THE GENERAL THEORY OF TAX AVOIDANCE^

THE GENERAL THEORY OF TAX AVOIDANCE^JOSEPH E. STIGLITZ*

IT used to be said that there were twothings that were unavoidable: death and

taxes. There is a widespread feeling todaythat under our present tax code only oneof these is unavoidable. What I wish todiscuss today is why this is so, and howthe extent of tax avoidance would be af-fected by some of the major tax reformspresently being discussed.

To do this, I shall first explain a gen-eral set of principles for tax avoidance,^(Section I) and then present four methodsof implementing these principles (SectionII). In Section III, I discuss what deter-mines the limits on the extent to whichindividuals can take advantage of taxavoidance schemes.

Many transactions, while they seem toreduce the tax liabilities to some partiesto the transaction, increase those of oth-ers. Because "prices" (the terms of thetransaction) adjust to reflect these changedtax liabilities, it is often difficult to as-certain who really benefits from many taxavoidance schemes. Moreover, the aggre-gate loss to the Treasury may be muchless than the seeming gain to the allegedbeneficiaries (when those calculations failto take account of the general equilib-rium effects of tax avoidance schemes).Thus, we follow our partial equilibriumanalysis of tax avoidance (Sections I-III)with an analysis of some of the more im-portant general equilibrium effects (Sec-tion IV). Some implications of our anal-ysis for tax reform are provided in SectionV.

I. Principles of Tax Avoidance

Tax laws constantly change the oppor-tunities for tax avoidance, but under-neath, there remain three basic princi-ples of tax avoidance within an incometax:^

(1) Postponement of taxes. The presentdiscounted value of a postponed tax is

'Princeton University.

much less than that of a tax currentlypaid.''

(2) Tax arbitrage across individualsfacing different tax brackets (or the sameindividual facing different marginal taxrates at different times). This is a partic-ularly effective method of reducing tax li-abilities within a family; but differentialtax rates may also induce transactionsamong individuals in different bracketswhich substantially reduce the aggregatetax liability; the availability of such op-portunities leads to what may be referredto as "tax induced transactions."

(3) Tax arbitrage across income streamsfacing different tax treatment. Under thecurrent law, long term capital gains aretaxed at lower rates than are other formsof income from capital. This provides aninducement to "convert" the returns tocapital (or to labor) into long-term capitalgains. Similarly, special treatment is af-forded to the return to capital in the formof housing, pensions, IRAs, etc.

Many tax avoidance devices involve acombination of these three. IRA accountscan be thought of as postponing tax lia-bilities until retirement; in effect, the in-terest earned on the IRA account is taxexempt.^ On the other hand, if the indi-vidual faces a lower tax rate at retire-ment than at the time he earns his in-come, then the IRA can be viewed as taxarbitrage between different rates.* Fi-nally, if the individual can borrow to de-posit funds in the IRA, and interest is taxdeductible, then the IRA is a tax arbi-trage between two forms of capital, one ofwhich is not taxed, and the other of whichis (tax deductible).'

Investing in assets yielding capital gainsinvolves a tax postponement, since taxesare paid only upon realization. Borrowingto invest in assets yielding capital gainsinvolves a tax arbitrage: the interest isdeductible at ordinary rates, the gain istaxed at favorable capital gains rates.

The tax savings from accelerated de-preciation with recapture result frompostponement. Without recapture, there

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326 NATIONAL TAX JOURNAL [Vol, XXXVIII

is the additional gain from the favorahletreatment of capital gains.

If depreciation allowances corre-sponded to true economic depreciation, andcapital gains were taxed on an accrualbasis at full rates, then there would be notax advantages (or tax induced distor-tions) from full expensing of maintenanceexpenses. If capital gains are taxed onlyupon realization, then full expensing ofmaintenance expenses (defined as thoseexpenditures required to maintain thevalue of the property) with depreciationwhich is rule based (i,e, not directly re-lated to the change in the value of theproperty) has a tax advantage: while theexpenses are currently deductible, the in-crease in the value (over what it other-wise would be) is only taxable upon re-alization; there is a gain frompostponement; if that gain is taxed at fa-vorable rates, there is a further gain fromarbitraging across rates.

Children's trusts involve tax arbitrageacross units facing different marginal taxrates,* The trusts are often set up so thattheir tax year does not coincide with thatof the child's; this enables a postpone-ment of the tax liability by almost a year.

The tax advantages that deep dis-counted bonds previously had arose morefrom the tax arbitrage across individualsfacing different rates and from the tax ar-bitrage from the differences in the treat-ment of capital gains and interest incomethan from the pure postponement effect.

Tax reduction schemes which take ad-vantage of the differences between ac-crual and cash accounting are, in effect,taking advantage of the gains from taxpostponement.

Note that the availability of these dif-ferent tax reduction-tax avoidance oppor-tunities depends on different aspects of thetax system: tax arbitrage across individ-uals depends on the progressivity of thetax system, or more accurately, on the factthat marginal tax rates increase with in-come.^ Many of the intra-family taxavoidance schemes entail capital trans-fers; if capital were not taxed, it would bemuch more difficult to engage in these taxavoidance schemes.

