Inflation, exchange rates and interest rates in Ghana: An autoregressive distributed lag model

Transcription

1 Inernaional Journal of Scienific and Research Publicaions, Volume 5, Issue 1, January ISSN Inflaion, exchange raes and ineres raes in Ghana: An auoregressive disribued lag model Dennis Nchor*, Samuel A. Darkwah**, LubošSřelec** * Deparmen of Saisics and Operaions Analysis, Mendel Universiy ** Deparmen of Terriorial Sudies, Mendel Universiy ABSTRACT This paper analyses he implicaion of exchange rae depreciaion and nominal ineres raes on inflaion in Ghana. I makes use of an auoregressive disribued lag model and an unresriced error correcion model. The resuls from he sudy show ha in he shor run a percenage poin increase in he level of depreciaion of he Ghana cedi leads o an increase in he rae of inflaion by.2%. A percenage poin increase in he level of nominal ineres raes however resuls in a decrease in inflaion by.98%. Inflaion increases by 1.67% for every percenage poin increase in he nominal ineres rae in he long run. The sudy could no prove a significan long run relaionship beween exchange rae depreciaion and inflaion. Key words: inflaion, exchange rae depreciaion, nominal ineres raes, auoregressive disribued lag model, error correcion model. 1. INTRODUCTION hana formally adoped inflaion argeing in 27 making i one of he firs group of emerging marke economies and as a Ghe ime one of he firs low income counries o do so. A 5 percen inflaion rae was se as he medium arge by he Bank of Ghana. This objecive was however affeced by negaive shocks which made i difficul o achieve he arge. Problems of his naure are common in he inflaion reducion phase of inflaion argeing counries and do no necessarily imply policy failure. I however means ha here is he need for flexibiliy in he implemenaion of inflaion argeing. Challenges in he implemenaion of inflaion argeing policies are expeced in he economy since i is vulnerable o shocks and has a hisory of high and variable inflaion. Inflaion raes dropped significanly o as low as 1.7% in 21, 8.7% in 211 and 9.2% in 212. I has however reurned o double digis, 13.5% as a he end of 213. In several insances, moneary policy auhoriies have reaced vigorously o shor-run deviaions from arges, in an aemp o mainain credibiliy. This had a desabilizing impac on he economy. Aemping o hi inflaion arges for every year is no desirable and migh no be feasible. The challenge should raher be o mainain he credibiliy of he ulimae arge, in he face of variaions in he pah of inflaion. This can be done by no jus focusing on annual inflaion arges bu also being mindful of shor-run rade-offs agains oupu and employmen. Ekholm K. (21). The sudy hus seeks o esimae he relaionship beween inflaion, exchange rae deprecaion and he level of nominal ineres raes in Ghana. Inflaion is one macroeconomic variable ha remains elusive o he policy makers in he counry. Though he much desired single digi level was aained in 21, 211 and 212, i could no be susained and has as expeced reurned o double digis and currenly sands a abou 13.5% a he end of he 213 fiscal year. This rend is prediced o prevail for a while as policy makers sruggle o discover he mix of policies ha will conrol boh inflaion and is causal facors. Lieraure on he relaionship beween inflaion and he level of exchange rae is sub divided ino wo groups. The firs group considers he responsiveness of he prices of radable goods o changes in he exchange rae. In oher words, i considers he validiy of he Purchasing Power Pariy. Dunn (197) and Magee (1973, 1974) suppored his asserion in heir sudy. More recen conribuions have aemped o use modern echniques and differen aspecs o esablish PPP condiions, paricularly since he work by Granger (1981), and Engle and Granger (1987) on co-inegraion relaionships. MacDonald (1995) in his sudy, suppored he idea of a long run Purchasing Power Pariy. The PPP heory was however no suppored by Krugman (1978) and Frenkel (1981). Sudies based on he macroeconomics of he Ghanaian economy have employed co-inegraion based models e.g. Bawumia and Abradu-Ooo, (23). Bawumia e al (23) examined he relaionship beween moneary growh, exchange rae and inflaion in Ghana from 1983 o An error correcion model (ECM) was applied in heir analysis and heir sudy showed he exisence of a long run equilibrium relaionship beween inflaion, money supply, he exchange rae, and real income. This sudy adops a similar approach however due o he fac ha he variables are inegraed of differen orders, an auoregressive disribued lag model (ARDL) is applied for he analysis.

