Yannis Bilias

Dimitris Georgarakos

Michael Haliassos

Equity Culture and the Distribution

of Wealth

Discussion Paper 2008 - 010

March 6, 2008

Equity Culture and the Distribution of Wealth#

Yannis Bilias, Dimitris Georgarakos, Michael Haliassos

March 6, 2008 Abstract

Household participation in stockholding has grown dramatically since the late 1980s, partly due to the demographic transition. Increased tendency of households to manage riskier portfolios and retirement financing creates challenges, especially for small investors, with unclear implications for financial markets and for the distribution of wealth. Our findings, based on SCF data, imply that during the stock market upswing the share of ‘small’ investors increased, but entries and exits during the subsequent decline resulted in a stockholding pool more prone to sizeable stock holdings, partly because of changes in configuration of financial attitudes and practices within the pool. Study of the reported incidence of cumulative stock market gains and losses reveals a significant role of heterogeneity in terms of characteristics, attitudes, and practices, especially during downswings. This role is quite pronounced for mutual fund holdings, contrary to beliefs that investments in managed accounts are ‘simpler’. As regards the broader implications for the distribution of wealth, we show that equity holdings, unlike housing, have become quite important for overall net wealth inequality, despite limited participation and portfolio shares in household assets. Inequality indices suggest that progressively widening access to the stock market was not associated with a more equal distribution of either stock wealth or net wealth. Yannis Bilias: University of Cyprus and CFS Dimitris Georgarakos: Goethe University Frankfurt and CFS Michael Haliassos: Goethe University Frankfurt, CFS, and MEA Keywords: Stockholding, equity culture, household finance, wealth distribution.

# We thank Chris Carroll, Gikas Hardouvelis, Dirk Krueger, José Machado, Miquel Pellicer, Luigi Pistaferri, Susan Rohwedder, Gregory Siourounis, Arthur van Soest, Jonathan Skinner, Nick Souleles, Maarten van Rooij, Paul Söderlind, Steve Zeldes, participants at the NBER Summer Institute, the Mannheim RTN Conference, the Utrecht Netspar conference; and seminar participants at Aberdeen, Athens University of Economics and Business, Central European University in Budapest, Frankfurt, Netherlands Central Bank, Oxford, Piraeus, and St. Gallen for very useful comments. We are grateful to NETSPAR for financial support through a competitive research grant. This work has also been supported by the Center for Financial Studies under Research Program ‘Household Wealth Management’, while early stages were supported by the European Community's Human Potential Program.

1

1. Introduction

Participation and portfolio shares of households in risky assets, especially

direct and indirect stock holdings grew substantially over the 1990s.1 The increase in

stockholding participation has been dramatic, mainly in response to stockholding

opportunities introduced through mutual funds, individual retirement accounts and

defined contribution pension plans. A major driving force has been – and will be in

years to come - the demographic transition and the need for households to accumulate

assets on their own in order to finance retirement.

The resulting expansion of the stockholder base is often thought of as

facilitating wealth enhancement and reduction in wealth inequality through wider

access to the equity premium. Yet stocks are a risky instrument and one complicated

to use, especially for households with limited experience, information, and financial

sophistication. Indeed, the stock market participation literature has established that

certain characteristics, such as being wealthier or more educated, make a household

more likely to overcome entry costs and become a stockholder.2 Thus, as stockholding

participation spreads, the composition of the stockholder pool changes through the

addition of households with no or limited previous experience with risky financial

assets. How people handle stockholding opportunities, whether and how

heterogeneity matters for stockholding levels and outcomes and ultimately for the

distribution of wealth are all difficult empirical questions with potentially important

implications for theoretical research on heterogeneous agent models and for policy

debates on expanding the use of retirement accounts, promoting financial education,

and regulating provision of financial advice.

