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Optimal Retrospective Capital Gains Taxation

Permanent Link: http://ncf.sobek.ufl.edu/NCFE004251/00001

Material Information

Title: Optimal Retrospective Capital Gains Taxation
Physical Description: Book
Language: English
Creator: Frazier, Nicholas
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2010
Publication Date: 2010

Subjects

Subjects / Keywords: Capital Gains
Taxation Lock-in Effect
Step-up of Basics
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This study surveys the present debate surrounding optimal capital gains taxation within the greater context of the United States individual income tax. Of particular interest is the requirement imposed of taxation upon realization, or an effective deferral of liability owed under a cash-flow methodology. This examination includes consideration of nature of capital gains as income, certain economic consequences of its taxation, and its inclusion, or exclusion, of our system�s broader social objectives. The approach applied relies on identifying certain issues within the current tax code and comparison of its mechanism for the calculation of tax liability to that Auerbach proposed in his 1991 work, Retrospective Capital Gains Taxation. This alternate scheme involves the imputation of growth over the holding period of the asset and charging the relevant compounded interest owed on those accrued gains as deferred payment. We also consider certain advantages and drawbacks inherent in Auerbach�s proposal and its overall treatment of capital gains as income. Finally, we conduct a simple application of Auerbach�s prescribed mechanism using the Internal Revenue Service�s Study of Capital Assets data estimating the relevant statistics concerning assets reported on the Schedule D for the tax years 1997 through 2003. The work seeks to summarize the ongoing debate and evaluate the various compromises between the social criteria and economic efficiency, implicit in all taxation but crucial to the taxation of capital income.
Statement of Responsibility: by Nicholas Frazier
Thesis: Thesis (B.A.) -- New College of Florida, 2010
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Coe, Richard

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2010 F8
System ID: NCFE004251:00001

Permanent Link: http://ncf.sobek.ufl.edu/NCFE004251/00001

Material Information

Title: Optimal Retrospective Capital Gains Taxation
Physical Description: Book
Language: English
Creator: Frazier, Nicholas
Publisher: New College of Florida
Place of Publication: Sarasota, Fla.
Creation Date: 2010
Publication Date: 2010

Subjects

Subjects / Keywords: Capital Gains
Taxation Lock-in Effect
Step-up of Basics
Genre: bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This study surveys the present debate surrounding optimal capital gains taxation within the greater context of the United States individual income tax. Of particular interest is the requirement imposed of taxation upon realization, or an effective deferral of liability owed under a cash-flow methodology. This examination includes consideration of nature of capital gains as income, certain economic consequences of its taxation, and its inclusion, or exclusion, of our system�s broader social objectives. The approach applied relies on identifying certain issues within the current tax code and comparison of its mechanism for the calculation of tax liability to that Auerbach proposed in his 1991 work, Retrospective Capital Gains Taxation. This alternate scheme involves the imputation of growth over the holding period of the asset and charging the relevant compounded interest owed on those accrued gains as deferred payment. We also consider certain advantages and drawbacks inherent in Auerbach�s proposal and its overall treatment of capital gains as income. Finally, we conduct a simple application of Auerbach�s prescribed mechanism using the Internal Revenue Service�s Study of Capital Assets data estimating the relevant statistics concerning assets reported on the Schedule D for the tax years 1997 through 2003. The work seeks to summarize the ongoing debate and evaluate the various compromises between the social criteria and economic efficiency, implicit in all taxation but crucial to the taxation of capital income.
Statement of Responsibility: by Nicholas Frazier
Thesis: Thesis (B.A.) -- New College of Florida, 2010
Electronic Access: RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE
Bibliography: Includes bibliographical references.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Local: Faculty Sponsor: Coe, Richard

Record Information

Source Institution: New College of Florida
Holding Location: New College of Florida
Rights Management: Applicable rights reserved.
Classification: local - S.T. 2010 F8
System ID: NCFE004251:00001


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OPTIMAL RETROSPECTIVE CAPITAL GAINS TAXATION BY NICHOLAS FRAZIER A Thesis Submitted to the Division of Social Sciences New College of Florida in partial fulfillment of the requirements for the degree Bachelor of Arts Under the sponsorship of Richard Coe Sarasota, Florida April, 2010

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Nick Frazier, Page 2 OPTIMAL RETROSPECTIVE CAPITAL GAINS TAXATION Nicholas Frazier New College of Florida, 2010 ABSTRACT This study surveys the present debate surrounding optimal capital gains taxation within the greater con text of the United States individual income tax. Of particular interest is the requirement imposed of taxation upon realization, or an effective deferral of liability owed under a cash flow methodology. This examination includes consideration of nature of capital gains as income, certain economic consequences of its approach applied relies on identifying certain issues within the current tax code and comparison of its mechanism for the calculation of tax liability to that Auerbach proposed in his 1991 work, Retrospective Capital Gains Taxation This alternate scheme involves the imputation of growth over the holding period of the asset and charging the relevant compound ed interest owed on those accrued gains as deferred payment. We also overall treatment of capital gains as income. Finally, we conduct a simple application of Assets data estimating the relevant statistics concerning assets reported on the Schedule D for the tax years 1997 through 2003. The work seeks to summarize the on going debate

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Nick Frazier, Page 3 and eval uate the various compromises between the social criteria and economic efficiency, implicit in all taxation but crucial to the taxation of capital income.

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Nick Frazier, Page 4 I. Introduction For much of human history the burden of taxes h as fallen predominantly on the peasant class. The principles of horizontal and vertical equity developed as decidedly modern notions While the wealthier households have long tended to draw their incomes from sources other than labor once again, the theor y and practice of how to tax these alternate sources of income still remain largely in flux today 1 Of concern here is a certain class of income derived from the appreciation in the value of capital that, while not always the principal source, is preponder antly located in the income of high income and wealthy households Even some of the more basic conclusions, such as the degree to which it represents a different form of income from wages or ordinary income, remain un resolved. In certain ways, capital gain s taxation shows potential as a vehicle for adding progressivity to the system but in others the very nature of its generation of value complicates or even precludes an efficient way to approach its taxation. Some economists have gone so far as to suggest that the optimal rate of taxation could never rise above zero in the long run 2 but the predominant work concerns improving and measuring the costs of such taxation. The conventional approach has been to assume that capital accumulation will bear some tax burden and discuss the considers how tax rates above than zero a ffects the equilibrium of risk taking for investors. For instance, we may see intuitively that as wealth increases, so does the 1 For an excellent summary of modern public finance and tax theory, see Salanie (2003). 2 See Ordover and Phelps (1979) for an approach using marginal rates of productivity to suggest a high sensitivity to tax rates. See Chamley (1986) and Judd (1985) for a discussion of the optimal rate from the perspective of an infinite horizon.

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Nick Frazier, Page 5 absolute am However, while we might expect, given a marginal utility of a dollar, that wealthier households may be less risk averse than comparable households, conclusive empirical evidence to support this assertion has not yet come forth. The analytics, as well, become murkier when we have a capital gains structure with a progressive rate schedule, as we may postulate that higher tax rates in centivize risk taking as an adjustment to achieve nor mal returns, but conversely because the net of tax returns are lower, wealthier households may seek other sources of income or seek less risky returns. Any empirical examination of how taxation changes preferences, however, suffers immediately from the in evitable complications located in our tax code. Notably, the majority of provisions in our tax code such as the higher tax rate for interest income, dividends, and ordinary income, seem to directly incentivize capital gains as a source of income. Anothe r topic of debate has been the importance of capital gains as a source of income. Mirlees (1971) suggested an ine scapable trade off between efficiency and equit y in income taxation which holds true for capital gain taxation in that any deviation from effic iency and equilibrium in the capital market to achieve social objectives comes with measurable economic costs Tax theorists and policy make rs weigh the consequences of such a tax on optimal portfolio balance, investor behavior, the choice between labor an d General Equilibrium Model, have been in the field of intergenerational analysis. Barro (1974) and Diamond (1965) consider the effect of taxation and debt on capital accum ulation and w hether the government can ultimately set t he equilibrium of capital stock in the long run Here, we may cite real examples to complement the theoretical

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Nick Frazier, Page 6 work that suggest its efficacy. For instance, t he social security system and federal publi c debt represent m odern examples of government intervention in private investment where the government effectively attempts to save and borrow, respectively, on behalf of individuals. The literature devoted to the consideration of taxing capital has prov ided some justifications for its practice. Some cite the empirical weakness of the assumption of separability in the choice between present and future consumption, where tax rates do not always appear directly correlated to levels of saving 3 One prominent reason for capital taxation has been the existence of large endowments and dynastical wealth, which may escape taxation on ordinary income sources and arguably faces a lower effective burden by virtue of arbitrary circumstance. Also public finance conside rs the possible corrective role of the government in sub optimal distributions of capital accumulation, between different levels of income, generations, and even regional which manifests in institutions like the Stafford loans, Social Security or the Tenn essee Valley Authority However, notably, none of the reasons mentioned directly suggest that capital gain represents income tantamount to ordinary income and should be taxed as such. One of the defining developments in modern public finance arrive d in th e classification of income. The Haig Simons comprehensive definition of income has been relatively wholly adopted by the Internal Revenue Service (IRS) of the United States to organize the individual i ncome tax s ystem. Their approach identifies income as t he amount an agent may consume in the specified period without reducing wealth. We may immediately recognize that capital gains represent a subtle case as under traditional 3 The recent introduction and popularity of IRAs [1981] and particularly Roth IRAs [1997] may provide some insight into the observable empirical relationship not considered in thi s work.

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Nick Frazier, Page 7 concepts of income, purchasing power has increased, but the ability to consume does not actually increase until realization of the asset 4 The IRS effectively treats cash distributions, such as interest or dividend payments, as ordinary income deserving a separate treatment from capital gains though all fall under the economic designatio n as capital income though based on a set criteria certain qualified dividends fall under capital gains We recognize, then, that the practical issue at hand entails how to treat realized capital gain comprehensively which inevitably requires a form of re trospective taxation during the period of accumulation. The current treatment of capital gains stems primarily from legislation since the Taxpayer Relief Act of 1997 (TRA97) 5 TRA97, discussed more in depth below, began the recent trend in lowering rates for capital income. The rates used in the current system through the tax year 2009 (TY2009), however, are derived from the Job Growth and Taxpayer Relief Reconciliation Act of 2003 (JGTRRA03) that lowered rates on all capital income and created max rate of fifteen percent for long term capital gains, considerably below the thirty five percent maximum rate for ordinary income. In particular, the recent decline in capital gains rates have significance for the income of hedge funds and private equity which eff ectively experience a much lower tax burden than other analogous institutions and households. An other major development with respect to capital gains taxation has been the move towards consumption taxation as emerging in two recent changes. The first appea rs as the increasing prefere nce towards deducting interest. For example, as the tax code presently exists, a taxpayer may take out 4 One caveat to this distinction arises in the empirical evidence suggesting that marginal propensity to consume does rise during a bullish period in the capital market. 5 For a more comprehensive history of capital gains taxation since the 1960s, see Steuerle 2008.

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Nick Frazier, Page 8 a mortgage and use that money to pay costs related their primary residence and invest the liquidity freed by the loan, deduct ing the interest paid on the mortgage and deferring realization of tax liability on the accumulated gain, essentially debt financed consumption that can create an effective tax rate of zero on the total gain at realization. The second major step towards co nsumption taxation arrived during the 1990s in the institution of qualified retirement plans, such as IRAs education and medical savings plans, 410Ks and, especially, the Roth IRA, in that they create significant incentives designed to induce saving amon g the American public. Generally, Steuerle (1985) estimates that, relative to interest income, almost eighty percent of returns to assets benefit from one tax preference or another. A full description of the current tax code would require more space than p ermitted but relevant provisions will be discussed as they arise later in our discussion. 6 As disc ussed in the first chapter, certain theoretical and even empirically proven distortions of the capital market result from the current treatment of capital gai ns. The discussion centers on the present method of imputing and calculating the tax liability due at realization. As currently s et the taxpayer face s a uniform rate of five or fifteen percent, depending on level of income, on net reported capital gains. Importantly, this system result s in a different total tax burden for a household that realized ass ets every year and one that deferred their realization for at least one year due to the implicit exclusion of interest owe d on the liability technically accrued during the holding period. We also consider the effect of t he loss offset provision that distor t s investor behavior in that, 6 This attribute has been a popular subject in recent work but, naturally, other perspectives might find other issues with capital gains taxation more serious.