2 Inernaional Journal of Scienific and Research Publicaions, Volume 5, Issue 1, January ISSN MATERIALS AND METHODS Time series daa from 1991o 213 was used and he daa was obained from he World Bank counry indicaors. The main variables for he sudy include: inflaion ( INFL ), exchange rae depreciaion ( EXR ) and he nominal ineres raes ( INTR ). The average yearly inflaion is used as a proxy for inflaion in he sudy. Exchange rae depreciaion was measured as he changes in he value of he Ghana cedi per he Unied Saes dollar. Nominal ineres rae was measured as he cenral bank s moneary policy rae. In oher words, he rae a which he cenral bank lends o commercial banks. The auoregressive disribued lag model approach is chosen due o he fac ha he variables had a mixure of I() and I(1) properies. This mehod also makes i possible o assign differen variables wih differen lag-lenghs as hey ener he model. The generaion of he models and all diagnosic ess were done in GRETL sofware. The leas squares regression mehod was used o esimae he model due o he fac ha i minimizes he sum of squares of he predicion errors. The variables were firs esed for non-saionariy properies using he Augmened Dickey Fuller mehod. Firs order differences were applied when necessary o remove non-saionariy properies. The basic auoregressive disribued lag model is given in Eq. 1. Equaion 1 INFL β β INFL... β INFL γ EXR γ EXR... γ EXR δ INTR δ INTR... δ INTR 1 1 f p 1 1 j q 1 1 k m Where ε is a random disurbance erm which is serially independen. The ARDL model for he variables will be esimaed as in Eq. 2. Equaion 2 i EXR INTR INFL EXR INTR 1 j j k k Where is an inercep, i, j, k are shor run coefficiens,, 1 and 2 are long run coefficiens and represens firs order difference. Eq. 2 can furher be expressed as in Eq. 3: Equaion 3 p q m i i jexr j kintr k INFL 1 1EXR 1 2INTR 1 From i1 j1 k1 : 1 2 esimaing he model in Eq. 3, an F es on he null hypohesis H is performed o deermine if he variables INFL 1 EXR, 1 INTR and 1 which have long run coefficiens are saisically significan. If he independen variables are saisically significan and co-inegraed hen an unresriced error correcion model (ECM) is used o esimae he given long run relaionships among hem. This is given in Eq. 4. Equaion 4 z 1 1 EXR INTR z ishe error-correcion erm and i is he OLS (Ordinary Leas Squares) residual from esimaing he model wih he level variables. The shor-run effecs can herefore o be exraced from he unresriced ECM as in Eq. 4. Eq. 3 shows ha, in he long-run equilibrium nominal ineres rae elasiciy of inflaion are given by, EXR INTR 1 and 2 exchange rae depreciaion and nominal ineres rae on inflaion in he long run.. Therefore exchange rae depreciaion and respecively. These represen he impac of boh 2.1 General rend in inflaion Generally, inflaion in Ghana has been declining since is hisoric high levels in he las wo decades. I reached as high as 122% in 1983 and 59% in Currenly he rae sands a abou 13.5%. Single digi levels were recorded in he years 21, 211 and 212. The rae has however reurned o double digis and also assuming an upward rend since 213. Fig. 1 illusraes he general rend in inflaion in Ghana.

