ELSEVIER Journal of Public Economics 58 (1995) 257-265

JOURNAL OF PUBLIC ECONOMICS

Taxation, uncertainty and the choice of a consumption tax base

G e o r g e R . Z o d r o w

Economics Department, Rice University, Houston, TX 77251-1892, USA

Received February 1993; revised version received May 1994

Abstract

Several observers have concluded that the equivalence between the cash flow and wage tax approaches to direct consumption taxation breaks down in the presence of uncertainty, as individuals with extraordinarily large gains are treated too generously under the latter approach. In particular, Ahsan (Journal of Public Economics, 1989, 40, 99-134; Canadian Journal of Economics, 1990, 23, 408-433) contends that equivalence obtains only if returns in excess of a safe rate of return are included in the wage tax base. This paper constructs an alternative and arguably more plausible model under which full equivalence between the two approaches obtains even i n t h e presence of uncertainty. It also derives Ahsan's result in a more general context, and demonstrates that the divergence between the two analyses is attributable to different assumptions regarding the cost to the government of an uncertain revenue stream.

Keywords: Consumption tax equivalence results; Taxation and saving; Tax with uncertainty

JEL classification: H2; D8

I . Introduction

T h e ques t i on of w h e t h e r i ncome or c o n s u m p t i o n is the p r e f e r a b l e base for d i rec t t a x a t i o n has s p a r k e d e x t e n d e d d e b a t e . 1 T h e issue is c o m p l i c a t e d by the ex i s t ence o f two a l t e rna t ive m e t h o d s of i m p l e m e n t i n g a c o n s u m p t i o n

For example, see the papers in Pechman (1980) and Rose (1990).

0047-2727/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0047-2727(94)01470-1

258 G.R. Zodrow / Journal o f Public Economics 58 (1995) 257-265

tax. The 'expenditure tax' approach allows individuals a deduction for saving, with full taxation of withdrawals of both the amounts saved and all earnings; since the tax base is net cash flow, this method is also called the 'individual cash flow' (ICF) approach. Under certain circumstances, includ- ing constant tax rates and certain returns, the ICF approach effectively exempts capital income from tax, as the benefit of tax deferral at the time of saving exactly offsets in present value future taxation of all withdrawals. This suggests that a 'wage tax' approach, which simply exempts capital income, provides an alternative means of implementing a consumption- based tax; indeed, under these same circumstances, the two approaches are equivalent in the sense that they result in tax burdens that are equal in present value (although the timing of tax payments is different) and identical individual consumption paths and utility levels. 2 This second approach is also te rmed the 'individual tax prepayment ' ( ITP) approach to a consumption tax since, relative to the ICF tax, tax liability is ' p r e p a i d ' - n o deduction is allowed for saving so subsequent taxation of withdrawals is unnecessary.

Several observers, however, have argued that this equivalence breaks down in a critical fashion in the presence of uncertainty, as extraordinarily large returns to 'lucky' investors will be entirely untaxed under the ITP approach, but such returns are included in the base of the ICF tax. 3 For example, the U.S. Treasury (1977, pp. 128-129) argues that under the ITP approach, "The major d i s advan tage . . , is t h a t . . , lucky investors might become very rich and owe no additional tax liability on future consumption of their wealth . . . . " Similarly, Graetz (1979) argues that fairness requires that taxpaying capacity be evaluated only on the basis of actual outcomes (that is, using an ex post measure such as the ICF approach), rather than on the basis of opportunities (that is, using an ex ante measure such as the ITP tax).

Other analysts, including Aaron and Galper (1985), Bradford (1986), and Zodrow and McLure (1991), conclude that this distinction is overstated. They argue that individuals subject to an ICF tax will anticipate future taxes on withdrawals and will increase the amount saved in the risky asset, relative to the ITP tax; each of these authors constructs simple numerical examples for which individual consumption outcomes are identical under the two approaches. 4

However , in two provocative papers Ahsan (1989, 1990) has constructed a model that he argues provides a formal proof of the Treasury /Grae tz

2 For a discussion of these points and some illustrative examples, see Zodrow and McLure (1991).

3 Similarly, 'unlucky ' investors will be able to deduct losses only under the ICF approach. 4 Note that Bradford et al. (1984, pp. 115-116) accept this line of reasoning in the revised

edit ion of Blueprints (U.S. Depar tment of Treasury, 1977).

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posi t ion. Specifically, he concludes that the ITP approach is equivalent to the I C F tax only if ex t raord inary capital gains - those in excess of a safe or riskless ra te of re turn - are included in the tax base under the ITP approach ; he calls this the 'modif ied wage tax' ( M W T ) approach. 5 This result is of course ent irely consistent with the rat ionale under ly ing the T r e a s u r y / G r a e t z a rgument , as it requires ' lucky ' investors to pay an extra tax on extra- o rd ina ry gains under the modif ied version of the ITP tax.

