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The Contribution of Mutual Funds to Taxable Capital Gains October 1999

APPENDIX: TESTING FOR THE NET IMPACT OF STOCK AND BOND FUNDS ON TAXABLE CAPITAL GAINS

Capital gains distributions paid out by stock and bond funds may substitute for gains that individuals would otherwise realize from selling stocks and bonds directly. The Congressional Budget Office (CBO) attempted to estimate the extent of that offset by adding measures of stock- and bond-fund activity to existing equations used to forecast the total taxable gains that will be reported on individual income tax returns. One type of equation explains the growth rate of capital gains, and another explains the ratio of capital gains to the size of the economy. CBO added three alternative measures of stock- and bond-fund activity to each equation: one measures the fraction of corporate stocks held in stock funds and two measure capital gains distributions. When the equations are reestimated with the added variables, they indicate that the activity of stock and bond funds is more likely to increase total capital gains than to completely substitute for other gains. Some of that increase probably is spurious, however, arising because stock- and bond-fund activity happens to be correlated with the selling of other assets.

Equations for Testing Net Impact

Forecasters at several institutions use equations to predict the capital gains reported on individual income tax returns as part of their forecasts of individual income tax revenues. Most of those equations--including the ones used by CBO--attempt to explain the annual growth rate of taxable capital gains. An alternative type of equation attempts to explain the ratio of capital gains realizations to the size of the economy. That type has been less widely tested, but it does produce a direct estimate of the dollar impact that distributions have on taxable gains. CBO used both growth-rate and ratio equations in the tests of stock- and bond-fund activity.

Growth-Rate Equations. CBO's growth-rate equations explain the annual growth rate of taxable capital gains in terms of the annual growth rate of accrued gains and annual changes in the cost of realizing gains.⁽¹⁾ The growth rate of accrued gains is approximated by the growth rates of the price level, real gross domestic product (GDP), housing starts, and real stock values. Housing starts are included to approximate changes in real estate prices, and real GDP is included to reflect changes in the value of personal and business assets other than real estate and corporate stocks. Fluctuations in real GDP growth also capture the tendency of people to realize more gains in boom years than in recessions. The cost of realizing gains is measured by the top federal tax rate on capital gains.

To project capital gains, CBO ordinarily uses four separate equations that include slightly different combinations of the explanatory variables. Two omit multifamily housing starts because of uncertainty about how well those starts reflect real estate prices. One of the equations with starts and one without also have an error-correction term that estimates how rapidly realizations rebound toward their normal level after a divergence. Normally, all four equations measure stock value as the total value of corporate equities and stock- and bond-fund shares held by households. Because that sum includes stock- and bond-fund assets, it could pick up some of the influence of those funds on taxable gains and thereby confuse the tests presented here. That potential distortion is explored in the tests below by substituting a pure stock-price index for the value of stocks and fund shares owned by households.⁽²⁾

Growth rates for the variables are measured as the yearly change in the logarithm of the variables. Data for estimating the equations are available for 1955 though 1997. The equation without housing starts or the error-correction term takes the form:
 

log(GAINS) =

c1 * log(PRICE LEVEL) +c2 * log(REAL STOCK PRICES) +c3 * log(REAL GDP) +c4 * log(REAL GDP) +c5 * TAX RATE +c6 * YEAR 1986 +c0 +random error

where means change from the previous year.

The variables are measured as follows:
 

GAINS		Net positive gains reported on individual income tax returns.
PRICE LEVEL		GDP chain-weighted price index from the national income and product accounts.
REAL STOCK PRICES		New York Stock Exchange Composite Price Index for December divided by the annual GDP price index.
REAL GDP		From the national income and product accounts.
TAX RATE		Top federal tax rate on long-term capital gains income.
YEAR 1986		1 in 1986, 0 in other years. (Reflects one-time bulge in realizations in 1986 because of impending tax increase.)

The following variables were added or substituted in alternative specifications of the above equation.
 

