Ramsey Taxation in the Global Economy. Working Paper 745 December 2017

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1 Ramsey Taxaton n the Global Economy V. V. Char Unversty of Mnnesota and Federal Reserve Bank of Mnneapols Juan Pablo Ncoln Federal Reserve Bank of Mnneapols and Unversdad D Tella Pedro Teles Banco de Portugal, Catolca Lsbon SBE, and CEPR Workng Paper 745 December 2017 DOI: Keywords: Captal ncome tax; Free trade; Value-added taxes; Border adjustment; Orgn- and destnaton-based taxaton; Producton effcency JEL classfcaton: E60, E61, E62 The vews expressed heren are those of the authors and not necessarly those of the Federal Reserve Bank of Mnneapols, the Federal Reserve System, Banco de Portugal, or the European System of Central Banks.. Federal Reserve Bank of Mnneapols 90 Hennepn Avenue Mnneapols, MN

2 Ramsey Taxaton n the Global Economy V. V. Char Unversty of Mnnesota and Federal Reserve Bank of Mnneapols Juan Pablo Ncoln Federal Reserve Bank of Mnneapols and Unversdad D Tella Pedro Teles Banco de Portugal, Catolca Lsbon SBE, CEPR December 2017 Abstract We study cooperatve optmal Ramsey equlbra n the open economy addressng classc polcy questons: Should restrctons be placed to free trade and captal moblty? Should captal ncome be taxed? Should goods be taxed based on orgn or destnaton? What are desrable border adjustments? How can a Ramsey allocaton be mplemented wth resdence-based taxes on assets? We characterze optmal wedges and analyze alternatve polcy mplementatons. Keywords: Captal ncome tax; free trade; value-added taxes; border adjustment; orgn- and destnaton-based taxaton; producton effcency JEL Codes: E60; E61; E62 We thank Charles Brendon, Isabel Correa, and Dejanr Slva for very helpful dscussons. Char thanks the NSF for supportng the research n ths paper and Teles acknowledges the support of FCT as well as the ADEMU project, A Dynamc Economc and Monetary Unon, funded by the European Unon s Horzon 2020 Program under grant agreement The vews expressed heren are those of the authors and not necessarly those of the Federal Reserve Bank of Mnneapols, the Federal Reserve System, Banco de Portugal, or the European System of Central Banks. E-mal addresses: varadarajanvchar@gmal.com, juanpa@mnneapolsfed.org, pteles@ucp.pt. 1

3 1 Introducton In ths paper we study cooperatve Ramsey equlbra n the open economy, addressng classc polcy questons such as: Should restrctons be placed on free trade and captal moblty? Should captal ncome be taxed? Should goods be taxed based on orgn or destnaton? What are desrable border adjustments? How can the Ramsey equlbrum be mplemented wth resdence-based taxaton of asset ncome? We take the Ramsey approach to optmal taxaton, n that the tax system s exogenously gven. We consder taxes wdely used n practce n developed economes. Those nclude consumpton and labor ncome taxes, taxes on captal ncome, equty returns, and returns on foregn assets, as well as value-added taxes wth and wthout border adjustments. As s well known, many tax polces yeld the same dstortons, and the theory pns down those dstortons n choces. Followng the publc fnance lterature, we refer to these dstortons as wedges. The frst man queston we address s, what are the optmal wedges? In partcular, we ask whether the Ramsey equlbrum yelds ntertemporal wedges. If t does, we say that future captal s taxed. If t does not, we say that future captal s not taxed. No ntertemporal wedges mples that ntratemporal wedges are constant over tme. Ths means that unform taxaton s optmal. We also ask whether the Ramsey allocatons dstort condtons for producton effcency assocated wth free trade. The second man queston addressed n ths paper s, how can the optmal wedges be mplemented? We consder mplementatons that, we beleve, are of nterest to polcy desgn. The model s a neoclasscal growth model wth two countres wth ntermedate goods that are traded nternatonally, as n Backus, Kehoe, and Kydland (1994). A useful feature of the model s that t nests the closed economy neoclasscal growth model. We characterze the optmal cooperatve Ramsey allocatons and determne what are optmal nter- and ntratemporal wedges as well as wedges on the movement of goods across borders. We determne the mnmal set of fscal nstruments that mplement those allocatons and study alternatve sets of nstruments that mplement those same allocatons. For general preferences, captal should not be taxed n the steady state, and there s no presumpton that t ought to be taxed along the transton. A subsdy may be optmal. Another man result s that free trade, requred for producton effcency, s also optmal. In addton, for standard macro preferences wth constant elastctes, t 2

4 s not optmal to ever mpose ntertemporal wedges, meanng that t s not optmal to tax captal. Ths result holds for the steady state but also for the transton. A mnmal set of nstruments to mplement the Ramsey allocaton are consumpton and labor ncome taxes. There s no need for taxes on ncome from assets. 1 For standard macro preferences, only a constant tax on ether labor or consumpton, possbly dfferent across countres, s necessary to mplement the Ramsey allocaton. We move on to study alternatve mplementatons n whch assets are taxed. We construct a resdence-based tax system wth captal ncome taxes on frms and a country-specfc, common tax on equty returns and returns from foregn assets. These taxes, together wth ether a labor ncome tax or a consumpton tax, mplement the Ramsey allocaton. Captal ncome taxes are optmally set to zero. We also consder alternatve ways of taxng goods, n partcular, value-added taxes wth and wthout border adjustments. A tax system wth value-added taxes wth border adjustments s equvalent to the system wth consumpton taxes. However, a value-added tax wthout border adjustment n general would dstort the allocaton of captal across countres. Compensatng, tme-varyng tarffs can undo those dstortons. We dscuss the mplcatons of these results for the desrablty of orgn- versus destnaton-based taxaton of consumpton. There s a lterature on value-added taxes wth and wthout border adjustments. 2 Grossman (1980), and Feldsten and Krugman (1990) show n statc models that border adjustments are rrelevant. 3 Barbero, Farh, Gopnath, and Itskhok (2017) make the same pont n a dynamc model wth labor only. In our model wth captal, border adjustments matter. Because the neoclasscal growth model s nested n the open economy model we study, the results on ntertemporal and ntratemporal wedges also apply n the closed economy model. So n the closed economy there s also no presumpton that captal ncome should be taxed, not only n the steady state but also along the transton. Ths result s n contrast wth nfluental results n the lterature on the optmal taxaton of captal. Chamley (1986) and Judd (1985) show that captal should be taxed at ts maxmum level ntally and for a number of perods. Bassetto and Benhabb (2006) 1 Ths does not mean that captal s not taxed, snce ntertemporal dstortons may be optmal along the transton for general preferences. 2 See Auerbach, Devereux, Keen, and Vella (2017) for a polcy evaluaton of the recent destnatonbased cash flow tax proposal. 3 See also Dxt (1985). 3