This result is t roub lesome for advocates of the ITP approach , since its simplicity advantages relative to the ICF tax - due largely to the absence of capital income in the b a s e - would evapora te under the M W T . 6 Indeed , the need to identify and tax only the ' ex t raord inary ' c o m p o n e n t of investment re turns under the M W T would likely render it more compl ica ted than the I C F tax. Since some observers argue that the latter approach is too compl ica ted to be practical, this suggests that considerat ions of tax simplicity m a y prec lude a direct consumpt ion tax.

H o w e v e r , in this paper I argue that such a conclusion is p rematu re , and is a rguably a misleading guide to tax policy. I construct an al ternative (more genera l ) mode l under which full equivalence be tween the ICF and ITP taxes obta ins even in the presence of uncertainty. The key assumpt ion of this mode l is that an uncer ta in revenue s t ream is costly to the gove rnmen t , so tha t it d iscounts future revenues at the expected rate of re turn in the e c o n o m y ra ther than at the riskless rate; I also show, within the context o f the same model , that Ahsa n ' s result obtains only when the gove rnmen t is a s sumed to be able to absorb such risk costlessly.

2. Equivalence results

2.1. Equ iva lence o f the I C F and I T P taxes with uncertainty

The mode l used in this paper is a general ized version of the Ahsan model . Individuals are expected utility maximizers , and utility is a strictly concave funct ion o f consumpt ion in two periods, C 1 and C2 .7 There are two a s s e t s - a safe asset with a certain re turn r, and a risky asset with an uncer ta in re turn x. 8 The f ract ion of total saving invested in the risky asset is a. L a b o r supply

5 Alternatively, an ITP tax is equivalent to an ICF tax only if the latter exempts extraordinary gains from taxation.

6 McLure and Zodrow (1990) discuss the relative simplicity advantages of the ITP approach. Ahsan considers the special case in which the utility function can be expressed in the form

g(C1) + E[h(C2) ]. Government services are assumed to be additively separable in the utility function in both formulations.

8As will be shown (footnote 10), the extension to the case of many risky assets is straightforward.

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is e x o g e n o u s , wi th f i r s t -per iod i ncome Y and no s e c o n d - p e r i o d income . C o n s u m p t i o n is t axed at ra te t c u n d e r the I C F a p p r o a c h , and wages are t a x e d at r a te t w u n d e r the ITP a p p r o a c h ; the I C F tax has full loss offset . I n d i v i d u a l s thus choose a and C l to max imize

E ( U { C 1, [ ( 1 - t w ) Y / ( 1 + t c ) - C1][1 + r + a ( x - r ) ] } ) , (1)

w h e r e the ind iv idua l budge t cons t r a in t impl ies the second a r g u m e n t is C 2, a n d t c = 0 u n d e r the ITP a p p r o a c h whi le t w = 0 u n d e r the I C F a p p r o a c h . T h e f i r s t -o rde r cond i t ions for a and C 1 are

E { U 2. [(1 - t w ) Y / ( 1 + / c ) - C~l(x - r)} = 0 , (2)

E { U 1 - U 2 • [1 + r + a ( x - r)]} = 0 . (3)

In the absence of unce r t a in ty , cons tan t g o v e r n m e n t r evenues (in p r e se n t va lues) r equ i r e 9

( 1 - t w ) = l / ( l + t c ) ::~ t w = t c / ( l + t c ) . (4) S u p p o s e (4) also holds wi th unce r t a in ty . If so, (2) and (3) a re ident ica l u n d e r the I C F and ITP reg imes , imply ing iden t ica l op t ima l va lues of a and C 1. M o r e o v e r , s ince saving u n d e r the ITP tax is S w = ( 1 - t w ) Y - C I and sav ing u n d e r the I C F tax is S c = Y - (1 + tc)C~, it is c lear tha t

S c = (1 + t c )S w (5)

w h e n (4) is sat isf ied; tha t is, as sugges ted above , saving increases u n d e r the I C F tax - by a fac tor of (1 + t c ) re la t ive to the ITP tax - in an t i c ipa t ion of t he l a rge r fu tu re taxes tha t mus t be pa id u n d e r the f o r m e r tax r eg ime . In a d d i t i o n , s ince a is ident ica l in bo th cases, the a moun t s inves ted in the r isky a n d safe assets also inc rease e q u i p r o p o r t i o n a t e l y u n d e r the I C F tax. m

