Is the Phillips curve useful for monetary policy in Nigeria? Carlos J. García ILADES- Georgetown University, Santiago Chile

Transcription

1 Is he Phillips curve useful for moneary policy in Nigeria? Carlos J. García ILADES- Georgeown Universiy, Saniago Chile 1

2 Is he Phillips curve useful for moneary policy in Nigeria? Carlos J. García Absrac The objecive of his aricle is o deermine if he Phillips curve is a relevan ool o conduc moneary policy in African counries wishing o adop an inflaion-argeing regime. I choose Nigeria as a case of sudy because i is in he early sage of he implemenaion of his regime. I esimae a medium-sized model for moneary policy analysis. The model reflecs a synhesis beween he New Keynesian and he Real Business Cycle (RBC) approaches. Then I esimae he model by using Bayesian economeric echnique in order o overcome he shorage of daa availabiliy. The sudy concludes ha here is evidence ha cenral banks can conrol he inflaion rae hrough a Phillips curve, a Taylor rule ha includes he exchange rae, and he serilizaion of he resources from oil expors. Neverheless, here are limis o he sabilizaion program. The same evidence suggess ha i is imporan o implemen a credible inflaionargeing regime o reduce inflaion gradually, insead of abrup sabilizaion aemps wih high coss in los oupu. JEL codes: E31, E52, E58, O23 Keywords: Moneary policy, Phillips curve, inflaion-arge regime. 2

3 1. Inroducion The main objecive of his aricle is o deermine wheher he Phillips curve is a relevan empirical ool for moneary policy conduc in Nigeria. The Phillips curve is in he hear of he new macro models ha have helped developed economies and some emerging ones o adop he inflaion-argeing regime. Are African counries prepared o adop his regime? Is here a Phillips curve in hese economies o implemen his regime as in oher regions? How could he cenral bank manage he reserves from naural resource expors o implemen an inflaion-argeing regime? In his aricle I explore he relevance of he Phillips curve in Nigeria, one of he bigges economies in he African coninen, an imporan oil exporer, and in he early sages of he implemenaion of an inflaion-argeing regime. If he Phillips curve is a relevan ool for guiding moneary policy, hen he cenral bank of Nigeria could conrol he nominal ineres rae and hus affec he oupu gap, he inflaion rae, and he exchange rae. All hese variables in urn affec moneary policy and so on hrough a kind of Taylor rule. Evenually his mechanism would resul in a decreasing inflaion rae oward a arge, which he cenral bank has defined below 10%. To measure he imporance of he Phillips curve, I buil a model which is sufficienly general o incorporae he basic srucures observed in his economy, including a wide range of shocks ha affec i. I propose an approach ha has been used in many counries (including Canada, he U.K., Japan and New Zealand) and inernaional organizaions (such as he IMF) for ha purpose. This combines he New Keynesian approach 1, wih an emphasis on nominal and real rigidiies and a role of aggregae demand in oupu deerminaion, wih he real business cycle radiion mehods of dynamic sochasic general equilibrium (DSGE), wih an emphasis on modeling wih raional expecaions 2 (Erceg e al.,2000; Chrisiano e al., 2005; Smes and Wouers, 2003, 2007; Galí 2008). 1 Ball and Romer (1990), Mankiw and Romer (1991), and Clarida e al. (1999). 2 See also Lucas (1976), Kydland and Presco (1977), Sims (1980), Sargen (1981), and Presco (1986). 3

4 The model is semi srucural since i includes equaions ha have a direc inerpreaion from he economic heory such as a modern Phillips curve and he oupu gap inerpreed as a Euler equaion (Woodford, 2003). I assume ha he agens have raional expecaions,.i.e., expecaions depend on he model s own forecass. In oher words, we assume ha agens in he Nigerian economy use all available informaion a heir disposal o calculae he expecaion of some crucial macroeconomic variables such as inflaion rae and exchange rae. 3 The model is esimaed by using Bayesian economerics. This is especially well suied for economies where daa availabiliy is limied, because his allows us o exclude values in our esimaions wihou economic sense ha are usually obained wih sandard economeric ools when ime series daa are shor. The use of prior informaion for he parameers is a sraegy ha could change dramaically he qualiy of he esimaion of macro models in developing economies and herefore avoid imporan policy misakes for spurious resuls. In summary, I conclude ha here is empirical evidence in Nigeria ha he cenral bank conrols he inflaion rae hrough a Phillips curve. Thus he adopion of a full-fledged inflaion-argeing regime in Nigeria is quie feasible. The moneary policy ransmission mechanism looks quie sandard: he cenral bank reacs o an upsurge in he inflaion rae by raising he ineres rae. The reacion is srong enough o conrol he inflaion rae Also, he cenral bank is relaively successful serilizing he reserve form nauralresources expors combined wih a fiscal policy ha delays he impac of oil prices on he economy. Bu he moneary policy works by inroducing a sacrifice raio in he Nigerian economy; herefore, i is imporan o implemen a credible inflaion-argeing regime o reduce he inflaion rae gradually insead of making abrup sabilizaion aemps wih high associaed coss in los oupu and employmen. 3 Even hough he model presened in his repor ignores a number of criical issues for moneary policy (a more complee descripion of he fiscal policy, curren accoun deerminaion, and he equilibrium levels for several variables), i has he advanage of relaive flexibiliy for analysis. In addiion, here is considerable scope o furher develop he model, hus he model for he Nigerian economy may be exended o include full microeconomic foundaions (DSGE), sock-flow dynamics, credi marke resricions, non-radable secors, fiscal policy, he implicaions for households ineremporal savings decisions, and so on. 4

