Moneary Insrumen Problem Revisied: The Role of Fiscal Policy Soyoung Kim Universiy of Illinois a Urbana Champaign Absrac The moneary insrumen problem is examined in an endowmen economy model wih various sochasic disurbances, wih minimizing he variance of inflaion as he policy objecive. Following curren developmens in he heory of fiscal deerminaion of he price level, for differen moneary policies, acive or passive fiscal policy is specified o guaranee a unique equilibrium. The responses of inflaion o various srucural disurbances in he consan money growh rae passive fiscal (he acive moneary passive fiscal regime, or he convenional regime where Ricardian equivalence and Quaniy Theory of Money hold) and he consan ineres rae acive fiscal regime (he passive moneary acive fiscal regime, or he regime where fiscal policy deermines he price level) are explained based on moneary and fiscal policies role in financing governmen defici changes and saisfying he governmen budge consrain in each regime, which is differen from he explanaions of pas research following Poole. One of ineresing findings is ha an increase in he seady sae real value of nominal governmen debs (bonds) reduces he variance of inflaion in he passive moneary acive fiscal regime. Published: 200 URL: hp://www.business.uiuc.edu/working_papers/papers/0 002.pdf
Moneary Insrumen Problem Revisied: The Role of Fiscal Policy by Soyoung Kim * Universiy of Illinois a Urbana-Champaign JEL Classificaion: E63, E52, E3 Keywords: moneary insrumen problem, variance of inflaion, fiscal policy, nominal governmen deb, fiscal deerminaion of he price level Absrac The moneary insrumen problem is examined in an endowmen economy model wih various sochasic disurbances, wih minimizing he variance of inflaion as he policy objecive. Following curren developmens in he heory of fiscal deerminaion of he price level, for differen moneary policies, acive or passive fiscal policy is specified o guaranee a unique equilibrium. The responses of inflaion o various srucural disurbances in he consan money growh rae-passive fiscal (he acive moneary-passive fiscal regime, or he convenional regime where Ricardian equivalence and Quaniy Theory of Money hold) and he consan ineres rae-acive fiscal regime (he passive moneary-acive fiscal regime, or he regime where fiscal policy deermines he price level) are explained based on moneary and fiscal policies role in financing governmen defici changes and saisfying he governmen budge consrain in each regime, which is differen from he explanaions of pas research following Poole. One of ineresing findings is ha an increase in he seady sae real value of nominal governmen debs (bonds) reduces he variance of inflaion in he passive monearyacive fiscal regime. * Universiy of Illinois, Deparmen of Economics, DKH, 225b, 407 W. Gregory Dr., Urbana, IL 0680, phone: (27) 265-0682, fax: (27) 333-398, e-mail: kim@uiuc.edu
. Inroducion The choice beween money and ineres rae as he moneary insrumen in he presence of differen srucural disurbances has long been discussed, even before Poole (970) s formalizaion. In his survey aricle, Friedman (989) explains he moneary insrumen problem as follows. The insrumen problem of moneary policy arises because of he need o specify how he cenral bank will conduc is open marke operaions. In paricular, he insrumen problem is he choice of a variable o be se direcly by he cenral bank via buying and selling securiies, and hence he value of which is o serve as he principal guide in carrying ou ha buying and selling funcion... In his explanaion, i is clear ha no only effecs of he changes in money or ineres rae bu also effecs of he changes in governmen securiies on he economy should be considered as a resul of open marke operaion. However, pas analyses following Poole (970), consider only one side of open marke operaion, changes in money and ineres rae. This probably is due o radiional analysis ha simplifies he governmen bond marke equilibrium by simplifying he consumer s choice beween governmen bond and money or by disregarding he implicaion of he governmen budge consrain. There have been recen heoreical developmens following Aiyagari and Gerler (985), Sims (988, 994), Leeper (99), and Woodford (995), which emphasize careful examinaions on he consumer s governmen bond holdings and he governmen budge consrain. These sudies asser ha here are wo equilibrium relaions deermining he price level; he one ha is consisen wih convenional models, and he oher ha depends on fiscal policy. These sudies incorporae he oher side of open 2
marke operaions. Based on hese sudies, his paper analyzes he role of fiscal policy on he choice beween money and ineres rae as he moneary insrumen. Following Leeper (99), moneary and fiscal policies are caegorized as acive or passive. The acive policy auhoriy ses policy variables wihou paying aenion o he governmen budge consrain while he passive policy auhoriy has he burden of saisfying he governmen budge consrain. Only when one of moneary and fiscal policies is acive (and he oher is passive), a unique equilibrium is obained. In paricular, a consan money growh rae policy is caegorized as an acive moneary policy so ha a passive fiscal policy is necessary for a unique equilibrium while a consan ineres rae policy is caegorized as a passive moneary policy so ha an acive fiscal policy is necessary. Pas research ha did no explicily specify fiscal policy and did no examine he implicaion of he governmen budge consrain proceeds in wo ways. Firs, he ineres rae pegging is claimed o lead o an indeerminacy in he raional expecaion model, for example, Sargen and Wallace (975) and Smih (988). Second, some special soluion mehods are used for he ineres rae pegging, for example, Parkin (978), McCallum (98, 983), Canzoneri e al (983). In conras, by specifying differen fiscal policies, his paper compares he consan money growh rae and he consan ineres rae policies in he model where a unique equilibrium is obained. Tha is, he consan money growh rae-passive fiscal regime and he consan ineres rae-acive fiscal regime are compared. In general, his paper compares he acive moneary-passive fiscal regime where moneary policy deermines he price level as in convenional models and he passive moneary-acive fiscal regime where fiscal policy deermines he price level as in he heory of fiscal deerminaion of he price level. To obain analyic soluions, a simple srucure of he model (an endowmen economy model wih he money-in-uiliy funcion framework) is assumed. Five kinds Appendix 2 provides some connecions beween he presen analysis and pas research. 3