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Nick Frazier, Page 9 through strategic realization of assets, a taxpayer may lower their effective tax burden in comparison to a comparable taxpayer who did not opt for more careful tax planning. We then summarize some of the empirical studies tha t attempt to evidence the mentioned theoretical distortions in market and tax activity. The second chapter introduces an alternate proposal for the taxation upon realization of capital gains developed by Auerbach in his 1991 aptly named paper: Retrospecti ve Taxation of Capital Gains His approach builds on work nominally begun by Vickrey (1939) who initially pointed out that much of the justification for the special provisions in the capital gains tax code, specifically that certain inconsistencies existed with respect to other types of income and between assets, had a better fix in a more even handed and comprehensive treatment of capital gains than expanding more arbitrary preferences Significantly, he proposed that the liability levied upon realization should include the interest on deferred payment of liability. This approach stands in contrast to the current and other popular scheme of taxation namely accrual taxation, where the taxpayer owes liability annually on actual changes in the value of capita l such that upon realization the taxpayer need only account for the change in asset value for the most recent year. Vickrey recommends the averaging of returns experienced by the asset and imputing the approximate tax owed at every year within the holding period and the accumulated interest owed on said liability, all to be paid upon realization. alternate system that would in effect resolve those issues. First of all, where some a ssets do not have readily observable market prices, a good estimation of the average rate of return may be impossible, to the extent in the extreme case which necessitates that the

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Nick Frazier, Page 10 final sales price minus the basis divided by the holding period proxy for t he actual pattern of accrual. This dilemma compounds the second problem wherein for an investor that does not have complete records of annual returns available for an asset that experienced above (below) average returns at some point in the holding period would likely stand to gain by holding (realizing) the asset so as to benefit from a smoothing out of the imputed returns. Essentially, the taxpayer may arbitrage the system by strategically picking the readily observable returns used in the averaging proce ss. Auerbach seeks, in contrast, a system of imputing gains that makes the investor at given point in time indifferent, with respect to their investment behavior, to considerations of previous and future tax owed and actual returns to the asset. To this e xtent, Auerbach develops a proposal that assumes an annual risk free rate of return during the holding period and taxes this return at the statutory rate and imputes the relevant liability owed but ignores the actual pattern of accrual. The advantage of th is system lies in the theoretical economic efficiency provided to the taxpayer and the capital market with respect to taxes. The second chapter contains a formal presentation and some additional explanation to his The discussion also develops formal definitions of economic efficiency as far as investor neutrality with respect to taxation and a short discussion of its unique nature in accomplishing said neutrality. The third chapter co ntextuali greater discussion of optimal capital gains taxation. While under the proposed definition of economic efficiency, his proposal rises as best contender, the general system does ostensibly fail to meet other criteria used in taxation theory to evaluate the optimality of any system. Of

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Nick Frazier, Page 11 concern are issues of equity across assets with different patterns of actual accrual, where the return deviates from the risk free rate of return, and the related concept of horizontal a nd vertical equity on the basis of applicable definition of income, as the increase of purchasing power or consumption during a specified period. We also highlight certain dist ortions of market behavior related to strategic realization and a perspective related to the taxation of property that lends some justification to a distinct ive classification for capital gains income. The chapter includes some of the more recent work publ ished Furthermore, we note the potentially increasing importance of capital gains taxation in the future of the individual income tax system based on recent theories o f income and wealth cycles. The fourth chapter contains a data based comparison of the current system and that relies on estimates of capital gains reported for the tax years 1997 2003 by the IRS Statistics of Income (SOI) division. The effort intends to provide a the most common types of assets and the overall tax revenue raised to give some qualification to the previously discussed differences in the two tax sche me. The chapter also notes and evaluates some important divergences in the alternate tax system and expresses some legitimate concerns of negative consequences for vertical equity across varying level of income. The chapter serves to conclude our discussion of issues wit hin the current treatment of capital gains in income taxation in contrast to the distinctive approach of Auerbach in an attempt to

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Nick Frazier, Page 12 clarify the principles involved and add to the ongoing debate characterized as dynamic compromise shaped by both the economic and political spheres.

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Nick Frazier, Page 13 II. Chapter 1 This paper owes much of its subsequent development of the lock in effect from the familiar models of Auerbach (1991) and Green and Shesinki (1978). In short, the lock in effect occu rs when the investor requires a lower before tax return on the currently held asset than other assets, due to amount to previous gains accrued in the asset over the holding period. This distortion of investment decision behavior occurs because the investor has implicitly decided to defer taxes otherwise due on the accrued gains by not realizing the asset earlier. Thus, we are concerned with assets held for longer than one tax year and primarily with accrued gains representing returns greater than or equal t o the risk free return. Here the rational investor will abstain from realization in certain conditions for tax reasons even though nominally they forego a higher before tax return and inefficiency in portfolio allocation. i. Single Period Model To illust rate, suppose an investor invests in some capital asset with value where signifies the original purchase price, in period (or fiscal year) s The investor sells the asset at the end of every period an d has appropriately balanced her portfolio with respect to her risk preferences. We assume the asset faces a rate of return ( ) in every period and the investor predicts this rate with certainty 7 There fore, the nominal gain, g s at the end of the period would be (1.1) 7 18.

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Nick Frazier, Page 14 which, signif icantly, represents the tax basis were the share realized at the end of this period. Now suppose a single statutory tax rate 8 t applies to all capital gains after realization, we calculate her expected wealth as follows, (1.2) Now suppose the investor considers realizing the asset at the end of the first period and then investing in a different asset with a rate of return, such that at the end of the second period she has (1.3) Should the investor then decide to realize the gains on her asset at the end of the second period, she faces expected wealth: (1.4) (1.5) We may interpret the equation by delineating the first part of the right hand side as the total gain and the second as an adjustment for the taxes paid in the first and second periods. Intuitively we know that a high statutory tax rate discourages investment by diminishing rate of return which we verify with (1.6) where for the relevant values of t between [0,1] imply We may also easily extend this analysis to incorpor ate transaction and compliance costs at realization and re 8 The effective tax rate rarely equals the statutory tax rate in the current capital gains tax system due to the provisions discussed in this chapter and also the possibility of double taxation of dividends and other corporate income.

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Nick Frazier, Page 15 investment by using a rate for as other costs as a percentage of the return 9 At any point, the decision to realize an asset to maximize net wealth will be sensitive and inversely related to the prevailing statutory tax rate. ii. Multi period Model A longer holding period at the date of realization amplifies the distortion created in single decisions. Investors who have repeatedly deferred the realization of an asset with accrued capital gains have effectively postponed payment of the tax liability on those gains and implicitly avoided the interest they would owe in a similar situation in the market. For instance, suppose our investor decided t o defer realization of the asset instead of realizing every period. We assume for simplicity. Thus, the relevant before tax wealth after two periods will be (1.7) g. ta x wealth after two periods as (1.8) or more generally, (1.9) 9 For a comprehe nsive estimate of transaction costs see Condon (1981).

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Nick Frazier, Page 16 To facilitate interpretation, we note the right hand side separates such that the first half represents total gains over n periods and the second half represents the tax liability owed at the end of the n period. In this case, the investor in effect defers paying the tax until the end of the period n. that the taxes are then paid without interest on previous liability owed the source of the incentive to defer realization and payment of taxes. Economists often refer to this f eature Where in an accrual based taxation system households would owe tax liability proportionate to the increase in total asset value, taxation upon realization en tails a deferral of payment similar to that accorded to student loans. The taxpayer eventually pays all liability owed (assuming asset value continuously increases in s ) but benefits substantially by strategic realization. This advantage afforded capital i ncome becomes considerably more expensive when used in conjunction with the deduction of losses and the stepping up of basis such that some capital gains escape taxation altogether 10 iii. General Model Form We extend our development of the lock in effect to a multi or indefinite holding period by considering investor behavior at some arbitrary date s (s>1). Ignoring transaction costs, the rational investor will every period decide to retain the original asset unless the differential between the current a 10 See Poterba (1998) for an empirical study examining the behavior of taxpayers responding to the capital gains tax. He suggests that some avoid the tax but the majority face a positive overall burden

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Nick Frazier, Page 17 return, at least satisfies the condition of indifference where the expected gain from holding the asset equals that of switching for a higher rate of return at the end of the second period: (1.10) The first strategy, then, yields an expected wealth in the second period of (1.11) The alternative strategy where the investor realizes the asset after the first period and re invests simultaneously in a new asset has expected wealth of (1.12) We then may make the strai ghtforward substitution setting 1.11 equal to 1 .12 and solving for an that satisfies the condition of indiff erence: (1.13) In the interest of greater clarity we multiply the right hand side by and note that from 1 .1, or the gains in the first period to see (1.14) Intuitively we see that the denominator represents the expected wealth in the first period using the second strategy or (1.15)

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Nick Frazier, Page 18 Finally, we discern that the numerator also represents the gains expected in the next period without realiz ation added to the taxes paid at realization in the present period such that the required rate of return must equal the return that would occur without realization plus the taxes paid with realization over the net of tax value of the asset in the decisive period or (1.16) Using the insight above, we may generalize a formula for calculating the lock in effect for an asset held for more than one period. For simplicity we assume the rates of return are constant over time for the two asset s. We note that the numerator term and denominator terms in 1.16 closely resemble 1 .9 where the tax has been added in the former and subtracted in the latter producing (1.17) In both cases the adjustment for t is a correction against including the principal amount in the tax base and signifies the return required in the decisive period s. The general solution then follows as (1.18) Once again, in the interest of clarity we perform the o p erations yielding 1 .16 and it follows that

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Nick Frazier, Page 19 (1.19) Immediately we observe that the value of the alternate rate proportionately relates to the original return, but to prove our assertions that the required alt ernate return, increases with a higher statutory tax rate and holding period we seek the derivative of the general case. We find relationship between t ax rate with the derivative of 1 .19 with respect to the t such that (1.20) (1.21) (1.22) Seeing that for we conclude that and strictly increasing for all s since the second derivative follows closely in form. To examine the connection between time and the alternate rate of return we seek the derivative of 1 .19 with respect to s : (1.23)

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Nick Frazier, Page 20 (1.24) (1.25) Noticing that and for leads us to deduce a nd a look at the second derivative bears out that the first derivative strictly increases for all s These findings confirm the advantage of deferring re alization increases over time, theoretically creating entrapment by a lock in effect mitigated or exacerbated by changes in the statutory tax rate. The model derived here describing the potency of the lock in effect as accumulating over time finds only the exact alternate return required to recuperate losses in a single period, thus an investor with a perspective beyond the next period would require a substantially lower alternate return. However, such a strategy does partially commit the investor to a long run strategy where a short term and more flexible approach may increase efficiency and profitability. Furthermore, any commitment to a long term strategy inevitably recommits the investor to the previous entrapment in the lock in effect. Thus, in both the short and long term, the tax rate works to lock in capital into an asset and discourage switching to a more profitable asset and the creation of a more efficient portfolio.