3 Rae of inflaion (%) Inernaional Journal of Scienific and Research Publicaions, Volume 5, Issue 1, January ISSN Figure 1. Trend in inflaion Inflaion 1.. Source: Bank of Ghana 2.2 Inflaion, exchange rae depreciaion and ineres raes The level of ineres raes in an economy plays a significan role in influencing he level of inflaion. Rising nominal ineres raes lead o rising inflaion raes and vice versa all hings being equal. The relaionship is however opposie in he case of real ineres raes. Rising real ineres raes lead o declining inflaion raes ceeris paribus. The relaionship is explained in he simple Fisher equaion where, r = R π R=Nominal ineres raes, r = real ineres raes and π = expeced inflaion The nominal exchange rae is basically an asse price ha affecs he real exchange rae in he shor run. Exchange raes ha are deermined freely by he marke are volaile and ha is no differen in he case of Ghana. The major rading parners of Ghana such as UK, USA and oher European counries have moneary policies ha differ from Ghana hence he inflaion differenial is very high. Thus, flucuaions in real exchange rae in he shor run are caused by boh he inflaion differenial and he nominal exchange rae. Depreciaion of he real exchange rae has a huge impac on he rae of inflaion. Declining rae of depreciaion is accompanied by declining rae of inflaion and vice versa ceeris paribus. An increase in he rae of depreciaion means higher cos of impors (impored inflaion) which is generally ransmied ino domesic prices. Fig. 2 shows he relaionship among he hree modeled variables: inflaion, exchange rae depreciaion and ineres raes.

4 Rae of change (%) Inernaional Journal of Scienific and Research Publicaions, Volume 5, Issue 1, January ISSN Inflaion Exchange rae depreciaion Ineres raes. Figure 2. Inflaion, ineres raes and exchange rae depreciaion Source: Bank of Ghana 3. RESULTS 2.1 Uni roo es for level variables Since he sudy employed ime series daa which are ofen non saionary and lead o spurious regression esimaes, (see e.g Granger and Newbold (1974)), he Augmened Dickey Fuller (ADF) mehod was employed o es he daa for uni roos. Based on he es resuls an appropriae economeric echnique is used in esimaing he model. The resuls (see Appendices, Tab. A.1) show ha, inflaion and nominal ineres raes were non-saionary a level bu saionary afer firs difference i.e. I(1). Exchange rae depreciaion was however saionary a level i.e. I(), (see Appendices, Tab. A.1). Giving he fac ha he variables were inegraed of differen orders, he sudy employed he auoregressive disribued lag model which was appropriae in his case. An error correcion model was hen used o esimae he shor run relaionship beween he variables when i was esablished ha he variables were co-inegraed. 2.2 Consrucing he auoregressive disribued lag model (ARDL) Since he uni roo es shows differen orders of inegraion for all hree variables. I became necessary o employ he ARDL model. The sudy firs esimaed an Ordinary Leas Squares (OLS) model using he level variables. The residual erm from his model was saved and used in he esimaion of he long run relaionship among he variables in he error correcion model. Tab. 1 shows he level model resuls. Inflaion ( INFL ) was he dependen variable while exchange rae depreciaion ( EXR ) and he nominal ineres raes ( INTR ) served as he independen variables. Table 1. OLS Level model: dependen variable - INFL Coefficien Sd. Error -raio P-value Consan EXR INTR *** R 2 =.55 n= 23 F(2,2)= 9.92, P(F) =.1 The aseriks * indicae he significance a 1% level, ** a 5% level and *** a 1% level. The sudy hen proceeds o esimae he ARDL model. Tab. 2 shows he resuls of he esimaed model. The firs order differenced inflaion was regressed on he firs order differenced independen variables including a maximum of wo lags. Two lags of he firs order differenced dependen variable are included in he sysem. The lagged level exchange rae depreciaion is no saisically

