Generalized Cash Flow Taxation

Transcription

1 Generalized Cah Flow Taxation by Alan J. Auerbach, Univerity of California, Berkeley, and NBER David F. Bradford, Princeton Univerity, NYU School of Law, NBER and CESifo CEPS Working Paper No. 69 May 2001 We are grateful to Ken Judd, Loui Kaplow, and participant in eminar at Harvard, Stanford and Texa for comment on earlier verion of thi paper.

2 Abtract We how the unique form that mut be taken by a tax ytem baed entirely on realization accounting to implement a uniform capital income tax, or, equivalently, a uniform wealth tax. Thi ytem combine element of an accrual baed capital income tax and a traditional cahflow tax, having many of the attribute of the latter while till impoing a tax burden on marginal capital income. Like the traditional cah-flow tax, thi ytem may be integrated with a tax on labor income. We alo how how uch a tax can be upplemented with an optional accounting for a egregated ubet of actively traded ecuritie, ubjected eparately to mark-to-market taxation at the uniform capital income tax rate, to permit a fully graduated tax ytem applicable to labor income. Alan J. Auerbach David F. Bradford Department of Economic Woodrow Wilon School Univerity of California Princeton Univerity Berkeley, CA Princeton, NJ auerbach@econ.berkeley.edu bradford@princeton.edu JEL No. H24, G11

3 Table of Content 1. Introduction 1 2. Generalized Cah-Flow Taxation 3 A. Derivation of the generalized cah-flow tax rule 3 B. Commentary 10 i. Intuition of the reult 10 ii. Portfolio balance and rik-taking 11 iii. Portfolio and other combination of aet 12 iv. Treatment of gain and loe 14 v. Choice of parameter, D and g 14 vi. Gift and bequet 17 vii. Enforcement Extenion 20 A. Time-dependent capital income tax rate, wealth taxation, and inflation adjutment 20 i. Time-dependent capital income tax rate and wealth taxation 20 ii. Inflation adjutment 21 B. Cloely-held aet and human capital accumulation 22 C. Lifetime progreivity and income averaging 24 D. Changing the tax parameter a a matter of changing policy Concluion 28 Reference 30 Appendix A. Baic Propoition 31 Appendix B. Intertemporal Optimization and Leiure 34

4 1. Introduction The growing flexibility of financial arrangement ha wreaked havoc on the income tax. The problem arie in connection with the treatment of financial and buine tranaction generally lumped under the heading of capital income. 1 Tranaction with imilar economic effect face tax rule that differ with repect to the timing and the rate of taxation, eentially providing taxpayer with the opportunity to elect the mot favorable tax treatment for any particular aet. Thi inconitency alo facilitate the contruction of offetting arbitrage poition that involve little net economic activity but that can be ued to reduce tax liability on income from other, unrelated ource. The dyfunctional conequence appear in variou guie, including the converion of ordinary income into capital gain, the deferral of capital gain by individual, and the recently publicized aggreive puruit of tax helter by corporation. To date, policy repone have attempted to limit taxpayer ability to engage in tranaction, to throw and in the gear of tax-motivated financial innovation. Such repone are inevitably imperfect, for there i no correct way to preerve a tax ytem that treat imilar tranaction inconitently. Wherever the line i drawn to identify tranaction with no economic ubtance, anti-abue proviion may alo catch taxpayer happening to chooe a imilar pattern of tranaction. Ultimately, the problem will exit unle all type of income from capital are ubject to the ame preent value tax burden, at leat ex ante at the time deciion are made. Directly impoing the ame rate of tax on all income a it accrue require a tax ytem that mark aet to market, a proce that i traightforward for frequently traded aet but quite 1 For the mot part in thi paper we implicitly invoke the traditional model, in which worker are paid a well-defined wage and eparately accumulate claim on aet that have poibly tochatic payoff in the future. In actuality, the reward to work effort may have intertemporal (for example, deferred compenation) and rik element (for example, tock option or hare-cropping), and may be intertwined with accumulated capital (for example, in a buine enterprie), o that an operational ditinction between capital and labor income i problematic. In part 3 we how how the ytem propoed could be extended to all cah flow, thereby eliminating any need for a ditinction.

5 2 difficult for other. Indeed, with the rie in derivative and ynthetic aet, it i not even clear where to draw the boundarie eparating one aet from another for purpoe of valuing and taxing each. An alternative repone i to ignore financial tranaction entirely, or to impoe a cah-flow tax on capital income. A variou author have hown, impoing a tax at a contant rate on all poitive and negative cah flow till impoe a zero effective tax rate at the margin on the normal, rik-free return to capital income from new invetment. But a hift to cah-flow taxation differ from elimination of capital income taxe with repect to timing and in taxing economic rent and, depending on tranition rule, return to exiting aet a well. A frequently cited advantage of cah-flow taxation i that it can collect revenue from capital income ource (i.e., rent, uch a the reward to entrepreneurhip and the upernormal return on invetment, and, in the cae of a tranition from a different regime, old capital) without having to meaure capital income. However, perhap becaue it i poorly undertood, or perhap becaue policy maker are committed to the attempt to include the rik-free return to wealth in the tax bae, the cah-flow tax ha not been adopted a an alternative to the income tax. In thi paper, we how that it i poible to generalize cah-flow taxation in a manner that preerve thi major advantage not having to meaure capital income while at the ame time effectively impoing an income tax at a contant rate on all capital income. Thi approach, to which we refer a generalized cah-flow taxation, reemble cah-flow taxation in that it taxe only cah flow and i not baed on any meaurement of income. However, unlike imple cahflow taxation, the tax aement levied on any particular cah flow depend on that cah flow date and the effective capital income tax rate that the government wihe to impoe. A we how, uch a tax ytem i equivalent, ex ante, from the viewpoint of both invetor and government to a pure accrual tax at the ame rate. It replace the requirement of aet valuation

