THE INTERACTIONS BETWEEN MONETARY AND FISCAL POLICY RULES. Amr Algarhi

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1 I- Inroducion: THE INTERACTIONS BETWEEN MONETARY AND FISCAL POLICY RULES Amr Algarhi Man sudies in he lieraure have been focused on analsing he performance of alernaive monear polic rules, however he ignores he behaviour of fiscal polic rules. In his assignmen, he analsis focuses on he monear and fiscal polic ineracion as se according o simple rules as adoped in he EJ2000 model b Leih and Wren-Lewis (2000). The analsis in his assignmen also relaed o Woodford (1996). The assignmen will examine he effec of differen shocks (consumpion shock, inflaion shock and suppl shock) under differen ineracions beween monear and fiscal polic (acive and passive regimes) when boh follows simple rules using he EJ2000 model. In he passive regime, is i beer for monear polic o be more passive or i would produce a worsen oucome. On he oher hand, in an acive polic, would furher increase in fiscal acivism dampen he effec of shocks? Addiionall, is he naure of he inflaionar process represened in Phillips curve (forward looking, backward looking or a combinaion of boh) criical o delineae he sabili of he dnamic of he model? And will considering a proporion of consumers as a credi consrained change he properies of he model. The assignmen will cover all he above quesions. The srucure of he assignmen is as follows. Secion II provides he descripion of he EJ2000 model. Secion III invesigaes he impac of differen shocks, including a emporar and auocorrelaed consumpion shock, a emporar fall in oupu suppl and a posiive shock o inflaion. Secion III also invesigae he change in he model properies if a proporion of consumers were credi consrained and how i affecs he model ogeher wih a backward looking inflaion. Finall, Secion IV gives some concluding remarks. II- The EJ2000 Model: The model was inroduced in Leih and Wren-Lewis (2000) as a micro-founded macro model which describes he Blanchard-Yaari model wih muli-good version and wih a presence of mone. In his model, he aggregae consumpion funcion can be wrien as, c = υ ( k+ σ )[ h + w 1 ] (1) where k is he probabili of deah and σ is he individual s subjecive discoun rae. Equaion (1) implies ha consumpion is a fixed proporion of human h ) and financial ( w ) wealh. The real mone demand is, ( 1

2 m 1 υ = υ r c. + (2) Where r is he real reurn and is he rae of inflaion. The dnamics of aggregaion discouned profi and labour income are, h+ 1 h = + ( τ ) (3) 1+ r + k On he oher hand, he financial wealh is represened in forms of mone and governmen bonds. As boh consiue he liabiliies of he governmen, financial wealh can be considered as governmen deb ( b = w m ). k is a ke parameer in equaion (3) as i is used as a mark up on he real ineres rae used o discoun income in human wealh. No capial is assumed in he model for simplici. Therefore, he governmen s dnamic budge consrain can be wrien in real erms as, w w + w r m r + + g τ (4) where. = ( ) g is he governmen spending and τ represen governmen axaion g = g f ( w 1 w) τ α + ( w 1 w) = α τ where f is he rae of fiscal feedback on deb. The aggregae demand is = c + g, and he aggregae price level is p = p 1 +. Using a se up due o Calvo (1983), he forward looking Phillips curve is derived as, (5) (6) 1+ ω( 1) = + (7) Philips curve describes he dnamics of inflaion in erms of expeced inflaion and he oupu gap. In modelphi, a simple generalized Phillips curve is considered as i allows for a combinaion of forward and backward looking inflaion, α 1 + ( 1 α) 1+ ω( 1) = + A purel backward or forward looking Phillips curve can be obained as special cases when α = 1and α = 0 respecivel. In his version of he mode, he Phillips curve is purel forward looking. The backward looking inflaion will be invesigaed a he end of secion III. The model adops a simple monear polic represened b, * r r +θ ( ) (8) = * where r is he sead sae of he ineres rae generaed b he model, is he arge level of inflaion and θ is an indicaor of he srengh of monear polic. The monear polic is acive when ineres rae mus rise following an increase in inflaion; his 2

