Application of Granger Causality Test in Forecasting Monetray Policy Transmision Channels for Nigeria

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1 Inernaional Journal of Saisics and Applicaions 2018, 8(3): DOI: /j.saisics Applicaion of Granger Causali Tes in Forecasing Monera Polic Transmision Channels for Nigeria ElemUche O. 1,*, Omekara C. O. 2, Nsude F. I. 1 1 Mahs / Saisics Deparmen, Akanu Ibiam Federal Polechnic Unwana - Afikpo, Eboni Sae, Nigeria 2 Saisics Deparmen, Michael Okpara Universi of Agriculure Umudike, Abia Sae, Nigeria Absrac This paper focused on he causali relaionship es wih applicaion o monear polic ransmission channels for Nigeria in he framework of vecor auoregressive (VAR) model. Daa used consis of hree main monear polic ransmission channels (credis, exchange rae and ineres rae) and are arranged on monhl basis, saring from Januar 2008 o June Granger causali analsis was carried ou on he daa in order o assess he poenial predicabili of one channel(s) o he ohers. The resul shows a unidirecional causali relaionship beween exchange rae channel and ineres rae channel, and beween credi channel and ineres rae channel. This reveals ha exchange rae channel and credi channel was useful in forecasing ineres rae, bu he converse is no rue. Also, a pair-wise Granger Causali es shows non-direcional causali beween credi channel and exchange rae channel, which indicaes ha boh channels canno affec each oher. Thus, exchange rae channel canno be used o forecas credi channel, also he converse is rue. Kewords Granger Causali, Monear polic, VAR 1. Inroducion Nigeria currenl is faced wih sagnaed growh, unsable business ccles and economic flucuaion which have led o unemplomen, inflaion, unproducivi and balance of pamen disequilibrium. Governmen on heir par has in one wa or he oher inroduced policies o regulae and conrol he econom in oher o maximize he welfare of he ciizens b ensuring ha he resources available are efficienl allocaed and used. Like an oher developing counr, Nigerian governmen adops hree pes of public policies o carr ou he objecive of allocaion of resources. These public policies include: monear polic, fiscal polic and income polic ools. In Nigeria, governmen has alwas relied on monear polic as a wa of achieving cerain economic objecive in he econom such economic objecives include; emplomen, economic growh and developmen, balance of pamen equilibrium and relaivel sable general price level. Monear polic refers o he combinaion of measures designed o regulae he value, suppl and cos of mone in an econom in consonance wih he level of economic aciviies. I can be described as he ar of conrolling he * Corresponding auhor: urchsa@gmail.com (ElemUche O.) Published online a hp://journal.sapub.org/saisics Coprigh 2018 The Auhor(s). Published b Scienific & Academic Publishing This work is licensed under he Creaive Commons Aribuion Inernaional License (CC BY). hp://creaivecommons.org/licenses/b/4.0/ direcion and movemen of monear and credi faciliies in pursuance of sable price and economic growh in he econom (CBN, 1992). The goal of monear polic is o induce changes in aggregae expendiures, which resul in changes in gross domesic produc, he price level, inflaion, emplomen, unemplomen, and balance of pamen equilibrium. The roue beween monear polic and aggregae expendiures works hrough a varie of channels. The hree main monear polic ransmission channels (variables) are: credi, ineres rae and exchange rae channels. These channels generall reinforce each oher, all moving aggregae expendiures in he same direcion. Also, hese channels increase aggregae expendiures wih expansionar monear polic and decrease aggregae expendiures wih conracionar monear polic (Hung, 2011). The relaionship beween monear polic ransmission variables and he econom (GDP) has been analzed b man auhors. For insance, Oneiwu (2012), Owalabi and Adegbie (2014), Adefeso and Mobolaji (2010), Chukwu (2009), Micheal and Ebibai (2014), Okwo, e al., (2012). These works were based on regressing one variable on he oher(s) wih no recourse o causali influences/effecs. Causali is he improvemen of a ime series variable b incorporaing he informaion abou anoher variable. Thus, would one ime series variable improve he predicion of he oher variable(s) if he informaion abou he firs is incorporaed? The major issue is in he forecasing abili of he polic channels in he econom visa-vise he predicing power of one o anoher.