This paper uses household portfolio data from three waves of the US Survey

of Consumer Finances between 1989 and 2001, which encompasses the period of

2

continuous spread of stock market participation through the stock market upswing and

the aftermath of the downswing, and a battery of econometric techniques to study a

number of questions. How did the composition of the stockholder pool change during

the 1990s upswing and in the aftermath of the downswing alongside continuous

increases in stock market participation? How did the changed composition influence

stockholding levels across the distribution of stockholders? What role did changes in

configuration of financial attitudes and practices play in determining stockholding

levels and outcomes? Do they matter less for making gains and avoiding losses in

mutual funds, which are run by professionals rather than by households themselves?

What happened to the wealth distribution through the upswing and the downswing? Is

there evidence that stock wealth seriously influences the overall distribution of net

wealth, despite limited participation and typically limited shares of stocks in

household portfolios?

Our findings imply that during the stock market upswing the share of ‘small’

investors increased, but entries and exits during the subsequent decline resulted in a

stockholding pool more prone to sizeable stock holdings across the distribution. Part

of these changes can be attributed to changes in financial attitudes and practices

within the stockholder pool (a ‘dilution’ during the boom and a subsequent

‘cleansing’ during the downswing). Study of the reported incidence of cumulative

gains and losses reveals a systematic role of heterogeneity in terms of characteristics,

attitudes, and practices, especially during downswings. This role is even more

pronounced for mutual fund holdings compared to direct holdings, contrary to popular

beliefs that investments in managed accounts are ‘simpler’. Moreover, we show that

stock market wealth has become quantitatively important for overall net wealth

inequality, despite limited participation and portfolio shares in household assets

3

(unlike the largest asset for most households: housing). Inequality indices show that

progressively widening access to the stock market was not associated with a

progressively less unequal distribution of either stock wealth or net wealth.

These questions seem particularly relevant in a world which, faced with the

demographic transition, is consciously shifting responsibility for financing retirement

away from Social Security and towards households themselves (e.g. through defined-

contribution pension plans and individual retirement accounts). Indeed, evidence for

the potential of households to mishandle stock investments is starting to accumulate.

Households with lower education and resources have been shown to be more prone to

‘investment mistakes’ in terms of (non)participation, (under)diversification, and (lack

of) debt refinancing (Campbell, 2006). Calvet, Campbell, and Sodini (2006) find,

using Swedish data, that mistakes are disproportionately present among groups of

lower education and resources. Poor understanding of investment options has also

been linked to lack of international diversification and planning for retirement

(Graham, Campbell, and Huang, 2005; Lusardi and Mitchell, 2007, respectively).

Wealth inequality is of interest both in its own right and because households at

different points of the wealth distribution tend to exhibit different financial and

entrepreneurial behavior.3 Existing theoretical literature on increased stock market

participation and wealth inequality is rather limited, but already points to conflicting

effects. Some papers emphasize that broadening access to a financial instrument

offering an expected return premium would tend to reduce wealth inequality (see

Arrow, 1987; Guvenen, 2006). Guvenen shows that limited stock market participation

can account for much of US wealth inequality, which suggests that expanding

participation should reduce wealth inequality. Ambiguities arise, however, even in

4

stylized models once full financial information and sophistication are not taken for

granted among all participating households (Peress, 2004).4

The rest of the paper is organized as follows. Section 2 investigates

econometrically whether the spread of equity culture drew progressively ‘smaller’

stockholders into the stockholder pool, i.e. households with characteristics, attitudes,

and practices that tend to be associated with smaller stockholding levels. Section 3

reports estimates of the systematic role that household characteristics, attitudes, and

practices play for the incidence of stockholding gains and losses, distinguishing

between direct stockholding and mutual funds; and between stock market upswing

and downswing. Section 4 measures and decomposes into various sources, net total

wealth inequality in the US over a period of growing participation, and a stock market

upswing followed by a downswing. It demonstrates, inter alia, the growth in

importance of stockholding for the overall distribution of net wealth. Section 5 offers

concluding remarks.

2. Increased participation and the transformation of the stockholding pool

In this section, we use data from SCF for 1989, 1998, and 2001 to uncover the

underlying transformation of the stockholding pool as participation spread. We provide

extensive details on the data, asset categories, and variable definitions in Appendix C.

