specrum, resuling in a measure for GC a every given frequency. Lemmens e al. (2008) reconsidered he original framework proposed by Pierce (1979), and proposed an easy esing procedure for Pierce (1979) specral GC measure. This GC es in he frequency domain relies on a modified version of he coefficien of coherence, which hey have esimaed in a nonparameric fashion, and for which hey have derived he disribuional properies. Le X and Y be wo saionary ime series of lenght. The goal is o es wheher X Granger causes Y a a given frequency. Pierce (1979) measure for GC in he frequency domain is performed on he univariae innovaions series, from filering he X and Y as univariae ARMA processes, i.e. x ( x x L ) X C ( L) u u and v, derived y y y ( L ) X C ( L) u (1) 5

6 where x (L) and y (L) are auoregressive polynomials, x (L) and y (L) are moving average polynomials and x C and y C poenial deerminisic componens. The obained innovaion series u and v, which are whie-noise processes wih zero mean, possibly correlaed wih each oher a differen leads and lags. The series u and v are building block for he GC es proposed by Lemmens e al. Le u ( ) and v ( ) be he specral densiy funcions, or specra, of u and v a frequency ] 0, [, defined by 1 i k u ( ) u ( k ) e and 2 k 1 i k v ( ) v ( k ) e (2) 2 k where (k) = Cov u, ) and (k) = Cov v, ) represen he auocovariances of u ( u k v ( v k u and v a lag k. The idea of he specral represenaion is ha each ime series may be decomposed ino a sum of uncorrelaed componens, each relaed o a paricular frequency. To invesigae he relaionship beween he wo sochasic processes under consideraion, hey consider he cross-specrum, () defined as, ( ) C ( ) iq ( ), beween u and v. This is a complex number, 1 ( k) e 2 k ik (3) 6

7 where he cospecrum C () and he quadraure specrum Q () are, respecively, he real and imaginary pars of he cross-specrum. Here (k) = Cov u, v ) ( k represens he cross-covariance of esimaed non-paramerically by, u and v a lag k. The cross-specrum can be M 1 ik ( ) wk ( k e ) (4) 2 k M wih (k) COV ( u, v k ) he empirical cross-covariances, and wih window weighs w k, for k M,.., M. Eq. (4) is called he weighed covariance esimaor, and he weighs w are seleced as, he Barle weighing scheme i.e. 1 k / M k. The consan M deermines he maximum lag order considered. The specra are esimaed in a similar way. This cross-specrum allows o compue he coefficien of coherence h () defined as. h ( ) u ( ) ( ) v ( ) (5) This coefficien gives a measure of he srengh of he linear associaion beween wo ime series, frequency by frequency, bu does no provide any informaion on he direcion of he relaionship beween wo processes. The squared coefficien of coherence has an inerpreaion similar o he R-squared in a regression conex. In paricular, Pierce (1979) indicaes ha he R-squared of a regression of v on all pas, presen, and fuure values of u is he inegral, across frequencies, of he squared coefficien of coherence. 7

8 Lemmens e al. have shown ha, under he null hypohesis ha h ( ) 0, he esimaed squared coefficien of coherence a frequency, wih 0 when appropriaely rescaled, converges o a chi-squared disribuion wih 2 degrees of freedom, denoed by. 2 2 where 2 1) d h( ) 2( n M d 2 sands for convergence in disribuion, wih n T w k M k 2 2 /. The null hypohesis h ( ) 0 versus h ( ) 0 is hen rejeced if h 2 2,1 ( ) (6) 2( n 1) wih being he 1 quanile of he chi-squared disribuion wih 2 degrees of 2 2,1 freedom. Following Pierce (1979), Lemmens e al decomposed he cross-specrum (E.q.3) ino hree pars: (i) u v, he insananeous relaionship beween u and v ; (ii) u v, he direcional relaionship beween v and lagged values of u ; and (iii) v u, he direcional relaionship beween u and lagged values of v, i.e., ( ) [ vu ] 1 1 ik (0) ( k) e 2 k k1 ( k) e ik (7) 8

