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Taxation, uncertainty and the choice of a consumption tax base
JOURNALOF Journal of Public Economics 58 (1995) 257-265
ELSEVIER
PUBLIC ECONOMICS
Taxation, uncertainty and the choice of a consumption tax base George
R. Zodrow
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 q u e s t i o n o f w h e t h e r i n c o m e o r c o n s u m p t i o n is t h e p r e f e r a b l e b a s e for d i r e c 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 existence of two alternative methods of implementing a consumption 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
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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, including 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 consumptionbased 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 t e r m e d 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, " T h e major d i s a d v a n t a g e . . , is t h a t . . , lucky investors might b e c o m e 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). O t h e r analysts, including Aaron and Galper (1985), Bradford (1986), and Z o d r o w and McLure (1991), conclude that this distinction is overstated. T h e y 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 T r e a s u r y / G r a e t z 2 For a discussion of these points and (1991). 3 Similarly, 'unlucky' investors will be 4 Note that Bradford et al. (1984, pp. edition of Blueprints (U.S. D e p a r t m e n t
some illustrative examples, see Zodrow and McLure able to deduct losses only under the ICF approach. 115-116) accept this line of reasoning in the revised of Treasury, 1977).
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position. Specifically, he concludes that the I T P a p p r o a c h is equivalent to the I C F tax only if e x t r a o r d i n a r y capital gains - those in excess of a safe or riskless rate of r e t u r n - are included in the tax base u n d e r the I T P a p p r o a c h ; he calls this the 'modified wage tax' ( M W T ) approach. 5 This result is of course entirely consistent with the rationale underlying the T r e a s u r y / G r a e t z a r g u m e n t , as it requires 'lucky' investors to pay an extra tax on extrao r d i n a r y gains u n d e r the modified version of the I T P tax. This result is t r o u b l e s o m e for advocates of the I T P a p p r o a c h , since its simplicity advantages relative to the I C F tax - due largely to the absence of capital i n c o m e in the b a s e - would e v a p o r a t e u n d e r the M W T . 6 I n d e e d , the n e e d to identify and tax only the ' e x t r a o r d i n a r y ' c o m p o n e n t of investment returns u n d e r the M W T would likely r e n d e r it m o r e complicated than the I C F tax. Since s o m e observers argue that the latter a p p r o a c h is t o o c o m p l i c a t e d to be practical, this suggests that considerations of tax simplicity m a y p r e c l u d e a direct c o n s u m p t i o n tax. H o w e v e r , in this p a p e r I argue that such a conclusion is p r e m a t u r e , and is a r g u a b l y a misleading guide to tax policy. I construct an alternative (more g e n e r a l ) m o d e l u n d e r which full equivalence b e t w e e n the I C F and I T P taxes obtains even in the presence of uncertainty. T h e key assumption of this m o d e l is that an uncertain r e v e n u e stream is costly to the g o v e r n m e n t , so that it discounts future r e v e n u e s at the expected rate of return in the e c o n o m y r a t h e r than at the riskless rate; I also show, within the context o f the s a m e m o d e l , that A h s a n ' s result obtains only w h e n the g o v e r n m e n t is a s s u m e d to be able to absorb such risk costlessly.
2. Equivalence results 2.1. E q u i v a l e n c e o f the I C F a n d I T P taxes with uncertainty
T h e m o d e l used in this p a p e r is a generalized version of the A h s a n model. Individuals are e x p e c t e d utility maximizers, and utility is a strictly c o n c a v e f u n c t i o n o f c o n s u m p t i o n in two periods, C 1 and C2 .7 T h e r e are two a s s e t s - a safe asset with a certain return r, and a risky asset with an uncertain return x. 8 T h e fraction 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 , with f i r s t - p e r i o d i n c o m e Y a n d no s e c o n d - p e r i o d i n c o m e . C o n s u m p t i o n is t a x e d at r a t e t c u n d e r t h e I C F a p p r o a c h , a n d w a g e s a r e t a x e d at r a t e t w u n d e r t h e I T P a p p r o a c h ; t h e I C F tax has full loss offset. I n d i v i d u a l s t h u s c h o o s e a a n d C l to m a x i m i z e E ( U { C 1, [ ( 1 - t w ) Y / ( 1 + t c ) -
C1][1 + r + a ( x -
r)]}),
(1)
w h e r e t h e i n d i v i d u a l b u d g e t c o n s t r a i n t i m p l i e s the s e c o n d a r g u m e n t is C 2, a n d t c = 0 u n d e r t h e I T P a p p r o a c h while t w = 0 u n d e r t h e I C F a p p r o a c h . T h e f i r s t - o r d e r c o n d i t i o n s for a a n d C 1 a r e 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)
I n t h e a b s e n c e o f u n c e r t a i n t y , c o n s t a n t g o v e r n m e n t r e v e n u e s (in p r e s e n t values) require 9
(1-tw)=l/(l+tc)
::~ t w = t c / ( l + t c ) .
