Monetary Policy, Taxes and the Business Cycle

Transcription

1 Moneary Policy, Taxes and he Business Cycle William T. Gavin Vice Presiden Research Deparmen Federal Reserve Bank of S. Louis P.O. Box 442 S. Louis, MO 6366 (34) Finn E. Kydland Professor of Economics Tepper School of Business Carnegie Mellon Universiy Pisburgh, PA 523 (42) June, 2004 Michael Pakko Senior Economis Research Deparmen Federal Reserve Bank of S. Louis P.O. Box 442 S. Louis, MO 6366 (34) Keywords: Inflaion, Taxaion, Business Cycle JEL Classificaion: E3, E32, E42 ABSTRACT In his paper, we model he ineracion of inflaion wih he ax code, examining he conribuion of his ineracion o aggregae flucuaions. Our innovaion is o combine persisen moneary policy shocks wih axes on nominal capial gains in a model in which he cenral bank operaes policy using an ineres rae rule. All hree feaures are necessary for us o generae large effecs of moneary shocks, bu hey are also realisic feaures of he U.S. economy. All hree have been examined in isolaion and, by hemselves, do no conribue much o aggregae flucuaions. Capial gains axes are imporan when here are persisen changes in he inflaion rae. Money growh shocks do no cause persisence changes in inflaion when he cenral bank uses a money growh rule. When he cenral bank operaes policy using an ineres rae rule persisen moneary policy shocks lead o persisence in inflaion, raising he effecive marginal capial gains ax rae, hereby suppressing capial accumulaion. We hank Ben Keen and Alex Wolman for helpful commens. The views expressed in his paper are hose of he auhors and do no necessarily reflec official posiions of he Federal Reserve Bank of S. Louis, he Federal Reserve Sysem, or he Board of Governors.

2 Inroducion Does he ineracion of inflaion and he ax code conribue o aggregae flucuaions? There is a large body of work showing ha he seady sae welfare effecs of moderae inflaion are large when nominal capial gains are axed. These include he parial equilibrium analyses of Fischer (98), Feldsein (997) and Cohen, Hasse, and Hubbard (999). The lieraure also includes he seady sae analysis of general equilibrium models in Abel (997), Leung and Zhang (2000), and Bullard and Russell (2004). In general equilibrium he welfare coss arise because, for any given capial income ax rae, an increase in he inflaion rae raises he real preax rae of reurn o capial and lowers he afer-ax reurn. The lower afer-ax reurn causes a decline in he capial sock and a reducion in labor produciviy. These analyses are abou seady saes and only suggesive abou he cyclical impacs. This paper examines he impac of he ineracion beween inflaion and he capial gains ax on business cycle flucuaions. We specify a DSGE model ha combines persisen shocks o he inflaion rend wih axes on nominal capial gains in a seing where he cenral bank operaes policy using an ineres rae rule. All hree feaures are necessary for us o generae large effecs of moneary shocks, bu hey are also realisic feaures of he U.S. economy. Cooley and Hansen (989) and Pakko (998) show ha he real effecs of persisen money growh shocks are large relaive o money supply shocks, bu sill small. Sudies wih models using money supply rules will no find much ineracion beween he ax sysem and moneary policy shocks because here is lile or no persisence in inflaion following a money growh shock. A persisen money growh shock leads o a large jump in he price level, bu inflaion does no persis and does no affec expeced reurns o invesmen.

3 Inflaion persisence is needed o induce changes in expeced ax raes. Dimar, Gavin and Kydland (2004) show ha ha inflaion persisence is common in models where he cenral bank uses an ineres rae rule. When he cenral bank is using an ineres rae rule, a persisen one-percen shock o he inflaion rend appears as a shock o he inflaion arge. I is followed by a persisen deviaion of inflaion from he seady sae and, in he presence of a nominal ax on capial gains, a persisen change in he effecive marginal ax rae on capial. Thus, a posiive shock o he inflaion arge disors he consumpion/saving decision and may have a longlasing effec on he capial sock. Alig and Carlsrom (99) use an overlapping generaions model wih nominal prices (bu wihou money explicily included) o show ha he lack of perfec indexaion for inflaion in he ax code could have a large cyclical effec in principle, bu find ha heir model could no accoun for he magniude of cyclical variaion in hours worked and i prediced a large decline in he capial sock in he 980s ha never maerialized. Having esablished ha moneary policy shocks can produce persisen deviaions of he inflaion rae from he seady sae, i is imporan o revisi he ineracion of such shocks wih he ax code. We begin by describing a model wih axes, including separae axes for income from labor, capial, bonds and capial gains. In he Unied Saes, he rise of inflaion in he 970s wihou indexaion of ax brackes and exclusion resricions led he governmen o index some aspecs of he ax code and o make ad hoc adjusmens in oher aspecs. We assume consan sauory ax raes in order o examine he ineracion of variable inflaion wih he nominal ax on capial gains. Then, we discuss he dynamics of he model, showing how inflaion affecs he business cycle hrough he ax on nominal capial gains. Finally, we use he 2

4 model wih esimaes of persisence in he inflaion objecive o show wha our model predics for capial, hours and produciviy in he U.S. economy. A Moneary Model wih Nominal Taxes Technology Oupu is produced wih a sandard CRTS producion echnology: () Y = z F α α ( K, x N ) = z K ( x N ) where z is a saionary echnology shock and x is an index of labor-augmening echnical progress ha increases a a (gross) growh rae γ /( α ) x. The implied growh rae for oupu, capial and consumpion, γ x, defines a seady-sae growh pah for he real economy. The firm sells oupu a price P, and purchases labor and capial services from he household a nominal wage, W, and renal price of capial, V. Along wih he CRTS assumpion, profi-maximizaion under perfec compeiion implies ha he real wage rae, w =W /P, and renal price, v =V /P, will be equaed wih he marginal producs of labor and capial. Capial owned by he households follows he law of moion (2) K + = ( δ ) K I, where I is gross invesmen and δ is he depreciaion rae on capial. Governmen wih a Nominal Tax Code A governmen issues nominal claims o money and bonds, and collecs revenues by imposing proporional axes on nominal income from labor, bond ineres and capial ownership (wih possibly differing ax raes). Governmen revenues, T, from income axes are: 3