STOCK VALUES		Sum of the household sector's holdings of corporate equities and stock-, bond-, and hybrid-fund shares from the flow-of-funds accounts.
STARTS		Starts of housing units in buildings with two or more units, according to the U.S. Census Bureau.
ERROR CORRECTION		Residual of previous year from an equation that explains logarithm of the gains-to-GDP ratio in terms of tax rates and the year 1986 variable.

Ratio Equations. The ratio specification, developed at the Federal Reserve Board, attempts to explain the ratio of taxable gains to the size of the economy.⁽³⁾ The size of the economy is measured by potential economic output (GDP) at full employment. The ratio of taxable gains to potential GDP has shown no long-run trend up or down in the past 40 years but has fluctuated considerably from year to year. The specification tries to explain those fluctuations in terms of fluctuations in stock prices, the business cycle, tax rates, and other variables. Explanatory variables such as stock prices and GDP are also measured relative to potential GDP.⁽⁴⁾

The ratio specification has been unable to explain the strong tendency for unusually high realizations in one year to be followed by high realizations in the next, and for unusually low realizations in one year to be followed by low realizations in the next. To correct for the statistical shortcomings of such an unexplained correlation, the equation is estimated with a first-order autoregressive correction.

The ratio equation shown below is a version specified to include explanatory variables similar to those in the growth equation. One simplification is that changes in the price level and real stock prices are forced to have the same effect on realizations. Another simplification is that business-cycle influences are measured by one variable, the ratio of actual to potential GDP.
 

GAINS / POTENTIAL GDP =		c1 * STOCK PRICE / POTENTIAL GDP +c2 * GDP / POTENTIAL GDP +c3 * TAX RATE +c4 * YEAR 1986 +c0 +ut
and:
		ut = c5 * ut-1 + random errort

The term u_t is the error term in year t that is correlated with the error term in the previous year. Potential GDP is CBO's measure of real potential GDP expressed in current dollars by multiplying by the implicit price deflator.

As with the growth equation, one alternative specification substitutes the total value of household holdings of stocks and stock- and bond-fund shares for the stock-price index. Another adds multifamily housing starts (measured relative to the number of households instead of potential GDP).

The above specifications were selected through theorizing and experimentation by several analysts.⁽⁵⁾ Nonetheless, they incompletely represent the factors that determine the accrued capital gains that people hold in a year and the decisions to sell assets with those gains. As a result, the estimated equations fail to explain annual realizations precisely. Additional variables, such as ones that reflect the activities of stock and bond funds, might improve the equations' ability to explain all realizations.

Variables Measuring the Activity of Stock and Bond Funds

CBO added three variables measuring stock- and bond-fund activity to the equations to estimate the extent to which those funds have a net impact on total taxable gains. One variable is the fraction of taxable stock holdings that is held in taxable stock funds. The other two variables are amounts of capital gains distributions: total distributions paid by stock and bond funds, and distributions reported by individuals on their tax returns.

Share of Individuals' Taxable Stock Holdings in Stock and Bond Funds. This variable provides a direct test of the hypothesis that more frequent trading by mutual funds raises total taxable gains. If the taxable distributions from stock and bond funds are raising taxable capital gains because fund managers realize gains that individual investors would not, then the increasing share of stocks that taxable investors hold in stock and bond funds should increase taxable gains. If, by contrast, fund managers are doing the same trading that individuals would do on their own, then the rising share of stocks held in stock and bond funds should have no impact on taxable gains.

The fraction of stocks that taxable individuals hold in stock funds is constructed from measures of the value of their stock-fund holdings and direct stock holdings. The first component--the value of taxable household stock-fund holdings--is measured as the sum of all stock-fund assets held in traditional accounts plus half of those held in trusts and estates. Those amounts came from data by the Investment Company Institute (ICI) for 1980, 1981, and 1985 through 1997 and from the Federal Reserve's flow-of-funds accounts for other years since 1955. The flow-of-funds data are adjusted in various ways to make them more consistent with the ICI data (see Box A-1 for details). The second component--the value of stocks held directly by taxable investors--is measured by flow-of-funds data on stocks held by the household sector plus half of the stocks held by trusts and estates.⁽⁶⁾ The fraction of stocks that taxable investors hold in stock funds is then measured as the ratio of the value of their stock-fund holdings to the sum of their stock-fund and direct holdings. That variable is referred to in the equations as MFSHARE.
 