The possibility of postponement is aconcomitant of a tax on a cash basis,'" The

effect of postponement is often to elimi-nate (part of) the tax on interest income.Thus, in a flat rate consumption tax, tim-ing is not of importance.^'

The possibilities of tax arbitrage acrossdifferent levels of income arise out of theattempts to use the tax system to encour-age particular kinds of activities (riskyventures, via capital gains; savings forretirement, via pensions and IRAs),

II. Some Basic Methods of TaxAvoidance

So potent are the opportunities for taxavoidance within our current tax struc-ture that, under the hypothesis that cap-ital markets are perfect (zero transac-tions costs, no restrictions on borrowingor short sales, for every security there isa linear combination of other securitieswhich yields an identical return), individ-uals could risklessly eliminate all taxeson capital, and indeed, with a little ad-ditional effort, they may be able to elim-inate their tax liabilities altogether. Thereis not just one way, but a multiplicity ofways by which taxes can be avoided. Letme briefly describe four modifications ofwhat are, in fact, familiar tax avoidanceschemes. The modifications/\arise be-cause, under my assumptions of a perfectcapital market, I need not concern myselfabout transactions costs; I assume thatindividuals can borrow against collater-alizable assets; if the probability of de-fault is zero, they pay the safe interestrate; if not, they will have to pay a higherinterest rate, but the interest rate will de-pend simply on the collateral available tocover the debt in the event of a default.We also assume that all securities can besold short, and that there are no trans-actions costs involved in doing so.'^

Consider first how an individual wouldhave allocated his portfolio over his life inthe absence of taxes, (For our purposes, itmakes no difference whether the individ-ual has chosen his portfolio to maximizehis lifetime expected utility or not,) Weconstruct tax avoidance strategies whichleave the individual's consumption andbequests in each state of nature and ateach date unchanged (and correspond-ingly, raise no revenue); the individual

No. 3] JOSEPH E, STIGLITZ 327

faces no more (or less) risk than he facedin the original situation. The tax has noreal effects on the economy. For simplic-ity, we assume a given marginal tax rate;thus none of the procedures we describeare based on taking advantage of the op-portunities for tax avoidance afforded bydifferent individuals facing different taxrates.

Method 1, Postponement of capitalgains. The first method is a modificationof the familiar technique of postponing therealization of capital gains, which givesrise to the locked-in effect. It is based ontwo aspects of the tax code: capital gainsare taxed only upon realization, and thereis a step up in basis at death. The usualdiscussions err, however, in not taking intoaccount the fact that the riskiness of anindividual's portfolio (and his consump-tion stream) will change if an individualholds on to an asset longer than he oth-erwise would simply to avoid taxes. Toavoid taxes and any change in the pat-tern of risk bearing or consumption, theindividual sells short a perfectly corre-lated security (or a set of securities, thereturns to which are perfectly correlatedwith his original securities), at preciselythe same moment that he would have, inthe absence of taxation, sold the given se-curity. The individual's (net) portfolio po-sitions and income flows are then iden-tical to what they would have otherwisebeen; but because no capital gain has beenrealized, no capital gain tax liability hasbeen incurred. It is thus apparent how anindividual can risklessly avoid payingcapital gains taxes.

But he can do still better for himself.Assume that at any date, the individualbuys a security and sells a perfectly cor-related (set of) security (securities) short.Again, the individual's net portfolio po-sition is unchanged. At the end of the year,one asset will have increased in value, theother decreased; the individual sells thelatter, using the loss to offset other in-come. At the same time, the individualfinds some other security (or linear com-bination of securities) which is perfectly(positively or negatively) correlated, andtakes an offsetting position in that secu-rity. Thus, again, the individual has beenable to avoid all risk (since throughout.

his net position in the set of perfectly cor-related securities remains zero). But nowhe has succeeded in obtaining losses, whichhe can use to offset against other in-

When the individual dies, his heirs closeout his positions; with the step up in ba-sis, no tax liabilities become due.

Two objections to this method that arecommonly raised are that it ignores theconsequences of limitations on loss offsetsand wash sales. These are importantquestions, to which I shall return later.

Method 2, Arbitraging between short-term and long-term capital gains rates.The previous method of tax avoidance tookadvantage of the fact that capital gainsare only taxed upon realization; it did nottake advantage of the lower rates whichare afforded capital gains. The secondmethod does. But while optimal portfoliostrategies in the previous method exhib-ited the "locked-in effect," with this methodthey do not.

Individuals again purchase and sellshort two perfectly correlated securities,so that the net position in the two assetstogether remains zero; no risk has beenincurred,^'' Just before the end of theminimum holding period required for el-igibility for long term treatment, the in-dividual will have made a capital gain onone, a capital loss on the other; he real-izes the capital loss, then the next mo-ment (when the security becomes eligiblefor long term treatment) he realizes thecapital gain. If the change in price is p(t-I- 1) - p(t), and long term capital gainsare taxed at 40 percent of full rates (T),then this tax arbitrage generates a taxsaving of

.6T[p(t + 1) - p(t)]

The major objection to this method is thatit ignores the special provisions by whichlong-term gains are used to offset short-term losses. This objection can be over-come, if there are methods by which or-dinary income (losses) can be convertedinto (short-term) capital gains.'^ There areseveral methods by which his can be done.For instance, in the options market, someof the capital gains that one attains maybe an implicit interest return; that is, one

328 NATIONAL TAX JOURNAL [Vol. XXXVIII

can (in principle, in the absence of trans-actions costs) engage in a set of transac-tions which involves borrowing and buy-ing options, which is perfectly riskless, butwhich generates an interest deduction anda short-term capital gain. One can do thisto the point that not only are all capitalgains offset, but all capital income, and alimited amount of wage income (the lim-itation of interest deductibility plus thelimitation on loss offsets).

Method 3, Indebtedness. The thirdmethod takes advantage of the differen-tial treatment afforded long-term capitalgains and interest. From an economic pointof view, interest and capital gains aresimply two alternative forms of return oncapital; there would be no reason to dif-ferentiate among them, (Indeed, what ap-pears to be a capital gain depends on thechoice of a numeraire; though moneyseems, for many purposes, a natural nu-meraire, it has increasingly been recog-nized that for purposes of taxation "con-sumption" provides a better numeraire;^®this is what has given rise to the strongsupport for indexing the tax system.) As-sume that there were no uncertainty aboutchanges in the price of gold. An exhaust-ible natural resource like gold should haveits price rise at the rate of interest. All ofthe returns, however, are realized in theform of capital gains. If an individualborrows to purchase gold, then his inter-est would be deductible against ordinaryincome, his capital gains taxed at favor-able rates. With a perfect capital market,there would be no reason that the bankwould not lend to the individual: he couldsimply put up the gold as collateral, andthere would thus be no risk to either party.

