During the period of the internet bubble 1996 to

The Persistence of Individual and Corporate Capital Gains and Losses The Persistence of Individual and Corporate Capital Gains and Losses* Abstract - We show that, for both individuals and corporations, there is an aggregate overhang of realized losses that can be expected to have persistent effects. At the taxpayer level, we use panel data to show that the transition probabilities between taxpayers states of capital realizations losses, gains, or zero do not meet the restrictions required for them to be modeled as following a simple time homogeneous Markov process. Further, a simple Markov model built around the long term transition probabilities would be too persistent to match short term transitions. We show that the summary statistics we consider are closely comparable between cohort panels and panels constructed from the overlap of annual cross sectional data. Nicholas Bull, James Cilke, & Christopher P. Giosa, Joint Committee on Taxation, Washington, D.C. 20515 C. Erik Larson Office of the Comptroller of the Currency, Washington, D.C. 20219 National Tax Journal Vol. LVII, No. 3 September 2004 INTRODUCTION During the period of the internet bubble 1996 to 2000 liability for individual capital gains transactions represented 11.8 percent of total individual and corporate liability. 1 While the collapse of the bubble creates considerable difficulty in forecasting capital gains, it also presents considerable difficulty in forecasting capital losses, which have exploded in recent years (see Figures 1 and 2). In addition, the explosion of losses has lead to proposals to expand the individual capital loss limitation (currently $3,000). In both these cases, our estimates of the path of future receipts and of the effect of proposed legislation on revenues and other key variables might be improved if we had a better understanding of how persistent losses are likely to be. This paper looks at the persistence of individual and corporate capital gains and losses, both in the aggregate and at the taxpayer level. In the aggregate, there is an overhang of realized losses and carryforwards that have only partially affected reported liability, and that can be expected to have persistent effects. This overhang results not just from the large amount of losses that have already been realized, but also from the fact that many of these losses have not affected current liability but will be carried forward to affect future * All views expressed in this paper are those of the authors and in no way reflect the views of the staff of the Joint Committee on Taxation or any Member of Congress, or the Office of the Comptroller of the Currency. 1 A number of authors have examined the effects of capital gains income on federal revenue, including Bull (2002), Jaquette, Knittel and Russo (2002), Kasten, Weiner and Woodward (1999) and Parcell (1999). 525

NATIONAL TAX JOURNAL liability. As will be seen, only by looking at both individual and corporate data can a full picture of the effects on liability be developed. At the individual and corporate taxpayer level, we use panel data to examine the transition probabilities between taxpayers states of capital realizations losses, gains, or zero. We show that these transitions cannot be modeled as a simple time homogeneous Markov process. Further, a Markov model built around the long term transition data would be too persistent to match up with the short term data. An additional contribution of the paper is that it provides a comparison between the two types of panels most widely used in tax analyses cohort panels and panels constructed from the overlap of annual cross sectional tax data. We show that the summary statistics that we consider are closely comparable between the two types of panels. The second section of this paper addresses the law relating to the inclusion of capital gains and losses in gross income, focusing on those rules related to losses. The third section provides a description of the cross sectional and panel data used for this study. The fourth section discusses aggregate capital gains data and shows why persistence of aggregate losses is likely to continue to affect liability. The fifth section discusses taxpayer level data, including capital realization transition matrices and the test we use to determine whether these transitions can be modeled with a time homogeneous Markov model. The last section provides conclusions and directions for future research. TAX LAW REGARDING THE INCLUSION OF CAPITAL GAINS AND LOSSES IN GROSS INCOME A brief summary of the tax law regarding capital realizations provides a useful background before we turn to the details. Individual taxpayers are generally allowed to deduct against ordinary income up to $3,000 ($1,500 in the case of a married individual filing a separate return) of net capital losses. Net capital losses in excess of that amount may be carried forward. Corporations are generally not allowed to deduct losses. However they can carry losses forward and, in some cases, backward. But there are notable exceptions to these rules, and there are implications of the way in which the rules as implemented interact between the individual and corporate level, that have significant implications for the persistence of capital losses. Individuals In general, capital gains can be offset to the extent that a taxpayer has capital losses. Since the Tax Reform Act of 1986, all net capital gains are included in gross income, though the applicable tax rate has varied. An individual taxpayer is allowed a deduction from ordinary income up to $3,000 ($1,500 in the case of a married individual filing a separate return) for each dollar of capital loss that exceeds the capital gains from the sales or exchanges of capital assets in a given taxable year (Internal Revenue Code hereafter IRC section 1211(b)). If such capital losses are attributable to the sale or exchange of a qualified small business stock, the taxpayer is allowed a deduction of up to $50,000 ($100,000 in the case of a joint return) (IRC section 1244). Individual taxpayers that were unable to use their capital losses to offset income in a taxable year may carry such losses forward for use in future taxable years. In general, individual taxpayers cannot carry back capital losses to offset income from previous taxable years. 2 A loss from 2 In the case of losses attributable to certain options, futures and currency contracts, an individual may use such losses to offset gains from such contracts realized in the previous three taxable years, according to IRC section 1212(c). 526