MFSHARE grew irregularly between 1955 and 1971, from 2.9 percent to a plateau of about 6.1 percent (see Table A-1). It then fell irregularly to 3.2 percent in 1980. MFSHARE went through a similar cycle between 1980 and 1992, peaking at 5.9 percent in 1987 before receding to 4.4 percent in 1992. Since then it has shot up to 12.2 percent. The growth of MFSHARE since 1980 has resulted from a combination of new investment in stock funds and disinvestment in directly held stocks.
 

MFSHARE follows a pattern similar to that of taxable capital gains, but its turning points lag behind those of taxable gains. When taxable gains are shown relative to potential GDP, as in the ratio equation, gains and MFSHARE rise from the mid-1950s through 1968 (see Figure A-1). Both subsequently turn downward, although the decline in MFSHARE begins and ends later. Both peak again in the 1980s, but taxable gains peak in 1986 whereas MFSHARE peaks in 1987. After bottoming out in the early 1990s, both rise through 1997, with MFSHARE growing much faster than taxable gains. The correlation between MFSHARE and taxable gains relative to potential GDP is .44.
 

FIGURE A-1. THE MFSHARE VARIABLE AND THE RATIO OF TOTAL CAPITAL GAINS TO POTENTIAL GDP, 1955-1997

SOURCE: Congressional Budget Office based on data in Table A-1 and from the Department of the Treasury.

NOTE: MFSHARE is the share of stocks that taxable individuals hold in stock funds.

Not only does MFSHARE lag behind the turning points in taxable gains, it misses many of the yearly fluctuations in the growth rate of taxable gains. The correlation between MFSHARE and the growth rate of taxable gains, the dependent variable in the growth equation, is .17.

Capital Gains Distributions. In principle, a second way to estimate the net impact of distributions from stock and bond funds on taxable gains would be to include a measure of taxable distributions from those funds in an equation that explains the amount of taxable gains on assets held outside those funds. If a dollar of taxable distributions reduced other taxable gains by a dollar, then stock and bond funds would have no net impact on taxable gains. (Gains from the funds would be substituting for gains on other assets.) At the other extreme, if a dollar of taxable distributions from stock and bond funds had no effect on other taxable gains, then no substitution would be occurring and all taxable distributions would be net additions to taxable gains.

Such a test cannot be carried out with the available data, however. Although total taxable gains are known for many years, their division according to source (from stock and bond funds and from other assets) is not known. The largest component of total gains coming from stock and bond funds is the amount of distributions reported by taxpayers. That amount is known only for 1981 through 1997. Those 17 years provide too few data points for reliable estimation of equations like the ones described above. The other components of gains from stock and bond funds that are included in total gains--distributions passed through estates and trusts, and gains realized from selling shares in the funds--are unknown for most years.

A feasible alternative is to add a measure of capital gains distributions to the equations described above. If a dollar of distributions is estimated to have no impact on taxable gains, then distributions are indeed substituting for other gains. If a dollar of distributions is estimated to raise taxable gains, the interpretation is less clear. The distributions may not be fully offset by reduced gains on other assets. Or some factor that affects all gains may be omitted from the basic equation. For example, the factors that lead investors to realize gains are probably not entirely captured by the equations, and they may be reflected in the decisions of fund managers to realize gains. Such correlations between realizations by the funds and by other investors would make distributions appear to explain total taxable gains. Hence, this alternative equation could be biased toward finding that distributions from stock and bond funds increase total taxable gains.⁽⁷⁾

Although measures of distributions have limited value in determining the net contribution of stock and bond funds to taxable capital gains, they may still be useful in forecasting. For instance, ICI reports total distributions paid by those funds before the IRS reports total taxable gains. Thus, if the distributions reflect amounts of capital gains realized by many other investors, equations including the distribution variable could provide advance information about total taxable gains.

CBO added two measures of capital gains distributions to the equations. The first is the amount of distributions reported by stock and bond funds, which is known in the equations as variable CGD (see Table A-1). That amount was included because it may be useful for forecasting total taxable gains. (CGD differs slightly in later years from the amounts shown in Table 2 because it does not reflect revisions incorporated in ICI's 1999 Mutual Fund Fact Book.)