5 and Straub and Wernng (2015) show that full taxaton of captal can last forever. 4 Ths lterature leads to the presumpton that captal taxes should be hgh at least for some tme. Two assumptons are mportant for the contrastng results. The frst assumpton concerns the confscaton of ntal wealth. We assume, n lne wth Armenter (2008), that confscaton s restrcted both drectly and ndrectly through valuaton effects. The lterature nstead only restrcts drect confscaton. The second assumpton s on the avalable nstruments. In contrast wth the lterature, we allow for a rch set of fscal nstruments. 5 The contrastng results are explaned n detal n a companon paper on captal taxaton n the closed economy by Char, Ncoln and Teles (2016). Char et al. (2016) also show, extendng results n Wernng (2007), that heterogenety n ntal endowments of captal does not affect the optmal wedges. They also relate the results on the optmal taxaton of captal to the ones on unform commodty taxaton n Atknson and Stgltz (1972) and optmalty of producton effcency n Damond and Mrrlees (1971). The paper s organzed as follows. In Secton 2, we present the two-country economy model wth consumpton and labor ncome taxes. We compute optmal Ramsey allocatons, show that trade should not be restrcted, and show that, for standard macro preferences, captal should never be taxed. In Secton 3, we consder alternatve tax systems that mplement the same Ramsey optmal allocaton. We frst consder a common tax on ncome from domestc equty and from foregn assets, together wth a proft tax (Secton 3.1). We also dscuss alternatve ways of taxng consumpton through value-added taxes wth and wthout border adjustment (Sectons 3.2 and 3.3). Secton 4 concludes. 2 A two-country economy There are two countres n ths economy ndexed by = 1, 2. The preferences of a representatve household n each country are over consumpton c t and labor n t, U = β t u (c t, n t ), (1) 4 Other relevant lterature ncludes Char, Chrstano, Kehoe (1994), Atkeson, Char and Kehoe (1999), Coleman (2000), Judd (1999, 2002), and Lucas and Stokey (1983). 5 Wth a rch set of nstruments, f ndrect confscaton through valuaton effects was allowed for, t would dstort captal accumulaton n the frst perod only. 4

6 satsfyng the usual propertes. Followng Backus, Kehoe and Kydland (1994) only ntermedate goods are traded. Fnal goods are not traded. Each country, = 1, 2, produces a country specfc ntermedate good, y t, accordng to a producton technology gven by y 1t + y 2t = y t = F (k t, n t ), (2) where y jt denotes the quantty of ntermedate goods produced n country and used n country j = 1, 2, k t s the captal stock, n t s labor nput and F s constant returns to scale. The ntermedate goods produced by each country are used to produce a country specfc fnal good that can be used for prvate consumpton, c t, publc consumpton, g t, and nvestment, x t, accordng to c t + g t + x t G (y 1t, y 2t ), (3) where G s constant returns to scale. Captal accumulates accordng to the law of moton x t = k t+1 (1 δ) k t. (4) If lump sum taxes and transfers across countres are avalable, the allocatons on the Pareto fronter satsfy the followng effcency: condtons, u ct u nt = 1 G,t F, = 1, 2 (5) nt u c,t βu c,t+1 = 1 δ + G,t+1F kt+1, = 1, 2 (6) G 1 j,t G 1 j,t+1 G 1 1,t+1 Fk,t δ ] = G2 j,t G 2 G 2 2,t+1 Fk,t δ ], j = 1, 2 (7) j,t+1 G 1 1,t G 2 1,t = G1 2,t, (8) G 2 2,t whch, together wth the resource constrants, characterze the Pareto fronter. The condtons above mean that there are no ntratemporal wedges (condtons (5)), no ntertemporal wedges ((condtons (7)), and no producton dstortons (condtons 5

7 (6) and (8)). Condtons (5) set the margnal rate of substtuton between consumpton and labor equal to the margnal productvty n each country. Condtons (6) equate the ntertemporal margnal rate of substtuton to the margnal productvty of captal. Condtons (7) equate the margnal rates of transformaton of the same ntermedate good n the two countres, and condtons (8) equate the margnal rates of techncal substtuton for the two ntermedate goods. We can use the ntratemporal and ntertemporal condtons, (5) and (6), to wrte the ntertemporal condton for labor, u nt βu n,t+1 = G,tFnt ] 1 δ + G G,t+1 F n,t+1,t+1 Fkt+1, = 1, 2. (9) We explctly characterze ths ntertemporal labor margn because are nterested n understandng when t s optmal not to dstort ths margn. Next we consder an economy wth dstortng taxes. Throughout we allow for transfers across governments. 6 We begn by consderng only country-specfc consumpton and labor ncome taxes. We then nclude a rcher tax system wth alternatve taxes and dscuss alternatve mplementatons. 2.1 Compettve equlbra wth consumpton and labor ncome taxes We now descrbe a compettve equlbrum wth taxes n whch governments fnance publc consumpton and ntal debt wth proportonal taxes on consumpton and labor ncome, τt c and τt, n as well as a tax on ntal wealth, l 0. Each country has two types of frms. Gven that the technologes are constant returns to scale, we assume, wthout loss of generalty, that there are two types of representatve frms. The ntermedate good frm n each country uses the technology n (2) to produce the ntermedate good usng captal and labor, purchases nvestment goods, and accumulates captal accordng to (4). Let V 0 be the value of the frm n perod zero after the dvdend pad n that perod, d 0. The ntermedate good frm 6 We solve for the whole Pareto fronter. It can be shown that there are welfare weghts such that transfers are zero. 6

8 maxmzes the value of dvdends V 0 + d 0 = Q t p t (y 1t + y 2t ) w t n t q t x t ] (10) subject to (2) and (4), where p t s the prce of the ntermedate good n unts of a numerare (or common money across countres) at t, w t s the wage rate, and q t s the prce of nvestment, or equvalently of the fnal good, all n unts of the same numerare. Q t s the ntertemporal prce of the common numerare at tme t n unts of the numerare at zero (Q 0 = 1). Because the ntermedate goods are traded, and there are no tarffs, the prces of each of the ntermedate goods are the same n the two countres. If we defne r f t+1 to be the return on one perod bonds n unts of the numerare between perod t and t + 1, then t must be the case that Q t Q t+1 = 1 + r f t+1, for t 0. (11a) The fnal goods frm n each country uses the technology n (3) to produce the fnal good usng foregn and domestcally produced ntermedate goods to maxmze the value of dvdends ] Q t qt G (y 1t, y 2t ) p 1t y 1t p 2t y 2t. (12) Ths problem reduces to a sequence of statc problems. wth Household The household budget constrant n each country s Q t q t (1 + τt) c c t (1 τt) n w t n t ] (1 l 0 ) a 0, (13) a 0 = V 0 + d 0 + Q 1 b 0 + ( ) 1 + r f 0 f 0, where a 0 denotes net holdngs of assets by the household of country, Q 1 b 0 denotes holdngs ( ) of domestc publc debt n unts of the numerare, nclusve of nterest, and 1 + r f 0 f 0 denotes holdngs of clams on households n the other country, n unts of 7