Actually, to take advantage of thismethod, long-term capital gains need noteven be taxed at lower rates: the individ-ual would gain simply from the postpone-ment effect. And if there is a step up ofbasis upon death, then the gains from thismethod are all the greater.

To implement this method, there neednot exist a perfectly safe asset; all that isrequired is that there exists an asset (ora linear combination of assets) which yielda strictly positive return in all states ofnature, and that one can issue an optionto divest oneself of all the risk associated

with returns in excess of the minimumreturn.

In some sense, this method can beviewed as a special case of Method1. borrowing is nothing more than sell-ing short a safe bond.

Method 4, Rollovers. This method takesadvantage of the arbitrariness of the unitof time over which taxes are levied. It doesnot, however, require that there be dif-ferential tax rates on long-term and short-term capital gains. As in Methods 1 and2, the individual purchases a security andsells short a perfectly correlated security(linear combination of securities), so thathe incurs no risk. But now, on December31, on one part of his position he will havea capital gain, on the other part a capitalloss. He realizes his loss; on January 1, herealizes his gain. The next year, of course,he must engage in similar transactions toa greater extent, not only to wipe out otherforms of capital income, but also to elim-inate the January 1 capital gain. Thoughthe 1981 Act eliminated some of the easyopportunities for these tax arbitrage ac-tivities, it by no means closed all of them.

This list of tax avoidance procedures isnot meant to be exhaustive. The incen-tives for engaging in these activities aresufficiently great that even fairly largetransaction costs should not have de-terred them. For most of the methods, nocapital is required: the individual simplyengages in two offsetting actions. Whereloans are required, the banks should bewilling to provide them, since there arealways offsetting assets; indeed, as wehave emphasized, these activities arereally tax arbitrage activities: the indi-vidual needs to undertake no additionalrisk, so the terms at which banks shouldbe willing to lend to the individual shouldbe the same as they were willing to lendin the absence of taxation.

III. Limits to Tax Avoidance

I am not an empirical economist; butthere are certain conclusions that one canmake about the so called real world with-out a detailed econometric study. One suchconclusion is that individuals do pay taxes,and that indeed, many individuals seemto be paying taxes on their capital in-

No. 3] JOSEPH E. STIGLITZ 329

come. There are four possible conclusionsone can reach from this empirical obser-vation:

(a) I erred in proving my theorems: theconclusions do not follow from the as-sumptions.

(b) I erred in failing to take into ac-count certain detailed provisions of the taxcode.

(c) I erred in assuming a perfect capi-tal market.

(d) I erred in ascribing more astute-ness (understanding of the tax code andthe economy) to the taxpayer than he has.

In a talk like this, you will simply haveto take my word that the error does notlie in (a).'^

In my analysis of the tax code, I havekept to the standard textbook formula-tion. To criticize (b) then is to suggest thatthe effects of the tax system depend crit-ically on provisions which these treat-ments have ignored. Among the specialprovisions, for instance, are those whichrestrict wash sales, the limitations on thedeductibility of losses, and the limita-tions on the deductibility of interest.

If, however, capital markets were per-fect, then these provisions would not bevery restrictive. Consider, for instance, therestrictions on wash sales, the purpose ofwhich is to ensure that an individual doesnot sell and then buy back the security,the only purpose of the transaction beingto gain some tax advantage. In a perfectcapital market, however, no security isunique: there are many securities (or lin-ear combinations of securities) which yieldthe identical pattern of returns. Thus, tomaintain a riskless position, the individ-ual does not have to buy and sell the samesecurity. Since what is relevant is the in-dividual's subjective judgements concern-ing the patterns of returns, ascertainingwhether the individual has engaged in ariskless arbitrage is a virtual impossibil-ity; and the administrative burdens of at-tempting to do so, even if subjective prob-abilities could be ascertained from previousreturns, would provide a nightmare of thecourts, though possibly a boon to litiga-tion-minded econometricians.

Part of the problem undoubtedly lies inthe third assumption: that of a perfectcapital market.'* As an aside, I find it re-

markable how almost a whole sub-disci-pline has developed, analyzing the behav-ior of financial markets, attempting to testwith sophisticated econometric tech-niques whether capital markets workperfectly and whether individuals "ra-tionally" allocate their portfolios, whichat the same time ignores tax considera-tions. Ignoring taxes is not ignoringsomething which should be viewed asleading to a third order refinement of thetheory: with wealthy individuals in re-cent history facing nominal tax rates of50 percent, 70 percent, or more, the taxeffects are first order effects, and any testof any attribute of financial markets whichignores them needs, at best, to be treatedwith skepticism. Indeed, there is avail-able a simple test of the perfect capitalmodel: do individuals pay taxes, or paytaxes on their capital income?

Moreover, the fact that individuals donot even take full advantage of the lim-itations on interest deductibility providesfurther evidence that the perfect capitalmarket/astute investor model is inappro-priate.'^ Whether this is because of cap-ital market imperfections, or because oflack of astuteness on the part of taxpay-ers, is difficult to ascertain.^" Probablyboth play an important role. In either case,however, the consequences of tax changesmay be markedly different from those thatwould be predicted by the conventionaleconomist's model assuming perfect capi-tal markets and "rational" tax avoidingfirms and consumers.^' As an example,with imperfect capital markets, an in-crease in the corporate tax rate might havea deleterious effect on firms' investmentbecause of a reduction in the internalfunds available for investment; a perfectmarket marginal analysis might suggest(with true economic depreciation, and in-terest deductibility) no effect on invest-ments, since returns and costs of capitalare reduced proportionally. (See Stiglitz[1973, 1976].)