Existing literature on participation in stockholding, direct and indirect, shows

consistently that certain characteristics make it more likely that a particular household

will be drawn into the stockholder pool. We report in Table 1 marginal effects from

probit regressions, for each of the three survey years, that control for a similar array of

demographic and pecuniary characteristics to that employed in relevant studies (see, for

example, the empirical contributions in Guiso, Haliassos and Jappelli, 2001).5

5

Consistent with existing literature, we find that being affluent, more educated, and less

risk averse contribute to the probability of owning stocks (held directly and indirectly),

controlling for other factors. These results imply that certain characteristics contribute

to the probability of being a stockholder, and that the composition of the stockholder

pool changes in general as stock market participation spreads.

In Table 2 we present summary statistics on three factors often considered as

key for stock investments, namely education, income and (non-equity) net wealth.

These statistics show notable changes in the composition of the expanding

stockholder pool, both in absolute terms and relative to the population. While they do

suggest an increase in the share of ‘marginal’ and less educated stockholders during

the upswing, they fail to indicate a continuation of this trend through the downswing.

Specifically, by 1998 the share of college graduates among equity holders was

somewhat reduced to 46.8%, while in the population it increased by almost 6

percentage points. In addition, both the mean and median non-investment income

among equity holders is lower in 1998 compared to 1989, while in the population it is

considerably higher, by 10% and 6%, respectively. A similar picture emerges when

we look at net wealth.

However, by 2001 college graduates among equity holders reach 49.6%, an

increase of almost 3 percentage points within just three years, while their population

share remains unchanged. They also show significant increases at all percentiles of

income and wealth distribution (for instance, median non equity net worth increased

two times more among equity holders compared to the population). If anything,

summary statistics suggest that the composition of stockholders shifted against

‘marginal’ investors during the downswing, despite increased participation.

6

2.1. The Composition of the Stockholder Pool: Counterfactual Distributions

Changes in stockholding levels across the entire distribution result partly from

changes in market conditions (such as an upswing or a downswing) and partly from

changes in the configuration of stockholder attributes. While summary statistics of

isolated household characteristics can be suggestive, they fail to give a picture of

changes in the overall configuration of relevant characteristics controlling for changes

in stock market conditions. In this section, we use recent advances in construction of

counterfactual distributions to decompose observed changes in equity holdings into

the influence of characteristics and the influence of market conditions. This allows us

to examine whether more and more ‘marginal’ stockholders likely to exhibit smaller

stockholding levels were drawn into the stockholder pool, as participation spread.

We apply a variant of a technique proposed by Machado and Mata (2005),

described in Appendix B, to decompose the change in the distribution of equity

holdings between two years into (i) a component due to the change in the distribution

of covariates; and (ii) a component due to changes in the coefficients on these

covariates at various percentiles. This is done by running quantile regressions6 and

constructing counterfactual distributions.

When comparing two different years, say 1998 to 1989, the relevant

counterfactual distribution is the (logarithm of) equity holdings that stockholders in

1989 would have if, given their own characteristics, they experienced the same

influence of characteristics on equity holdings (‘coefficient effects’) as those

experienced by stockholders in 1998. The difference between the 1998 and 1989

distributions of equity holdings at each percentile is decomposed into:

98 89 98 * 89 98 * 89 98 89( ) ( ) { ( ) ( ; )} { ( ; ) ( )}f y f y f y f y X b f y X b f y− = − + − (1)

7

where y represents the log of equity wealth, X is the data matrix and b is a vector of

estimated quantile regression coefficients evaluated at various percentiles. The

difference in the first curly brackets represents the contribution of household

characteristics to the overall difference between the 1998 and 1989 distributions of

equity holdings. The difference in the second curly brackets measures the contribution

of differences in coefficients.

The coefficient and covariate effects for 1998-1989 are presented in Figure 1a.