of srucural disurbances are examined money demand shocks, aggregae demand shocks (discoun rae shocks), endowmen shocks, moneary policy shocks, and fiscal policy shocks. Since he producion side is simplified, policy regimes are compared in erms of he variance of inflaion, in conras o Poole (970) ha assumes a fixed price level and compares policies in erms of he variance of oupu. 2 When a fiscal policy is explicily specified o guaranee a unique equilibrium for each moneary policy, Poole s resuls and reasoning are no useful. The difference of he regimes resuls from he role of moneary and fiscal policy in financing governmen defici and saisfying he governmen budge consrain. Poole s resuls and reasoning are resriced o he acive moneary-passive fiscal regime; for example, a combinaion policy (using boh ineres rae and money growh rae) is no beer han he consan ineres rae policy in he passive moneary-acive fiscal regime. In addiion, some ineresing resuls are found. Firs, in he passive monearyacive fiscal regime, an increase in he seady sae real value of nominal governmen deb (bonds) reduces he variance of inflaion in he presence of money demand and endowmen shocks. In he regime, any shocks generaing changes in he presen value of ne governmen deficis are financed by inflaion ax, which depends on he seady sae real value of nominal governmen liabiliies (money and governmen bonds). An increase in he seady sae real value of nominal governmen bonds decreases he size of inflaion ha is required o collec he given amoun of inflaion ax. 2 The uiliy funcion defined in he model may be explicily used o evaluae he policy regimes. However, since an endowmen economy is assumed, here are no many ineresing welfare quesions and he welfare changes are minor. So, he variance of inflaion, which ofen shows up in he policy lieraure as one objecive, is used. In addiion, he resuls in he presen model are similar o hose in Poole (970) wih he policy objecive as minimizing he variance of inflaion, when we use a convenional soluion mehod, which does no ake care of he governmen budge consrain. Therefore, he resuls in his paper can be direcly compared o hose in Poole (970). Refer o Appendix 2. On he oher hand, following he radiion of moneary regime comparison wihin general equilibrium models (for example, Sargen and Wallace (982)), we compare a consan money growh rae rule and a consan ineres rae rule, in conras o sudies following Poole (970) ha choose beween money and ineres rae. A similar resul is obained when a consan money and a consan ineres rae rules are compared. 4
Second, using he resul ha he effecs of passive policy on he conemporaneous inflaion rae is almos null, we infer he following. ) I is beer for he auhoriy wih superior informaion on curren disurbances and srucural parameers and wih less implemenaion errors o be acive. 2) Only changes in he parameers of he acive policy can generae he radeoff in reducing he variance of inflaion in he presence of differen srucural disurbances. Beside he main objecive of he paper, as a by-produc, his paper provides careful examinaions on dynamics of he passive moneary-acive fiscal regime in he presence of differen srucural disurbances. I may be separae ineress o see how moneary and fiscal policies ineracs in response o differen srucural disurbances in order o saisfy he governmen budge consrain and wha are he effecs of differen srucural disurbances in he passive moneary-acive fiscal regime (or in he model of fiscal deerminaion of he price level). Secion 2 consrucs he model and reviews he meaning of acive and passive policies. Secion 3 compares he consan money growh rae-passive fiscal and he consan ineres rae-consan ax regimes. Secion 4 exends he analysis o general acive moneary-passive fiscal and passive moneary-acive fiscal regimes. Secion 5 concludes he paper wih fuure research subjecs. 2. The Model 2. The Srucure of he Model Each individual is endowed wih exogenous income each period. There is fia money and real money balance provides uiliy. For analyical racabiliy, we assume a log uiliy funcion in which consumpion and real money balance are separable. Each individual maximizes his lifeime uiliy subjec o his ineremporal budge consrain. Income is consiss of endowmens (Y) and gross ineres income receips from oneperiod nominal governmen bond holdings (R-B-/P, where B- is one-period nominal 5
governmen bond holdings, P is he price level, and R- is he gross ineres rae of he bonds). He allocaes his income o consumpion (C), changes in money holdings ((M- M-)/P), and nominal governmen bond holdings afer paying ne lump-sum ax (ransfer if negaive) o he governmen (τ). Each individual chooses C, M, and B, given P, Y, τ, V, K, and R. max M E β K logc + Vlog s.. =0 {C,M,B } P M M B R B τ Y () C + + + = P P where M 0, B 0 and Y, V, and K are i.i.d. processes., Firs order condiions of he consumer opimizaion problem are: VC P M = R and (2) R E CPK + = β. (3) C P K + + Equaion (2) is he money demand relaion and equaion (3) is an ineremporal version of he aggregae demand relaion. Therefore, we can inerpre V as money demand shocks and K as a kind of aggregae demand shocks (or discoun rae shocks). In response o a posiive shock in K, each individual becomes less paien and he demand for curren consumpion increases. The governmen should saisfy he budge consrain. I issues deb and money and collecs lump-sum (ne) ax (or ransfer if negaive). 6