9 The proposed specral measure of GC is based on he key propery ha X does no Granger cause Y if and only if ( k) 0 for all k 0. Our goal of esing he predicive conen of X relaive o Y is given by he second par of Eq. (7), i.e. ( ik ) ( k) e (8) k The Granger coefficien of coherence is hen given by, h ( ) u ( ) ( ) v ( ) (9) Therefore, in he absence of GC, h ( ) 0 for every in ] 0, [. The Granger coefficien of coherence akes values beween zero and one, as shown by Pierce (1979). An esimaor for he Granger coefficien of coherence a frequency is given by h ( ) u ( ) ( ) v ( ), (10) wih () as in Eq. (4), bu wih all weighs w for k 0pu equal o zero. k In his sudy we have applied above discussed mehodology for he period April 1991 o March 2009, which can be fairly considered as pos liberalisaion period in India. We have considered broad money (M 3 ) as a measure of money supply repored a he end of he monh by RBI. Oupu has been proxied by IIP manufacuring and prices by WPI manufacuring. For IIP he base year was and , whereas for WPI he 9

10 base year was and The IIP and he WPI daa have been spliced using symmeric mean mehodology. Geomeric mean has been applied as symmeric mean because i generaes a spliced series ha is invarian o rebasing of eiher of he original series (see. Hill and Fox (1997)). Daa on all hese variables was colleced on monhly basis from RBI daabase on Indian economy, from RBI daabase on Indian economy (RBI Websie) and RBI occasional repor, RBI Annual repors ec. All he variables have been aken in heir naural logs. 3. Empirical Finding We invesigae wheher money supply Granger cause he oupu or prices or boh. Furher, we also invesigae wheher oupu and prices granger causes money supply or no. ince he es requires saionariy of he ime series, we have applied HEGY monhly uni roos es developed by Beaulieu and Miron (see. Beaulieu and Miron (1993)). The seasonal uni roos es resuls are repored in he Appendix. The es suggess presence of uni roos a seasonal frequency as well as a zero frequency in all he hree ime series, M 3, IIP and WPI. We have seasonally differenced he hree series and hen performed firs difference on he seasonally differenced series. We filered he hree series using ARMA modeling by making use of AIC and BIC informaion o obain whie noise processes. Boh AIC and BIC suggesed he same ARMA model. We 4 We have used WPI manufacuring as measure of price Index because i excludes primary producs (whose prices are more vulnerable o emporary supply shocks) and fuel and energy (whose prices are ofen adminisered). Excluding primary producs and fuel and energy from WPI, allows us o come over he variaion in prices caused due o srucural influences, e.g. crop failures, commodiy shorage, adminisered pricing policies ec. In selecion of oupu variable GDP would have been a beer measure bu using ha as a measure of oupu would leave us wih few observaion. Our excuse for he choice of IIP manufacuring as a measure of oupu is ha, i is available on monhly basis and has nearly 80 percen weigh in IIP General. One can argue ha why we have dropped mining and elecriciy secor from IIP. The reason is ha demand of credi mainly comes from manufacuring secor compared o Mining and Elecriciy. Moreover, Mining and Elecriciy are inpus of producion which will ge refleced in IIP manufacuring. 10

11 compue he Granger coefficien of coherence, given by E.q (10), using lag lengh 5 M T. Fig. 1 shows he Granger coefficien of coherence beween M 3 and IIP a all frequency (). This coefficien assesses wheher and o wha exen M 3 Granger causes IIP a ha frequency. The higher is he esimaed Granger coefficien of coherence, he higher he Granger causaliy a ha paricular frequency. The frequency () on he horizonal axis can be ranslaed ino a cycle or periodiciy of T monhs byt 2 / (for monhly daa). Fig. 1 shows a M 3 Granger causes IIP a higher frequencies reflecing shor-run componens. In erms of monhs M 3 Granger causes IIP a 3-4 monhs and hen a 6-9 monhs, which clearly reflecs wihin a year movemen. The esimaed shor erm Granger coefficien of coherence beween M 3 and IIP reaches 50% (a frequency corresponding o 8 monh). On he oher, a 5% significance level M 3 does no Granger causes IIP a lower frequencies reflecing long -run componen. Granger coefficien of coherence M3 Granger Causing IIP Figure 1. The dashed line represens he criical value, a he 5% level, for he es for no GC. 5 Following Diebold (2001, p.136) we ake M equal o he square roo of number of observaionst