(4)
S u p p o s e (4) also h o l d s with u n c e r t a i n t y . If so, (2) a n d (3) a r e i d e n t i c a l under the ICF and ITP regimes, implying identical optimal values of a and C 1. M o r e o v e r , since saving u n d e r t h e I T P tax is S w = ( 1 - t w ) Y - C I a n d s a v i n g u n d e r t h e I C F tax is S c = Y - (1 + tc)C~, it is c l e a r t h a t S c = (1 + t c ) S w
(5)
w h e n (4) is satisfied; t h a t is, as s u g g e s t e d a b o v e , saving i n c r e a s e s u n d e r t h e I C F t a x - b y a f a c t o r o f (1 + t c ) r e l a t i v e to t h e I T P tax - in a n t i c i p a t i o n o f t h e l a r g e r f u t u r e t a x e s t h a t m u s t be p a i d u n d e r t h e f o r m e r tax r e g i m e . In a d d i t i o n , since a is i d e n t i c a l in b o t h cases, the a m o u n t s i n v e s t e d in t h e risky a n d safe assets also i n c r e a s e e q u i p r o p o r t i o n a t e l y u n d e r t h e I C F tax. m T h e critical issue is t h u s t h e v a l i d i t y o f (4) in t h e p r e s e n c e of u n c e r t a i n t y . U n d e r t h e I T P m e t h o d , t h e p r e s e n t v a l u e o f r e v e n u e s (which a r e c o l l e c t e d e n t i r e l y in t h e first p e r i o d ) , is s i m p l y R w = t w Y . U n d e r t h e I C F tax, t h e e x p e c t e d p r e s e n t v a l u e o f r e v e n u e s is R c = tc[C 1 + E ( C 2 ) / ( 1 + p)], w h e r e p is t h e g o v e r n m e n t ' s d i s c o u n t rate. S u b s t i t u t i n g for C2 (as in (1)) a n d simplifying yields R c = [tc/(1 + tc)]OY+ tcC,(1-
0),
w h e r e 0 = E[1 + r + a ( x - r ) ] / ( 1 + p). T h u s ,
(6) (4) o b t a i n s u n d e r t h e e q u a 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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e x p e c t e d r e v e n u e constraint R w = R c if the g o v e r n m e n t discount rate equals the e x p e c t e d return to saving, or p = r + E [ a ( x - r)]. This r a t h e r plausible condition can be interpreted in several ways. O n e i n t e r p r e t a t i o n is that the deduction for saving u n d e r the I C F tax effectively m a k e s the g o v e r n m e n t a silent p a r t n e r in risky investments, sharing in b o t h gains and losses. 11 A c c o r d i n g l y , the g o v e r n m e n t should in this case a c c o u n t for the uncertainty of future revenues by discounting t h e m at the e x p e c t e d rate o f r e t u r n in the e c o n o m y (rather than the riskless rate); 12 such an a p p r o a c h is consistent with several recent analyses, including M a y s h a r (1977), Mintz (1981), B u l o w and S u m m e r s (1984), G o r d o n (1985) and H a m i l t o n (1987), w h o argue that the g o v e r n m e n t c a n n o t a b s o r b risk costlessly. 13 F o r example, G o r d o n (1985, pp. 5 - 6 ) concludes that "risk in g o v e r n m e n t tax revenues is as costly to bear as privately t r a d e d risks" since g o v e r n m e n t s bear the risks of " r a n d o m tax rates on o t h e r i n c o m e , r a n d o m g o v e r n m e n t expenditures, or r a n d o m g o v e r n m e n t deficits". A n alternative i n t e r p r e t a t i o n is that the r e v e n u e s which are o b t a i n e d earlier u n d e r the I T P a p p r o a c h than u n d e r the I C F tax can be invested by the g o v e r n m e n t to yield a r e t u r n equal to the expected private rate of return in the e c o n o m y . Such a view is also a plausible one, and is generally consistent with s o m e recent results on relative returns to public and private investment. 14 T h u s , w h e n the g o v e r n m e n t accounts for the costs of uncertain future r e v e n u e s by discounting t h e m at the expected rate of return, full equivalence b e t w e e n the I T P and I C F a p p r o a c h e s is established. T h a t is, c o n s u m p tion in b o t h periods and the expected present value of g o v e r n m e n t r e v e n u e s are identical u n d e r b o t h c o n s u m p t i o n tax regimes. 15