5 Inernaional Journal of Scienific and Research Publicaions, Volume 5, Issue 1, January ISSN significan hence i was removed from he model. The resuls in Tab. 2 represen he resriced model wihou all insignifican variables. The sudy hen proceeded o es for he sabiliy of parameers in his ARDL model using he CUSUM es (see Appendices, Tab. A.2). The resuls show ha he model parameers were sable and he model fulfills all diagnosic es requiremens (see Appendices, Tab. A.2). Table 2. ARDL. Dependen variable - INFL Variable Coefficien Sd. Error -raio P-value Consan *** INFL *** 1 INTR ** 1 1 EXR *** 1 INTR *** ** ** R 2 =.61, F(6,13)=33.3 and P-value(F) =3.67e-7, n=2 The subscrip -q where q=1,2,3 shows he various lagged erms of he variables and he symbol, Δ before he variables denoes firs order difference. The aseriks * indicae he significance a 1% level, ** a 5% level and *** a 1% level. The esimaed ARDL equaion is given in Eq. 5. Equaion EXR 1.83INTR INFL 1. 81INTR 1 To esablish wheher he model variables had a long run relaionship or no, he sudy esed for he saisical significance of he coefficiens of INFL 1 and INTR 1. Using he Wald es, he resuls (see Appendices, Tab. A.2) show ha inflaion and ineres rae had a long run relaionship Consrucing he error correcion model (ECM) The long run relaionships can herefore be esimaed using an unresriced error correcion model if he variables are co-inegraed using he ADF es on he lagged residual erm from he level model, z. If he coefficien of z 1 is negaive and significan in he ECM hen i validaes he long run relaionship. In boh cases of esing he uni roos in z (see Appendices, Tab. A.3),he p-values were less han 5% indicaing ha he variables were co-inegraed. An unresriced error correcion model could herefore be used o esimae heir shor run relaionships. I is given by he expression: 1 Where is he speed of adjusmen parameer and EXR INTR z z is he residual erm from he esimaed level model. The Error Correcion model resuls are displayed in Tab. 3. The firs order differenced inflaion is regressed on he lagged erms of he firs order differenced inflaion, nominal ineres raes and exchange rae depreciaion. The model also includes he lagged erm of he residual erm z from he level model. Tab. 3 shows he resuls of he resriced ECM wihou all insignifican variables.

6 Inernaional Journal of Scienific and Research Publicaions, Volume 5, Issue 1, January ISSN Table 3. ECM model: dependen variable- INFL Coefficien Sd. Error -raio P-value Consan EXR *** 1 INTR *** ** ** z ** 1 R 2 =.57, F(5, 14) = 1.53 and P(F) =.2, n=2. The aserisk * indicae he significance a 1% level, ** a 5% level and *** a 1% level Saisical significance of he shor-run coefficiens Afer esimaing he error correcion model, i is necessary o es wheher exchange rae depreciaion and nominal ineres raes affec inflaion in he shor run. This was done by resricing he coefficiens of he shor run variables, EXR 1and INTR 1o zero. The p-value obained (see Appendices, Tab. A.4) from he es was less han he 5% significance level used indicaing ha he shor run coefficiens were saisically significan. z was significan and negaive hus validaing he long run relaionship beween inflaion and he nominal The coefficien of 1 ineres rae. The negaive sign of he z 1 indicaes ha previous year s deviaion from equilibrium is resored by 133% in he curren year. This indicaes an overshooing adjusmen. Model parameers of he ECM were also sable (see Appendices, Tab. A.4). The long run relaionship beween he nominal ineres raes and inflaion is hen calculaed using he coefficiens from he ARDL model. The resuls are displayed in Tab. 4. Table 4. Long run impacs Variable Long run coefficien Symbols Formula Long run impac (elasiciy) INTR.81 θ 2 θ 1.67 θ 2 INFL 1.35 θ θ, θ 2 are he esimaed coefficiens from ARDL Inerpreaion In he shor run, a percenage poin increase in he rae of depreciaion of he Ghana cedi leads o an increase in inflaion by.2% ceeris paribus. Inflaion rae however decreases by.98% for every percenage poin increase in he level of nominal ineres raes. In he long run, exchange rae depreciaion has no impac on inflaion. The nominal ineres rae elasiciy in he long run is 1.67% (nominal ineres rae elasiciy). Implying ha a percenage poin increase in he nominal ineres rae will lead o inflaion of abou 1.67% in he long run. 4. DISCUSSION Exchange rae and nominal ineres rae play vial roles in deermining he level of inflaion in Ghana. The resuls from he sudy show ha inflaion is affeced by boh facors in he shor run and in he long run. The shor run relaionships were esimaed using an unresriced error correcion model. The resuls show ha a depreciaion in he Ghana cedi by a percenage poin leads o an increase in he rae of inflaion by.2%. I however decreases by.98% for every percenage poin increase in he nominal ineres rae. The resuls from his sudy confirm he sudy