Leith, C., Moldovan, I., and Rossi, R. (2014) Monetary and fiscal policy under deep habits. Journal of Economic Dynamics and Control.

Transcription

1 nn Leih,., Moldovan, I., and Rossi, R. 214) Moneary and fiscal policy under deep habis. Journal of Economic Dynamics and onrol. ISSN opyrigh 214 The Auhors hp://eprins.gla.ac.uk/1634/ Deposied on: 17 December 214 Enlighen Research publicaions by members of he Universiy of lasgow hp://eprins.gla.ac.uk

2 Auhor's Acceped Manuscrip Moneary and fiscal policy under deep habis ampbell Leih, Ioana Moldovan, Raffaele Rossi PII: DOI: Reference: S )32-9 hp://dx.doi.org/1.116/j.jedc DYNON313 To appear in: Journal of Economic Dynamics & onrol Received dae: 16 March 214 Revised dae: 6 November 214 Acceped dae: 7 November 214 ie his aricle as: ampbell Leih, Ioana Moldovan, Raffaele Rossi, Moneary and fiscal policy under deep habis, Journal of Economic Dynamics & onrol, hp: //dx.doi.org/1.116/j.jedc This is a PDF file of an unedied manuscrip ha has been acceped for publicaion. As a service o our cusomers we are providing his early version of he manuscrip. The manuscrip will undergo copyediing, ypeseing, and review of he resuling galley proof before i is published in is final ciable form. Please noe ha during he producion process errors may be discovered which could affec he conen, and all legal disclaimers ha apply o he journal perain.

3 Moneary and Fiscal Policy under Deep Habis 1 ampbell Leih 2 Ioana Moldovan 3 Raffaele Rossi 4 1. Inroducion Deep habis see Ravn, Schmi-rohe and Uribe, 26 and 212), which occur a he level of he individual goods, raher han oal household consumpion, can improve he empirical performance of sandard DSE models in various dimensions. Aside from replicaing he hump-shaped response of key variables o moneary policy shocks and adding inerial behavior more generally as do oher forms of habis), hey also imply, consisenly wih he daa, counercyclical markups and he crowding in of privae secor consumpion following increases in governmen spending. The laer propery raises he governmen spending muliplier from well below one in he benchmark New Keynesian model, o above one.,6 The ineremporal naure of he pricing problem for firms, which face a dynamic demand curve as a resul of deep habis, furher implies ha he ransmission mechanism of moneary policy is alered oo, wih moneary policy affecing pricing decisions direcly. Finally, deep habis, which are of an exernal ype, imply ha he disorions presen in he modelled economy, which effecively define he rade-offs facing he policy maker, are significanly differen from hose ypically found in New Keynesian models. In his paper, we explore he implicaions for opimal moneary and fiscal sabilizaion policy of inroducing his new disorion o policy making and he implied fundamenal changes in he macroeconomic response o shocks. We now urn o moivae our exploraion of he policy problem under deep habis more fully, before oulining he key resuls and plan of he res of he paper. An alernaive, commonly used exension o he benchmark model which is designed o achieve he crowding in of privae consumpion is o assume a proporion of households only consume ou of curren income and neiher borrow nor save - see ali, Lopez-Salido, and Valles, 27) and Bilbiie, 29). We prefer o use he deep habis device for boh heoreical and empirical reasons. While he assumpion ha some households are credi consrained may be jusifiable, precluding he possibiliy of saving seems less so. Moreover, olciago, 211) argues ha he mechanism hrough which he crowding in occurs and he number of households ha mus be hand-o-mouh consumers for he crowding in effec o be achieved are no consisen wih he daa. 6 Recen work looking a opimal moneary and fiscal policy in sicky-price New Keynesian models see, for example, Schmi-rohe and Uribe, 24a) and Benigno and Woodford, 23)) ypically finds ha fiscal policy should be largely devoed o ensuring fiscal solvency, while moneary policy plays a demand managemen role. However, such models conain he usual crowding ou effecs from public consumpion such ha he efficacy of fiscal policy as a sabilizaion device may be hough o necessarily be limied. Preprin submied o Elsevier November 24, 214

4 Lieraure on Deep Habis Empirical evidence generally finds ha oupu, consumpion and real wages increase in response o an unexpeced increase in governmen spending, see iner alia Faas and Mihov, 21), Blanchard and Peroi, 22), ali, Lopez-Salido, and Valles, 27), Zubairy, 21b), Zubairy, 21c), and Ravn, Schmi-rohe, and Uribe, 212). onrary o his evidence, sandard Real-Business ycle models, for example Baxer and King, 1993), and New Keynesian models, such as Faas and Mihov, 21), find insead a crowding ou effec: privae consumpion falls afer a posiive governmen spending shock. This resul comes from he fac ha afer a governmen spending shock households face a negaive wealh effec and ineviably lower heir consumpion and increase hours worked. The increase in labor supply also causes real wages o fall, anoher resul a odds wih he empirical evidence. Ravn, Schmi-rohe, and Uribe, 26) show ha he crowding in effec of public spending on privae consumpion can be induced in a sandard RB model where firms have some monopolisic power and agens preferences conain deep habis in consumpion of individual goods. Deep habis imply a downward-sloping demand funcion ha depends on he lagged level of consumers purchases of ha specific good. Since firms ake his demand funcion as a consrain in heir opimal price-seing problem, deep habis have pronounced implicaions for aggregae supply. In paricular, he inelasic par of he demand funcion due o he impac of consumers pas purchases of a specific good, implies ha, ceeris paribus, an increase in demand for he good, generaes an incenive for firms o lower markups. Hence, deep habis can successfully mimic he counercyclicaliy of firms markups generally found in he daa. Accordingly, an increase in governmen spending, which raises aggregae demand, leads o a decline in firms markups. This shifs he labor demand curve ouward, increasing real wages. In urn, he rise in wages induces households o subsiue consumpion for leisure. A plausible esimaes of he degree of deep habis, his subsiuion effec may be srong enough o offse he negaive wealh effec coming from he increase in public consumpion, resuling in an equilibrium increase in privae consumpion, see Ravn, Schmi-rohe and Uribe 26, 212) and Zubairy, 21b). When considering deep habis in an open economy conex, Ravn, Schmi-rohe and Uribe 212) find ha a wo-counry RB model augmened wih deep habis can no only provide a raionale for he counercyclical markup and increase in privae consumpion, bu also for an iniial depreciaion in he real exchange rae following a governmen spending shock, a feaure consisen wih he empirical evidence. Moreover, deep habis share wih heir superficial counerpar 7 he same aggregae demand behavior, such ha models feauring deep habis sill reain he empirically desirable hump-shaped response of key aggregae variables afer 7 Superficial habis refer o habis ha are formed a he level of he household s consumpion baske, raher han a he level of individual iems in he baske. 2