6 3 (which may not be feaible) with the aumption that invetor have the ability arbitrarily to adjut their rik poition. That i, our approach aume the exitence of a complete, competitive capital market in which price-taking invetor can buy or ell aet in any quantitie deired in order to adjut their portfolio to accommodate the timing of taxation. The impact of realitic deviation from thee aumption i a quetion that mut be left for future reearch. 2. Generalized Cah-Flow Taxation Our approach repreent an extenion of two previou paper, Auerbach (1991) and Bradford (1997), and may be mot eaily undertood by tarting with a brief review of thee paper reult, uing dicrete time for clarity and mathematical implicity. We tart with the mot baic of invetor deciion, whether or not to ell (and therefore realize the income from) an aet with no intermediate cah flow between purchae and ale. The cla of tranaction conidered initially conit of arm length purchae, ale, and holding of financial aet traded in active public market. Later we extend the cope of aet conidered in everal repect. A. Derivation of the generalized cah-flow tax rule Under a typical capital gain tax ytem with a contant tax rate, realization of a net gain i dicouraged the invetor i locked in becaue there i a deferral advantage to delaying, without interet, the taxation of gain. Put another way, the invetor i willing to accept a lower before-tax rate of return on the aet than i available on other aet, becaue the tax on additional return i effectively reduced by the eroded tax liability on gain already accrued. Thi deferral advantage could be offet, and the additional return on current and alternative aet ubjected to uniform treatment, by charging (deductible) interet on unpaid

7 4 taxe a gain accrued, a firt enviioned by Vickrey (1939), with the tax liability at realization, T, evolving according to the expreion (1) T + = [1 + i(1 ] T + tr A 1, where A i the value of the aet at date (with time meaured from the acquiition date), i i the afe rate of interet, t i the income tax rate, and r i the aet rate of appreciation between date and +1. Unfortunately, implementation of the unique tax ytem baed on (1) and the initial condition T 0 = 0 would require u to oberve the path of A, i.e., the value of r, over time. Following Auerbach (1991), we oberve that Vickrey approach i too retrictive if the objective i to eliminate the lock-in effect at each date. Let V( ) be an operator that convert a date uncertain return into their certainty equivalent. 2 A hown in Appendix A, the condition (2) V ( T+ 1 ) = [1 + i(1 ] T + tia, i neceary and ufficient for an aet held from date to date +1 to yield a before-tax return equal in certainty-equivalence to the before-tax interet rate. Thi i equivalent to the propective gain on the aet facing an effective tax rate of t. Vickrey ytem obey (2), becaue in portfolio equilibrium the certainty-equivalent before-tax return on any riky aet equal the afe rate of return when aet are taxed uniformly, i.e., V ( r ) = i. But if we decompoe the riky aet return into two component, the afe return plu the exce return, then any tax ytem that impoe a tax rate t on the afe return will atify (2). That i, a ufficient condition for (2) i that the tax liability, T, evolve according to 2 One may think of thi a applying tate-contingent price to uncertain return in order to expre them in unit of a certain return.

8 5 * (3) T 1 = [1 + i(1 ] T + tia + t ( r i) A +, where t * i an arbitrary contant, becaue applying the operator V( ) to (3) eliminate the lat term on the right-hand ide of the expreion. One can chooe any value for t *, and need not et t * = t. The underlying reaon for thi flexibility with repect to the choice of t* i that invetor can offet change in pure rik-haring (i.e., variation in the tax rate on the exce return) with portfolio hift between afe and riky aet (ee, e.g., Sandmo 1985). Thu, an invetor will not imply be indifferent, ex ante, with repect to the choice of t*, but alo in an equal poition ex pot, when the invetor entire portfolio i conidered. Further, hould the private ector rikpooling be efficient, thi variation in tax collection will alo have no effect on the reulting equilibrium, once account i taken of the impact of the rik characteritic of government revenue (Gordon 1985, Konrad 1991, Kaplow 1994). Replacing condition (1) with condition (3) doe not directly indicate a olution to the problem of not being able to oberve the path of A. However, a widened et of admiible tax tructure might include ome that do not require thi information. Indeed, thi turn out to be the cae for one particular choice, t * 1+ i(1 = 1, which reult if T i decribed by 3 : 1+ t 1+ i(1 (4) T = 1 A. 1+ i Under (4), the tax liability upon realization at date i independent not only of the evolution of A over time, but alo of the initial purchae price. The tax T depend only on the amount realized, 3 it A period length decline, thi expreion approache T = (1 e ) A, preented in Auerbach (1991).

9 6 A, the realization date (and holding period), the afe interet rate, i, and the income tax rate, t. 4 The liability in (4) i what would reult if one aumed that the oberved ale proceed A had reulted from accumulation at the afe rate from date 0 onward, and then impoed Vickrey ytem on the aumed pattern of gain, tarting with the imputed date-0 value, 1+ i) A. ( In Appendix A, we retate two other proof baed on the preentation in Auerbach. Firt, the expreion in (4) i unique among tax regime that (i) depend only on the ame information et (notably, not on aet value at any other date) and (ii) impoe no tax liability upon realization at date 0. Second, the final realization deciion would till be unditorted by taxation for aet with intermediate ditribution, if each ditribution were alo ubject to taxation baed on (4). Thi reult will turn out to be important for our current invetigation, becaue it pave the way for aggregating different aet under the ame tax regime, not requiring that we identify the ource of ditribution a long a they face a particular predetermined tax formula. Bradford (1997) found that one could implement a more general tax ytem than the one decribed in (4) and yet till achieve holding-period neutrality. Conidering again the imple cae of an invetment at date 0 with a realization at date and no intermediate cah flow, he propoed the following tax regime. Let D be the gain reference date and g be the gain tax rate. For the ake of intuition, imagine that 0 D, although thi doe not affect the algebra. What i crucial i that D i fixed in advance of commitment to the cah flow equence covered by the tax. The tax liability at date i computed in two tep. Firt, we calculate an imputed gain at date D, equal to the difference between the purchae price A 0, inflated at the afe rate of return to 4 Expreion (4) embodie the aumption that both the rikle interet rate and the capital income tax rate are + i t contant. If they vary over time the tax rate correponding to (4) i T = 1 1 ξ (1 ξ ) 1 A. i ξ = 0 1+ ξ