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Nick Frazier, Page 21 iv. Empirical Evidence A considerable body of theoretical and empirical work on t he lock in effect and other investment behavior distortions exists in the fields of finance and economics. Essentially the studies aim to evidence the degree to which the relevant capital income taxes affect portfolio allocation, asset pricing, and realiza tion behavior. Most studies indicate that taxes are not irrelevant to the asset markets, though certainly no consensus exists as the magnitude of that effect. Zodrow (1995) provides a comprehensive review of important studies and various proposed alternati ve systems, noting in particular, the deficiencies in empirical studies but a trend towards an effect with significant magnitude. Brown and Nichols (1969) represents one of the earliest studies to directly address the lock in effect. They postulated that i lock into a higher tax bracket with greater accumulated gains later in their investment horizon. Consequentially, then, t hey noted that the elderly and households facing the highest capital gains tax rate would face a significant distortion and provide a summary of various perspectives and historical responses to this issue 11 Since their study, the subject has been given con siderable attention in financial and tax theory journals, though its overall direct inclusion in policy decision remains minimal. The majority of research concerning the lock in effect has been time series or cross sectional analysis of tax return data pr ovided by the Internal Revenue Service. Dyl (1977, 1978) first empirically evidenced that households engaged in strategic realization as a response to the capital gains tax both in the timing within year and the type of asset 11 Interestingly, Brown and Nichols (1969) proposed allowing households to deduct capital gains taxes

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Nick Frazier, Page 22 (re: short selling). These res ults were supported by Yitzhaki (1979) who found that capital gains tax rates effectively reduce the rate of return on stocks for high income households which established that the presumed arbitrage of short selling and strategic realization to escape capi tal gains tax did not hold for the predominant holder of capital assets. The first study to evidence the sensitivity of corporate stock sales and overall realization of capital assets to capital gains tax rates, Feldstein, Slemrod, and Yitzhaki (1980), use d the IRS data for tax returns in 1973. Their study initiated the trend of estimating an elasticity of realization with respect to tax rates that became the dominant approach until recently. This methodology has produced results with significant variance, summarized by Zodrow (1995), contingent on a time series versus panel study and the period studied 12 In accordance with the demonstrated variance, considerable attention has been afforded the deviations in estimated elasticity. In particular, Boskin and S hoven (1980) build upon similar studies estimating the elasticity of saving to the capital gains rate, which they find to be significant and negative, to argue for the elimination of capital gains taxation to improve market efficiency. Burman and Randolph (1994) suggest that much of the deviation relates to the focus on temporary versus permanent changes, where temporary changes tend to be large whereas permanent changes tend to be close to negligible 13 Consequentially, they caution that the interference be tween the two compromises any estimation or other results from the above studies. 12 Auerbach and Poterba (1988) provide a detailed analysis of the deficiencies and correct adjustments for estimation of the elasticity of realization. 13 A conclusion supported by Auerbach and Poterba (1988).

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Nick Frazier, Page 23 Contemporary inquiries have sought to address the complication of interference by changing the approach away from estimating the elasticity of realization towards that of eva luation of two complementary effects that of capitalization and lock in. Dai et. al. (2008) directly addresses this approach as being able to separate the long and short term behavio r changes (respectively). Their study presents a regression analysis on ma rket prices and realization behavior during the natural experiment of the Taxpayer Relief Act of 1997 (TRA97) where the statutory capital gains rates were reduced. We expect the assets with a more favorable treatment to experience capitalization, or a mark et wide price adjustment, relative to the new pricing. Thus, as Dai et. al. finds during the week before the TRA97 became effective, asset prices increased as demand shifted upward, reflecting the new expected relevant rate of return. Dai et. al. also foun d evidence of a lock assets so as to qualify for the new lower rates and realized a large total value of assets. Since he studied investor behavior on the cusp of change, Dai et. al. concluded that both effects exist at a change in tax law but that the general result of the change, as to which effect dominates the other, depends on the time period or types of assets involved. Ayers et. al. (2003) also stands out among thi s group as a regression analysis on asset prices and statutory capital gains rate during the period 1975 to 2000. They find evidence of premiums for taxable asset acquisitions in relation to non taxable acquisition suggesting that firms bid for investors a nd thus compensate for individual who face a capital gains tax. Their results suggest that the market does internalize the cost of the lock in effect into the market price in the long run and therefore evidences capitalization of this distortion cost a pos itive permanent effect for changes in tax rates.

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Nick Frazier, Page 24 Shackelford (2000) presents similar conclusions in an empirical analysis of TRA97 and the Internal Revenue Service Restructuring and Reform Act of 1998 (IRSRRA98). His results demonstrated a reaction in gene ral asset pricing to both the change and in the capital gains rate and news concerning the likelihood of changes in the tax policy. He found a material magnitude of adjustment in the market prices for capital assets and that such adjustments were complete by the final announcement of the enactment of the legislation. He also provides a detailed summary of other work concerning the TRA97 and the IRSRRA98 all suggesting that the legislated changes in tax policy caused significant repercussions in the asset ma rket 14 A related line of recent research has been into the modeling of microeconomic decision behavior for household portfolio building. Klein (1998) develops a coherent asset pricing model that incorporates the horizons of other investors and transaction costs in short term selling to show that the present evaluated price depends on the accrued capital gains in the presently held assets and the overall horizon of the investor. His results demonstrate the trade offs that occur especially for retired and ol der households where the accumulated gains may be large and the horizon can be relatively long or short depending on bequests or other circumstances. Klein (2001) builds on these results and runs a regression analysis on a cross section of assets with a lo ng holding period and finds evidence of a significant lock in effect that causes investors to accept lower returns from assets with large amounts of accrued gains. Balcer and Judd (1986) note similar results from a theoretical perspective. Their work sugge sts that the current tax system 14 The findings of Blouin, Raedy, and Shackelford (2003), in their regression analysis on the S&P 500 for tax based distortions, support this conclusio n. Here, characteristic of these studies, many of the actual estimates are modest in their significance, but seem to defy other plausible explanations.

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Nick Frazier, Page 25 distorts the decision to hold debt versus equity, changing in proportion over the lifetime of the household, and that the result would hold even for a nominally flat income tax implying the importance of tax considerations i n efficient portfolio allocation. They, in particular, are also interested in developing an estimated effective accrual tax rate for the current tax system but find that, due to the distortion of consumption and saving equilibriums, specification of a sing le rate is unlikely. v. Step up of Basis Another important qualification concerning the lock in effect in the current tax system arises especially when considering long term gains and dynastical wealth. The step up of basis for inherited capital assets p resents a substantial potential disincentive to efficient investment behavior. Suppose a taxpayer with a large portfolio begins planning estate will not trigger the estate tax or the related gift tax and that they maximize utility relative to their total wealth. When contemplating the planned bequest, the taxpayer will weigh present consumption against the consumption of future generations. We specify two periods, s and s+ 1 to denote the current generation and the future generation and assume that the present generation has some interest in or utility from a bequest to the next generation following the model originally developed by Barro (1974). Here, w e implicitly assume the bequest is not entirely accidental which seems reasonable for the amount of effort given to estate planning for the current tax system. Thus, we identify a temporal consumption function, another function that maps an investo bequest motive, h ( j ), and an error term, to account for other considerations, such as

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Nick Frazier, Page 26 transaction and compliance costs, such that the calculation for the net utility for a bequest follows from (1.26) w here we expect However, because upon inheritance, the beneficiary may take the total applicable value of the asset as the new basis (having a tax liability of zero if realized within the same fiscal year), we propose that a wealth and utility maximizing recipient should make payments up to the present tax liability to the benefactor 15 The present generation benefits from increased consumption and a bequest while the future generation either gains or i s indifferent (ignoring any utility derived from payments to previous generations for simplicity). Thus, we observe (1.27) where We immediately notice the potential for a substantial distortion in the beha vior that would otherwise occur without the stepping up of the basis and suppose that if the payment aforementioned were made in lump sum, the benefactor would continue to 15 For empirical evidence of such retrospective inter generational transfer see Bernheim, Shleifer, and S ummers (1986).

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Nick Frazier, Page 27 garner annual payments of until the bequest assuming th e portfolio earns a return greater than zero. Finally, we note that the step up of basis radically changes the calculation of the lock in effect for taxpayers engaged in planning a bequest. Here all the assets in the portfolio generate untaxed dividend dis tributions as long as the asset is unrealized and the federal government forgoes almost all revenue from the assets, extending substantial tax expenditure to a certain subset of likely wealthy taxpayers. Due to the nature of the records the IRS collects, a definitive empirical study on the step up of basis would be difficult at best. However, the sunset provision from the Economic Growth and Taxpayer Reconciliation Act of 2001 (EGTRA01) represents a natural experiment with the potential to generate usable empirical data. In the fiscal year 2010, the estate tax will effectively be repealed but the basis for all asset bequests will the property at the date of the deced 16 The issue of relevant interest, then, households subject to the estate tax as stipulated before EGTRA01. Assuming they can plan the date of their death, such households have a choice between transferring the basis to the next generation and the related capital gains tax liability and paying the estate tax in 2011. Conversely, for households with assets but not subject to the estate tax, they will face a st rong incentive to not die until 2011 so as to avoid leaving a bequest subject to capital gains tax. The resultant consequences on household behavior and tax planning could create significant patterns in the asset market for the three relevant tax years 200 9, 2010, and 2011 and will likely generate considerable academic interest. 16 U.S.C. § 1022 (a)

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Nick Frazier, Page 28 III. Chapter 2 We begin by outlining a tax schedule and scheme for capital gains that eliminates the deferral and realization strategies that distort investor behavior in the curr ent tax system. We define such a scheme as holding period neutral with respect to the investment decisions where the decisions to retain or realize the asset are independent of the length of time held and previous pattern of gain accrual. We then offer an exponential function that when used to impute the growth of tax liability over the holding period satisfies holding period neutrality on an ex ante basis or before the actual asset yield for the relevant period is known. To achieve the described holding pe riod neutrality for any given period, the function developed to compute current tax liability must have a derivative that meets two separate requirements. The increase in tax liability for a given fiscal year must be equal to (1) the interest owed on defer red payment of liability for previous gains and (2) the increase in tax liability attributed to gains during the current period. Importantly, as discussed earlier, the former requirement is not met by the current system and the second becomes a function of the holding period and pattern of returns Since the relevant function will necessarily be sensitive to these imposed conditions and its holding period neutrality contingent upon their satisfaction, they merit a discussion. The relevant interest rate on d eferred tax liability should be equal to the opportunity cost to the government of the accrued but unre alized tax liability, which at minimum is the risk free market rate of return. However, because the presumably the federal government does not owe income tax, the rate must be adjusted to be the risk free

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Nick Frazier, Page 29 market rate of return net of tax, or ( 1 t)i Should the government charge their whole opportunity cost, i the taxpayer will be forced to realize their asset annually to avoid accruing interest or assum e some risk to cover the share owed as taxes and result in distortion of investment behavior. To see this effect, consider a n entirely risk averse investor who purchases an asset and after every year purchases another complementary asset equal to the incre ase in tax liability for the original asset. All the complementary assets would have yields equal to (1 t)i and thus every year the investor deferred realization on the original asset, her accrued interest owed on previous liability is ti greater than the value of her complementary assets. Thus, in the interest of efficient taxation, the government should charge a rate of return equal to the risk free and after tax market return, removing both government arbitrage and profit from deferred realization and th e behavioral distortions. n ex ante approach to achieve indifference from an investor standpoint to the increase in tax liability for current gains. Since we hold that knowledge of the pattern of accrual at realization is bey ond the informational capacity of the government or the investor, the calculation of tax liability must be based on equality ex ante By defining the framework for our analysis on an ex ante basis, we choose to impose an effective tax rate that is uniform across all assets before the actual gains in the period have occurred as distinguished from an ex post basis in which the latter would entail an increase in tax liability directly proportional to the actual gains realized in the current period, similar to the system proposed by Vickrey (1939) 17 The accrual in any period would in either case be subject to the same tax rate legislated for capital gains. 17 A discussion of the repercussions in ex ante and ex post framework on overall equity follows in Chapter 3.

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Nick Frazier, Page 30 equal to what the inv estor could expect from the risk free rate of return while excess gain is taxed at a lower rate. We denote the instantaneous return as the risk free rate of return i and the reward to risk, accounting for any deviation from the expected return. From a n ex ante perspective, represents an unknown adjustment conditioned on the expected minimum return for the investor. In order for to realistically be conditioned on a risk free return we assume that the entire set of investor portfolios and capital mar ket automatically adjusts to balance d at all times, relative to risk preferences and avai lability of appropriate assets. The value of basing tax liability on ex ante decisions arrives in the low informational requirements imposed upon the government and th e investor. The government assumes that the investors adjust their portfolios to earn at least the risk free rate and therefore can assess tax liability based on that certainty of that return. The investors manage their portfolios without the distortion of multi period tax planning and are only required to report the final sales price upon realization. The government need only observe the instantaneous rate of return for risk free assets for the period and the reported asset value at the end of the period t o calculate the increase in tax liability. Contrasted with the current system which requires basis, holding period, and asset value considerably lowers the information distortion, and compliance costs.