M M P B R B + P - + τ = 0. (4) From he privae budge consrain and he governmen budge consrain, he social resource consrain is: Y=C. (5) The moneary auhoriy is assumed o conrol a combinaion of growh rae of money and ineres rae: 3 M α m + α rr = ρ + η. (6) M - αm= and αr=0 imply ha he moneary auhoriy fixes he money growh rae a ρ. On he oher hand, αm=0 and αr= imply ha he moneary auhoriy fixes he ineres rae a ρ. The fiscal auhoriy ses he ne ax level as a feedback rule from ousanding governmen bonds in real erms: 4 B τ = γ 0 + γ + µ. (7) P - The disurbance erms in he moneary and fiscal policy rules (η and µ, respecively) are inerpreed in wo ways. Firs, hey are inerpreed as implemenaion errors. The effec of implemenaion errors on he economy is also a sandard for 3 Moneary policy is described as choosing a combinaion of he ineres rae and he money growh rae, in order o examine he choice beween hem. This moneary policy can specify he complee region of acive and passive moneary policy. Sims (988) and Leeper (99) describe moneary policy as ineres rae seing rule in response o curren inflaion. Any combinaion of wo variables among money growh rae, ineres rae, and inflaion can specify he complee region. 7
comparing differen policy rules. Second, hey are inerpreed as discreionary policy. Under his inerpreaion, he effeciveness of discreionary policy in he presence of non-policy disurbances can be analyzed. 2.2. Seady Sae By defining h = M/M-, b = B/P, π = P/P-, and m = M/P, he seady sae relaions follow. π β R = (8) h=π (9) m = Y/V, YV m = (0) R γ 0 m π b = - + γ β () α m h + α rr = ρ (2) τ = γ 0 + γb (3) By choosing differen values of policy parameers (αm, αr, and ρ), he moneary auhoriy deermines he seady sae inflaion rae. Under specific values of αm and αr, by choosing an appropriae seady sae value of ρ, any inflaion rae can be achieved. 5 4 This fiscal policy rule, used by Sims (988) and Leeper (99) (similar rules are used in Aiyagari and Gerler (985) and Sims (994)), can describe he complee region of acive and passive fiscal policy rule. Oher fiscal policy rules such as he AR- rule of ne ax level also can describe he complee region. 5 When he moneary auhoriy fixes he money growh rae (αm=, αr=0, and h=ρ), he seady sae inflaion rae is ρ from equaion (9), R is deermined from equaion (8), m and V are deermined from 8
2.3. Specificaion of Fiscal Policies for he Unique Equilibrium The model is linearized around he seady sae. Using he seady sae relaions, he sysem of equaions is summarized as: h π + R = R + Y Y + V V (4) (R ) (R ) E π R = Y K (5) + b b β m m + + π R β bπ b(r ) m + R β bπ (R ) = m b m bπ ( Y + V ) + ( Y + V ) τ (6) hα h + Rα R = η (7) m r ττ = γ bb + µ (8) where each variable wihou subscrip is he seady sae values and each variable wih subscrip is he deviaion from he seady sae divided by is seady sae value (for boh policy shocks, hey are jus deviaions from he seady sae values, no divided by heir equaions (0) given Y. In his case, fiscal policy deermines only b and τ by choosing γ0 and γ. On he oher hand, in he case of he consan ineres rae rule (αm=0, αr=, and R=ρ), equaion (8) deermines he seady sae inflaion rae (βρ). Noe ha even in he case of he consan ineres rae rule, he fiscal auhoriy canno deermine he seady sae inflaion rae. The fiscal auhoriy only deermines he seady sae direc axaion and bonds. Noe ha he moneary auhoriy deermines he seady sae inflaion ax on money holdings and seignorage. In conras, from equaions () and (3), he fiscal auhoriy deermines he size of direc axaion. Inflaion ax on bond holdings is deermined from he seady sae inflaion rae se by he moneary auhoriy and bond holdings which can be conrolled by he fiscal auhoriy. 9
seady sae values). 6 When he policy auhoriies se he policy parameers (αm, αr, ρ, γ0, and γ) and he exogenous processes (K, Y, V, η, and µ)are realized, h, b, π, C (=Y), m, and R are deermined. The seady sae nominal ineres rae (R) is assumed o be greaer han, which implies he seady sae inflaion rae (π) and he seady sae money growh rae (h) are greaer han β from he seady sae relaions. 7 In his sysem, here are wo roos ha can lie ouside he uni circle, /β-γ and hrαm/(hαm+rαr-r 2 αr). Since his sysem includes only one expecaional erm (E-π), only one roo should lie ouside he uni circle o have a unique equilibrium. 8 While he firs roo depends on he fiscal parameer γ, he second roo depends on moneary parameers αm and αr. When he firs roo lies ouside he uni circle and he second roo lies inside, he fiscal auhoriy has he burden of keeping he governmen budge consrain saisfied by changing he ne ax level in response o governmen defici changes (acive moneary-passive fiscal policy). 9 On he oher hand, when he firs roo lies inside he uni circle and he second lies ouside, he moneary auhoriy saisfies he governmen budge consrain by changing he growh rae of money and by collecing seignorage and inflaion ax (passive moneary-acive fiscal policy). In he firs case, Quaniy Theory of Money and Ricardian Equivalence hold as in convenional models 6 Equaion (4), (5), and (7) can be expressed wih m insead of h. I use h o simplify he moneary policy equaion (7). 7 Firs, i makes he seady sae governmen bond and money holdings posiive (equaion (0)). Second, when R is less han, he behavior of he sysem is unusual in he sense ha he demand for (he growh rae of) real money balance is an increasing funcion of he ineres rae (from equaion (4)). Third, we can inerpre a money growh rae rule as an acive moneary policy wihou reference o he seady sae value (Refer o he nex secion). 8 This is he condiion from Blanchard and Kahn (980). In general, we need addiional condiions found by Sims (995). In he presen model, he condiion from Blanchard and Kahn (980) is a necessary and sufficien condiion for a unique equilibrium. 9 More precisely, he firs roo needs o be less han /β. When he firs roo is equal or greaer han and less han /β, real deb (and ax) explodes bu his equilibrium violaes neiher he ransversaliy condiion nor he feasibiliy condiion. Refer o McCallum (983) and Sims (995). Here, I exclude his equilibrium for simpliciy. Also, his equilibrium seems unrealisic. 0
