Dynamic asset pricing effects and incidence of realization-based capital gains taxes

Journal of Monetary Economics 46 (2000) 465}488

Dynamic asset pricing e!ects and incidence of realization-based capital gains taxes夽 Alan D. Viard* Research Department, Federal Reserve Bank of Dallas, Dallas, TX 75265-5906, USA Received 6 July 1999; received in revised form 2 November 1999; accepted 30 November 1999

Abstract Many analyses of capital gains taxation assume that realization-based taxes are economically similar to accrual-based taxes. In equilibrium, however, the distinctive implications of realization taxes for asset trading through the lock-in e!ect are associated with distinctive dynamic asset pricing e!ects. Asset prices are increased by the current realization tax, to partly o!set the sale disincentive that the tax would otherwise impose. The resulting division of the tax burden between buyers and sellers of assets is similar to traditional public "nance models of excise-tax incidence in product markets.  2000 Elsevier Science B.V. All rights reserved. JEL classixcation: G11; G12; H22 Keywords: Capital gains taxation; Asset pricing; Tax incidence; Lock-in e!ect

夽

I am grateful for helpful comments by Thomas A. Barthold, Stephen G. Cecchetti, Margaret Mary McConnell, David A. Marshall, James M. Peck, V. Brian Viard, seminar participants at Ohio State University, University of South Florida, Utah State University, University of ColoradoDenver, and the Federal Reserve Banks of Kansas City, Chicago, New York, and Dallas, and Midwest Economic Association. I am solely responsible for any errors. The views expressed here are solely my own and do not represent those of the Federal Reserve System or the Federal Reserve Bank of Dallas. * Tel.: 214-922-5172; fax: 214-922-5194. E-mail address: [email protected] (A.D. Viard). 0304-3932/00/$ - see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 9 3 2 ( 0 0 ) 0 0 0 3 4 - 9

466

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

1. Introduction Most countries tax capital gains when they are realized through asset sales rather than as they accrue. It has long been recognized that the dynamic impacts of realization-based taxes on the volume of asset transactions di!er sharply from those of accrual-based taxes, but there has been little attention to the corresponding implications for equilibrium asset pricing. Instead, the pricing e!ects of realization taxes are generally assumed to be qualitatively similar to those of accrual-based capital gains taxes. In this paper, I address the dynamic asset pricing implications of realization taxes, relate them to the change in asset transactions, and distinguish them from the e!ects of accrual taxes. While I "nd that the responses of asset prices to anticipated future accrual and realization taxes are similar, the responses to current tax rates are quite di!erent. I also show that the asset pricing e!ects can be interpreted in terms of tax incidence theory. Unlike accrual taxes, realization-based taxes penalize asset sales and induce a lock-in e!ect. Due to the lock-in e!ect, the trading volume in each asset during a period is negatively related to the current capital gains tax rate. I show that, in equilibrium, the asset's price is positively related to the current tax rate. For consumers who sell shares of the asset in the period, the capital gains tax liability penalizes sales of the asset and thereby increases the return to holding the asset into the next period. If the asset price did not change, the tax would induce sellers to hold more (sell less) of the asset, while buyers' desired asset holdings would be unchanged. In equilibrium, this disparity is prevented by a price increase that reduces the quantity of the asset demanded by buyers and dampens the reduction in the quantity demanded by sellers. This price increase has a ready interpretation in the framework of tax incidence theory. The price increase partially compensates sellers for the marginal tax on sales, thereby shifting part of the tax burden to buyers. The ratio of buyers' and sellers' tax burdens is proportional to the two groups' absolute risk tolerances, implying that each group's burden is inversely proportional to its combined ability to substitute consumption between periods and states. This division of the tax burden between buyers and sellers of each asset resembles the standard public "nance conclusion about the incidence of productmarket excise taxes, in which each side of the market bears a tax burden that is inversely proportional to the elasticity of its participation in the market. It di!ers dramatically, however, from the incidence of an accrual tax, which falls on the consumers who hold the asset at the time that the tax is announced. I examine these issues in a stochastic discrete-time exchange economy with complete markets and in"nite-lived consumers whose preferences satisfy an aggregation condition. I derive the "rst-order equilibrium asset pricing e!ects of current and future capital gains taxes from their e!ects on each consumer's

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

467

marginal cost of holding each asset and the marginal cash #ows generated by the asset. The paper is organized as follows. In Section 2, I specify the model economy and characterize the no-tax equilibrium. In Section 3, I examine the e!ects of taxes on consumers' "rst-order conditions. I analyze the equilibrium asset-price e!ects in Section 4 and I discuss tax incidence in Section 5. I discuss extensions in Section 6 and conclude in Section 7. 2. Speci5cation of economy and no-tax equilibrium I begin by specifying a simple asset-pricing model of a stochastic discrete-time exchange economy without transaction costs and solving for its no-tax equilibrium. The economy contains in"nite-lived consumers, a representative intermediary, and a government. 2.1. Endowment and consumer preferences To focus the analysis on price e!ects, I follow the common strategy of assuming an exchange economy with exogenous aggregate consumption. I assume that part of the consumption endowment is paid directly to consumers. The representative intermediary receives the remainder of the endowment. Endowment } In each period, the economy receives a (generally stochastic) exogenous endowment C of a single perishable consumption good. Each R consumer directly receives a (generally stochastic) non-negative portion of the endowment, with = received by consumer i during period t and GR = , = denoting consumers' aggregate endowed income. The represenR G GR tative intermediary receives the (generally stochastic) non-negative remainder of the endowment, C != . R R I restrict consumer preferences in a manner that facilitates aggregation (as discussed below). Consumer preferences } Consumers are in"nite-lived. Each consumer i has preferences of the form ;(i)"  bRE+(C !M )\A!1,/(1!c), with R GR GR curvature parameter c and utility-discount factor b identical across consumers. If c equals unity, the utility function is logarithmic, ;(i)"  bRE+ln(C !M ),. As c approaches in"nity and M approaches negative R GR GR in"nity, with (c/M) equal to !k, the utility function approaches the negative exponential (constant absolute risk aversion) form,  bRE+!exp(!kC ),. R GR The parameters M , which can be interpreted as subsistence levels of conGR sumption, may di!er across consumers and periods and may be stochastic. A consumer whose subsistence parameter equals zero in every period and state of the world has isoelastic utility, with constant relative risk aversion equal to c.