9 the numerare, also nclusve of nterest. Wthout loss of generalty, households wthn a country hold clams to the frms n that country as well as the publc debt of the government of that country. There s an nternatonally traded bond. The household s problem s to maxmze utlty (1) subject to (13). by Government The budget constrant of the government of each country s gven Q t τtq c t c t + τtw n t n t q t g t ] + l 0 a 0 = Q 1 b 0 T 0, (14) where T 0 denotes transfers receved by the government of country from other governments, so that T 10 + T 20 = 0. (15) The budget constrants of the government and the household (wth equalty) n each country mply ( ) Q t p t y t q t (c t + g t + x t )] = 1 + r f 0 f 0 T 0, (16) whch can be wrtten as the balance of payments condton wth ( ) Q t p t y jt p jt y jt ] = 1 + r f 0 f,0 T 0 (17) ( ) ( ) 1 + r f 0 f 1, r f 0 f 2,0 = 0. A compettve equlbrum for ths economy conssts of a set of allocatons {c t, n t, y jt, k t+1, x t } and d 0, prces {q t, p t, w t, Q t, V 0 }, and polces {τ c t, τ n t, l 0, T 0 }, gven { k 0, Q 1 b 0, such that households maxmze utlty subject to ther constrants, frms maxmze value, the balance of payments condtons (17) hold, and markets clear n that (2), (3), and (4) together wth (15) are satsfed. ( 1 + r f 0 Note that we have not explctly specfed the governments budget constrants because they are mpled by the other constrants. We say that an allocaton {c t, n t, y jt, k t+1, x t } s mplementable f t s part of a compettve equlbrum. ) f 0 } 8

10 The frst order condtons of the household s problem nclude u c,t u n,t = (1 + τ t) c q t (1 τt n) w, (18) t u c,t (1 + τt c) = Q tq t βu c,t+1 ( ), (19) Q t+1 q t τ c t+1 for all t 0, where u c,t and u n,t denote the margnal utltes of consumpton and labor n perod t. The frst order condtons of the frms problems are, for all t 0, p t F n,t = w t (20) Q t q t = Q t+1 p t+1 F k,t+1 + Q t+1 q t+1 (1 δ), (21) where Fn,t and Fk,t together wth denote the margnal products of captal and labor n perod t, q t G j,t = p jt. (22) By combnng the household s and frm s equlbrum condtons, t can be shown that the value of the frm n (10) s V 0 + d 0 = q 0 1 δ + G,0 F k,0] k0. (23) The frst order condtons can be rearranged as u c,t u n,t = (1 + τ c t) (1 τ n t ) G,t F n,t (24) u c,t βu c,t+1 = (1 + τ c t) ( 1 + τ c t+1 ) G,t+1F k,t δ ], (25) as well as (7) and (8), repeated here, G 1 j,t G 1 j,t+1 G 1 1,t+1 Fk,t δ ] = G2 j,t G 2 G 2 2,t+1 Fk,t δ ], j = 1, 2 j,t+1 G 1 2,t G 1 1,t = G2 2,t G 2 1,t 9

11 for all t 0. Comparng these condtons wth the ones for the Pareto fronter wth lump sum taxaton, (5), (6), (7), and (8), we have that the consumpton and labor taxes create an ntratemporal wedge n (24), and that tme varyng consumpton taxes create ntertemporal wedges n (25). Taxes do not affect the producton effcency condtons (7) and (8). Usng condtons (24) and (25), we can wrte u n,t βu n,t+1 = ( (1 τ t) n G ),tfn,t 1 τ n G t+1 G,t+1 F n,t+1,t+1 Fk,t δ) ], (26) whch makes t clear how the taxes affect the labor ntertemporal margn. A compettve equlbrum has no ntertemporal dstortons n consumpton from perod s onward f the frst order condtons (25) and (6) concde for all t s. Smlarly, a compettve equlbrum has no ntertemporal dstortons n labor from perod s onward f the frst order condtons (26) and (9) concde for all t s. Fnally, a compettve equlbrum has no ntertemporal dstortons from perod s onward f t has no such dstortons for both consumpton and labor. Wth the taxes that we consder here, t s not possble to create producton dstortons n the use of the traded goods, so that (7) and (8) always have to be satsfed. These margnal condtons wll have to be mposed as restrctons to the Ramsey problem, but as we show below, they wll not be bndng at the Ramsey optmum Implementablty In order to characterze the Ramsey equlbrum, we begn by characterzng the set of mplementable allocatons. An allocaton {c t, n t, y jt, k t+1, x t } and perod zero polces and prces, {l 0, τ0, c T 0, q 0 }, gven {k 0, b 0, f 0 } s mplementable as a compettve equlbrum f and only f they satsfy the resource constrants (2), (3), (4), and the mplementablty condtons ] β t u c,tc t + β t u n,tn t = W0, (27) 10

12 where W 0 = (1 l 0 ) u c,0 (1 ( δ + G (1 + τ0 c ),0Fk,0) k0 + Q 1 b r f 0 ) f,0 q,0 ] (28) together wth (7) and (8). The proposton follows. Proposton 1 (Characterzaton of the mplementable allocatons): Any mplementable allocaton and perod zero polces and prces satsfy the mplementablty constrants (27), together wth (7) and (8), as well as the resource constrants (2), (3), (4). Furthermore, f an allocaton satsfes these condtons for some perod zero polces and prces, then t s mplementable by a tax system wth consumpton and labor ncome taxes. 2.2 Cooperatve Ramsey equlbra A (cooperatve) Ramsey equlbrum s a compettve equlbrum that s not Pareto domnated by any other compettve equlbrum. The Ramsey allocaton s the assocated mplementable allocaton. We say that the Ramsey planner s unrestrcted f the planner can choose polces and allocatons n all perods subject only to the constrant that the resultng allocatons, prces, and polces consttute a compettve equlbrum. Consder the followng programmng problem, referred to as the unrestrcted Ramsey problem, whch s to choose allocatons and perod zero polces to maxmze a weghted sum of utltes of the households of the two countres, θ 1 U 1 + θ 2 U 2 (29) wth weghts θ 0, 1], subject to the condtons (27) and the resource constrants. Assume polces are unrestrcted n the sense that for any allocaton, l 0 (or any of the other ntal taxes) can be chosen to satsfy (27). Then the unrestrcted Ramsey problem reduces to maxmzng welfare subject to the resource constrants, and therefore t mmedately follows that t s possble to mplement the lump-sum tax allocaton as the Ramsey equlbrum. 11