5 a moneary shock, see Ravn, Schmi-rohe, Uribe, and Uuskula, 21) and Leih, Moldovan, and Rossi, 212). iven ha deep habis imply empirically appealing impulse responses o key macroeconomic shocks, i is no surprising ha esimaion of models wih deep habis are ypically preferred o heir superficial counerpars. Ravn, Schmi-rohe, Uribe and Uuskula 21) inroduce deep habis ino a sandard medium scale sicky-price/ sickywage model and esimae he key parameers using a limied informaion approach. They find ha he model wih deep habis provides a superior fi o he idenified dynamic effecs of moneary policy shocks compared wih superficial habis. Moreover, he model wih deep habis can accoun simulaneously for he persisen impac of moneary policy shocks on consumpion, for he price puzzle, and inflaion persisence. Similar evidence in favor of deep habis is found by Zubairy 21a, 21b). Lubik and Teo, 211) derive and esimae a New Keynesian Phillips curve NKP) in a model wih deep habis and show ha such habis aler he NKP in a fundamenal manner as i inroduces expeced and conemporaneous consumpion growh, as well as he expeced marginal value of fuure demand, as addiional driving forces for inflaion dynamics. Esimaing he srucural parameers of he model using a MM echnique, hey find ha he fi of he deep habis NKP is much improved over he sandard NKP. Moivaion and Plan Aside from poenially raising he efficacy of governmen spending policy, as suggesed by he evidence discussed above, he modelling of deep habis has furher imporan implicaions for policy. Firsly, firms curren pricing decisions affec he sock of habis possessed by heir cusomers and herefore fuure levels of demand for he good hey produce. This ineremporal aspec o pricing decisions, on op of ha implied by nominal ineria, means ha moneary policy will have a direc effec on firms pricing decisions and hence inflaion. Secondly, he habis exernaliy, whereby households do no ake accoun of he impac of heir consumpion decisions on he welfare of ohers, implies ha here is an addiional disorion in he economy beyond hose associaed wih monopolisic compeiion and nominal ineria. For sandard esimaes of he exen of habis formaion, his disorion will dominae o such an exen ha i implies a highly disored economy, as in Levine, Pearlman, and Pierse, 28). As a resul, in an economy wih deep habis, here is a poenial role for fiscal sabilizaion policy, using governmen spending and/or ax insrumens, alongside moneary policy, as we have moved a long-way from he special case implied by approximaing an economy around an efficien seady-sae. The curren paper explores he robusness of he crowding in resul in he conex of a New Keynesian model of opimal moneary and fiscal policy, where households possess deep habis in consumpion. We also explore he abiliy of fiscal and moneary policy insrumens o conribue o macroeconomic and fiscal sabilizaion in such an economy. 3

6 To his end, we consruc a sicky-price New Keynesian economy along he lines of Benigno and Woodford, 23), where households provide labor o imperfecly compeiive firms who are subjec o price adjusmen coss. As in Benigno and Woodford, 23), axes are disorionary. We begin exploring he fiscal policy ransmission mechanism by varying he relaive exen of habis in privae and public goods consumpion and by allowing firms o discriminae beween pricing for privae and public goods. In ligh of hese resuls, we hen assess he abiliy of fiscal policy o sabilize an economy wih price-sickiness, monopolisic compeiion and deep habis in privae and public consumpion. In doing so, unlike Benigno and Woodford, 23), we also allow governmen spending o be used as a policy insrumen, raher han reaing i as an exogenous sream which needs o be financed. In he nex secion, we describe our model. Secion 3 hen examines he fiscal policy ransmission mechanism, before we explore opimal sabilizaion policy. We find ha, governmen spending shocks can lead o a subsanial crowding-in of privae secor consumpion in he shor-run. However, despie he fac ha governmen spending mulipliers are now greaer han one and ha our benchmark calibraion implies a large consumpion exernaliy as a resul of he deep habis, when we urn o augmen opimal moneary policy wih he governmen spending insrumen, we find ha his insrumen acually adds very lile o sabilizaion policy in our model economy. The public consumpion gap he difference beween he acual variable and he value ha would be chosen by a benevolen social planner) is several orders of magniude smaller han he corresponding consumpion and oupu gaps. Moreover, i barely moves in response o eiher echnology or mark-up shocks. 8 Neverheless, he opimal moneary policy response o echnology and mark-up shocks can be significanly differen in he presence of deep habis, ofen resuling in a moneary policy sance which is he opposie of ha wihou such habis effecs. Furher enriching he policy problem o include governmen deb and consider disorionary axaion o be a policy insrumen, we find ha i remains opimal o allow seady-sae governmen deb o follow a random walk. 9 A he same, ime moneary policy essenially acs o sabilize he consumpion gap in he face of echnology shocks and ax policy deals wih he mark-up shocks and he consumpion exernaliy, wihou generaing significan inflaion beyond he iniial periods of he shock in eiher case. Therefore, alhough governmen spending conribues lile o macroeconomic sabilizaion, ax policy is very useful in offseing he consumpion exernaliy. 8 Noe ha he fac ha he governmen spending gap does no move does no mean ha governmen spending iself is no varied in response o shocks. In he case of posiive echnology shocks he social planner would choose o expand boh public and privae consumpion, afer correcing for he consumpion exernaliies implied by habis. Therefore mainaining he public consumpion gap in he face of such a shock implies ha public consumpion would increase. 9 As in, for example, Benigno and Woodford, 23), Schmi-rohe and Uribe, 24a), and Leih and Wren-Lewis, 213). 4