The Persistence of Individual and Corporate Capital Gains and Losses the sale of a principal residence is treated as a nondeductible personal loss and may not be used to offset any income unless the property was used for a business purpose. Corporations Corporations may also use their capital losses to offset capital gains. However, in general, corporations are not permitted to use capital losses to offset other types of income (IRC section 1211(a)). An exception to this rule is for certain insurance companies that may deduct losses to the extent that the proceeds from the sale or exchange of a capital asset are used to cover abnormal insurance losses and to provide for distributions to shareholders (IRC section 834(c)(6)). In general, corporations may carry back their losses to offset capital gains from the previous three taxable years, or carry forward such losses to offset gains for the succeeding five taxable years. 3 Corporations filing as regulated investment companies (RICs) and real estate investment trusts (REITs) may not carry back capital losses to offset gains from previous years (IRC section 1211(a)(3)), nor may they distribute such losses to their shareholders. However, RICs may carry losses forward for eight taxable years and REITs may carry losses forward for ten years (IRC section 1212(a)(1)(C)). S corporations may distribute losses to their shareholders and, as such, typically do not carry losses into future tax years. 4 Business Property and Inventory Conversions Internal Revenue Code section 1231 addresses the gains and losses realized on sales of property used in a trade or business or on business property that has been involuntary converted. In general, an involuntary conversion is the result of the destruction, theft, seizure, condemnation or other disposal of property that led to its conversion into similar property or money (IRC section 1033). Losses from the sales of property used in a trade or business and from involuntary conversions of business property are not limited and may be used to the extent the taxpayer has taxable income (IRC section 1231(a)(4)(A)(ii)). Hence, for individual taxpayers, IRC section 1231 losses are not subject to the $3,000 limitation on their deduction from ordinary income. For corporate taxpayers, such losses are not limited by other net gains, and may be used to offset other income. However, for individual and corporate taxpayers, if IRC section 1231 losses are used to offset ordinary income, such losses are subject to be recaptured by net IRC section 1231 gains that are realized during the succeeding five taxable years (IRC section 1231(c)). Section 1231 gains and losses are calculated on Form 4797. In general, net long term gains are carried over to Schedule D. Net long term losses and short term gains and losses are carried to Form 1040 by individuals and to Form 1120 by corporations. DESCRIPTION OF CORPORATE AND INDIVIDUAL DATA The Statistics of Income division of the Internal Revenue Service (SOI) provided the data used for this paper. These data are based on samples of corporation and individual income tax returns filed from 1987 through 2002. The corporate data are the annual cross sectional samples from 1987 through 2001 (plus the advance 3 But a corporation that acquires a corporation that has loss carryforwards may not be able to use them, under IRC section 384. 4 An S corporation that had previously been a C corporation may have built in gains or losses carried forward from when it was a C corporation these are taxed differently than gains or losses realized by an S corporation (see IRC section 1374). 527

NATIONAL TAX JOURNAL file for 2002). 5 This paper uses two types of individual income tax samples: annual cross sectional samples from 1987 through 2001 (plus the advance file for 2002), and a cohort panel of tax returns that were followed from 1987 through 1996 (the last year available to us). Both the individual and corporate samples are stratified random samples. Also, we present income tax return information that has been publicly released by SOI (see Individual Income Tax Returns, Publication 1304; Corporation Income Tax Returns, Publication 16; and Corporation Source Book, Publication 1053). These public data provide aggregated taxpayer information that does not betray any particular taxpayer return. Because the SOI publications describe the cross sectional tax data in detail, we will not repeat the description here, except to comment on how we used these data for this study. For both corporations and individuals, we present data using standard definitions of capital gains realizations, such as positive net capital gains in AGI (the sum of net capital gains over all taxpayers for whom net capital gains are positive), and we introduce two new definitions of capital gains realizations: New Net and Total Net capital gains or losses. By New Net capital gains or losses, we mean the net of capital gains realized in the given year, without taking account of any loss carryforwards, and without taking account of limitations on taxpayers ability to use these losses to offset ordinary income in the current year. This definition would be potentially useful for looking at the effect of proposed legislation that would change the treatment of capital gains or losses e.g., the loss limit because it isolates the pattern of current year losses from that of carryforwards. By Total Net capital gains or losses, we mean the same as New Net, but adding in the effect of loss carryforwards. This definition might be useful for forecasting current law tax receipts, since those are affected both by the pattern of loss realizations, and by the pattern of carryforwards, (which are themselves a result of the loss limitations imposed on both individual and corporate taxpayers). Published SOI Corporate Capital Gains Data As mentioned above, SOI publishes statistics on corporation income tax returns. We note that we present a different aggregation of corporate net capital gains from the SOI published data. When SOI tabulates corporation net short term gains in excess of net long term capital losses, those statistics are calculated from the returns of C corporations, RICs, and REITs. However, when SOI tabulates corporation net long term gains in excess of net short term capital losses, those statistics are calculated from the returns of C corporations and REITs (but not RICs). Neither of these tabulations includes S corporations. Unless otherwise noted, the data we present for corporations includes the gains and losses of C corporations, RICs, REITs, and S corporations. For S corporations, we use positive net capital gains reported on their Schedule K. As an example, Table 1 reconciles tax year 2001 between SOI s published data and the data we present in this paper. For 2001, total net gains reported by SOI amount to $138,213 million. To that, we add $41,098 million of RIC net long term gains over net short term losses, and $27,808 million of S corporation gains to show a total of $207,120 million of corporate gains. Of these, $127,036 million are C corporate gains. 5 Relative to the final file, the advance file is incomplete because it does not contain returns from the many high income taxpayers who file their final return on extension. 528