5 The sudy is organized as follows: Secion 2 provides a deailed descripion of sylized facs o suppor he srucure of he model. Secion 3 presens he model and he empirical sraegy, while Secion 4 shows he resuls of he esimaions; parameers and impulse response funcions. Secion 5 concludes. 2. Sylized Facs In his secion I presen he evidence o suppor he heoreical srucure of he model. Thus, i is very imporan o check wheher or no some sylized facs are presen in he Nigerian economy ha le he cenral bank carry ou a sandard moneary policy. The firs one is he exisence of a sable Phillips curve, which allows i o affec he inflaion rae hrough he oupu gap. The idea behind his is ha he cenral bank can affec he demand side of he economy, which implies ha he cenral bank is able o reduce he inflaion rae via a lower aggregae demand or an acual GDP below is poenial level. In fac Figure 1 confirms his posiive relaionship beween inflaion and oupu gap in he Nigerian economy. Bu wha is he moneary ransmission mechanism o conrol he inflaion rae? Figure 1 also shows he connecion beween he Moneary Policy Rae (MPR) and he oupu gap. I is observed ha an increase in he MPR reduces he oupu gap in he period From he IS equaion, i is eviden ha he bridge connecing he inflaion rae and he MPR is he negaive link beween he oupu gap and he MPR. This could explain he influence of he ineres rae on boh privae consumpion and invesmen, probably via he expansion and conracion of he credi marke. Figure 1: Inflaion, GDP gap, and ineres rae (MPR) in Nigeria The nex issue is how he cenral bank is seing he MPR. Figure 2 shows he acual MRP and he MPR following a Taylor rule. I calibrae his rule by assuming a response for he inflaion rae of 1.5 and a response of oupu gap of 0.5. I also assume ha here is a lag of 0.7 in he MPR. As i is eviden from Figure 2, he cenral bank follows very closely a sandard Taylor rule. This shows ha he complee mechanism of moneary policy in he Nigerian economy could be explained as follows: a higher level of inflaion causes he cenral bank o raise he MPR above he inflaion rae o ensure a posiive real ineres rae. This slows down privae consumpion and privae invesmen, ulimaely moderaing he increase in prices. 5

6 Figure 2: MPR and he Taylor Rule in Nigeria There is an addiional issue relaing o inflaion sabilizaion in Nigeria ha is imporan o discuss. Theoreically, he righ connecion in he Phillips curve is beween he inflaion rae and he oupu gap (or unemploymen rae), and no for oher measures of economic aciviy. This is also esablished in he Nigerian economy. For insance, Figure 3 shows ha he posiive relaionship beween inflaion and economic aciviy is clearly valid only for he oupu gap and no for oupu growh. Even for a same level of economic growh, we can observe a wide range of inflaion raes. Anoher imporan issue is how we can measure he oupu gap. Should we use he poenial oupu as researchers do in developed economies or jus a rend o indicae when here is excess demand? In Figure 4 I show he possible discrepancy ha can occur beween hese conceps in an economy such as Nigeria. Moreover, here is difficuly in measuring he poenial oupu in developing economies (for insance, wha is he level of capial sock?, labor force? and Toal Facor Produciviy?) and hus, he poenial oupu can be inappropriae for planning moneary policy in he shor run in developing counries like Nigeria. Probably all he disorions presen in hese economies hinder hem from reaching heir poenial oupu no only in he shor run bu also in he long run. Therefore, he correc proxy o measure he oupu gap seems o be he acual GDP rend as opposed o he ideal poenial oupu. Figure 3: GDP gap, GDP growh, and inflaion rae Figure 4: GDP gap: poenial oupu gap vs. oupu rend Sill anoher issue ha is srongly relaed o moneary policy ransmission in a small open economy is he impac of he exchange rae on prices. Firs, from he ineres rae pariy condiion, a relaionship beween he ineres rae and he exchange rae can be esablished. Under a flexible exchange rae sysem, a higher ineres rae produces capial inflows ha appreciae he exchange rae. Conversely, a lower ineres rae causes capial ouflows ha produce a depreciaion of he exchange rae. Figure 5 shows some evidence of a negaive link beween he exchange rae and he ineres rae in he Nigerian economy. Second, i could be ha he exchange rae has a direc impac on he economy via impor secor (boh final goods and inpus). So an appreciaion (depreciaion) of he exchange rae can have a posiive (negaive) impac on he 6

7 inflaion rae. Undoubedly all his depends on wheher he pass-hrough coefficien of he exchange rae o inflaion is high or no, which is an empirical quesion. For insance, a lower coefficien can moderae he impac of he exchange rae on prices due o he exisence of price sickiness. Figure 6 shows ha in he Nigerian economy here is a direc relaionship beween he inflaion rae and exchange rae depreciaion. Figure 5: Real exchange rae and ineres rae in Nigeria Figure 6: Exchange rae pass-hrough in Nigeria One of he main subjecs in he Nigerian economy is he role of he price of oil. Bu wha is he real impac of his price on he inflaion rae and on he moneary policy mechanism? I find a leas hree channels hrough which he oil price is affecing he inflaion rae. The firs one is he influence of he oil revenues on he money supply. In effec, Figure 7 shows he posiive connecion beween he money supply, ne foreign asses (NFA) and he cenral bank s inernaional reserves. Therefore, if he cenral bank does no serilize, he excess supply of money can impac negaively on he inflaion rae. The second channel is he influence of exchange rae on he inflaion rae. Figure 8 shows ha an appreciaion of he exchange rae is associaed wih a higher oil price. As we have observed, appreciaions are also conneced wih lower inflaion raes. Figure 7: Ne foreign asse (NFA), foreign reserve, and money Figure 8: Real exchange rae and oil price Neverheless, he mos difficul ask was o find some prior link beween he price of oil and he oupu gap. Figure 9 indicaes ha his relaionship seems o be inexisen in he Nigerian economy; even his associaion becomes negaive for he period The reason may no be unconneced wih he ype of fiscal policy he governmen implemened during hese years. In fac, he Figure 10 shows ha he correlaion beween he oil price and he governmen expendiure gap is almos non-exisen. This means ha he governmen would no be ransmiing emporary oil price shocks o is expendiure and herefore o he aggregae demand. However, we do no mean o say ha he price of oil is no imporan o explain he dynamic of he level of oupu in he Nigerian economy. Figure 11 shows ha here is always a posiive correlaion beween hese wo variables. However, he imporan concep for explaining he inflaion rae as we said above is he oupu gap and no he level of GDP. 7