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Nick Frazier, Page 31 ex ante we introduce some valuation operator 18 V( ) which converts the uncertain distribution of returns, i +e to their certainty equivalent returns from the ex ante perspective of the investor. Thus the valuation operator assesses the expected rate of return adjusted for risk which will always be at least equal to the risk free return. We implicitly assume here that the market investors attempt to maximize wealth within risk preferences The government by basing its imputation of tax liability on the observed risk free rate for the holding period when the asset in realized, does not have to observe actual changes in asset value nor the actual drift rate for the asset. To demonstrate the first define sufficient conditions for holding period neutrality and then establish that If we define the total tax liability generated by an asset at date s as T s, we effectivel y wish to demonstrate that the change in tax liability, T s+1, as anticipated by the investor is holding period neutral, or independent of holding period and the pattern of accrual. We assign t as the relevant capital gains tax rate, A s as the value of the asset at s and i is the risk free rate of return, and propose (2.1) where the increase in tax liability is based on ex post knowledge of the actual gains at r s, the rate of return, for the asset at s and T s is equivalent to the previous tax liability assessed i(1 t ) where the government would obtain r s for all s to calculate the accrued tax liability. As a 18 The mechanism of this valuation operator is not addressed in this paper though Auerbach presented general qual ifications in an early draft of his 1991 paper, see Auerbach (1991) footnote 3.

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Nick Frazier, Page 32 matter of clarification the present model approaches s as being discrete in fiscal years, in line with how taxes are imposed on an annual basis. The Auerbach model will be presented in a continuous time framework which is more realistic with how investm ent behavior occurs but both models effectively hold for either framework and the difference is predominantly notational. We further assume that the investor will require at minimum the same return, adjusted for risk, on any capital asset as they would on a risk free asset ex ante So, (2.2) and applying the valuation o perator to equation 3.1 yields (2.3) ex ante T he increase in liability equals the sum of the interest on the unpaid liability and the new liability on accrued gains during period s, independent of actual gains and holding period, and is therefore holding period neutral. If we take net of tax value of the asset as and assume that the rational investor will seek out at least the net of tax risk free rate of return, i(1 t), it follows that: (2.4) and so the before tax value of the asset will be: (2.5) Therefore, investors are indifferent to the risk free interest rate when considering tax. However, yet to specified is the function, which can effectively calculate tax liability retrospectively wi thout behavioral distortions.

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Nick Frazier, Page 33 (2.6) satisfies this requirement. The derivate of with respect to time is (2.7) (2.8) (2.9) and thus (2.10) Where represents a random re turn satisfying and (the risk (2.11) (2.12) where and such that

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Nick Frazier, Page 34 (2.13) or 2 .3, thus proving holding period neutrality for this taxation function. To explain the process we observe (2.14) (2.15) Here the first term represents the tax liability due to interest on the previous liability. The second term represents the tax liability due to excess return (taxed at the rate ) The third term represents tax rate on the gain in peri od s that accrues no liability due to interest. Thus the taxation breaks down into the imputed taxation of interest accrued on unpaid taxes for the previous gains for both the risk free interest and then on any excess gains plus the taxes accrued in the pr esent period. Furthermore as holding period, s, increases, decreases which entails that the total tax liability increases in s This aspect of the function is what lends it its multi period holding period neutrality. A formal pr period holding period neutrality involves demonstration that tax liability at the end of some period is the same regardless of realization strategy. Once again the proof works from the perspective of the investor ex ante expecting certainty equivalent normal returns. We suppose the investor may choose between strategies: (1) realize an asset at s 1 and then immediately repurchase the asset and realize again at s 2 ; and (2) where she holds the asset and realizes the asset at s 2 In th e former case she faces a tax liability at s 1 and s 2 equal to (2.16) and in the latter case she faces the regular liability

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Nick Frazier, Page 35 (2.17) We now hold that this tax scheme is time independent and thus that (2.18) (2.19) (2.20) 1 and s 2 is (2.21) which we may solve for and substitute such that (2.22) (2.23) We also note the possibility of retaining special tax treatment of certain types of income which has been used to cite the deferral as positive tax expendi ture for encouraging capital investment. Suppose we introduce a preferential rate for capital gains income as opposed to regular income, as exists i n our current system. The opportunity cost of investm ent in a system with a universal tax rate, is equal to i whereas with a preferential tax rate, it is now and for the opportunity cost for investing in capital gains is now lower encouraging investm ent. Our relevant tax liability must then be

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Nick Frazier, Page 36 (2.24) And, similar to 2 .11, the expected increase in tax liability: (2.25) The new effective tax is discounted where gains are taxed with respect to the capital gains rate while interest is char ged on unpaid tax liability at reflecting the correct opportunity cost to the government of deferred realization. We note here that differences in and will cause variation i n the composition of portfolios as investors seek to maximize the trade off between risk and return. Based on dissimilar opportunity costs driven by effective tax rates, two investors may evaluate risk premia differently for the same asset. For a more comp rehensive discussion of how the market will still achieve efficient equilibrium see Auerbach and King (1983). Finally, we demonstrate a useful capacity of the system that makes it generally applicable to current markets in that it can retain its efficient properties when the asset realized produced cash distributions at previous dates. Where dividends are payments from assets with arbitrary patterns of cash flows apart from capital appreciation and the household holding said asset must pay the tax due on t hem concurrent with the receipt of the distribution. To be time independent, we must suppose that dividends represent capital appreciation that is partially realized and thus the household pre pays part of the tax and therefore no imputed interest should b e accrued by those payments apart from the

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Nick Frazier, Page 37 gain since they represent part of the capital appreciation and thus part of the applicable rate of return. To prove thi s assertion, suppose an asset at s sheds cash distributions, D s making s such that any transaction costs involved in holding, selling, or purchasing an asset are tantamount to negative distributions as well. For the investor to be holding period neutral their perceived ex ante liability sh ould be (2.26) where the liability equal to interest on unpaid liability and increased liability on new accretions, as before, and less any payment now made in s From 2 .4 we can see (2.27) which suggests that dis tributions are in fact partial realizations that if subject to a different tax rate should be a candidate for the differentiated tax rate treatment demonstrated before. Auerbach proposes an alternate tax scheme, (2.28) that effectivel y taxes the entire asset and then credits back the interest and taxes for period neutrality see Auerbach (1991).

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Nick Frazier, Page 38 IV. Chapter 3 ion of capital gains ultimately seeks to amend certain structural failures in the current system. He retains the retrospective approach agreeing with the consensus view that (1) paying taxes annually on recorded accrual represents an unfair burden on some taxpayers who have a predominant share of their wealth tied up in assets and also that (2) the informational burden required by keeping annual records of accrual to be disclosed upon realization discriminates against certain assets that do not have regular ly observable market values and taxpayers who are otherwise unable or unwilling to retain such records 19 His proposal addresses the same difficulty in retrospective taxation as the current system, though with a decidedly different approach. Where the curre nt system requires the taxpayer provide the purchase an d sale s price ( with adjustment of basis) and levies a single rate on that defined gain, the alternate proposal requires the final sales price and the holding period, ascribing at least risk free return to asset and taxing accordingly. Fundamentally, both of the systems weaknesses and strengths reflect the type of information compelled from the taxpayer. i. Ex Post Equality tal equity in the uniform taxation of ex post capital gains. The current system by definition 19 The current tax system also discriminates against taxpayers without the basis of the asset in that the purchase price is included in the calculation of tax liability.

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Nick Frazier, Page 39 solves this issue by levying a single rate on reported gains, though notably not without certain distortions like the exclusions of gain for the sale of a primary residence and the carryover of long term losses. The holding period neutrality for ex ante decisions, a notional response to the theoretical distortions created ex ante by the current system, arrives at a cost of uniform taxation on basis of ex post gain s, or deviations from the risk free return. The most accessible explanation of how deviations can occur relies once calculates the portion of gains retrospectively using the risk free rate of return independent of actual drift rates and returns for the asset. The results would play out such that assets that experience exceptional returns will pay a lower effective tax rate on the portion of gains than in the current tax syste m. The opposite will occur for assets with sustained below risk free returns where the imputed return will be higher and the original asset value will be assumed to represent gains and thus be partially taxed. To bear out this deviation in effective rate s we equate the two tax systems. To to equal that of the ex post rate current system, we begin with (3.1) and bo rrow our earlier notation that g is the percent of gains in the asset such that (3.2) (3.3)

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Nick Frazier, Page 40 Here we can see that the statutory tax rate required is inverse to the holding period and the risk free interest rate a nd directly related to the percent of gains included in the final sale price. As such, a risk free rate of return that does not accurately reflect the overall hold ing period. Ironically, this exact issue in retrospective taxation is eliminated under a Vickrey like system, illustrating the complex negotiation of feasible taxation. Menoncin and Panteghini (2009) address the failure of ex post equality concisely by d eveloping a continuous categorically fail to satisfy horizontal equity differentiated on rates of accrual different from the risk free rate. The result furthermore proves that a s ystem that could provide such equivalence would necessarily require past prices and therefore subject to the same flaw as a Vickrey like scheme. They, in particular, specify that such a system would be a state contingent tax that used the same mechanics of the proposal to calculate liability but adjusting the interest rate to reflect the state of the asset or differences in the pattern of period neutrality but at a cost of considerably higher complia nce cost in information required. Auerbach (1991) admits the merit of such a critique but also notes that ex ante equality should not be dismissed as basis for horizontal equality. He notes that, even with a known pattern of accrual, tax liability could b e owed on a capital loss by virtue of interest on deferred liability. He cites an example where an asset purchased for one dollar that increases to two dollars at the end of the first period and to ninety nine cents by the end of the second would owe liabi lity under any condition where the net of tax interest

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Nick Frazier, Page 41 rate is greater than one percent 20 system with respect to the ability to pay criteria, if not the overall premise of income taxation, in that a cap ital loss would still be assessed tax liability. For an investor with an appropriately adjusted portfolio, we would expect that such a loss would automatically be offset by other diversification; however, investors who experienced capital losses and no oth er gains to offset that loss, would still owe tax liability assessed on their final sale price, despite the lack of actual income generated. This concern is somewhat mediated by the observation that even in the current tax system, where assets bearing net losses should be realized immediately, reported gains on income returns far outweigh the reported losses, even in poor markets. Furthermore, presumably, a comprehensive or epidemic increase in the ratio to the absolute value of losses to gains should be r eflected in the risk free rate for that period as investors adjusted their portfolios to new market conditions as suggested by the results reported in the next section Once again, though, certain types of assets are not easily liquefiable in a systemic ma rket correction, for instance, property and certain portfolios could suffer serious transaction costs when trying to adjust to sudden market deviations. Ultimately, this aspect deserves weighed consideration over its consequences for vertical and horizonta l equity. ii. Wealth Taxation Perspective One possible mitigating understanding of the equity of assumed return for capital offered by Auerbach is that of the perspective of wealth taxation. By changing the point 20 From Auerbach (1991) footnote 12.