The second measure is the amount of distributions that individuals reported on their tax returns, known as CGDTAX. That variable is only available for 1981 through 1997. For earlier years, CGD is used. It is probably a good substitute in the 1950s and early 1960s because flow-of-funds data indicate that at that time most stock- and bond-fund assets were held in taxable form by individuals. CGD is an increasingly less reliable approximation starting in the late 1960s, when trusts and estates, pensions, and other institutions began to increase their holdings of stock and bond funds. By 1980, ICI shows that only 66 percent of stock funds were held by individuals in traditional fashion.

The amounts that individuals reported on their tax returns in 1981 and 1982 are larger than the amounts that, according to ICI, stock and bond funds paid out. The variable CGDTAX uses ICI's distributions in those years on the assumption that individuals overstated their distributions. That overstatement, if it existed, should have diminished in later years as the Internal Revenue Service improved its monitoring of income from mutual funds.

The amounts that taxpayers reported as distributions between 1983 and 1997 omit distributions passed through trusts and estates. That omission should have a relatively small effect because trusts and estates hold many fewer stock-fund assets than individuals do, and not all of the distributions paid to trusts and estates are passed through. Also, annual fluctuations in pass-through distributions caused by changes in stock prices and other market forces are likely to be similar to fluctuations in distributions paid to traditionally held funds and thus reflected in distributions reported by taxpayers.

CGD and CGDTAX omit capital gains that taxpayers realize from selling shares in stock and bond funds, but that omission is unlikely to affect the estimated coefficients. For one thing, the amount of omitted gains is small. And for another, the sale of fund shares is likely to offset trading that individuals would have done on directly held assets.

CGDTAX falls progressively behind the upward trend in CGD after 1983, but it shows similar fluctuations around the trend. Distributions reported by taxpayers fall progressively behind total distributions, apparently because traditional holdings of stock funds grew less rapidly than tax-deferred, fiduciary, and institutional holdings, as discussed earlier.

CGDTAX has always been a small component of total taxable gains, although it has grown from less than 5 percent in the early 1980s to more than 12 percent in 1997 (see Table 3 in the main text). In spite of its small size relative to total gains, its trends over time match some of the trends in total taxable gains (see Figure A-2). Both measures of gains rose gradually from 1955 through 1968, dropped in the early 1970s, peaked dramatically in the mid-1980s, and then dipped again before jumping up in the 1990s. The major difference between the two is that reported distributions (CGDTAX) have far surpassed their last peak, in the mid-1980s, whereas total taxable gains have pulled only slightly ahead of their mid-1980s peak.
 

FIGURE A-2. TOTAL TAXABLE GAINS AND CAPITAL GAINS DISTRIBUTIONS REPORTED ON TAX RETURNS, 1955-1997

SOURCE: Congressional Budget Office based on data in Table A-1 and from the Department of the Treasury.

The growth rate of CGDTAX, which will be entered into the growth-rate equation, has a correlation of .62 with the growth rate of taxable gains. CGDTAX relative to potential GDP, which will be entered into the ratio equation, has a correlation of .70 with gains relative to potential GDP.

Results

When the measures of stock- and bond-fund activity are added to the equations individually, all of the estimated coefficients are positive, suggesting that stock and bond funds do increase taxable gains. Only the coefficients of MFSHARE are statistically different from zero, however, and they may be reflecting realizations by other investors.

Ratio Equations. The basic ratio equation, using data from 1955 through 1997, estimates coefficients that are statistically different from zero (as indicated by t-statistics greater than 2.0) and have their expected signs. The equations explain 90 percent of the variation in the ratio of taxable gains to potential GDP (see Table A-2).
 

When MFSHARE is added to the basic ratio equation, its estimated coefficient is 0.126. Its t-statistic of 2.0 means that a true coefficient of zero is very unlikely. Coefficients on the other variables in the equation are close to their values in the basic equation without MFSHARE, indicating that the contribution of MFSHARE largely comes from reducing the unexplained residual in the basic equation. In particular, adding MFSHARE helps explain the increasing amount of taxable gains relative to potential GDP in 1993, 1996, and 1997.