The Persistence of Individual and Corporate Capital Gains and Losses TABLE 1 RECONCILIATION WITH SOI PUBLISHED DATA, TAX YEAR 2001 ($ in millions) Published SOI C Corporations REITs RICs Estimates RICs S Corporations Schedule D Net Short Term Gains Over Net Long Term Losses 11815 + 62 + 8893 = 20770 All Corporate Filers Schedule D Net Long Term Gains Over Net Short Term Losses 115221 + 2223 = 117443 41098 Schedule K Net Positive Capital Gains 2001 Totals 127036 + 2285 + 8893 Note: Details may not sum to totals due to rounding. Corporate Overlap Panel We matched employee identification numbers to create a panel of corporation income tax returns for tax years 1987 through 2001. 6 Each year, SOI prepares a cross sectional stratified random sample of tax returns. Because of the specific sample design used by SOI, certain taxpayers are likely to be included in the sample year after year. For fiscal year tax filers, we defined the corporate tax filing year in terms of the 12 months spanning the end of the calendar year. For example, the data for corporate tax year 2001 include corporate tax returns filed for accounting periods that ended July 2000 through June 2001. Most corporate accounting periods do end on December 31 (in 2000, for example, 82 percent of corporations reported a December ending period; these corporations represent 75 percent of aggregate corporate assets and 73 percent of corporate tax liability). Two panels were created to examine the transition probabilities between capital gains positions of corporate taxpayers. = 138213 + 41098 + 27808 = 207120 One panel linked all corporate taxpayers regardless of their filing status and included over 18,000 corporations. The second panel linked only C corporations (thereby excluding pass through entities, such as RICs, REITs, and S corporations) and included over 12,000 C corporations. Individual Overlap Panel 27808 In addition to the corporate overlap panel, we also constructed an individual overlap panel. 7 The overlap panel used in this study consists of the 3,362 returns where each of their 1987 to 2001 tax returns appears on SOI s annual cross section files. As appropriate for such overlap panels, the panel weight used on these returns is the maximum weight observed over the 15 tax years. Shorter overlap panels would contain more tax returns. We chose a starting date that matched with the cohort panel, and an ending date that included all of the final SOI cross sections currently available. 6 A single cross section file may contain two or more tax returns for the same corporation or individual. For instance, this would happen if a taxpayer filed a prior year s tax return at the same time as the current year s tax return. 7 Individual overlap panels have been used a number of times by researchers (e.g., Carroll (1998)). 529

NATIONAL TAX JOURNAL Individual Cohort Panel SOI along with the Office of Tax Analysis (OTA), Department of the Treasury, have developed an individual panel sample, one in which the same taxpayers were sampled over a ten year period (Cilke et al., 2000). For purposes of this paper, we used a subset of the panel known as cohort returns. The cohort returns were drawn from the 88,000 non dependent individual income tax returns for tax year 1987 that were included in the 1988 SOI cross section. All taxpayers who were represented on these sampled tax returns including secondary taxpayers on joint returns and their dependents were designated as members of the cohort panel. For the next nine years SOI included in the cohort panel sample any tax return filed that reported any panel member as a primary or secondary taxpayer. Each record in the sample contains the tax return information reported on Form 1040 as well as the major accompanying forms and schedules. The sample is augmented with several additional data items. Of particular relevance to the current paper, OTA obtained year of death for panel members from an exact match to Social Security Administration data. For the sake of computing transitions between states of capital gains realizations for panel members, we used the tax return as the unit of analysis, and a base year return could only be linked to one return filed in a successive year (an out year return). This assumption becomes an issue when the base year return consists of a married couple filing a joint return, and the couple splits up (e.g., divorces) and one or both spouses file their own separate return in the out year. In such cases, we calculated our gains transitions by linking the base year joint return to the primary taxpayer s out year return. If the primary s out year return was unavailable (e.g., because of death), we linked the base year return to the surviving spouse. A feature common to Markov transition estimates is the absorbing state or death state. When attempting to compute and analyze transition rates between gains states, we must define the ways in which a panel member enters this death state. In the case of taxpayers that do not file a joint return in the base year, the return enters the absorbing state in the tax year following the taxpayer s death. (A taxpayer normally files a final return in the year of death.) In the case of joint returns, the return enters the absorbing state when both taxpayers die, and in the tax year following the second death. If taxpayers income in an out year falls below the filing threshold, they may not file a tax return in that year. We assumed that all taxpayers have zero capital gains in years when they are non filers. PERSISTENCE IN THE AGGREGATE CAPITAL GAINS DATA Figures 1 and 2 show positive net capital gains and New Net losses for individuals and for all corporations. The figures show both the striking run up in capital realizations in the late 90s, and the explosion in capital losses in the early 00s. For purposes of exposition, it is useful to first discuss capital gains and then capital losses and carryforwards. Capital Gains Individual positive net capital gains peaked at $644 billion in 2000 (Figure 3 shows capital gains for individuals, all corporations, and C corporations). 8 This year marked the height of the era of irrational exuberance, which ended with a sharp decline of asset prices and investor 8 Figure 3 does not include section 1231 short term gains or losses or section 1231 long term losses. 530

The Persistence of Individual and Corporate Capital Gains and Losses Figure 1. Individual Capital Gains Realizations (in billions of dollars) Figure 2. Corporate Capital Gains Realizations (in billions of dollars) confidence. This decline was followed by the events of September 11, 2001 and several corporate malfeasance scandals, which continued to limit investor confidence. As a result, capital gains realizations fell to $247 billion by 2002. 9 Capital gains realizations reported by corporate filers also peaked in tax year 2000 at $594 billion and have since dropped to $118 billion in 2002. A majority of the capital gains realized by corporations are not subject to corporate taxes, 9 Any information contained in this report addressing tax year 2002 is preliminary and will most likely be revised. 531