8 Figure 9: Oil price and oupu gap Figure 10: Governmen spending, GDP gap, and oil price gap Figure 11: Oil price gap and GDP The las sylized fac is relaed o he lack of credibiliy. This can affec he power of moneary policy o conrol he inflaion rae if expecaions are no anchored. Figure 12 indicaes ha he inflaionary rend was no exacly consan in he period Acually, his rend has flucuaed around a level of 10% of inflaion. This evidence means wo hings for he model: firs, we need o inroduce a variable arge ino he Taylor rule; and second, he model mus be able o measure he cos in erms of higher inflaion and los oupu of a emporary deviaion of inflaion from he arge. Figure 12: Inflaionary rend in Nigeria To sum up, he acual evidence indicaes ha he model has o consider hese following elemens o explain he inflaion rae in Nigeria: The posiive connecion beween inflaion and he oupu gap (Phillips curve); An IS curve where he oupu gap is dependen on he real ineres rae gap; An ineres pariy condiion o incorporae he effec of he MPR on he exchange rae; A channel of ransmission from exchange rae o inflaion rae (pass-hrough coefficien); and The impac of he price of oil on he money supply and he exchange rae. 3. The Model The Nigerian economy is analyzed using a medium sized New Keynesian macroeconomic model wih raional expecaions (Berg e al., 2006). The core equaions in he model consis of an oupu gap relaion; an inflaion equaion, an exchange rae equaion, and a moneary policy reacion funcion. The model expresses each variable in erms of is deviaion from he equilibrium (gap erms). The model emphasizes he flow dynamics of he Nigerian economy. Thus, he firs of hese equaions is an aggregae demand (IS curve) ha relaes he level of real aciviy o expeced and pas real aciviy, he real ineres rae, and oher variables o properly reflec he Nigerian economy, especially governmen expendiure 8

9 and he oil price. The second equaion is a Phillips curve ha relaes inflaion o pas and expeced inflaion, he oupu gap, he oil price, and he exchange rae. Then he hird equaion is he exchange rae, assuming an uncovered ineres pariy condiion wih some allowance for backward-looking expecaions and a variable o measure he counry risk premium. The fourh equaion is a moneary rule for seing he policy ineres rae as a funcion of he oupu gap, expeced inflaion and money supply. I add some addiional equaions o capure some specific characerisics of he Nigerian economy. I le he model incorporae he money supply as an endogenous variable dependen on exernal reserves and ne foreign asses (oil revenues). So he ineres rae is parially defined by a kind of Taylor rule and for an endogenous money supply. In addiion I inroduce he possibiliy of an inflaion arge ha depends on pas inflaion and influences he formaion of inflaionary expecaions. So if his variable increases, i will push up inflaion hrough he expecaion of higher inflaion. I use his as a measure of lack of credibiliy of he moneary policy. Noaion and Srucure of he Model The variables of he model are defined as follows: ygap is he oupu gap rrgap is he real ineres rae gap zgap is he real exchange rae gap x* denoes foreign variables π is inflaion Δ is he firs difference operaor z is he real exchange rae rr is he real ineres rae rs is he moneary policy rae rs is he equilibrium nominal ineres rae ε denoes error erms βs, δs, φ, Θ, γs, θs, ζs, κs, νs, ρs, and αs are he parameers. Oupu depends on aggregae demand and hence he real ineres rae, as well as pas and fuure oupu iself. The equaion (1) can be derived from a sandard Euler equaion 9

10 wih habi persisence, which yields an equaion relaing he nominal ineres rae o he expeced pahs of oupu and expeced inflaion. Moreover, he oupu gap also depends on specific characerisic of he Nigerian economy, all of hem relaed o he oil indusry, he weigh of he governmen secor in he economy, and he impor secor. These variables are he oil price gap (pogap), he real exchange rae gap, he governmen expendiure gap (gregap) and he foreign ineres rae gap (rrgap * ). ygap = β ygap + β ygap + β rrgap + β rrgap + β zgap * β gregap + β pogap + ε I assume ha governmen expendiure depends on he oil price gap, he exchange rae gap, and he oupu gap. The firs wo variables are associaed wih he oil indusry and he foreign secor, respecively. I inroduce he oupu gap o measure he impac of economic aciviy on governmen revenues. (1) gregap = fiscal pogap + fiscal zgap + fiscal ygap + ε (2) Inflaion depends on expeced and lagged inflaion, he oupu gap, he exchange rae gap, and he oil price. * ( 1 ) ygap z π = απ + α π + α + α Δ + απ + ε (3) This equaion indicaes how moneary policy affecs inflaion rae. Firs, moneary policy influences inflaion hrough is effecs on oupu and he exchange rae. In oher words, he coefficiens of he oupu and exchange rae gaps mus be greaer han zero. Oherwise, moneary policy would have no effec on inflaion. A common problem wih many models ha assume ineres pariy condiion is ha hey ypically do no provide enough persisence o generae a hump-shaped response of he real exchange rae afer a shock o moneary policy, which is commonly found in esimaed VARs (see, e.g., Eichenbaum and Evans, 1995; Faus and Rogers, 2003). We suppose ha he ineres pariy condiion holds parially and he real exchange rae depends on a lag of iself. Two addiional variables are included he oil price and 10