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Nick Frazier, Page 42 of reference from income to wealth taxatio that the equity concerns reverse for taxpayers with rates of return deviating from the risk free rate. The idea develops along the lines that the overall principal represents initial wealth taxed at a rate of ti p er period where the tax liability depends on the initial value of the investment. An asset that experiences sustained greater than normal returns will have an imputed initial value greater than actually existed and have a higher imputed annual increase for interest and thereby a higher tax liability. The opposite would occur for an asset with sustained lower than normal returns. While from the perspective of income taxation, the high yield asset has a lower effective tax rate on gains, a wealth tax perspect ive would hold the opposite high yields face a higher effective rate than lower yields. Here, higher than normal returns face the discrimination attributed to lower returns before. The justification for such a perspective offered by Auerbach is that of pro perty taxation, the predominant source of income for local and state government. His argument follows that the inequality present in ex post taxation of capital gains holds true in ex post wealt h taxation as well. To extricate the idea, consider four conti guous houses, A, B, C, and D, with the following constant and respective rates of return .03, .06, .06, and .09 over a period of three years. Suppose furthermore that all three houses are worth $100,000 at the beginning of the first period and that this pr ice is readily observable to the tax assessors. The local government levies an ad valorem property tax set at twenty percent of the projected annual .06 percent growth rate for the next three years (so as not to discourage investment by consuming the annua l return). Finally, suppose that on the third year, house C and D sell for the full value and the local assessors then use that basis

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Nick Frazier, Page 43 to adjust the market value of all four houses using a simple average. So we may illustrate the tax burdens of the three ho uses as follows: House A B C D Year Value Tax Value Tax Value Tax Value Tax 0 $100,000.00 $1,200.00 $100,000.00 $1,200.00 $100,000.00 $1,200.00 $100,000.00 $1,200.00 1 $103,000.00 $1,200.00 $106,000.00 $1,200.00 $ 106,000.00 $1,200.00 $109,000.00 $1,200.00 2 $106,090.00 $1,200.00 $112,360.00 $1,200.00 $112,360.00 $1,200.00 $118,810.00 $1,200.00 3 $109,272.70 $1,200.00 $119,101.60 $1,200.00 $119,101.60 $1,200.00 $129,502.90 $1,200.00 4 $112,550 .88 $1,491.63 $126,247.70 $1,491.63 $126,247.70 $1,491.63 $141,158.16 $1,491.63 Sum of Tax $6,291.63 Tax/Total Value 0.056 0.050 0.050 0.045 Fig. 1 By calculating total tax burden as a percentage of total wealth we can see that, ex post, the house with below (above) normal returns suffers a higher (lower) burden than those experiencing the projected returns. Despite a theoretical soundness to the assessment of a property tax contingent upon expected growth, without observing the act ual accrual pattern, horizontal equity is impossible under the condition that all houses do not face uniform rates of return. However, the pervasiveness of property taxation in the United States creates a strong argument that advantages in ex ante equality and administrative ease may outweigh concerns of ex post equality. iii. Step up of Basis The step up of basis on bequest of an asset represents another serious concern in effect genera ted by the step up of basis in 1 .27 but in contrast the applicable tax rate will

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Nick Frazier, Page 44 likely now be greater than the current long term statutory rate of fifteen percent, increasing the overall advantage of deferring realization to the next generation. Th us, (3.4) where the conditional equality of the effective rates fro m the two systems applies from 3 .3. Assuming the general set of assets affected by the step up of basis represents long term gains, we expect that the lock in effect created by deferring realization to the next generation will increase under the alternate tax system ceteris paribus We also implicitly assume that the set of assets modeled would not qualify for the estate tax which in the present system recaptures some otherwise untaxed income from particularly wealthy estates 21 While recently the trend in tax policy has been to reduce liability for wealthy up of basis. Much of the complication from documenting the basis and necessary adjustments to the basis for assets that undergo intergenerational transfer evaporates by reducing the required documentation necessary to the accumulated holding period for any a nd all holders of the asset. This system removes some of the justification for and may work well in place of the estate tax, as well, by carrying over imputed liability, though wealth not contained in unrealized assets, otherwise included in gross estate, would escape taxation. The metric of applicability would be to determine the share of gross estate not tied up in assets for households subject to the estate tax. 21 The current system applies a statutory rate of 45% to taxable estate above $3,500,000, however, for 2010 the relevant statutory rate is temporarily zero and rises to 55% on January 11 th 2011.

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Nick Frazier, Page 45 iv. Risk free Rates of Returns ssumption of an observable risk free rate of return. In practice the actual specification of how to observe a 22 and risk free rate rests beyond the scope of this paper and interested parties should see the considerable attention given to it in finance journals 23 To qualify the free rate, we address two fundamental concerns: (1) that a risk free rate remains independent of the risk adjusted rates and (2) that all assets are not subject to the same annual rate of return. As mentioned above, Auerbach explicitly assumes that the risk free rate of return is deterministic and posits that the scheme would retain its holding period neutrality for 24 As pointed out in Hess an d Kamara (2005), even Treasury bill rates, the traditional bench mark for a risk free rate, may contain some risk premium for relates to the implicit assumption that the risk free rate conforms to a random walk, such that it is serially uncorrelated. In fact, Fama and French (2004) assert a lack of empirical directly address this aspect i n the construction of their continuous time model by proving 22 Beta, here, is the correlatio n of the particular rate with the general market. A zero beta rate is uncorrelated with the market, while a positive (negative) beta has a direct (inverse) price relationship. 23 For instance, for a discussion of the difficulties in defining a risk free spo t rate see Yuan and Savickas (2009 ) or Hess and Kamara (2005). 24 Auerbach (1991) footnote 2.

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Nick Frazier, Page 46 that the risk period neutrality. Of particular concern, as well, is the likely impact of fiscal and monetary policy on market retu rns, generally, as a taxpayer would be wise to be suspicious of a tax authority that can set the tax rates and have an endogenous effect on taxed returns. However, these concerns relate to the current tax system to varying degrees as well. The emergent sig nificance, then, lies with the degree of care requisite in specifying an appropriate risk free return. The second concern confronts the heterogeneity of the capital market in the United States such that a single risk free rate may poorly reflect the divers ity of assets and returns possible. During the development of the model, we assumed a market in equilibrium where possibilities for arbitrage or regional and/or sector related deviations in the market rate were ruled out by balanced portfolios and sufficie nt knowledge. However, even under the unrealistic instantaneous adjustment assumption to an exogenous shock to a localized asset market, we note that transaction costs and differences in preference structures among investors will likely create losers and/o r winners. To address this situation would seem to require a more discretionary approach to assigning an interest rate. Such discretion, though, comes at a cost of administrative ease. v. Discretionary Tax Policy The current tax code undoubtedly already c ontains discretionary allowances and tax expenditures to account for the diversity of situations amongst taxpayers. For instance, the Midwestern Disaster Relief provisions from the Heartland Disaster Tax Relief Act of 2008 specify tax breaks to residents o f certain states that were strongly

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Nick Frazier, Page 47 affected by the unusually destructive natural disasters during late May to July in 2008. The provisions include tax incentives regarding charitable donations to that region, retirement account contributions, education cr edits for qualified expenses, and the deduction of clean up costs. They also contain direct tax relief for the replacement period for non recognized gains, net operating losses, and the cancellation of debt (IRS Publication 4492 B) that would not apply to non designated regions. The economic toll on the region seems to qualify as an exogenous shock like that described above and somewhat compensated by discretionary tax policy. The ultimate applicability or feasibility of such discretionary decisions in re lation to adjusting the risk free rate would lie with empirical trials. One particularly difficult obstacle emerges in avoiding behavioral or market distortions in a multi period policy. The likelihood of creating expectations that the government must, rat her than can, use tax policy to respond to a situation may cause legislated relief for capital gains whether or not such provisions represent effective vehicles for delivering relief. However, the ability to effectively vary the tax rate and imputed rate o f interest represents an important facility as relief would likely arrive in the form as a partial exemption of gains such as that for small business qualified stock sal es or, like the Jobs and Growth Tax Relief Act of 2003, an overall cut in applicable tax rates. Especially in the latter case, in which the 15% long term capital gain rate rises to 20% at the end of 2010, the temporary nature of the reduction in rates will clearly cause distortion in multi period investor behavior, as allows for a lasting effect of such tax provisions, a lasting memory, so to speak.

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Nick Frazier, Page 48 vi. Lasting Memory The function defined in 2 .6, though alluring in its simplicity, does not sufficiently account for a case when either t or i varies in s The extension relies on defining two functions f(i) and g(t) that account for such variation. Presumably, due both to seri al non correlation and exogenous factors, neither of these two functions could be specified as a continuous and likely will best be described as piecewise. To begin we may propose f(i) maps the historically observed risk free rates and hold the tax rate co nstant on s and that we calculate the tax liability for an asset realized on s as (3.5) The tax liability calculated in 3.5 is demonstrably the same as 2 .6 where f(i) does not vary in s The extension, then, from 3 5 to inclusion o f a varying tax rate requires an adjustment for the term but otherwise follows: (3.6) That the scheme retains its holding period neutrality should result from treating f(i) and g(i) as constant and the earl ier proof for 2 .6.

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Nick Frazier, Page 49 The significance of the capacity to retain changes in both relevant risk free rates and statutory tax rate changes arrives as an improvement in horizontal equality. Where the current tax system has no memory and thus any statutory change s introduce an elasticity of realization on the cusp of the change (including fiscal year to fiscal year) 25 triggered by tax reasons 26 Taxpayers would still benefit from su ch favorable provisions despite realizing their asset after the designated expiration date. This capacity of the scheme allows for more efficient, in economic terms, behavior in investment and greater horizontal equity on a time continuum comparison, both gains over the current system. behavior does not adjust accordingly, the pr ojected cost analysis of such relief provisions at enactment would seriously underestimate the true long term cost. We could certainly estimate the spot cost of the provision by multiplying the applicable risk free rate for the relevant years and multiply them by the total value of capital assets that will eventually be subject to the tax; however, that the total value is deterministic is a questionable proposition. This difficulty is compounded by the added cost of the interest lost to that relieved liability that could be calculated only if certain assumptions where made to the eventual realization date s of the various portions of the total asset value outstanding. Thus, the economic efficiency gains may increase administrative costs appreciably. 25 See the discussion of Dai et. al. (2008) in Chapter 2. 26 Balcer and Judd (1986) note that the income effects for an accrual tax outweigh those for the current ta x system making it a potentially more effective tool for tax policy for social and economic ends

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Nick Frazier, Page 50 The informational burden on the taxpayer would not change but certain other compliance costs would be imposed by the expansion of the scheme. The difficulty of immediately calculating the tax liability exists within the original scheme represented in eqn. 2 .6 but faces a considerable increase in eqn. 3.5 as it requires an understanding of integral calculus. Furth ermore, the tax tables available for calculating ordinary income would be unwieldy if t and i varied significantly between tax payers since they would have been computed by holding period and the ability to average would depend on s as the effective tax r ate grows with increasing elasticity. While arguably capital gains would be concentrated in households where a paid preparer is used, even then the burden is only slightly shifted to concentrate it among a certain subset of the population. This burden coul d be lightened to a large degree by the use of some computer application or software, even supplied for free by the IRS, that could calculate the appropriate tax liability, but certainly some taxpayers would suffer heavier compliance costs 27 To even approa ch a rough estimate for an appropriate cost benefit analysis would require extensive research and is beyond the scope of this paper. vii. Vertical Equity effective capital gain s tax rates on assets that have long holding periods and represent good candidates for a lock in effect and also a significant loss of tax revenue for the U. S. government. We may reasonably suppose that households waiting to realize assets after a long ho lding period have either available liquidity or a preference for saving. We can also 27 An example of how the IRS could lower compliance costs is the goal set by Congress to achieve an 80% e file rate among U.S. tax payers (which was at 60% in FY2008) (Advancing E file Study Phase 1).

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Nick Frazier, Page 51 infer that such assets signify either wealth or high income in the former case or retirement savings in the latter. A high income household that manages to receive a predo minant portion of their income in long term gains will necessarily receive a more favorable tax treatment than a similar household that relies on wages, due to the difference in ordinary rates and capital gains rates 28 Solid arguments exist for both the el imination and the extension (see the Flat Tax) of this special treatment and, due to the complicated issues of economic efficiency and equity involved, is unlikely to be resolved in the near future. If we posit that any dynastical wealth that derives a sub stantial portion of its annual income from capital income and gains, represents profiteers from the windfall given long term capital gains and nominees for a higher burden in a progressive tax system, given the smaller share of earned income, then the degr enhance vertical equity and progressivity merits an examination. Unquestionably, high income households receive the majority of capital gains income as a group. For instance, between 1999 and 2003, households that claim ed $10,000,000 or more in adjusted gross income represented less than .05% of all tax returns but had an average of 30% of all capital gains claimed during that period (SOI Tax Stats). However, that the majority of gains rest with the high income household s does not prove that it represents an effective vehicle for progressive taxation. Rather such an assertion requires that capital gains correspond to a substantial portion of their total taxable income. Thus, if the majority of their income comes from wage s, wages would be the more effective vehicle for progressive taxation. One difficulty lies in the nature of 28 At the writing of this paper, this conclusion will still hold in 2011 for every ordinary income bracket above 15% at the new rate of 20% for long term gains. The 15% ordinary income bracket will actually experi ence a higher statutory rate of 20% (instead of 0%) for capital income.