10 7 date D, and the ale price at date, dicounted at the afe rate of return back to date D. We accumulate thi date-d liability to date at the after-tax interet rate: (5) g[ A (1 + i) ( D) A (1 + i) 0 D ](1 + i(1 ) ( D) Second, we compute tax at rate t on all the imputed interet on the aumed accumulation from A 0 at date 0 to A ) D 0 (1 + i at date D, plu all the imputed interet on the aumed accumulation from A (1 i ( D) + ) at date D to A at date, and carry thee liabilitie forward at the after-tax interet rate to date : ( D) D D D D ( D) (6) [ ] [ ] (1 + i(1 ) (1 + i) (1 + i(1 ) A 0 + (1 + i) (1 + i(1 ) A (1 + i) Combining thee liabilitie, the total tax under Bradford ytem at date i: D D 1 + i(1 1 + i(1 (7) 1 (1 g) A (1 + i(1 ) 1 (1 g) A i 1 + i Figure 1 provide a graphical repreentation of thi tax cheme, for an aet that appreciate from date 0 to date following the path hown by the thick line. The cheme ue only the initial and final aet value, A 0 and A, to generate two hypothetical projection of the aet value at date D, each baed on the interet rate, i (ee expreion (5)). The difference between thee hypothetical value i taxed at rate g, and the interet aumed to be earned until date D and after date D along the two hypothetical appreciation path i taxed at rate t, with all tax liabilitie determined at date and accumulated to that date.

11 8 A Actual A 0 Imputed 0 D Figure 1. Actual and Imputed Aet Value Trajectorie under Bradford Tax Scheme In relation to current tax rule, one may think of the econd term in (7) a a reduction in tax liability reflecting the initial bai of the aet. In hi original preentation, Bradford how that the ytem in (7) leave unditorted the realization deciion for an aet on which the invetor expect to earn the afe rate of return. He alo note that, for D = g = 0, the ytem reduce to that outlined by Auerbach, given in (4) above. Bradford preentation enviion that all tax conequence are concentrated at the date of realization,. In particular, it i neceary when applying (7) to take into account the aet initial purchae price, A 0. Thu, the ytem would appear to impoe greater informational requirement than that outlined by Auerbach. However, it i clear from inpection of (7) that the ame economic impact would reult from impoing eparate taxe on the two cah flow aociated with the project at their repective date, A 0 at date 0 and A at date. That i, one

12 9 could impoe a cah-flow tax at rate D 1+ i(1 1 (1 g) on the ale at date and a cah- 1+ i flow tax at rate D 1 + i(1 1 (1 g) on the initial purchae (i.e., provide a deduction at 1 + i that rate) at date 0, which ha the ame preent value a the deduction of D 1 + i(1 ( 1 + i(1 ) 1 (1 g) A 1 + i 0 at date. The advantage in impoing the tax eparately with repect to each cah flow i that each one may then be treated without reference to the other. It follow intuitively that, jut a in Auerbach ytem, the tax ytem would continue to work with intermediate cah flow, with each flow being ubject to the ame tax formula a the initial and final cah flow. Indeed, thi i hown in Appendix A. We refer to thi modified verion of Bradford approach, taxing each date-v cah flow (poitive and negative) from an aet at rate v D 1 + i(1 1 (1 g), a generalized cah- 1 + i flow taxation. Like cah-flow taxation, it impoe a tax on each cah flow without reference to the aet value or cah flow at other date. Unlike a tandard cah-flow tax, though, which would reult at rate g by etting the income tax rate t = 0, the generalized cah-flow tax effectively impoe a tax at rate t on accruing capital income. Given that the tax liability at date depend only on the ame information et a Auerbach ytem, one may be led to quetion Auerbach proof of uniquene for hi approach. Note, though, that the tax liability aociated with the aet ale under the generalized cah-flow tax i not zero for a realization at date 0, a aumed in Auerbach proof of uniquene. Rather, there may be a poitive (or negative) tax on ale proceed, even for an aet old at the ame time

13 10 a it i purchaed. For example, if the gain reference date D = 0, then a ale at date 0 generate a tax liability of ga 0. Note, though, that a purchae at the ame date would generate a deduction of A 0 at rate g, reulting in a net tax liability of zero. The reult i identical to Auerbach in thi cae, in which the aet i purchaed and old at the ame time. However, the net tax liability would not necearily equal zero if the taxpayer acquired the aet by mean other than a market purchae, a ditinction that will prove important. Relaxing the retriction of a zero-tax liability at date 0, the ytem of generalized cahflow taxation i unique given it informational requirement. Thi, too, i hown in Appendix A. B. Commentary i. Intuition of the reult It i well known that the zero tax on a zero net preent value invetment that i characteritic of the conventional cah-flow tax fail when the tax rate applied i varying over time. A declining cah-flow tax rate ha the effect of encouraging current deductible invetment, while a riing tax rate dicourage it. A tax rate riing at jut the right rate in a conventional cah-flow tax will reproduce the effect of an accrual income tax a far a the opportunitie preented to and hence the incentive of the invetor are concerned. Specifically, if the fraction of a cah flow that the invetor get to keep (or ha to give up, in the cae of an outflow) i falling at a rate equal to ome fraction of the interet rate, then the tax ha the ame impact a an income tax at that ame fractional rate. To pell thi out, note that, with an income tax, an invetment of 1 today would generate 1 + (1 ti ) in a year. With a cah-flow tax at rate f v at the current date v, one could invet 1, taking into account the rebate due to the cah-flow tax. A return at interet rate i implie f 1 v