while in he second case, he inflaion rae depends on he oal governmen liabiliies and fiscal policy. 0 In conras o pas research on he moneary insrumen problem, acive or passive fiscal policy is specified in order o guaranee a unique equilibrium under a paricular moneary policy. Firs, a consan money growh rae policy implies ha he second roo (R) lies ouside he uni circle and he moneary auhoriy canno change he money growh rae in order o collec seignorage and inflaion ax in response o governmen defici shocks. In his case, o guaranee a unique equilibrium, fiscal policy should be passive or he fiscal parameers should lie in he range of /β-γ < (he second roo lies inside he uni circle). Tha is, fiscal policy should adjus ne ax level enough o saisfy he governmen budge consrain in response o governmen defici changes. However, in he case of a consan ineres rae policy, acive fiscal policy should be specified for a unique equilibrium. Since he second roo (0 since αm=0) lies inside he uni circle, he firs roo should lie ouside he uni circle o achieve a unique equilibrium ( /β-γ > ). Tha is, fiscal policy does no adjus enough so ha he moneary auhoriy should collec seignorage or inflaion ax o saisfy he governmen budge consrain. 3. Consan Money Growh Rae-Passive Fiscal Regime vs. Consan Ineres Rae- Consan Tax Policy Regime In his secion, he consan money growh rae-passive fiscal and he consan ineres rae-consan ax regimes are compared. I assume ha he policy objecive is 0 In he firs case, he equilibrium inflaion rae is deermined from equaions (4), (5), and (7) wihou referring o equaions (6) and (8). Equaions (6) and (8) deermine ne ax level and he real governmen deb only. In conras, in he second case, he equilibrium inflaion rae is deermined from equaions (5), (6), (7), and (8). Equaion (4) deermines he growh rae of money only. The consan ax policy is chosen as he represenaive case of acive fiscal policies since he consan ax policy implies ha he fiscal auhoriy does no change ax in response o governmen defici changes. In
minimizing he variance of inflaion under differen sources of disurbances, given he seady sae inflaion rae. 2 Five kinds of disurbances are considered -- money demand shocks, aggregae demand shocks (discoun rae shocks), endowmen shocks, moneary policy shocks, and fiscal policy shocks. 3 Finally, he policy auhoriies are assumed no o have informaion on he curren disurbances excep for he case ha moneary policy shocks and fiscal policy shocks are considered as discreionary policy on curren disurbances. 4 3.. Equilibrium From he linearized sysem (equaions (4)-(8)), soluions are obained following Sims (995). The complee soluions in boh regimes are repored in Appendix 2. In he case of he consan money growh rae-passive fiscal regime, he soluion for inflaion is: R V V Y Y h R K = ( ) ( ) + + ( K ) π η - (9) In his regime, he effecs are he same as hose in he convenional models in which Quaniy Theory of Money and Ricardian Equivalence hold. A posiive money demand and a posiive endowmen shock decrease he inflaion rae while a posiive aggregae demand shock increases he inflaion rae. In he nex period, since he money growh addiion, soluion is simple under he consan ax policy, compared o oher acive fiscal policies. In Secion 4, more general forms of acive fiscal policies are analyzed. 2 The mean of inflaion rae (or seady sae inflaion rae) is no considered as a policy objecive since boh regimes (in general, any policy combinaion ha can achieve a unique equilibrium in his model) can achieve any seady sae inflaion rae by adjusing he consan erm (ρ). Refer o Secion 2.2. 3 The opimal policy rule is no formally derived since he objecive of he analysis is o reexamine he moneary insrumen problem and Poole (970) s resuls by considering he implicaion of governmen budge consrain and fiscal policy. Furher major insighs do no seem o be obained by deriving opimal policy rule formally. 4 In some cases, we do no discuss he lagged effecs. If he policy auhoriy is allowed o se up a feedback rule on lagged variables which offses he lagged effecs, hen only conemporaneous effecs maer. In addiion, once no serial correlaions of he srucural disurbances are assumed, here are only few cases where he lagged effecs change he qualiaive conclusion in he presen analysis. Therefore, in some cases where he lagged effecs do no change he resuls much, we do no discuss he lagged effecs. 2
rae and he seady sae inflaion are consan, he price level reurns o he original growh pah. Tha is, he absolue values of he firs and second period inflaion raes are he same, bu hey have opposie signs. However, moneary policy shocks (money growh rae shocks) have only conemporaneous effecs. In response o moneary policy shocks, he price level does no reurn o he original growh pah in he second period because he money sock jumps from he original growh pah. Noably, fiscal policy (neiher fiscal policy shocks nor he seady sae values of b, τ, γ0, and γ) does no have any effecs. 5 In he case of he consan ineres rae-consan ax regime, he soluion for inflaion is: βm(r -) β β π β η- µ β - m+br V mr ) m+br Y Y R = K K ( + + + R + (20) m+br For his regime, deailed explanaions are provided since he effecs are differen from hose in convenional models. In response o a posiive money demand shock (V), since he ineres rae is consan, he money growh rae and he real money balance (from equaion (4)) increase, and seignorage increases. Since ne ax is consan in his regime, he moneary auhoriy should offse he increase in seignorage by negaive inflaion ax in order o saisfy he governmen budge consrain. Therefore, he curren βm(r -) inflaion rae decreases. The size of he inflaion rae decrease depends on m+br he seady sae real balance (m) and he seady sae real value of oal nominal governmen liabiliies or overall inflaion ax base (money and gross ineres paymen of bonds, m+br). This is because he real money balance deermines he iniial increase in seignorage and he oal governmen liabiliies deermines he amoun of inflaion ax 5 Fiscal policy does no have effecs on any variables excep for fiscal variables. Refer o Appendix. 3