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Nick Frazier, Page 52 capital gains realization, in that, as Feenberg and Poterba (2000) show using Statistics of Income data, households that rely on capital income may only periodically realize portions of their holdings and then perhaps not even enough to merit inclusion into higher income groups. Thus, insightful data would have to be tied to the return and even then on a time series analysis with that same return to s how true patterns of income. A seminal study on the sources of income for high income households by Piketty and Saez (2001) may serve to answer the current effectiveness of capital gains taxation as a vehicle for implementing progressivity. They argue tha t the prominent capital incomes and wealth that existed before World War I suffered precipitous decline during the war and depression periods that exists between 1913 and 1945. They assert that the high taxes and other societal factors have prevented the r e accumulation of large holdings of capital until recently, and thus, most high income households today do not received a prominent share of their total income from capital gains and dividends. Consequently, the period from 1913 to present has seen a decli ne in the importance and presence of income as capital gains income during this period, like that of rent, interest, and royalties, have remained a relatively stable p ercentage of income for the top households, but the decline 1920s to about 25% in the 1950 Piketty and Saez, 14). Another importan t observation is that capital income has not declined on a whole over the 1913 to present period, but rather diminished in concentration in the accounts of high income households. Piketty and Saez (2001) note that the overall percentage of

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Nick Frazier, Page 53 capital gains in total income in the United States has remained relatively constant over the time period. Where income inequality in the United States can be accurately modeled by a Pareto distribution, or a normal distribution with a strong positive skew, we would expect that fiscal years with a strong stock market would affect the high income households, or the positive skew portion, proportionate to their accumulation of capital stock. Feenberg and Poterba (1993) estimate income with a Pareto distribution and compare to the actual known distribution and find that the large share of capital gains in 1986 likely contribute to the error across the entire distribution, suggesting that capital gains are not necessarily realized according to a Pareto distribution. Feeberg and Poterba (2000) further support this assertion by showing that the inclusion of capital gains in adjusted gross income does not increase but decreases the total share of adjusted gross income attributed to the top .5 percent of households. Altogether, recen t studies cast serious doubts as to whether capital gains taxation contains the potential for an effective instrument for increasing progressivity in personal income taxation. The discussion merits a couple of final qualifications to the evidence presented above. P iketty and Saez (2001) note that part of the decline in dividends reported represent an increase in distributions from qualified savings and retirement plans, where for high income households we would tend to think that this portion of their portf olio represents a small share of the total. Their paper also suggests that, as an extension of the rising importance of wages recently combined with rising inequality, the possibility that large capital wealth may once again begin to occur in the upper per centiles of adjusted growth income as the high marginal ordinary income rates that prevented high wage earners from funding the general accumulation of wealth for much of the second half of

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Nick Frazier, Page 54 the twentieth century have recently and rapidly declined. They poi nt to France, where the literal destruction of large capital holdings occurred during the war periods, but now shows a concentration of dividends as a substantial source of income for high income households that developed over time Thus capital income tax ation may soon pose an alluring instrument for protecting the vertical equity of the personal income tax system in the upper echelons of wealthy households. viii. Special Case Assets certain assets regularly realized as capital gains transactions. Generally, any asset realized after a long holding period grants a significant reprieve of tax liability through deferred payment and would likely be fully recaptured through his proposal. Wh ile serious administrative and compliance difficulties would result by attempting to impose an alternative tax scheme on assets that might otherwise be subject to a lower effective tax rate, the uneven treatment imparted by the current system gives merit t o a general discussion. One of the most expensive tax expenditures in our current system occurs where gains on primary residences extensively escape equitable tax treatment. In 1985, the most recent fiscal year for which the specific data is readily avail able, the IRS reported approximately 1.5 billion dollars in taxable gain. These transactions occurred under the 29 where the current 29 The exact provisions were that a taxpayer under age 55 could buy a house of greater value than the one sold to qualify to rollover, or defer until sale of the new asset, the gains or a taxpayer over 55 years

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Nick Frazier, Page 55 provision of automatic exclusion of $250,000 (500,000 for MFJ) provides even more favorable treatment 30 As we would expect primary residences to predominantly qualify for long term holding periods and even have an exceptionally long average holding period, the potential for a strong lock in effect for residences with a high percentage of gains included in the sales price represents an added distortion to assets that can be liquefied more easily. A tax scheme that adjusted appropriately for holding period would work to recompense the serious shortfalls created by hous vertical equity across households and the horizontal equity across assets. dividends and interest. The current system schedules dividends and intere st to ordinary income and taxes them at the appropriate marginal tax rates a treatment that belies their actual status as capital income 31 Given their nature as partial realizations of a capital asset which favorably generates annual income instead of defe rred until realization, their taxation incur more subtle consequences. Were realized assets subjected to the proposed scheme but interest and dividends left off of the capital income schedule then we would expect an increased lock in effect for the assets generating such income as a function of holding period. Arguably, the deferral advantage would be alleviated by returning this income to the capital gains schedule, covered under the proposed scheme as discussed above, such that a net gain in revenue would result from dividends with long holding received an exclusion up to $125,000 in gains from the transaction. The current exclusions came into effect under the Taxpayer Relief Act of 1997. 30 See Chambers, Garriga, and Schlagenhauf (2007) for an intergenerational model of asymmetric tax treatment and consequences for progressivity. See also Ling and MacGill (2007) for a microlevel examination of the tax preferences differentiated by income, age, and wealth. 31 For a comprehensive discussion of the tax burden on dividends and an estimate of the effective tax rate on dividends, factoring in the lower general capital gains rates, after the Jobs Growth and Taxpayer Relief Reconciliation Act of 2003 (JGTRRA03) see Poterba (2004).

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Nick Frazier, Page 56 periods. The targeted dividend and interest payouts would likely be those distributed in retirement where the marginal rates for ordinary income rates would likely fall; however, the inclusion of this capital income avoids the negative consequences of heavily taxing retirement income as presumably low income households receive their income from qualified retirement plans or have their gross income reduced by the applicable tax preferences for the elderly and retired 32 The difference in the proposed treatment occurs for households that receive large amounts of capital income as a continued income stream rather than retirement savings and would likely pay a considerably lower rate in taxes were it included with other in come. The final class of assets that would benefit from a different treatment than the current system is those that have a long holding period but no basis. The issue can originally be presented as a loss in horizontal equity as the government taxes them on their initial contribution or purchase price a penalty levied effectively for insufficient record keeping. Complications arise especially in the sale of residences where the original sales price or improvements added years before could adjust the basi s no longer have evidenced values but also arise for other assets like a variable rate certificate of deposit. The ramification of a missing cost basis causes asymmetric treatment of assets, violating horizontal equity, and also should create a lock in eff ect especially assuming the asset qualifies for a step up of basis and the household benefits from transferring the 32 The general $5,700 ($11,400 for MFJ) standard ded uction increases by $1,100 ($1,400 for single of head of household) for each taxpayer over 65 years of age which is augmented by the non refundable Credit for the Elderly and Disabled worth $5,000 ($7,500 for both qualified and MFJ) per taxpayer assuming t hey under the applicable income limits (AGI is under $17,500 or non taxable Social Security and pension benefits are under $5,000).

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Nick Frazier, Page 57 asset to a new generation or other party 33 The immediate benefit here follows from ibuted as gains occurs less arbitrarily and the taxpayer should have holding period neutrality with respect to the decision to sell 34 To apply the scheme to only this subset of assets, however, would invite an administrative nightmare as we might expect as sets with long holding periods to be subject to considerably more than the current fifteen percent tax rate accorded to long term gains and voluntary election of the applicable tax rate would allow for tax shopping, mitigating the benefits of a discretiona ry treatment. 33 For an illustration of why a household would benefit from a bequest current wealth see Barro (1974). 34 As discussed earlie r, the eligibility for a stepped up basis in the current tax code could increase the lock

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Nick Frazier, Page 58 V. Chapter 4 The discussion presented below involves a side by side comparison between the estimate the total liability for regular capita l gains income under both systems using a straightforward calculation based upon historical data from the United States Individual Publication 1304 for years 1997 to 1999 whi ch takes a biased sample of individual tax returns to extrapolate the aggregate data of the general population 35 Our approximation of the total liability necessitates considerable simplification of the actual tax code and holds behavior constant across bot h schemes. Thus, we regard the actual figures developed as weak approximations and focus instead on general inferences as to how the liabilities differ. Notably, the years sampled represent those following the historic Taxpayer Relief Act of 1997 that redu ced many effective tax rates for the majority of taxpayers. President Clinton signed the legislation on August 5 th 1997 as a reduction of taxes on capital gains and estates and the introduction of the Child Tax Credit, the Hope Education Credit, and the $ 250,000 ($500,000 MFJ) exclusion of gains from the sale of personal residences. The top capital gains rate fell from 28% to 20% and the 15% bracket fell to 10%, with 35 See the Publication 1304 for a detailed review of their methodology and its limitations.

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Nick Frazier, Page 59 certain phase in restrictions for 1997 and for assets realized after July 19 th 1997 with a holding period of 18 months or greater 36 Lower rates of 18% and 8%, respectively, were also introduced for assets bought in 2001 and held for at least six years 37 These tax rate reductions led to a period of significant increase in the realization of cap ital gains assets across all income levels 38 The analyses also confirm that losses realized in December account for around one quarter of all losses tied to a determined holding period for every year in SOCA study, a trend predicted under the strategic rea lization approach for tax arbitrage 39 Furthermore, we remember the 1997 1999 period as a relatively strong one for capital asset growth as reported net capital gains increased by approximately 40%, 22%, and 22%, respectively, from the year previous. Altoge ther, the period represented unusually high revenues and realizations compared to contiguous periods and thus not necessarily representative of historic or future results. The Sales of Capital Assets Study (SOCA) data utilized in this comparison relies o n a probability subsample of the larger cross sectional Individual Income Tax Returns project of the SOI division. The SOI constructs their original sample from unaudited Individual Tax Returns randomly selected from certain subpopulations designated by sp ecified characteristics or variables of interest. Importantly, the data in aggregate represents a time series take on cross sectional data, but the selected returns are randomly chosen and therefore no assumptions about the continuity of any particular hou sehold(s) in the subsample, such as in a panel study, should be made. Similarly, the total subsample 36 This 18 month requirement was later re pealed in favor of the traditional 366 day requirement for gains realized after December 31 st 1997. 37 The maximum statutory rates for the general class of capital gains fell to 15% and 10% under after the Job Growth and Tax Relief Reconciliation Act of 20 03 due to sunset in 2010. 38 See Dai et. al. (2008), Shackelford (2000) and Chapter 2. 39 See Dyl (1977, 1978) and Zodrow (1995) and Chapter 2.

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Nick Frazier, Page 60 for the Sales of Capital Assets Study represents less than one percent of the total population of returns filed. However, since variables of interest for t he designation of subpopulations over select high income households, where the majority of capital income occurs, the returns selected for this study, though randomly selected from the sample, represent over sixty percent of the of the total original sampl e size, considerably larger than the typical proportion of returns with capital gains in the general population 40 Due to the difficulty involved in collecting accurate data from high income households and the temporal sensitivity of capital gains realizati ons, data from tax returns likely represents the best source of data readily available, though its use should come with reservations. The SOI SOCA database contains several tables of relevant information extrapolated from the subsample of returns compiled They record short and long term gains and losses by (1) asset type, (2) size of adjusted gross income, and (3) asset class. They also provide short and long term transactions classified by (1) asset type and month of sale and (2) asset type and length of holding period. Due to the informational requirements of either tax system, we will primarily concern ourselves with the asset transactions ordered by length of holding period. The table breaks short term gains and losses into number of months held and those where the holding period is greater than one year or not determinable (a designation that combined equal around one sixth of all short term transactions). Long term gains and losses have been classified by the following holding periods: (1) under 18 mon ths (includes some un reclassified short term transactions) 40 For a discussion of the confidence intervals and sampling error for the SOI estimations see Section II: Descript ion of the Sample from Publication 1304.