3 monear rule is he Talor principle (where θ is posiive), if i is no he case inflaionar shocks will become persisen wih global insabili. So passive monear polic is when nominal ineres rae does no rise due o an increase in inflaion, whereθ = 1 implies ha he polic is fixing he nominal ineres rae (Kirsanova e al., 2005). From he above equaions, i is obvious ha he model conains hree main dnamic processes: consumpion, wealh and inflaion. Consumpion is forward looking, wealh is backward looking and inflaion can be eiher (a pure forward or backward) or boh. The above discree ime model is used and a se of parameers are adoped o examine he deail of he dnamic pahs of he variables following shocks. Table (1) presens he parameers and he sead-sae values of model variables. Table 1: Parameers and Sead-Sae Values of Variables. Parameers Base Values υ c 0.66 k 0.06 g 0.34 σ 0.02 h 7.87 f 0.08 w 0.40 τ 0.35 r 0.03 ω 0.1 θ 0.5 The preferences of he polic-maker in his model is o minimize he loss funcion: L γ 2 2 = L ( 1) he loss funcion ever period penalizes deviaions of inflaion and oupu from is arges and β denoes he relaive weigh given o deviaions of oupu from is arge (Kirsanova e al, 2005). β III- Simulaions and Resuls: Auocorrelaed Consumpion Shock Consider a emporar bu auocorrelaed negaive consumpion shock (1% decrease) which dies awa graduall over five ears. The impac of such a shock on consumpion, oupu, and inflaion is shown in figure 1 where all variables are measured as absolue deviaions from he base andθ = Consumpion deviaes from he base in a similar wa as he shock, however no in he exac same wa. Oupu also deviaes from is base similarl o consumpion which shows ha his model is demand deermined in he shor run because of he presence of nominal ineria. As he consumpion shock dies awa afer five ears, is impac on oupu and inflaion dies oo. Figure (1) shows ha afer he 3

4 shock is over, oupu and inflaion reurn o is base. The reason is ha afer period 5 he governmen spending falls b an amoun ha is equivalen o he increasing amoun of consumpion because boh consumpion and governmen spending depends on financial wealh (governmen deb) wih opposie signs (see equaion c and g) ha simpl offse each oher as he wo parameers, ( k + σ ) and f happen o be he same (=0.08). Figure 1: Deviaion of Inflaion, Oupu and Consumpion Inflaion Consumpion Oupu Figure 2 shows he shock impac on governmen spending and financial wealh. Wealh increases in he beginning due o less consumpion and more savings. On he oher hand, governmen spending can be considered as he mirror image of wealh. Once he shock dies ou, lower governmen spending reduces deb and consumers spend he wealh he have buil up. However, unlike oupu and inflaion, disequilibrium in wealh is much more long lasing due o he slow fiscal feedback Figure 2: Deviaion of governmen spending and wealh Financial wealh Governmen Spending

5 Consider he same consumpion shock, however his ime i is under a passive polic regime, where θ = 0. 1 and f = Inflaion is above base in all periods under he passive regime due o he dnamic behaviour of he governmen deb, as shown in Figure (3), alhough he direc effec of a demand shock is deflaionar. The negaive consumpion shock increases saving which implies a higher sock of governmen deb. As here is no feedback from deb o governmen spending ( f = ), he onl wa governmen deb can sabilise is for monear polic o cu deb ineres pamens and boos ax revenues hrough higher oupu. Therefore under a passive monear polic his implies higher inflaion in order o achieve his ineres rae. Passive polic is beer han acive polic a reducing he iniial inflaion disequilibrium following he shock, bu ha is no he case in he medium run, as inflaion reurns o base under he acive polic. However, under he passive regime, he econom suffers he inflaionar consequences of a high price level in he long run as shown in Figure Figure 3: Inflaion under he Acive and Passive Regime Passive Regime Acive Regime In he passive regime ( f = 0. 01), he changes in monear polic rule from θ = 0. 1 o θ = 0.2 can be examined wih he same consumpion shock. Figure 4 shows he wo differen inflaion pahs wih he more passive monear polic θ = 0. 2 wih he greaer inflaion sabili. Tha is shows ha if monear polic is passive, i is beer for i o be more raher han less passive. Wih no fiscal feedback, monear polic sabilizes governmen deb b reducing he sensiivi of nominal ineres raes o inflaion. 5