11 ygap o measure he effec of he counry risk premium on he exchange rae. Consisenly wih he empirical evidence, he idea here is ha hese variables measure occasionally he percepion of foreign invesors abou he Nigerian economy. ( ) ( 1 ) ( ) * 4 z = γ1z 1+ γ1 z+ 1 rr rr + γ2pogap + γ4ygap +ε (4) I assume ha he moneary policy insrumen is based parially on some shor-erm nominal ineres rae, and ha he cenral bank ses his insrumen in order o achieve a arge level for inflaion, π T. I may also reac o deviaions of oupu from he equilibrium. Neverheless, cenral banks also use someimes as he moneary policy insrumen he money supply; hus, he nominal ineres rae depends on he money supply as well. To do ha, I use money demand o obain he ineres rae in erms of money supply. ( ( ) ) T ( 1 ) ( π π ) rs = epsilon rs + epsilon grama rs + epsilon + epsilon ygap au3 ( ) ( 1 epsilon ) ( 1 grama ) au y ( m p ) + grama zgap + grama Δ z + ε (5) In addiion, I consider in equaion (5) ha he ineres rae also responds o he real exchange rae. Accordingly, if domesic currency appreciaes in real erms, he cenral bank of Nigeria decreases he ineres rae wih he aim of offseing he appreciaion (fear of floaing). We can measure he same phenomenon by replacing he exchange rae by he level of inervenion of he cenral bank in he currency marke, which is measured by he divergence beween he official rae and he rae in he black marke. In order words, as his difference ges larger, he cenral bank decides o change he ineres rae o encourage capial flows, hereby moderaing he difference beween he wo markes. Le us assume ha cenral bank decides o increase money supply when inernaional reserves also increase. Equaion (6) formalizes his assumpion, where he parameer θ deermines he level of serilizaion of he cenral bank. If he cenral bank makes a decision of serilizing compleely he increase in he reserves, θ is equal o zero; oherwise θ is beween 0 and 1. 11

12 6 ( ) ε Δ m = θ Δ res + (6) Le inernaional reserves depend on, among ohers, he oil price, he exchange rae, he oupu gap, and ne foreign asses (equaion 7). I add an equaion o explain ne foreign asses in erms of he difference beween he domesic and he foreign ineres rae. 7 ( ) ( ) ( ) ( ) ε Δ res = money Δ po + money Δ z + money ygap + money Δ nfa + (7) ( ) ( ) ( ) * 8 Δ = 5 Δ + 6 Δ ε (8) nfa money po money z money rr rr Credibiliy issues We inroduce he credibiliy issues by endogenising he inflaion arge (equaion 9) in he formaion of inflaionary expecaions. T T T π = ρπ 1+ (1 ρ)( π 1 π 1) (9) In oher words, if he parameer ρ is equal o one, he inflaion arge is consan. Oherwise, he inflaion arge also depends on he difference beween he pas inflaion rae and he pas inflaion arge. So in his laer case, he cenral bank accommodaes a higher rae of inflaion by seing also a arge higher for he nex period. This accommodaion will produce lack of credibiliy if he inflaion arge is inroduced direcly in he expecaions of he inflaion rae. Thus we need o adjus all he equaions of he model involving expecaion of he fuure inflaion rae. The changes are he following: T * ( ) ygap = β1ygap+ 1+ β11ygap+ 1+ β2 rrgap φπ 1 + β3rrgap + β4zgap + β gregap + β pogap + ε (1) ( ) * 3 π = α ( π + φπ ) + 1 α π + α ygap + α Δ z + α π + ε (2) T ( ) T ( 1 ) ( ) * 4 z = γ1z 1+ γ1 z+ 1 rr φπ 3 rr + γ2pogap + γ4ygap +ε (4) T * ( ) ( ) ( φ π ) 8 Δ nfa = money Δ po + money Δ z + money rr rr + ε (8)

13 The φ parameers quanify he relevance on he inflaionary expecaions of a cenral bank s deparure from a consan inflaion arge. Posiive values of each parameer signify an increase in expecaions and hen more inflaionary pressures. For he sake of simpliciy, all he equilibrium values o calculae he gaps (oupu, ineres rae, inflaion, and exchange rae) were esimaed by using he Hodrick-Presco filer. Finally, I represen he foreign secor of he Unied Saes and he price of oil. I assume as exogenous variables (AR process) he oupu gap, he Fed fund rae, and he inernaional oil price. 4. Economeric Mehodology: Bayesian Economerics The model is esimaed by Bayesian economerics, which is a mix beween calibraion (economic inuiion) and maximum likelihood. The calibraion par is he specificaion of priors, and he maximum likelihood approach eners hrough sandard economerics based on adjusing he model wih daa. Thus priors can be seen as weighs on he likelihood funcion in order o give more imporance o cerain areas of he parameer subspace according o economic inuiion. This is especially well-suied for economies such as Nigeria where daa availabiliy is limied and herefore priors for parameers are helpful in seing he parameers of he model by excluding values wihou economic sense for lacking of proper daa for he economeric esimaion. On he one hand, he priors are described by a densiy funcion of he form p ( θ A A) Where A indicaes a specific model, θ A represens he parameers of model A, p ( ) is he probabiliy densiy funcion. 4 On he oher hand, he likelihood funcion describes he densiy of he observed daa, given he model and is parameers: ( θa T ) (, T θa ) L YA py A Where Y T are he observaions unil period T. In order o obain p( θ Y T ), he poserior kernel densiy, I use he Bayes heorem: 4 Such as a normal, gamma, shifed gamma, inverse gamma, bea, generalized bea, or uniform funcion 13