Differences in distributions of equity holdings over this period are mainly driven by

coefficient effects, and these become progressively more important at higher

percentiles of the distribution. This is consistent with the exceptionally strong upward

movement of stock market indices over this period and it suggests that a given change

in characteristics has more important effects, during upswings, on the equity wealth of

households with sizeable equity holdings.

On the other hand, covariate effects are negative, implying that the

combination of 1989 characteristics with 1998 coefficients would generate even

higher equity holdings than what was actually observed for the 1998 stockholders. In

other words, the overall distribution of shareholder characteristics in the wider

stockholder base at the end of the 1990s was not as conducive to high equity levels as

the 1989 distribution. This was most evident among households with large equity

holdings.7

On the basis of 1989-1998 comparisons, one might be tempted to conclude

that the conjecture of progressive dilution of the stockholder base with smaller

stockholders as participation grows is accurate. However, when we compare 1998

with 2001, findings are actually reversed (Figure 2a). The decomposition is as

follows:

8

2001 98 2001 * 2001 98 * 2001 98 98( ) ( ) { ( ) ( ; )} { ( ; ) ( )}f y f y f y f y X b f y X b f y− = − + − (2)

We find that coefficient effects are negative, but covariate effects on equity holdings

(displayed in the second curly brackets) are positive and increasing beyond the 40th

percentile of the distribution of stock wealth. This implies that a stockholder pool with

the configuration of stockholder characteristics of 2001 would have had higher equity

levels in 1998, compared to those actually observed for 1998 stockholders. In turn,

this suggests an improvement of the pool between 1998 and 2001, despite the

continuing overall increase in participation. These, combined with our findings for

1989-1998, point to the conclusion that stock market conditions are crucial: increased

participation appears to draw ‘marginal’ investors during booms, but during

downswings the balance is tilted towards bigger investors, presumably through more

pronounced exits among small investors.

2.2. A Role for Financial Attitudes and Practices?

So far, we have used the terms ‘large’ or ‘small’ (‘marginal’) investor merely

to depict their likely level of stockholding, but without asking whether this level is

‘optimal’ for stockholders with these characteristics, or whether it can be traced partly

to (possibly suboptimal or misguided) financial attitudes and practices. Are ‘marginal’

investors small simply because this is optimal given their characteristics, or also

because of the way they approach stock investments? This issue is particularly

relevant for understanding the implications of increased reliance on household

decision making for managing riskier portfolios and providing for retirement.

As a first step, we extend our counterfactual analysis in order to estimate the

effect of changes in configurations of financial attitudes and practices within the

stockholder pool. We are conservative in what we include under attitudes and

9

practices, in that we do not include factors such as education, which help shape

attitudes and inform practices but also determine the income process faced by the

household. In this sense, we are likely – if anything - to underestimate the quantitative

importance of attitudes and practices. We consider three factors under financial

attitudes and practices, namely reported willingness to take more than average risk,

reporting a long investment horizon (in excess of 10 years), and ‘financial alertness’

(defined as shopping around extensively for the best terms before making major

borrowing and saving decisions).

We perform the following sequential decomposition:

98 89 98 ** 98 89 98

** 98 89 98 * 89 98

* 89 98 89

( ) ( ) { ( ) ( ; , , )}

{ ( ; , , ) ( ; )}

{ ( ; ) ( )}

f a

f a

f y f y f y f y X X b

f y X X b f y X b

f y X b f y

− = −

+ −

+ − (3)

where the counterfactual f** represents the equity wealth distribution that would have

prevailed in 1998 if the configuration of financial attitudes in the stockholder pool

were distributed as in 1989. The term in the second curly bracket shows the relative

contribution of other household characteristics (which we can call ‘fundamentals’).

Figure 1b exhibits this decomposition of covariate effects for the 1989 to 1998

period. The shaded area represents the effects of changes in covariates conservatively

assigned to ‘economic fundamentals’. Our estimates based on this exercise imply a

considerable contribution of financial attitudes and practices throughout the

distribution of equity holdings, but especially at the upper end of the distribution.