2.2. Equivalence o f the I C F approach and the M W T In contrast, A h s a n concludes that equivalence obtains b e t w e e n the I C F tax and the M W T . His analysis follows earlier analyses of taxation and risk-taking, including D o m a r and M u s g r a v e (1944), Mossin (1968), Stiglitz
1~This point is well known in the consumption tax literature; for example, see Zodrow and McLure (1991). ~2Similarly, 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 A r r o w and Lind (1970), in assuming the government can absorb risk costlessly. 16 In this case, the appropriate 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 I T P tax than u n d e r the I C F 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 p a p e r as follows. Consider the model detailed above for the case in which a R is the absolute a m o u n t 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 M W T . In this case, the first-order conditions for a R and C~ are E { U 2. [ ( 1 - tw)/(1 + / c ) ] ( x -
r)} = 0 ,
E{U, - U 2. ( 1 + r)} = 0.
(2') (3')
If (4) is satisfied, then (2') and (3') imply that the optimal a R and C i are identical under the I C F and M W T taxes. In addition, since saving under the I C F 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 M W T , saving goes up proportionately (by a factor of (1 + tc) ) under the I C F approach; however, since a R is constant, all of the increase in saving goes into the safe asset. T o determine the validity of (4), note that expected revenues under the MWT-under the assumption that the government discounts future revenues at the riskless return r - a r e R M = tw{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 I C F approach is equivalent to the M W T . 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 I C F and I T P approaches in the previous s u b s e c t i o n - an increase in investment in the risky asset u n d e r the I C F 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 I C F tax goes into the safe asset.
3. Conclusion
In s u m m a r y , this p a p e r identifies conditions under which the well-known equivalence between the I C F 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 streams by discounting future revenues at the expected rate of return. By comparison, if the g o v e r n m e n t 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 I C F approach, and the government must alter the structure of the I T P 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 'modified wage tax'. H o w e v e r , 'equivalence' might also be established in alternative ways; in particular, rates under the ITP tax could simply be raised to reflect the absence of costless government risk-sharing, relative to the I C F tax; such an approach would have the clear administrative advantage of avoiding attempts to characterize returns as ' n o r m a l ' and 'extraordinary'. In any case, the nature of the equivalence results presented a b o v e 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. T h e results of the p a p e r also highlight an important feature of cash flow taxes. Such taxes are often asserted to generate positive revenues by taxing economic rents or a b o v e - n o r m a l returns to risky investment. 17 H o w e v e r , this is true only in the limited sense that such revenues reflect economic rents or a b o v e - n o r m a l returns on the g o v e r n m e n t ' s share of the investment (which arises due to deductions for expensing rather than for economic depreciation u n d e r a cash flow tax). Indeed, the above analysis demonstrates that g o v e r n m e n t revenues are zero in present value terms for a b o v e - n o r m a l returns to risky investment if the government discounts uncertain future 17For a recent example, see Musgrave (1992, p. 180).