13 2.2.1 Ramsey problem Suppose now that polces and ntal condtons are restrcted n the sense that households n each country must be allowed to keep an exogenous value of ntal wealth W, measured n unts of utlty. Specfcally, we mpose the followng restrcton on the Ramsey problem: W 0 = W, (30) whch we refer to as the wealth restrcton n utlty terms. Wth ths restrcton, polces, ncludng ntal polces, can be chosen arbtrarly, but the household must receve a value of ntal wealth n utlty terms of W (see Armenter (2008) for an analyss wth such a restrcton). 7 The Ramsey problem s to maxmze (29), subject to the resource constrants (2), together wth (3) and (4), that are combned as c t + g t + k t+1 (1 δ) k t G 1 (y 1t, y 2t ), (31) together wth the mplementablty condtons (27), the wealth restrcton (30), (7) and (8). Condton (28) does not restrct the problem snce t s satsfed by the choces of the ntal taxes. We are gong to wrte the problem wthout mposng the condtons for producton effcency, (7) and (8). We wll show that they are satsfed at the optmum. Defne v ( c t, n t ; ϕ ) = θu (c t, n t ) + ϕ ] u c,tc t + u n,tn t, where ϕ s the multpler of the mplementablty condton (27). We can now use the effcency condtons for the case wth lump-sum taxes, (5), (6), (7), and (8), replacng the margnal utltes of u by the dervatves of the functon v. The soluton of the Ramsey problem s gven by v c,t v n,t = 1 G,t F, = 1, 2 (32) n,t 7 Char et al. (2016) study equlbra wth partal commtment n whch the assumpton n Armenter (2008) apples every perod. The government n each perod has partal commtment to one perod returns on assets n utlty terms. The Markov equlbrum concdes wth the full commtment equlbrum wth wealth restrctons n utlty terms. Thus, partal commtment provdes one ratonalzaton for studyng Ramsey equlbra wth wealth restrctons n utlty terms. 12

14 v c,t βv c,t+1 = 1 δ + G,t+1F kt+1, = 1, 2 (33) G 1 j,t G 1 j,t+1 G 1 1,t+1 Fk,t δ ] = G2 j,t G 2 G 2 2,t+1 Fk,t δ ], j = 1, 2 (34) j,t+1 G 1 1,t G 2 1,t = G1 2,t. (35) G 2 2,t Every Ramsey soluton must satsfy the producton effcency condtons, (7) and (8), even f the condtons were not mposed as a restrcton to the problem. Ths means that f we had consdered tarffs as possble nstruments, they would not need to be used. The proposton follows. Proposton 2 (Optmalty of free trade ): Unrestrcted nternatonal trade s optmal. where In order to further characterze the optmal wedges, t s useful to wrte σt = u cc,tc t, σ u t n c,t v c,t = u c,t v n,t = u n,t θ + ϕ ]] 1 σt σt cn θ + ϕ 1 + σ n t = u nn,tn t, σ u t nc n,t ]] σt nc, = u nc,tc t, σ u t cn = u cn,tn t n,t u c,t are own and cross elastctes that are only functons of consumpton and labor at tme t. Note also that f consumpton and labor are constant over tme, then the relevant elastctes are also constant, so v c,t and v n,t are proportonal to u c,t and u n,t, respectvely. It then follows that t s optmal to have no ntertemporal dstortons. Ths observaton leads to the followng proposton. Proposton 3 (No ntertemporal dstortons n the steady state): If the Ramsey equlbrum converges to a steady state, t s optmal to have no ntertemporal dstortons asymptotcally. For standard macro preferences, ] U = β t c 1 σ t 1 nt 1+σn η 1 σ, (36) 1 + σ n 13

15 the margnal condtons are u c,t u n,t = θ + ϕ (1 + σ n ) θ + ϕ (1 σ ) 1 G,t F, (37) n,t together wth the ntertemporal effcency condtons, (6), and the producton effcency condtons, (7) and (8). The proposton follows. Proposton 4 (No ntertemporal dstortons ever): Suppose that preferences are gven by (36). Then, the Ramsey soluton has no ntertemporal dstortons for all t 0. Corollary: The Ramsey allocatons can be mplemented wth consumpton or labor taxes that are constant over tme, but possbly dfferent across countres. The two-country model nests the closed economy neoclasscal growth model for G (y 1t, y 2t ) = y t. It follows that the results on the optmal taxaton of captal also hold n the neoclasscal growth model. Ths s n contrast wth the nfluental results of Chamley (1986) and Judd (1985), whch argue that captal should not be taxed n the steady state but should be heavly taxed along a transton. They are also n contrast wth the results n the more recent lterature, n Bassetto and Benhabb (2006) and Straub and Wernng (2015), that t may be optmal to tax captal at the maxmum rate forever. To obtan our result that there s no presumpton that captal ought to be taxed also along the transton, t s mportant that the ntal confscaton be restrcted not only drectly, as s common to assume n the lterature, but also ndrectly through valuaton effects, as proposed by Armenter (2008). Ths assumpton s related to partal commtment to asset returns, as argued by Char et al. (2016). Another mportant assumpton to shorten the transton of heavy captal taxaton s that the tax system may be rch enough, n the sense that no taxes that are avalable n advanced economes may be left out f relevant for polcy. We consder such a rch tax system, but that s not the common assumpton n the lterature. The assumptons that ndrect confscaton s possble whle drect confscaton s not, together wth a restrcted tax system, explan the contrastng results n the lterature. Note that the preferences consdered n Proposton 4 are separable and homothetc n both consumpton and labor. These propertes are used n Char et al. (2016) to 14