6 Figure 4: Inflaion afer increasing he Passivi of Monear Polic θ = 0.2 θ = However, fiscal polic operaes hrough governmen spending, and he feedback from deb o governmen spending exacl offse he wealh in he consumpion funcion. Now consider he rae of fiscal feedback on deb f o be doubled from 8% o 16%. Figure 5 shows ha governmen spending reacs more quickl in he laer, as well as wealh will reurn o is base more rapidl. Figure 5: Deviaion of governmen spending and wealh (wih double fiscal feedback on deb) g wih double fiscal feedback on deb w wih double fiscal feedback on deb g: governmen spending w: financial wealh On he oher hand, oupu differs from is base afer he shock dies ou and he inflaion disequilibrium becomes worse as show in Figure 6. This shows ha he fiscal feedback akes place on governmen spending influence inflaion and he opimal monear polic. 6

7 Figure 6: Deviaion of Inflaion and Oupu (wih double fiscal feedback on deb) Inflaion wih double fiscal feedback on deb Oupu wih double fiscal feedback on deb Inflaion Oupu Suppose he addiion of oupu deviaion o he monear polic rule where Equaion (8) is wrien as, * r = r + ( ) + θ ( ) θ This monear polic rule (Talor rule) relaes he real ineres rae o inflaion and oupu deviaion. θ shows ha if inflaion rises, hen he real ineres rae will be raised o weaken demand, which will reduce inflaion. θ shows ha he real ineres rae is raised if oupu rises. In equaion (8) θ is zero, and for he sabili condiions θ is required o be posiive. However a posiive large value of θ wih inflaion above arge can cause a large ineres-rae increase, which leads o a large reducion in oupu, hen o a reducion in inflaion, which ma lead inflaion o overshoo below arge, and hen converge in a cclical manner. Including a posiive value for θ can preven such overshooing. If oupu in equaion (7) is wih lag -1 hen i is considered as a predicor of fuure inflaion which helps polic maker o lower he real ineres rae when oupu has fallen, wihou waiing for he reducion in inflaion which he fall in oupu will cause. A Talor rule wih θ = along wihθ = 0. 5 will conrol he model. 7

8 Figure 7: Oupu deviaion in he monear polic rule Consumpion wih θ =0.35 Consumpion Inflaion wih θ =0.35 Inflaion Oupu wih θ =0.35 Oupu Figure 7 shows ha b adding oupu deviaion o he model, oupu and inflaion have less deviaion from is base han when θ = 0 ; however he reurns o heir base when he consumpion shock is over. Figure 8 shows ha governmen spending reacs more quickl aθ = hanθ = 0. Financial wealh reurns o is base more rapidl wih oupu deviaion included. As a resul, adding oupu deviaions o he monear polic rule did help, as his monear sabilisaion had some effec in dampening he consumpion shock represened in less oupu and inflaion deviaion. Figure 8: Oupu deviaion in he monear polic rule governmen spending wih θ =0.35 governmen spending wealh wih θ =0.35 wealh

9 A emporar fall in oupu suppl Turning o anoher kind of shock, consider now a emporar fall in oupu suppl which dies awa graduall over four ears. Inflaion will rise as a response o he oupu suppl fall, and via Talor rule real ineres rae will follow inflaion. The rise in ineres rae will decrease consumpion via human capial. This decrease in consumpion increases saving and in reurn increases wealh, which implies a higher sock of governmen deb. Afer he shock in oupu suppl is over, oupu and inflaion reurn o is base. The reason is ha afer period 5 he governmen spending falls b an amoun ha is equivalen o he increasing amoun of consumpion because boh consumpion and governmen spending as menioned before Figure 9: Inflaion and Oupu deviaion Inflaion Oupu Now suppose an acive regime fixing θ = 0. 5 and how differen degrees of fiscal feedback will reac o he emporar fall in oupu suppl. Table 2 presens he effec of emporar fall in oupu suppl under differen degrees of fiscal feedback ( f = 0. 08, f = 0.16 and f = ). From able 2, he increase in fiscal feedback can lead o generae greaer disequilibrium in oupu, however i dampen he rae of inflaion. As he fall in oupu suppl increase governmen deb, which reduce governmen spending (via equaion 5) depending on he value of he fiscal feedback. The larger he feedback, he larger he deviaion of oupu from he base and he longer ime i will ake he oupu o reurn back o base. 9