A coefficient of 0.126 means that a 1 percentage-point increase in the share of stocks that taxable individuals hold in stock and bond funds increases the ratio of taxable gains to potential GDP by 0.126 percentage points. Applied to the 1990-1997 period, the coefficient implies that the increase in MFSHARE of 7 percentage points raised total taxable gains by $67 billion. In comparison, distributions reported on tax returns rose by $42 billion during that period; distributions passed through trusts and estates may have risen by at most another $8 billion, for a total increase of no more than $50 billion in actual taxable distributions.

An estimated increase in taxable gains greater than the actual increase in distributions is inconsistent with the hypothesis being tested. The coefficient of MFSHARE is intended to estimate the extent to which shifting stocks into stock funds raises capital gains on those stocks. An estimated increase equal to the amount of taxable distributions ($50 billion) would indicate that all distributions by stock funds were net increases in taxable gains. That is, individuals would not have realized any gains on those stocks if they had held them directly. An estimated increase of less than $50 billion would imply that gains in stock and bond funds partially substituted for gains by individuals. But an estimated increase of $67 billion implies that shifting stocks to stock funds increases gains by more than the amount realized by the funds.

One explanation for that discrepancy is statistical error. The standard error of the estimate is 0.061, so the true coefficient of MFSHARE has a 95 percent chance of lying between zero and 0.25. If the true coefficient was, say, half of its estimated size (0.63), the increase in MFSHARE during the 1990s would have raised taxable gains by $34 billion. An increase of that magnitude when total taxable distributions rose by about $50 billion would mean that two-thirds of distributions from stock and bond funds were net increases in taxable gains. Higher net increases are more probable than the two-thirds figure, and lower net increases are less probable.

Although statistical error is a plausible explanation for the apparent overestimate, it is not the most likely explanation. Statistical error is as apt to mean that the true effect could be half as much above the estimated impact as below it. The most likely explanation is that other activity involving the realization of capital gains is correlated with the rising share of stocks held in stock funds. That could occur because some omitted variable both encourages realizations of gains and encourages people to invest in stock funds, or simply because some omitted variable happens to be correlated in recent years with the rapid increase in MFSHARE. Unfortunately, if other realizations activity is contaminating the estimated impact of stock and bond funds themselves, the net contribution of those funds cannot be isolated.

The impacts of CGD and CGDTAX are directly observable from their estimated coefficients in the ratio equations (see Table A-2). When CGD is added to the basic ratio equation, its coefficient is 0.31, which means that an additional dollar of capital gains distributions raises taxable gains by 31 cents. Capital gains distributions increased by $174 billion between 1990 and 1997, so the coefficient implies that their increase raised taxable capital gains by $54 billion. That amount is close to the estimated $50 billion increase in distributions appearing on tax returns, which implies that nearly all taxable distributions are net increases in taxable capital gains. The strength of that finding is limited, however, because of the large standard error of the estimate. That error is large enough to allow the possibility of no impact, negative effects, or much larger positive effects. The lack of statistical significance for the coefficient (t = 1.33) also means that total distributions from stock and bond funds are not useful for forecasting total taxable gains.

When CGDTAX is added to the basic ratio equation, its estimated coefficient is 1.47, which means that an additional dollar of distributions paid to taxable individuals increases total taxable gains by $1.47. That increase is larger than gains on stock and bond funds can account for. If distributions by stock and bond funds are not offset by reduced gains on other assets, then each dollar of distributions reported by taxpayers will raise total taxable distributions by no more than $1.20. (The $1.00 is the amount reported by taxpayers, and the $0.20 is the unidentified distribution passed through trusts and estates.) An impact much in excess of $1.20 would have to reflect realizations activity on other assets as well as stock and bond funds.