16 provde ntuton for the results on the optmal taxaton of captal by relatng them to results on unform commodty taxaton and producton effcency, as n Atknson and Stgltz (1972) and Damond and Mrrlees (1971). The Ramsey allocaton characterzed n Propostons 2 through 4 can be mplemented n a varety of ways. The followng sectons descrbe alternatve mplementatons. 3 Alternatve mplementatons In ths secton, we dscuss a varety of other tax systems, ncludng taxes on the ncome from dfferent assets and alternatve ways of taxng consumpton. Our analyss s motvated by the observaton that these alternatve tax systems are wdely used n practce. We show that no tax system can yeld hgher welfare than the tax system wth only consumpton and labor ncome taxes. We show that a varety of tax systems can mplement the Ramsey allocaton assocated wth those taxes. Furthermore, some tax systems do yeld lower welfare. 3.1 Taxes on captal ncome, equty returns, and foregn assets In ths secton, n addton to captal ncome taxes, we consder a common tax on the returns from foregn assets and on the equty returns ncludng captal gans. Ths s a resdence-based system where captal from dfferent sources s treated the same. We assume that frms are resdents of the country where they produce. For convenence, we keep both consumpton and labor ncome taxes, but we dscuss whether any of these wll be made redundant. We now descrbe the problems of the frms and the household n each country and defne a compettve equlbrum. We mantan the assumpton that ownershp of frms s domestc, but we wll see that ths s wthout loss of generalty. Frm The representatve ntermedate good frm n each country produces and nvests n order to maxmze the present value of dvdends, V 0 + d 0 = Q td t. 15

17 Dvdends, n unts of the numerare, d t, are gven by d t = p t F (k t, n t ) w t n t τ k t p t F (k t, n t ) w t n t q t δk t ] q t k t+1 (1 δ)k t ], where τ k t s the tax rate on captal ncome net of deprecaton. The frst order condtons of the frm s problem are now (20), together wth (38) Q t q t = 1 + ( ) ( ) 1 τ k p t+1 t+1 Fk,t+1 δ. (39) Q t+1 q t+1 q t+1 Substtutng for d t from (38) and usng (20) and (39), t s easy to show that the present value of the dvdends at tme zero n unts of the numerare s gven by V 0 + d 0 = Q t d t = 1 + ( ) ( )] 1 τ0 k p 0 F k,0 δ p 0 k 0. (40) q 0 The problem of the fnal good frm s as before. The frst order condtons are gven by (22). Households The flow of funds constrant n perod t for the household n country n unts of the numerare s gven by b t+1 + V t s t+1 + f t+1 (41a) = Q ( t 1 b t + (V t + d t ) s t τ t V t V t 1 + d t (q ) t q t 1 ) V t 1 s t + Q t q t 1 ( ) ( 1 + r f t f t τ t r f t q ) t q t 1 f t + (1 τ q t) n w t n t (1 + τt) c q t c t. t 1 In perod 0, the constrant s b 1 + V 0 s 1 + f 1 (42) ( = (1 l 0 ) Q 1 b 0 + (V 0 + d 0 ) s 0 τ 0 V 0 V 1 + d 0 (q ) ] 0 q 1 ) V 1 s 0 + q ( 1 (1 l 0 ) 1 + r f0 τ 0 r f 0 q )] 0 q 1 f 0 + (1 τ q 0) n w 0 n 0 (1 + τ0) c q 0 c 0. 1 Dvdends and captal gans are taxed at rate τ t wth an allowance for numerare nflaton. Returns on foregn assets are also taxed at the same rate, τ t, also wth an 16

18 allowance for numerare nflaton. The returns on publc debt, b t, are country specfc, Q t 1 Q t, because assets can be taxed at dfferent rates n the dfferent countres. The household s problem s to maxmze utlty (1), subject to (41a), (42), and no-ponz-scheme condtons, lm T Q T +1 b T +1 0, and lm T Q T +1 f T The frst order condtons of the household s problem n each country are, for t 0, (18), and together wth and Q t Q t+1 = whch mples that u c,t (1 + τt c) = Q tq t βu c,t+1 ( ), (43) Q t+1 q t τ c t+1 Q ( ) t = (1 τ t+1 ) 1 + r f q t+1 t+1 + τ t+1 wth Q 0 = 1 (44a) Q t+1 q t (V t+1 + d t+1 ) τ t+1 (V t+1 V t + d t+1 q t+1 q t q t V t ) V t, (45a) 1 + r f t+1 = V t+1 + d t+1 V t. (46a) Ths condton on the two returns can be wrtten, usng 1 + r f t+1 = Qt Q t+1, as Q t V t = Q t+1 V t+1 + Q t+1 d t+1. (47a) Imposng that lm T Q T +1 V T +1 = 0, then V t = s=0 Q t+1+s Q t d t+1+s. The present value of dvdends for the households of country s a dfferent expresson from the expresson above because they pay taxes on the asset ncome. Usng (45a), we have that V 0 = ( ) 1 ˆτ a t+1 Qt+1 d t+1, where 1 ˆτ a t+1 = Π t s=0 (1 ˆτ s+1 ), and 1 ˆτ t+1 = (1 τ t+1 ) ( q 1 τ t+1 Q t+1 t+1 q t Q t ). The values are the same snce ( 1 ˆτ a t+1) Qt+1 = Q t+1. Ths condton s obtaned from (44a). 17

19 The value of the frm for the households n country ncludng the dvdends n perod 0 s ( V 0 + d 0 τ 0 V 0 + d 0 q ) 0V 1 q 1 = (1 τ 0 ) (V 0 + d 0 ) + τ 0 q 0 V 1 q 1. Notce that the market prce of the frm before dvdends, V 0 + d 0, s a lnear functon of the value for the frm for the households of each country, so that the soluton of the maxmzaton problem of the frm also maxmzes shareholder value. That would also be the case f the stocks were held by the households of the foregn country. Ths means that the restrcton that frms are owned by the domestc households s wthout loss of generalty. Usng the no-ponz scheme condton, the budget constrants of the household, (41a) and (42), can be consoldated nto the sngle budget constrant, where (49) Q t q t (1 + τt) c c t (1 τt) n w t n t ] = (1 l 0 ) a 0, (50) a 0 = Q 1 b 0 + (1 τ 0 ) (V 0 + d 0 ) + τ 0 q 0 V 1 q 1 + ( 1 + r f0 τ r f 0 q )] 0 f 0. q 1 (51) Usng (40) as well as s 0 = 1, the ntal asset holdngs n (51) can be wrtten as a 0 = Q 1 b 0 + (1 τ 0 ) q 0 k0 + ( ) ( 1 τ0 k G,0 F k,0 δ ) ] q 0 V 1 k 0 + τ0 q ( r f0 τ r f 0 q )] 0 f 0 q 1 The nterest rate party condton s obtaned from for = 1, 2, or Q t = q t ( ) ( )] 1 τ k p t+1 t+1 Fk,t+1 δ Q t+1 q t q t+1 (52) 18