468

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

2.2. Financial markets Finite-duration "nancial securities are issued and traded without transaction costs by consumers and the representative intermediary. Securities } In some or all periods, the representative intermediary and consumers issue "nite-duration securities without transaction costs. Each share of security n pays a (possibly stochastic) non-negative dividend D during each period t after the period in which it is issued through its LR terminal period. Each share of the security also pays a (possibly stochastic) non-negative liquidating payment ¸ in its terminal period (whose date may LR be stochastic). Let N(t) denote the (stochastic) set of securities active at the end of period t (securities issued in or before period t that have not liquidated in or before period t), with N(0) exogenous. These securities may include equity instruments, debt instruments (with ÷nds' de"ned to include interest payments) and hybrid instruments. Securities are assumed to be of "nite, although possibly stochastic, duration. This assumption re#ects the turnover of "rms in a production economy, in which even equity securities with unlimited stated life are liquidated when the issuing "rm ceases operations. Several sources of uncertainty potentially a!ect individual consumption choices in each period, including the allocation of the endowment between the intermediary and consumers and among individual consumers, consumers' subsistence parameters, and changes in the probability distributions of future values of all of the above. I assume that the available securities are su$cient to span these uncertainties but that no redundant securities exist. Market completeness } Markets are complete, but no redundant security or portfolio exist (no security or portfolio has returns perfectly correlated with the return on any other security or portfolio). An in"nite number of sets of securities could be used to complete the market, since securities can be arbitrarily repackaged (combined and divided). Each set of securities would imply a di!erent trading sequence in equilibrium. For example, a set of Arrow-Debreu state-contingent securities would complete the market, with no trading after the initial period. In the no-tax equilibrium, under

 In the limiting case of negative exponential (constant absolute risk aversion) utility, the assumptions that markets are complete and that the time preference parameter b is constant across individuals are not necessary for aggregation and may be relaxed.

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

469

the maintained assumption of no transaction costs, the identity of the securities used to complete the markets is irrelevant, as is the distinction between dividend and liquidating payments. As will be seen, these matters become relevant in the presence of taxes. Consumers costlessly trade the active securities ex-dividend at the end of each period at market-clearing prices. An adding-up constraint requires that the net holdings of all securities by consumers and the representative intermediary equal zero. Securities trading } The intermediary does not buy securities and, apart from initial issues of new securities, does not sell securities. At the end of each period t, consumers trade ex-dividend all securities in the set N(t). Let P denote the (endogenously determined) ex-dividend price (in terms of the LR consumption good) of security n at the end of period t. Let Z denote the GLR number of shares of each security n held by each consumer i at the end of period t (beginning of period t#1), i.e., after the period t trading session has concluded. Consumers' aggregate net holdings of each active security Z , Z equal the quantity issued by the intermediary (zero for securities LR G GLR issued only by consumers). Each consumer's holdings of each security at the end of period zero, Z , are exogenous. GL The intermediary has zero net cash #ow in every period and state of the world, implying that consumers ultimately receive all of the endowment. The intermediary's net payments to consumers during each period (consisting of dividend and liquidating payments on outstanding securities minus the sale proceeds from the issuance of new securities) exhaust the intermediary's endowed income. Distribution of intermediary's income } In each period and state, the intermediary makes aggregate net payments to securities holders equal to its endowed income, Z (D #¸ )! ! Z P "C != . ,R\ LR\ LR LR ,R ,R\ LR LR R R Based on the above assumptions, each consumer faces the following budget constraint in each period, Z P "= # Z (D #¸ #P )!C , ∀i, t. GLR LR GR GLR\ LR LR LR GR ,R ,R\

(1)

Each consumer's wealth at the end of each period equals her endowed income during the period plus the dividends and liquidating payments on the shares held from the previous period's trading plus her wealth at the beginning of the period minus her consumption during the period.

470

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

2.3. No-tax equilibrium Because markets are complete, the ratio of marginal utilities across consumers is a deterministic constant. De"ning the aggregate subsistence level M , M , the following condition holds in each period and state of the world, R G GR C !M "j (C !M ), (2) GR GR G R R where each j is a constant determined by the consumer's initial "nancial wealth, G expected endowed income, and expected subsistence requirements. Also, since the no-tax equilibrium of this economy lies on the Pareto frontier, it can be represented as the solution to a planner's problem, in which the planner attaches weight j to agent i's utility. By construction, these constants sum to unity. G Each consumer's equilibrium decisions satisfy a transversality condition, with the expected marginal-utility value of her wealth converging to zero, lim E+bR(C !M )\A( Z P ),"0, ∀i. Also, each consumer's equilibR GR GR ,R GLR LR rium decisions satisfy "rst-order conditions equating the marginal cost of holding each active security to the present discounted value of its expected cash #ow, with discount factors given by the consumer's marginal rates of substitution, bQ\RE +(D #¸ )(C !M )\A, R LQ LQ GQ GQ P " QR , ∀i, t, n3N(t). (3) LR (C !M )\A GR GR The market-completeness condition (2) permits (3) to be rewritten in terms of discount factors linked to aggregate consumption, bQ\RE +(D #¸ )(C !M )\A, R LQ LQ Q Q P " QR , ∀t, n3N(t). (4) LR (C !M )\A R R Eq. (4) states the familiar result that each security's price equals the present discounted value of its expected future dividends.

3. E4ect of dividend, accrual, and realization taxes To analyze the e!ects of realization taxes and compare them to the e!ects of other taxes, I consider the institution of a tax system that includes dividend taxes, as well as taxes on accrued and realized capital gains. 3.1. Specixcation of tax system I allow a general pattern of tax rates and lump-sum rebates. Tax rates and rebates } At the beginning of period one, the government unexpectedly announces sequences of non-negative tax rates q on dividend GLR

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

471

payments, a on accrued capital gains and r on realized capital gains. GLR GLR These rates may vary across consumers and securities and over time and may be stochastic. Tax revenues are contemporaneously rebated back to consumers in lump-sum form, with X denoting each consumer's rebate in each GR period. The allocation of rebates among consumers is unrestricted and may be time-varying and stochastic. By allowing each set of tax rates to di!er by consumer, asset, and time period, this assumption is su$ciently general to encompass many of the complexities of actual tax systems. Most tax systems apply realization taxes to some assets (such as equity securities and real estate), while applying accrual taxes to other assets (such as debt securities). Also, consumers are taxed at di!erent rates, with some consumers exempt from tax. I now describe the design of the three components of the tax system, beginning with the taxes on dividends and accrued capital gains. For simplicity, I assume that the dividend and accrual taxes are linear, with full deductibility of accrued losses. Liquidating payments are exempt from the dividend tax, but subject to the tax on accrued capital gains. Taxes on dividends and accrued capital gains } The period-t dividend tax imposed on each consumer with respect to each security in each period equals q Z D . The corresponding accrual tax equals a Z GLR GLR\ LR GLR GLR\ (¸ #P ![P /n ]). The accrual tax applies to the capital gain (or loss) LR LR LR\ R that accrued on each share since the end of the previous period, including any liquidating payment, and is imposed on the consumer who held the share during the period in which the appreciation occurred. In the speci"cation of the accrual tax, the n term captures the interaction of consumer price in#ation with the capital gains tax. If the tax system is not indexed, so that nominal capital gains are taxed, n is de"ned to equal the ratio of the single consumption good's price (in terms of the economy's unit of account) in period t to its price in the preceding period. If the tax system is fully indexed and only real gains are taxed, n is de"ned to equal unity. If the tax system is partially indexed to in#ation, n is de"ned as the relevant function of the in#ation rate. The speci"cation of the realization tax poses more complex issues, because the tax treats buyers and sellers di!erently. Let S be an indicator variable equal to GLR one if the consumer sells security n in period t (if Z (Z ) and zero GLR GLR\ otherwise, so that S (Z !Z ) equals Max(0, Z !Z ). I assume GLR GLR\ GLR GLR\ GLR that the realization tax is also linear, with full deductibility of realized losses. Tax on realized capital gains } The period-t realization tax imposed on each consumer with respect to each security equals r (¸ Z #S P GLR LR GLR\ GLR LR (Z !Z )!B ), where B is the consumer's basis deduction. GLR\ GLR GLR GLR