2 120 ElemUche O. e al.: Applicaion of Granger Causali Tes in Forecasing Monera Polic Transmision Channels for Nigeria Therefore, his aricle presens a plaform on how knowledge informaion of one ime series variable would be a precursor o predic oher(s). In oher words, he paper seeks o presens fundamenal casual connecivi of ime series variables vis-à-vis monear polic ransmission channels in an econom Granger Causali A ime series variable is called causal o anoher if he abili o predic he second variable is improved b incorporaing informaion abou he firs. The noion of causali was firs proposed in (Wiener, 1956). However, a ha ime Wiener lack pracical implemenaion of his idea and Granger (1969) came up wih he implemenaion forma in conex of ime series linear auo regressive models of sochasic processes. Granger causali is a echnique for deermining wheher one ime series is useful in forecasing anoher. Granger (1969) defined causali as follows: A variable Y is causal for anoher variable X if knowledge of he pas hisor of Y is useful for predicing he fuure sae of X over and above knowledge of he pas hisor of X iself. So if he predicion of X is improved b including Y as a predicor, hen Y is said o be Granger causal for X. Granger-causali es can be applied in hree differen pes of siuaions: 1. In a simple Granger-causali es here are wo variables and heir lags. 2. In a mulivariae Granger-causali es more han wo variables are included, because i is supposed ha more han one variable can influence he resuls. 3. Granger-causali can also be esed in a VAR framework; in his case, he mulivariae model is exended in order o es for he simulanei of all included variables. Causali beween wo variables can be unidirecional, bidirecional (or feedback) and neiher bilaeral nor unilaeral (i.e. independence means no Granger-causali in an direcion). Granger causali esing applies onl o saisicall saionar ime series. If he ime series are non-saionar, hen he ime series model should be applied o emporall differenced daa raher han he original daa. The es procedure as described b (Granger, 1969) is saed below as n Y = αy + β X + u i i j j 1 i= 1 j= 1 n n X = λy + σ X + u i i j j 2 i= 1 j= 1 n The firs equaion posulaes ha he curren Y is relaed o is pas values as well as ha of X and vice versa. Unidirecional causali from X and Y is indicaed if he esimaed coefficien on he lagged X are saisicall differen from zero as a group (i.e. β j 0 ) and he se of esimaed coefficien on he lagged Y are no saisicall differen from zero if λ i 0. The converse is also he case for unidirecional causali from Y o Feedback or bilaeral causali exis when he ses of X. and Y coefficiens are saisicall differen from zero in boh above regressions (Gujarai, 2009). 2. Mehodolog The daa used in his paper consis of hree monear polic ransmission channels, namel Ineres rae channel (IR), Exchange rae channel (ER) and Credi channel (CR). The daa are monhl and were sourced from he Cenral Bank of Nigeria Saisical bullein. The daa has 102 observaions, saring, Januar 2008 o June The daa sourced were analzed o deermine he causali beween CR and ER, CR and INT, and finall ER and INT. Before analzing he causal relaionship beween he monear ransmission channels, daa were ransformed o naural logarihms, and hen examined for possible exisence of uni roos in he daa o ensure ha he model consruced laer is saionar in erms of he variables used. If a ime series has a uni roo, hen he firs difference of he series which is saionar should be used. The saionari of each series is invesigaed b emploing Augmened Dicke-Fuller uni roo es. We furher proceed wih he VAR lag order selecion crieria o choose he bes lag lengh for he VAR ime series model o examine he Granger causali and we perform he pair wise Granger Causali es for all he series. To carr ou he analsis of he daa, we used he saisical package, E-views version 9 which is used mainl for economeric analsis Modeling/ Theoreical Approach 1. Deermine if here exiss a uni roo or saionari. 2. Obain he VAR lag order selecion 3. Perform he pair Granger causali es Saionari Waler (2004) defined Saionari as follows: A ime series is covariance (or weakl) saionar if, and onl if, is mean and variance are boh finie and independen of ime, and he auo-covariance does no grow over ime, for all and -s. Non-saionari exiss when he variance is ime dependen and goes o infini as ime approaches o infini. A ime series which is no saionar wih respec o he mean can be made saionar b differencing. Differencing is a popular and effecive mehod of removing a sochasic rend from a series. X