IV. Tax Avoidance and GeneralEquilibrium Analysis

One of the important lessons to emergefrom the analysis of taxes during the pastdecade is that one cannot analyze the ef-

330 NATIONAL TAX JOURNAL [Vol, XXXVIII

fects of a single tax in isolation from othertaxes; for instance, the effects of the cor-porate income tax depend on the struc-ture of the individual income tax (includ-ing its provisions for the taxation of capitalgains [Stiglitz, 1973]),

Similarly, the effects of a tax structurecannot be analyzed by looking at its ef-fects on a single individual This is par-ticularly true of the analysis of tax avoid-ance. Transactions which reduce oneindividual's tax liability may increase thetax liability of others. The terms of thetransaction will reflect this. Thus, look-ing at the first individual's tax savingsmay give a wrong impression both con-cerning the total cost to the governmentof the tax avoidance activity and the in-cidence of the benefits from tax avoid-ance.

This general principle has been recog-nized for a long time. If all individualsfaced the same marginal tax bracket, thenexempting state and local bond interestwould simply reduce the rate of return onthese bonds to the point where it equalledthe after-tax return of taxed bonds (ofequal risk). The individual would be nobetter off than he would have been if hehad not bought the tax exempt bonds. Thebenefits all accrue to the communities is-suing

How does this general equilibrium per-spective alter our analysis of the previoussection? Two questions need to be posed.

Consistency of tax avoidance activities.First, if all individuals attempted to pur-sue the policies indicated, would they beable to avoid taxes?

At first blush, the answer seems to beno: assume two individuals A and B werepursuing tax avoidance method #2, As-sume securities x and y are perfectly cor-related. Individual A buys a share of x andsells short a share of y; individual B buysa share of y and sells short a share of x.Their actions are offsetting: the net de-mand for shares in x and y are unaf-fected. At the end of six months assumethe price of x (and y) has in fact de-creased. Thus A sells x, and B sells y: theiractions are not offsetting. It appears as ifmarkets do not clear. But this ignores the

fact that both A and B will want to covertheir exposed position for the moment fromjust before six months to just after sixmonths: A will wish to buy y and B willwish to buy x; hence the net demand re-mains zero,

A similar analysis applies for the roll-over method. Now, on December 31, A sellsX and buys y, while B sells y and buys x.These methods work even if the "asset"purchased is a contract on the futuresmarket. In such markets, whenever oneindividual takes a position, another in-dividual takes the opposite position. Thus,if A sells B a contract for future deliveryof wheat at a fixed price, when the priceof wheat goes up, A is worse off, B is bet-ter off. Assume A sells B a contract forwheat, and B sells A a contract for a per-fectly correlated commodity, which weshall refer to as Commodity Z. The posi-tions are offsetting so neither individualis bearing any risk! Assume just before theend of six months the price of wheat hasrisen. A sells his contract for delivery ofwheat to C, realizing a short-term capitalloss; at the same time he buys from C acontract for delivery of commodity Z; sim-ilarly C buys from B a contract for the de-livery of Z, and sells a contract for the de-livery of wheat. At the end. A, B, and Cremain perfectly hedged. Then, just aftersix months has passed, all positions areclosed out: A realizes a long-term gain onhis commodity Z contract, B a long-termgain on his wheat contract, and C realizessmall, offsetting gains and losses.

Note that this tax arbitrage possibilitywas not eliminated by provisions for con-structive realization on December 31.These were aimed at our fourth methodof tax avoidance, recording losses in oneyear and gains the next.

Note that tax avoidance schemes basedon borrowing would not be effective in aneconomy in which all individuals faced thesame marginal tax rate: any tax savingsfrom an interest deduction by one indi-vidual would give rise to an offsetting taxliability by another.

Though the general equilibrium per-spective alters one's views concerning thetax savings which can be achieved by


purely financial arbitrage activities, atleast in a world in which all individualsface the same tax rate, the basic taxavoidance principles we described earliercan be used to reduce, and possibly elim-inate, taxes on the return to real capitalassets. Thus, the present discounted valueof tax liabilities are reduced as a resultof postponing the realization of gains andtaking losses as soon as possible^^ and theyare reduced by holding on to assets whichhave increased in value at least to the timeat which they are eligible for long-termtreatment.

The Relative Importance of DifferentTax Avoidatice Devices

We have thus shown that some of thetax avoidance strategies described earlierare effective, even in a world in which allindividuals faced the same tax rate, andeven when the tax counsequences for allindividuals were appropriately taken intoaccount. But the aggregate tax savingsassociated with various transactions maybe far different from what appear^* to bethe tax savings to one individual. As a re-sult, the relative importance of differenttax avoidance schemes may look quitedifferent from a general equilibrium^^perspective than from a partial equilib-rium perspective. In particular, many ofthe tax savings which appear as arisingfrom postponement are really tax savingswhich arise from arbitraging across rates.We have noted one example earlier: thereal tax savings (at least in a perfect cap-ital market) from IRA accounts arise notfrom the postponement of taxes, but fromarbitraging between the tax deductibilityof interest and the non-taxability of in-terest accruing in IRA accounts. ®

Installment purchases. As another ex-ample consider the tax consequences of adelay in the "official" transfer of the own-ership of an asset (for tax purposes). Itappears as if there has been a gain frompostponement. Assume the two individu-als involved in the transaction are in thesame tax bracket; A is selling the asset toB. Assume, moreover, that A wishes toreceive the cash today. If the sale was

completed today, A would incur a tax li-ability of, say, tg, where g was the capitalgain on the asset. Assume, instead, thatB lends him the money at a zero interestrate^^; A effectively turns over control ofthe asset, but the sale is not officiallycompleted until the next period. Then theonly implications for either party is thatthe present discounted value of the tax li-ability on the capital gains has been re-duced. Since capital gains taxes are paidonly upon realization, there is a generalequilibrium tax savings from postponingrealization.