NATIONAL TAX JOURNAL Figure 3. Individual and Corporate Capital Gains Realizations, 1992 2002 because RICs, REITs, and S corporations may distribute their capital gains to shareholders, thus avoiding a corporate tax on such income. 10 Restricting attention to C corporations alone, this data series also peaked in 2000 at $189 billion before falling to $79 billion by 2002. Clearly, total corporate gains are highly correlated with individual gains, in part because some individual shareholders of pass through entities must include the distributed gains in income. For example, approximately one quarter of net long term gains distributed by RICs are reported on individual tax returns. But C corporation gains are also highly correlated with individual gains, a fact which is somewhat puzzling in light of their different tax treatment. 11 The components of corporate capital gains realizations by organizational types are shown in Figure 4. Each of the pass through organizational types RICs, REITs, and S corporations had their highest level of realizations in 2000. RICs had the most with $360 billion of realizations, followed by S corporations with $39 billion, and REITs with six billion dollars. By 2002, net capital gains on the tax form of RICs declined to $20 billion, S corporations to $15 billion, and REITs to four billion dollars. As will be discussed later, these decreases in net capital gains are not only due to the fall of asset prices, but also due to the accumulation of capital loss carryovers. These decreases in the corporate sector also contribute to the fall of capital gains claimed on individual tax returns. This can be seen most directly by comparing RIC capital gains at the corporate and individual level (see also Ozanne (1999)). Figure 5 shows how the fall of net long term capital gains realized by RICs (from $297 billion in 2000 to $41 billion in 2001) contributed to the decrease in gains distributions reported on individual returns (from $79 billion in 2000 to $14 billion in 2001). Based on advanced data, these gains variables continued to slide into 2002 as asset prices have failed to return to early 2000 levels, and an increasing stock of loss carryovers are used to offset gains. As can be seen in the figure, approximately one quarter of net long term 10 Corporations may also be the recipients of capital gains distributions from RICs, thus causing some double counting in the corporate capital gains data series. 11 For a further discussion of this phenomenon, see Burman and Plesko (2002) or Desai and Gentry (2003). 532

The Persistence of Individual and Corporate Capital Gains and Losses Figure 4. Corporation Capital Gains Realizations, By Organizational Type, 1992 2002 Figure 5. Net Long Term Gains of RICs and Long Term Distributions Reported on Individual Tax Returns, 1997 2002 533

NATIONAL TAX JOURNAL gains distributed by RICs are reported on individual tax returns. Much of the remainder benefits from tax deferral or tax exemption, such as income distributed to tax exempt organizations, individual retirement accounts, employer sponsored retirement plans, and certain foreigners. Net Capital Losses and Carryforwards Turning to loss realizations and loss carryforwards, we will see that the interrelationship between corporate losses and individual losses implies potentially persistent effects on tax liability that have been only partially seen in corporate and individual tax receipts thus far. Not only have individual and corporate carryforwards exploded in recent years, but the fact that RIC and REIT losses cannot be passed through to shareholders means that carryforwards will depress net capital gains in these entities for years to come. Individual Losses Individual losses and carryforwards (Figure 6) grew quite slowly during the period when gains were expanding rapidly, but recently have grown significantly. Individual taxpayers filed 130.3 million returns for tax year 2001. Of these returns, 12.6 million returns reported a taxable net gain from their Schedule D of $348.1 billion, and 10.8 million returns reported a taxable net loss of $23.0 billion from their Schedule D. However, 6.1 million of these returns were subject to the $3,000 limitation (or $1,500 in the case of a married individual filing a separate return). These returns carried $248.7 billion in losses into tax year 2002. This represents an average annual increase of 69.1 percent over the 2000 to 2002 period (since individual taxpayers carried $87.0 billion in losses into tax year 2000). The average annual increase beginning in 1989, into which $39.1 billion in losses were carried, through 2000 was only 7.5 percent. A similar pattern can be seen when we turn from the dollars of losses carried forward to the number of returns carrying them. The number of returns reporting a short term loss carryover grew slowly from 0.5 million returns in 1989 to 1.0 million returns in 2000, before increasing to 2.8 million by 2002. Returns with long term loss carryovers grew even more slowly from Figure 6. Individual Loss Realizations, 1987 2001 534