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r e v e n u e s at the e x p e c t e d rate of r e t u r n . T h u s , a cash flow tax does n o t affect p r i v a t e rates of r e t u r n a n d thus does n o t r e d u c e the rate at which private i n v e s t o r s e a r n e c o n o m i c r e n t s or a b o v e - n o r m a l r e t u r n s ; only the private s h a r e of the i n v e s t m e n t is r e d u c e d . 18 F i n a l l y , two a d d i t i o n a l qualifications to the e q u i v a l e n c e b e t w e e n the I C F a n d I T P taxes should b e n o t e d . First, e q u i v a l e n c e does n o t o b t a i n u n d e r a p r o g r e s s i v e tax system, since tax rates will differ across p e r i o d s u n d e r the I C F tax. S e c o n d , a l t h o u g h the a s s u m p t i o n that rates of r e t u r n are ind e p e n d e n t of the level of private i n v e s t m e n t is o f t e n plausible, it m a y be i n a p p r o p r i a t e in the case of u n i q u e i n v e s t m e n t o p p o r t u n i t i e s (e.g. e n t r e p r e n e u r i a l i n n o v a t i o n ) .19 I n v e s t i g a t i o n of the i m p o r t a n c e of these p o i n t s is left to f u t u r e research.
Acknowledgments I h a v e b e n e f i t e d greatly from the c o m m e n t s of two a n o n y m o u s referees a n d f r o m discussions with C h a r l e s M c L u r e a n d P e t e r Mieszkowki. A n y r e m a i n i n g errors are m y own.
References Aaron, H.J. and H. Galper, 1985, Assessing tax reform (Brookings Institution, Washington, OC). Ahsan, S.M., 1989, Choice of tax base under uncertainty: Consumption or income, Journal of Public Economics 40, 99-134. Ahsan, S.M., 1990, Risk-taking, savings, and taxation: A re-examination of theory and policy, Canadian Journal of Economics 23, 408-433. Arrow, K. and R. Lind, 1970, Uncertainty and the evaluation of public investment decisions, American Economic Review 60, 364-378. Aschauer, D.A., 1989, Is public expenditure productive?, Journal of Monetary Economics 23, 177-200. Atkinson, A.B. and J.E. Stiglitz, 1980, Lectures on public economics (McGraw-Hill, New York). Bradford, D.F., 1986, Untangling the income tax (Harvard University Press, Cambridge, MA). Bulow, J.l. and L.H. Summers, 1984, The taxation of risky assets, Journal of Political Economy 92, 20-39.
18For further discussion of this point, see Zodrow and McLure (1991). ~9Note, however, that such issues are avoided under an ITP tax to the extent that many investment activities, including those of entrepreneurs, are subject to a business level cash flow tax that complements ITP treatment at the individual level. See Hall and Rabushka (1985), Bradford (1986) and McLure et al. (1990).
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Domar, E.D. and R.A. Musgrave, 1944, Proportional income taxation and risk taking, Quarterly Journal of Economics 58, 382-422. Gordon, R.H., 1985, Taxation of corporate capital income: Tax revenues versus tax distortions, Quarterly Journal of Economics 100, 1-27. Graetz, M.J., 1979, Implementing a progressive consumption tax, Harvard Law Review 92, 1575-1661. Hall, R.E. and A. Rabushka, 1985, The fiat tax (Hoover Institution Press, Stanford). Hamilton, J.H., 1987, Taxation, savings, and portfolio choice in a continuous time model, Public Finance 42, 264-282. Mayshar, J., 1977, Should the government subsidize risky projects?, American Economic Review 67, 20-28. McLure, C.E., Jr. and G.R. Zodrow, 1990, Administrative advantages of the individual tax prepayment approach to the direct taxation of consumption, in: M. Rose, ed., Heidelberg Congress on taxing consumption (Springer-Verlag, Berlin). McLure, C.E., Jr., J. Mutti, V. Thuronyi and G.R. Zodrow, 1990, The taxation of income from business and capital in Colombia (Duke Univ. Press, Chapel Hill). Mintz, J.M., 1981, Some additional results on investment, risk taking, and full loss offset corporate taxation with interest deductibility, Quarterly Journal of Economics 96, 631-642. Mossin, J., 1968, Taxation and risk taking: An expected utility approach, Economica 35, 74-82. MunneU, A.H., 1990, ed., Is there a shortfall in public capital investment? (Federal Reserve Bank of Boston, Boston). Musgrave, P.B., 1992, Substituting consumption-based direct taxation for income taxes as the international norm: A comment, National Tax Journal 45, 179-184. Pechman, J.A., 1980, What should be taxed: Income or expenditure? (Brookings