472

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

The realization tax applies to sellers of each security and all holders of a security when it is liquidated. Consumers are taxed on their sale proceeds and liquidating payments minus a `basisa deduction for the cost of purchasing the shares being sold or liquidated. Since each consumer generally will have purchased shares of each security in many past periods at di!erent prices, the tax system must specify basis-selection rules to allocate purchase costs among subsequent sales. Basis deductions } The basis deductions claimed with respect to each security in each period by each consumer selling or liquidating shares of the security depend on the history of the asset's real price and the in#ation rate and the consumer's current and past holdings of the security, B " GLR f (Z ; P , n ), s4t. The function is di!erentiable with respect to Z except GLQ LQ LQ GLQ (possibly) on a space of measure zero. Let b ,!*B /*Z denote the GLR GLR GLR basis deduction for the marginal share sold. Conditional on the path of real security prices, consumer price in#ation, and the consumer's security holdings, basis deductions do not depend upon tax rates in any period. The basis deduction is identically zero in each period for a consumer who purchases shares of a security. This assumption is su$ciently general to encompass several major basisselection rules. It includes the "rst-in "rst-out (FIFO) rule, which is the default rule in the United States, and the average-cost rule studied by Klein (1999), which is an alternative rule that United States taxpayers may apply to mutual fund shares but not to other securities. It also encompasses the last-in-"rst-out (LIFO) rule, which is not used in the United States tax system. However, the assumption does not accommodate the speci"c identi"cation rule, under which the consumer may designate which shares are being sold, because the basis deductions allowed in each period then depend upon the pattern of tax rates. Although speci"c identi"cation is permitted in the United States, relatively few taxpayers use it. Since the assumption allows real basis deductions to depend upon current and past rates of consumer price in#ation, it accommodates tax systems in which basis deductions are unindexed (as in the United States), partially indexed, or fully indexed. Also, if the in"nite-lived consumers are actually dynasties of "nite-lived individuals linked by operative bequest motives, the assumption allows a variety of tax treatments when an individual dies and bequeaths assets. The assumption accommodates basis carryover (in which the heir takes the same basis as the decedent) and basis stepup (the United States system, in which the heir takes a basis equal to the asset's market value on the date of death). For realization taxes to be viable, consumers must be unable to replicate the real e!ects of asset sales through transactions that are not taxed as sales.

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

473

Stiglitz (1983) and Constantinides (1983) noted that, under certain conditions, consumers could avoid realization taxes with strategies that do not require changes in their consumption in any period or state of the world. New securities that repackage the previous securities in a manner that implies di!erent trading sequences or di!erent mixes of dividends and liquidating payments could also be introduced. However, as recognized in the literature, taxpayers' actual ability to employ such strategies appears to be quite limited. I therefore assume that these strategies are not available. Tax avoidance } Short sales `against the boxa (selling short shares of a security while holding other shares of the same security) and wash sales (both buying and selling shares of a security during the same period) are not permitted. The cost of introducing new securities is bounded away from zero, so that new securities will not be introduced by consumers or by the intermediary in response to a su$ciently small tax. This assumption ensures that a small realization-based capital gains tax (to which this analysis will be specialized below) raises revenue. I discuss these tax-avoidance strategies and the propriety of this assumption further in Section 6. 3.2. Ewects of taxes on consumers The taxes and rebates modify the budget constraints (1) to Z P "= #X !C GLR LR GR GR GR ,R



(1!q

)D Z

#(1!a

!r

)¸ Z

#(1!a

)P Z



GLR LR GLR\ GLR GLR LR GLR\ GLR LR GLR\ , # !r S P (Z !Z )#a [P /n ]Z #r B ,R\ GLR GLR LR GLR\ GLR GLR LR\ R GLR\ GLR GLR ∀i, t. (5)

With realization taxes, the presence of the S indicator variable in Eq. (5) GLR implies that each consumer's payo! function is non-di!erentiable at the point at which she neither buys nor sells shares of a security, when the variable changes discretely between zero and unity. As noted by Cook and O'Hare (1992) and others, discrete realization taxes induce a ®ion of inaction,' which is a range of shocks for which a consumer, who sold shares of a security in the no-tax equilibrium, neither buys nor sells. With a discrete realization tax, there is a positive probability that, in any given period, a consumer chooses a corner solution in which she neither buys nor sells, locating at this `kinka in her payo! function. Kupiec (1996, pp. 119}120) made the same observation for securitiestransaction taxes.

474

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

However, for small realization taxes, consumers remain at interior solutions with arbitrarily high probability. (Since points at which a consumer neither buys nor sells shares of an asset are a space of measure zero, I assume that no consumers are at such points along the no-tax equilibrium path.) At interior solutions, consumers continue to satisfy "rst-order conditions similar to (3), equating the marginal cost of holding the security (the cost of purchasing one more or selling one less share) to the present discounted value of its expected marginal cash #ows. With taxes, these "rst-order conditions take the form P !r S (P !b ) LR GLR GLR LR GLR




 