The Persistence of Individual and Corporate Capital Gains and Losses 1.4 million returns in 1989 to 1.8 million in 2000, before increasing rapidly to 4.6 million in 2002. Figure 6 also shows individuals Total Net losses, which grew from $102 billion in 1999 to $266 billion in 2001 (to $413 billion in the advance data for 2002 a fourfold increase from 1999). Note that this increase would not be attributable to the loss realizations of RICs, since RICs do not distribute losses to their shareholders. However, with RICs distributing fewer net capital gains, there are fewer individual capital gains to offset other individual capital losses. While these losses and carryforwards have partially affected receipts to date, they can be expected to persistent in holding liability for some time to come. Finally, to fill in the remaining detail on individual losses, in tax year 2001, approximately 843,000 individual returns reported a loss of $9.1 billion on Form 4797. Of these returns, an estimated 4,000 returns reported a capital loss that was attributable to the sale or exchange of a qualified small business stock that was restricted by the $50,000 ($100,000 in the case of a joint return) limitation. Approximately 153,000 individual returns reported $3.1 billion in non recaptured net IRC section 1231 losses from previous tax years. Of this amount, only $238 million was recaptured as ordinary income. Corporate Losses But individuals are only part of the story. When we turn to corporations, we will see that not only do corporate losses and carryforwards have significant implications for future corporate liability, but also for future individual liability. This is both because carryforwards at the corporate level will have direct effects on corporate after tax income (or on RIC and REIT net capital gains), and because there may be an interaction between the expected sequence of lower tax payments and the value of the firm (or of RIC and REIT shares). 12 Corporate taxpayers filed 5.1 million returns for tax year 2001. Fewer than 800,000 of these returns reported taxable income. These returns with taxable income reported $91.8 billion of net capital gain income from their Schedule D. New net capital losses of $452.9 billion were reported on 135,700 corporate returns in tax year 2001. Approximately 53,400 corporate returns carried over $107.3 billion of unused capital losses into tax year 2001 (see Figure 7). In this case, 95 percent of losses carried into tax year 2001 remained unused. Of the returns that reported a carryover loss, only 6,400 reported net capital gain income on their Schedule D and only 2,100 returns reported taxable income. Advance data for 2002 show New Net capital losses realized by corporations rose to $865 billion in 2002, plus there were a total of $416.4 billion of loss carryforwards for all corporations, almost quadruple those on 2001 returns. This represents a sharp increase compared to an annual average of 10.2 percent since 1989 when $26.2 billion of unused capital loss carryovers were brought into tax year 1989. The number of returns reporting unused carryover losses grew 4.5 percent per annum over the 1989 to 2000 period. However, even though these losses grew by 41 percent from 2000 to 2001, the number of returns reporting such losses grew by only five percent. The additional New Net loss realization combined with the unused carryovers led to approximately $1.3 trillion in Total Net losses on 2002 corporation income tax returns. But most of this increase in corporate losses was attributable to RICs, which carried over $383.6 billion of losses into 12 A full analysis of the potential price effect of the expected path of future tax payments is beyond the scope of this paper, but would require a discussion of new view versus old view firms (see Auerbach (2001)). 535

NATIONAL TAX JOURNAL Figure 7. Loss Realizations, By All Corporations, 1992 2002 2002, and realized an addition $766 billion in additional net losses for the same year. When pass through entities are removed from the corporate loss data, Figure 8 shows that the C corporations show the same trend in loss accumulation. C corporate Total Net losses have grown from $51 billion in tax year 2000 to $126 billion in 2002. While it is not possible to determine exactly how much of RIC loss carryforwards accrue to taxable individuals or corporations, it is clear that there are a great many losses that have not yet affected individual or corporate liability, and that can be expected to happen in the coming years. Finally, to complete the story on corporate losses, in tax year 2001, approximately 145,800 corporate returns reported a loss of $41.0 billion on Form 4797. Nearly 97,000 returns reported $4.0 billion in non recaptured IRC section 1231 net losses from previous tax years. These returns recaptured about $1.6 billion. However, only 4,500 of these returns reported taxable income. In tax years 1999 through 2001, capital loss deductions taken by all insurance companies averaged $350 million per year. TAXPAYER LEVEL GAIN AND LOSS TRANSITIONS Having examined aggregate data, we next turn to taxpayer level data. Recall that one of the initial motivations for interest in looking at the persistence of capital gains and losses is that with the explosion of losses have come proposals to expand the individual capital loss limitation (currently $3,000). But such a provision would lower the path of loss carryforwards in the initial year, the taxpayer would be able to claim more losses against ordinary income, which would reduce the amount of loss carryforwards taken into the subsequent year. In the subsequent year, the combination of the smaller carryforward combined with the ability to use up more of the second year losses reduces carryforwards at an accelerating rate. As a first step toward estimating the effects of such a proposal on revenue or other key variables, it is useful to gain a better understanding of the patterns of taxpayer behavior with respect to realizations of capital gains and losses. To that end, we use individual and corporate taxpayer panel data to look at taxpayer s intertemporal transitions between 536

The Persistence of Individual and Corporate Capital Gains and Losses Figure 8. Loss Realizations, By C Corporations, 1992 2002 Figure 9. Individual and Corporate Capital Loss Carryovers, 1988 2002 states of capital realizations i.e., whether they are realizing (or reporting) net losses, net gains, or are non realizers. It is natural when looking at such data to think in terms of transition probabilities between these states of capital realizations. Markov Transitions Further, it is natural having constructed these probability transition matrices to think in terms of building a simple stochastic model that would make use of 537

NATIONAL TAX JOURNAL the data. The simplest such model is a time homogeneous Markov model. Such a model assumes that all that is necessary to characterize the probability distribution over taxpayer states in a subsequent year is knowledge of their initial state and of the transition probability matrix. However, the adoption of the simple Markovian transition framework is not without cost; restrictive assumptions on the nature of transitions are required for the validity of this simple model. In fact, many of these assumptions are unrealistic, and are likely to be violated by the types of transitions considered by practitioners. Therefore, it would appear that a diagnostic test for the validity of the simple Markov chain model specification would be a valuable tool to add to the transitions modeler s toolkit. We present results from a test for time homogeneity. This is not required by the general Markov specification, but seems to be a featured assumption in practice (and is an assumption that makes much empirical work possible!). Time homogeneity means that the transition matrix P, whose ij th element is the probability that a taxpayer is in state j next period given it is in i this period, is constant over time. This is a strong assumption. For example, it might be thought that these transition probabilities would depend on macroeconomic conditions, or conditions specific to the taxpayer, such as whether they are retired. Time homogeneity is sometimes referred to as the property of having stationary transition probabilities. This is probably bad terminology, as it may cause confusion with stationarity of the stochastic process determined by these transition probabilities. Markov chains are not usually stationary, in the sense that the joint distribution of N successive observations may be different depending on where the N are taken. Nevertheless, a test for time homogeneity of ratings transitions is one diagnostic test that can be used to evaluate 538 the adequacy of the simple Markov specification. The following discussion follows that in Kiefer and Larson (forthcoming), which provides a recent illustration of how such a test can be constructed and applied to credit rating data. For a more formal statistical treatment, see Anderson and Goodman (1957). Before proceeding, it is useful to put our empirical goals in perspective. Our goal is not to determine whether gains state transitions are or are not truly Markovian; this is not the issue. The issue instead is whether the Markovian specification adequately describes transitions over rather short periods. The test that we apply allows researchers to determine which state transitions look Markovian and over what periods. More technically, a Markov process consists of a set of states in period t S t = {S 1, S 2, } and a set of transition probabilities P t. ij Pt is the probability that an ij observation in state i in period t will move to state j in period t + 1. We estimate the probabilities P t by observing the transition between states S t ij and S t+1. Note that sole determinant of the transitions probabilities are states S t and S t+1. In our case we have four possible states: with capital gains, with capital losses, with neither, and death. In matrix form: P 11 P 12 P 13 P 14 p t = P 21 P 22 P 23 P 24 and P 31 P 32 P 33 P 34 P 41 P 42 P 43 P 44 S t = S 1 S 2 S 3 S 4. Note that summing across each of the rows in P t, the sum must be 1 (since the columns contain all states of the world to which one can transition). Further, state 4 is our death state, so P 41 = P 42 = P 43 = 0 (i.e., once deceased, no further transitions are possible).