7 Finally, we assess he abiliy of a se of simple policy rules o mimic he fullyopimal Ramsey policy. In an Appendix, we consider he deerminacy properies of hese rules and find ha he usual classificaion of he deerminae acive and passive policy rules due o Leeper, 1991) depends upon he exen of deep habis formaion presen. Our analysis shows ha he combinaion of opimized simple, bu inerial, moneary policy rules which respond o inflaion and ax rules which respond o governmen deb can effecively achieve he level of welfare found under he Ramsey plan. However, he opimal coefficiens of hese rules are radically differen wheher or no he model includes habis effecs, wih a subsanial fall in he moneary policy response o inflaion and an associaed rise in he response of axaion o governmen deb, when habis are presen. This combinaion of ineres rae and ax policy successfully manages he unwinding of he sock of habis following shocks, wihou generaing significan inflaion. Sensiiviy analysis indicaes ha he main resuls are generally robus o variaions in he degree of labor supply elasiciy and nominal ineria. The final secion concludes. 2. The Model The economy consiss of households, a monopolisically compeiive producion secor, and he governmen. Households derive uiliy from consumpion of boh privae and public goods and hey form exernal consumpion habis a he level of he individual privae/public) goods in heir baskes - Ravn, Schmi-rohe, and Uribe, 26) call his ype of habis deep. Furhermore, firms are subjec o nominal ineria in he form of price adjusmen coss and hey may price discriminae beween sales o households or he governmen Households The economy is populaed by a coninuum of households, indexed by k and of measure 1. Households derive uiliy from consumpion of composie privae and public goods and disuiliy from hours spen working. Deep Habis. When habis are of he deep kind, each household s privae consumpion baske, X k, is an aggregae of a coninuum of habi-adjused goods, indexed by i and of measure 1, ) η 1 ) η 1 η 1 X k = i k η θ i 1 di, where i k is household k s consumpion of good i and i 1 k idk denoes he crosssecional average consumpion of his good. η is he ime-varying elasiciy of subsiuion beween habi-adjused varieies, assumed o follow a saionary AR1) process, as in Ireland, 24): ln η = ) 1 ρ η ln η + ρη ln η 1 + ϱ η, wih persisence parameer ρ η, 1) and random shocks ϱ η iidn,σ 2 η). The parameer θ measures he degree

8 of exernal habi formaion in consumpion of each individual privae good i. Seing θ o reurns us o he usual case of no habis in privae consumpion. The composiion of he consumpion baske is chosen in order o minimize expendiures, and he resulan demand is ) P i k η = i P X k + θ i 1, i where P represens he overall price index or PI), defined as an average of prices of privae goods, P 1 ) 1/1 η P 1 η ) i di). Aggregaing across households yields he oal privae consumpion demand for good i, i [, 1], ) P η i = i P X + θ i 1. 1) Due o he presence of habis, his demand is dynamic in naure, as i depends no only on curren period elemens bu also on he lagged value of consumpion. This, in urn, will make he pricing/oupu decisions of he firms producing hese goods, ineremporal. Remainder of he Household s Problem. For he remainder of he households problem, households choose he habi-adjused privae consumpion aggregae, X k, hours worked, N k, and he porfolio allocaion, D+1 k, o maximize expeced lifeime uiliy, E = β subjec o he budge consrain, 1 ) X k 1 σ ) N k 1+υ 1 σ + χ 1+υ X,k 1 σ ) 1 σ P i k idi + E Q,+1 D k +1 =1 τ ) W N k + D k +Φ 2) and he usual ransversaliy condiion. E is he mahemaical expecaion condiional on informaion available a ime, β is he discoun facor <β<1),χ he relaive weigh on uiliy from consumpion of public goods, and σ and υ are he inverses of he ineremporal elasiciies of habi-adjused consumpion and work σ, υ > ; σ 1). The household s period- income includes: afer-ax wage income from providing labor services 1 τ ) W N k, dividends Φ, and paymens on he porfolio of asses D k. Financial markes are complee and Q,+1 is he one-period sochasic discoun facor for nominal payoffs. τ is he labor income ax rae. In he maximizaion problem, households ake as given he processes for 1, W,Φ,andτ, as well as he iniial asse posiion D 1 k. The firs order condiions for labor and habi-adjused consumpion are: ) N k υ X k ) σ =1 τ )w 6

9 and where w W P ) X k σ Q,+1 = β +1 P X k P+1, is he real wage. The Euler equaion for consumpion can be wrien as 1=βE [ X k +1 X k ) σ ] P P+1 R, = E [Q,+1 ] denoes he inverse of he risk-free gross nominal ineres rae where R 1 beween periods and + 1, while π 2.2. The overnmen P /P 1 is inflaion. Deep Habis We follow he lieraure Ravn, Schmi-rohe, and Uribe, 26), Ravn, Schmi-rohe, and Uribe, 27)) and allow for deep habis effecs in public consumpion, bu will assess how opimal policy varies as we aler he exen of such exernaliies, including he special case where here are no habis effecs in governmen spending. As wih he consumpion habis in privae consumpion, he governmen purchases individual goods so as o maximize he aggregae X ha eners he represenaive household s uiliy funcion, given he allocaed level of aggregae spending, i 1, from he previous period, max X { k = i} i s i θ i 1 ) η 1 η P i k idi P k. ) η η 1 di Tha is, he governmen does no inernalize he impac of is expendiure decisions on household habi formaion over publicly funded consumpion when deciding how much of an individual good o purchase. Since firms could poenially discriminae beween sales o he privae and he public secors, we allow for a disinc se of public purchased goods prices, { Pi }, and a corresponding price index, P i. 1 θ gives a measure of he level of habis formaion in he consumpion of public goods. In he maximizaion problem, he governmen akes as given he pas consumpion of individual public goods, as i respecs he habis formaion behavior of households. The demand for public goods i, i [, 1], is ) P η i = i P X + θ i 1, 3) 1 Ravn, Schmi-rohe, and Uribe, 26) and he res of he lieraure on deep habis assume ha here is no price discriminaion beween privae and public cusomers. 7