But if A and B are in different taxbrackets, the tax savings may be farlarger: If the gain is "recognized" today,A has, after tax, (1 + g - gtA), where 1is his basis; and if he invests this, at theafter tax return of r'A, he will have (1 +g ~ gtA)(l + T'A). On the other hand, ifthe trade is not "consummated" until nextperiod, B will have (1 -H g) (1 + r's). As-sume B turns this over to A. A will thenhave, after tax,

(1 + g)(l + r'B)(l - tA) + tA,

a gain of

(r's - r'A)(l + g (1 - tA)) + tAr'e;

the first term represents the gain from taxarbitrage across individuals; the secondterms represents the gain from postpone-ment. As the limiting case, assume B hasa zero marginal tax bracket, and A is inthe 50 percent tax bracket, with capitalgains taxed at 20 percent. Then the taxsavings is .5r(l + .8g) + .2r; the tax sav-ings are largely due to arbitraging acrossindividuals.

Early recognition of gains. In the ex-ample we have just described, we haveshown how it inay pay to delay the "of-ficial" transfer by ownership (and thus therecognition of a capital gain). But this isnot always the case. With depreciable as-sets, there is a step up in basis upon thetransfer of ownership, and the tax advan-tages of this may well outweigh the dis-advantages of paying the capital gains tax.


Take, as an example, a machine whichwill last for one more year. It was ex-pected to produce an output of $1; at a 10percent discount rate, its current value isapproximately $.9. Assume now that the(net) output that it is expected to producedoubled; this would imply that its marketprice would double; the owner would havea $.9 capital gain. But note that we willtax the extra income as it accrues. To taxthe capital gain, representing the expec-tation of future income and to tax the ex-tra future income seems to be taxing thesame extra income twice, and this seemsunfair. But, if we have true economic de-preciation, there is not any real "double"taxation; the new owner will have higherdepreciation allowances reflecting thehigher capital value. With true economicdepreciation, full taxation of (accrued)capital gains would be required in thissituation to avoid distortions within anincome tax. With a flat rate tax, the dif-ference between doing this, and simplytaxing the income as it accrued is the taxon the (implicit) interest income. In ourexample there will be a capital gain of 1/1 + r = .9, in the absence of taxation; withtaxation, but true economic depreciation,the present discounted value of this in-crease is unchanged.^* Hence, the in-crease in tax liabilities is t /[l + r] thisperiod; next period net income is 1 - de-preciation = 1 - 1/[1 + r] = r/[ l + r]and the tax next period is thus tr /[ l + r].The present discounted value of tax pay-ments, using the discount rate, r*, is justt[(l/l 4- r) + (r/(l + r)(l -h r*)] = t[l +(r/1 + r*)]/l + r.

If there had been no tax on capital gain,but no concurrent increase in the depre-ciation allowance, the increase in tax li-ability (as a result of the increased pro-ductivity of the asset), next period is justt. Thus, the difference in the present dis-counted value of tax liabilities is just t /(1 + r) + [t/(l + r)][l - (1/(1 + r)] - t /(1 + r*) = tr /( l + r) ' -t- t(r* - r)/(l +r*)(l + r).

On the other hand, if the asset were sold,by individual A to individual B, with trueeconomic depreciation, the total presentdiscounted value of the difference in tax

liabilities (between what it would havebeen without the realization of the capi-tal gain and the corresponding step up inbasis and with it) is^^

tA/1 + r -f (te/l + ri)[l - (1/1 + r)]

- tA/1 + rS = [tA(r* - r)(l + rg) + tsr

rg).

Thus, with a flat rate tax, with r = r*,with full taxation of capital gains, andwith true economic depreciation, it wouldalways pay to postpone the realization ofthe gain. But if r*A = (1 - tA)r, then earlyrealization may be desirable. All of thischanges dramatically, however, whenthere is not true economic depreciation andwhen capital gains are taxed at favorablerates. Consider first the consequences oftaxing capital gains at favorable rates, say.4 of ordinary rates. Then the net changein aggregate tax liabilities from thetransfer is .4tA/l + r + (tg/l + r*B)[l -1/1 + r] - tA/1 + r*A = [-tAZ + r te/ l +r]/l + r*B, z = (1 -H rg)/(l -f rj) - .4(1+ rg)/(l + r) = .6 if rg = r j = r. Thus,for short lived assets (low r) or highly taxedindividuals (high tA), it pays to realize thecapital gain early.^"'^'

The tax consequences of recognizing acapital gain are somewhat different ifthere is accelerated depreciation. Con-sider a two period asset, whose return ateach date unexpectedly increases by adollar. With straight line depreciation theincrement in value is given by the solu-tion to

V = (1 - ts) 8 + tB8V/2

where

8 = 1 / 1 + r*B + 1/(1 + r*B)'

Hence

V = (1 - tB)8/[l - tB8/2]

Hence the change in tax liability fromtransferring ownership is (using B's dis-count rate)


(.4tA - .58tB)V + (tB - tA)5.

The accelerated depreciation presumablyincreases the value of an asset. Notice,however, that with a flat rate tax, withno favorable treatment of capital gains,the magnitude of the tax change fromtransferring ownership is relatively small.Thus, with a flat rate tax, the distortionsassociated with the failure to tax capitalgains on depreciable assets upon accrualmay be relatively small.

Our general equilibrium analysis of thetax consequences of the realization ofcapital gains has thus uncovered a fun-damental error in the standard partialequilibrium treatment. The gains from thestep-up in basis have to be contrasted withthe losses from the early recognition of again: though with true economic depre-ciation and full taxation of capital gains,it remains true that early recognition isundesirable, with favorable treatment ofcapital gains and with depreciation thatis faster than true economic depreciation,early recognition may well be desirable;the gains become particularly significant,however, when individuals are in mark-edly different tax brackets.