10 Table 2: Alernaive degrees of Fiscal Feedback ( θ = 0. 5 ) Years f Inflaion % deviaion Oupu % deviaion Inflaion Shock Consider a posiive shock o inflaion (1%) a ime. he real ineres rae will follow inflaion and will raise hrough Talor rule under acive monear polic and hen go back o base a +1 when he shock is over. The ineres rae rise will affec boh human capial and financial wealh. Once ineres rae increases, human capial will decrease (see equaion 3), which leads o a decrease in consumpion in ime, and hen oupu decreases. On he oher hand, he fall in consumpion a rises saving which in urn increases wealh a, his implies a higher sock of governmen deb a +1. in he long run he real deb will go back o is original level. The increasing wealh leads o an increase in consumpion and hen increase in oupu; While he increase in governmen deb via equaion 5 will lead o a decrease in governmen spending (fiscal conracion), ha will cause falls in oupu. However, he increase in consumpion and he decrease in governmen spending offse each oher as k +σ = f leading oupu o reurn o is base once he inflaion shock is over, and his decrease in oupu will decrease inflaion o is original via he Phillips curve. Therefore, he inflaion shock had no effecs on fuure inflaion ha is because he Phillips curve is a purel forward looking, and hen he econom reurns o is base equilibrium once he shock is over. Alernaive degrees of fiscal polic in an acive regime are considered. Suppose he degree of monear polic srengh is fixed aθ = Then i is examined if a furher increase in fiscal acivism (changing from f = 0. 08, f = o f = ) would reduce he consequence of he inflaion shock. Table 2 shows he impac of he inflaion shock considered differen degrees of fiscal feedback. I can be observed ha wih he increase of fiscal acivism, he impac of inflaion shock las for a longer period (especiall when f f k+ σ ), which shows ha increase in fiscal feedback can generae disequilibrium, e i is no a radical one. As he inflaion shock raises governmen deb, and ha decrease governmen spending depending on he degree of fiscal feedback. he shor erm oupu falls more when feedback is sronger (see able 3), and he greaer he fiscal feedback he more ime i ook oupu o reach is base. 10

11 Table 3: Alernaive degrees of Fiscal Feedback ( θ = 0. 5 ) Years f Inflaion % deviaion Oupu % deviaion Adding oupu deviaion o he monear polic rule (Equaion 8), i was found haθ = minimize he loss funcion givenθ = Oupu has less deviaion from is base b including oupu deviaion o Talor rule. Governmen spending reacs more quickl a θ = hanθ = 0 and financial wealh reurns o is base more rapidl. Thus monear sabilisaion had some effec in dampening he inflaion. However, including oupu deviaion had a bigger effec on inflaion in he firs period more han before, bu inflaion once again reurns o base afer he shock is over. On he oher hand, including lagged ineres rae o he Talor rule will worsen he effec of he shock especiall he higher he response of he ineres rae o is lagged values as disequilibrium will be generaed in boh oupu and inflaion. The inflaion shock wih he addiion of he lagged ineres rae o he monear polic rule will las for longer period; however is effec is relaivel small. Credi Consrained Consumers and Backward looking inflaion A sud b Kirsanova, Vines and Wren-Lewis (2006) has shown ha he sabili of such dnamic model depends on he naure of he inflaionar process, wheher Phillips curve is considered as a purel forward looking, backward looking or a combinaion of forward and backward price seers. If inflaion is forward looking, hen he econom will follow saddle pah equilibrium. However, if inflaion is backward looking (predeermined variable), hen here is a danger ha he econom will exhibi significan cclical behaviour which ma be unsable. The exen of his danger depends on he dependence of aggregae demand on he level of real ineres raes. In his par o be closer o reali, i is assumed ha some consumers are credi consrained, and he res are unconsrained consumers. The difference is ha he former are unable o borrow all he need o achieve heir opimal consumpion plan. Those consumers are consrained due o he imperfec and asmmeric informaion, as lenders do no have knowledge of human capial (expecaions abou fuure income of consumers). Accordingl he are no willing o lend consumers. As a resul consumers will no be able o implemen heir opimal consumpion plans. However, some 11