5 N B K G (3) T = τ WN + τ RB + τ ( v δ) PK + τ ( P P ) K, where R is he nominal ineres rae on bonds from he previous period. The hird erm in equaion (4) represens he revenue from axes assessed on capial reurns ne of depreciaion charges. The fourh erm represens he income from he ax on nominal capial gains. Revenues from he income axes are reurned o he household via a lump-sum rebae. This allows us o consider he pure disorionary effecs of axaion, absracing from wealh affecs associaed wih reallocaions beween he public and privae secors. The governmen also carries ou ransfers of bonds and money o he public direcly in he form of nominal asses, B and M. Households and leisure, A represenaive household maximizes a discouned sream of uiliy from consumpion = 0 max β u( C, L ), θ θ σ wih u( C, L ) = ( C L ) /( σ ), subjec o a nominal budge consrain and a consrain on he allocaion of ime. The household s nominal budge consrain can be wrien: (4) ( N K G τ ) W N + ( τ )( v δ ) P K τ ( P P ) K + T + [ + ( ) ] + + = + [ ] + +, B τ R B M M PC P K+ K B+ M+ where M is he ransfer of money in period. The bar over T, he lump sum ransfer of governmen revenue, indicaes ha he household akes he lump-sum ransfer as exogenous o is maximizaion problem. 4

6 The household endowmen of ime (normalized o one) can be allocaed o leisure, labor inpu o he producion process, or o ransacion relaed aciviies such as shopping-ime, rips o he bank, ec.: (5) L N + S =. + Transacions-relaed coss are minimized via a shopping-ime funcion ha is assumed o be increasing in he nominal value of consumpion purchases and decreasing in he quaniy of money held for faciliaing ransacions, PC (6) S = ξ M η, wih ξ, η>0. This specificaion of shopping ime may appear o be nonsandard because money received in he ransfer is no used in he shopping ime funcion. The iming was used Kydland (989). I is a consisen wih cash-in-advance iming. If we included he ransfer, hen i would be equivalen o end-of-period balances and more comparable wih ypical analysis of models in which money eners he uiliy funcion direcly. Boh varians of his shopping ime funcion are discussed in Goodfriend and McCallum (987). The only imporan resul ha depends on his iming is he real deerminacy of he equilibrium wih a conemporaneous policy rule. Carlsrom and Fuers (200) show ha he deerminacy condiions depend crucially on hese somewha arbirary iming convenions. Saionary Transformaion and Household Opimizaion The model conains wo sources of nonsaionariy: Technological progress implies growh in all real variables, while nominal variables are also subjec o growh due o inflaion. Allowing for he echnology growh rae and inflaion o have sochasic componens, he 5

7 saionary represenaion of he model approximaes he dynamics of a difference-saionary economy. The real-valued variables oupu, consumpion and invesmen share a common rend, γ x. The price level is assumed o be difference saionary, so all nominal values also share a common rend wih he (sochasic) rend inflaion rae, γ p. To assure ha he governmen s ineremporal budge consrain is saisfied, we impose he condiion ha he growh rae of bonds and money are coinegraed wih he nominal growh rend, γ xγ p. In he compuaional experimens, we rea γ p as sochasic, allowing for shocks he inflaion rend. To model he model s dynamics, we require a saionary represenaion, which can be derived by deflaing all real variables by (γ x ) and deflaing all nominal variables by a similar index of he rend rae of inflaion, (γ p ). The resuling ransformed household opimizaion problem, in which all nominal and real variables are saionary, can be wrien: θ θ σ max β ( c L ) /( σ ) subjec o N K G p (7) ( τ ) wn + ( τ )( v δ) k τ k + γ p p p = 0 b m m b m + [ + ( τ ) R ] + + = c + [ γ k k ] + γ γ + γ γ B + + x+ + p+ x p+ x p p p p p pc (8) L + N + ξ = m η This ransformaion also affecs he value of he appropriae discoun facor (as described in King, Plosser and Rebelo (988). 6

8 In he ransformed problem, lower-case variables represen inflaion-adjused, growh-adjused saionary values. The iming convenion is such ha R +, and γ p+ represen growh raes from o +. The firs-order condiions o he household s opimizaion problem can be expressed as follows: (9) U ) = λ + ω η( S / c ) c ( (0) U L ( ) = ω () N λ ( τ ) w = ω (2) β [ λ + ω η S / m )] γ γ λ ( p / p ) + + p + ( + + = p+ x + B (3) βλ [ + ( τ ) ] γ γ λ ( p / p ) + + R + = p+ x + v K G (4) βλ + [( τ + )( + δ )] τ + = γ x + γ p+ p+ where λ and ω are uiliy-denominaed, presen-valued shadow prices of goods and ime, respecively. Equaion (9) ses he marginal uiliy of consumpion equal o he shadow goods-price plus a facor reflecing he shopping-ime cos. Equaions (0) and () deermine he shadow value of ime, and reflec he opimal condiion ha he marginal uiliy of leisure is equal o afer ax wage rae (denominaed in uiliy-unis). Equaions (2)-(4) deermine porfolio allocaions for money, bonds and capial. From (3), he gross nominal rae of reurn on a ax-free bond would be: p λ (5) ~ ( + R + = ) π + γ xλ βλ + 7