14 ( θa T, ) ( T θa, ) ( θa ) κ( θa T, ) p Y A p Y A p A Y A This is he equaion ha will allow us o rebuild all poserior momens of ineres Resuls 5.1 Esimaed parameers The resuls for all parameers of he model are presened in he Appendix. I focus on his secion in he equaions ha measure essenially he moneary policy ransmission mechanism hrough he Phillips curve o conrol he inflaion rae. Table 2 shows he esimaion of he Phillips curve. The priors for he esimaion are in line wih he esimaions in oher counries. The esimaed effec (prior) of he oupu gap on he inflaion rae is lower han our prior (alpha2). Neverheless, i exiss and gives he cenral bank an imporan ool o conrol inflaion via he oupu gap. In oher words, here is a Phillips curve ha allows he cenral bank o sabilize he economy aking advanage of some level of price sickiness in he economy. Anoher ineresing resul is ha in he Nigerian economy 57% (=1-alpha1) of he agens se he acual inflaion by considering heir pas inflaion. This backward-looking characerisic of he economy implies ha he inflaion rae shows a high level of ineria and herefore i may be difficul for policy makers o reduce he inflaion rae. Also, he impac of he exchange rae on prices is smaller han our prior (alpha 3), indicaing ha he pass-hrough coefficien of he exchange rae o he inflaion rae is quie low. In addiion and consisenly wih his las resul, he influence of foreign inflaion (alpha4) is only This akes place even hough impors are an imporan secor in he Nigerian economy; I believe ha all hese resuls are indicaing ha he prices in he Nigerian economy are sicky downward raher han flexible. Inse Table 2: Parameers esimaed for he Phillips curve The second se of resuls is shown in Table 3, conaining he parameers esimaed for he IS curve. This able indicaes for he second ime ha he Nigerian economy 5 In he appendix I explain in deail he economeric procedure. 14

15 displays a high level of ineria (bea11=0.91). Pracically, he acual oupu gap is no affeced by he expecaions abou he fuure rajecories of he ineres rae, he exchange rae, ec. (bea1=0.0063). Neverheless, wha influences he oupu gap are he acual values of he domesic and foreign real ineres rae gaps (bea2 and bea3). The oher variables, namely he governmen expendiure gap (bea4), he oil price gap (bea5), and he exchange rae gap have a nil impac on he oupu gap (bea6). Thus, his gives he cenral bank some level of conrol of he inflaion rae by changing he aggregae demand hrough he ineres rae. Bu his impac is only limied and i can ake many quarers due o he high ineria in he oupu gap. Inser Table 3: Parameers esimaed for he IS curve Regarding he parameers involved in he deerminaion of he ineres pariy condiion (Table 4), we have ha his condiion holds only parially. The poserior mode for gamma1 indicaes ha he exchange rae depends only on 50% of he expecaions abou he fuure rajecory of he difference beween he domesic and he foreign ineres rae. Regarding he impac of he oher variables on he exchange rae, we have ha he oil price gap (gamma2) and he oupu gap (gamma4) have some small effec on he exchange rae. This resul is consisen wih all he previous evidence ha in he Nigerian economy he ineria is an imporan elemen o explain he dynamic of many macroeconomic variables. Inser: Table 4: Parameers esimaed for he Ineres Pariy Condiion Nex in he moneary policy rule, I find (see Table 5) ha he cenral bank mos of he ime is following a Taylor rule very closely (gamma1=0.95). So he cenral bank is responding o he inflaion rae (epsilon2=1.33) and he oupu gap (epsilon3=0.34) in a very sandard manner. On he conrary, he cenral bank used very moderaely he money supply o affec he ineres rae in he period Oher ineresing resuls indicae ha he oupu elasiciy of he money demand is close o 1 (au2) and he ineres rae elasiciy of money demand is 0.29 (au3). We do no find any evidence ha he cenral bank is using he ineres rae o inervene he exchange rae marke (gamma2 and gamma3 are close o zero). However, from all hese resuls, he cenral bank is very conservaive when changing he ineres rae. Thus, our esimaion indicaes ha he acual ineres rae depends on a 0.98% (epsilon1) of changes in is own lag. 15