14 11 1 fv+ 1 a payoff of (1 + i), net of cah-flow tax, in a year. The net return to the taxpayer who 1 f v invet 1 at date v will be 1 + (1 ti ), that i the cah-flow tax will mimic the income tax, if the fraction retained, 1 f v, evolve according to 1 fv (1 ti ) =. 1 fv (1 + i) In the generalized cah-flow tax, the fraction of a cah flow that the invetor get to keep at date v i v D 1 + i(1 t) (1 g). 1+ i The ratio of thi fraction at a given time to it value a year earlier i 1 + (1 ti ), (1 + i) exactly fulfilling the requirement to imulate an accrual tax at rate t. ii. Portfolio balance and rik-taking A with Auerbach original cheme, the generalized cah-flow tax effectively impoe a tax at rate t on the afe return, i, but a different tax rate on the exce return, r -i at date. It i + 1 D * 1 + i(1 traightforward to how that thi tax rate i t = 1 (1 g). An invetor in a 1 + i riky aet eeking to undo the impact of taxation on rik taking would then need to increae the holding of the riky aet not by the factor 1/(1-t), a would be the cae under a tandard income + 1 D * 1 + i(1 tax, but by the factor 1/(1 t ), or (1 g ). For the pecial cae of a 1 + i imple cah-flow tax (t=0), the repone would increae the riky aet holding by the factor 1/(1-g), a well-known reult. More generally, the invetor would need to hold an increaing hare of the riky aet over time. Thi concluion preume, however, no change in the background rik impoed on the invetor by government policy. A dicued above in relation to the literature on taxation and rik taking, if market for rik haring are efficient, then 1

15 12 the increaing rik of government revenue will undo the rik-reducing apect of taxation on aggregate invetment in riky aet. Still, each individual hare of the riky aet would need to grow over time to offet the rik-reducing impact of taxation, unle the government allocation of tax revenue rik among individual grew ufficiently with age to counter the direct impact of taxation. That i, with tax rate riing with age, the individual would normally have to take on more and more before-tax rik to deliver the ame after-tax rik. Only if the government allocation of rik roe fat enough with age would uch increaed rik-taking through portfolio deciion be unneceary. iii. Portfolio and other combination of aet Becaue the generalized cah-flow tax may be applied to any aet, regardle of it cah flow, it propertie are preerved if it i impoed on any combination of aet, a long a the ame tax parameter (i, t, D, and g) apply. That i, if we chooe two aet in an invetor portfolio and apply the ame generalized cah-flow tax to each, the outcome i identical to aggregating the two aet and then applying the generalized cah-flow tax with the ame parameter to the combined cah flow of the two aet. Similarly, hould the invetor break a ingle aet into piece, thi will have no tax conequence. Thi invariance lead to an important concluion: the ytem not only impoe an income tax rate t on the return to any particular invetment, but will do o regardle of how the invetment i characterized by the invetor or, indeed, even whether the invetment exitence i acknowledged. Example 1: Conider the put-call parity theorem of finance, which etablihe the equivalence between an equity poition combined with a put option and a call option at the ame trike price, and a afe zero-coupon bond with a ingle payment equal to that trike price. Both poition convey a rik-free return; the bond doe o directly, while the equity poition i perfectly hedged

16 13 by the invetor ability to dipoe of the aet if it value fall below the trike price (by exerciing the put option) and the invetor being required to relinquih the aet if it value rie above the trike price (through the exercie of the call option by it purchaer). Under current law, thee two equivalent poition face different tax treatment; the bond would be taxed over time ubject to the original iue dicount rule, while the equity and option would not. However, under a generalized cah-flow tax, the combined cah flow of thee two poition would be identical and o, therefore, would be their pattern of tax payment. Example 2: A problem under current tax rule i when to combine two ide of a hedging tranaction. If one aet i a mirror image of another, logic and practice ugget that they hould be combined for tax purpoe to avoid a pure arbitrage tranaction. But one poition may hedge a combination of everal other poition, no one of which i a cloe match to the firt poition by itelf. Such portfolio hedging i typically ignored by tax rule, but offer the ame arbitrage potential a the imple hedge. Both et of poition would be automatically merged under generalized cah-flow taxation, without any action required on the part of tax authoritie. Example 3: Some aet may not even be identifiable until they begin generating cah flow. Thi may be epecially the cae for cloely held aet. We take up below the extenion of the generalized cah-flow tax beyond arm length financial aet. The flavor of that extenion i uggeted by the example of a firm or individual poeing the knowledge required to develop a certain technology. Thi knowledge ha value, and the value of thi aet will change over time. Generalized cah-flow taxation will effectively impoe an income tax on thee change in value, through it anticipated impact on future cah flow. Thi implicit taxation of accruing gain will alo make the tax ytem neutral with repect to the invetor deciion regarding when to reveal the aet exitence by implementing the aociated technology in production.