C !M \A (1!qGLQ )DLQ #(1!aGLQ !rGLQ )¸LQ GQ GQ " bQ\RE , R C !M !a (P ![P /n ])#r S F GR GR QR GLQ LQ LQ\ Q GLQ GLQ GLQR ∀i, t, n3N(t), (6) where F , Q *B /*Z is the e!ect on period-s basis deductions of OR GLQ GLO GLQR acquiring or retaining an additional share in period t and holding it thereafter. The introduction of taxes alters the "rst-order conditions in several ways. Future dividend, accrual, and realization taxes reduce the expected cash #ows from holding an additional share of each security, while current realization taxes reduce the opportunity cost (for sellers) of holding an additional share. First, note that the future dividend and accrual taxes expected to be imposed on the share, q D #a (¸ #P ![P /n ]), reduce the marginal cash GLQ LQ GLQ LQ LQ LQ\ Q #ows from holding an additional share and make the security less attractive. However, the current dividend and accrual tax rates do not enter the "rst-order condition. The current taxes in period t are sunk costs that must be paid by the period-t holder, regardless of her trading decisions at the end of the period. Second, the expected marginal cash #ows are reduced in a similar manner by the future realization taxes expected to be imposed upon liquidation of the asset, r ¸ . These expected taxes also reduce the reward to holding an additional GLQ LQ share. Third, the expected marginal cash #ows are also modi"ed by the marginal e!ects of asset holding on future basis deductions, which are captured by the term r S F . This term includes the additional basis deduction in the GLQ GLQ GLQR period of liquidation (because the marginal share is liquidated), but also includes changes in basis deductions claimed against sale proceeds prior to liquidation. This term is somewhat di!erent from the "rst term, the present discounted value of the dividend and accrual taxes imposed in period s. While the accrual and dividend taxes apply to shares held during period s, the period-s realization tax applies to shares sold during period s (holdings during period s!1 minus holdings during period s). If the realization tax applied to gross sale proceeds with no basis deductions, the period-s tax would not change the marginal cash #ows from acquiring or retaining an additional share in period t((s) because

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

475

the acquisition or retention increases holdings in both period s and s!1. Stated di!erently, the expected tax in period s would not penalize (or reward) purchases or sales in period t(s, but would only penalize sales in period s. However, transactions in period t generally change the amount of basis deductions available on subsequent sales, with the sign and magnitude of these e!ects depending upon the basis selection rule and the consumer's trading sequence. In general, the addition of another share to the consumer's inventory has e!ects on which shares are deemed sold in arbitrarily many future periods. Under FIFO, for example, if the consumer is a purchaser of a security in period t, the purchase of an additional share has no e!ect on basis deductions until the period in which cumulative subsequent sales exceed the holdings in period t!1, because all of these sales are deemed to be from shares purchased before period t. In the period in which that occurs, the share purchased in period t is deemed sold, displacing a later purchased share that would otherwise be deemed sold. Of course, the deemed sale of that displaced share is then pushed into a subsequent period, when it displaces a share purchased still later, and so on. If the consumer is a seller in period t, the sale of one less share causes a similar sequence of displacements of later-purchased by earlier-purchased shares, beginning with the very next sale period. If the security's price has generally risen over time, these displacement e!ects tend to reduce future basis deductions and increase the taxes on future sales, r S F (0. However, under LIFO, the displaceGLQ GLQ GLQR ment e!ects resulting from acquiring or retaining an additional share generally increase basis deductions and reduce taxes on future sales, r S F '0. GLQ GLQ GLQR Klein (1999, pp. 366}367) analyzed the properties of this term (which he called the &average deferral' term) under the average-cost basis selection rule. The fourth e!ect captures the most salient di!erence of realization-based taxes from dividend and accrual taxes. This term states that the opportunity cost of holding the marginal share of the security is reduced by the term r S (P !b ). As re#ected by the presence of the S indicator variable, this GLR GLR LR GLR GLR term is zero for consumers who buy security n in period t, creating a divergence between buyers' and sellers' "rst-order conditions. Each buyer's marginal opportunity cost (the cost of buying one more share) equals the price, but each seller's marginal opportunity cost (the revenue foregone by selling one less share) equals the price minus the tax imposed on the sale of the marginal share, r (P !b ). The realization tax rewards sellers for holding (not selling) the GLR LR GLR security, because retaining the security reduces the current tax liability. Note that this term depends only upon the current tax rate in period t.

4. Equilibrium asset pricing e4ects of taxes I now specialize the analysis to the "rst-order e!ects of introducing a sequence of small taxes. To obtain the "rst-order e!ects, I linearize Eq. (6) around the

476

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

no-tax equilibrium. The "rst-order changes in security prices and individual consumption must satisfy, dP !dr S (P !b ) LR GLR GLR LR GLR " bQ\RE R QR

 

!dq D !da (¸ #P ![P /n ]) GLQ LQ GLQ LQ LQ LQ\ Q C !M \A GQ GQ !dr ¸ #dr S F GLQ LQ GLQ GLQ GLQR C !M GR GR dC dC GR ! GQ #c(D #¸ ) LQ LQ C !M C !M GR GR GQ GQ









∀i, t, n3N(t).





,

(7)

Since aggregate consumption is "xed in this exchange economy, dC "0, ∀s in each state of the world. Also, recall that C !M is proporG GQ GQ GQ tional to j along the no-tax equilibrium path described by Eq. (2). For each G security and time period, multiplying Eq. (7) for each consumer by j and G imposing the zero change in aggregate consumption yields, dP " j dr S (P !b ) LR G GLR GLR LR GLR G !j dq D !j da (P #¸ ![P /n ]) C !M \A G GLQ LQ G GLQ LQ LQ LQ\ Q Q Q # bQ\RE R C !M !j dr ¸ #j dr S F R R G GLQ LQ G GLQ GLQ GLQR G QR







∀t, n3N(t).

, (8)

Eq. (8) describes the "rst-order e!ects of introducing an arbitrary combination of dividend, accrual and realization taxes into a no-tax economy. Under the maintained aggregation assumption, the price of each security is a!ected (to a "rst-order approximation) only by its own tax rates. Before examining the e!ects of realization taxes, it is useful to review the familiar e!ects of dividend and accrual taxes, which are con"rmed by Eq. (8). 4.1. Equilibrium asset pricing ewects of dividend and accrual taxes The responses of asset prices to anticipated dividend and accrual taxes in an exchange economy are well-understood. Eq. (8) states that the current security price is reduced by the present discounted value of the k-weighed sum of

 This is an application of the aggregation result of Rubinstein (1974), which holds when markets are complete and all consumers' preferences are of the hyperbolic absolute risk aversion (HARA) form (1), with identical curvature parameters and discount factors.