Statistical uncertainty about the 1.47 estimate is substantial. The standard error of the estimate is such that the actual impact of CGDTAX has a 95 percent chance of lying between -0.08 and 3.01. That range barely includes zero, so a complete offset is possible but unlikely. Effects as high as 3.01 are also possible, and those could arise only if taxable distributions were reflecting realizations activity on other assets as well as any impact from stock and bond funds. As noted above, the coefficient of CGDTAX is likely to be biased upward, both because distributions are likely to be correlated with realizations activity by other investors and because CGDTAX is itself a component of taxable gains.

The estimated impact of CGDTAX is slightly smaller than the estimated impact of MFSHARE. The $42 billion increase in CGDTAX between 1990 and 1997 multiplied by the estimated coefficient of 1.47 implies that taxable distributions raised total taxable gains by almost $62 billion, compared with the $67 billion figure suggested by MFSHARE. Given the statistical uncertainty of the estimated coefficients, the difference between $62 billion and $67 billion is statistically insignificant.

Growth-Rate Equations. The basic growth-rate equation estimates that all coefficients have their expected signs. Four of the estimated coefficients are statistically different from zero, but the coefficients for price level and the acceleration of real GDP are not (see Table A-3).⁽⁸⁾ The equation explains nearly 80 percent of the variation in the growth rate of taxable gains.
 

When the change in MFSHARE is added to the basic growth-rate equation, its coefficient is more certainly above zero than in the ratio equation, and its implied impact is much larger. The coefficient of 7.86 suggests that the increase in MFSHARE between 1990 and 1997 raised taxable gains by $140 billion--far above the estimated $50 billion of taxable distributions from stock and bond funds during that period. Statistical uncertainty is unlikely to explain such a large impact if the true effect is $50 billion or less.

The larger impact of MFSHARE in the growth-rate equation than in the ratio equation appears to arise from that variable's interaction with the price-level variable in the growth-rate equation. Adding the change in MFSHARE to the basic growth-rate equation causes the coefficient of the price-level term to double. In the basic equation, the coefficient of the growth rate of the price level implies that a 1 percent increase in inflation will raise the growth rate of taxable gains by a plausible 1.2 percent. But when the change in MFSHARE is added, a 1 percent increase in inflation is estimated to raise the growth rate of taxable gains by 2.6 percent. That amount is implausible because it means that inflation has three times as much impact as increases in real stock prices and nearly the same impact as increases in real GDP. The implausibly large impacts estimated for the inflation rate and the change in MFSHARE are offset by a larger negative value for the constant term. That pattern suggests the two variables are interacting to explain realizations activity outside mutual funds that happens to be correlated with the combination of the two variables. In short, the estimated impact of MFSHARE appears to be more distorted in the growth-rate equation than in the ratio equation. The distortion is avoided in the ratio equation because the inflation term does not appear by itself there.

When the growth rates of CGD and CGDTAX are added separately to the growth-rate equation, their estimated coefficients are again positive but are smaller relative to their standard errors than in the ratio equation (see Table A-3). Compared with the ratio equation, no net impact or even a negative impact on total taxable gains is plausible. So too is the possibility that a dollar of taxable distributions raises total taxable gains by more than could be attributable to stock and bond funds. The 0.064 coefficient of CGDTAX implies that the growth of distributions reported by taxpayers between 1990 and 1997 raised total taxable gains by $35 billion, or 83 cents for each dollar of growth in reported distributions. The statistical error in the estimate means that the actual change per dollar of growth in taxable distributions has a 95 percent chance of being as low as a 40 cent reduction or as high as a $2 increase in total taxable gains. The portion of the range between zero and $1.20 is consistent with a pure test of the impact of stock and bond funds.⁽⁹⁾ The coefficients of CGDTAX seem to be less biased by the realizations activity of other investors than the coefficients of MFSHARE do.

Alternative Specifications of the Basic Equations. Of the three changes in the basic equations discussed above, only one causes a noticeable change in the estimated coefficients of MFSHARE. Substituting the value of household stock holdings for the stock-price index causes the estimated impact of MFSHARE to increase by between 20 percent and 30 percent (see Table A-4). That increase occurs primarily because the value of stock holdings explains less of the variation in taxable gains than the stock-price index does. When MFSHARE is added to the basic equations with stock values, it explains some of the variation in taxable gains that is unexplained by stock values. Thus, substituting stock values further obscures the net impact of stock and bond funds on taxable gains.
 