12 consrained consumers are willing o borrow so he will hold some deb. This case will moderae he impac of he borrowing consrain (Kirsanova e al., 2006). The proporion of credi consrained consumers is larger in developing counries wih undeveloped financial ssems. Equaion (1) in he model will be modified ino wo equaions one for consrained consumers u c affec aggregae demand and inflaion. c and he oher for unconsrained consumers c c.boh u c and Using differen values for he proporion of backward looking price seers as in Kirsanova, Vines and Wren-Lewis (2006), i was found ha he higher his proporion, he more unsable he model. The model s dnamic is ill cclical for lower proporions and his cclical movemen are no so obvious as he proporion of backward looking price seers decreases, however overshooing could sill occur wih he exisence of credi consrained consumers. As a resul backward looking inflaion differs from forward looking inflaion as he former help generaing inflaion momenum. Now consider one uni posiive shock o inflaion. As menioned before, he effec of such a shock when he Phillips curve is a purel forward looking, his shock iself had no effecs on fuure inflaion, and hen he econom reurns o is base equilibrium once he shock is over. However b assuming a backward looking inflaion, inflaion ineria is generaed and hen he same one uni posiive shock o inflaion will have implicaions on he fuure inflaion. Assuming he exisence of credi consrained consumers, his inflaion persisence will amplified, as higher inflaion will reduce hose consumers deb burden because he rise in inflaion will reduce he real value of heir ineres pamens, which will lead direcl o an increase in heir curren consumpion and herefore aggregae demand. The sronger he combinaion of inflaion persisence presened in backward looking Phillips curve and consrained consumers he higher he inflaion momenum. Credi consrained consumers pla a vial role in amplifing he inflaion persisence, unlike he case if all consumers are unconsrained. Higher inflaion will influence he expeced change in consumpion for unconsrained consumers raher han he level of consumpion for credi consrained consumers. If all consumers are unconsrained, he model will be sable, unless he case of a purel backward looking Phillips curve (Kirsanova e al., 2006). c IV- Conclusions: This assignmen has looked a he ineracion beween fiscal and monear polic when boh follow simple rules. I was found ha in a passive regime, monear polic should be more passive o secure sabili facing a consumpion shock. However, furher increase in fiscal acivism- in an acive regime facing a consumpion shock- generaes greaer disequilibria, however i is no radical. In oher words, he impac of changes in fiscal feedback is relaivel small and here is no need o respond immediael on a rapid fiscal correcion of deb equilibrium. For he emporar fall in oupu under an acive regime, he increase in fiscal feedback lead o generae greaer disequilibrium in oupu, however i dampen he rae of inflaion. When for he inflaion shock, i was found ha 12

13 increasing fiscal acivism helped he impac of inflaion shock o las for a longer period e is deviaion from he base is no a radical one. Changes he model assumpion b including a proporion of consumers, he changes in curren inflaion will affec he level of curren consumpion, no jus he expeced consumpion, and consequenl aggregae demand which changes he properies of he model. On he oher hand, he naure of he inflaionar process represened in Phillips curve (forward looking, backward looking or a combinaion of boh) is ver vial as i criicall delineaes he sabili of he dnamic of he model. Backward looking inflaion will generae inflaion ineria. Wih a proporion of backward looking inflaion and in he presence of credi consrained consumers, an inflaion shock will persis and amplified leading he econom o a cclical dnamic. The larger he credi consrained consumers proporion and he greaer he backward looking inflaion proporion, he more he cclical dnamic will appear (Kirsanova e al., 2006). 13

14 References: Calvo, G. (1983), Saggered Prices in a Uili Maximizing Framework, Journal of Monear Economics, vol.12 (3), pp Kirsanova, T., S. Sehn and D. Vines (2005), The Ineracions Beween Fiscal Polic and Monear Polic, Oxford Review of Economic Polic, Vol.21, No.4, pp Kirsanova, T., D. Vines and S. Wren-Lewis (2006), Credi Consrained Consumers, Inflaion Ineria and Insabili under Fixed Exchange Raes, Universi of Exeer, mimeo, available a Leih, C. and S. Wren-Lewis (2000), Ineracions beween Monear and Fiscal Polic Rules, The Economic Journal, 110, pp Woodford, M. (1996), Conrol of he Public Deb: A Requiremen for Price Sabili, Naional Bureau of Economic Research, Working Paper No