9 where π + = γ p+ + p / p. In general equilibrium, equaion (5) represens he afer-ax nominal ineres rae. Relaive o he real afer-ax ineres rae, ( + r + ) = ( + R + ) / +, he ax disorions in equaions (2)-(4) can be summarized in he following relaionships: ~ (6) ( + r + ) = [ + ( ω+ p+ / λ+ )( S+ / m+ ) ]/ π + η (Money) B [ + ( + ) R+ ] / π + = τ (Bonds) K G { + [( )( δ )] τ ( / )} = + v + + π + τ (Capial) The disoring effecs of axes on ineres and capial income are direcly represened by he ax B K wedges, ( τ ) and ( τ ). An increase in he ax on ineres income lowers he demand for bonds, raising he nominal bond rae. The direc effec of an increase in he capial ax is o lower real afer ax reurns, reducing invesmen demand and capial accumulaion. The seigniorage ax (inflaion) lowers real reurns on money and bonds. For a given baseline real reurn, an increase in inflaion requires a higher nominal bond rae and a higher reurn o money holdings in equilibrium. In he case of money, higher reurns are associaed wih a lower demand for real money balances and an increase in shopping-ime coss. Inflaion also ineracs wih he ax srucure in he expression for capial reurns hrough he las erm, which reflecs he axaion of nominal capial gains. A higher inflaion rae lowers afer ax reurns o capial hrough his channel, lowering invesmen demand and capial accumulaion. I is his mechanism ha primarily drives he model dynamics in response o shocks o he inflaion rend. ~ ~ π 8

10 Sochasic General Equilibrium Equaions (8), (0) and () in he household s opimizaion problem deermine he household allocaion of ime beween labor and leisure (ne of shopping-ime) implying a labor demand funcion and deermine he shadow price of ime. The firm s profi-maximizaion condiion seing he marginal produc of labor equal o he real wage, (7) w = α)( y / N ), ( complees he labor marke and deermines he equilibrium real wage. Similarly he firm s demand for capial deermines ha he real renal price will be equal o capial s marginal produc: (8) v = α y / k ). ( Equaions (9) and (4), along wih a ransformed saionary represenaion of he capial accumulaion equaion, (2 ) γ k + = ( δ ) k + i imply household demand funcions for consumpion and real invesmen and hence, he fuure capial sock, k +. The presence of marginal shopping-ime coss in he consumpion-demand equaion (9), defined by he shopping-ime funcion (6 ) η pc ξ S =, m demonsraes one source of non-neuraliy in he model. In addiion, he presence of π in equaion (4) implies anoher source of ineracion beween he goods marke and he nominal asse marke. Assuming equilibrium in he nominal asse markes, he condiion for equilibrium in he goods marke can be derived from he household s budge consrain: (4 ) y = c + i 9

11 by imposing he consrain ha his demand for goods equals he supply of goods, defined by he producion funcion, α α ( ) y = z k N. Equilibrium in he goods marke deermines consumpion, invesmen, and oupu wih he equilibraing price being he shadow value of capial, λ + ; i.e., he afer-ax real ineres rae, ( + ~ r ) + = γ xλ βλ +. Summarizing o his poin, ( ), (2 ), (4 ), (6 ), (8)-(), (4), (7) and (8) comprise eleven equaions deermining equilibrium values for y, c, i, k +, N, L, S, v, w, ω and λ +. The remaining firs-order condiions from he household s problem, (2) and (3), represen demand funcions for bonds and money. Togeher wih governmen supply processes, specified below, equilibrium in he asse marke deermines he price level and he nominal ineres rae (inflaion). Wih lump-sum rebaes of ax revenue and no real governmen asses, he bond marke plays no independen role in erms of equilibrium allocaions. Wihou loss of generaliy, we will assume ha governmen borrowing is zero in each period. Equaion (3) herefore sands as a definiion of he nominal ineres rae. Equaion (2) describes a relaionship ha can be inerpreed as a money demand funcion. Subsiuing (), (3), (7) and (6 ), equaion (2) can be solved for real money balances o yield: (20) m p + + = N η ηξ ( τ α + η + )( )( y+ / N + ) c+. B ( τ + ) R + Calibraing he shopping-ime funcion wih η= implies an ineres elasiciy of -½. Noe also ha because consumpion and produciviy are coinegraed, he scale variable in he numeraor of (20) implies a long-run income elasiciy equal o one. Because boh consumpion and labor 0

12 produciviy end o be procyclical bu wih smaller ampliude han oupu he shor-run income elasiiciy of he money demand relaionship will be less han one. Policy Funcions and Exogenous Processes Closing he model requires he specificaion of he policy funcions deermining he money supply process and ax raes. In his paper we rea he ax raes as consan. We consider wo alernaive moneary policy sraegies a money growh rule and an ineres rae rule aimed a achieving an inflaion arge. In boh cases, we define he moneary policy shock o be a shock he inflaion rend (γ p ). When he cenral bank is using a money growh rule, we refer o his shock as a shock o money growh and when i is using an ineres rae rule, we refer o he shock as a shock o he inflaion arge. I is common in he lieraure on money growh rules o specify he policy shock as a shock o he money growh rae. However in he lieraure on ineres rae rules, he shock is usually appended o he equaion in which he cenral bank deermines he one-period ineres rae. We hink of his as a shock o liquidiy. In he money growh rule, he liquidiy shock is an innovaion o he level, raher han o he growh rae of he money supply. In his paper we do no consider shocks o shor-erm liquidiy because here is no special role for liquidiy excep ha embodied in he shopping ime funcion. These effecs are small in a model wih flexible prices. Under he ineres rae rule, he cenral bank arges he inflaion rae, wih he money sock deermined endogenously from he money demand relaionship (2). As ypically wrien, an ineres rae rule specifies ha he moneary auhoriy adjuss he nominal ineres rae in response o deviaions of inflaion from a arge rae, π*, and o deviaions of oupu from poenial (he oupu gap). Alhough we examined some rules wih oupu in hem, our model does no