Figure 2b carries out an analogous exercise for the period between 1998 and

2001. Here we use the following sequential decomposition:

10

2001 98 2001 * 2001 98

* 2001 98 ** 98 2001 98

** 98 2001 98 98

( ) ( ) { ( ) ( ; )}

{ ( ; ) ( ; , , )}

{ ( ; , , ) ( )}

f a

f a

f y f y f y f y X b

f y X b f y X X b

f y X X b f y

− = −

+ −

+ − (4)

Results are quite similar, with greater room for effects of attitudes above roughly the

70th percentile of the distribution of equity holdings.

Thus, counterfactual analysis suggests that the period 1989-1998 has

witnessed a dilution of the composition of the stockholder base, as more ‘marginal’

stockholders were drawn into the market. The subsequent, 1998-2001 period is even

more interesting, as it seems to combine an improvement in the composition of the

stockholder base coupled with an increase in overall participation. To put it

differently, our findings suggest that the stock market downswing has had a

‘cleansing effect’ on the stockholder pool, by encouraging investors with poorer

financial attitudes and practices to leave and (a slightly larger number of) investors to

enter with attitudes and practices more conducive to high equity wealth levels.8

3. Who Gains and Who Loses in the Stock Market?

We now turn to examining directly the systematic role of household

characteristics, attitudes, and practices in making overall gains in the stock market and

in avoiding losses. The SCF contains responses on the incidence of stockholding gains

or losses based on the cumulative experience of each stockholder by 1998 or 2001

(though without knowledge of when stocks were initially acquired). We first present

some tables describing the incidence of these responses in the population and across

different education categories. We then report our findings from econometric analysis

of the contribution of various household characteristics, including financial attitudes

11

and practices, to experiencing cumulative gains or losses in stockholding by 1998 and

then by 2001, separately for direct and indirect stockholding through mutual funds. 9

3.1. Descriptive analysis

Table 3 shows the experience that the three education categories had with stock

market gains and losses by the end of 1998 and 2001. By 1998, 80% of all direct

stockholders were experiencing cumulative gains on their direct stock investments. The

incidence of gains was increasing in education, but the incidence of losses was the same

across the board. By 2001, the percentage of equity holders declaring cumulative gains

in direct stock investments dropped to 53%, with a steeper education gradient, both for

gains and for losses.

Mutual fund investments are generally considered as being less demanding for

households, since portfolios are diversified and managed by professional fund

managers. However, in view of the proliferation of mutual funds, whose number is now

of the same order as the number of individual stocks, the question of which stocks to

hold has been replaced by the equally pressing questions of which mutual funds to hold

and of how to pick qualified advisors. In Table 3, one does find greater incidence of

cumulative gains and smaller incidence of cumulative losses for mutual funds in each

of the two years, though marginally so for losses in 2001. Yet, Table 3 also shows that,

in both 1998 and 2001, cumulative gains and losses for mutual funds were much more

differentiated across education categories than the corresponding rates for direct

holdings of stock.

3.2. Regression Analysis

We turn next to regression analysis of the incidence of gains and losses from

12

stockholding, conditional on participation, in order to estimate the contributions of

given household characteristics, attitudes, and practices, controlling for the remaining

ones. We model the incidence of cumulative gains and losses using two-stage probit

regressions that allow for selection. The first step models the probability of owning

directly stocks (or mutual funds, respectively), and the second is observed only if

households are direct stockholders (or mutual fund shareholders, respectively). The first

step specification is the same to the one presented in Table 1. The model uses as

exclusion restrictions the variables ‘intension to leave a bequest’ and ‘save for rainy

days’, which are assumed to affect the probability of owning the asset in question but

not to determine the incidence of gains or losses.10 We run two such estimations for

1998 (one for gains and one for losses), and two for 2001, separately for direct and

indirect stockholding.11

Our estimation allows for correlation among unobserved factors contributing to

the probability of the cumulative outcome and to the probability of stock ownership of

the relevant type. When the correlation is statistically significant, we report conditional

marginal effects from two-stage probits that have taken into account selection bias.