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

477

consumers' marginal tax liabilities, bQ\RE R QR






C !M \A Q Q (j dq D #j da (P #¸ ![P /n ])) . G GLQ LQ G GLQ LQ LQ LQ\ Q C !M R R G



If all consumers are subject to the same future dividend and accrual tax rates with respect to a particular security, then the security's price declines in each prior period by the present discounted value of the common tax burden. This is Ricardo's famous result for the e!ect of a tax on the price of an asset in "xed supply in the absence of income e!ects. Continuing to assume that tax rates are the same for all consumers, it is instructive to examine the e!ects of a dividend or accrual tax levied in period s on the price path of the security. The anticipation of the period-s tax reduces the equilibrium price in all periods from when the price is announced (period one) through period s!1, but has no e!ect on the price in period s, immediately after the tax is collected. Unlike the no-tax-equilibrium price path, the new price path includes an anticipated price jump at the end of period s, when the price reduction disappears. This abnormally high pretax return to holding the security in period s is necessary to maintain equilibrium. The higher pretax return o!sets the tax imposed on holding the security during period s, leaving the aftertax rate of return unchanged. Since aftertax rates of return are unchanged, each consumer's holdings are una!ected and the allocation of consumption across periods and states is also unchanged. In an exchange economy, dividend and accrual taxes in which all consumers face the same tax rate (for each security) are lump sum. More generally, if tax rates vary across consumers, the price decline equals the present discounted value of a j-weighted combination of consumers' marginal tax burdens. The net e!ect of the tax and price change is that some (tax-exempt or low-tax-rate) consumers face aftertax rates of return higher than the no-taxequilibrium return and hold more of the security, while other (high-tax-rate) consumers face lower aftertax rates of return and hold less of the security. By altering securities holdings, the divergence of aftertax returns changes the allocation of consumption across periods and states and inducing exchange ine$ciency. The equilibrium price changes are more sensitive to the tax rates imposed on consumers with higher values of j, because, along the no-tax equilibrium path, j is proportional to consumers' absolute risk tolerance - ;/;. Each consumer's absolute risk tolerance measures her absolute willingness to substitute consumption between periods and states of the world (her absolute consumption changes in response to changes in rates of return). Gordon and Bradford (1980) noted that, when tax rates di!er across consumers, the equilibrium price depends upon a weighted combination of individual tax rates, with weights given by absolute risk tolerance.

478

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

4.2. Equilibrium asset pricing ewects of realization taxes Eq. (8) states that the equilibrium price of each security in period t declines by the present discounted value of a j-weighted combination of the future taxes imposed on liquidation of the security and the tax burden associated with the changes in future basis deductions, bQ\RE R QR








C !M \A Q Q (j dr ¸ !j dr S F ) . G GLQ LQ G GLQ GLQ GLQR C !M R R G

The e!ects of future realization taxes are broadly similar to the e!ects of future dividend and accrual taxes. The distinctive equilibrium e!ect of realization taxes arises from the current tax rate. The current security price rises by j dr S (P !b ), a jG G GLR GLR LR GLR weighted combination of the sellers' marginal tax liabilities. Like the price changes induced by future taxes, this price change is a necessary equilibrium response to changes in consumers' demand for securities, implied by the changes in their "rst-order conditions. It is well understood that realization taxes impose a penalty on sales of appreciated assets. The tendency of realization-based capital gains taxes to ine$ciently reduce asset trading is known as the &lock-in e!ect' and has been a major focus of study and policy discussion. Empirical studies, critically surveyed by Gravelle (1994 pp. 144}151), have usually found a signi"cant lock-in e!ect, although its magnitude remains controversial. Revenue estimates of proposals to reduce capital gains tax rates invariably include a revenue feedback from increased sales and generally conclude that such tax reductions increase revenue in the short run. However, most of these studies have not considered the impact of the lock-in e!ect on equilibrium asset prices. Instead, due to the complexity of realization taxes, the overwhelming majority of economic analyses of the e!ects of capital gains taxation on asset pricing (and, in production economies, investment) assume that gains are taxed on an accrual basis. Because deferral of the tax liability until the date of sale reduces its present value, these studies generally model the capital gains tax as an accrual tax levied at an &accrual-equivalent' rate lower than (usually one-quarter of ) the stated rate of the actual realization tax. McGee (1998), Turnovsky (1995, p. 288), and Jorgenson and Landau (1993) are recent examples. Similarly, policy analysts, implicitly or explicitly relying on these models, often argue that reducing the tax rate on capital gains will increase asset prices. These models assume that, despite their disparate e!ects on trading volume, realization and accrual taxation have economically similar asset pricing e!ects, if magnitudes are properly adjusted. In equilibrium, however, the distinctive e!ects of realization taxes must be manifested in prices as well as trading volumes. Market clearing requires that an

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

479

increase in the security's price accompanies the lock-in e!ect. If the price remained unchanged, buyers, who are not directly a!ected by the current tax, would continue to purchase the same number of shares, while sellers would sell fewer shares, yielding a disequilibrium outcome. The equilibrium price change stated by Eq. (8) restores market clearing. The price increase dampens the reduction in sellers' desired sales, while also reducing buyers' purchases. Since the sum of j across all sellers is strictly less than unity (recall that the sum for all G consumers is unity), the price rises by less than the cross-sectional average of sellers' marginal tax liabilities. Sellers with average capital gains liability still reduce the number of shares they sell, while buyers respond to the higher price by reducing the number of shares they purchase. By causing marginal opportunity costs to di!er across buyers and sellers (and across sellers with di!erent marginal basis in the asset), a realization tax induces exchange ine$ciency, even if tax rates are the same for all consumers. Since the average seller's opportunity cost of holding the security is too low, sellers hold an ine$ciently high amount (sell an ine$ciently low amount) of it. Since each buyer's opportunity cost of holding the security is too high, buyers hold (buy) an ine$ciently low amount of it. Relative to the "rst-best, trading is too low. Eq. (8) indicates that the asset pricing e!ects of realization taxes are sensitive to the dynamics of tax rates. A temporary realization tax that expires after the current period increases asset prices through the lock-in e!ect. A realization tax that is announced with a future e!ective date reduces current asset prices. An immediate permanent realization tax may increase or reduce asset prices, depending upon the strengths of the relevant e!ects. 4.3. Potential magnitude of the asset pricing ewects I now provide a rough calibration of the price increase induced by the lock-in e!ect to assess its practical signi"cance, compare it to the price reduction induced by the anticipated future taxes, and examine the factors a!ecting its magnitude. The analysis reveals that omitting the increase can dramatically distort the e!ects of capital gains tax policies, particularly when the policies are temporary and when assets have experienced rapid price appreciation in the past. The price increase induced by the lock-in e!ect is j dr S (P !b ). G G GLR GLR LR GLR Although the covariances (across sellers) between j, tax rates, and ratio of gain  In this model, accrual taxes are superior to realization taxes, because realization taxes inescapably induce exchange ine$ciency, while accrual taxes are e$cient if tax rates are the same for all consumers. Introducing transaction costs, liquidity constraints, or valuation di$culties would diminish the attractiveness of taxing unrealized gains and could alter the superiority of accrual taxes. Also, in a production economy, both taxes distort the allocation of resources between consumption and investment, although they do so in di!erent ways.