13 include he sandard noion of an oupu gap. In models where prices do no adjus o clear markes, he oupu gap is defined as he difference beween he models oupu and he level ha would occur in a flexible price equilibrium. In he pas we have defined he oupu gap as he deviaion of oupu from he seady sae. In preliminary resuls for his sudy, we found ha none of our qualiaive resuls depended on having oupu in he policy rule. 2 Therefore we focus on policy in which he cenral bank responds only o inflaion. (2) R = r + π * + ϕπ ( π + π* ). Assuming a consan inflaion arge, his rule can be wrien (2 ) R = ( r ϕ π π *) + ( + ϕ ) π. + π In he conex of his model, a rule of his ype can be specified as π (22) ( + R+ ) = ( + r) π π * ϕ π. In erms of log-deviaions from a consan seady-sae, (22 ) Rˆ = ˆ ( + + ϕπ ) π Recall ha π includes boh he endogenous rae of change in prices, p /p -, and an exogenous componen represening he inflaion rend, γ p. Inerpreing he exogenous componen as a arge rae of inflaion ha is subjec o occasional deviaions from he consan seady-sae, he rule can be generalized o allow for changes in he inflaion arge: (23) Rˆ = ˆ ˆ ( + ϕπ) π + ϕπγ. p The remaining exogenous variables z, and γ p are similarly assumed o follow independen firs order auoregressive processes ha are calibraed from he daa. 2 We also confirmed he resul in Edge and Rudd (2002) ha adding axes o he model resrics he size of he 2

14 z = ρ z + ε z z γ = ργ + ε π p π p π The moneary policy shock, ε, is a shock o he inflaion rend. The model s dynamics are simulaed in erms of proporional deviaions from a baseline, consan seady sae. Seady-Sae and Model Calibraion The model s dynamics will be approximaed as proporional deviaions from a baseline seady sae, defined by he model parameers (including he baseline growh raes of echnology and prices, γ x and γ p ). The model is calibraed by maching he seady-sae values o long-run macroeconomic daa (see Table ). [Table ] Some of he model s parameers are calibraed direcly using long-run average values for pos-960 U.S. daa: he capial share is se equal o 0.38, and he depreciaion δ=.02. The discoun facor, β, is se o We se he relaive risk aversion parameer equal o 2. The shopping-ime parameer, η is se a one, implying an ineres-elasiciy of money demand equal o minus one half. Seady sae allocaions of ime are se exogenously, wih marke labor comprising 30 percen of ime, and shopping ime equaling 0.3 percen of ime and he remaining percen of ime allocaed o leisure. The growh rae parameers are se a γ x =.004 and γ p =.0, reflecing he average annual growh raes of produciviy growh and inflaion equal o approximaely.6 percen and 4 percen, respecively. The money growh rend is a produc of he echnology and inflaion growh rends. parameer space for which he model has a unique equilibrium. In our model, increasing he weigh on oupu resrics he space even more. 3

15 Several key seady-sae raios are useful for deriving values for he remaining model parameers, and for specifying he linear approximaions used o calculae he model s dynamics. Firs, equaions (4) and (8) can be used o derive he seady sae capial/oupu raio: (24) k y = γ x K αβ ( τ ) K β ( δ ) + βτ [( γ ) / γ δ ] p p. From (2 ) he share of oupu used for invesmen will be (25) i y k = [ γ x ( δ )], y and from (4 ) he consumpion share is (26) c y i =. y From (9) and (0), he marginal rae of subsiuion beween consumpion and leisure is relaed o he wo shadow-prices and he parameers of he shopping-ime funcion. Subsiuing he values of he relaive shadow prices from (), we can derive he following relaionship: θ L c S (27) = + η. θ N ( τ N )( α) y N Given a calibraed allocaion of ime among labor, leisure, and shopping along wih a value of η (seleced o generae money demand elasicies) and he consumpion/oupu raio from (27) equaion (28) deermines he value of he parameer θ o be used. Combining equaions () and (2) yields (28) γ γ N py S x p + ( τ )( α) η =, m N β 4

16 which defines he seady sae raio of nominal oupu o money (velociy), Wih his value in hand, we can use he shopping-ime definiion (6 ), along wih he consumpion-oupu raio above, o specify a value for he scale parameer, ξ, consisen wih he calibraed allocaion of ime o shopping. 3 Seady sae ax raes are all se o equal he average marginal ax raes for 960 o 2002 calculaed using he NBER TAXSIM model and repored in Table 9 of Feenberg and Poerba (2003). They are 24 percen for labor, 26 percen for ineres income, 34 percen for capial income and 20 percen for capial gains. In his paper, we consider only wo shocks: he firs is o he level of echnology and he second is o he inflaion rend. 4 We calibrae he echnology shock wih a 0.95 firs-order auocorrelaion parameer and a sandard deviaion equal o 0.75 percen a a quarerly rae, calibraions widely used in he real business cycle lieraure. In principle, he ime-series process for he inflaion rend can be calibraed using eiher money growh or inflaion daa. Because he daa were generaed in an era in which he cenral bank usually followed an ineres rae rule, he model suggess ha we should calibrae he model o he persisence in he inflaion daa. Gavin and Kydland (2000), among many ohers, show ha he auocorrelaion of inflaion dropped significanly afer he policy change in Ocober 979. Therefore, we esimae he persisence in he inflaion rae separaely for pre and pos 979 periods. Using an augmened Dickey Fuller mehod, we esimae he persisence o be 0.97 before 979 and 0.84 aferwards. The sandard deviaion of he residual is approximaely Alernaively, equaion (29) can be used o calibrae S and ξ o be consisen wih a pre-seleced value for velociy. 4 See Pakko (2002) for an analysis of persisen shocks o he growh rend in echnology. 5