When it is statistically insignificant, we report marginal effects from standard probits

on the restricted subsamples of direct (or mutual fund) shareholders.

Results for direct stockholding and mutual funds in 1998 and 2001 are reported

in Tables 7 and 8, respectively. As before, we examine the effects of three aspects of

financial attitudes and practices, namely willingness to take more than average risk,

long investment horizon, and financial alertness. In addition, we control for portfolio

breadth (the number of shares or mutual funds held), and for whether the household

reports that it makes use of professional advice (this information is available only for

waves 1998 and 2001).12

13

Portfolio breadth has a positive and statistically significant contribution to the

probability of achieving cumulative gains in direct stockholding by 1998 (Table 4).

Neither having a long investment horizon (in excess of 10 years) nor using professional

advice make a statistically significant contribution to cumulative gains among

stockholders in the stock market boom of 1998, controlling for other factors.

Interestingly, once we control for financial attitudes and practices, we no longer find a

statistically significant role for educational attainment in achieving cumulative gains in

1998. Findings in column 3 which examines the incidence of the less likely outcome of

cumulative losses by 1998 are consistent with those.

Education, some financial attitudes and practices, and certain other factors that

made no significant contribution in boom times, gain statistical and quantitative

significance in the period encompassing the downswing (cols. 4 and 5). As in the boom,

portfolio breadth is statistically significant in facilitating cumulative gains among direct

stockholders and in reducing the probability of cumulative losses. However, the same is

true now for having an investment horizon longer than 10 years, with marginal effects

of the order of 6 percentage points. In addition, willingness to take more than average

financial risk significantly affects the probability of making gains. Estimated marginal

effects of using professional advice are insignificant (marginally for gains) and of the

wrong sign for direct stockholders.

Even after controlling for financial attitudes and practices, a college degree is

estimated to make a difference in producing good outcomes in bad times. It has a

remarkably large and significant positive effect on the probability of surviving the

downswing with cumulative gains, raising it by 15 percentage points. Although it is

also estimated to reduce the probability of losses, the effect is not statistically

significant.

14

Having received an inheritance or substantial assets in a trust or in some other

form also makes statistically significant and sizeable contributions to the incidence of

cumulative gains and to avoiding cumulative losses in bad times, of the order of about 9

percentage points. Since wealthier households are more likely to be leaving bequests,

households who have received an inheritance are likely to have also inherited a

portfolio structure and some of the financial expertise that contributed to making the

previous generation wealthy.

Table 5 presents results for indirectly held equity. In the period ending in 1998

(cols. 2 and 3), the only notable statistically significant effects refer to breadth in

mutual fund holdings and willingness to take above average financial risks. The

relevance of the former suggests that the degree of diversification inherent in any given

mutual fund, though greater than that typically observed among direct stockholders, can

be further improved upon by combining a number of different mutual funds. In these

good times, education, length of investment horizon, financial alertness and use of

professional advisors made no significant contribution to the outcomes.

As for direct stockholding, a number of factors become significant for making

gains and avoiding losses in the period encompassing the downswing. A college degree

is estimated to have increased the probability of cumulative gains among mutual fund

holders by a staggering 28 percentage points, and to have reduced the probability of

losses by 23 percentage points, controlling for other factors. Indeed, college education

is estimated to have greater impact on the probabilities of gains and of losses for the

commonly thought as “softer” option of indirect stockholding than for direct

stockholding.

Financial attitudes and practices are also important. Portfolio breadth is found to

have a strongly statistically significant marginal effect, despite the diversification

15

inherent in holding even a single mutual fund. Holding shares in more funds increases

the probability of cumulative gains and reduces that of losses in mutual funds by 2001.

Having an investment horizon longer than 10 years also contributes to gains and to

avoidance of losses, by about 7 percentage points.