3 Inernaional Journal of Saisics and Applicaions 2018, 8(3): Tesing of Saionari If a ime series has a uni roo, he series is said o be non-saionar. Tess which can be used o check he saionari are: 1. Parial auocorrelaion funcion and Ljung and Box saisics. 2. Uni roo ess - a es designed o deermine wheher a ime series is sable around is level (rend saionar) or sable around he differences in is levels (difference-saionar). To check he saionari and if here is presence of uni roo in he series, he mos famous of he uni roo ess are he ones derived b Dicke and Fuller and described in Fuller (1976), also Augmened Dicke-Fuller (ADF) or Said-Dicke es has been mosl used Dicke-Fuller (DF) Tes Dicke and Fuller (DF) considered he esimaion of he parameer α from he models: 1. A simple AR (1) model is: µ + α + = 1 ε 2. µ + β + α + ε = 1 α + = 1 3. I is assumed ha 0 = 0 and ε ~ independen idenicall disribued, i.i.d (0, σ2) The hpoheses are: H0: α = 1 vs. H1: α <1 Alernaive hree versions of he Dicke-Fuller es of he parameer α from he models: 1. Pure random walk model. = 1 So, α + 2. Drif + random walk. ε = α + ε = ( α 1) + ε 1 1 = γ + ε Null hpohesis is: H0: γ = 0 = + γ 1 µ + ε Null hpohesis is: H0: μ = 0; γ = 0 3. Drif + linear ime rend. = + γ 1 µ + β + ε Null hpohesis is: H0: β = 0; γ = 0 Where, μ is a drif or consan erm, β is a ime rend, and is he firs-order difference of he series Augmened Dicke-Fuller (ADF) or Said-Dicke Tes Augmened Dicke-Fuller es is an augmened version of he Dicke-Fuller es o accommodae some forms of serial correlaion and used for a larger and more complicaed se of ε ime series models. If here is higher order correlaion hen ADF es is used bu DF is used for AR (1) process. The esing procedure for he ADF es is he same as for he Dicke-Fuller es bu we consider he AR (p) equaion: = α + γ + β + ε i i i= 1 p p = µ + γ + α + β + ε 1 i i i= 1 Each version of he es has is own criical value which depends on he size of he sample. In each case, he null hpohesis is ha here is a uni roo, γ = Vecor Auo-regression (VAR) Vecor Auo-regression (VAR) is an economeric model which has been used primaril in macroeconomics o capure he relaionship and independencies beween imporan economic variables. The do no rel heavil on economic heor excep for selecing variables o be included in he VARs. The VAR can be considered as a means of conducing causali ess, or more specificall Granger causali ess. VAR can be used o es he Causali as; Granger-Causali requires ha lagged values of variable X are relaed o subsequen values in variable Y, keeping consan he lagged values of variable Y and an oher explanaor variables. In connecion wih Granger causali, VAR model provides a naural framework o es he Granger causali beween each se of variables. VAR model esimaes and describe he relaionships and dnamics of a se of endogenous variables. For a se of n ime series variables = (, 2,..., 1 n can be wrien as: ), a VAR model of order p (VAR(p)) = A0 + A1 1 + A Ap p... + ε Where, p = he number of lags o be considered in he ssem. n = he number of variables o be considered in he ssem. Y is an (n 1) vecor conaining each of he n variables included in he VAR. A 0 is an (n 1) vecor of inercep erms. A i is an (n n) marix of coefficiens. ε is an (n 1) vecor of error erms Deerminaion of Lag-Lengh for VAR Model A criical elemen in he specificaion of VAR models is he deerminaion of he lag lengh of he VAR. Various lag lengh selecion crieria are defined b differen auhors like, Akaike (1969) final predicion error (FPE), Akaike Informaion Crierion (AIC) suggesed b Akaike (1974), Schwarz Crierion (SC) (1978) and Hannan-Quinn Informaion Crierion (HQ) (1979).