The Persistence of Individual and Corporate Capital Gains and Losses A Markov process is time homogeneous if the transition probabilities P t ij are constant over time (i.e., P t ij = P ij ). Time homogeneity is not required of a Markov process, but it is a convenience. Such a model might provide a powerful tool for estimating future levels of gains and losses and analyzing the revenue and other effects of proposed legislation regarding capital transactions. Let S t+x be the observed states distribution x periods in the future. We can then calculate P t+x = S t+x /S t. Let E[S t+x ] be the expected states distribution x periods in the future. In a simple Markov process, E[S t+1 ] = S t. P t. Under a Markov time homogeneous process, we would expect: E[S t+2 ] = E[S t+1 ]. P t+1 = S t. (P) 2, and therefore, E[S t+n ] = S t. (P) n. We tested the null hypothesis that the data can be represented as a time homogeneous Markov process against several cuts of the three panel data sets (individual cohort and overlap, and corporate overlap). In particular, we computed transition matrices in every length possible for each panel. For example, for the individual cohort panel, which extends from 1987 to 1996, we computed the sequence of one year transitions, of two year transitions (1987 to 1989,..., 1994 to 1996), of three year transitions (1987 to 1990,..., 1993 to 1996), up to the longest transition possible the nine year transition from 1987 to 1996. Transition Probability Matrices Tables 2 to 7 show transition probability matrices for each of the three panel data sets, for varying transition lengths, and (for individuals) for the two definitions of capital realizations (discussed in the third section). Each transition probability 539 matrix has rows that correspond to the initial state and columns that correspond to the final state. For example, in the first panel of Table 2, the first row shows transition probabilities for a taxpayer who has a zero net capital realization in 1989. The columns show the probability associated with each capital gain transition to 1990. The probability of moving to a zero capital gain is 94.4 percent; to a positive net capital gain it is 3.5 percent; and to a capital loss it is 2.1 percent. For individuals, Table 6 allows a direct comparison between results for the individual cohort panel and for the individual overlap panel the two types of panels most widely used in tax analyses. The table shows average transitions for the cohort panel that are directly comparable to the same length transition in the overlap panel. At least for capital gains data, even the worst case comparison between the two panels the nine year transition probability from 1987 to 1996, a length of time that maximizes the tendency of taxpayers to fall out of the cross section and, thus, out of the overlap panel we find that the two transition matrices are not a great deal different. The probability of ending up in a gains state is a bit higher in the overlap panel, as should be expected, since one way to stay in the cross section from year to year (and, thus, to be observed in the overlap panel) is to have high capital gains realizations. Given that a cohort panel is available, the researcher would probably tend to choose it. But for some key tax law changes such as the Tax Reform Act of 1997 no edited cohort panel data are available. The results found in this paper may provide some comfort in using overlap panels to analyze such tax law changes. It may also provide some comfort in interpreting the results of such studies. Tables 3, 5, and 7 allow a direct comparison for Total Net capital realizations, for the individual overlap and cohort panels and for the corporate overlap

NATIONAL TAX JOURNAL TABLE 2 TRANSITION MATRICES, INDIVIDUAL OVERLAP PANEL, NEW NET REALIZATIONS (percentages) One year transitions 1989 to 1990 1996 to 1997 2000 to 2001 Average 1987 to 2001 1987 to 1990 1995 to 1998 1998 to 2001 Average 1987 to 2001 Five Year Transitions Seven Year Transitions Ten Year Transitions Fourteen Year Transition, 1987 to 2001 94.4 29.1 43.5 91.1 14.4 28.2 92.3 26.2 31.2 93.1 23.0 32.7 93.6 35.5 42.5 85.3 19.2 27.9 88.6 26.6 32.4 90.0 27.9 36.5 84.8 26.1 32.4 81.9 27.4 31.5 77.8 27.9 29.5 78.2 33.4 32.2 3.5 54.1 28.0 7.2 78.2 50.4 5.4 49.2 28.1 5.2 64.8 41.5 Three year transitions 4.4 46.8 30.8 12.4 71.8 54.3 7.4 48.0 30.1 7.9 60.0 43.1 12.2 61.9 48.5 14.6 60.4 50.1 17.8 60.1 53.4 13.8 44.6 35.8 2.1 16.8 28.4 1.8 7.4 21.4 2.4 24.7 40.7 1.7 12.2 25.8 2.0 17.8 26.7 2.2 9.0 17.8 4.0 25.4 37.5 2.2 12.1 20.4 Average transitions from 1987 to 2001 3.0 12.0 19.1 3.5 12.2 18.2 4.4 12.0 17.1 8.0 22.1 32.0 panel. At the aggregate level, we saw that C corporate capital realizations have the same pattern as individual, but with dampened movement. To some extent, we see a similar relationship at the taxpayer level. For instance, comparing Table 3 with Table 7, we see that the probability that a corporation transitions from gains to gains is smaller at every time interval than for individuals. 540