480

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

to price could be positive or negative, data limitations impel the assumption that they are zero. Then, the proportional price increase equals j S multiplied G G GLR by the average seller's marginal tax rate multiplied by the average seller's marginal capital gain (as a fraction of the sales price). The sum of j across sellers must lie strictly between zero and unity. There is G no general reason to expect that sellers of the typical asset would have higher or lower absolute risk tolerances than the buyers, particularly since the same consumers are likely to move between the two groups in response to economic perturbations. I therefore assume that this sum typically equals one-half, j S "0.5. Since 1997, most individuals in the United States have faced G G GLR a 20% federal capital gains tax rate, plus additional state taxes. However, a signi"cant amount of assets are held in tax-sheltered retirement accounts that do not face realization-based capital gains taxation. I assume an average marginal capital gains tax rate of 15%. Under these assumptions, the proportional price increase for each asset is 0.075 times the ratio of capital gain to sales price for the average seller of the asset, (P !b )/P . This ratio will vary dramatically across assets. While LR GLR LR expected rates of price appreciation may be similar across assets (with di!erences re#ecting risk and dividend yield), ex-post rates of price appreciation will vary widely in a stochastic economy. For an asset that has experienced very rapid price appreciation, the average value of (P !b )/P would be close to LR GLR LR unity and the capital gains tax would increase asset prices by almost 7.5%. Conversely, the average ratio would be close to zero for assets that have experienced little price appreciation, or negative for assets that have declined in price. IRS data for 1985 (the most recent year for which such data have been reported) show that, in the aggregate, individual taxpayers' basis deductions equaled 74% of sales proceeds, Auten and Wilson (1999, p. 123). With a 26% ratio of capital gain to price, the capital gains tax would increase asset prices by 1.9%. A higher ratio might now apply, in view of the recent rapid appreciation of corporate equity. It is useful to compare the price increase induced by the current tax to the price reduction induced by future taxes. The approach used in the literature suggests that a permanent 15% capital gains tax would, under a speci"c set of reasonable parameters, reduce the price by 6.3 percent. Even for a permanent tax, the price increase induced by the lock-in e!ect o!sets a signi"cant fraction of

 The standard approach assumes that a 15% realization tax induces the same price reduction as a 3.75% accrual tax. For an asset with expected annual nominal appreciation g, required annual nominal return o, and arbitrarily distant liquidation date, the present value of accrued nominal capital gains is g/(o!g) times the current price. Note that (o!g) is the annual dividend yield and that the present value of nominal capital gains exceeds the asset price (the present value of dividends) if nominal appreciation exceeds dividend yield. For o"0.08 and g"0.05, the present value of nominal capital gains is 1.67 times the price and a 3.75% accrual tax reduces the price by 6.3%.

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

481

the price reduction for many assets and fully o!sets it for assets with very rapid past appreciation. But, as noted above, the relative importance of the price increase is greatest in the case of temporary tax policies, because the price impact of the future taxes is then smaller. This case is empirically relevant; Gravelle's description of the history of U.S. capital gains taxation (1994, pp. 268}271) reveals that major changes have occurred at a rate of about one per decade. For the parameters used above, the price reduction from future taxes would be 1.6% if the tax expires after 10 years (0.9% after 5 years and 2.8% after 20 years). In this case, the price increase induced by the lock-in e!ect would frequently outweigh the price reduction induced by future taxes. The above analysis implies that omission of the lock-in e!ect from the analysis of asset pricing e!ects of capital gains tax policies can seriously distort the conclusions. The distortion is greatest when the policies are temporary and when assets have experienced rapid recent appreciation. 4.4. Comparison to previous literature The conclusion that asset prices are increased by current realization-based taxes through the lock-in e!ect is not new. Lang and Shackelford (2000, pp. 74}75) informally sketched the argument that asset sellers would obtain compensation for the tax liability triggered by selling and noted that this argument has sometimes appeared in the business press (in addition to their references, see Norris, 1997; and Lohse, 1997). Two recent papers by Klein (1998, 1999), that I became aware of after writing an earlier version of this paper, explicitly modeled the realization nature of capital gains taxes. Under the assumption of exponential utility and a terminal date for the economy, Klein derived expressions for the e!ect of a time-invariant capital gains tax that included both the price increase resulting from the current tax and the price reductions induced by future taxes. Englund (1986) similarly found that time-invariant realization-based capital gains taxes could increase housing prices. But, this e!ect has been suppressed in most of the literature by treating realization taxes as the economic equivalent of accrual taxes. Modeling realization-based and accrual taxes as having similar asset pricing e!ects, while recognizing that they have dramatically di!erent e!ect on asset transactions, is internally inconsistent.

 Klein (1999, pp. 371}372, 1998, pp. 1551}1552) also explained how the cross-sectional asset pricing implications (discussed above) might account for empirical "ndings of mean reversion in pretax security returns.

482

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

5. Tax incidence The burden of the current realization tax on each security is divided between the consumers who sell the security and those who buy it. The tax is collected from the sellers, but the price increase shifts a portion of the tax payment to the buyers in that period. I now demonstrate that the extent of this shifting is determined by the same factors that govern the shifting of excise taxes in product markets. Consider the special case in which all sellers have the same tax rate r and the same marginal basis in the security b, so that all sellers have the same marginal tax liability. Inspection of Eq. (8) reveals that the ratio of the buyers' tax burden to the sellers' tax burden is inversely proportional to the sum of j across each G group. Recall that j measures each consumer's absolute willingness to substiG tute consumption between periods and states of the world (the absolute change in consumption in response to a change in rates of return). Therefore, each group's share of the burden is inversely proportional to its aggregate absolute willingness to substitute consumption. This result is an application of the standard inverse-elasticity result from the partial-equilibrium analysis of excise-tax incidence (see Kotliko! and Summers, 1987, pp. 1045}1047). This formula states that the ratio of the buyer's burden to the seller's burden equals the supply elasticity divided by the demand elasticity, so that burden is divided between buyers and sellers in inverse proportion to their ability to substitute out of the market. The excise-tax analogy also explains why the weights in Eq. (8) depend upon each seller's value of j , rather than upon the quantity she sells. The incidence of G a tax depends upon consumers' ability to substitute at the margin, not on the quantities of their inframarginal transactions. These results explain why the incidence of a realization-based tax di!ers from that of accrual and dividend taxes. These taxes, which apply to holdings rather than sales, fall upon the initial holders of the assets. That incidence result can also be interpreted in terms of the inverse-elasticity incidence result, since the holdings of the initial owners are perfectly inelastic with respect to the tax while those of subsequent holders are elastic. Because the initial holdings are perfectly inelastic, the initial holders bear the full burden of accrual and dividend taxes. 6. Extensions This analysis can be extended in a variety of directions. 6.1. Production economy Since the above analysis assumes an exchange economy, it is of interest to consider the extension to a production economy. Although the exact solution of