20 q 1t ( ) ( )] 1 τ1t+1 k p 1t+1 Fk,t+1 1 δ = q 2t ( ) ( )] 1 τ k p 2t+1 2t+1 Fk,t+1 2 δ. q 1t q 1t+1 q 2t q 2t+1 (53) Usng (22) to replace the relatve prces of the ntermedate and fnal goods, t follows that G 1 j,t 1 + ( 1 τ k 1t+1 ) ( G 1 1,t+1 F 1 k,t+1 δ )] (54) G 1 j,t+1 = G2 j,t ( ) ( τ k G 2 2t+1 G 2 2,t+1 Fk,t+1 2 δ )], for j = 1, 2. j,t+1 To get producton effcency, that s, to satsfy (8), we need ether to set the two tax rates to zero or to pck τ k 1t+1 and τ k 2t+1 accordng to ( τ1t+1 k G 1 1,t+1 Fk,t+1 1 δ ) (55) ( ( G 1 = τ2t+1 k G 1 1,t+1Fk,t+1 1 j,t+1 /G 2 )) j,t+1 δ 1, for j = 1, 2. G 1 j,t /G2 j,t In order to ensure producton effcency, there has to be an adjustment to the movements n the real exchange rate. The tax revenue on the return on captal n the consumpton of one country must be equal to the tax revenue on the return on captal n the consumpton of the other country mnus the proportonate change n the real exchange rate. Usng the ntertemporal condton of the household (43), and Q t Q t+1 = (1 τ t+1 ) Q t Q t+1 + τ t+1 q t+1 q t (56a) obtaned from (44a), together wth Qt Q t+1 condton (39), together wth (22), we obtan = 1 + r f t+1, and combnng t wth the frm s ( ) u c,t 1 + τ c t+1 βu c,t+1 (1 + τt c) = 1 + (1 τ t+1) ( ) ( 1 τt+1 k G,t+1 Fk,t+1 δ ). (57) 19

21 The margnal condtons n ths economy can be summarzed by u c,t u n,t = (1 + τt) c (1 τt n) G,t F, (58) n,t the ntertemporal condton (57), the nterest rate party condton (54), and condton (8), for all t 0. In ths economy wth a common tax on equty and foregn returns, t s possble to set to zero ether the consumpton tax or the labor ncome tax, but not both. The Ramsey allocaton can be mplemented wth a (possbly tme-varyng) common tax on home and foregn assets. Captal ncome taxes n both countres ether must be set to zero or must be set accordng to the dfference n real returns n the goods of the two countres to ensure producton effcency. For standard macro preferences, all the taxes on assets are set to zero and the labor ncome tax s constant over tme. In ths economy wth a common tax on domestc equty and foregn returns, frms use a common prce to value dvdends. If relaxed, the restrcton that frms are owned by the domestc resdents would not change the mplementable allocatons. Consder the tax systems that do not tax ether consumpton or labor, but do have the other taxes. We refer to a tax system n whch consumpton taxes are set to zero as a no-consumpton tax system, and smlarly for the labor tax. The proposton follows. The proof s straghtforward. Proposton 5 (Common tax on domestc equty and foregn returns) : None of the tax systems consdered here gve hgher welfare than the tax system wth only consumpton and labor ncome taxes. The Ramsey equlbrum under the noconsumpton tax or the no-labor ncome tax system requres the taxaton of domestc and foregn assets at the same rate. Captal ncome taxes can be set to zero. For standard macro preferences, only the consumpton tax or the labor tax wll be used, and t wll be constant over tme. 3.2 Border-adjusted value-added taxes and labor ncome taxes Consder next an economy n whch consumpton taxes are replaced by value-added taxes leved on frms wth border adjustment. Border adjustment means that frms n a country do not pay VAT taxes on exports and cannot deduct mports. Taxes on assets are set to zero, but labor ncome taxes are not. The value-added taxes are denoted by 20

22 τt. v The setup s the same as n the economy wth only consumpton and labor ncome taxes, except that we dstngush prces n ths economy wth carets. Because taxes on assets are zero, there s a sngle ntertemporal prce of the numerare. The ntermedate good frm now maxmzes ˆQ t (ˆp 1t y 1t + ˆp 2t y 2t ) ŵ t n t ˆq t x t ] (59) ˆQ t τ v t ˆp t y t ˆq t x t ] subject to (2) and (4), where ˆp jt s the prce of the ntermedate good produced n country and sold n country j. The fnal goods frm now maxmzes ˆQ t ˆqt G (y 1t, y 2t ) ˆp 1t y 1t ˆp 2t y 2t ] (60) ˆQ t τ v t ˆqt G (y 1t, y 2t ) ˆp t y t ]. The household problem s the same as above, except that the consumpton taxes are set to zero. The frst order condtons of the household s problem now nclude u c,t u n,t = ˆq t (1 τt n) ŵ, t 0 (61) t u c,t = ˆQ tˆq t ˆQ t+1ˆq t+1 βu c,t+1, t 0. (62) The frst order condtons of the frms problems for an nteror soluton are ˆp t (1 τ v t) F n,t = ŵ t (63) ˆQ tˆq t (1 τ v t) = ˆQ t+1ˆp t+1 ( 1 τ v t+1 ) F k,t+1 + ˆQ t+1ˆq t+1 ( 1 τ v t+1 ) (1 δ)) (64) ˆp t (1 τ v t) = ˆp jt (65) ˆq t G,t = ˆp t (66) 21

23 ˆq t (1 τt) v G j,t = ˆp jt, for j. (67) In order to show equvalence between these two tax systems, consder the followng prces wth value-added taxes. Let ˆq t (1 τt) v = q t (68) ˆp t (1 τ v t) = p t (69) ˆp jt = p t, j, ŵ t = w t, ˆQt = Q t. (70) Replacng the prces wth caret n the frst order condtons n the economy wth valueadded taxes, we get q t u c,t = u n,t (1 τt v) (1 τ t n) w, t 0 (71) t u c,t = Q ( ) tq t 1 τ v t+1 Q t+1 q t+1 (1 τt v) βu c,t+1, t 0 (72) p t F n,t = w t (73) p t = p t (74) Q t q t = Q t+1 p t+1 F k,t+1 + Q t+1 q t+1 (1 δ)) (75) q t G j,t = p jt. (76) These are the same condtons as n the economy wth consumpton taxes wth 1 τt v = 1. (77) 1 + τt c The budget constrants of households n the two cases are (13) and ˆQ t ˆq t c t (1 τ n t) ŵ t n t ] (1 l 0 ) a,0, (78) where a,0 = ˆq 0 (1 τ v 0) 1 δ + G,0F k,0] k0 + Q, 1 b 0 + ( ) 1 + r f 0 f,0. Usng the condton establshng the equvalence between the prces n the two economes, (68) and (70), t follows that the budget constrant n the value-added 22