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Nick Frazier, Page 61 (2) 18 months to under 2 years (3) 2 years under 3 years (4) 3 years under 4 years (5) 4 years under 5 years (6) 5 years under 10 years (7) 10 years under 15 years (8) 15 years under 20 years (9) 20 years or more (10) Holding period not determinable. Importantly, the last category represents at least half of all transactions reported since the treatment under the current system for assets held 366 days or greater remains effectively the same and thus record keeping requirements are no t as stringent as for short term transactions. This paper takes the relatively conservative assumption that assets qualifying for category (9) have a holding period of 25 years and those for (10) as 15 years 41 The limitations of available data require this unfortunate strong assumption. Another substantial shortcoming in the calculation of the liability from the data available arrives in the inability to offset gains with losses 42 While the data contains total losses realized in the year, calculating the t ax liability owed under the current system based only on net gain would require strong assumptions about how those losses accrued. 41 The underlying assumption leading to 15 years is that records are more readily available for assets with shorter holding periods though the majority (around 85 percent) of transactions report holding periods of 10 years or less. Notably, for the Other Asset category, the holding period is often listed as non determinable for around three quarters of all transactions. We treat the non determinable holding period for short term transactions as deterministically less than one year. 42 The current tax code allows for short and long term losses to offset total gains and, if a net loss occurs, ordinary income can be offset by up to $3,000. Furthermore, if net losses in any tax year exceed $3,000, the tax payer may carry forward those losses into the next tax year to offset future gains.

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Nick Frazier, Page 62 A more precise estimate necessitates specific transactions tied to particular taxpayers data that the IRS does not make publi cly available for reasons of confidentiality, administration costs, etc. Furthermore, the SOI SOCA database does not contain any information on short and long term losses carried forward, which can have a substantial effect on calculation of liability fol lowing years where large numbers of taxpayers experienced net capital losses. The pattern of capital gains transactions prevents even conservative assumptions about how the losses were distributed. For instance, in 1997 taxpayers with an adjusted gross inc ome of over $1 million reported around 29.9 short term transactions, compared to an average of 3.3 short term transactions for an adjusted gross income of under $20,000, though no metrics are reported to clarify how loss transactions are distributed 43 The resultant distortion will considerably overestimate the amount of tax liability owed under the current system and also ignore the behavioral factors inherent in the realization patterns of households. A simplification used in this comparison also require d by the nature of the data but more limited in its qualitative impact entails the statutory tax rate used. While a study on household realization behavior would likely devote substantial consideration to differences in tax rate, as the focus of this study lies in how overall liability develops, we apply a decidedly simplified tax scheme to simulate the current tax code. We levy a 15% rate on all gains realized to generate total liability, regarding the ultimate estimate as independent of actual revenue for the relevant tax year. Analogously, we use a 15% tax term gains, and use six percent risk free interest rate derived from a rough average of U.S. 43 See Figure 1 in the Appendix for an example of the difficulty and consequences of assigning losses based on AGI.

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Nick Frazier, Page 63 Treasury bill rates duri ng the same period. In this way, we derive some clarity and suggestions as to how ex ante and ex post equality create different effective outcomes based on actual data on reported realizations. Thus, the ultimate simulation will demonstrate differences in the calculated liability with generally similar tax rates as an effort to provide some context as to the differences in expected assessed liability. To realize the comparison, we consider the liability of separate asset classes and finally all asset liabi lity together over relevant period. The desired result will largely arrive in the differences in total liability calculated in that large deviations in two estimated liabilities indicate problems in ex post equity as the inherently uniform taxation of gain s by the current system delivers a different effective tax rate than an ex ante a lower (higher) owed liability we expect a lower (higher) effective tax rate than the current system. The division of the assets and reported gains utilized here follows that presented in the SOI SOCA data as: corporate stock, bonds, real estate, and all other assets. The advantage in individual analysis arrives in the ability to observe ho w the calculation of liability in the two schemes affects the different types of assets. Furthermore, we may thus conduct a more detailed discussion of the considerations and the limitations respective to the asset types. To conclude, we will estimate tota l liability across all assets reported without regard to type. i. Corporate Stock Corporate stock is the most readily identifiable and common class of capital assets in the United States market. In every year considered, corporate stock accounts for

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Nick Frazier, Page 64 around 4 0% of net gains reported and over half of total losses reported. The corporate stock asset class represents perhaps the best candidate for an approach such as and return than that of other assets classes. Furthermore, unless we assume perfect efficiency with respect to risk and return, we expect a certain premium over the risk free rate of return for the relevant years due to the bullish market circumstances in that the cu rrent system will levy higher tax in ex post Observing figure 5.1, we notice this assertion bear out, though notably, without loss deductions and other previously mentioned provisions in the current tax system. Figure 5.1 ii. Bonds and other securities

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Nick Frazier, Page 65 The second class of assets consists of regularly traded securities from government and private sources. Included within this class are state and local bonds from which the interest is generally tax fr ee. Since the various sources and guarantors of the bonds do get recorded in the SOCA study records, all securities are assumed taxable under both schemes which create an equal treatment for total gains. In this case, we might expect a significantly smalle r premium included in the pattern of accrual as bonds would generally be considered close to risk free assets if not such outright, adjusting for the variety of other securities available and realized. Figure 5.2 From Figure 5.2 we confirm that the total calculated liabilities remain roughly consistent during our relevant period though the TY1998 shows a marked discrepancy which is

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Nick Frazier, Page 66 largely explainable by the data reported to the IRS for that year. The year showed high realiza tions for bond and other security assets in general but had a significantly higher Figure 5.3. Figure 5.3 This difference, given the conservat ive assumed holding period with respect to levies a uniform 15% across the repo scheme and the relevant assumed rates results in a tax liability equal to 12.6% of the total asset price which partially suggests that more gains exist than might otherwise be expected for a holding period of 15 years. However, we also observe from Figure 5.3 that

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Nick Frazier, Page 67 as we could expect given the nature of securities, the predominant holding period falls under 10 years or less, suggesting that that final category of assets follows a distribution un the under 10 ye ar division but faced a higher than risk free rate of return, or that it represents a surge in bonds with longer holding periods being realized than in the two contiguous years. Altogether, the results remain fairly consistent with those from the corporate stock estimation. iii. Real Estate Real estate represents one of the most difficult assets to reconcile the over simplified tax schemes applied in this study with the actual treatment. The complications arise from the considerable advantages afforded real est ate for primary residences and its place in the United States economy as a primary vehicle for investment for the general population. Importantly, the real estate analyzed here accounts for residential property, rental property, depreciable business proper ty, farmland, and all other land in individual income returns. The approach utilized in this comparison has been to ignore the various incentives and other provisions in the tax code and focus on how liability develops for real estate. Theoretically, real estate assets represent another strong candidate for better time with returns at least equal to the risk free rate of interest, since for a sizeable portion of the inves tor base it represents the majority of the portfolio. Though the data available prevents such analysis, a possible avenue would be to exclude taxpayers who qualify for prop erty. Figure 5.4 suggests that real estate follows a reasonably akin pattern of liability

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Nick Frazier, Page 68 calculated as with the previous assets considered, though it should be noted that the years considered represent relatively strong years for the housing market, a cir cumstance that has since deteriorated perhaps beyond general equilibrium 44 Figure 5.4 The dramatic increase in realizations during the period considered can likely be wholly contributed to the favorable treatment initiated in TRA97 but hold also an interesting insight when we consider the realized gains for the period as in Figure 5.5. 44 The immediate implication of a depressed market arrives in lower than r isk free returns which would result in a higher tax burden for this type of asset due to market failures. Furthermore, considering the equity based nature of purchasing homes, forced realizations due to liquidity constraints would affect horizontal equity across taxpayers with access to liquidity.

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Nick Frazier, Page 69 Figure 5.5 Though missing 1996 as a pre TRA97 base line, Figure 5.5 clearly suggests that the assets with considera bly more gain accrued in the sales price were realized in TY1999 than in TY1997. Furthermore, we note a substantial difference particularly for assets with holding periods of greater than 20 years and indeterminate, suggesting that the exclusion provision provided a way to unlock some real estate assets. The increase in assets with a holding period slightly greater than one year can also be explained by the incentive provided to relatively short term real estate investors seeking to effectively escape taxat considerable gains in efficiency in this particular asset market if it made households holding period neutral, rather than resorting to expensive tax expenditures such as the housing ex clusion or the pre

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Nick Frazier, Page 70 iv. Other Assets The final class of assets include put and call options, futures contracts, mutual funds, and all other not already mentioned types of assets. This class represents around forty fiv e percent of all gains and transactions reported on individual income tax returns a substantial portion of all capital income. For instance, pass through gains, capital gain distributions and mutual funds combined accounted for an average of 67.6%, 43.1%, and 39.5% of net gain reported for the tax years 1997, 1998, and 1999, respectively 45 The diversity in accrual pattern, liquidity, and even election of classification make taxation of this class of assets difficult under any system. In particular, the fea sibility of ex ante holding where labor and capital incomes blend in the returns to the assets. Immediately we see that using the holding period to tax labor income rests on a tenuou s theoretical base, at best, but similarly taxing capital income at ordinary rates higher than the capital gains rates discourages holding such assets 46 Determining a definite holding period could also prove a source of added compliance and administrative cost for some assets. The dissolution and reincorporation of some subchapter S corporations and limited liability corporations could provide taxpayers a way to evade some taxation. For example, n that, the calculation depended on the date of incorporation for the business. Were the business to spin off a 45 For comparison, corporate stock accounted for 37.8%, 39.6%, and 42.4% of net reported gain for the same respective tax years. 46 Auerbach (1991) in particular points out that a system based on ex ante neutrality will fail to account for a premium earned from intellectual or idea capital invested in the asset. Where this return would be

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Nick Frazier, Page 71 new corporation with the same relative ownership for any investments that proved profitable, they would be able to lessen their total burden, de pending on the transaction costs of spinning off business 47 Related to the previous discussion and also to minimal requirements for assets that generally fall into the long term or short term categories, the data for Other Assets contains a large number o f transactions with an undetermined holding period over sixty percent of all transactions for tax years 1997 99 which detracts from the overall usefulness of the data as a reliable estimator of realization behavior. To see the difference, presented are Fig Figure 5.6 with that group excluded. Figure 5.5 47 This argument ha s been used to counter proposals to reduce taxation of venture capital.

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Nick Frazier, Page 72 Figure 5.6 arr ives in the way certain capital gains are reported, in that, for all three tax years, total gains are more than double the reported sales price, leading to large differences in the calculated liability. Noticeably, from Figure 5.6, we observe that the inco ngruence then, the addition of that final category has a strongly deterministic effect on the overall liability. However, to adduce the correct treatment of this category w ould require unavailable details such as the distribution of undetermined holding periods across the pertinent other categories and to discuss the exact rules from the tax code for reporting for the various types of included assets. Therefore, without grea ter specification and more

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Nick Frazier, Page 73 detailed data regarding the asset holding periods, solid conclusions remain outside the capability of this treatment. v. All Assets The final estimation we present centers on the data available for all assets reported on individua l tax returns. We define this category as the aggregation of the above mentioned classes of assets, organized by length of holding period. Thus, the estimated liability will represent the total expected revenue including the various deficiencies and simpli fications of the separated assets. Similarly, we ignore off setting losses and retain the simplified tax rates used in the previous estimates. One facility of this approach is that we may include the results from 1993 2003 SOCA panel study. The SOI cross s ectional study used earlier no longer collected records on realizations classified by type and holding period, but the panel study did generated estimates for all assets based on holding period 48 Since the panel study followed certain taxpayers over the fi ve year period, the estimates deviate from those of the cross sectional study. The cross sectional analysis for TY1999 represents the base year for the panel study from which a smaller sub sample was selected, creating some variation in the data 49 Overall, we may posit that TY2001 saw a severe reversal in the upward trend of capital gains growth that led to lower imputed returns and higher reported losses. We observe this discordance in Figure 5.7 where the previously converging estimated liabilities diverg e for the remainder of the 48 The SOI division notes that these estimates should be regarded with extreme caution, even relative to the cross panel estimates, as the attrition and nature of capital gains realizat ion may preclude accurate representation from such a small sample. 49 To see figures relating and comparing the 1997 99 cross sectional reports to those of the 1999 03 period see Appendix.

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Nick Frazier, Page 74 period. However, based on that exact circumstance, we suspect that the hereto proffered risk free rate of return of six percent likely over approximates the actual return. Figure 5.7 Therefore, in Figu four percent which provides a closer convergence in the resultant liabilities.