by Bawumia e al (23) which also proved a long run relaionship beween inflaion and ineres rae using co-inegraion and error correcion analysis. Their sudy also concluded ha he level of exchange rae depreciaion affecs inflaion posiively. The impac is however ransmied wih a one-monh delay. This sudy however found a posiive relaionship beween nominal ineres raes and inflaion in he long run which explains he overwhelming negaive effec on he economy of raising ineres raes for longer periods. As menioned earlier, sable single digi inflaion has no been possible due o he fac ha he economy is vulnerable o shocks. Wih exchange rae volailiy and an inflaion argeing mechanism, he Bank of Ghana is emped o focus is effors unduly on he exchange rae flucuaions. This case implies ha he Bank of Ghana will be reacing o almos every or several of he flucuaions in

7 Inernaional Journal of Scienific and Research Publicaions, Volume 5, Issue 1, January ISSN he exchange rae. Moneary policy will herefore also be volaile. This is obviously undesirable as i means ha he cenral bank iself becomes a source of unnecessary disrupions in he economy. Volaile exchange rae such as seen in Ghana for he pas few years will be problemaic if he Bank of Ghana allows he exchange rae o ake a very prominen posiion in is analysis. Higher ineres raes need o only be emporary. Once he exchange rae is sabilized, ineres rae should be allowed o decline given he cos of persisenly high ineres raes. Temporary igh policies may signal he deerminaion of he moneary auhoriy o pursue exchange rae sabiliy and low inflaion. Even when he igh policies are wihdrawn, he exchange rae would sabilize a a higher level. Drazen and Masson (1994). When here are imporan srucural issues aside he repuaion of he moneary auhoriies, raising ineres raes may no necessarily solve exchange rae crises. Even if ineres raes as a moneary policy ool can sabilize exchange raes, he coss of raising ineres raes may be oo high. 5. SUMMARY The sudy employed an auoregressive disribued lag model and an unresriced error correcion model o esimae he long run and shor run relaionships among inflaion, exchange rae depreciaion and he nominal ineres raes. The error correcion model was applied due o he fac ha he variables were co-inegraed. The long run relaionships were esimaed using he coefficiens from he auoregressive disribued lag model. The ARDL model was also applied because variables were found o be inegraed of differen orders. The resuls from he sudy show significan effecs of ineres rae and exchange rae on inflaion in boh he shor run and he long run. However in carrying ou moneary policy which aims a price sabiliy, here is he need o reconcile he radiional ineres raeexchange rae rade-off, Goldfajn and Gupa (1998). This should be done being mindful of he inflaion-oupu rade-off and he inflaion-unemploymen rade-off. The cos incurred in raising ineres raes o sabilize he currency could be overwhelming if he banking secor is fragile such as he case in Ghana. This policy is only appropriae if he corporae secor is heavily exposed o foreign deb. The Bank of Ghana needs o ouline a credible view of he ransmission mechanism, from policy insrumens o objecives. This can be done using a model which will inform he decision making process so as o provide clear and consisen explanaions for policy acions. Inflaion expecaion should be incorporaed in his model of disinflaion. The Bank of Ghana builds is credibiliy as i makes progress in he bid o achieve low inflaion. I is however worh admiing ha modeling inflaion in he Ghanaian economy will be challenging given he fac ha, he economy is highly vulnerable o shocks and inflaion expecaions are unsable. Appendices Table A.1 Variable Tes Saisic 1% criical 5% criical 1% criical MacKinnon approx. p- value for Z() INFL Z() INFL Z() INTR Z() INTR Z() EXR Z() Decision Uni roos No uni roos Uni roos No uni roos No uni roos The absolue value of he Z() is compared wih he absolue criical values a 5% level of significance. Z() > 5% criical value indicaes a rejecion of he null hypohesis of uni roos. Table A.2. Diagnosic es Tes P values (5%) Lineariy es Lagrange muliplier es.15 Model specificaion RESET es.66 Heeroskedasiciy Whie es.19 Normaliy of residuals Chi-square.7 Auocorrelaion Breusch-Godfrey es.76 Parameer sabiliy es (CUSUM es) Harvey-Collier.39 Tes for long run relaionship ( INFL 1 and INTR 1.) Wald es.