Ownership of "capital gain assets."Similarly, the tax structure potentially hasimportant implications for the pattern ofownership of assets. Assume, for in-stance, that A owns an asset which nat-urally yields its return in the form of cap-ital gains (like gold). Assume that the realrate of capital gain is g. If A lends B themoney to buy the asset, charging an in-terest rate equal to r*, where

r*(l - tA) = g(l - .4tA)

then A is indifferent: A has received thesame after tax return. But B's net incomeis

1 + g(l - .4tB) - (1 + r*(l - tB))

= g[(l - .4tB) - (1 - to)

(1 - .4tA)/(l - tA)]

= .6g(tB - tA)/l - tA > 0,

if B faces a higher tax rate than A. This

suggests that all of the capital gain yield-ing assets should be owned by individualsin the high tax brackets. (High tax bracketindividuals should engage in this kind ofarbitrage until either there are no moresuch opportunities (and additional oppor-tunities cannot easily be created) or untiltax brackets are equalized.)

These calculations suggest that muchof the gain from tax avoidance activitiesunder our present tax structure arise fromarbitraging across rates, rather than frompostponement. Indeed, there is somequestion about the significance to be at-tached to the postponement effect. Realrates of interest on government securities'^have, from 1950 to 1984, averaged lessthan .75 percent. Thus the loss to the gov-ernment from a tax which is postponed forfive or ten or even twenty years is rela-tively small. Individuals' gains may bemuch higher: they face higher real inter-est rates.^' Because of limitations on col-lateralizable assets, the government maybe in a better position to serve as a "lender"(through the tax system) than are privatelenders.

(With a progressive tax system, thegovernment may not be in an advanta-geous position relative to a private lender.While limited liability limits in general,what a private lender can get back, a pri-vate lender can require the owner of a firmto sign a personal note guaranteeing partor all of a loan. The government cannot,and individuals thus can design contractsunder which losses accrue to those in highmarginal tax rates, gains to those in lowmarginal tax rates, in effect yielding thegovernment a negative return on its loan.)

To the extent that the government candevise tax systems which allow individ-uals discretion in the timing of their taxliabilities, the government may be im-proving the efficiency of the capital mar-ket and this in turn will have a beneficialeffect on the economy. But though theremay be some beneficial effects associatedwith "postponement" many of the taxavoidance activities have a deleterious ef-fect.

Real resource allocation effects. Most ofthis paper has focused on how paper


transactions can, without cost to soci-ety, * enahle the reduction in tax liabili-ties. In the presence of a perfect capitalmarket, presumably all tax liahilities couldhe eliminated. But we do not have a "per-fect" capital market, and all tax liabili-ties are not, therefore, eliminated simplyhy means of "paper" transactions. To re-duce tax liahilities distorting actions areresorted to. Some of these are closelylinked to the very reason that capitalmarkets are not perfect.

Elsewhere, I have argued why imper-fections (and, in particular, asymmetries)of information result in the capital mar-ket being fundamentally different fromhow it is envisaged in the traditional neo-classical paradigm. ® In that model, own-ership makes no difference: the managersimply maximizes the market value of thefirm. But with imperfect information (orincomplete markets), ownership is of im-portance. And ownership entails havingthe claim on residual income (and havingother residual rights not specified in acontractual arrangement). Thus, in ourearlier discussion, we noted that there wasan incentive to delay the recognition of acapital gain, by delaying the completionof a transaction, i.e. delaying the turningover of all residual claims with respect toincome and other rights.

Similarly, we noted there was an in-centive to have higher income individualsreceiving income in the form of capitalgains, lower income individuals in the formof interest; while the latter are usuallyassociated with debt, the former are as-sociated with "ownership"^^; thus, our taxsystem encourages the perpetuation ofcontrol of productive assets hy the wealthy.

These are, by no means, the only realdistortions associated with our tax sys-tem: since there are some sectors whereit seems easier to convert ordinary in-come into capital gains (real estate, inparticular), investments in these sectorsare encouraged, since they increase theopportunities for tax avoidance.

V. Tax Reform

This analysis of tax avoidance behaviorhas some striking implications for tax re-

form. Many of the tax avoidance schemeslose their force (within a general equilib-rium context) with a flat rate tax (or withgreatly reduced differences in marginaltax rates).

With a flat rate income tax, for in-stance, all interest received could be madetax deductible (with interest payments nottax deductible). In a closed economy, theonly net interest payments would be fromthe government. Given the current taxdeductibility of state and local interestpayments, the only effect would be to de-crease the interest rate the federal gov-ernment would have to pay (it would beas if the government collected the tax onits interest payments at source).^' (In anopen economy, the effect of making inter-est income non-taxable would depend onthe treatment of payments to and fromforeign sources.)

Similarly, as we have noted, some of thecentral problems of capital gains taxationare reduced with a flat rate tax.

We have emphasized so far the impor-tant role that differences in marginal taxrates play in tax avoidance under the in-come tax. Similar problems might wellarise in the consumption tax. Consider,for instance, the Blueprints proposal tohave registered and unregistered assets.Assume A is in a higher tax bracket thanB. Assume A and B swap registered forunregistered assets, so that it appears asif A's consumption has decreased and B'sconsumption has increased. Then currenttax liabilities would have reduced (for Aand B together) by tA - ts. To avoid risk,A and B sign contracts promising to swapback again next year. It will then appearas if A's consumption has, at that date in-creased, and B's consumption has de-creased. Whether the present discountedvalue of tax liabilities will have increasedor decreased (in the aggregate) as a resultof this tax swap depends on the relativevaluation of the assets at the two dates.If the values increase by the market rateof interest, there will be no change in thepresent discounted value of aggregate taxliabilities. But if the values increase lessthan the rate of interest, then such a swapreduces the aggregate tax liabilities, andif the values increase by more than the


rate of interest, then the reverse swapwould reduce the aggregate tax liabili-ties. One of the main arguments in favorof the consumption tax, that it would avoidthe difficult and arbitrary valuationproblems which are pervasive under theincome tax, seems less persuasive in thecontext of a consumption tax which doesnot have a flat rate. And such tax avoid-ance activities may have quite similardistortionary effects to the kinds of taxavoidance activities currently observedunder the income tax.

Conclusions

We have outlined in this paper a gen-eral set of principles for tax avoidance;most of at least the common tax avoid-ance schemes can be reinterpreted asmaking use of one or more of these prin-ciples.