12 Fig. 2 shows he Granger coefficien of coherence beween M 3 and WPI. The esimaed Granger coefficien of coherence beween M 3 and WPI is no significan in he shor -run corresponding o higher frequency. However a lower frequency equivalen o 7-22 quarers, we find M3 significanly Granger causes WPI and he Granger coefficien of coherence beween M3 and WPI reaches 42% (a frequency corresponding o 11 quarer). Granger coefficien of coherence M3 Granger Causing WPI Figure. 2. The dashed line represens he criical value, a he 5% level, for he es for no GC. The empirical resuls from above fig.1 and fig.2 sugges ha he effec of money supply on oupu has remained a shor run phenomenon in he pos-liberalisaion period, in India. On he oher hand, effecs of money supply on prices ge refleced only a business cycle frequency. These finding are in line wih monearis views and subsaniae he monearis proposiion in Indian conex. Fig. 3 repors he es resul for IIP Granger causing M 3. I is imporan o noe ha wihin our sample period he Granger coefficien of coherence resul indicaes ha IIP does no Granger causes M 3 in shor -run as well as in he long -run a 5% significance level. Clearly, here is absence of bidirecional Granger causaliy beween money supply and 12

13 oupu in our sample period. The causaliy beween money supply is unidirecional, running from money supply o oupu. IIP Granger Causing M Granger coefficien of coherence Fig. 3. The dashed line represens he criical value, a he 5% level, for he es for no GC. WPI Granger Causing M Granger coefficien of coherence Fig. 4. The dashed line represens he criical value, a he 5% level, for he es for no GC. Fig. 4 presens he resuls for he null hypohesis, wheher WPI Granger causes M 3 or no. The resuls clearly sugges ha a 5% significance level WPI does no Granger causes M 3. This finding is in line wih earlier finding of Masih and Masih (1994) ha feedback effec of prices on money supply were no srong enough o be saisically significan a 13

14 5% probabiliy level. The Granger causaliy beween money supply o prices is also unidirecional, running from money supply o prices. The above discussed empirical resul indicaes ha here is no feedback relaion beween money supply-oupu and money supply-prices. The causaliy is unidirecional in boh he cases running from money supply o oupu and prices. However, he srengh of causaliy varies over frequencies. The absence of bidirecional causaliy beween money supplyoupu and money supply-prices indicaes ha money supply can be considered as exogenous in our bivariae framework. The implicaion of his finding is supply of money (M 3 ) can be considered as an effecive conrol variable. 4. Conclusion The sudy invesigaes he causal relaionship beween money, oupu and prices for he pos liberalisaion period in India. The Granger causaliy es was performed in bivariae frequency-domain seup. The empirical finding indicaes ha money supply (M 3 ) Granger causes oupu (IIP manufacuring) only in shor -run, whereas money supply (M 3 ) Granger causes prices (WPI manufacuring) a business cycle frequencies. Any feedback running from oupu (IIP manufacuring) and prices (WPI manufacuring) o money supply (M 3 ) was rejeced in our bivariae seup. 14