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

483

a production-economy model is quite di$cult, particularly with multiple assets, some general conclusions can be stated. The above analysis indicates that future dividend, accrual, and realization taxes tend to reduce current asset prices in an exchange economy. The corresponding conclusion for a production economy is that these future taxes tend to reduce current investment in assets. Investment is penalized by the future taxes to be imposed on the new assets. However, the above analysis indicates that, in an exchange economy, the current realization tax increases asset prices. The corresponding e!ects on current investment in a production economy are also altered, in a manner that depends upon the tax treatment of new production relative to secondary trading. Assume that consumers who produce new assets receive a basis deduction for the cost of production, on the same terms that consumers who purchase existing assets receive a basis deduction for the cost of purchase. This is generally true for non-corporate investment in the United States. Then, asset production responds positively to the current realization tax; investment increases until the marginal production cost equals the new higher price of the asset. New production is e!ectively exempt from the current realization tax, because a sale of the newly produced asset is tax-free (its market price equals its marginal production cost, which equals its basis). In contrast, purchases of existing shares from sellers are subject to tax. As a result, buyers of the asset produce more of it, substituting away from taxed purchases. Auerbach (1992, p. 266), using a threeperiod model with one safe and one risky asset, found that realization taxes result in greater investment than accrual taxes. The availability of a production choice dampens the price increase that the tax would otherwise produce, placing less of the tax burden on buyers and more on sellers. The option to produce the asset or buy it from new producers gives buyers greater ability to substitute out of the market and diminishes the extent to which they bear the incidence of the tax. However, the tax treatment of reinvested corporate earnings in the United States is quite di!erent, as noted by Gravelle (1994, p. 126) and other authors. The reinvestment increases the value of the existing shares, but shareholders are not allowed a basis deduction for the reinvested earnings. Since the production of new assets is then subject to the current realization tax, production should respond negatively to the current tax rate. More formal analysis of the e!ects of realization taxes in production economies is required. It is apparent that the analysis would yield rich implications,  Sole proprietors receive a basis deduction for capital investment expenditures. The taxation of investments by partnerships and small (&S') corporations taxed as pass-through entities is economically similar, since partners and S shareholders receive basis deductions for their pro-rata shares of the business's reinvested earnings.

484

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

particularly with respect to the allocation of investment between the corporate and non-corporate sectors. 6.2. Transaction costs and xnite lives A crucial methodological simpli"cation in this analysis is that all consumers are at an interior optimum in all periods and all states, along the no-tax equilibrium path (and after arbitrarily small taxes are introduced). The marginal opportunity cost of holding each security then always equals the in"nitehorizon present discounted value of its expected marginal cash #ows. Any of several changes to the model's assumptions would negate this feature. For example, transaction costs would induce some individuals to choose corner solutions with respect to some securities in the no-tax equilibrium. These individuals are in a no-transaction region, in which they neither buy nor sell shares, as described by Davis and Norman (1990). Kiefer (1990) considered a model in which investors hold only a single stock at a time and are at corner solutions with respect to other stocks. Cook and O'Hare (1992) also considered a model in which the choice variable is how often to transact. Although transaction costs would complicate the analysis, they are unlikely to alter the qualitative properties of the solution. In a model with transaction costs, where the choice variable is transaction frequency, two-period lives, and a deterministic economy, Englund (1986) found that realization-based capital gain taxes can increase asset prices through the lock-in e!ect. Klein (1998, 1999) analyzed transaction costs by including shadow prices for consumers at corner solutions and continued to "nd asset pricing implications from the lock-in e!ect. 6.3. Tax avoidance In this analysis, I have assumed that realization taxes cannot be avoided through strategies that do not require real changes in the allocation of consumption across periods and states of the world. This assumption appears to be a roughly accurate description of how capital gains taxes a!ect most investors. Stiglitz (1983, pp. 259}271) and Constantinides (1983, pp. 623}626) demonstrated that, with perfect capital markets and a stylized tax code, utilitymaximizing consumers can use borrowing and short sales against the box to completely avoid capital gains taxes and obtain interest and capital-loss deductions o!setting taxes on their other income. In a short sale against the box, an investor, before selling shares of a security, borrows shares of the same security from her broker or another investor and uses the speci"c-identi"cation basis rule to designate the borrowed shares as the ones sold. She then avoids tax until she closes the transaction by selling her own shares and delivering them to the lender as repayment for the borrowed shares. I assume that short sales against the box are not permitted for tax purposes.

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

485

Similarly, if redundant securities exist, a consumer can avoid tax on an appreciated asset by selling a perfectly correlated security with a di!erent tax basis. Dammon and Spatt (1996, pp. 910, 928 no.10) observed that the lock-in e!ect has no impact on asset prices in the extreme case in which all securities subject to capital gains tax have identical tax-exempt counterparts. While costless avoidance of capital gains tax requires the use of identical securities, near-costless avoidance can be achieved by using almost-identical securities (writing deep-in-the-money calls, purchasing deep-in-the-money puts, or entering into equity-swap transactions), as described by Henriques and Norris (1996). I assumed that no redundant securities existed and that none would be introduced in response to a small realization tax. Before 1997, these tax avoidance strategies were generally permitted in the United States. A few wealthy investors used them, particularly during the few years before 1997, Henriques and Norris (1996), and some investors continue to use them, despite legal restrictions adopted that year. However, as noted by Auerbach et al. (1998, pp. 2, 25), Mariger (1995, p. 448), Haliassos and Lyon (1994, p. 283), Kiefer (1990, p. 92 no.13), Auerbach (1989, p. 395), Balcer and Judd (1987, pp. 745}746), Poterba (1987, pp. 165}169), and Stiglitz (1983), most taxpayers make little or no use of these strategies. Dammon and Spatt (1996, p. 948) comment that &what is puzzling about investors' observed trading behavior is the relative infrequency of capital loss realizations'. In 1997, individual taxpayers in the United States realized $339 billion of capital gains, net of capital losses, Cruciano (1999, p. 138). Stiglitz concluded (1983, pp. 258, 273) that capital market imperfections prevented widespread use of these strategies. Klein (1998, pp. 1536}1537; 1999, pp. 356}357) reinforced this explanation by describing the transaction costs that might inhibit the use of these techniques. I have also abstracted from several other features of the actual tax systems, such as rate di!erentials between long- and short-term capital gains. Constantinides (1984) and Bossaerts and Dammon (1994) also discussed tax-avoidance strategies which exploit this di!erential. I also precluded wash sales; incorporating them in this model would add terms re#ecting the savings from the resulting deductions, but would not otherwise a!ect the analysis since wash sales do not have real portfolio e!ects.

 On August 5, 1997, Congress and President Clinton enacted section 1259 of the Internal Revenue Code, which, subject to certain exceptions, taxes as &constructive sales' short sales against the box and equity swaps entered into after June 8, 1997. Section 1259 also empowers the IRS to extend this treatment to the issuance of deep-in-the-money calls, purchases of deep-in-the-money puts, and similar transactions, but the IRS has not yet done so. Paul (1997) thoroughly described these intricate rules and Schizer (1998) analyzed the extent to which they still permit some tax avoidance. Schultz (1999) described the recent growth of explicitly &tax-managed' stock mutual funds.