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Nick Frazier, Page 75 Figure 5.8 To ignore this key variable would be to discount a key feature of that the imputed risk free rate of return represents a powerful tool to adjust overall burden on the public. On a final note on the importance of the specified risk free rate of return, we use a proxy for the risk free rate for the199 7 2003 period. We opt for the 3 month Treasury bill rate in their annual average form from the Federal Reserve Economic Database as representative of the general spot rate for those years, though as discussed above, actual specification requires more subtl e calculation 50 Thus, in Figure 5.9, we see 50 For reference, we provide the rates below: 3 Month 1997 1998 1999 2000 2001 2002 2003 T Bill Rates 5.20 4.91 4.78 6.00 3.48 1.64 1.03

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Nick Frazier, Page 76 Figure 5.9 a considerably different approximation of liability. Here, the approximation of the realizat ion behavior was constant but that for the current system is still grossly over estimated 51 For instance, consider an investor in the top ordinary income bracket of 35% who invests $12,000 dollars that after one year is realized and equals either $0 or $24 ,000. Here the investor will either receive a loss or gain equal to $12,000. However, assuming the investor does not realize any other assets, since losses may be carried over to offset ordinary income, that loss is worth $1050 per year to the investor or $4,200 total, while the net of tax value of the gain would be $10,200. Conversely, if the investor realized exactly $3,000 of gain per year, she would escape a total tax of $1,800. The 51 Excluding even special provisions for real estate and differences in tax rates for lower income households.

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Nick Frazier, Page 77 distortions indicated here demonstrate the complexity that accounting f or losses in the present system entails, since losses are not always random and nor are they always complementary to capital gains. Thus, to determine to what degree the presented estimate reflects actual capital gains revenue under the current system rema ins well beyond the capability of the data available. Altogether, the aim of this exercise was to compare the predicted liabilities generated by the two different schemes of capital gains taxation. Given the serious concern of ex post equality, the relati ve convergence of the two estimations suggests that the risk free return does not represent an unrealistic departure point for imputing gains. Furthermore, where we assume that length of holding period increases in the level of income and/or wealth, certai n potential gains in vertical equity, relatively minimal in the current system, exist in the alternate system. A more insightful study might use a panel approach that could also incorporate the way taxpayers used losses to improve the estimates of liabilit y under the current system and also better represent the distortions in investment behavior exhibited in the data above. Finally, the large percentage of transactions and gain included in the data without a determined holding period hindered the accurate e required informational burdens upon the taxpayers were increased, this quality may remain inherent in the data.

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Nick Frazier, Page 78 VI. Conclusion: Capital gains taxation will likely never re ach the status of a primary source of revenue for the United States government, nor ever dominate the national public discourse. At the same time, as an institution we expect capital gains taxation to retain a prominent place in individual income taxation and the literature accompanying it. The aim of this discussion centers on improving the fairness and efficacy of the treatment of comprehensive approach to income. Th e compromise between notions of social equality and economic efficiency, the basis of tax policy, remain the decisive issue in the debate over capital gains taxation. Where we suppose that the current system, in its simplified version, imposes a uniform b urden across a more or less horizontal spectrum of taxpayers, with a small provision for vertical differentiation, its arbitrary levying of taxes without regard to economic performance or behavioral distortions incur real economic costs and consequences. H owever, a perfectly efficient system may generally fail to satisfy the criteria included within the variety of social objectives built into our tax structure. If we place the current system at one end of a constructed spectrum, where it ignores certain eco nomic considerations concerning capital gains income, we posit that at the other end economic circumstance. The scheme Auerbach developed in his 1991 paper, Retrospective Capital Gains Taxation, represents something closely akin to that latter end.

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Nick Frazier, Page 79 Part of the divergence between the ends of the spectrum occurs in the treatment and applied definition of income. Where the traditional definition of income runs along the line capital gains complicates application of the type of direct taxation imposed on earned income or distributions. Using this understanding, the original proposals for accrual taxa This approach fails to account for neither the illiquid nature of unrealized gains nor the continuously evolving nature of capital income. As discussed above, a taxpa yer could be forced to realize an asset prematurely to pay for its tax bill, or even find that she owes positive liability for the previous year on an asset that has since depreciated to point of being worthless. To address this dilemma, the IRS has effect ively adopted the Haig Simons definition, which suggests that capital gains ought to be taxed on realization but even as such offers no prescription for a correct approach to the taxation. Thus, the relevant discussion surrounds not whether a capital gain represents taxable income but the best mechanism to bridge the gap between ordinary income and the accumulated gain. As a general rule, we may further characterize the debate as taking the current system as a starting point and working to improve its defic iencies. For assets with a holding period longer than one year, the mechanism in the current system effectively treats all gain as having accrued in the most recent year. In fact, total liability decreases on the cusp on a holding period of one year, encou raging longer holding periods. This approach implicitly creates an advantage for deferring realization through an interest free loan from the U.S. Treasury on the liability in earlier years. While technically accurate when we consider the Haig nition, as a

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Nick Frazier, Page 80 sudden increase in income upon realization where none existed before, this method produces distortions both between ordinary income and capital gains, and then again, even within capital gains, as the calculation of liability rests as almost e ntirely independent of the actual generation of the taxed income. The character of capital gains justifies the call for a more nuanced design. Nonexistent in the sphere of wage or other earned income, the issue created by a capital loss establishes certain complications for our definition of income. For instance, theoretically, since a capital gain entails an increase in tax burden, a capital loss should incur a proportionate decrease in tax burden. We observe this distinction between earned income and inve stment income in the current individual income tax code, where generally taxpayers may reduce their total taxable income by losses realized a logical extension and conclusion under the our definition of income. This practice recognizes the difference in th e two types of income but ignores the possibility that a capital loss is not tantamount to a loss of ordinary income and that they may merit two different approaches to taxation to preserve efficiency. Here, the academic literature and debate supposes that capital income may benefit from an alternate form of taxation, unique and specific to its nature and location within a market. In the modern academic literature, the first comprehensive attempt to bridge this Ultimately, his system of averaging annual accrual as a way of imputing taxes owed on an annual basis partially fails for the same reason that taxation of annual accrued sums did namely, some assets do not have readily observable prices until realization. Furthermore, his system approached an economically efficient system but also suffered from certain issues related to the

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Nick Frazier, Page 81 differences in averaged returns and actual returns and the ability of the taxpayer to effect the calculation used through tax arbitrag e. Notably, he did, however, consider the complication of interest owed on deferred taxes for assets with a holding period longer than one tax year. His seminal study represents an initial foray into an alternative approach to capital gains income, separat e and distinct from that afforded ordinary income. system rests the responsibility to alleviate and even eliminate the distortions inherent in the current system. As discussed ab ove, these distortions of behavior and overall market investment, primarily tax arbitrage through strategic realization and incentives to hold certain types of assets, define a condition of economic efficiency for a tax system as where investor decisions r emain independent of tax considerations with respect to their investment behavior. The efficient tax system leaves the investor neutral in the timing of any investment or realization and also the type of asset chosen, with exception for direct provisions f avoring or discouraging certain types of assets in the tax code, such as IRAs or personal residences. Significantly, such a tax system stands as second best for economic efficiency behind accrual taxation, but in contrast to the current system where consid erable evidence exists for significant distortions in behavior. Auerbach (1991) attempted to design just such a tax system, furthermore proving that his proposed scheme exists as the only one that satisfies the requirements without requiring the actual pa tterns of accrual from the taxpayer. His design entails the assumption of a risk free rate of return for all assets and then imputing the accrued tax liability over the holding period and the liability accumulating on that unpaid liability.

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Nick Frazier, Page 82 Therefore, the scheme requires a minimal informational burden of the taxpayer, namely gov ernment. The system satisfies the defined holding period neutrality requirement, tantamount to the described condition of economic efficiency, and contains several additional desirable properties. As proposed, the function to calculate the liability owed u pon realization uses an exponential operator that retrospectively imputes the growth of the asset and is robust to earlier partial payments of the liability, assets with cash distributions and also varying tax and interest rates. ce between a payment of the liability earlier or later represents an essential requirement of holding period neutrality as otherwise there would be an advantage for either immediate payment or deferral. The liability evolves on the assumption of a risk fre would be assumed to make a net return of at least the risk free rate of return over time. partial re alization and partial payment of the ultimate liability. Finally, the exponential nature of the function used to calculate liability allows for variation in tax and interest rates with respect to time with the use of straightforward integration. Importantl y, this last facility of the scheme also improves a serious deficiency in the current system where empirical evidence suggests that realization and investment behavior is sensitive to changes in the tax code. The method used to calculate liability retains the ability to confer those temporary changes to the calculation of liability well after their expiration, thus

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Nick Frazier, Page 83 making the taxpayers indifferent to tax legislation, allowing for more efficient investment to its satisfaction of the criteria beyond economic efficiency. For one, since it assumes an annual risk free rate of return on the asset, even an asset that deprec iated every year during the holding period would still owe tax liability based on its holding period. This circumstance does not pose a concern if we assume that households have well adjusted portfolios balanced relative to risk, but this assumption become s stronger when considering smaller relative portfolios, whether in terms of total capital or diversity of assets. Importantly, this aspect of retrospective taxation also violates the definition of income used in income taxation as the government levies ta xes for a transaction where no or negative income was generated. This distinction suggests the difficulty of treating capital income as analogous to ordinary income since to do so would incorrectly assume its cause and pattern of generation occurs similarl y. Furthermore, while ex ante all investors should expect to obtain at least the risk free rate of return from their portfolio, from an ex post perspective, the taxation of actual gains would face decidedly different effective rates. Here, the tax system f ails to satisfy an ex post horizontal equity in taxation burden as taxpayers with lower or greater returns would ultimately pay amounts of tax based on the actual experience and returns generated by the asset realized. To qualify and evaluate the latter co ncern, we conducted an empirical examination using data provided by the IRS SOI division that estimates the capital gains transactions, gains, and overall reporting from the ongoing study of individual income taxation. The procedure required considerable s implification of actual circumstances and

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Nick Frazier, Page 84 tax codes that influenced the data produced and sought to generally evaluate how different a uniformly imposed tax rate of fifteen percent differed from the rates generated rison suggest a reasonably close total tax burden when adjusted for the offsetting loss provision in the current system, meaning that the imputed gains at a risk free return taxed at a fifteen percent and adjusted for interest owed on deferred liability ap proached an effective tax rate of fifteen percent across reported gains. These results should not altogether discredit the concerns mentioned, but serve as a call for further research. In particular, this study failed to examine exact burden in a horizonta l or vertical structure because of the aggregated nature of the data and the general difficulty of obtaining data on the capital gains and income of households across time. The study also suffered from certain limitations in the data related to the differe nces complicated nature and behavioral elements inherent in using data from the current tax system as the basis for evaluating an alternate one. The potential gains in economi c efficiency and simplification of the tax code by discussion of the optimal taxation of capital gains. Unsettled, even, is the correct definition for capital gains as income a nd how that income arrives, whether realized gain represents an instantaneous increase, or an annual accumulation. Where previously we intuitively guess that a practical sy stem might combine elements of both. For instance, if free rate of return we could potentially achieve

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Nick Frazier, Page 85 satisfaction of horizontal and vertical equity principles. Though such an approach would come at a cost of distorting investor behavior, as assets with high returns would benefit from deferring realization, we submit that the resultant system might possess net gains over the curren would be not to dismiss the existence of an efficient way to tax capital gains but that any such system will always be an optimization of a second best rule.

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Nick Frazier, Page 86 Appendix : Figure 1 SOCA Panel Data, Tax Years 1999 2003 SOI Bulletin We see rather immediately that being taxed on losses would cause a net tax burden to be imposed on taxpayers who did not have net gains only for the lower end of the income scale, creating se rious questions concerning horizontal equity.

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Nick Frazier, Page 87 Figure 2 Sales price and gross gains reported for the tax years 1997 2003.

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Nick Frazier, Page 92 2008. Co ntemporary U.S. Tax Policy 2d ed. Washington, D.C: Urban Institute Press. Yitzhaki, Shlomo. 1979. An empirical test of the lock in effect of the capital gains tax. The Review of Economics and Statistics 61 (November): 626 29. Yuan, Jianhua and Robert Savi ckas. 2009. Cross sectional estimation biases in risk premia and zero beta excess returns. SSRN . Zodrow, George R. 1995. Economic issues in the taxation of capital gains. Canadian Public Policy 21 (November): 27 57.


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