ha is colleced by he inflaion decrease. The larger he seady sae real value of nominal governmen bond holdings is, he smaller he changes in he inflaion rae. A posiive aggregae demand shock (K) increases he curren inflaion rae, which generaes a posiive inflaion ax oday. This increase in inflaion ax should be offse by negaive inflaion ax. Therefore, in he nex period, here is a deflaion. 6 Noe ha he changes in he inflaion rae (β) do no depend on he size of nominal governmen liabiliies. This is because he iniial inflaion is generaed from he disurbance, no from he moneary reacion o a disurbance changing governmen defici in order o collec inflaion ax. Endowmen shocks (Y) aler boh goods marke and money marke equilibria, so he effecs are he combinaion of he effecs of a negaive aggregae demand and a posiive money demand shock. Fiscal policy shocks affec he inflaion rae conemporaneously. In response o a posiive ne ax shock (µ), he moneary auhoriy generaes a deflaion and collecs a negaive inflaion ax (he size of which depends on he seady sae real value of oal governmen liabiliies (m+br)) o saisfy he governmen budge consrain. Moneary policy shocks (η) have only lagged effecs on he inflaion rae. They aler only he composiion of governmen liabiliies (an increase in bond holdings and a decrease in he real money balance, caused by an increase in he nominal ineres rae), bu no he size of he oal governmen liabiliies, which deermines he curren inflaion rae. In he nex period, he inflaion rae increases and inflaion ax is colleced o offse he increased deb service. The seady sae governmen liabiliies do no affec he size of he lagged inflaion change because boh he inflaion ax collecion and he increased deb service are affeced by he seady sae governmen liabiliies and hey are canceled ou. 3.2 Comparison 6 Noe ha he discouned value of he deflaion in he nex period is equal o he curren inflaion. 4
In his secion, wo regimes are compared, wih minimizing he variance of inflaion as he policy objecive. Table (a) repors resuls when he seady sae inflaion rae is one (π=) and he seady sae governmen bond holdings are zero (b=0). Table (b) repors general resuls. In each case, conemporaneous and lagged effecs are repored separaely. The firs column shows he ype of disurbances. The second and he fourh columns repor he inflaion responses in he consan money growh-passive fiscal and he consan ineres rae-consan ax regimes, respecively. The hird column under rel. var. compares he size of inflaion responses (absolue values) in wo regimes. > ( < ) implies ha he inflaion response is larger (smaller) in he consan money growh-passive fiscal regime han in he consan ineres raeconsan ax regime. b, π, and b, π in Table (b) imply ha he resuls depend on he seady sae value of b, π, and boh b and π, respecively. The effecs of non-policy disurbances are examined firs. 7 When π= and b=0, he conemporaneous effecs on he inflaion rae are he same in boh regimes. However, in some sense, he consan ineres rae policy is beer in he presence of money demand shocks while he consan money growh rae policy is beer in he presence of aggregae demand shocks, as in Poole (970), even hough he reasoning is differen; The difference in wo regimes resuls from differen mehods of financing governmen defici changes. Firs, in erms of he lagged effecs, resuls are similar o hose of Poole (970). In he presence of aggregae demand (money demand) shocks, he lagged inflaion response is smaller (larger) in he consan money growh rae-consan ax regime (he consan ineres rae-acive fiscal regime), and he consan money growh rae-consan ax regime (he consan ineres rae-acive fiscal regime) is beer. In addiion, in he presence of money demand shocks, he variance of inflaion can be reduced by non-zero 7 We skip he resuls on he endowmen shocks since he inflaion response in he presence of endowmen shocks are he same as he one in he presence of boh a negaive aggregae demand and a posiive money demand shock. 5
seady sae governmen bond holdings in he consan ineres rae-consan ax regime, since non-zero seady sae governmen bond holdings increase inflaion ax base (shown in Table (b) and equaion (20)). 89 As discussed in he previous secion, hese differences resul from he differen mehod of financing governmen defici changes in each regime. Table (b) shows ha in general, which regime is beer depends on he value of π or/and b. The effecs in each regime depends on he seady sae inflaion rae. 20 More ineresingly, he effecs in he consan ineres rae-consan ax regime depends on he seady sae real value of nominal governmen bond holdings (We provide deailed explanaions for his in he nex secion.). Again, he difference beween hese wo regimes resuls from differen mehods of financing governmen defici changes. 8 Noe ha he fiscal auhoriy can choose differen values of he seady sae governmen bond holdings by choosing γ 0 and γ. Refer o he seady sae relaions in Secion 2.2 and foonoe 5. 9 We discuss how serial correlaion of shocks (wihou any couner-cyclical policy on lagged effecs) affecs he resuls (when π and b are zero). In he consan money growh rae-passive fiscal regime, in response o non-moneary policy shocks, he price level reurns o he original growh pah in he nex period. However, in he consan ineres rae-consan ax regime, he price level does no. Firs, in he case of money demand shocks, he lagged effec is zero in he consan ineres rae-consan ax regime. In his case, a negaive (a high posiive) correlaion of he shocks resuls relaively large reducion of he variance of he inflaion rae in he consan money growh rae-passive fiscal regime (he consan ineres rae-consan ax regime). Second, in he case of aggregae demand shocks, he lagged effec becomes even larger han he curren effec in he consan ineres rae-consan ax regime. In his case, any serial correlaion does no make he consan ineres rae-consan ax regime beer han he consan money growh rae-passive fiscal regime. 