486

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

6.4. Aggregation Allowing incomplete markets or more general preferences would negate the aggregation technique employed in this analysis. It would not be possible to take a weighted combination of the relevant Euler equations with "xed weights given by j , because the appropriate weights would be time-varying, stochastic, G and endogenous. The introduction of a tax could itself induce a "rst-order change in the weights. With incomplete markets, the choice between accrual and realization taxes would also have implications for risk-sharing, as in Haliassos and Lyon (1994). Aggregation would also break down if consumers were "nite lived, as would occur if individuals were not linked by operative bequest motives. Accrual or realization taxes would redistribute resources across generations and the resulting income e!ects would alter asset prices. Chamley and Wright (1987) noted that accrual taxes on land could actually raise land prices in an overlapping generations economy, due to income e!ects from intergenerational redistribution. While the inclusion of risk-sharing and income e!ects would complicate the comparison of accrual and realization taxes, it would not change the fact that the two taxes have dramatically di!erent incentive e!ects and therefore di!erent asset pricing e!ects. 7. Conclusion In this paper, I demonstrate that accrual and realization taxes on capital gains have quite di!erent dynamic asset-pricing e!ects and incidence. While the impact of future taxes is similar, asset prices are positively related to current realization taxes in a manner that has no counterpart for accrual or dividend taxes. This pricing e!ect is an equilibrium implication of the lock-in e!ect that is distinctive to realization-based taxation. The incidence of the current realization tax is divided between buyers and sellers of the asset, with each group's burden determined by an inverse-elasticity formula similar to the public-"nance analysis of excise tax incidence. These results cast serious doubt on the practice of assuming that realization and accrual taxes have fundamentally similar economic properties. But, since the e!ects of realization-based capital gains taxes are sensitive to the speci"cation of the economic environment and tax rules, further theoretical and empirical research is necessary to clarify the impact of actual realization taxes. References Auerbach, A.J., 1989. Capital gains taxation and tax reform. National Tax Journal 42, 391}401.

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

487

Auerbach, A.J., Burman, L.E., Siegel, J.M., 1998. Capital gains taxation and tax avoidance: new evidence from panel data. National Bureau of Economic Research Working Paper 6399. Auten, G., Wilson, J., 1999. Sales of capital assets reported on individual income tax returns, 1985. Statistics of Income Bulletin 18, 113}136. Balcer, Y., Judd, K.L., 1987. E!ects of capital gains taxation on life-cycle investment and portfolio management. Journal of Finance 42, 743}758. Bossaerts, P., Dammon, R.M., 1994. Tax-induced intertemporal restrictions on security returns. Journal of Finance 49, 1347}1371. Chamley, C., Wright, B.D., 1987. Fiscal incidence in an overlapping generations model with a "xed asset. Journal of Public Economics 32, 3}24. Constantinides, G.M., 1983. Capital market equilibrium with personal tax. Econometrica 51, 611}636. Constantinides, G.M., 1984. Optimal stock trading with personal taxes: implications for prices and the abnormal January returns. Journal of Financial Economics 13, 65}89. Cook, E.W., O'Hare, J.F., 1992. Capital gains redux: why holding periods matter. National Tax Journal 45, 53}76. Cruciano, T., 1999. Individual income tax returns, preliminary data, 1997. Statistics of Income Bulletin 18, 137}145. Dammon, R.M., Spatt, C.S., 1996. The optimal trading and pricing of securities with asymmetric capital gains taxes and transaction costs. Review of Financial Studies 9, 921}952. Davis, M.H.A., Norman, A.R., 1990. Portfolio selection with transaction costs. Mathematics of Operations Research 15, 676}713. Englund, P., 1986. Transaction costs, capital gains taxes, and housing demand. Journal of Urban Economics 20, 274}290. Gordon, R.H., Bradford, D.F., 1980. Taxation and the stock market valuation of capital gains and dividends. Journal of Public Economics 14, 109}136. Gravelle, J.G., 1994. The Economic E!ects of Taxing Capital Income. MIT Press, Cambridge, MA. Haliassos, M., Lyon, A.B., 1994. Progressivity of capital gains taxation with optimal portfolio selection. In: Slemrod, J. (Ed.), Tax Progressivity and Income Inequality. Cambridge University Press, Cambridge, pp. 275}304. Henriques, D.B., Norris, F., 1996. Wealthy, helped by Wall Street, "nd new ways to escape tax on pro"ts. New York Times, December 1. Jorgenson, D.W., Landau, R. (Eds.), 1993. Tax Reform and the Cost of Capital: An International Comparison. Brookings Institution, Washington, DC. Kiefer, D., 1990. Lock-in e!ect with a simple model of corporate stock trading. National Tax Journal 43, 75}94. Klein, P., 1998. The capital gains lock-in e!ect with short sales constraints. Journal of Banking & Finance 22, 1533}1558. Klein, P., 1999. The capital gains lock-in e!ect and equilibrium returns. Journal of Public Economics 71, 355}378. Kupiec, P.N., 1996. Noise traders, excess volatility, and a securities transaction tax. Journal of Financial Services Research 10, 115}129. Lang, M.H., Shackelford, D.A., 2000. Capitalizations of capital gain taxes: evidence from stock price reactions to the 1997 rate reduction. Journal of Public Economics 76, 69}85. Lohse, D., 1997. Would tax cut ignite a "re? Don't be sure. Wall Street Journal, March 3. Mariger, R.P., 1995. Taxes, capital gains realizations, and revenues: A critical review and some new results. National Tax Journal 48, 447}462. McGee, M.K., 1998. Capital gains taxation and new "rm investment. National Tax Journal 51, 653}673. Norris, F., 1997. With rates down, will investors sell? New York Times, August 3.

488

A.D. Viard / Journal of Monetary Economics 46 (2000) 465}488

Paul, W.M., 1997. Constructive sales under new section 1259. Tax Notes 76, 1467}1479. Poterba, J.M., 1987. How burdensome are capital gains taxes? Evidence from the United States. Journal of Public Economics 33, 157}172. Rubinstein, M., 1974. An aggregation theorem for securities markets. Journal of Financial Economics 1, 225}244. Schizer, D.M., 1998. Hedging under section 1259. Tax Notes 80, 345}356. Schultz, A., 1999. As big gains increase the bite, more funds try to o!set taxes. New York Times, April 4. Stiglitz, J., 1983. Some aspects of the taxation of capital gains. Journal of Public Economics 21, 257}294. Turnovsky, S.J., 1995. Methods of Macroeconomic Dynamics. MIT Press, Cambridge, MA.