As in all our previously reported regressions, use of professional advice failed to

make a significant difference to the cumulative outcome (beyond any influence it may

have had in lengthening the horizon and in broadening the portfolio of the household)

and showed counterproductive signs during downswings. These findings cast some

doubt on the overall quality or scope of professional advice given to households, as

long as we view the use of such advice as being a function of exogenous factors, such

as ignorance or lack of time on the part of the household to delve into the intricate

details of financial decision making.13

Finally, being a male or white non-Hispanic mutual fund shareholder raises the

probability of surviving the downswing with cumulative gains and lowers the

probability of experiencing cumulative losses. Estimated conditional marginal effects

are sizeable in both cases. Part of these effects may be due to the race variable proxying

for future income prospects, but it may be additionally suggesting that the mutual fund

sector is targeting minority households less aggressively.

All in all, results in this Section suggest that the incidence of cumulative gains

or losses in direct stockholding or in mutual funds is not simply determined by overall

stock market performance but also by household characteristics, including financial

attitudes and practices of investing households.14 Education, portfolio breadth, and

length of investor horizon are both statistically and quantitatively significant for making

gains and avoiding losses in stockholding, especially in the aftermath of stock market

downswings.

16

Given that household participation in stockholding is far from universal; and

that invested amounts cannot be compared to the major asset for most households,

namely the value of the primary residence, how important can stocks be for the overall

wealth distribution? Even if stock market swings change the levels of household equity

wealth and even if some households are better able to handle the challenges of

stockholding, can we expect the increased participation and the amounts that are

invested in stocks to have a visible effect on the distribution of net wealth and its

changes over time? It is to these questions that we now turn.

4. How important is Stockholding for Net Wealth Inequality?

In this Section, we document changes in inequality of net total wealth among

US households between 1989 and 2001 and investigate the importance of

stockholding for these changes.15 The first subsection computes net wealth inequality

indices to show that different parts of the distribution of net wealth have been affected

quite differently over this period, rendering blanket statements about net wealth

inequality misleading. The second subsection presents inequality decompositions by

asset components to show that, despite the rich pattern of inequality changes,

stockholding has become dramatically more important for net wealth inequality

regardless of whether we focus mainly on inequality at the upper end or in the middle

of the distribution.

4.1. How has Net Wealth Inequality Changed?

Data from SCF are particularly well suited for analysis of the wealth

distribution, since they over sample the rich and they are not subject to top-coding of

wealthy households carried out in other surveys.16 We first compute four commonly

17

used measures of inequality, which are sensitive to changes in different parts of the

distribution17: Mean logarithmic deviation (MLD), Theil, Half of Squared Coefficient

of Variation (HSCV), and Gini. Theil’s index is influenced by the relative distance

between the rich and the poor, attaching more weight to transfers at the lower and

upper ends. HSCV is very sensitive to changes in the upper tail of the distribution: it

is very sensitive to inequality at high wealth levels but less so to inequality at other

regions of the distribution (Cowell, 1977; Shorrocks, 1980). Gini is more sensitive to

the middle of the distribution.

Table 6 reports computed values of four inequality indices for net overall

wealth in 1989, 1998, and 2001.18 MLD records a sizeable decrease in inequality

between 1989 and 1998, followed by an increase to a level in 2001 that falls short of

inequality at the starting point. Theil and HSCV record increased inequality in 1998

compared to 1989, followed by a reduction in inequality between 1998 and 2001.

Finally, Gini records a slight increase in net wealth inequality over time.

The patterns we observe, especially the movements in HSCV and Theil,

suggest that net wealth inequality at the upper end of the wealth distribution increased

during the stock market upswing of the 1990s and diminished during the subsequent

downturn. The increase in the Gini coefficient suggests some increase in inequality

among middle net-wealth classes throughout the period under examination.