17 percen a a quarerly rae in boh periods. Under his specificaion, he lower uncondiional variance of inflaion afer 979 is all due o lower persisence. 5 Seady-sae welfare coss The main operaive mechanism of he model he ineracion of inflaion wih he nominal ax code is illusraed in he seady-sae welfare calculaions presened in Table 2. [Table 2] The small welfare coss of inflaion aribuable o non-neuraliy from he shopping-ime funcion are shown in he firs row. These losses are associaed wih ypical welfare riangle ype calculaions: Higher raes of inflaion induce households o economize on real money holdings, requiring greaer shopping-ime (a he expense of leisure and work-effor). For an inflaion rae of 0 percen, oupu and consumpion are only 0.42 percen lower han hey would be in a zero-inflaion seady-sae. Leisure is only marginally lower han in he zero-inflaion environmen. The final wo columns of he able show he combined effecs of lower consumpion and leisure on household uiliy, using a measure of compensaing variaion calculaed as he κ ha solves U ( c, L ) U (( κ ) c, L = ), where superscrips denoe he sead-sae inflaion rae. For he firs row, his value represens a cos of only 0.47 percen of seady-sae consumpion in he zero-inflaion environmen. As a fracion of oupu, his amouns o lile more han one-hird of one percen. 5 Using Bayesian mehods, Kim, Nelson, and Piger (2003) find ha he poserior mean of he persisence parameer falls from 0.94 before 979:Q2 o 0.72 aferwards. They also esimae a separae breakpoin for he innovaion variance which occurs in 99. 6

18 The second row shows ha wih he excepion of he capial gains ax he addiion of axes o he model have no effec on he welfare coss of inflaion. In fac, he coss of 0 percen inflaion are even smaller in his case because he zero-percen baseline economy is already disored by axes on real labor and capial income. The hird row shows he dramaic effec ha nominal axaion of capial gains has on he seady sae. In he high-inflaion environmen, oupu is abou 2 percen lower han i would be a zero inflaion, while consumpion is lower by abou 8 percen. The main effec of inflaion is revealed in he capial/oupu raio, which is nearly 3 percen lower in he 0 percen inflaion regime. As a resul, wages and employmen are suppressed (so ha leisure is acually higher for his case). In erms of he compensaing variaions, 0 percen inflaion represens a cos of abou 7 percen of seady-sae consumpion, or abou 5 o 6 percen of oupu. These calculaions confirm ha our model framework capures he effecs highlighed by Feldsein, Fisher, and ohers; namely, ha he nominal axaion of capial gains implies ha inflaion suppresses capial accumulaion. In he model dynamics presened below, our ineres is in evaluaing how his mechanism generaes aggregae flucuaions in response o sochasic inflaion. Model Dynamics We show how he model economy responds o moneary policy shocks under alernaive assumpions abou ax policy and he cenral bank policy rule. In general, he real effecs of moneary policy shocks are magnified if he cenral bank follows an ineres rae rule. The reason for his is shown in Figure which plos he response of inflaion o a moneary policy shock under boh moneary policy rules wih he baseline ax raes. Wih a money growh rule, a 7

19 persisen one-percen money growh shock leads o a jump in he price level of 0 percen wih lile persisence in he inflaion rae. Wih an ineres rae rule, however, inflaion rises o percen on impac, and persiss for many years. Noe ha he bond ax magnifies he effec on inflaion. Wihou he bond ax, a one percen shock o he inflaion rend causes he inflaion rae o jump o 0.7 percen before gradually reurning o he seady sae. By using an ineres rae rule, he cenral bank eliminaes he price jumping ha occurs in general equilibrium models wih money supply rules. 6 Insead, he money supply endogenously accommodaes he shif in money demand. [Figure ] The effec on he real economic dynamics of our model is bes seen by comparing he response of he capial sock under hese alernaive regimes. Figure 2 shows he no ax and all axes cases under boh moneary policy regimes. Wih no axes, here is almos no measurable effec of a moneary policy shock under eiher moneary policy regime. Including axes makes hese effecs measurable. Under a money growh rule, he capial sock gradually falls o a rough abou percen below he seady sae level afer five years. Wih he ineres rae rule, a one percen shock o he money growh rae causes he capial sock o fall much furher more han 2-/2 percen afer 7 years and i says well below he seady sae for 25 years. For all of he resuls below, he paern of responses for real variables is similar under boh money growh rules and ineres rae rules. The effecs under ineres rae rules, however, are magnified. Since mos cenral banks implemen policy wih some form of ineres rae argeing and none do so wih moneary aggregaes, we consider only he case wih ineres rae rules for he remainder of he paper. 6 See Friedman (969) for an early exposiion of he jumping ha occurs in models wih money supply rules. Miller 8

20 [Figure 2] The impulse responses of he capial sock a moneary policy shock under four ax regimes are shown in Figure 3. The ax regime wih he smalles impac is he one wih he seigniorage ax only. Here a persisen percen shock o he inflaion arge causes capial o decline only a iny fracion of a percen. When we include all axes excep capial gains axes, he decline, on impac, is abou 0. percen. The decline is enirely due o he bond ax because i drives a larger wedge beween he before- and afer-ax ineres rae. Braun (994) and McGraan (994) show ha boh he labor ax and he capial ax have large welfare effecs, bu he size of he ax wedges do no change wih inflaion and do no inerac wih flucuaions in he inflaion rae as does he bond ax. 7 In he hird ax regime, we reinsae he capial gains ax bu eliminae he ax on bond income. Here he large effec of he capial gains ax is clearly eviden. The impac effec is.3 percenage poins larger han he impac effec wih no axes. When we include all axes, a percen increase in he inflaion arge reduces he capial sock by 2.7 percen. The bond ax is imporan because i raises he impac on inflaion by abou half and herefore magnifies he increase in he effecive ax on nominal capial gains. [Figure 3] Figure 4 shows he impulse-responses of some key macroeconomic variables following a one percen inflaion shock. Boh oupu and hours worked decline sharply upon impac wih he decline in invesmen demand. Oupu follows capial sock along a proraced pah of belowrend growh. Hours converge back o he seady sae over ime he rae convergence has halflife of abou 4 years. The model produces a counerfacual increase in consumpion because here is no cos of adjusing capial and i is freely consumed if he sock is oo high. Figure 4 and Upon (974) refer o his jumping as he Friedman surge. 9