Institution, Washington, DC). Rose, M., 1990, ed., Heidelberg Congress on taxing consumption (Springer-Verlag, Berlin). Stiglitz, J.E., 1969, Effects of wealth, income, and capital gains taxation on risk taking, Quarterly Journal of Economics 83, 263-83. Summers, L.H., 1987, Investment incentives and the discounting of depreciation allowances, in: M. Feldstein, ed., The effects of taxation on capital accumulation (Univ. of Chicago Press, Chicago). U.S. Department of Treasury, 1977, Blueprints for basic tax reform (Government Printing Office, Washington, DC). Revised second edition issued as D.F. Bradford and the U.S. Treasury Tax Policy Staff, 1984 (Tax Analysts, Arlington, VA). Zodrow, G.R. and C.E. McLure, Jr., 1991, Implementing direct consumption taxes in developing countries, Tax Law Review 46, 405-487.
ELSEVIER
PUBLIC ECONOMICS
Taxation, uncertainty and the choice of a consumption tax base George
R. Zodrow
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 q u e s t i o n o f w h e t h e r i n c o m e o r c o n s u m p t i o n is t h e p r e f e r a b l e b a s e for d i r e c 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 existence of two alternative methods of implementing a consumption 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
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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, including 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 consumptionbased 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 t e r m e d 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, " T h e major d i s a d v a n t a g e . . , is t h a t . . , lucky investors might b e c o m e 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). O t h e r analysts, including Aaron and Galper (1985), Bradford (1986), and Z o d r o w and McLure (1991), conclude that this distinction is overstated. T h e y 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 T r e a s u r y / G r a e t z 2 For a discussion of these points and (1991). 3 Similarly, 'unlucky' investors will be 4 Note that Bradford et al. (1984, pp. edition of Blueprints (U.S. D e p a r t m e n t
some illustrative examples, see Zodrow and McLure able to deduct losses only under the ICF approach. 115-116) accept this line of reasoning in the revised of Treasury, 1977).
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position. Specifically, he concludes that the I T P a p p r o a c h is equivalent to the I C F tax only if e x t r a o r d i n a r y capital gains - those in excess of a safe or riskless rate of r e t u r n - are included in the tax base u n d e r the I T P a p p r o a c h ; he calls this the 'modified wage tax' ( M W T ) approach. 5 This result is of course entirely consistent with the rationale underlying the T r e a s u r y / G r a e t z a r g u m e n t , as it requires 'lucky' investors to pay an extra tax on extrao r d i n a r y gains u n d e r the modified version of the I T P tax. This result is t r o u b l e s o m e for advocates of the I T P a p p r o a c h , since its simplicity advantages relative to the I C F tax - due largely to the absence of capital i n c o m e in the b a s e - would e v a p o r a t e u n d e r the M W T . 6 I n d e e d , the n e e d to identify and tax only the ' e x t r a o r d i n a r y ' c o m p o n e n t of investment returns u n d e r the M W T would likely r e n d e r it m o r e complicated than the I C F tax. Since s o m e observers argue that the latter a p p r o a c h is t o o c o m p l i c a t e d to be practical, this suggests that considerations of tax simplicity m a y p r e c l u d e a direct c o n s u m p t i o n tax. H o w e v e r , in this p a p e r I argue that such a conclusion is p r e m a t u r e , and is a r g u a b l y a misleading guide to tax policy. I construct an alternative (more g e n e r a l ) m o d e l u n d e r which full equivalence b e t w e e n the I C F and I T P taxes obtains even in the presence of uncertainty. T h e key assumption of this m o d e l is that an uncertain r e v e n u e stream is costly to the g o v e r n m e n t , so that it discounts future r e v e n u e s at the expected rate of return in the e c o n o m y r a t h e r than at the riskless rate; I also show, within the context o f the s a m e m o d e l , that A h s a n ' s result obtains only w h e n the g o v e r n m e n t is a s s u m e d to be able to absorb such risk costlessly.