17 14 iv. Treatment of gain and loe The Auerbach rule reult in what may eem, at firt ight, to be an odd treatment of gain and loe; to wit, a gain, in itelf, give rie to no extra tax and a lo to no reduction in tax. The ale value of the aet with no intermediate ditribution i, in effect, treated a the reult of accumulation at the afe interet rate ince the date of acquiition. No extra tax i due if, in fact, the aet ha jumped in value ince that date; no allowance i given if, in fact, the aet ha lot value. A emphaized by both Auerbach and Bradford, there i nothing wrong with thi feature of the rule applied to tranaction at arm length in a capital market that permit cotle contruction of all zero-value bet. Gain or loe relative to accumulation at the rik-free interet rate are the reult of good or bad outcome of uch bet. Any rate of tax applied to a bet ha the effect of reducing it cale but not it eential tochatic character. (Thi tatement will not hold if the tax rate depend on the ize of the gain or lo, a it may in a graduated-rate ytem.) A a reult, any tax applied to bet can be completely offet, at the dicretion of the invetor/gambler, imply by changing the cale of a zero-value bet in the financial market. A decribed in the expoition of the concept, the generalized cah-flow tax ha the effect of ubjecting to tax, at rate g, gain and loe, relative to the rik-free reult, all brought by appropriate back or forward dicounting to gain reference date, D. We ugget below that thi feature of the generalized cah flow rule may have a ueful practical role to play. A long a we are dealing with arm length tranaction in a dene capital market, however, the invetor i theoretically indifferent to the gain tax, ince it can be completely offet with zero-value bet. v. Choice of parameter, D and g The original Bradford cheme conceived of etting (perhap by free choice of the invetor) the capital gain parameter, g and D, that would apply to each aet in iolation; D

18 15 wa decribed a a time ince the acquiition date of the aet. So long a there i no ambiguity about the identity of an aet (o that, in particular, it acquiition date i well defined), it i conceptually permiible for each aet to have it own value of D and g. A ha been uggeted above, the identity of aet in thi ene i, however, problematic when one take into account tranaction uch a merger and ale of ome right pertaining to an aet. Thee problem vanih when the ame value of D and g apply to all aet, where D now ha the interpretation of a particular calendar date, rather than a time ince acquiition. Conceivably, one could pecify uch common value to apply to all invetor at all time. The implication would be a rate of taxation of gain and loe that tend over time toward 100 per cent (reminder: the tax rate at time v i given by v D 1 + i(1 1 (1 g) ). A a 1 + i theoretical matter thi i no problem, o long a we confine our attention to arm length invetment choice, where only intertemporal and rik allocation are involved. If invetor want to take a particular rik poition, they can do o, independently of the tax applicable to gain and loe, by taking appropriate zero-value hedging poition. A a practical matter, however, one can imagine ome problem with an invetor getting a tax rebate of 99.9 percent of the amount inveted, and paying percent on the return flow in a few year time. Among other problem, thi would require the invetor to take a huge poition in the riky aet to offet the nearly complete aborption of rik by the government. A way around thi practical problem would be to pecify eparate pair of value of g and D for each taxpayer. (Throughout we aume taxpayer are natural people, not companie.) Suppoe, for example, D were choen to be either the taxpayer date of birth or 40 th birthday.

19 16 Age (in Year) at Gain Reference Date (D) 0 40 Gain Tax Rate (g) Age Aume interet rate (i) of 2 percent and capital income tax rate (t) of 25 percent. Table 1. Generalized Cah-Flow Tax Rate (in percent) at Variou Age for Gain Reference Date, D, Equal 0 or 40 and Variou Gain Tax Rate, g Table 1 diplay the tax rate that would apply at variou age for variou choice of gain tax rate, g, auming a rik-free interet rate of 2 percent and capital income tax rate of 25 percent. (A negative entry mean that the taxpayer get a ubidy upon a poitive realization and pay a tax upon making an invetment.) For the (D, g) combination (40,.3), for example, a 40- year-old would face a tax rate of 30.0 percent. That ame individual would face a tax rate of 36.7 percent 20 year later, at age 60, the riing cah-flow tax rate imulating the effect of an income tax. All of thee age-tax rate tructure are identical in their effect on intertemporal choice. In particular, applied to any given portfolio they generate the ame value of tax revenue, dicounted at the after tax rate of return. The age-tax rate tructure in the Auerbach cheme, with it implicit gain tax rate of zero, i hown in the firt column of each panel. A illutrated, the tax rate increae with g and decreae in D. Although the variable g and D each have an intuitive definition, any given chedule can be replicated by an infinite combination of value of g and D. In our baic cae of contant rikle interet and capital

20 17 income tax rate, uch combination atify the equation D 1 + i(1 ( 1 g) = x for ome 1 + i value of x. Thi reult ha a ueful application if the future interet rate or capital income tax rate are uncertain. If the date D i in the future, the generalized cah-flow tax rate applicable in the current period depend on thoe future rate. By chooing intead a lower value of D (for example, 0) and a correpondingly higher value of g, one obtain a ytem that i baed on currently or hitorically oberved interet rate only. (The flexibility to chooe D and g i reduced if the ytem i extended to labor income, a alo dicued below.) vi. Gift and bequet Where the tax parameter are pecific to the taxpayer a new iue arie: the treatment of tranfer between taxpayer. Important example would include tranfer between poue and between parent and children. The ubject of interpoual tranfer would take u on too long an excurion into the treatment of married veru unmarried couple for adequate dicuion here. With repect to the treatment of intergenerational tranfer, the dicuion in the U.S. Treaury Blueprint for Tax Reform (Bradford et al., 1984; hereinafter Blueprint) of the ame problem in the framework of that tudy cah-flow tax may be relevant. A way to think about the tranfer iue i whether amount given away hould een a conumed by the giver, or not. There eem to be no particularly compelling a priori theoretical anwer to thi quetion. Blueprint favored excluding gift from the tax bae of the giver and including them in the tax bae of the recipient. Thi approach ha an adminitrative advantage in that in the typical cae (in which the aet i not dipoed of) there are no tax conequence at the time of tranfer of an aet. 5 5 We can think of uch a tranfer a involving an implicit ale, taxed to the tranferor, a gift, deducted by the tranferor, taxable receipt by the tranferee, and deductible aving by the tranferee.