T h e cr i t ical issue is thus the va l id i ty of (4) in the p re sence of unce r t a in ty . U n d e r the ITP m e t h o d , the p re sen t va lue of r evenues (which are co l l ec ted en t i r e ly in the first p e r i o d ) , is s imply R w = twY . U n d e r the I C F tax, the e x p e c t e d p r e s e n t va lue of r evenues is R c = tc[C 1 + E ( C 2 ) / ( 1 + p)] , w h e r e p is the g o v e r n m e n t ' s d i scoun t ra te . Subs t i tu t ing for C2 (as in (1)) and s impl i fy ing y ie lds

R c = [ t c / (1 + t c ) ]OY+ t c C , ( 1 - 0 ) , (6)

w h e r e 0 = E[1 + r + a (x - r ) ] / (1 + p) . Thus , (4) ob ta ins u n d e r the equa l

9 For example, see Atkinson and Stiglitz (1980, pp. 69-70). l0 Note that this result can easily be extended to the case of many risky assets. For

k = 1 . . . . , K risky assets, there are K conditions analogous to (2) - one for each a k, the share of saving in an asset with a risky return x k. The equivalence result still obtains, however, as the K + 1 first-order conditions are identical under the ICF and ITP taxes.

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expec ted revenue constraint R w = R c if the gove rnmen t discount rate equals the expec ted re turn to saving, or p = r + E [ a ( x - r)].

This ra ther plausible condi t ion can be in terpre ted in several ways. O n e in te rpre ta t ion is that the deduct ion for saving under the ICF tax effectively makes the gove rnmen t a silent par tner in risky investments , sharing in bo th gains and losses. 11 Accordingly , the gove rnmen t should in this case account for the uncer ta in ty of future revenues by discounting them at the expec ted rate o f re turn in the e c o n o m y (rather than the riskless rate); 12 such an approach is consistent with several recent analyses, including Mayshar (1977), Mintz (1981), Bulow and Summers (1984), G o r d o n (1985) and H a m i l t o n (1987), who argue that the gove rnmen t cannot absorb risk costlessly. 13 For example , G o r d o n (1985, pp. 5 - 6 ) concludes that "r isk in g o v e r n m e n t tax revenues is as costly to bear as privately t raded risks" since gove rnmen t s bear the risks of " r a n d o m tax rates on o ther income, r a n d o m g o v e r n m e n t expendi tures , or r a n d o m gove rnmen t deficits". A n al ternative in terpre ta t ion is that the revenues which are obta ined earlier under the ITP app roach than under the I C F tax can be invested by the gove rnmen t to yield a re turn equal to the expected private rate of re turn in the economy . Such a view is also a plausible one , and is general ly consistent with some recent results on relative returns to public and private investment . 14

Thus , when the gove rnmen t accounts for the costs of uncertain future revenues by discounting them at the expected rate of re turn, full equiva- lence be tween the ITP and ICF approaches is established. That is, consump- t ion in bo th per iods and the expected present value of gove rnmen t revenues are identical under bo th consumpt ion tax regimes. 15

2.2. Equivalence o f the ICF approach and the M W T

In contras t , A h s a n concludes that equivalence obtains be tween the ICF tax and the M W T . His analysis follows earlier analyses of taxat ion and r isk-taking, including D o m a r and Musgrave (1944), Mossin (1968), Stiglitz

1~ This point is well known in the consumption tax literature; for example, see Zodrow and McLure (1991).

~2 Similarly, Summers (1987) argues that firms should use a relatively high discount rate for uncertain cash flows.

l~These studies effectively assume that individuals face perfect capital markets and are sufficiently diversified that aggregate uncertainty is not reduced when risk is transferred from private individuals to the government; see Hamilton (1987).

t4 See Aschauer (1989) and the papers in Munnell (1990) for discussions of this controversial issue.

~ However, note that the private valuations of taxes paid in the two cases depend on the individual discount rate.

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(1969) and Arrow and Lind (1970), in assuming the government can absorb risk costlessly. 16 In this case, the appropr ia te government discount rate is the riskless rate of return (p = r), and the above analysis indicates that if (4) were satisfied, expected revenue would be lower under the ITP tax than under the ICF alternative (since future revenues under the latter tax are discounted at a lower rate). Accordingly, Ahsan argues that the wage tax base must be expanded to include extraordinary gains ( x - r ) to obtain equivalence with the ICF; his result can be generalized within the context of the model utilized in this paper as follows.