2. Equivalence results 2.1. E q u i v a l e n c e o f the I C F a n d I T P taxes with uncertainty
T h e m o d e l used in this p a p e r is a generalized version of the A h s a n model. Individuals are e x p e c t e d utility maximizers, and utility is a strictly c o n c a v e f u n c t i o n o f c o n s u m p t i o n in two periods, C 1 and C2 .7 T h e r e are two a s s e t s - a safe asset with a certain return r, and a risky asset with an uncertain return x. 8 T h e fraction 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 , with f i r s t - p e r i o d i n c o m e Y a n d no s e c o n d - p e r i o d i n c o m e . C o n s u m p t i o n is t a x e d at r a t e t c u n d e r t h e I C F a p p r o a c h , a n d w a g e s a r e t a x e d at r a t e t w u n d e r t h e I T P a p p r o a c h ; t h e I C F tax has full loss offset. I n d i v i d u a l s t h u s c h o o s e a a n d C l to m a x i m i z e E ( U { C 1, [ ( 1 - t w ) Y / ( 1 + t c ) -
C1][1 + r + a ( x -
r)]}),
(1)
w h e r e t h e i n d i v i d u a l b u d g e t c o n s t r a i n t i m p l i e s the s e c o n d a r g u m e n t is C 2, a n d t c = 0 u n d e r t h e I T P a p p r o a c h while t w = 0 u n d e r t h e I C F a p p r o a c h . T h e f i r s t - o r d e r c o n d i t i o n s for a a n d C 1 a r e 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)
I n t h e a b s e n c e o f u n c e r t a i n t y , c o n s t a n t g o v e r n m e n t r e v e n u e s (in p r e s e n t values) require 9
(1-tw)=l/(l+tc)
::~ t w = t c / ( l + t c ) .
(4)
S u p p o s e (4) also h o l d s with u n c e r t a i n t y . If so, (2) a n d (3) a r e i d e n t i c a l under the ICF and ITP regimes, implying identical optimal values of a and C 1. M o r e o v e r , since saving u n d e r t h e I T P tax is S w = ( 1 - t w ) Y - C I a n d s a v i n g u n d e r t h e I C F tax is S c = Y - (1 + tc)C~, it is c l e a r t h a t S c = (1 + t c ) S w
(5)
w h e n (4) is satisfied; t h a t is, as s u g g e s t e d a b o v e , saving i n c r e a s e s u n d e r t h e I C F t a x - b y a f a c t o r o f (1 + t c ) r e l a t i v e to t h e I T P tax - in a n t i c i p a t i o n o f t h e l a r g e r f u t u r e t a x e s t h a t m u s t be p a i d u n d e r t h e f o r m e r tax r e g i m e . In a d d i t i o n , since a is i d e n t i c a l in b o t h cases, the a m o u n t s i n v e s t e d in t h e risky a n d safe assets also i n c r e a s e e q u i p r o p o r t i o n a t e l y u n d e r t h e I C F tax. m T h e critical issue is t h u s t h e v a l i d i t y o f (4) in t h e p r e s e n c e of u n c e r t a i n t y . U n d e r t h e I T P m e t h o d , t h e p r e s e n t v a l u e o f r e v e n u e s (which a r e c o l l e c t e d e n t i r e l y in t h e first p e r i o d ) , is s i m p l y R w = t w Y . U n d e r t h e I C F tax, t h e e x p e c t e d p r e s e n t v a l u e o f r e v e n u e s is R c = tc[C 1 + E ( C 2 ) / ( 1 + p)], w h e r e p is t h e g o v e r n m e n t ' s d i s c o u n t rate. S u b s t i t u t i n g for C2 (as in (1)) a n d simplifying yields R c = [tc/(1 + tc)]OY+ tcC,(1-
0),
w h e r e 0 = E[1 + r + a ( x - r ) ] / ( 1 + p). T h u s ,
(6) (4) o b t a i n s u n d e r t h e e q u a 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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e x p e c t e d r e v e n u e constraint R w = R c if the g o v e r n m e n t discount rate equals the e x p e c t e d return to saving, or p = r + E [ a ( x - r)]. This r a t h e r plausible condition can be interpreted in several ways. O n e i n t e r p r e t a t i o n is that the deduction for saving u n d e r the I C F tax effectively m a k e s the g o v e r n m e n t a silent p a r t n e r in risky investments, sharing in b o t h gains and losses. 