21 18 Following thi approach under the generalized cah-flow tax would preent no problem in the univeral D cae but would poe adminitrative challenge in the ytem involving a eparate D for each individual. In thi world it would probably be neceary to treat a gift or bequet a a realization event for the tranferor (preumably with no deduction by the tranferor and no incluion of amount received in the tax bae of the tranferee). Thi requirement would preent an arguably minor breech in the trict cah-flow accounting involved in the cheme, a breech tempered to the extent that valuation i required for tranfer tax purpoe in any event. 6 vii. Enforcement Both the Auerbach and Bradford concept were motivated by interet in the poibility of taxing conitently the yield from aet that could and could not be readily marked to market. The former yield were aumed taxed on an accrual bai, wherea taxation of the latter had inevitably to be on what Warren (1993) call a wait and ee bai. The preumption wa that ome aet are taxed on an accrual bai, which tranlate in the model a a tax on the bai of the oberved interet rate. The alternative modified taxation of realized cah amount, developed here a generalized cah-flow taxation, wa thought of a the treatment that would hypothetically be impoed on aet for which accrual taxation wa impractical, much a realization accounting i done in the exiting income tax. Our current analyi ha emphaized an additional benefit to generalized cah-flow taxation that obtain from ubjecting all invetment or capital income cah flow to the ame tax ytem, namely elimination of the opportunity to take advantage of difference in tax treatment. 6 An alternative approach would be to maintain the donor D even after the tranfer and not treat the gift a a realization event, which parallel the exiting treatment of gift of appreciated aet, which are not realization event and for which the donor bai i tranferred to the recipient. While thi approach ha the advantage of avoiding realization and a change in the aet tax attribute, it would require recipient to maintain eparate account with different value of D, even after the dipoition of the aet initially tranferred.

22 19 However, if the new tax ytem i to be applied only on a limited bai, thi raie the quetion of how one ditinguihe the cah flow to which the modified cah-flow tax applie from thoe aociated with tranaction ubject to accrual accounting. One poibility would be to ue a device analogou to the Qualified Account uggeted in the Blueprint cah-flow tax. In the Blueprint cah-flow tax, in which a zero rate of tax on capital income i the objective, the default treatment of financial flow involving arm length aet i to ignore them. Net flow from a Qualified Account are, by contrat, included in the cah-flow tax bae (o net depoit are deducted). In the context of the generalized cah-flow tax on capital income, the default would be to ubject all capital income aociated cah flow to the propoed time-varying rate, with deduction in the cae of negative flow. 7 A taxpayer that wanted to elect the preent tyle treatment of capital income would have acce to a Tax Anticipation Account. Net flow from a Tax Anticipation Account, limited to aet traded on active ecurity market, would be excluded from the generalized cah-flow tax bae. That mean the invetor would get no deduction for a depoit and pay no tax on a withdrawal. Intead, the Tax Anticipation Account would be ubjected to tax on a mark-to-market bai at the appropriate capital income tax rate. It i important to tre here that eligibility for the Tax Anticipation Account mut be limited to aet held at arm length. Otherwie, the taxpayer could arbitrage the difference in tax treatment by contructing aet with below-market return to be taxed on an ex pot bai and aet with above-market return to be taxed on an ex ante bai. 7 At thi point we are auming individual invetment flow are ditinguihable from labor income flow; we take up below the problem of making uch ditinction.

23 20 3. Extenion A. Time-dependent capital income tax rate, wealth taxation, and inflation adjutment i. Time-dependent capital income tax rate and wealth taxation Our derivation of the generalized cah-flow tax how how it i poible to duplicate in eential economic effect a capital income tax impoed at ome pecified rate on accruing income. We have mentioned how the Auerbach tax can be adjuted for time-varying rikle interet and capital income tax rate. In the generalized cah-flow tax, the correponding refinement of the tax rate would be ν 1 + iξ(1 t ) ξ 1 (1 g) Aν. ξ = D 1+ i ξ When the rikle interet and capital income tax rate are tochatic, we need to conider how to deal with the generalized cah-flow taxation of receipt and outlay occurring before the date D in the formula. One poibility, contemplated in Bradford cheme, would be to potpone reolving the tax liability until the arrival of D, with appropriate dicounting of tax implication to the time of tax payment. The other option, mentioned earlier, would be to chooe a value of D that would alway be in the pat for the affected invetor. A more ignificant iue, to which we return below, i the poibility that the gain tax rate, g, will change in the future. By ubjecting all capital income cah flow to the generalized cah-flow tax, one could implicitly impoe any tax rate trajectory, uncontrained by arbitrage condition with repect to aet ubject to accrual taxation. In particular, one could imulate any deired capital income D tax rate trajectory. Think of the generalized cah-flow tax rate a obeying 1 (1 g) γ, 1 + i(1 t) where γ i a parameter to be choen a a matter of policy. If we chooe γ =, 1+ i where i and t have the tandard interpretation, we produce the effect of an accrual tax at rate t on