In a perfect capital market, these prin-ciples of tax avoidance are so powerful asto enable the astute taxpayer to eliminateall taxation on capital income, and pos-sibly all taxation on wage income as well.The fact that the tax system raises reve-nue is thus a tribute to the lack of as-tuteness of the taxpayer and/or the lackof perfection of the capital market.

This in turn has an important impli-cation: one should treat with some skep-ticism models which attempt to analyzethe effects of taxation assuming rational,maximizing taxpayers working within aperfect capital market.

Some (perhaps most) of the imperfec-tions of the capital market are attribut-able to imperfections (including asym-metries) of information. In economies withimperfect information ownership/controlis important; many of the tax avoidancedevices necessitate altering patterns ofownership, and this may have importantimplications for real resource allocation.

A full analysis of tax avoidance cannotbe conducted within a partial equilibriummodel; when one individual reduces a taxliability through some transaction, thattransaction may at the same time in-crease the tax liability incurred by an-other. In that case, the terms at which thetransaction are conducted will reflect this

"shifting" of tax liabilities. If the two in-dividuals are in the same tax bracket, noreal tax avoidance may have occurred.Such is the case when an individual bor-rows from another; while the interest isdeductible by one, it is taxable to the other.We have delineated those tax avoidanceschemes which do indeed reduces the ag-gregate tax liabilities of all those whoparticipate in them.

We have noted, in particular, that muchof the "general equilibrium" gain from taxavoidance arises from differences in taxrates, both across individuals and acrossclasses of income (rather than from "post-ponement"). If this is true, then reformsaimed at reducing the differences in mar-ginal tax rates may be effective in reduc-ing tax avoidance; there may be signifi-cant gains to be had from going to a flatrate tax, whether of the income or con-sumption variety.

FOOTNOTES

'Financial support from the National Science Foun-dation is gratefully acknowledged.

I focus on the individual income tax, and do notdiscuss the role of the corporation tax in tax avoid-ance, or the methods by which corporate tax liabili-ties may be reduced.

In terms of the Cordes-Galper classification of taxshelters, the tax avoidance schemes on which I focusare pure arbitrage schemes ("pure tax shelters") asopposed to "tax-preferred activities" such as gas andoil.

In my analysis, I do not discuss, moreover, the eco-nomic, political, or social arguments behind thoseprovisions of the tax code which give rise to taxavoidance opportunities. My concern is rather to de-scribe the consequences of these provisions. To the ex-tent that these tax avoidance activities run counterto the intent of these provisions, these consequencesclearly have to be borne in mind in evaluating theirdesirability.

'A fuller discussion of these tax avoidance princi-ples is contained in Stiglitz, [19861 Chapter 24, "AStudent's Guide to Tax Avoidance".

Ûnless, of course, the tax liability is increased asa result of postponement. We shall note instances ofthis below.

*rhat is, if the individual's marginal tax rate at thedate he earned the income and at retirement were thesame, T, then, if he paid the tax at the time he earnedthe income, but if interest income were tax exempt,he would have at retirement, T years later, (1 - rje'",whereas if he used an IRA account, at retirement hewould have, before taxes e'", and after taxes he wouldhave had (1 - T)e"' , precisely the same amount.

^Though the term "tax avoidance" suggests that in-dividuals are not paying taxes that they "should" this


is not necessarily the case: even apart from the al-leged beneficial incentive arguments often raised inbehalf of special tax provisions by their advocates,there may be equity arguments as well. For instance,lifetime income seems a more equitable tax base thanannual income; but provisions for income averagingare inadequate. Hence, "arbitrage" by individualsacross different marginal tax rates they face at dif-ferent times of their lives increases the equity of thetax system.

'For a fuller discussion of the incentive and equityeffects of IRAs, see Stiglitz, [1986], Chapters 22 and23.

^Though the maximum tax savings from this kindof tax arbitrage is limited. If a wealthy, married cou-ple with four children set up eight trusts, their max-imum total tax savings in 1983 was $90,700. Theminimum income required to achieve this is $745,400.Somebody with this income has his average tax ratereduced from 47.9% to 35.7%.

'A flat rate tax with an exemption is progressive,in the sense that the average tax rate increases withincome.

'"Though under accrual, there are often opportun-ities for postponement, taking advantage of particu-lar rules which define when income or expenses areaccrued.

"Later, we shall show that, at least for some ver-sions of a progressive consumption tax, there may stillbe tax avoidance possibilities.

""We ignore all the institutional details associatedwith short sales. If a security costs p and yields astream of returns of x(e,t), in state 6 at date t, thenif an individual sells the security short, he receivesp, and must pay out -x{e,t) in state 9 at date t.

"Note that in our perfect capital market world, theindividual needs no capital to engage in these trans-actions.

"Again, the individual could buy two perfectly neg-atively correlated securities; or he could identify twoperfectly correlated sets of securities, buying one andselling the other short.

'^Note that the objective in converting ordinary in-come losses into short term capital gains is not to gaina direct tax savings—the two are taxed at the samerate; but rather to overcome other limitations withinthe tax code which might restrict the ability to takeadvantage of the favorable treatment of long-termcapital gains.

'Êlsewhere, I have argued that the main distortionto our economy from inflation arises from the failureto appropriately index the tax system. See Stiglitz[1981].

"For sketches of proofs, see Stiglitz [1983]."The term "imperfect capital markets" is used to

cover a whole host of sins. The imperfections withwhich we are concerned here need not reflect "irra-tionalities" of the market. Rather, they may be theconsequence of real costs of transactions and imper-fect and costly information. Simple transactions costs(i.e., those not associated with imperfect information)probably cannot account for the failure of individualsto take full advantage of the available tax avoidanceschemes. Imperfect information can account both forcredit rationing and the high costs of raising fundsby issuing new equity. See Stiglitz and Weiss [1981,1983], and Greenwald, Stiglitz, and Weiss [1984].