20 In he consan money growh rae-passive fiscal regime, as he seady sae inflaion rae (and he seady sae nominal ineres rae) increases, he ineres rae elasiciy of money demand decreases (equaion (4)). So, he inflaion rae changes more in response o money demand shocks. Bu in response o aggregae demand shocks, he inflaion rae changes less since less offseing effecs work as a resul of he decrease in he ineres rae elasiciy of money demand. (A posiive aggregae demand shock increases demand for curren consumpion, so he curren inflaion increases bu he curren increase in inflaion is offse by an increase in he demand for real money balance due o he increase in he demand for curren consumpion.) In he consan ineres rae-consan ax regime, as he seady sae inflaion rae increases, he elasiciy of inflaion wih respec o he real money balance increases and he inflaion response increases in he presence of money demand shocks. (We can see his elasiciy by ransforming equaion (6) o an equaion wih m insead of h.) Therefore, he fundamenal difference beween wo regimes resuls from wheher equaion (4) or equaion (6) is used o deermine he price level, ha is, from differen mehods of financing governmen defici changes. 6
We can also compare hese wo regimes based on he effecs of policy shocks. Firs, hose shocks are inerpreed as implemenaion errors, and we choose he regime ha does no allow hose errors o affec inflaion much. In he consan money growh rae-passive fiscal regime, implemenaion errors in fiscal policy do no affec he inflaion rae. In he consan ineres rae-consan ax regime, implemenaion errors in moneary policy have only lagged effecs on inflaion rae, which may be offse by fiscal discreion. Therefore, when here are implemenaion errors in fiscal policy (moneary policy), he consan money growh rae-passive fiscal regime (he consan ineres rae-consan ax regime) is beer. Tha is, i is beer for he auhoriy wih less implemenaion errors o be acive. Second, hose shocks are inerpreed as discreion or couner reacions o curren disurbances under he assumpion ha policy auhoriies have some informaion on curren disurbances and srucural parameers. 2 Since only he acive policy can have conemporaneous effecs on he inflaion rae, only he acive auhoriy can effecively perform discreionary policy agains curren disurbances. Even wih curren informaion on disurbances, he passive auhoriy canno reduce he variance of inflaion. Therefore, if boh policy auhoriies have curren informaion on he disurbances and srucural parameers bu one has beer informaion han he oher, hen i is beer for he auhoriy wih beer informaion o be acive. In summary, Poole (970) s basic resuls do no necessarily hold in his model. Even when he resuls are similar, he reasoning is differen: he resuls are based on he role of moneary and fiscal policies in financing governmen defici changes and saisfying he governmen budge consrain in each regime. In addiion, here are some ineresing findings. Firs, i is beer for he auhoriy wih superior informaion and less implemenaion errors o be acive. Second, he variance of inflaion depends on he 2 Of course, when boh auhoriies have exac informaion on curren disurbances (also if hey know he srucural parameers), hen hey can perfecly offse changes in inflaion rae due o curren disurbances. 7
seady sae real value of nominal governmen deb (bonds) in he consan ineres raeconsan ax regime. In he nex secion, he laer resul is discussed in deails. 3.3. Nominal Governmen Deb (Bonds) Reduces he Variance of Inflaion In he consan ineres rae-consan ax regime, an increase in he seady sae real value of nominal governmen deb (bonds) reduces he variance of inflaion in he presence of money demand shocks, endowmen shocks, and fiscal policy shocks. 22 Any shocks alering he presen value of he governmen defici are financed by inflaion ax in his regime, which in urn depends on oal nominal governmen liabiliies. When nominal governmen bond holdings increase, oal nominal governmen liabiliies increase, and he size of inflaion required collecing he given amoun of inflaion ax decreases. In Woodford (995) s erm, when here are larger nominal governmen liabiliies, wealh effecs from holding he governmen liabiliies per changes in he inflaion rae become larger and he size of changes in he inflaion rae becomes smaller when here is a shock ha needs differen level of equilibrium inflaion rae. Then, we may claim ha larger seady sae nominal governmen deb is beer for reducing he variance of inflaion since he seady sae nominal governmen deb does no have any effecs on he variance of inflaion in oher cases (he consan ineres rae-consan ax regime in he presence of aggregae demand shocks and moneary policy shocks, and he consan money growh rae-passive fiscal regime in he presence of any ypes of shocks). 23 22 When we inerpre he fiscal policy shocks as implemenaion errors, if we assume ha implemenaion errors become larger as he seady sae ax level increases, hen here may be an opimal size of nominal governmen deb (in he presence of fiscal policy implemenaion errors) since an increase in he seady sae governmen deb decreases he variance of inflaion hrough smaller inflaion given he required inflaion ax bu increases he variance of inflaion hrough larger seady sae governmen ax level and larger implemenaion errors. For example, if we assume ha he implemenaion errors (he size of fiscal policy shocks) are proporional o he seady sae governmen ax level, hen he opimal size of governmen deb is m(βr-)/(r(-β)). 23 The sraegy of large seady sae nominal governmen deb o reduce he variance of inflaion may be especially valuable when policy auhoriies do no have an exac idea on he curren regime or he naure of disurbances in he economy. Oher sraegies need some informaion on he naure of major disurbances in he economy and if he informaion is no precise, hen here may be some coss. In 8