4 122 ElemUche O. e al.: Applicaion of Granger Causali Tes in Forecasing Monera Polic Transmision Channels for Nigeria 2.7. Informaion Crieria AIC= SC = HQIC = T In + 2N T In + N InT T In + 2N InT Where, = deerminan of he variance/covariance marix of he residuals. N = oal number of parameers esimaed in all equaions. T = number of usable observaions. 3. Resuls of Graphical Presenaion and Applicaion This secion consiss of graphical presenaion of daa and applicaions of uni roo es, VAR lag order selecion crieria and pair-wise Granger Causali. The research sars b showing he graphs of he raw daa, which comprises he series CR, ER and INT in order o know how he behave in heir naural sae. The (Fig. 1, Fig. 2 and Fig. 3) are shown below CREDIT (M'N) EXCHANGE RATE Figure 1. (Graph of CR) Figure 2. (Graph of EX) INTEREST RATE (%) Figure 3. (Graph of INT) From he above hree figures, he impression is ha he series are no saionar. Our nex sep is o make he series linear. We ake he logarihms of he original series: CR, EX, and INT and produce heir graphs. To conclude ha he series are saionar or no, we also produce he correlograms of he hree logarihmic series: LNCR, LNEX, and LNINT (Fig. 4, Fig. 5 and Fig. 6).

5 Inernaional Journal of Saisics and Applicaions 2018, 8(3): LNCR Figure 4. (Graph and Correlogram of LNCR) LNEX Figure 5. (Graph and Correlogram of LNEX)

6 124 ElemUche O. e al.: Applicaion of Granger Causali Tes in Forecasing Monera Polic Transmision Channels for Nigeria LNINT Figure 6. (Graph and Correlogram of LNINT) From he above graphs, we conclude ha all he hree series are no saionar also he above correlograms do no show saionari. I is clear from correlograms ha he non-decaing behavior of he sample Auocorrelaion Funcion (ACF) is due o lack of saionari because ACFs are suffered from linear decline bu he Parial Auocorrelaion Funcion (PACFs) decaing ver quickl and here is onl one significan spike of PACFs. To make he above conclusion more confirm, we perform a uni roo es (Augmened Dicke-Fuller) o observe wheher he series are saionar or no. Table 1. (Augmened Dicke-Fuller ADF Tes on LNCR, LNEX, LNINT) Null hpoheses: LNCR, LNEX, LNINT has a uni roo LNCR ADF es saisic Tes criical values: -saisic Prob* (0.9737) Lag Lengh: 0 (Auomaic - LNEX ADF es saisic Tes criical values: -saisic Prob* (0.5466) Lag Lengh: 1 (Auomaic - LNINT ADF es saisic Tes criical values: -saisic Prob* (0.9929) Lag Lengh: 2 (Auomaic - *MacKinnon (1996) one-sided p-values. Above able is he summar of resuls of Augmened Dicke-Fuller es. According o (Table.1), we conclude ha here is presence of uni roo according o he P-values of all he hree series as he P-values are insignifican. Since he values of compued ADF es-saisic of he hree series are greaer han he criical values a 1%, 5% and s of

7 Inernaional Journal of Saisics and Applicaions 2018, 8(3): significance, respecivel wih differen lag lenghs (based on Schwarz Informaion Crierion). So, he null hpoheses canno be rejeced ha means all he hree series have a uni roo. Hence, from he uni roo es, we conclude ha he hree series are no saionar, so we make hese hree non-saionar series, saionar b aking firs difference as: DLNCR, DLNEX and DLNINT. Below graphs and correlograms clearl shows he firs difference of he series DLNCR Figure 7. (Graph and correlogram of DLNCR).4.3 DLNEX Figure 8. (Graph and correlogram of DLNEX)