21 shows ha his effec is quie shor-lived compared o he long period of depressed consumpion ha follows an inflaionary shock. Labor produciviy also displays a shor-lived increase upon impac, followed by a long period of convergence back o he rend. [Figure 4] Business Cycle Effecs This model can also be used o show how much cyclical oupu variaion migh be aribued o he ineracion of inflaion wih he ax code. As shown by Gavin and Kydland (999), Kim, Nelson and Piger (2003) and ohers, here has been a leas one significan srucural break in he inflaion process over he sample period. In paricular, he persisence of shocks o inflaion diminished significanly afer 979. Consequenly, we calculae he business cycle effecs of inflaion innovaions under wo separae regimes for inflaion: In he firs regime (corresponding o he pre-979 period) he auoregressive parameer ρ π is se o 0.97, while for he laer period we simulae he model using a value of In each of he simulaions, he echnology shock is assumed o have a firs-order AR parameer of 0.95 and a shock variance of [Table 3] 7 Chang (995) considered he capial income ax, bu also did no invesigae he ineracion wih inflaion. 8 These values were esimaed using Dickey-Fuller regressions for sample periods of 954:Q-979:Q3 and 979:Q4 2003:Q4. The esimae for he early period should probably be adjused upward for he bias repored in Sock (99). If we were o delee he ransiion years, 980 o 982, he esimae of he persisence would fall o 0.72 for he laer period. 20

22 Analysis of HP Filered Momens: Table 3 shows sandard deviaions and correlaions wih oupu for some key macroeconomic variables (HP filered), comparing versions of he model wih and wihou he nominal capial gains ax. I is clear from he op panel of Table 3 ha he ineracion beween inflaion and he nominal capial gains ax has a subsanial effec when inflaion is highly persisen as before 980. In he early period, he RBC model wihou capial gains axes explains 72 percen of he variabiliy in he cyclical variance in oupu. In his simple model wihou axes, he variabiliy of hours and produciviy are unrealisically low and he co-movemen beween oupu and oher variables far o high relaive o he daa paricularly for produciviy. These simulaed momens are nearly idenical o hose ha would obain in a model wihou eiher axes of inflaion. Persisen shocks o he inflaion objecive have no measurable impac on oupu in he model wihou a capial gains ax. Adding he capial gains ax increases he sandard deviaion of each of he variables considered. The variabiliy of oupu rises o accoun for 80 percen of he variabiliy in he daa. Hours and produciviy variabiliy rise considerably. In addiion, he inclusion of capial gains axes inroduces a propagaion channel for inflaion shocks ha lowers he high correlaion beween oupu and oher macroeconomic variables ha is ypical of sandard RBC models. As we saw in Figure 4, when he shock o inflaion is highly persisen, he resuling increase in he expeced fuure effecive capial gains ax causes households o consume capial, generaing a low conemporaneous correlaion wih oupu and very volaile invesmen. Indeed, in he model wih capial gains axes, he correlaion of consumpion and oupu is far oo low relaive o U.S. daa. On he oher hand, he shor-run dynamics illusraed in Figure 4 also imply a lower 2

23 correlaion of oupu and produciviy, brining ha saisic very close o is observed value in he daa. In he laer period, wih ρ π = 0.84, he qualiaive resuls are similar bu much smaller. The sandard deviaion of oupu deviaions is no higher han wihou he capial gains ax. Boh hours and produciviy are slighly more volaile and less highly correlaed wih oupu. Wih he lower persisence, he variabiliy of consumpion, invesmen and hours are only slighly higher han in he model wihou a capial gains ax. The firs-order auocorrelaions are slighly lower in he model ha includes capial gains axes, bu he effec is no nearly as pronounced as in he high-persisence case. Frequency Decomposiion: The impulse responses in Figures 2-4 showed ha he effecs of persisen moneary policy shocks operaing hrough he capial gains ax have effecs a a frequency ha is ends o be lower han ha of business cycles. Therefore, we invesigaed he model s dynamics a differen frequencies using a band-pass filer. 9 The resuls of hese decomposiions repored in Table 4 show ha when inflaion has high persisence (Panel A), he ineracion of inflaion wih he capial gains ax has significan effecs on he model dynamics a all frequencies. For example, he inroducion of capial gains axes o he model raises he sandard deviaion of oupu by 9.4 percen a high frequencies, by.2 percen a business cycle frequencies, and by 6.5 percen a low frequencies. The sandard deviaion of hours is approximaely wice as large in he model wih a capial gains ax han wihou. This is rue across he full range of frequency bands. Noe ha he low correlaion 9 The saisics for U.S. daa repored in Table 4 are calculaed using he band-pass filer suggesed by Chrisiano and Fizgerald (2003). Saisics for he model simulaions are filered using ideal band-pass filers applied o a 22

24 beween oupu and consumpion noed above is no inconsisen wih he corresponding highfrequency componen of he daa. When he persisence in he inflaion process is calibraed a 0.84 (Panel B) he impac of inflaion shocks declines dramaically. Along many dimensions, he versions of he model wih and wihou capial gains axes generae nearly idenical implicaions for volailiy across all frequencies. However, here remains a noiceable increase in he variabiliy of invesmen and hours when capial gains axes are inroduced. For invesmen, he effec of inroducing capial gains axes is greaes in he high-frequency range. For hours, he effec is larges a business cycle frequencies. The saisics for U.S. daa repored in Tables 3 and 4 illusrae he widely-documened decline in he volailiy of real macroeconomic variables since 979. The analysis he model suggess ha he lower persisence of inflaion since 979 migh have played a role in his volailiy decrease. Wih high persisence in he inflaion process, inflaion shocks inerac wih he capial gains ax o have large effecs on real variables. This impac declines dramaically wih he decline in inflaion persisence. Simulaions of U.S. Daa: The model simulaions sugges ha we should see imporan cyclical effecs from he ineracion of inflaion and he capial gains ax before 980, bu he effecs may be oo small o be measurable aferwards. To illusrae his feaure of he model, we use esimaed shocks o he inflaion rend o see wha our model implies for movemens of capial, hours worked and labor produciviy for U.S. hisory wih a policy break in 979:Q3. We use he same calibraion for he policy process as was used in Table 3. The conribuion of esimaed inflaion shocks o he real economy are summarized in Figure 5. frequency domain decomposiion of he model s populaion momens. The parameers of he bands are as follows: 23