10 where P = 1 ) ) 1 P 1 η 1 η i di. overnmen Budge onsrain ombining he series of he represenaive consumer s flow budge consrains, 2), wih borrowing consrains ha rule ou Ponzi schemes, gives he ineremporal budge consrain see Woodford, 23), chaper 2, page 69), E [P T T ] D + E [Q,T Φ T + W T N T 1 τ T ))]. T = T = Noing he equivalence beween facor incomes and naional oupu, P Y + P Y = W N +Φ T, and he definiion of aggregae demand, we can rewrie he privae secor s budge consrain as, D = E [Q,T PT T W T N T τ T )] T = which implies ha some combinaion of moneary accommodaion, disorionary axaion and spending adjusmens is required o service governmen deb as well as sabilize he economy. 11 Noing ha, in aggregae, he households ne porfolio consiss of governmen bonds D = R 1 B 1 allows us o wrie he flow budge consrain as, or in real erms, B = R 1 B 1 + P τ W N 4) b = R 1 π ) 1 b 1 + ζ τ w N where b B /P is real value of deb and ζ P /P is he relaive price of public goods in erms of privae goods ζ = 1 when firms charge he same price o boh households and he governmen) Firms oods are produced by a coninuum of monopolisically compeiive firms indexed by i and of measure 1), which are subjec o nominal ineria in he form of quadraic price adjusmen coss, as in Roemberg, 1982). Firms may also differeniae heir oupu/pricing decisions according o he secor hey are supplying, eiher privae or public. Each firm i produces a unique good using only labor as inpu in he producion 11 In secions 3.1 and 3.2 below, we emporarily absrac from he fiscal financing needs of he governmen by allowing access o lump-sum axaion. We do so in order o explore he implicaions of removing governmen deb from he policy problem, before excluding lump-sum axes and reurning o he more realisic case where all axes are disorionary. 8

11 process Y F i = A N F i, ) wih F = {, } denoing he specific secor goods are supplied o. Toal facor produciviy, A, affecs all firms symmerically and follows an exogenous saionary process, ln A = ρ A ln A 1 + ϱ A, wih persisence parameer ρ A, 1) and random shocks ϱ A iidn,σ 2 A). The nominal profis from sales o he privae secor are given as Φ i P i Y i W N i ϕ 2 while hose from sales o he public secor are Φ i P i Y i W N i ϕ 2 Pi π Pi 1 1 Pi π Pi 1 1 ) 2 P ) 2 P Y Y where he las erm in each expression represens he nominal coss of price adjusmen. Noe ha we disinguish beween he prices charged for public goods and privae goods o allow firms o price discriminae beween he wo secors. We also consider wha happens when such price discriminaion is no possible. We le Z Fi) denoe he price adjusmen coss of firm i in real erms) when supplying goods o secor F = {, }, Z Fi) ϕ 2 ) 2 Pi F πpi 1 F 1 Y F and we assume ha hese adjusmen coss are expressed in erms of a ES aggregae of he differeniaed goods bu which does no feaure habis 12 here we index he differeniaed firms/goods by j o avoid confusion when aggregaing), Z Fi) = 1 Z Fi) j ) η 1 η dj ) η η 1 6) For any given level of Z Fi), he demand for individual varieies j mus be such ha oal expendiures 1 P j FZFi) j dj are minimized, subjec o he consrain 6). This hen yields he individual demand Z Fi) j = ) P F η j P F Z Fi) 12 While i seems naural o allow for habis formaion by households in he consumpion of privae and public goods, a similar assumpion does no appear paricularly plausible when applied o firms. 9

12 where P F = ) 1 1 Pj) F 1 η 1 η dj is he price index and he associaed oal expenses are 1 P j FZFi) j dj = P FZFi). Aggregaing across all firms, he demand for each differeniaed good j associaed wih he price adjusmen coss is where Z F j 1 ZFi) j di and Z F 1 Z F j = P F j P F ZFi) di. ) η Z F 7) Profi maximizaion: In providing goods o households or o he governmen, firms choose Pi F, F i, Zi F,andN i F for F = {, } o maximize he presen discouned value of profis, E Q,+s Φ F i+s, subjec o he dynamic demand consrains 1) or s= 3), he consrain in 7), he producion echnology ), and under he resricion ha all demand be saisfied a he chosen price, F i + Zi F = Y i F. Q,+s is) he s-sep ahead sochasic discoun facor for nominal payoffs Q,+s = β +s u X,+s P u X,. The associaed P+s firs order condiions are: v i = Pi ) M + θe [Q,+1 v i+1 ] vi = Pi M ) + θ [ E Q,+1 vi+1 ] P i = η i Y and +ϕ P P i = η i Y +ϕ P ) η 1 ) P 1 [ P ) Pi π Pi 1 1 i M ) Z + v i X ] [ P Y π Pi 1 ϕe ) η 1 ) P 1 [ ) P i M Z ) Pi π Pi 1 1 [ P Y π Pi 1 ϕe Q,+1 P i+1 π P i + v i X ] 1 P Q i+1,+1 π Pi 1 ) P i+1 π P i ) P i+1 π P i ) 2 P +1 Y +1 ) 2 P +1Y+1 where M = W A represens he nominal marginal cos of producion, while v i and vi are he Lagrange mulipliers on he dynamic demand consrains and represen he shadow prices of producing privae and public good i, respecively. These shadow values equal he marginal benefi of addiional profis from each ype of good, Pi M and Pi M, respecively, plus he discouned expeced payoffs from higher fuure sales, θe [Q,+1 v i+1 ]andθ [ E Q,+1 vi+1]. In he presence of deep habis in consumpion, increasing sales o he privae public) secor leads o an increase in sales of θ θ )in ] ] 1