The Persistence of Individual and Corporate Capital Gains and Losses TABLE 3 TRANSITION MATRICES, INDIVIDUAL OVERLAP PANEL, TOTAL NET REALIZATIONS (percentages) Average transitions from 1987 to 2001 One Year Transitions Five Year Transitions Ten Year Transitions Fourteen Year Transition 92.7 20.0 20.1 84.5 25.9 27.7 77.3 27.1 26.9 77.2 32.4 29.7 5.6 67.8 29.1 11.8 59.7 41.6 17.2 58.0 47.9 13.2 42.3 31.1 1.7 12.1 50.8 3.6 14.4 30.7 5.5 14.9 25.2 9.5 25.2 39.2 TABLE 4 TRANSITION MATRICES, INDIVIDUAL COHORT PANEL, NEW NET REALIZATIONS (percentages) Average transitions from 1987 to 1996 Deaths One Year Transitions Three Year Transitions Five Year Transitions Nine Year Transition, 1987 to 1996 93.8 25.4 35.3 91.4 32.2 40.4 89.0 35.8 41.0 86.0 39.5 41.9 4.0 61.9 38.1 6.1 55.3 39.1 8.1 52.7 41.5 11.0 50.7 43.2 1.4 11.3 25.5 1.8 10.9 19.1 2.0 9.5 16.2 2.0 7.7 13.5 0.7 1.4 1.1 0.8 1.7 1.3 0.9 2.0 1.3 1.0 2.1 1.5 TABLE 5 TRANSITION MATRICES, INDIVIDUAL COHORT PANEL, TOTAL NET REALIZATIONS (percentages) Average transitions from 1987 to 1996 Deaths One Year Transitions Three Year Transitions Five Year Transitions Nine Year Transition, 1987 to 1996 94.0 25.8 24.1 91.2 31.8 33.8 88.7 35.3 36.7 85.5 38.5 38.8 541 4.0 61.9 26.2 5.9 53.4 31.4 7.8 50.3 34.9 10.7 48.3 37.2 1.3 10.9 48.8 2.1 13.0 33.6 2.6 12.4 27.2 2.8 11.0 22.7 0.7 1.5 1.0 0.8 1.7 1.2 0.9 2.0 1.2 1.0 2.1 1.4

NATIONAL TAX JOURNAL Cohort Panel Overlap Panel Cohort Panel Overlap Panel Cohort Panel Overlap Panel TABLE 6 COMPARISON OF TRANSITION PROBABILITIES IN INDIVIDUAL COHORT PANEL VERSUS INDIVIDUAL OVERLAP PANEL (percentages) 93.8 25.4 35.3 93.1 23.0 32.6 91.4 32.2 40.4 90.0 27.9 36.5 86.0 39.5 41.9 83.3 31.4 35.6 Average one year transitions from 1987 to 1996 542 4.1 61.9 38.1 5.2 64.8 41.5 6.1 55.3 39.1 7.9 60.0 43.0 11.0 50.7 43.2 14.2 60.0 50.2 1.4 11.3 25.5 1.7 12.2 25.8 1.8 10.9 19.1 2.2 12.1 20.4 2.0 7.7 13.5 2.6 8.6 14.2 Deaths 0.7 1.4 1.1 n.a. n.a. n.a. Average three year transitions from 1987 to 1996 Deaths Nine year transition from 1987 to 1996 TABLE 7 TRANSITION MATRICES, C CORPORATE OVERLAP PANEL (EXCLUDING RICs, REITs, AND S CORPORATIONS), TOTAL NET REALIZATIONS (percentages) Average transitions from 1987 to 2001 One Year Transitions Three Year Transitions Five Year Transitions Seven Year Transitions, 1987 to 2001 Ten Year Transitions Fourteen Year Transition 93.8 39.7 19.5 91.6 47.0 32.9 89.8 51.7 40.8 88.4 53.6 47.7 87.2 56.5 53.6 86.7 58.2 61.4 5.2 52.8 17.4 6.4 43.5 23.1 7.5 39.1 26.4 8.2 36.5 28.2 9.0 34.9 28.4 8.6 29.3 21.5 1.0 7.5 63.1 2.0 9.5 44.0 2.7 9.2 32.8 3.4 9.9 24.1 3.9 8.6 18.0 4.7 12.5 17.1 0.8 1.7 1.3 n.a. n.a. n.a. Deaths 1.0 2.1 1.5 n.a. n.a. n.a.