Some pas research suggess ha large governmen deficis are responsible for high inflaion when i is moneized or even when i is financed by governmen bonds. As Leeper (99) emphasized, he disincion beween wo policy regimes in his paper is based on he mehod of financing defici changes, ha is, he marginal finance mehod, and no based on he average level of finance. In he model, a negaive µ, and governmen defici changes due o oher srucural shocks, increase he inflaion rae in he consan ineres rae-consan ax regime since he moneary auhoriy finance he defici changes by collecing inflaion ax, bu he seady sae inflaion does no change and he inflaion rae increase is only emporary. 24 On he average finance level, in he passive moneary-acive fiscal regime, governmen deficis are already backed by seignorage and direc axaion. 25 Therefore, he finding can be rephrased as: a larger conras, his sraegy works wihou any coss. In addiion, his sraegy does no require any knowledge on srucural parameers. In oher words, his sraegy is no an empirical maer in he presen model. On he oher hand, his resul may serve as a favorable argumen for non-indexed governmen bonds. If he governmen indexes some facions of bonds, hen he policy auhoriy canno collec inflaion ax from he indexed bond holdings. Therefore, in response o disurbances changing governmen deficis, larger changes in inflaion is required and he variance of inflaion becomes larger. Bohn (988) also provides a reason for non-indexaion. Under he assumpion ha welfare losses from disorionary axaion is a convex funcion of he ax rae, a smooh pah for ax rae changes or a smaller variance of ax raes is opimal. In he case of real shocks ha increase governmen deficis and increase inflaion, inflaion ax compensaes for he governmen deficis. The larger he nominal governmen bonds, he larger he inflaion ax, he smaller he variance of direc ax, and he larger he welfare. Therefore, in his model, governmen nominal deb is a device for hedging. As he emphasized, his argumen is based on assumpions on disorionary axaion. In conras, in he presen analysis, even wihou he assumpion of disorionary axaion, nonindexed governmen bonds can be beer han indexed governmen bonds. Bu, he assumpion of disorionary direc axaion may work as a couner argumen agains non-indexed bonds in he presen model. As in equaions () and (3), larger seady sae governmen bond implies larger seady sae direc axaion and here may be some penalies or disorions when he seady sae nominal governmen bonds increase. Therefore, in he model wih disorionary direc axaion, he opimal size of governmen deb requires ha he marginal coss of nominal governmen deb (from disorion) and he marginal benefi of nominal governmen deb (from reducing he variance of inflaion) are equalized. In addiion, as discussed in a previous foonoe, if he implemenaion errors of fiscal policy increase as he size of seady sae governmen direc axaion increases, hen his increase in implemenaion errors will generae larger variance of he inflaion rae, and hus here will be anoher penaly incurred wih larger seady sae nominal governmen deb. 24 Remember ha any seady sae level of inflaion can be achieved by differen values of ρ. 25 Refer o foonoe 5. 9
nominal governmen deb is beer for reducing he variance of inflaion in he passive moneary-acive fiscal regime when he governmen deb is fully backed. 26 4. Exension: Acive Moneary-Passive Fiscal Regime vs. Passive Moneary-Acive Fiscal Regime This secion exends he analysis o general comparison beween he acive moneary-passive fiscal regime and he passive moneary-acive fiscal regime by allowing αm, αr, and γ o be non-zero. When non zero αr (/(R(R-)) αr > -/R) is allowed, he inflaion rae in he acive moneary-passive fiscal regime (afer normalizing αm as /h ) is: π = ( ) α ( ) ( ) η ( ) ( ) - R V V R V Y Y R K K α R K r + + r Now, he relaive effecs of money demand shocks and aggregae demand shocks change. There is a radeoff. By increasing he negaive (posiive) weigh on ineres rae, he variance of inflaion due o money demand shocks decreases (increases), bu he variance of inflaion due o aggregae demand shocks increases (decreases). The minimum variance in he presence of money demand shocks is achieved when αr is close o -/R while he minimum variance in he presence of aggregae demand shocks is achieved when αr is /(R(R-)). We can derive he opimal policy ha reduces overall variance of inflaion once he relaive variance of each shock is specified. The resul is consisen wih Poole (970), in he sense ha a combinaion policy (using boh ineres rae and money growh rae) dominaes he pure ineres rae pegging or he 26 Aiyagari and Gerler (985) suggesed ha in he region of a paricular ype of acive fiscal policy (heir non-ricardian regime ), inflaion rae and he price level are higher. The exac definiion of heir non- Ricardian regime is differen from he definiion of an acive fiscal policy in his paper. Again, any seady sae inflaion rae can be achieved in boh regimes of he presen analysis. 20