8 Inernaional Journal of Scienific and Research Publicaions, Volume 5, Issue 1, January ISSN Table A.3 Wih consan Wih consan and rend Tes saisic: au_c(1) Asympoic p-value..3 Sample size (n) P-values less han 5% indicae a rejecion of he null hypohesis of non-saionariy. Table A.4 Diagnosic es Tes saisic P-values (5%) Lineariy es Lagrange muliplier es.1 Model specificaion RESET es.6 Heeroskedasiciy Whie es.24 Normaliy of residuals Chi-square.11 Auocorrelaion Breusch-Godfrey es.92 Parameer sabiliy es (CUSUM es) Harvey-Collier.46 Tes for shor run relaionships ( EXR 1and INTR 1 ) Wald es. References 1. M. Bawumia., P. Abradu-Ooo, Moneary growh, exchange raes and inflaion in Ghana: an Error Correcion Analysis. Working paper W/P BOG 23/5, Bank of Ghana. 2. A. Drazen., P. Masson, Credibiliy of policies versus credibiliy of policymakers. Quarerly Journal of Economics, 1994, pp R. M., Dunn Jr, Flexible exchange raes and oligopoly pricing: A Sudy of Canadian Markes. Journal of Poliical Economy. 197, 78, pp K. Ekholm, Moneary policy and he exchange rae, speech a HQ Bank, Sockholm 12 January R. F. Engle., C. W. J Granger, Co-inegraion and error-correcion: represenaion, esimaion and esing. Economerica, , pp J. Frankel, The collapse of purchasing power pariy during he 197 s. European Economic Review 16, 1981, pp D. Ghura., T. J. Greenes, The real exchange rae and macroeconomic performance in Sub-saharan Africa. Journal of Developmen Economics, 1993, 42, pp I. Goldfajn, R. O. Valdés. The afermah of appreciaions. Quarerly Journal of Economics. 1998, Vol. 114 (February), pp. pp C. W. J. Granger, Some properies of ime series daa and heir use in economeric model specificaion. Journal of Economerics, 1981, 1, pp P. Krugman, Purchasing power pariy and exchange raes. Journal of Inernaional Economics 1978, 8, pp R. Macdonald. Long-run exchange rae modelling: a survey of he recen evidence. 1995, Saff Papers 42, No.3. Inernaional Moneary Fund, Washingon DC 12. S. P. Magee, U. S. Impor prices in he currency conrac period. Brookings Papers on Economic Aciviy, 1,1974, pp AUTHORS Firs Auhor Dennis Nchor, MSc, Mendel Universiy and dennis_nchor@yahoo.com. Second Auhor Samuel A. Darkwah, Ph.D, Mendel Universiy and darkwah@mendelu.cz Third Auhor Luboš SřelecPh.D, Mendel Universiy and darlingmikki@yahoo.com. Correspondence Auhor Dennis Nchor, dennis_nchor@yahoo.com, xnchor1@node.mendelu.cz,