13 he nex period. The oher firs order condiions indicae ha an increase in price Pi Pi ) brings addiional revenues of Y i Yi ), while simulaneously causing a decline in demand and affecing price adjusmen coss. In conras, if we do no allow producers o discriminae beween privae and public sales of heir producs, hen he firs order condiions reduce o, and v i = Pi M ) + θe [Q,+1 v i+1 ] vi = Pi ) M + θ [ E Q,+1 vi+1 ] Y i = η P i +ϕ P ) η 1 ) P 1 [ ) P i M Z + v i X + vi X ) P Y ϕe Q i+1,+1 Pi π Pi π Pi 1 P π P i ] 1 ) P i+1 π P i ) 2 P +1Y +1 wih he addiional consrain ha Pi = Pi. The combined firs order condiion indicaes ha he common price should be increased unil he exra revenue generaed by selling o boh secors, Y i = Yi + Y i, maches he value of he decline in demand and he changes in price adjusmen coss Equilibrium All households and firms in his economy are symmeric. The producion of privae and public goods amouns o Y = A N and Y = A N, which can be aggregaed o an economy-wide level of oupu Y Y + Y = A N 8) where N = N + N represens aggregae labor. The markes for privae and public goods mus clear, so we have + ϕ 2 π ) 2 π 1 Y = Y 9) + ϕ 2 ) π 2 π 1 Y = Y 1) which reduces o he usual aggregae resource consrain, when firms do no price discriminae beween sales o households and he governmen, + + ϕ 2 ) π 2 π 1 Y = Y 11) Noe ha we generally have wo measures of aggregae prices - he usual consumer price index P and he index of he prices of goods supplied o he governmen P - 11

14 and consequenly wo measures of inflaion, π P and π P 1 P. There are also P 1 wo markups of price over marginal cos associaed wih sales o he privae and public secor, μ P M and μ P M,whereμ is he inverse of he real marginal cos. The symmeric equilibrium is characerized by equaions 8) - 11), ogeher wih he governmen budge consrain and he equilibrium condiions defining he households and he firms behavior Appendix Appendix A.3 liss he enire se of equilibrium condiions), o which we add he moneary and fiscal policy specificaion as deailed in Secions 3 and 4 below). 2.. Soluion Mehod and Model alibraion Since we are ulimaely ineresed in assessing he welfare benefis of allowing fiscal policy o conribue o he sabilizaion of our New Keynesian economy feauring deep habis, we canno rely on linear approximaions o our model s equilibrium condiions when evaluaing opimal policy. Kim and Kim, 23) have shown ha such approximaions can give rise o spurious welfare rankings amongs alernaive policies. Insead, we employ he perurbaion mehods of Schmi-rohe and Uribe, 24b) o obain a second-order accurae soluion o he model which can be used o validly rank he welfare consequences of alernaive policies. In order o solve he model, we mus selec numerical values for some key srucural parameers. Table 1 repors our choices. The bulk of our benchmark calibraion comes from he esimaion/calibraion of Ravn, Schmi-rohe, and Uribe, 26). The model is calibraed o a quarerly frequency and, following Ravn, Schmi-rohe, and Uribe, 26), we assume an annual real rae of ineres of 4%, which implies a discoun facor β of.992. From he same source, he risk aversion parameer σ issea2.andυ he inverse of he Frisch labor supply elasiciy) is equal o 1/ The Roemberg price adjusmen parameer, ϕ =26.34, is chosen o mach he alvo no-price change probabiliy of.6 from Schmi-rohe and Uribe, 26) which in urn is consisen wih an average price conrac lengh of 7. monhs), given he reduced-form equivalence beween he wo forms of nominal-ineria o a firs-order approximaion. Finally, our habis formaion parameer, θ =.86, is aken from he cenral esimae in Ravn, Schmi-rohe, and Uribe, 26) and we assume a similar benchmark for he habis in public consumpion, θ. These values fall wihin he range of esimaes idenified in he lieraure. 14 The remaining parameers are calibraed as follows. The weigh aached o public consumpion in uiliy, χ, is.143, such ha he seady sae under he Ramsey plan implies a governmen spending o DP raio of.2, consisen wih he U.S. daa average 13 Esimaes of his elasiciy vary quie widely and Secion below considers a sensiiviy analysis wih respec o his parameer. 14 Macro-based esimaes of habis formaion of he deep kind range from relaively lower values of.3, as in Ravn, Schmi-rohe, and Uribe, 212), o very high values of.9-.97, as repored by Ravn, Schmi-rohe, and Uribe, 26), Lubik and Teo, 211), and Zubairy, 21c). 12

15 beween 1947 and 24. We se seady-sae governmen consumpion o be in line wih he same level, when we assume follows an exogenous process, raher han lying in he se of opimal policy insrumens. The elasiciy of subsiuion parameer η is se o 8.128, which implies a seady-sae markup of 1%, as a cenral calibraion relaive o he ypical values in he lieraure, which range from 1-2%. We furher assume a seady sae governmen deb o DP raio ha corresponds o an annual average of %, again based on U.S. daa from 1947 o 24. Under he opimal Ramsey policy, he implici seady sae ax rae akes an empirically plausible value of.36 under no habis and.2 under he benchmark calibraion of habis, reflecing primarily he fiscal financing role of axes. 1 Technology shocks are assumed persisen wih persisence parameer ρ A =.86 and sandard deviaion σ A =.6. These values are aken from Schmi-rohe and Uribe, 26), who esimae he process joinly wih a Taylor rule o mach inflaion and DP momens over he pos-war period. In he case of an exogenous governmen spending process, is characerisics are also aken from he esimaes in Schmi-rohe and Uribe, 26) and are based on he esimaion of an AR1) process using HP-filered daa for governmen spending beween 1947 and 24, ρ =.87 and σ =.16. The mark-up shocks follow he esimaed process in Ireland, 24), ρ η =.962 and σ η =.12. Finally, he seady-sae inflaion rae of 3.% per year is based on he U.S. daa average beween 1947 and 24, and implies ha, under our various descripions of policy, he nominal ineres rae never breaches he zero-lower bound for plausible draws of he shocks. 3. Opimal Ramsey Policy In his secion, we consider he naure of opimal policy in response o exogenous shocks. The opimal policy problem can be se up in erms of a Lagrangian as, L = max y E β [Uy +1, y, y 1, u ) λ fy +1, y, y 1, u )] = where y and u are vecors of he model s endogenous and exogenous variables, respecively, Uy +1, y, y 1, u )= X)1 σ 1 σ N)1+υ 1+υ + χ X ) 1 σ 1 σ, fy +1, y, y 1, u )= are he model s equilibrium condiions equaions A.2) - A.21) in Appendix Appendix A.3), and λ is a vecor of Lagrange mulipliers associaed wih hese consrains. The opimizaion implies he following firs order condiions, E [ U.) y + βf U.) + β 1 1 f.) f.) λ 1 F + λ + βλ +1 F f.) ] y 1 y +1 y y 1 = 12) 1 In he case where he governmen has access o lump-sum axes o balance he budge, he opimal seady sae ax rae would be.14 wih no habis, reflecing he long-run inefficiency due o monopolisic compeiion, and a very large.83 under he benchmark value of habis, reflecing he consumpion exernaliy. 13