11 A c c o r d i n g l y , the g o v e r n m e n t should in this case a c c o u n t for the uncertainty of future revenues by discounting t h e m at the e x p e c t e d rate o f r e t u r n in the e c o n o m y (rather than the riskless rate); 12 such an a p p r o a c h is consistent with several recent analyses, including M a y s h a r (1977), Mintz (1981), B u l o w and S u m m e r s (1984), G o r d o n (1985) and H a m i l t o n (1987), w h o argue that the g o v e r n m e n t c a n n o t a b s o r b risk costlessly. 13 F o r example, G o r d o n (1985, pp. 5 - 6 ) concludes that "risk in g o v e r n m e n t tax revenues is as costly to bear as privately t r a d e d risks" since g o v e r n m e n t s bear the risks of " r a n d o m tax rates on o t h e r i n c o m e , r a n d o m g o v e r n m e n t expenditures, or r a n d o m g o v e r n m e n t deficits". A n alternative i n t e r p r e t a t i o n is that the r e v e n u e s which are o b t a i n e d earlier u n d e r the I T P a p p r o a c h than u n d e r the I C F tax can be invested by the g o v e r n m e n t to yield a r e t u r n equal to the expected private rate of return in the e c o n o m y . Such a view is also a plausible one, and is generally consistent with s o m e recent results on relative returns to public and private investment. 14 T h u s , w h e n the g o v e r n m e n t accounts for the costs of uncertain future r e v e n u e s by discounting t h e m at the expected rate of return, full equivalence b e t w e e n the I T P and I C F a p p r o a c h e s is established. T h a t is, c o n s u m p tion in b o t h periods and the expected present value of g o v e r n m e n t r e v e n u e s are identical u n d e r b o t h c o n s u m p t i o n tax regimes. 15
2.2. Equivalence o f the I C F approach and the M W T In contrast, A h s a n concludes that equivalence obtains b e t w e e n the I C F tax and the M W T . His analysis follows earlier analyses of taxation and risk-taking, including D o m a r and M u s g r a v e (1944), Mossin (1968), Stiglitz
1~This point is well known in the consumption tax literature; for example, see Zodrow and McLure (1991). ~2Similarly, 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 A r r o w and Lind (1970), in assuming the government can absorb risk costlessly. 16 In this case, the appropriate 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 I T P tax than u n d e r the I C F 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 p a p e r as follows. Consider the model detailed above for the case in which a R is the absolute a m o u n t 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 M W T . In this case, the first-order conditions for a R and C~ are E { U 2. [ ( 1 - tw)/(1 + / c ) ] ( x -
r)} = 0 ,
E{U, - U 2. ( 1 + r)} = 0.
(2') (3')
If (4) is satisfied, then (2') and (3') imply that the optimal a R and C i are identical under the I C F and M W T taxes. In addition, since saving under the I C F 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 M W T , saving goes up proportionately (by a factor of (1 + tc) ) under the I C F approach; however, since a R is constant, all of the increase in saving goes into the safe asset. T o determine the validity of (4), note that expected revenues under the MWT-under the assumption that the government discounts future revenues at the riskless return r - a r e R M = tw{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 I C F approach is equivalent to the M W T . 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 I C F and I T P approaches in the previous s u b s e c t i o n - an increase in investment in the risky asset u n d e r the I C F 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 I C F tax goes into the safe asset.