16 Inser Table 5: Parameers esimaed for he Moneary Policy Rule Anoher imporan issue relaed wih he moneary policy rule is he level of serilizaion of he inernaional reserves ha he cenral bank carried ou in he period Table 6 indicaes ha he cenral bank serilized mos of he ime he reserves ha came from he oil revenues. Thus, he parameer hea, which can ake values beween 0 and 1 (one being no serilizaion and zero complee serilizaion), has a poserior of only 0.1. This resul is also consisen wih he previous evidence ha he cenral bank is using almos all he ime a Taylor rule o implemen moneary policy in he Nigerian economy. Inser: Table 6: Parameers esimaed for he Money supply Finally, he las imporan issue is abou he credibiliy of he moneary policy in he Nigerian economy. To do so, we repea he equaion for he Phillips curve and he equaion for he inflaion arge of Secion III. I menion in ha secion ha if ρ is smaller han one he inflaion arge is no consan. Moreover, if φ is greaer han zero, agens are inroducing changes in he inflaion arge ino he expecaion formaion, indicaing a lack of credibiliy of he moneary policy, i.e., hey expec a higher inflaion due o changes in he inflaion arge. ( ) π = α ( π + φπ ) + 1 α π + α ygap + α Δ z + α π + ε T * π = ρπ + (1 ρ)( π π ) T T T Table 7 shows ha he inflaion arge has been very sable in he las en years in Nigeria (rho=0.98); however, small changes in he inflaion arge have some effec in he formaion of inflaionary expecaions (phi=0.13). Thus, he deparure of a consan inflaion arge has some imporan consequences. So, if he cenral bank increases is inflaion arge emporarily, i will cause a emporary bu very persisen increase in he rae of inflaion. Inser: Table 7: Parameers esimaed for he Phillips curve and he dynamic of he inflaion arge 5.2 Impulse response funcions 16

17 Firs, he moneary shock (Figure 13) is consisen wih wha he economic heory predics o sabilize he economy (Woodford, 2003). 6 Afer he increase in he moneary policy rae (rs), here is a decrease in he oupu gap and he inflaion rae. This happens because he real ineres rae has a negaive effec on he oupu gap (see equaion 1) and hen his brings abou a decline in he inflaion rae (see equaion (3), Phillips curve). This shock also produces an appreciaion (in nominal and real erms) of he Naira because he uncovered ineres rae pariy holds parially, i.e., he higher ineres rae generaes capial inflows ha appreciae he Naira (see equaion 4). Then, subsequen o he shock all variables end o reurn o heir equilibrium values. This akes place because he decline in oupu and inflaion riggers a downward adjusmen in he ineres rae (see equaion 5). Inser Figure 13 MPR shock Therefore, an increase of 200 bsp causes a reducion in he inflaion rae of up o 2% afer wo years. This is evidence of he high degree of price sickiness presen in Nigeria, as in many oher economies. The reducion in he oupu gap is abou 0.6% (annually) afer wo years wih a real appreciaion in he exchange rae of 20%. In oher words, he moneary policy ransmission works by inroducing a sacrifice raio in he Nigerian economy. For insance, if he cenral bank decides o reduce quickly he inflaion rae by 10%, he oupu gap will drop by -3.0%. In addiion, he policy is effecive in a horizon of up o wo years. Consequenly, i is advisable o implemen a credible inflaion-argeing regime o reduce he inflaion rae gradually and avoid oupu coss. Figure 14 shows wha happens if he cenral bank raises he inflaion arge emporarily. The esimaion indicaes ha an increase in he inflaion arge of 3.6% (hisorical variance of he inflaion arge) has imporan effecs in he economy. The inflaionary expecaions affec quickly he inflaion rae, which goes up o 2.0%. Hisorically afer hese episodes, he cenral bank reurns o is sabilizaion policy by raising he ineres rae. This change in he moneary policy has a direc impac on economic aciviy. The increase in he ineres rae brings abou a conracion in aggregae demand which in urn reduces he oupu gap and decreases he inflaion rae in a horizon of wo years. As 6 Each shock corresponds o an increase of one sandard deviaion. 17

18 he Figure 17 shows, he deparure from a consan inflaion arge of 3.6% has a cos implicaion on he oupu gap ( ha is, reducing he oupu gap up o 0.7%). Inser Figure 14 Inflaion Targe shock Figure 15 shows he impulse response funcion for a shock in he ineres rae pariy condiion. This allows o measure direcly he impac of a pure exchange rae shock on he inflaion rae. An exchange rae shock of approximaely 18% increases he inflaion rae by around 1.8%. Therefore, he exchange rae pass-hrough in he Nigerian economy is around 0.1 (=1.8/18) and occurs in he firs wo quarers approximaely. The moderae response in he inflaion rae is due no only o he high inerial in he inflaion rae bu also o he reacion of he cenral bank o increases he ineres rae. These wo effecs go in he same direcion: a lower oupu gap ha weakens aggregae demand and real appreciaion ha finally reverse he risk premium shock. Inser Figure 15 Risk Premium shock The oil price shock (Figure 16), produces a very moderae expansion in he oupu gap (see equaion 1). The response of he auhoriy is o increase ineres rae (see equaion 5), ha riggers an appreciaion in he exchange rae; consequenly, his appreciaion pushes down he inflaion rae (equaion 3). However, all variables end o reurn o heir equilibrium values when he oil price shock disappears. The main imporan effec of he oil price shock is an appreciaion of he real exchange rae. The impac of he oil price shock on he inflaion rae is no srong because here are wo opposing facors a work. Firs, he appreciaion of he exchange rae ha pushes down he inflaion rae as Figure 16 shows. Bu here is a second-round effec ha is no incorporaed in he Figure 16. When he price of oil goes up, foreign inflaion also increases, pushing up he domesic inflaion rae (see Figure 17). Inser Figure 16 Oil Price shock Inser Figure 17 Foreign Inflaion shock Finally, demand and supply shocks in he Nigerian economy are in line wih he predicion of he economic heory (Figures 18-19). The demand shock produces an expansion of he economy (oupu) and increases in he inflaion rae in he medium erm as expeced. On he conrary, he supply shock causes an increase in inflaion ha 18