16 Parameer Value Descripion 1/β 1.4) 1/4 Real ineres rae σ 2 Inverse of ineremporal elasiciy of subsiuion ɛ Nw 1.3 Frisch labor supply elasiciy η 8.13 Elasiciy of subsiuion beween goods ϕ Price adjusmen cos parameer θ.86 Degree of habi formaion in privae goods consumpion θ.86 Degree of habi formaion in public goods consumpion χ.143 Relaive weigh on uiliy from public goods consumpion π 1.3) 1/4 ross PI inflaion rae. B/DP. 4 Deb o DP raio ρ A.86 Persisence of echnology ρ η.962 Persisence of markup shock process ρ.87 Persisence of exogenous governmen spending σ A.6 Sandard deviaion of echnology process σ η.12 ϕ Sandard deviaion of markup shock process σ.16 Sandard deviaion of exogenous governmen spending Table 1: Parameer values used in simulaions where F is he lead operaor, such ha F 1 is a one-period lag. A second-order accurae soluion o opimal policy hen involves solving hese firs order condiions in combinaion wih he non-linear equilibrium condiions of he model, fy s+1, y s, y s 1, u s )=, using he perurbaion mehods of Schmi-rohe and Uribe, 24b). In order o explore he conribuion of fiscal policy insrumens o opimal sabilizaion in a sicky price economy feauring deep habis, we gradually inroduce fiscal consideraions o he policy problem. To begin wih, we consider he naure of he fiscal policy ransmission mechanism by inroducing exogenous governmen spending shocks o a model varian where moneary policy is opimal. This allows us o explore he crowding-in resuls of Ravn, Schmi-rohe, and Uribe, 26) in an economy where moneary policy is conduced opimally and where we can make differen assumpions abou he pricing of privae and public goods. We hen allow governmen spending o be varied as par of opimal policy, o assess wheher or no governmen spending as a proxy for he manipulaion of aggregae demand hrough fiscal policy) conribues o sabilizaion policy. In boh cases, we emporarily absrac from fiscal solvency issues by assuming he policy maker has access o a lump-sum ax hrough which o balance he budge. We hen relax his assumpion and consider he opimal policy response o echnology and cos-push shocks, when axes are disorionary and Ricardian equivalence no longer holds. In all cases, we consider opimal policies wih commimen. Finally, in Secion 4 we explore he abiliy of a se of simple linear) policy rules o replicae he Ramsey policy. 14

17 3.1. Exogenous overnmen Spending and Opimal Moneary Policy We firs consider he case when fiscal policy is exogenous, while moneary policy is se opimally under commimen, and he governmen has access o lump-sum axes o balance is budge. We assume ha governmen spending follows an exogenous saionary process, ln =1 ρ )ln + ρ ln 1 + ϱ, wih persisence parameer ρ, 1) and random shocks ϱ iidn,σ 2 ). Even hough governmen spending is exogenous, households sill derive uiliy from he consumpion of public goods and form habis accordingly. The moneary auhoriy ses he nominal ineres rae o maximize households welfare subjec o he privae secor s response and given he exogenous processes. We analyze he implicaions of his policy in erms of impulse responses o a governmen spending shock since his allows us o explore he naure of he fiscal policy ransmission mechanism in a model wih deep habis. A Posiive overnmen Spending Shock Figure 1 deails he impulse responses o a posiive governmen spending shock in hree cases - no habis, habis of θ = θ =.86 and common pricing across privae and public goods and, finally, he same degree of habis, bu wih price discriminaion across public and privae goods. onsider he case wihou habis: he increase in governmen spending resuls in an increase in aggregae demand which he moneary auhoriy offses by raising real ineres raes and discouraging household consumpion. The policy maker does his unil consumpion falls by enough ha labor supply increases essenially mach he increase in labor demand and he marginal coss of producion are largely unchanged alhough hey acually fall slighly in he iniial period, as does inflaion). Therefore, he essence of he opimal policy in he absence of habis lies in ensuring he inflaionary consequences of he increase in governmen spending are largely negaed. Wihin his policy response, here is acually a feaure of opimal policy under commimen which is no easy o discern from he plos of he impulse response funcions - he presence of price level conrol. As noed by Woodford 23), under commimen, a policy maker facing he consrain implied by he New Keynesian Phillips curve will find i opimal o no only sabilize inflaion following shocks, bu will also seek o sabilize he price level iself. Accordingly, he policy maker acually maches he iniial fall in inflaion wih a prolonged period of slighly posiive inflaion. This miigaes he inflaionary consequences of he governmen spending shock while achieving he bes balance beween privae and public consumpion. This feaure of opimal policy will be more apparen when we consider he same shock in he presence of deep habis. We hen consider he case where household preferences include deep habis over boh privae and public goods θ = θ =.86) and where he suppliers of hese goods are consrained o supply o he privae and public secors a he same price. Here, he increased demand for goods emps firms o reduce heir mark-ups in order o capure a larger share of he increased overall produc demand. eeris paribus, his will end 1