24 economy (78) becomes (13). by The budget constrants of the governments n the value-added economy are gven ˆQ t τ v t ˆp t y t ˆq t x t ] + τ v t ˆqt G (y 1t, y 2t ) ˆp t y t ] + τ n t ŵ t n t q t g t ] ] = l 0 a 0 + Q, 1 b 0 T 0. (79) The balance of payments condtons are ( ) ˆQ t ˆp jt y jt ˆp jt y jt ] = 1 + r f 0 f,0 T 0, (80) ( ) ( ) where 1 + r f 10 f 1, r f 20 f 2,0 = 0. Snce ˆp jt = p t, for j, the balance of payments condton concdes wth the one wth consumpton and labor ncome taxes. The two economes are equvalent. Ths s stated n the followng proposton. Proposton 6 (Value-added taxes wth border adjustment): Compettve equlbrum allocatons n the economes wth consumpton and value-added taxes concde f the taxes n the two systems satsfy (77). 3.3 Value-added taxes wthout border adjustment: The role of tarffs Consder next an economy just lke the one n the prevous secton, except that valueadded taxes are leved on frms wthout border adjustment. Ths means that the taxaton of ntermedate goods wll be source based. We wll also consder tarffs. The tarff leved by country j on the good mported from the other country s denoted by τ y jt. The value-added taxes n country are denoted by τ t. v The ntermedate goods frm now maxmzes ˆQ t (1 τ v t) (ˆp 1t y 1t + ˆp 2t y 2t ˆq t x t ) ŵ t n t ] (81) subject to (2) and (4), where ˆp jt s the prce of the ntermedate good produced n 23

25 country and sold n country j. The fnal goods frm n country 1 now maxmzes ˆQ t (1 τ v 1t) ˆq 1t G 1 (y 11t, y 21t ) ˆp 11t y 11t (1 + τ y 21t) ˆp 21t y 21t ] (82) and smlarly for country 2. The household problem s the same as above, except that the consumpton taxes are set to zero. The frst order condtons of the household s problem are u c,t u n,t = ˆq t (1 τt n) (1 τ t v) ˆp, t 0 (83) tfn,t u c,t = ˆQ tˆq t ˆQ t+1ˆq t+1 βu c,t+1, t 0. (84) The frst order condtons of the frms problems for an nteror soluton are ˆp t (1 τ v t) F n,t = ŵ t (85) ˆQ tˆq t (1 τt) v = ˆQ ( ) t+1ˆp t+1 1 τ v t+1 F k,t+1 + ˆQ ( ) t+1ˆq t+1 1 τ v t+1 (1 δ)) (86) ˆp t = ˆp jt ˆp t (87) ˆq t G,t = ˆp t, = 1, 2 (88) ˆq t G j,t = ( 1 + τjt) y ˆpjt, for j. (89) We can rearrange the frst order condtons as u c,t u n,t = 1 (1 τt n) (1 τ t v) G,t F, t 0 (90) n,t u c,t (1 τ v t) = ( 1 τ v t+1) βu c,t+1 G,t+1 F k,t δ) ]. Usng (88) and (89), t follows that ˆq 1t ˆq 2t = (1 + τ y 21t) G 2 2,t G 1 2,t = G 2 1,t (1 + τ12t) y. (91) G 1 1,t 24

26 Usng (86) and (88), we have that 1 τ v 1t+1 1 τ v 1t ˆq 1t+1 G 1 ˆq 1,t+1 Fk,t δ ] = 1 τ 2t+1 v ˆq 2t+1 G 2 1t 1 τ2t v ˆq 2,t+1 Fk,t δ ]. (92) 2t The margnal condtons are summarzed by u c,t u n,t = 1 (1 τ n t ) (1 τ v t ) G,t F n,t (93) u c,t (1 τt) v = ( 1 τt+1) v βu c,t+1 G,t+1 Fk,t δ) ] (94) ( ) 1 τ v 1t+1 (1 τ v 2t ) ( 1 + τ21t+1) y G 1 2,t ( ) 1 τ v 2t+1 (1 τ v G 1 1t ) (1 + τ21t) y G 1 1,t+1 Fk,t δ ] = G2 2,t G 2 2,t+1 G 2 2,t+1 Fk,t δ ] 2,t+1 ( ) (95) 1 τ v 1t+1 (1 τ v 2t ) (1 + τ12t) y ( ) 1 τ v 2t+1 (1 τ v 1t ) ( ) G1 1,t G τ y 12t+1 G 1 1,t+1 Fk,t δ ] = G2 1,t G 2 1,t+1 G 2 2,t+1 Fk,t δ ] 1,t+1 (96) G 1 2,t G 1 1,t = (1 + τ 21t) y (1 + τ12t) y G 2 2,t. (97) G 2 1,t In order to have producton effcency, verfyng (7) and (8), t must be that ( ) 1 τ v 1t+1 (1 τ v 2t (1 τ1t) ( ) = 1 + τ y 12t+1 v 1 τ2t+1 v 1 + τ y 12t and ( ) ( ) 1 + τ y 12t τ y 21t+1 = (1 + τ y 12t) (1 + τ21t) y = 1. The Ramsey allocaton n the economy wth consumpton taxes can be mplemented n ths economy wth a VAT wthout border adjustment and tarffs. The tarffs have to compensate each other 1 + τ y 12t = 1/ (1 + τ21t), y so that f the tarff s postve n one country, t must be negatve n the other. The compensatng tarffs must be tme varyng to undo the dstortons mposed by the VAT taxes on the (dynamc) producton effcency condton, (7). The value-added taxes wll have to move over tme, dfferently n the two countres to mplement the optmal ntertemporal dstortons, and the labor ncome tax wll mplement the optmal ntratemporal dstorton. Wthout tarffs, the Ramsey allocaton n the economy wth both consumpton and labor ncome taxes cannot n general be acheved. 25