8 126 ElemUche O. e al.: Applicaion of Granger Causali Tes in Forecasing Monera Polic Transmision Channels for Nigeria DLNINT Figure 9. (Graph and Correlogram of DLNINT) A firs difference of all he hree series looks saionar and correlograms also verifies he same as we see ha ACFs end o zero raher quickl. We appl uni roo es wih Augmened Dicke-Fuller afer aking he firs difference o check wheher he series are now saionar or no. Table 2. (Augmened Dicke-Fuller ADF Tes on DLNCR, DLNEX, DLNINT) Null hpoheses: DLNCR, DLNEX, DLNINT has a uni roo DLNCR ADF es saisic Tes criical values: -saisic Prob* (0.0000) Lag Lengh: 1 (Auomaic - DLNEX ADF es saisic Tes criical values: -saisic Prob* (0.0000) Lag Lengh: 0 (Auomaic - DLNINT ADF es saisic Tes criical values: -saisic Prob* (0.0000) Lag Lengh: 1 (Auomaic - *MacKinnon (1996) one-sided p-values. According o he summar resuls of Augmened Dicke-Fuller es above (Table. 2), we conclude ha here is absence of uni roo according o he P-values of all he hree series as he P-values are significan. The values of compued ADF es-saisic of he hree series are smaller han he criical values a 1%, 5%, and s of significance, respecivel wih differen lag lenghs (based on Schwarz Informaion Crierion). Therefore, we rejec he null hpoheses ha all he hree series do no have a uni roo. We conclude ha all he hree series are saionar according

9 Inernaional Journal of Saisics and Applicaions 2018, 8(3): o he resuls of Augmened Dicke-Fuller (Table. 2). Since he hree series are saionar, we precede wih he lag order selecion crieria for esing he Granger Causali. Lag lengh selecion crieria was deermined using he VAR model. We selec he bes lag lengh for he VAR ime series model on which Granger causali is based (Table. 3). Table 3. VAR lag order selecion Crieria Endogenous variables: DLNCR DLNEX DLNINT Exogenous variables: C Included observaions: 96 Lag LogL LR FPE AIC SC HQ NA 4.12e-08* * * * e e e e * 5.34e * indicaes lag order seleced b he crierion According o he resuls of VAR lag order selecion crieria (Table. 3), we decide o use lag lengh 5 for he Granger Causali es. This is due o he fac ha FPE, Akaike, Schwarz and Hannan-Quinn choose 0 lags bu LR chooses 5 lags. We use he LR es [sequenial modified LR es saisic (each es a )] as a primar deerminan of how man lags o be include. Wih coninuaion of analsis, we proceed o perform he pair-wise Granger Causali es for all he series DLNCR, DLNEX and DLNINT (Table. 4) b using he above seleced lag lengh 5. Table 4. Pair-wise Granger Causali Tess Null Hpohesis: Obs F-Saisic Prob. Decision DLNEX does no Granger Cause DLNCR Accep DLNCR does no Granger Cause DLNEX Accep DLNINT does no Granger Cause DLNCR Accep DLNCR does no Granger Cause DLNINT Rejec DLNINT does no Granger Cause DLNEX Accep DLNEX does no Granger Cause DLNINT Rejec Pair-wise comparison of series, DLNCR VS DLNEX According o he resuls of (Table 4), he P-value (0.9888) is no significan so, we accep he null hpohesis and we conclude ha DLNEX does no Granger Cause DLNCR. The P-value (0.4819) is also no significan so, we accep he null hpohesis and we conclude ha DLNCR does no Granger cause DLNEX. So, DLNEX does no affec DLNCR and he converse is also rue, i means ha here is no Granger Causali beween he series, running from DLNEX o DLNCR and he oher wa. Hence, he Granger Causali is non-direcional beween he series. Pair-wise comparison of he series, DLNCR VS DLNINT According o (Table 4), he P-value (0.7474) is no significan so, we accep he null hpohesis and we conclude ha DLNINT does no Granger cause DLNCR. Bu he converse is no rue as P-value (0.0094) is significan. So, we rejec he null hpohesis and we conclude ha DLNCR Granger Cause DLNINT. So, DLNCR affecs DLNINT bu he converse is no rue, i means he Granger Causali is unidirecional beween he series, DLNCR and DLNINT, running from DLNCR o DLNINT and no he oher wa. Pair-wise comparison of series, DLNEX VS DLNINT According o (Table 4), he P-value (0.7374) is insignifican so, we canno rejec he null hpohesis and we conclude ha DLNINT does no Granger Cause DLNEX. The P-value (0.0476) is significan so, we rejec he null hpohesis and we conclude ha DLNEX Granger Cause DLNINT. So, DLNEX affecs DLNINT, bu he converse is no rue, i means he Granger Causali is unidirecional beween he series. 4. Summar and Conclusions The main objecive of his paper is o analze he causali relaionship wih applicaion o credi channel CR, exchange raes channel EX and ineres rae channel IR of monear