19 causes a recession. This maerializes as he cenral bank mus raise he ineres rae o reduce inflaion o is original level. Inser Figure 18 Demand shock Inser Figure 19 Domesic Inflaion shock 5. Conclusions I develop a semi-srucural dynamic general equilibrium model o undersand how moneary policy is working in he Nigerian economy. This model is based on he Phillips curve and capures mos of he channels hrough which policymakers believe moneary policy o influence a small open economy wih a managed floaing exchange rae. The model was esimaed wih Nigerian quarerly daa beween 1995 and 2007, o replicae some rue facs. The esimaion confirms ha he cenral bank in he Nigerian economy can conrol he inflaion rae hrough a Phillips curve. Moreover, here is an IS curve, an ineres pariy condiion o incorporae he effec of he MPR on he exchange rae, a channel linking he exchange rae o he inflaion rae (pass-hrough coefficien), and a well-defined moneary policy rule. Thus he adopion of a full-fledged inflaion-argeing regime in Nigeria is quie feasible and i could be a good example for oher African economies The moneary policy ransmission mechanism acs like his: he cenral bank reacs o an upsurge in inflaion by raising he ineres rae. This reacion is srong enough o produce an increase in he real ineres rae gap, which in urn diminishes he oupu gap. Finally, he inflaion rae umbles hrough a Phillips curve. In oher words, moneary policy ransmission works by inroducing a sacrifice raio in he Nigerian economy. For insance, if he cenral bank decides o reduce quickly he inflaion rae by 10%, he oupu gap will narrow by -3.0%. In addiion, our esimaes indicae ha he policy is effecive in a horizon of up o wo years. Consequenly, i is preferable o implemen a credible inflaion-argeing regime o reduce he inflaion rae gradually. I also find ha a deparure from a consan inflaion arge has imporan coss 19

20 in erms of los oupu, and ha he pass-hrough coefficien of he exchange rae o he inflaion rae is around 0.1 in Nigeria. Appendix Bayesian Economerics To ge he poserior kernel I need o esimae he likelihood funcion py ( T θ, A A) of he model. I express he model as linear o calculae easily he log-likelihood funcion. A model wih raional expecaions can be wrien in his form: { f ( y + 1 y y 1 u )} Ε,,, = 0, and he soluion is an equaion of he ype ha we call he decision rule ( ) y g y u, = 1. This can be rewrien in he following linear manner: ( θ) ˆ ( θ ) yˆ = gy y 1 + gu u ( ) ( ) y = My θ + My θ + η * ˆ ' ( η η ) ( θ) Ε = V ' ( uu ) Q( θ ) Ε =, where yˆ represens all he endogenous variables in deviaions from he seady sae, y is he vecor of seady-sae values, u are exogenous variables, and θ is he vecor of parameers o be esimaed. The firs equaion is he decision rule expressed in lineal erms, bu he second equaion expresses a relaionship among he rue endogenous variables ha are no direcly observed observed, * y. Boh variables are relaed hrough an error erm y ˆ and he endogenous variables ha are η. 20

21 The nex sep is o esimae he likelihood of he sysem. Noice ha, if all endogenous variables are observed, he previous sysem is a VAR model wih a sandard loglikelihood funcion (see Hamilon, 1994). Second, if a group of he endogenous variables are no observed, we need o use a Kalman filer recursion o derive he loglikelihood. The only condiion o be considered is ha he number of observed endogenous variables has o be equal o he number of he shocks (see Hamilon, 1994). The resul is he following log-likelihood funcion: ( θ ) ( π) Tk ln L Y ln 2 F v F v * = T ' = 1, where F and v come from he Kalman filer procedure or a simple VAR if all variables are observed. Then he log poserior kernel can be expressed hus: * * ( Y ) = L( Y ) + p( ) lnκ θ ln θ ln θ. The nex sep is o ge he poserior disribuion. To do ha hrough he Meropolis- Hasings algorihm: 0 1. Choose a saring poin θ ha is he poserior mode * 2. Draw a proposal θ from a jumping disribuion J ( * 1 θ θ ) N( θ 1, c m ) he poserior mode. = Σ where Σ m is he inverse of he Hessian compued a 3. Compue he accepance raio κ θ r = κ θ * ( YT ) 1 ( YT ) * 4. Finally, accep or discard he proposal θ according o he following rule, and updae, if necessary, he jumping disribuion: * θ θ = 1 θ ( ) wih probabiliy min r,1 oherwise 21

22 In pracice, he model for he Nigerian economy was esimaed wih wo programs. The firs one obains he saring poin ha is he poserior mode considering 1,200 draws in he Meropolis Hasings algorihm. Afer ha a second program carries ou a second simulaion of he Meropolis Hasings algorihm considering 250,000 draws o obain he final resuls. Acknowledgmens This research was conduced while García was visiing scholar in he Cenral bank of Nigeria, for whose hospialiy he is graeful. I hank Charles N.O. Mordi, Abwaku Englama, and Adebiyi Michael Adebayo for very useful commens and discussion. Especially I wan o hank o Professor Eddy Ndekwu for inerminable conversaions abou moneary policy in Nigeria during our ea ime. Also I hank o Solange De Vids for her suppor during my visi in Nigeria. All remaining errors are he auhor s own. References Ball, L. and D.H. Romer (1990) Real Rigidiies and he Nonneuraliy of Money, Review of Economic Sudies, 57(April): Berg, A., P. Karam and D. Laxon (2006) A Pracical Model-Based Approach o Moneary Policy Analysis: A How-To Guide, Inernaional Moneary Fund Working Paper, 06/81 (Washingon: Inernaional Moneary Fund). Chrisiano, L.J., M. Eichenbaum and C.L. Evans (2005) Nominal Rigidiies and he Dynamic Effecs of a Shock o Moneary Policy Journal of Poliical Economy, 113(1): Clarida, R., J. Galí and M. Gerler (1999) The Science of Moneary Policy: A New Keynesian Perspecive, Journal of Economic Lieraure, 37(4): Eichenbaum, M. and C. Evans (1995) Some Empirical Evidence on he Effecs of Shocks o Moneary Policy on Exchange Raes, Quarerly Journal of Economics, 110: Erceg, C., D. Henderson and A. Levin (2000) Opimal Moneary Policy wih Saggered Wage and Price Conracs, Journal of Moneary Economics, 46(2): Faus, J. and J. Rogers (2003). Moneary Policy s Role in Exchange Rae Behavior, Journal of Moneary Economics, 50: Galí, J., (2008) Moneary Policy, Inflaion, and he Business Cycle. Princeon Universiy Press. 22