18 o simulae consumpion. The policy maker wishes o discourage he formaion of such habis effecs and so aggressively raises ineres raes a he sar of he simulaion, which encourages households o save raher han consume and reduces he discouned value of he sales generaed by price cus offered by firms. Despie his, he desire o gain marke share is so grea ha he increase in governmen spending crowds in privae consumpion. As he shock passes, he policy maker wishes o miigae he coss of falling habis-adjused consumpion and so relaxes policy for a ime, before ulimaely ighening i again. This cyclical behavior in policy making reflecs he combined effecs of he dynamics of habis-adjused consumpion and he implemenaion of a policy of price level conrol. Finally, we consider a varian wih he same degree of habis bu where he producers can charge differen prices o he privae and public secors. Here, he markup charged o he public secor is subsanially reduced, bu he governmen spending shock does no have a direc impac on he markup charged o he privae secor s consumpion goods, and privae consumpion is crowded ou. The increase in aggregae demand due o he increase in public consumpion does raise marginal coss and consumer price inflaion. In he presence of nominal ineria, his implies ha markups in he producion of he privae consumpion goods fall. However, his decline is significanly smaller han he corresponding fall in he markup charged o he public secor. Also, in order o reduce he inflaionary effec, moneary policy is ighened by more in he iniial period han i would be under common pricing, which furher discourages privae consumpion. There is hen he same relaxaion and subsequen ighening of policy which minimizes he coss of inflaion and habis-adjused consumpion gaps, parly by relying on he expecaional benefis of price-level conrol. The crowding-in effecs are effecively he resul of he common pricing behavior by firms, combined wih sufficien degrees of habis formaion in privae and public goods consumpion. 16 Figure 2 shows he response of consumpion under differen combinaions of habis. For common levels of habis across privae and public goods, he exisence of crowding-in effecs when moneary policy is opimal requires a degree of habis in excess of.72. However, for differing levels of habis in public and privae goods consumpion, a higher degree of habis in one can compensae, o varying degrees, for a lower degree of habis in he oher and sill suppor he crowding-in of privae consumpion. The crowding-in effecs disappear if, for example, privae goods consumpion habis are a heir benchmark level, θ =.86, bu here are no habis in public goods consumpion, θ =, or vice versa he laer is shown by he dash-do lines in Figure 2). However, as he markup effecs on privae consumpion are imporan in generaing hese resuls, higher degrees of habis formaion in privae consumpion can resore he crowding-in effecs, as is he case when θ = bu θ =.96 which is he upper bound 16 Our resuls also differ from early sudies in ha we are assuming an opimal moneary policy. 16

19 of he esimaes in Ravn e al 26)). Similarly, mainaining habis in public consumpion a heir benchmark level of.86 will resul in crowding-in effecs, provided he level of habis in privae goods θ is of a leas.4 he sars impulse response in Figure 2 illusrae such a case) Endogenous overnmen Spending and Opimal Moneary Policy In his subsecion, we analyze he opimal policy response o echnology and markup shocks, where he nominal ineres rae and governmen spending serve as policy insrumens. We coninue o ignore he budgeary consequences of policy by assuming fiscal auhoriies have access o a lump-sum ax wih which o balance he budge. A Technology Shock Figure 3 analyses he response o a posiive echnology shock and includes hree cases - no habis effecs and he case of deep habis wih eiher common or discriminaory pricing across privae and public goods. In he absence of habis effecs, policy seeks o eliminae he inflaionary consequences of he shock, leaving consumpion, governmen spending and oupu subopimally low due o he disorionary effecs of monopolisic compeiion. If he policy maker were forced o behave in a ime consisen manner, hen his permanen disorion would resul in an inflaionary bias, bu under commimen he policy maker is able o resis he empaion o inroduce policy surprises in order o offse his disorion. Therefore, he policy maker raises public consumpion and relaxes moneary policy o boos privae consumpion. These policies exacly balance he reducion in marginal coss ha would oherwise arise as a resul of he echnology shock, so ha inflaion is zero hroughou he simulaion. When we inroduce significan deep habis effecs, he naure of he disorion changes as households now over-consume, due o he habis exernaliy, hus implying significan consumpion and oupu gaps he difference beween acual oupu and he efficien level of oupu, as a percenage of he efficien level 17 ) of 68% and 2%, respecively. 18 In he face of his enormous exernaliy, moneary policy no longer seeks o solely sabilize inflaion. Real ineres raes are iniially ighened o preven he formaion of such damaging habis exernaliies, while inflaion falls iniially. As he shock dissipaes, policy is slowly relaxed o suppor he slow unwinding of increased sock of consumpion habis. iven he expecaional benefis of price level conrol in a forward looking model, moneary policy acually swiches from is iniial ighened sance o a more accommodaive sance and he iniial fall in inflaion is offse by a subsequen rise. Therefore, we can see ha he conduc of moneary policy has been significanly affeced by he inroducion of deep habis. In conras, i is ineresing o 17 See Appendix Appendix A. for he deails of he social planner s problem. 18 In he absence of habis, he monopolisic compeiion and ax disorions would imply ha oupu is sub-opimally low. However, as he degree of habis increases, he consumpion exernaliy begins o dominae rendering oupu inefficienly high. 17

20 noe ha he governmen spending gap is small relaive o he very large consumpion and oupu gaps. Therefore, despie he fac ha inroducing deep habis implies he economy faces a massive disorion and he oupu mulipliers associaed wih he governmen spending insrumen rise from significanly below o above one, here is sill lile reliance on he governmen spending gap as a ool of sabilizaion policy. This is a paern ha will re-emerge hroughou our simulaions. 19 A Mark-Up Shock We hen consider he response of policy o a markup shock, aken as a 1% increase in η, which represens a decrease in he firms desired markup. In his case, he policy maker faces a rade-off beween inflaion and oupu sabilizaion even in he absence of habis, as inflaion falls while oupu rises. Wih lile change in governmen spending, ineres raes are iniially raised in order o reduce aggregae demand and he size of he oupu gap, while allowing for addiional deflaion. This is illusraed by he doed lines in Figure 4. Again, he iniial deflaion is offse by a subsequen period of slighly lower ineres raes and raised inflaion, which is difficul o discern in he Figure, and he governmen spending gap is negligible in comparison o he oupu and consumpion gaps, which bear he brun of he economic adjusmen o he shock. In he presence of deep habis, he reducion in markup reduces he value of reaining marke share and firms seek o raise he prices of heir goods, and we observe a rise in inflaion. As a resul he iniial ighening of moneary policy is even sronger, as he policy maker aemps o curb he large oupu gap ha can ensue due o overconsumpion effecs. Following his iniial ighening of policy, here is he now familiar relaxaion of policy which suppors habis-adjused consumpion as he mark-up shock fades away. This relaxaion of policy is laer moderaed o achieve a sligh fall in inflaion, expecaions of which reduce he iniial rise in inflaion and is a feaure of he abiliy o make credible policy promises under commimen. While he abiliy o price discriminae across privae and public goods does no have much bearing on he resuls, 2 he ime-varying markups ha arise under deep habis are shown o play an imporan role in he opimal policy response o cos-push shocks Opimal Moneary and Fiscal Policy We now urn o he analysis of opimal Ramsey policy when policy makers have conrol over moneary policy and boh fiscal policy insrumens - governmen spending and income axes, bu where hey no longer have access o lump-sum axes o saisfy 19 I should be noed ha, even hough he governmen spending gap is ofen small, his need no imply ha governmen spending iself does no respond o shocks. The governmen spending gap is measured relaive o he efficien level of public goods consumpion and his responds o echnology shocks bu no o markup shocks. Hence, under he Ramsey policy, here will be relaively significan movemens in he level of governmen spending in he former case. 2 Impulse responses across he wo ypes of pricing behavior are virually he same. 18