27 For standard macro preferences, there s no need for tarffs, and the Ramsey allocaton can be acheved wth VAT taxes that, n general, are dfferent across countres but constant over tme. Border tax adjustments n ths case are rrelevant. We state these results n the followng proposton. Proposton 7 (Value-added taxes wthout border adjustment): The Ramsey allocaton can be mplemented wth consumpton taxes replaced by value-added taxes wthout border adjustment and tarffs. The tarffs must compensate each other and have to be tme varyng to compensate value-added taxes that may move dfferently across tme n the two countres. For standard macro preferences, the value-added tax rates are constant over tme, and therefore there s no need for tarffs. Corollary: In general, the Ramsey allocaton cannot be mplemented wth a tax system wth labor ncome taxes and value-added taxes wthout border adjustment. Orgn- versus destnaton-based taxaton In order to dscuss restrctons on tax systems based on orgn and destnaton, we need to be clear about what we mean by a destnaton-based system and an orgn-based system mean. One possble meanng s the followng. A destnaton-based system s one n whch taxes are set by the destnaton country; smlarly, an orgn-based system s one n whch taxes are set by the country from where the goods orgnate. In such a destnaton-based system there s no reason to tax mports at the same rate as domestcally produced goods. Smlarly, n an orgn-based system, there s no reason to tax exports at the same rate as domestcally used goods. In such a system, whether destnaton-based or orgn-based, there would be four tax rates that would allow to mplement the Ramsey allocaton. Under the destnaton based system, the Ramsey polcy would set the rate on mports equal to the rate on domestcally produced goods, and under the orgnbased system, the rate on exports would be equal to the rate on the goods produced n the destnaton country. Another nterpretaton of destnaton- versus source-based systems s more restrctve but s also closer to what most people have n mnd. That s, a destnaton-based system s one where tax rates do not depend on orgn, and an orgn-based system s one where tax rates do not depend on destnaton. In ths case, the VAT system wth border adjustment would be a destnaton-based system, and the VAT system wthout border adjustment would be an orgn based system. In the case of value-added taxes wth border adjustment, the goods leave the country untaxed and are taxed n 26

28 the destnaton country at the sngle value-added tax rate n the destnaton country. In the case wth value-added taxes wthout border adjustments, however, goods are taxed at the sngle rate of the orgn country. For ths nterpretaton of destnatonand orgn-based systems, the destnaton-based system does not mpose relevant restrctons on the set of mplementable allocatons, but the orgn-based system, would n general mpose such restrctons. Wthout tarffs, the destnaton-based system s superor, snce n general t s not possble to mplement the Ramsey allocaton wthout tarffs when no border adjustments are made. Those restrctons would be undone by tarffs, but tarffs would convert an orgn-based system nto a destnaton-based one. 4 Concludng remarks We characterze cooperatve Ramsey allocatons n the open economy. We show that free trade s also optmal n the second best Ramsey allocaton and that for standard macro preferences, captal should never be taxed. For general preferences there s no presumpton that captal should also be taxed along the transton. We study alternatve mplementatons of the Ramsey allocaton ncludng resdence-based taxaton of equty returns, foregn asset returns and frms profts. We also consder value-added taxes wth and wthout border adjustments. In these envronments wth captal accumulaton, border adjustments matter for the optmal allocatons. We dscuss the desrablty of destnaton- versus orgn-based taxaton of goods. The results on the taxaton of captal are related to the nfluental results of Chamley (1986) and Judd (1985) whch argue that captal should not be taxed n the steady state but should be heavly taxed along a transton. They are also related to the more recent lterature, n Bassetto and Benhabb (2006) and Straub and Wernng (2015), that challenge the optmalty of zero taxaton of captal n the steady state. The contrastng results are explaned n Char et al. (2016). References 1] Armenter, Roc, 2008, A Note on Incomplete Factor Taxaton, Journal of Publc Economcs 92 (10-11), ] Atkeson, Andrew, V. V. Char, and Patrck J. Kehoe, 1999, Taxng Captal 27

29 Income: A Bad Idea, Federal Reserve Bank of Mnneapols Quarterly Revew 23 (3), ] Atknson, Anthony B. and Joseph E. Stgltz, 1972, The Structure of Indrect Taxaton and Economc Effcency, Journal of Publc Economcs 1 (1), ] Auerbach, Alan, Mchael P. Devereux, Mchael Keen, and John Vella, 2017, Destnaton-Based Cash Flow Taxaton, Oxford Unversty Center for Busness Taxaton WP 17/01. 5] Backus, Davd K., Patrck J. Kehoe and Fnn E. Kydland, 1994, Dynamcs of the Trade Balance and the Terms of Trade: The J-Curve?, Amercan Economc Revew 84 (1), ] Barbero, Omar, Emmanuel Farh, Gta Gopnath, and Oleg Itskhok, 2017, The Economcs of Border Adjustment Tax, mmeo, Harvard Unversty. 7] Bassetto, Marco, and Jess Benhabb, 2006, Redstrbuton, Taxes, and the Medan Voter, Revew of Economc Dynamcs 9(2), ] Chamley, Chrstophe, 1986, Optmal Taxaton of Captal Income n General Equlbrum wth Infnte Lves, Econometrca 54 (3), ] Char, V.V., Lawrence J. Chrstano, and Patrck J. Kehoe, 1994, Optmal Fscal Polcy n a Busness Cycle Model, Journal of Poltcal Economy 102 (4), ] Char, V. V., Juan Pablo Ncoln, and Pedro Teles, 2016, Optmal Captal Taxaton Revsted, mmeo, Federal Reserve Bank of Mnneapols. 11] Coleman, Wlbur John II, 2000, Welfare and Optmum Dynamc Taxaton of Consumpton and Income, Journal of Publc Economcs 76 (1), ] Damond, Peter A and James A. Mrrlees, 1971, Optmal Taxaton and Publc Producton I: Producton Effcency, Amercan Economc Revew 61 (1), ] Dxt, Avnash, 1985, Tax Polcy n Open Economes, n Handbook of Publc Economcs, Vol. 1, ed. Alan Auerbach and Martn Feldsten. Amsterdam: North- Holland. 28

30 14] Feldsten, Martn S., and Paul R. Krugman, 1990, Internatonal Trade Effects of Value-Added Taxaton, n Taxaton n the Global Economy, ed. Assaf Razn and Joel Slemrod, Unversty of Chcago Press, ] Grossman, Gene M., 1980, Border Tax Adjustments: Do They Dstort Trade?, Journal of Internatonal Economcs, 10(1), ] Judd, Kenneth L., 1985, Redstrbutve taxaton n a smple perfect foresght model, Journal of Publc Economcs 28 (1), ] Judd, Kenneth L., 1999, Optmal Taxaton and Spendng n General Compettve Growth Models, Journal of Publc Economcs 71 (1), ] Judd, Kenneth L., 2002, Captal-Income Taxaton wth Imperfect Competton, Amercan Economc Revew, Papers and Proceedngs 92 (2), ] Lucas, Robert E., Jr. and Nancy L. Stokey, 1983, Optmal Fscal and Monetary Polcy n an Economy wthout Captal, Journal of Monetary Economcs 12 (1), ] Straub, Ludwg and Iván Wernng, 2015, Postve Long Run Captal Taxaton: Chamley-Judd Revsted, mmeo, MIT. 21] Wernng, Iván, 2007, Optmal Fscal Polcy wth Redstrbuton, Quarterly Journal of Economcs 122 (3),