10 128 ElemUche O. e al.: Applicaion of Granger Causali Tes in Forecasing Monera Polic Transmision Channels for Nigeria polic ransmission channels. We perform uni roo es, VAR lag order selecion crieria and pair-wise Granger Causali es o esablish he causali which exiss beween he hree monear polic ransmission channels of our sud. According o he resuls of his research wih original daa, we found ha he hree series have a uni roo which means all he series do no show saionari. Afer aking firs difference of he series, he resuls of uni roo es show saionari a he levels of significance: 1%, 5% and 10% wih differen lag lenghs. According o he resuls of pair-wise Granger Causali ess, we observed non-direcional causali relaionship beween CR and EX, which means ha he pas hisor of boh series canno predic heir fuure values. Thus, we conclude ha EX canno be used o forecas CR, also he converse is rue. Also, we observed unidirecional causali running from CR o INT which means ha he pas hisor of CR is useful o forecas he fuure values of INT, bu he converse is no rue. Finall, we observed anoher unidirecional causali running from EX o INT which shows ha EX is useful o forecas INT, bu he converse is no rue. Furhermore, according o he resuls of Granger-Causali of our research, we observe ha he casual relaionship which exiss beween CR, EX and INT adjus o reflec changes in he monear polic ransmission channels of Nigeria. The leading role of he Credi channel and Exchange rae channel affecing Ineres rae channel is clearl visible in he causali relaionship ess. REFERENCES [1] Adefeso, H. & Mobolaji, H. (2010). The fiscal monear polic and economic growh in Nigeria: Furher Empirical Evidence. Pakisan Journal of Social Sciences, 7 (2), [2] Akaike, H. (1969). Fiing auoregressive models for predicion. Annals of he Insiue of Saisical Mahemaics, (21), [3] Akaike, H. (1974). A new look a he saisical model idenificaion. IEEE Transacions on Auomaic Conrol, (19), [4] CBN (2008). Cenral Bank of Nigeria (CBN), Monear Polic Deparmen Series 1, 2008.CBN/MPD/Series/01/ [5] CBN (2016). Saisical Bullein; [6] Enders W. (2004). Applied Economeric Time Series. 2nd Ediion, New York: Wile. [7] Granger, C. W. J. (1969). Invesigaing Causal Relaionship b Economeric Model and Cross-specral Mehods. Economerica, (37), [8] Granger, C. W. J. (1981). Some properies of ime series daa and heir use in economeric model specificaion. Journal of Economerics, (16), [9] Gujarai, D. N. & Porer, D.C. (2009). Basic economerics. Fifh ediion, New York, McGraw-Hill/Irwin. [10] Hannan, E. J. & B. G. Quinn (1979). The deerminaion of he order of an auo-regression. Journal of he Roal Saisical Socie, Series B 41, [11] Hung, L. V. (2011), AVecor Auoregression Analsis of Monear Transmission Mechanism in Vienam, Naional Graduae Insiue of Polic Sudies (GRIPS). [12] Michael, B. & Ebibai, T. S. (2014). Monear polic and economic growh in Nigeria ( ). Asia Economic and Financial Review, 4(1) [13] Okwo, I. M. Eze, F. & Nwoha, C. (2012). Evaluaion of monear polic oucomes and is effec on price sabili in Nigeria. Research Journal Finance and Accouning, 3 (11), [14] Oneiwu, C. (2012). Monear polic and economic growh of Nigeria. Journal of Economic and Susainable Developmen. 3(7) [15] Owalabi, A. U. & Adegbie, T. A. (2014). Impac of monear polic on indusrial growh in Nigeria. Inernaional Journal of Academic Research in Business and Social Sciences, 4 (1), [16] Schwarz, G. (1978). Esimaing he dimension of a model. The Annals of Saisics, (5), [17] Wiener, N. (1956). The heor of predicion. In: Beckenbach, E. (Ed.), Modern Mahemaics for Engineers. New York, McGraw-Hill.