''See Feenberg [1981].^"There are many other instances in which tax-

payer behavior seems inconsistent with perfect mar-kets with perfectly rational individuals. These in-clude the "dividend paradox" [Stiglitz, 1973], the"inventory valuation paradox," and the "managerialcompensation paradox." In each case, the behavior canbe "explained" by rational managers dealing with ir-rational shareholders or by non-maximizing (non-as-tute) managers. See Stiglitz [1982b, 1985a, 1985b].

^'Similarly, optimal portfolio behavior with taxesand imperfect capital markets is markedly differentfrom what it would be without taxes and perfect cap-ital markets. See Stiglitz [1983].

^ Of course, if no restrictions are imposed on com-munities issuing these bonds, they could engage intax arbitrage, raising funds by issuing tax exemptbonds and then lending out the money.

În particular, even if there were not favorabletreatment of long term capital gains, losses should berecognized in the year in which they occur. Assumethere are two perfectly correlated assets, x and y, whichhave decreased in price. If A owns x and B owns y,they can achieve a tax savings by swapping on De-cember 31; this leaves unaltered their risk position.

'"The actual tax savings to the individual may alsobe quite different from what they appear to be be-cause the terms of the transaction may be markedlydifferent from what they would have been in the ab-sence of taxation.

Ît should be emphasized that our general equilib-rium analysis is still not completely general: we ig-nore effects on prices and before-tax interest rates.These are crucial for assessing the incidence of taxavoidance schemes such a real estate, and gas and oilinvestments, as opposed to the pure tax arbitrageschemes. See Stiglitz [1986].

'°It obviously makes no difference whether individ-uals are restricted from borrowing to deposit funds inIRA accovmts. Individuals simply borrow more for otherreasons, leaving them more money available for de-positing in their IRA accounts. The only real effectsarise if IRA accounts are not collateralizable.

"The interest rate charged makes no difference toaggregate tax liabilities, since the tax liability of Bis offset by the tax deduction of A.

^ h e incremental value, with true economic depre-ciation, is

V = (1 - t)/[l + r - rt - t]

V = (1 - t)/[(l + r)(l - t)]

= 1/1 + r

^ h i s calculation discounts each individual's tax li-abilities at his own discount rate.

^Remember these calculations have nothing to dowith the transfer of "money," only with the transferof ownership claims in the asset.

"The critical condition for the desirability of own-ership transfer is

.6tA s rtfl/l + r.

Thus, if tA = ts, asset transfer is desirable if r s 1.5.^^hree month Treasury bill rates minus the rate

of inflation.


^'Presumably, reflecting the greater risk to lendingto them. They may also face credit rationing. SeeStiglitz and Weiss [1981].

Other than the direct transactions costs.^'See, for instance, Stiglitz [1982a and 1985a].'*rhere are some subtle and difficult questions as-

sociated with why this is so, and whether it must nec-essarily be so.

"With a flat rate tax, interest rates on state andlocal bonds would presumably fully reflect the tax ex-empt status; the only inefficiency associated with thetax deductibility of state and local interest is the in-centive that it would provide for excessive capital ex-penditures.

REFERENCES

Atkinson, A. and J. E. Stiglitz [1980], Lectures in.Public Economics. New York and London: McGraw-Hill Book Company.

Cordes, J. J. and H. Galper [1985], "Tax Shelter Ac-tivity: Lessons From Twenty Years of Evidence,"paper presented at a Symposium of the NationalTax Association—Tax Institute of America, May1985.

Feenberg, D., [1981], "Does the Investment InterestLimitation Explain the Existence of Dividends?,"Journal of Financial Economics, pp. 265-269.

Greenwald, B., J. E. Stiglitz and A. Weiss, [1984] "In-formational Imperfections in the Capital Market andMacroeconomic Fluctuations," American EconomicReview. May, Vol. 17, pp. 194-199.

Stiglitz, J. E., [1973], "Taxation, Corporate FinancialPolicy and the Cost of Capital," Journal of PublicEconomics, Vol. 2, February, pp. 1-34.

Stiglitz, J. E., [1976], "The Corporation Tax." Journalof Public Economics. April-May, pp. 303-311.

Stiglitz, J. E., [1981], "On the Almost Neutrality ofInflation" in Development in an Inflationary World.eds. M. June Flanders and Assaf Razin, AcademicPress.

Stiglitz, J. E., [1982a], "Information and Capital Mar-kets" in Financial Economics: Essays in Honor ofPaul Cootner. William Sharpe and Cathryn Coot-ner eds., (Englewood Cliffs, New Jersey: PrenticeHall).

Stiglitz, J. E., [1982b], "Ownership, Control and Ef-ficient Markets: Some Paradoxes in the Theory ofCapital Markets," in Economic Regulation: Essaysin Honor of James R. Nelson, Kenneth Boyer andWilliam G. Shepherd eds., (East Lansing, Michi-gan: Michigan State University Press), pp. 311-341.

Stiglitz, J. E., [1983], "Some Aspects of the Taxationof Capital Gains," Journal of Public Economics. Vol.21, pp. 257-294.

Stiglitz, J. E., [1985a], "Credit Markets and the Con-trol of Capital," Journal of Money, Credit andBanking. May, Vol. 17, pp. 133-152.

Stiglitz, J. E., [1985b], "Information and EconomicAnalysis: A Perspective," Economic Journal Sup-plement. Spring, Vol. 95, pp. 21-42.

Stiglitz, J. E., [1986], Economics of the Public Sector,Norton and Company, New York.

Stiglitz, J. E. and A. Weiss, [1981], "Credit Rationingin Markets with Imperfect Information," AmericanEconomic Review, June, Vol. 71, No. 3, pp. 393-410.

Weiss, A. and J. E. Stiglitz, [1983], "Incentive Effectsof Termination: Applications to the Credit and La-bor Markets," American Economic Review, Decem-ber, Vol. 73, pp. 912-927.

Documents

THE GENERAL THEORY OF TAX AVOIDANCE^