21 he governmen s budge consrain. I is imporan o noe ha, if we did coninue o remove he need o adjus eiher governmen spending or disorionary axes o saisfy he ineremporal budge consrain, hen he policy maker can achieve he firs bes allocaion using he income ax insrumen o offse he consumpion exernaliy and he mark-up shocks, while using he ineres rae o offse he nominal ineria coss of echnology shocks. Before considering he response o echnology and mark-up shocks, i is ineresing o consider he iniial seady-sae of he Ramsey policy. This is compued by solving he seady-sae of he Ramsey firs-order condiions and he equilibrium condiions describing our New Keynesian economy, condiional on an iniial governmen deb o DP raio. In he case of our model wihou habis, he combinaion of he monopolisic compeiion and ax disorions suppresses oupu below is socially efficien level. Ineresingly, he opimal policy implies ha he absolue size of he governmen spending gap is significanly smaller han he consumpion gap. The inuiion for his paern lies in he desire o suppor he deb sock wih he opimal combinaion of efficiency gaps in variables wihou generaing any seady-sae inflaion. In he case of habis, he consumpion exernaliy renders he level of oupu oo high despie he presence of monopolisic compeiion and disorionary axaion. As a resul he consumpion and governmen spending gaps are posiive, bu he consumpion gap is four imes he size of he governmen spending gap. We now consider he naure of he policy response o echnology and cos-push shocks, in his highly disored environmen. Figure deails he response o a 1% posiive echnology shock. A key elemen of he policy response is ha he seady-sae of governmen deb follows a random walk as in Benigno and Woodford, 23), Schmi- rohe and Uribe, 24a), and Leih and Wren-Lewis, 213). The basic inuiion for his is ha in a sicky-price environmen adjusing fiscal insrumens o offse fiscal shocks is cosly, such ha policy makers ensure ha policy insrumens are adjused o service he new seady-sae deb ha emerges following shocks, bu he policy maker commis o no aemping o do more. In he absence of habis, gap variables are adjused o heir new seady-sae values from he second period onwards, and deb slowly evolves o is new seady-sae consisen wih hose variables. Real ineres raes are adjused in he face of he echnology shock o mainain consumpion a is new consan gap value. Wih a posiive echnology shock, ax raes fall and governmen spending, consumpion and oupu rise o suppor he lower seady-sae deb sock wihou affecing inflaion. As shown in Leih and Wren-Lewis, 213), he behavior in he iniial period is slighly differen as he policy maker explois he fac ha expecaions are given o reduce he impac of he shock on deb. Accordingly, in he iniial period he fall in real ineres raes is moderaed o miigae he fall in deb service coss and offse he increase in he ax base) and encourage a surprise deflaion in he iniial period alhough axes rise o parially offse his deflaion) - he combined impac of his is o reduce he evenual 19

22 decline in deb ha would oherwise emerge. 21 When here are deep habis in consumpion, he policy maker needs o minimize boh he consumpion exernaliy and he coss of nominal ineria. Despie his addiional rade-off, he assignmen of insrumens remains similar, alhough he sabilizaion of gap variables a heir new long-run levels is no longer immediaely afer he iniial period i should be noed ha he ransiion o he new seady-sae sill reains he propery ha inflaion is effecively zero beyond he firs wo periods). Moneary policy adjuss ineres raes o help sabilize he consumpion gap in he face of he echnology shock, and ax raes are adjused o largely offse he exra consumpion generaed by he echnology shock in he presence of habis, while ogeher ensuring ha inflaion is near zero from he hird period onwards. The paern of adjusmen in he firs wo periods is ineresing and capures he essence of he rade-off facing he policy maker. In he firs period, he policy maker ighens moneary policy o reduce he formaion of undesirable habis effecs, which ends o reduce inflaion i amouns o a negaive inflaion surprise in he firs period), while he ax rae is slighly reduced. The combined effecs of hese changes are o acually increase he real value of governmen deb iniially, despie he posiive echnology shock resuling in an increase in he ax base. This iniial increase in deb hen reduces he size of he seady-sae fall in deb which ulimaely emerges once he shock has passed. In he nex period, here is a sligh swich in he assignmen of policy insrumens as moneary policy is relaxed and higher axaion is used o discourage over-consumpion. Anicipaion of his second period ax increase miigaes he iniial fall in inflaion which is cosly given he price adjusmen coss. Using axaion in his way in he iniial period is undesirable as he inflaionary consequences of he ax increase would have reduced he iniial deb level and implied greaer adjusmen o suppor he new lower seady-sae deb level ha would have implied. We now consider he mark-up shock, deailed in Figure 6. In he absence of habis, he ax rae is employed o miigae he impac of he mark-up shock while mainaining he consumpion, governmen spending and oupu gaps close o heir new seady-sae values. In he iniial period, here is an aemp o offse he long-run reducion in governmen deb following he negaive mark-up shock, primarily hrough ighening moneary policy which increases deb service coss, reduces he size of he ax base and suppors a surprise deflaion). When we inroduce deep habis, he policy maker has o consider boh he consumpion exernaliy and he mark-up shock. As a resul, he ax rae is raised more aggressively han in he absence of habis and inflaion rises raher han falls. This reduces he iniial sock of deb, which is undesirable, bu helps reduce 21 Leih and Wren-Lewis, 213) show ha he combinaion of insrumens used in he iniial period depends crucially upon he degree of price sickiness and he seady sae deb-dp raio. In our benchmark calibraion, deb service coss and inflaionary surprises are paricularly effecive in influencing he level of governmen deb. 2