23 Hamilon, J. (1994) Time Series Analysis. Princeon Universiy. Kydland, F. and E.C. Presco (1977) Rules Raher Than Discreion: The Inconsisency of Opimal Plans, Journal of Poliical Economy, 85(3): Lucas, R.E. (1976) Economeric Policy Evaluaion: A Criique, Carnegie-Rocheser Conference Series on Public Policy, vol. 1, pp Mankiw, N.G. and D. Romer (1991) New Keynesian Economics, Cambridge: MIT Press. Presco, E. (1986) Theory Ahead of Measuremen, Federal Reserve Bank of Minneapolis Quarerly Review, Fall: Sargen, T. (1981) Inerpreing Economic Time Series, Journal of Poliical Economy, 99(2): Sims, C. (1980) Macroeconomics and Realiy, Economerica, 48(1): Smes, F. and R. Wouers (2003) An Esimaed Dynamic Sochasic General Equilibrium Model of he Euro Area, Journal of he European Economic Associaion, 1(5): Smes, F. and R. Wouers. (2007) Shocks and Fricions in U.S. Business Cycles: A Bayesian DSGE Approach, American Economic Review, 97(3): Woodford, M. (2003) Ineres and Prices: Foundaions of a Theory of Moneary Policy. Princeon: Princeon Universiy Press. 23

24 Tables Table 1: Parameers esimaed for he Phillips curve Prior Poserior Disribuion alpha bea alpha gamm alpha gamm alpha gamm Table 2: Parameers esimaed for he IS curve Prior Poserior Disribuion bea bea bea gamm bea gamm bea gamm bea gamm bea gamm bea gamm Table 3: Parameers esimaed for he Ineres Pariy Condiion Prior Poserior Disribuion gamma bea gamma gamm gamma gamm Table 4: Parameers esimaed for he Moneary Policy Rule Prior Poserior Disribuion epsilon bea epsilon bea epsilon gamm grama bea grama gamm grama gamm au gamm au gamm Table 5: Parameers esimaed for he Money supply Prior Poserior Disribuion hea bea 24

25 Figures Figure 1: Inflaion, GDP gap, and ineres rae (MPR) in Nigeria Inflaion Inflaion GDP gap GDP gap Inflaion Q2 1996Q3 1997Q4 1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q GDP gap GDP oupu gap MPR gap Source: CBN Figure 2: MPR and he Taylor Rule in Nigeria MPR Tyalor Rule.7*MPR(-1)+.3*(1.5*(INF-10%)+.5*GDP gap) Source: CBN and auhor s calculaions 25

26 Figure 3: GDP gap, GDP growh, and inflaion rae Inflaion Inflaion GDP gap GDP growh Source: CBN Figure 4: GDP gap: poenial oupu gap vs. oupu rend Poenial oupu Acual rend Acual GDP ?? 26

27 Figure 5: Real exchange rae and ineres rae in Nigeria Real exchange rae MPR Source: CBN Figure 6: Exchange rae pass-hrough in Nigeria Exchange Rae Pass Through Inflaion Inflaion Exchange rae depreciaion Exchange rae depreciaion Inflaion Source: CBN Exchange rae depreciaion 27

28 Figure 7: Ne foreign asse (NFA), foreign reserve, and money NFA growh Source: CBN Money supply growh Foreign Reserve growh Money supply growh Figure 8: Real exchange rae and oil price Real exchange rae Oil price gap Source: CBN 28

29 Figure 9: Oil price and oupu gap oil price gap GDP gap oil price gap GDP gap Source: CBN Figure 10: Governmen spending, GDP gap, and oil price gap Governmen Exp. gap Governmen Exp. gap GDP gap oil price gap Source: CBN 29

30 Figure 11: Oil price gap and GDP oil price gap oil price gap GDP GDP Source: CBN Figure 12: Inflaionary rend in Nigeria Q2 1996Q3 1997Q4 1999Q1 2000Q2 2001Q3 2002Q4 2004Q1 2005Q2 2006Q3 2007Q4-5 Sources: CBN and auhor s calculaions 30

31 Figure 13 Impulse response funcion: Moneary policy shock Source: Auhor s calculaions 31

32 Figure 14 Impulse response funcion: Inflaion arge shock Source: Auhor s calculaions 32

33 Inser: Figure 15 Impulse response funcion: Risk premium shock Source: Auhor s calculaions 33

34 Inser: Figure 16 Impulse response funcion: Oil price shock Source: Auhor s calculaions 34

35 Inser: Figure 17 Impulse response funcion: Foreign inflaion shock Source: Auhor s calculaions 35

36 Inser: Figure 18 Impulse response funcion: Demand shock Source: Auhor s calculaions 36

37 Inser: Figure 19 Impulse response funcion: Supply shock Source: Auhor s calculaions 37