15 References A, unil., C, aumen., & C, Kaushik., (2004). Defici, Money and Price: The Indian Experience. Journal of Policy Modeling, 26, Beaulieu, J. J. and Miron, J. A., (1993). easonal Uni Roos in Aggregae U Daa. Journal of Economerics, 55, Biswas, B., & aunders, P. J. (1990). Money and Price Level in India: An Empirical Analysis. Indian Economic Journal, 35, Cagan, P. (1965). Deerminans and effecs of changes of sock of money, ( ). Princeon Univ. Press (for he Naional Bureau of Economic Research). Friedman, Milon, (1968). The Role of Moneary Policy. American Economic Review 58, 1968, Friedman, Benjamin and Kenneh Kuner (1993), Anoher Look a he Evidence on Money-Income Causaliy, Journal of Economerics, 57, Geweke, J. (1982). Measuremen of Linear Dependence and Feedback beween Muliple Time eries. Journal of he American aisical Associaion, 77, Ghil, M., Allen, M. R., Deinger, M. R., Ide, K., Kondrashov, D., Mann, M. E., Roberson, A. W., aunders, A., Tian, Y., Varadi, F. and Yiou, P., (2002). Advanced pecral Mehods for Climaic Time eries. Reviews of Geophysics 40(1): Granger, C. W. J. (1969). Invesigaing Causal Relaions by Economeric Models and Cross-pecral Mehods. Economerica, 37, Granger, C. W. J. and Haanaka, M., (1964). pecral Analysis of Economic Time eries. Princeon, NJ: Princeon Universiy Press. Hamilon, J. D. (1994): Time eries Analysis. Princeon Universiy Press, Princeon, 15

16 NJ. Hill R. J. and Kevin, J. Fox., (1997). plicing Index Numbers. Journal of Business & Economic aisics, 15, Iacobucci, A. (2003) pecral Analysis for Economic Time eries. OFCE Working Papers, Lemmens, A., Croux, C., & Dekimpe, M.G., (2008). Measuring and Tesing Granger Causaliy Over he pecrum: An Applicaion o European Producion Expecaion urveys, Inernaional Journal of Forecasing, 24, Masih, A. M. M. and R. Masih (1994). Temporal Causaliy beween Money and Prices in LDCs and he Error-Correcion Approach: New Evidence from India. Indian Economic Review, 29(1), pp Medio, A., (1992). Chaoic Dynamics - Theory and Applicaions o Economics. Cambridge: Cambridge Universiy Press. Nachane, D. M., & Nadkarni, R. M. (1985). Empirical Tess of Cerain Monearis Proposiions via Causaliy Theory. Indian Economic Journal, 33, Phelps, Edmund, (1967). Phillips Curves, Expecaions of Inflaion and Opimal Unemploymen Over Time. Economica, 34, Phillips, A.W., (1958), The Relaion beween Unemploymen and he Rae of Change of Money Wages in he Unied Kingdom, Economica 25, Pierce, D. A. (1979). R-quared measures for Time eries. Journal of he American aisical Associaion, 74, Priesley, M. B., (1981). pecral Analysis and Time eries. London: London Academic Press. 16

17 Ramachandra, V.. (1983). Direcion of Causaliy beween Moneary and Real Variables in India-An empirical Resul. Indian Economic Journal, 31, Ramachandra, V.. (1986). Direcion of Causaliy beween Moneary and Real Variables in India-An exended Resul. Indian Economic Journal, 34, harma, R. (1984). Causaliy beween Money and Price Level in India. Indian Economic Review, 19(2), pp ims, Chrisopher (1972), Money, Income, and Causaliy, American Economic Review, 62(4), ingh, B. (1989). Money upply- Price Causaliy Revisied. Economic and Poliical Weekly, 24, pp

18 Appendix Beaulieu and Miron es for inegraion a seasonal and non-seasonal frequencies 0 / 2 2 / 3 / 3 5 / 6 / 6 IIP (a.) (P-value) (0.1)* (0.01) (0.01) (0.1) * (0.07) (0.1)* (0.02) WPI (a.) (P-value) (0.1)* (0.06) (0.1)* (0.1)* (0.1)* (0.1)* (0.05) M 3 (a.) (P-value) (0.1)* (0.04) (0.1)* (0.1)* (0.1)* (0.1)* (0.1)* The parenhesis associaed P-value has been given. The (*) reflecs ha we can no rejec he null hypohesis of presence of uni roos a 5% level of significance. The es has been performed using he R sofware. (R Developmen Core Team (2008). R: A language and environmen for saisical compuing. R Foundaion for aisical Compuing, Vienna, Ausria. IBN , URL hp:// 18