The Persistence of Individual and Corporate Capital Gains and Losses Testing for Time Stationarity To test whether our observed transition probabilities are time homogeneous, we compare E[S t+n ] with the data observed S t+n. We use a maximum likelihood ratio statistic, as described by Kiefer and Larson (forthcoming). We find that for each of the data sets, for each transition length, and for each definition of capital realizations, the null hypothesis that the data can be represented as a time homogeneous Markov process is soundly rejected (the probability of acceptance is below a millionth of a percent). But closer examination of the maximum likelihood transition matrices with the one period transition matrices is quite revealing. For each of the tests performed, the on diagonal elements in the maximum likelihood transition matrices is uniformly larger than the corresponding element in the one period transition matrix. Table 8 shows a typical case. For New Net gains for the individual cohort panel, the top panel in the table shows the average one period transition matrix. The bottom panel in the table shows the maximum likelihood one period transition matrix that is consistent with the five period average transition. That is, the five fold product of this one period transition matrix would produce a five year transition consistent with that observed in the data. The on diagonal elements are uniformly larger for the matrix in the bottom panel. The interpretation is that if a Markov model were built around the maximum likelihood matrix, it would be too persistent to be consistent with the short term properties reflected in the one period average transition matrix. Alternatively, a Markov model built around the one period average transition matrix would not be sufficiently persistent to be consistent with the long term properties of the data, as reflected in the maximum likelihood matrix that is consistent with the multi period transitions. 13 A possible reason that the data fail the time homogeneous Markov test is that aggregate positive net capital gains grew rapidly through the period in which much of the data were collected, thus potentially causing persistent increases in the probability that a taxpayer would end up with positive capital gains. Thus, as a first step toward testing whether an alternative specification of the model would not be rejected, we detrended the data series using aggregate capital gains data. Specifically, in the individual cohort panel data, we detrended positive gross gains for each taxpayer by aggregate positive net gains, and we detrended negative gross losses by aggregate net losses. Because aggregate net gains rose rapidly over the period, while aggregate net losses were nearly TABLE 8 TRANSITION MATRICES, INDIVIDUAL COHORT PANEL, NEW NET REALIZATIONS (percentages) Markov Test Matrices Deaths Actual Average One Year Transitions 1987 to 1996 93.8 25.4 35.3 4.0 61.9 38.1 1.4 11.3 25.5 Maximum Likelihood One Year Transition Consistent with Five Year Average Transition 96.2 13.8 21.7 2.6 74.6 41.6 0.9 11.0 36.3 0.7 1.4 1.1 0.3 0.6 0.5 13 Auerbach, Burman, and Siegel (2000) examine capital gains persistence in a panel model, and discuss tax avoidance behavior that would provide one motivation for persistence of losses. In addition, there are demographic reasons to expect persistence of gains during retirement, taxpayers would tend to be drawing down assets and, therefore, would tend to realize a sequence of positive gains. 543

NATIONAL TAX JOURNAL constant, this would tend to detrend each taxpayer s gross gains considerably, while leaving gross losses little changed, thereby flipping more people from a net gains state to a detrended net loss state. This would offset the growth in the probability of moving to a positive net gains state that is evident in the data. Nonetheless, the null hypothesis that the data can be represented as a time homogeneous Markov process is again rejected. CONCLUSION AND DIRECTIONS FOR FURTHER RESEARCH We have presented evidence regarding the persistence of capital realizations at the aggregate and at the individual and corporate taxpayer level. We show that the summary statistics that we consider are closely comparable between cohort panels and panels constructed from the overlap of annual cross sectional data. We show that a simple, time homogeneous Markov model is inconsistent with the underlying data. But it may be possible that a non time homogenous Markov model consistent with the underlying data could be developed, which would be useful for forecasting receipts and estimating the revenue effect of proposed tax law. Possibly, detrending using aggregate variables would be helpful, though we found that this was not the case when we detrended using aggregate capital gains and losses. However, our data span several different tax law regimes, and also span two business cycles, so it might be useful to take these into account. It might also be of interest to consider different demographic groups, such as elderly taxpayers. Acknowledgments We would like to thank Rosanne Altshuler, Larry Ozanne, and our discussant, Len Burman, for helpful comments. All errors and omissions are solely the responsibility of the authors. All views expressed 544 in this paper are those of the authors and in no way reflect the views of the staff of the Joint Committee on Taxation or any Member of Congress, or the Office of the Comptroller of the Currency. REFERENCES Anderson, Theodore W., and Leo A. Goodman. Statistical Inference about Markov Chains. Annals of Mathematical Statistics 28 (August, 1957): 89 109. Auerbach, Alan J. Taxation and Corporate Financial Policy. NBER Working Paper No. 8203. Cambridge, MA: National Bureau of Economic Research, April, 2001. Auerbach, Alan J., Leonard E. Burman, and Jonathan M. Siegel. Capital Gains Taxation and Tax Avoidance; New Evidence from Panel Data. In Does Atlas Shrug? The Economic Consequences of Taxing the Rich, edited by Joel B. Slemrod, 355 88. New York: Russell Sage Foundation; Cambridge and London: Harvard University Press, 2000. Bull, Nicholas. The Effect of Asset Price Changes on Federal Tax Liability. In Proceedings of the Ninety Fourth Annual Conference on Taxation, 156 63. Washington, D.C.: National Tax Association, 2002. Burman, Leonard, and George Plesko. Individual and Corporate Capital Gains are Highly Correlated. Tax Notes (October 28, 2002): 553. Carroll, Robert. Do Taxpayers Really Respond to Changes in Tax Rates? Evidence from the 1993 Tax Act. OTA Working Paper No. 79. Washington, D.C.: Office of Tax Analysis, November, 1998. Cilke, James, Julie Anne M. Cronin, Matthew Eichner, Janet McCubbin, James R. Nunns, and Paul Smith. Developing a Panel Model for Tax Analysis. In Proceedings of the Ninety Second Annual Conference on Taxation, 419 26. Washington, D.C.: National Tax Association, 2000.