pure money (growh rae) pegging. Also, noe ha he fiscal parameers and fiscal policy shocks sill do no have any effec on he inflaion rae in his regime. In he case of he passive moneary-acive fiscal regime, we repor he resul from allowing eiher non-zero αm or non-zero γ, bu no boh since he soluion is very complicaed when boh parameers are allowed o be non-zero and since some basic inuiions can be obained wihou doing ha. When non-zero αm ((R-)/(h(R+)) αm -/h) is allowed, he inflaion rae in he passive moneary-acive fiscal regime (afer normalizing αr as /R) is: π = s= hα mr R--hα m -s βm(r -) h α m(r-)( m+ βm+ br) h α m (R-) Vs Vs- + V m+br (R -- h α m )(m + br) R--hαm βrm ( + b) αm β α m s s- m+br Y h (R-)( m+ m+ br) h + Y (R -- h α m )(m + br) R--hαm hα mr + Ys-2 R--hαm hα m R hαm( + β ) + βks + Ks Ks 2 R--hαm R--hαm R h mr R β m+br α R--h m β µ s µ s α m+br h αm (R-) βr R- + 2 + (R--hα m+br-br β +mr β ) µ s η )( (R -- hα ) R m m s-2 s- The curren effec of each shock on he inflaion rae is exacly he same as in he consan ineres rae policy case and αm does no affec conemporaneous inflaion a all. Therefore, in erms of he conemporaneous response of he inflaion rae, we do no observe any radeoffs by changing αm and a combinaion policy is no beer han he pure ineres rae pegging, which is differen from he resuls of Poole (970). 27 27 There are prolonged lagged effecs of disurbances on he inflaion rae. So, even in erms of lagged responses of he inflaion rae, he pure ineres rae pegging dominaes he combinaion policy. The reason for he delayed effecs is ha he moneary auhoriy sill collecs he same size of inflaion ax in he curren period, which needs he same size of inflaion and he same size of he increase in he growh rae of money. Bu since he moneary auhoriy conrols only he combinaion of money growh rae and 2
On he oher hand, as in he consan ineres rae-consan ax regime, an increase in he seady sae nominal governmen deb decreases he variance of he inflaion rae in his regime, regardless of he value of αm. In addiion, moneary policy shocks sill have only delayed effecs on inflaion rae. When non-zero γ is allowed ( /β-γ > ), he inflaion rae is: b βmr- βr β ( β - γ ) β ( β - γ ) +m π = V Y m+br m+br + Y βγm βr + η η µ + ( β - γ )(R-)(m+ br) R + m+br ( β - γ ) K K - - Now changes in he fiscal parameer γ generae he radeoff beween reducing he variance of inflaion due o money demand shocks and reducing he variance of inflaion due o aggregae demand shocks. Also, by allowing non-zero γ, he variance of inflaion may be reduced. 28 In he passive moneary-acive fiscal regime, here are neiher he radeoff nor he possibiliy of reducing he inflaion rae when moneary parameers are changed, bu here are he radeoff and he possibiliy when fiscal parameers are changed. Also, as in he previous case, an increase in he seady sae nominal governmen deb decreases he variance of he inflaion rae, regardless of he value of γ. On he oher hand, now moneary policy shocks have curren effecs on he inflaion ineres rae, he ineres rae also changes. This change in he ineres rae changes he deb service nex period, and i is financed by inflaion ax in he nex period, which changes he deb service in he following period and so on. 28 For example, when /β - > γ > 0, pars of he governmen defici shocks are financed by direc ax in he nex period. As a resul, in response o money demand shocks, he amoun of necessary inflaion ax decreases, and variance of inflaion decreases. In conras, in he case of aggregae demand shocks, he variance of inflaion increases. In response o aggregae demand shocks, real bond holdings decrease, which leads o direc ax decreases in he nex period. Therefore, o offse he nex period direc ax decrease, he increase in he curren inflaion should be larger han he previous case. When /β-γ is close o /(Rβ), he variance due o money demand shocks are minimized. As /β-γ increases, he variance due o aggregae demand shocks and endowmen shocks become smaller. 22
rae, bu he discreionary moneary policy offseing he effecs of curren disurbances is sill no simple. I requires he exac informaion on fiscal policy parameer γ, in addiion o he informaion on disurbances and oher srucural parameers. Especially, he sign of he inflaion rae response o moneary policy shocks is sensiive o γ. When he fiscal auhoriy ses γ close o zero bu he moneary auhoriy is no sure of he sign of γ, he moneary auhoriy canno perform he appropriae discreionary policy even wih he precise knowledge of he naure and size of curren disurbances and oher srucural parameers. In summary, previous findings can be generalized. Firs, he difference of wo regimes resuls from he role of moneary and fiscal policies in financing he governmen defici changes and saisfying he governmen budge consrain. Second, an increase in he seady sae real value of he nominal governmen bonds decreases he variance of he inflaion rae in he passive moneary-acive fiscal regime. Third, i is beer for he policy auhoriy wih beer informaion and wih less implemenaion errors o be acive. In addiion, here is a new finding a combinaion policy is beer han he pure ineres rae or he pure money growh rae pegging in he acive moneary-passive fiscal regime, bu no in he passive moneary-acive fiscal regime. Poole (970) s resuls and reasoning hold only in he acive moneary-passive fiscal regime, no in he passive moneary-acive fiscal regime. 5. Conclusion By consrucing an endowmen economy model wih various sochasic disurbances, which specifies fiscal policy explicily o guaranee a unique equilibrium, he moneary insrumen problem is examined, wih minimizing he variance of inflaion as he policy objecive. As in Poole (970), which regime is beer depends on he naure of disurbances, and he choice of he opimal policy regime is an empirical maer. However, Poole (970) s exac resuls and reasoning do no apply, especially in 23
he passive moneary-acive fiscal regime. Difference of inflaion responses in differen regimes should be explained by he role of moneary and fiscal policies in financing he governmen defici changes and saisfying he governmen budge consrain in each regime. Fuure research on he comparison beween he acive moneary-passive fiscal and he passive moneary-acive fiscal regime under more general seup may be ineresing. Firs, comparison in he model wih nominal rigidiies using boh oupu and inflaion variabiliy or formal welfare crierion as he policy objecive seems o be fruiful. 29 Second, he model wih disorionary axaion may be anoher direcion. 29 See Leeper (993) for some simulaion resuls. 24
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