3. Conclusion
In s u m m a r y , this p a p e r identifies conditions under which the well-known equivalence between the I C F 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 streams by discounting future revenues at the expected rate of return. By comparison, if the g o v e r n m e n t 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 I C F approach, and the government must alter the structure of the I T P 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 'modified wage tax'. H o w e v e r , 'equivalence' might also be established in alternative ways; in particular, rates under the ITP tax could simply be raised to reflect the absence of costless government risk-sharing, relative to the I C F tax; such an approach would have the clear administrative advantage of avoiding attempts to characterize returns as ' n o r m a l ' and 'extraordinary'. In any case, the nature of the equivalence results presented a b o v e 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. T h e results of the p a p e r also highlight an important feature of cash flow taxes. Such taxes are often asserted to generate positive revenues by taxing economic rents or a b o v e - n o r m a l returns to risky investment. 17 H o w e v e r , this is true only in the limited sense that such revenues reflect economic rents or a b o v e - n o r m a l returns on the g o v e r n m e n t ' s share of the investment (which arises due to deductions for expensing rather than for economic depreciation u n d e r a cash flow tax). Indeed, the above analysis demonstrates that g o v e r n m e n t revenues are zero in present value terms for a b o v e - n o r m a l returns to risky investment if the government discounts uncertain future 17For a recent example, see Musgrave (1992, p. 180).
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r e v e n u e s at the e x p e c t e d rate of r e t u r n . T h u s , a cash flow tax does n o t affect p r i v a t e rates of r e t u r n a n d thus does n o t r e d u c e the rate at which private i n v e s t o r s e a r n e c o n o m i c r e n t s or a b o v e - n o r m a l r e t u r n s ; only the private s h a r e of the i n v e s t m e n t is r e d u c e d . 18 F i n a l l y , two a d d i t i o n a l qualifications to the e q u i v a l e n c e b e t w e e n the I C F a n d I T P taxes should b e n o t e d . First, e q u i v a l e n c e does n o t o b t a i n u n d e r a p r o g r e s s i v e tax system, since tax rates will differ across p e r i o d s u n d e r the I C F tax. S e c o n d , a l t h o u g h the a s s u m p t i o n that rates of r e t u r n are ind e p e n d e n t of the level of private i n v e s t m e n t is o f t e n plausible, it m a y be i n a p p r o p r i a t e in the case of u n i q u e i n v e s t m e n t o p p o r t u n i t i e s (e.g. e n t r e p r e n e u r i a l i n n o v a t i o n ) .19 I n v e s t i g a t i o n of the i m p o r t a n c e of these p o i n t s is left to f u t u r e research.
Acknowledgments I h a v e b e n e f i t e d greatly from the c o m m e n t s of two a n o n y m o u s referees a n d f r o m discussions with C h a r l e s M c L u r e a n d P e t e r Mieszkowki. A n y r e m a i n i n g errors are m y own.
References Aaron, H.J. and H. Galper, 1985, Assessing tax reform (Brookings Institution, Washington, OC). Ahsan, S.M., 1989, Choice of tax base under uncertainty: Consumption or income, Journal of Public Economics 40, 99-134. Ahsan, S.M., 1990, Risk-taking, savings, and taxation: A re-examination of theory and policy, Canadian Journal of Economics 23, 408-433. Arrow, K. and R. Lind, 1970, Uncertainty and the evaluation of public investment decisions, American Economic Review 60, 364-378. Aschauer, D.A., 1989, Is public expenditure productive?, Journal of Monetary Economics 23, 177-200. Atkinson, A.B. and J.E. Stiglitz, 1980, Lectures on public economics (McGraw-Hill, New York). Bradford, D.F., 1986, Untangling the income tax (Harvard University Press, Cambridge, MA). Bulow, J.l. and L.H. Summers, 1984, The taxation of risky assets, Journal of Political Economy 92, 20-39.
18For further discussion of this point, see Zodrow and McLure (1991). ~9Note, however, that such issues are avoided under an ITP tax to the extent that many investment activities, including those of entrepreneurs, are subject to a business level cash flow tax that complements ITP treatment at the individual level. See Hall and Rabushka (1985), Bradford (1986) and McLure et al. (1990).
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