24 21 the actual interet rate, i. But we could chooe the parameter γ directly. Thi will be equivalent to an effective capital income tax on nominal capital income at rate (1 + i)(1 γ ) t =. One may i alo view the reult a equivalent to a uniform wealth tax (applied each period to the amount carried into the next period) at rate ( 1 γ ). Under thi incluive approach, one need not oberve the rik-free interet rate to implement a tax ytem with a ingle effective rate of tax on all capital income. Only the parameter γ need be pecified, although the effective rate of capital income tax will depend on the actual value of the interet rate. The requirement that all capital income cah flow be covered i important. If the taxpayer had the alternative of electing accrual income taxation, there would generally be an inconitency between the two (unle the capital income tax rate actually were et at (1 + i)(1 γ ) t = ). i ii. Inflation adjutment A emphaized by Bradford (1997), the capital income tax effected by the generalized cah-flow tax i certainly not correct if taxation of real capital income i the objective. With a poitive rate of inflation, taxing nominal interet income at a contant rate would imply taxing real interet income at a higher, perhap time-varying rate. The previou dicuion relating to wealth taxation indicate that it would be conceptually eay to ue the generalized cah-flow tax to impoe an inflation-corrected capital income tax: if i * i the real interet rate, then one would ubtitute i * 1 + i(1 t) for i in determining γ =, the generalized cah-flow tax formula. 1+ i

25 22 B. Cloely-held aet and human capital accumulation A dicued in Auerbach (1991), the original approach to retropective taxation of individual aet encounter problem when aet are cloely held; in particular, the ytem yield the wrong reult when invetor can mirepreent the return tream and cot aociated with a particular aet. A already dicued here, thi problem i overcome to the extent that alternative aet are alo included under the propoed tax regime, for then the tax calculation aggregate all cah flow, regardle of the aet with which they are aociated by the invetor. But a key borderline remain between labor and capital income. If an invetor ha the choice of purchaing an aet or contructing it himelf through hi own effort (think of a venture capital operation), the choice hould not be ditorted by taxation. Yet a ditortion will exit if the propoed ytem applie only to capital income. Under the Auerbach cheme, for example, the individual would avoid tax on imputed labor income ued to produce a elf-contructed aet, but would be taxable on labor income ued to finance the aet market purchae. Even under the generalized cheme, the ditortion will remain unle the labor income tax and the generalized cah-flow tax are equal at each date, in which cae the invetor deciion to report imputed labor income would have no tax conequence, the extra tax being exactly offet by the extra cah-flow deduction aociated with the aet purchae. Two policy repone ugget themelve. On the one hand, perhap taxing labor income at rate riing over time i undeirable and the incluion of labor income under the generalized cah-flow ytem unneceary. For individual facing only the claic labor-leiure deciion, the level and pattern of labor tax rate over time hould be determined by the ditortion aociated with thi deciion. Even in thi cae, the riing tax chedule might make ene. A hown in Appendix B, the houehold intertemporal marginal rate of ubtitution for leiure under thi

26 23 regime will be baed on the before-tax interet rate, a would be true in the abence of taxation. It i not clear that a zero intertemporal labor ditortion i optimal in thi econd-bet world, in which the intertemporal conumption and labor-leiure ditortion remain. But conidering the optimality of intertemporal labor taxation raie the broader quetion of how the income tax rate t i determined in the firt place. Thi iue i important but lie beyond the cope of thi paper. Where the definition of labor i unclear, a common tax rate for labor and capital i an adminitrative advantage. Another attractive feature of the ytem of riing tax rate i that, if individual make deciion about human capital invetment, uch invetment would not longer be favored by the tax ytem a they are in a conventional income tax. The riing rate would eliminate the relative tax benefit given human capital (or other) invetment that i financed with foregone earning when labor income tax rate are contant over time. To ee thi intuitively, note that uch invetment receive it favorable treatment becaue imputed labor income that i foregone when uch an invetment occur i not ubject to taxation. If individual were forced to report uch imputed income and receive bai in the capital invetment, the tax advantage would go away (auming economic depreciation for all invetment). The propoed incluion of labor income under the generalized cah-flow tax would eliminate the net tax conequence of deciding to report uch imputed income and an aet purchae of equal ize. Human capital invetment would be treated no better or wore than other invetment, a point made in a related context by Kaplow (1996). Human capital i jut another intance of a elf-contructed phyical aet, the only potential difference being in how the future income i characterized. With all cah flow being taxed at the ame rate regardle of being categorized a labor income or capital income the treatment of elf-contructed phyical aet and human capital are identical to each other and to the treatment of purchaed aet.

27 24 Indeed, thi effect of riing labor income taxe over time ha been ubmitted a a defene of the Nordic approach to dual income taxation, which impoe a proportional tax on capital income but a progreive tax (typically inducing riing marginal tax rate over the productive part of the life cycle) on labor income (Nielen and Sørenen 1997). C. Lifetime progreivity and income averaging Once the capital income tax rate ha been et, the propertie of the tax on earning at different age are determined by the D and g combination. Table 1 give a ene for the pattern of tax rate at variou age implied by typical choice. Although the tax rate vary over the life cycle, they do not vary with the level of lifetime income. A natural quetion i whether one could, alternatively, apply ome ort of graduated rate tructure to cah flow in order to achieve progreivity in the ytem. The difficulty i that, if earning or cah flow are not uniform over time, a graduated rate tructure will generate intertemporal variation in the rate that will upet the uniform capital income taxation aimed for by the ytem. A imilar problem confronted the Blueprint cah-flow tax. In that cae, where a zero rate of capital income taxation wa an objective, the aim wa to aure that a taxpayer would alway confront the ame marginal rate on cah flow, thereby eliminating the inefficiency that would reult from a time-varying rate of tax and effecting a tax burden baed on an arguably appropriate average of lifetime conumption. Becaue of variation in conumption over time (and the fact that ome aet, notably owner-occupied houe, were excluded from the ytem), thi would be an unlikely reult if a graduated rate tructure were trictly applied to all cah flow. Intead, under the Blueprint cah-flow tax, the taxpayer i given the option to chooe between two form of accounting for cah flow aociated with arm length inveting. Net