25 [Figure 5] In he period leading up o 980, he effecs of he ineracion beween inflaion and he capial gains ax are of he same order of magniude as he effecs of echnology shocks. As we saw in Figure 2, he effecs on he capial sock ake such a long ime o peak ha he damage from rising inflaion in he 960s and 970s coninued o have a depressing effec on he capial sock ino he 990s. The impac on hours worked works hough he economy quickly. The upward drif upward of inflaion caused hours worked o fall below he seady sae level for mos of he 970s. Corresponding o he inflaionary effecs of he oil price shocks of he 970s, he model implies sharp declines in employmen associaed wih hose evens. Since 980, he effec on hours worked is insignifican. The impac on produciviy reflecs a combinaion of he effec on he capial sock and on hours worked. The upward drif in inflaion combined wih he nominal ax on capial o exer an increasingly negaive impac on labor produciviy from he lae 960s unil afer 980. Since he 980s, his effec has helped o raise labor produciviy slighly. Conclusion When he cenral bank operaes wih an ineres rae, persisen shocks o he rend in money growh (or, equivalenly, he inflaion arge) can have large real effecs on he business cycle if he ax sysem is no indexed for inflaion. In our model, here is a ax on nominal capial gains. The business cycle effecs are large when he shocks o he expeced inflaion objecive are highly persisen. We found hose effecs o be large in he Unied Saes before high frequency, 2-6 quarers; business cycle frequency, 6-32 quarers; and low frequency, quarers. 24

26 980, bu no aferwards. The reducion of persisence in shocks o he inflaion arge was he criical aspec of he change in moneary policy. Before 980, he inflaion objecive appeared o follow a random walk. Afer 980, we esimaed he larges roo in he inflaion process o be no larger han A his level, he shocks do no have much impac on he cycle, raising he cyclical deviaions by only abou 5 percen above he case wih no moneary policy shocks. Using a common calibraion for all parameers excep he persisence in he shock o he long-run inflaion objecive, we find ha bad moneary policy may parially explain he slowdown in produciviy growh before 980. The upward rend in he average inflaion rae probably ineraced wih he ax on nominal capial gains o reduce produciviy growh in he 960s and 970s. Beer policy afer 980 may parially explain he revival of produciviy and he lower variabiliy of real variables since hen. 25

27 References Abel, Andrew B. Commen on The Coss and Benefis of Going from Low Inflaion o Price Sabiliy, by Marin Feldsein in Reducing Inflaion : Moivaion and Sraegy, eds. Chrisina D. Romer and David H. Romer, Chicago: Universiy of Chicago Press Alig, David, and Charles Carlsrom, Inflaion, Personal Taxes, and Real Oupu: A Dynamic Analysis, Journal of Money, Credi and Banking 23(3) Par II (Augus 99) Braun, R. Anon. Tax Disurbances and Real Economic Aciviy, Journal of Moneary Economics 33 (994) Bullard, James B., and Seven H. Russell. "How Cosly is Susained Low Inflaion for he US Economy?" Federal Reserve Bank of S. Louis Working Paper #997-02B, Revised March 998. Carlsrom, Charles T., and Timohy S. Fuers. "Timing and Real Indeerminacy in Moneary Models," Journal of Moneary Economics 47 (200), Chang, Ly-June. Business Cycles wih Disoring Taxes and Disaggregaed Capial Markes, Journal of Economic Dynamics and Conrol, 9 (995) Chrisiano, Lawrence J. and Terry J. Fizgerald, The Band Pass Filer, Inernaional Economic Review 44 (2003), Cohen, Darrel, Kevin A. Hasse, and R. Glenn Hubbard. Inflaion and he User Cos of Capial: Does Inflaion Sill Maer? in The Coss and Benefis of Price Sabiliy, ed. Marin Feldsein, Chicago: Universiy of Chicago Press Cooley, Thomas F., and Gary D. Hansen. The Inflaion Tax in a Real Business Cycle Model, American Economic Review 79 (Sepember 989), Dimar, Rober D., William T. Gavin, and Finn E. Kydland. Inflaion Persisence and Flexible Prices, Federal Reserve Bank of S. Louis Working Paper, E. Revised April 2004, Forhcoming Review of Inernaional Economics. Edge, Rochelle M., and Jeremy B. Rudd. Taxaion and he Taylor Principle, Division of Research and Saisics, Federal Reserve Board, Ocober 3, 2002 Feenberg, Daniel R., and James M. Poerba. The Alernaive Minimum Tax and Effecive Marginal Tax Raes, NBER Working Paper 0072, November