The two other changes made to the basic equations are the addition of multifamily housing starts and, in the growth-rate equations, of an error-correction term. Those additions improve the fits of the basic equations shown in Tables A-2 and A-3 but cause small changes in the estimated coefficients of MFSHARE.

Conclusions

All of CBO's estimates find that stock and bond funds increase taxable capital gains, but the sizes of the increase are so large that the estimates probably overstate the net impact of those funds. The estimated coefficients of MFSHARE appear to be distorted in the growth-rate equations and in the ratio equations with stock values. In the ratio equations with stock prices, the estimated coefficients are consistent with the hypothesis that stock and bond funds raise taxable gains by two-thirds or more of the amount that they distribute. However, those coefficients are also consistent with the hypothesis that MFSHARE is reflecting realizations activity by other investors, and that hypothesis is more probable. The estimated effect of CGDTAX in the ratio equations is slightly smaller than that of MFSHARE, but it is subject to the same uncertainties about the net impact of the funds. In the growth-rate equations, the coefficient of CGDTAX does not appear to suffer the same distortion as the coefficient of MFSHARE. In fact, it implies a modestly smaller impact than the coefficient of CGDTAX in the ratio equation does. Finally, distributions paid by stock and bond funds (CGD) are not useful in forecasting taxable gains, even though data on those distributions are generally available earlier than IRS data on taxable gains.

The uncertainty about the impact of stock- and bond-fund activity results partly from the relatively few years of experience that exist with such funds at their current size. The uncertainty also arises from weaknesses in the historical data, such as the absence of direct information about the amount of distributions reported by taxpayers before 1981 and the fraction of household stocks held in stock funds before 1980. Finally, the inability of the basic equations to explain other realizations raises the likelihood of bias in the estimated effects of stock- and bond-fund activity. Indeed, the inclusion of stock- and bond-fund variables in the forecasting equations highlights their shortcomings. The overestimate of the effect of mutual funds--particularly in the case of MFSHARE in the ratio equation--results largely from the sharp spike in taxable gains and MFSHARE in 1996 and 1997. Because the basic equations fail to adequately explain that spike in taxable gains, the addition of stock- and bond-fund variables appears to do so.

1. Additional information about the equations can be found in Congressional Budget Office, Projecting Capital Gains Realizations, CBO Memorandum (November 1995).

2. A stock-price index differs from a measure of household stock values because it does not reflect changes in the number of shares that households own. That distinction has modest significance for CBO's statistical estimation because most of the variation in stock values in the estimation period arises from variation in stock prices. The number of shares held by households changed relatively little. Conceptually, stock prices and values have different limitations for measuring accrued gains; neither is necessarily superior.

3. Randall Mariger, Forecasting Individual Capital Gains Realizations, Federal Reserve Board Memorandum (August 27, 1997).

4. Changes in the ratio of stock prices to GDP are similar to changes in the ratio of stock value to GDP because the number of shares changes slowly.

5. See Congressional Budget Office, Projecting Capital Gains Realizations, and the references cited therein.

6. Federal Reserve Board, Flow of Funds Accounts of the United States (March 12, 1999), p. 102. The March data differ slightly from the June 1999 data used earlier in this memorandum.

7. The net impact of distributions on total taxable gains could also be overstated by the mathematical fact that distributions are a component of taxable gains.

8. The estimated coefficient of real GDP is 3.0, implying that a 1 percent change in the growth rate of real GDP leads to a 3 percent change in the growth rate of taxable gains. The size of that coefficient reflects the great sensitivity of taxable gains to the business cycle. The size is implausible, however, for the long-term response of taxable gains to real GDP growth.

9. When CGD is added to the basic growth-rate equation, its coefficient is 0.031, which implies that the growth in distributions paid by stock and bond funds between 1990 and 1997 raised taxable gains by $20 billion, or 48 cents for each dollar of growth in reported distributions. The statistical error in the estimate indicates a 95 percent chance that the actual impact per dollar of growth in taxable distributions could be as low as a 78 cent reduction or as high as a $1.68 increase.

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