28 25 depoit to a Qualified Account are deducted from the tax bae; other nonqualified invetment and diinvetment tranaction in arm length financial aet are ignored by the ytem. A nonqualified invetment acrifice the benefit of deduction for up-front outflow from the taxpayer, but the return i free of tax. Under thi approach, a taxpayer anticipating a riing cah-flow tax rate would find it advantageou to remove fund from Qualified Account (adding to the current tax bae, thereby inducing a higher current marginal tax rate) and invet them in nonqualified form (reducing the future tax bae, thereby inducing a lower future marginal tax rate). Such a tranaction would add to the current tax bae and reduce the future tax bae by the ame amount in preent value. The reult would be a reduction in the dicounted lifetime tax flow (becaue the marginal tax rate i lower in the preent than in the future). Continuing thi proce, the taxpayer would eek to maintain a contant anticipated marginal tax rate. For taxpayer with higher lifetime inflow, for example owing to high labor earning, the marginal tax rate that would reult from uch (deirable) tax planning would be higher than for taxpayer with lower lifetime inflow. In the framework of the generalized cah-flow tax, the Tax Anticipation Account could be deployed to imilar effect. Net depoit to the Tax Anticipation Account, ubject to accrual income taxation, would be excluded from the generalized cah-flow tax bae. The generalized cah-flow tax would be determined by applying to included cah flow a graduated rate tructure, derived from a conventional graduated rate tructure by making it age dependent in uch a way that the marginal net of tax rate at each tax bae level decline at the after-tax interet rate. A potential complication of thi approach to averaging i that it depend on the taxpayer ability to allocate aet acro the two type of account. A treed above, thi open up the poibility of tax arbitrage unle the taxpayer allocation deciion i contrained to aet held

29 26 at arm length. But ucceful averaging would till be poible. For example, it could be accommodated even if the taxpayer choice were retricted to government bond pecially created for thi purpoe. The government could permit each individual to etablih a pair of pecial government bond account, the balance of which would be updated on the taxpayer annual tax return. One account would be ubject to generalized cah-flow taxation, the other to accrual taxation. The two account would carry the ame rate of interet, and the balance in either could be negative, a long a the net balance of the two account remained non-negative. By borrowing in one account and depoiting an equal amount in the other, the taxpayer would be able to decelerate or accelerate lifetime cah flow to enure adequate lifetime averaging. But, becaue the two account would impoe the ame effective tax rate under ucceful averaging, there would be no cope for arbitrage beyond that ued to accomplih the averaging. 8 One ubtle point to recognize about thi approach to averaging (whether under the Blueprint cah-flow tax or the generalized verion) i that it would not generally leave the invetor in a ituation in which the rik-adjuted before-tax return to invetment equal the interet rate, i.e., V ( r ) = i. Even with averaging, future tax rate would till be uncertain. A a conequence, the taxpayer portfolio deciion would depend not imply on the expected tax rate, but alo on the covariance between the tax rate and each aet before-tax return. For example, an aet offering higher return when the tax rate i higher (a would be the cae if higher than expected aet return are aociated with a higher tandard of living) would erve a a hedge againt tax rate variation, leading the invetor to accept a lower before-tax return than if the aet before-tax return were independent of tax rate variation. Thi incentive to offet tax- 8 It i poible ome form of explicit averaging could be ued intead of the elf-averaging ytem enviioned here. Typical averaging mechanim, however, bring with them, at leat in ome degree, the ort of intertemporal tax rate variation, and hence intertemporal ditortion, that the GCFT ytem i deigned to avoid.

30 27 rate rik might eem a ource of inefficiency, ditorting taxpayer behavior in repone to individual rik that are ocially diverifiable. But rik that could be diverified need to be taken into account if no mechanim actually exit for diverification. Once tax-rate rik ha been introduced, it i privately and ocially optimal for taxpayer to offet the rik unle there i ome other mechanim that allow them to do o, i.e., to pool tax-rate rik with other taxpayer. D. Changing the tax parameter a a matter of changing policy One of the under-appreciated feature of a proper accrual tax on capital income i that time-variation in the rate of a tax ha no allocative effect, apart from whatever follow from variation in after-tax rate of return. So, for example, with mark-to-market accounting (if it were feaible), variation in tax rate, whether anticipated or not, would have no conequence for aet price, including the relative price of aet of different durability or different vintage. 9 A we have already dicued, thi i not the cae for cah-flow taxe. In the claic cah-flow implementation of a conumption tax, for example, the contancy of the rate through time i critical for all of the conumption-type propertie of the ytem. In the generalized cah-flow tax, we have ued a carefully articulated intertemporal variation in the tax rate to produce the equivalence of an accrual income tax. Any dependence of the generalized cah-flow tax rate on time mut be appropriately coordinated with change in the capital income tax rate in a way anticipated by the invetor in the ytem for it to work. In the conventional income tax, a ingle rate applie to both capital and labor income. In the generalized cah-flow tax, the taxation of capital income i implicit, and at a rate that typically bear no reemblance to the current rate of tax on cah flow. We have dicued above the poibilitie for varying the implicit rate of capital income tax, t, via the lope of the tax 9 A concie preentation of thi reult may be found in Samuelon (1964).