28 Feldsein, Marin. The Coss and Benefis of Going from Low Inflaion o Price Sabiliy, in Reducing Inflaion : Moivaion and Sraegy, eds. Chrisina D. Romer and David H. Romer, Chicago: Universiy of Chicago Press Fischer, Sanley. Towards an Undersanding of he Coss of Inflaion : II, Carnegie-Rocheser Conference Series on Public Policy 5 (98) Friedman, Milon. The Opimum Quaniy of Money and Oher Essays, Chicago, Aldine Publishing Company, 969. Gavin, William T., and Finn E. Kydland, Endogenous Money Supply and he Business Cycle, Review of Economic Dynamics (999), pp.???? Gavin, William T., and Finn E. Kydland, The Nominal Facs and he Ocober 979 Policy Change, Federal Reserve Bank of S. Louis Review 82 (November/December 2000) Goodfriend, Marvin S., and Benne T. McCallum. Money: Theoreical Analysis of he Demand for Money, in The New Palgrave: A Dicionary of Economic Theory and Docrine. 987, pp.????? Kim, Chang-Jin, Charles R. Nelson, and Jeremy Piger. The Less-Volaile U.S. Economy: A Bayesian Invesigaion of Timing, Breadh, and Poenial Explanaions, Journal of Business and Economic Saisics, King, Rober G., Charles I. Plosser and Sergio T. Rebelo. Producion, Growh, and Business Cycles, Journal of Moneary Economics 2 (988) Kozicki, Sharon, and Peer A. Tinsley. Permanen and Transiory Policy Shocks in an Empirical Macro Model wih Asymmeric Informaion, CFS Working Paper No. 2003/4, Ocober Kydland, Finn E. Moneary Policy in Models wih Capial, in Dynamic Policy Games, van der Ploeg, F. and A. J. de Zeeuw eds. Elsevier Science Publishers B. V. (Norh-Holland), 989. Leung, Charles Ka Yui and Guang-Jia Zhang, Inflaion and Capial Gains Taxes in a Small Open Economy, Inernaional Review of Economics and Finance 9 (2000) McGraan, Ellen R. The Macroeconomic Effecs of Disorionary Taxaion, Journal of Moneary Economics 33 (994) Miller, Meron H., and Charles Upon. Macroeconomics: A Neoclassical Inroducion, The Universiy of Chicago Press,

29 Pakko, Michael R. Wha Happens When he Technology Growh Trend Changes? Transiion Dynamics, Capial Growh, and he New Economy. Review of Economic Dynamics 5 (2002), Pakko, Michael R. Shoe-Leaher Coss of Inflaion and Credibiliy, Federal Reserve Bank of S. Louis Review 80(6) (November/December 998), Sock, James H. Confidence Inervals for he Larges Auoregressive Roo in U.W. Macroeconomic Times Series, Journal of Moneary Economics 28 (99)

30 Table : Parameer Calibraion for he Baseline Case Parameer Symbol Value Depreciaion rae δ 0.02 Discoun facor β 0.99 Relaive risk aversion σ 2 Labor ax rae τ N 0.24 Capial ax rae τ K 0.34 Bond ax rae τ B 0.26 Capial gains ax rae τ Kg 0.20 Seady sae oupu growh γ x.004 Seady sae money growh γ p.0 Shopping ime parameer η Capial share in producion α 0.38 Seady sae share of shopping ime S Seady sae share of ime supplying labor services N 0.3 Fed's reacion o inflaion φ π 0.5 Fed's reacion o oupu gap φ y 0 Persisence in he echnology shock ρ z 0.95 Persisence in he money growh shock ρ π 0.95 Sandard deviaion of Shocks Producion Technology σ z Moneary policy σ π

31 Table 2: Welfare Effecs of a Seady-Sae 0 percen Inflaion Rae Effecs on Seady-Sae Values (Percen) Compensaing Variaion As Percen of: Y C L W K/Y C Y No Taxes Taxes w/o Capial Gains Taxes Incl. Capial Gains

32 Table 3: Second Momens (HP Filered) Panel A: ρ π = 0.97 U.S. daa 954: 979:3 Model w/o Capial Gains Tax Model wih Capial Gains Tax SD( ) Corr(,y) SD( ) Corr(,y) SD( ) Corr(,y) Oupu Consumpion Invesmen Hours Produciviy Panel B: ρ π = 0.84 U.S daa 979:4-2003:4 Model w/o Capial Gains Tax Model wih Capial Gains Tax SD( ) Corr(,y) SD( ) Corr(,y) SD( ) Corr(,y) Oupu Consumpion Invesmen Hours Produciviy

33 Table 4: Frequency Analysis of Second Momens (Band Pass Filer) Panel A: ρ π = 0.97 U.S. daa 954: 979:3 Model w/o Capial Gains Tax Model wih Capial Gains Tax High Frequency SD( ) Corr(,y) SD( ) Corr(,y) SD( ) Corr(,y) Oupu Consumpion Invesmen Hours Produciviy Business Cycle Frequency SD( ) Corr(,y) SD( ) Corr(,y) SD( ) Corr(,y) Oupu Consumpion Invesmen Hours Produciviy Low Frequency SD( ) Corr(,y) SD( ) Corr(,y) SD( ) Corr(,y) Oupu Consumpion Invesmen Hours Produciviy

34 Table 4: Frequency Analysis of Second Momens (Band Pass Filer) Panel B: ρ π = 0.84 U.S. daa 979:4 2003:4 Model w/o Capial Gains Tax Model wih Capial Gains Tax High Frequency SD( ) Corr(,y) SD( ) Corr(,y) SD( ) Corr(,y) Oupu Consumpion Invesmen Hours Produciviy Business Cycle Frequency SD( ) Corr(,y) SD( ) Corr(,y) SD( ) Corr(,y) Oupu Consumpion Invesmen Hours Produciviy Low Frequency SD( ) Corr(,y) SD( ) Corr(,y) SD( ) Corr(,y) Oupu Consumpion Invesmen Hours Produciviy

35 Figure : Inflaion Response o a % Moneary Policy Shock (Wih all axes) Percen deviaions from he seady sae 2 0 Money Growh Rule 8 (ρ π = 0.95 in boh cases) Taylor Rule Quarers following shock 34

36 Figure 2: Capial Response o a % Moneary Policy Shock (Effecs of Differen Policy Rules) No axes All ax raes and a money growh rule -.5 All axes and an ineres rae rule

37 Figure 3: Capial Response o a % Moneary Policy Shock (Effecs of differen axes) 0.0 No axes All axes excep capial gains All axes excep bond ax All axes

38 Figure 4: Responses o a % Moneary Policy Shock 0.0 Y 0.0 N C 0.6 Y/N

39 Figure 5: Conribuion of Moneary Policy Shocks 8% 6% 4% 2% 0% -2% -4% -6% Capial % 2% Hours 0% -2% -4% -6% % 2% % 0% -% -2% -3% Produciviy