Consider the model detailed above for the case in which a R is the absolute amount of saving invested in the risky asset. In this case, individuals choose O~ R and C~ to maximize

E(U{C1, [(1 - t w ) r / ( 1 + tc) - Ct](1 + r)

+ [(1 - tw)/(1 + tC)]aR(X -- r ) ]}) , (1 ' )

where the second argument is again C 2, taking into account the individual budget constraint under the taxation of extraordinary returns (x - r) at rate t w under the MWT. In this case, the first-order conditions for a R and C~ are

E { U 2. [ ( 1 - tw)/(1 + / c ) ] ( x - r)} = 0 , (2 ' )

E{U, - U 2. ( 1 + r)} = 0 . (3 ' )

If (4) is satisfied, then (2 ' ) and (3 ' ) imply that the optimal a R and C i are identical under the ICF and M W T taxes. In addition, since saving under the ICF approach is S c = Y - (1 + t c ) C ~, and saving under the M W T approach is S M = (1 - t w ) Y - C1, S c = (1 + tc)S M when (4) is satisfied. Thus, relative to the MWT, saving goes up proport ionately (by a factor of (1 + tc) ) under the ICF approach; however, since a R is constant, all of the increase in saving goes into the safe asset.

To determine the validity of (4), note that expected revenues under the M W T - u n d e r the assumption that the government discounts future re- venues at the riskless return r - a r e

R M = t w { Y + E[aR(X-- r)]/(1 + r )} . (7)

Substituting for C 2 into R c = tc[C 1 + E(C2)/(1 + r)] and simplifying shows that (4) implies R M = R c.

Thus, when the government discounts future revenues at the riskless rate of return, the ICF approach is equivalent to the MWT. It is interesting to

~6This assumption is at the opposite extreme from that made by the studies noted in the previous subsection- individuals are not perfectly diversified and government risk-spreading reduces aggregate uncertainty costlessly.

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note that the M W T is constructed so that the behavioral response that is critical to establishing the equivalence between the ICF and ITP approaches in the previous subsec t i on - an increase in investment in the risky asset under the ICF tax in anticipation of future larger tax p a y m e n t s - does not occur; all of the increase in saving that occurs when switching from the M W T to the ICF tax goes into the safe asset.

3. Conclusion

In summary , this paper identifies conditions under which the well-known equivalence between the ICF and the ITP approaches to the direct taxation of consumption in the presence of certain returns to investment also obtains in the presence of uncertainty; the key assumption is that the government cannot absorb risk costlessly and accounts for the costs of uncertain revenue s t reams by discounting future revenues at the expected rate of return. By compar ison, if the government can absorb risk costlessly it should discount future uncertain revenues at the riskless rate of return. This implies that the expected present value of revenue is lower under the ITP tax than under the ICF approach, and the government must alter the structure of the ITP tax to obtain an equivalent amount of revenue. Ahsan (1989, 1990) shows that one way this might be done is by including extraordinary capital gains in a 'modif ied wage tax'. However , 'equivalence ' might also be established in al ternative ways; in particular, rates under the ITP tax could simply be raised to reflect the absence of costless government risk-sharing, relative to the ICF tax; such an approach would have the clear administrative advantage of avoiding at tempts to characterize returns as 'normal ' and 'ext raordinary ' . In any case, the nature of the equivalence results presented above clearly depends on the extent to which the government can absorb risk costlessly; although this issue clearly is still controversial, there seems to be increasing support in the literature for the view that bearing such risk imposes costs on the government .

The results of the paper also highlight an important feature of cash flow taxes. Such taxes are often asserted to generate positive revenues by taxing economic rents or above-normal returns to risky investment. 17 However , this is true only in the limited sense that such revenues reflect economic rents or above-normal returns on the government ' s share of the investment (which arises due to deductions for expensing rather than for economic depreciat ion under a cash flow tax). Indeed, the above analysis demonstrates that government revenues are zero in present value terms for above-normal returns to risky investment if the government discounts uncertain future

17 For a recent example, see Musgrave (1992, p. 180).

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r evenues at the expected rate of re turn . Thus , a cash flow tax does no t affect pr iva te rates of r e tu rn and thus does no t reduce the rate at which private inves tors ea rn economic rents or above -no rma l re turns ; only the private share of the inves tmen t is reduced. 18

F ina l ly , two addi t ional qualif ications to the equiva lence be tween the I CF and ITP taxes should be noted. First , equiva lence does no t ob ta in u n d e r a progress ive tax system, since tax rates will differ across per iods unde r the I C F tax. Second, a l though the assumpt ion that rates of re tu rn are in- d e p e n d e n t of the level of pr ivate inves tmen t is of ten plausible , it may be i napp rop r i a t e in the case of un ique inves tmen t oppor tun i t i es (e.g. en- t r ep r eneu r i a l innova t ion) . 19 Inves t iga t ion of the impor tance of these points is left to fu ture research.

Acknowledgments

I have benef i ted greatly from the commen t s of two a n o n y m o u s referees and f rom discussions with Charles McLure and Peter Mieszkowki. A n y r e m a i n i n g errors are my own.

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