4.2. The Growth in Importance of Stockholding for Net Wealth Inequality

Appropriate decompositions of inequality indices allow us to investigate the

relative importance of different asset components of net total wealth for generating

inequality at different points in the distribution. Inequality in a variable W in a given

18

year, WI , can be expressed as an exact sum of the contributions made by its various

factor components:

W ff

I S=∑ (5)

A factor component contributes to increased (reduced) inequality if fS > 0 (<0). The

share of a particular factor f, fs , in generating inequality is defined as: ff

W

Ss

I= , and

thus: 1ff

s =∑ . Here we focus on the top of the distribution (which accounts for the

main bulk of equity holdings) using the HSCV, and on the middle of the distribution

using the Gini. Despite their recorded differences, both point to the substantial growth

in importance of stockholding.

4.2. Decomposition of HSCV by Source

HSCV has desirable decomposability properties and it can handle the regular

incidence of zero assets.19 Shorrocks (1982) proved that, under certain axioms, there

is a unique ‘decomposition rule’, according to which the proportionate contribution of

factor f can be derived − for a broad set of inequality measures − from:

2

cov( , )f

W

f Wsσ

= (6)

This is actually equivalent to the OLS estimated slope coefficient from the regression

of wealth factor f on net total wealth W.

When inequality is summarized by HSCV,

ff fW f

W

Is

Iρ χ= (7)

19

This expresses the proportionate contribution of factor f in terms of factor correlation

with total net wealth fWρ , the factor’s share in net total wealth fχ , net total wealth

inequality WI and the factor inequality fI , both measured by the HSCV. Thus, the

absolute contribution of factor f is: f fW f W fS I Iρ χ= .

The percentage of factor owners fn+ and the inequality they exhibit among

them fI + have a - disproportionate and proportionate, respectively - effect on the

factor contribution to inequality, given in approximation by: 1 ( 1) 1f ff

I In

++

⎛ ⎞= + −⎜ ⎟⎜ ⎟⎝ ⎠

(Jenkins, 1995). Hence, in our tables presenting wealth decompositions, we report

along with factor correlations, factor shares, and factor inequalities, percentages of

factor owners, and within factor inequalities.

Finally, we also compute a measure of each factor’s contribution to the

evolution of inequality over time. A factor making an important contribution to total

inequality in a given year does not necessarily play a prominent role in inequality

changes over time. Following Jenkins (1995) we decompose HSCV trends over time

as: 1% %t tf f

ft

I II s SI

+ −Δ = = Δ∑ , where a large positive value of sƒ%ΔSƒ suggests an

important role for factor f in raising total inequality over time.

Table 7 shows decompositions of inequality by source, as measured by

HSCV.20 Stock holdings are not the dominant source of net wealth inequality, but

neither is primary residence that forms the biggest part of most households’ portfolio.

Indeed, wealth in primary residence has a much smaller effect on net wealth

inequality than stockholding, and one not consistent with the overall trend.21

20

The factor with the greatest proportional contribution to net wealth inequality

is risky real assets (business equity and investment real estate excluding primary

residence), which make a more than 50 percent contribution in all three years (1989,

1998, 2001). Yet ownership rates of risky real assets do not exhibit any strong trend

between 1989 and 2001, hovering around 27 percent. Risky real assets exhibit high

degree of inequality and high correlation with overall net wealth, but in 1998, the year

that overall inequality spikes by the HSCV measure, the absolute factor contribution

of risky real assets and business equity increases only slightly (from 10.16 to 11.63).22

Given the much higher increase in net total wealth inequality, the proportionate factor

contribution actually drops (from 0.72 to 0.60).

Stock holdings, on the other hand, represent the factor with the biggest growth

in importance and they exhibit changes in inequality consistent with those of net

wealth. By 1998, wealth in equity holdings accounts for more than 25 percent of net

total wealth inequality, compared to just 7 percent a decade before.23 Directly and

indirectly held equity plays the dominant role in the increase of overall net wealth

inequality by 1998, based on the percentage change in source contributions. Between

1998 and 2001, reduction in inequality of equity holdings (attributable mainly to the

significant reduction in inequality among equity holders but also to the higher

percentage of owners) more than outweighs the increase in their relative correlation

and share, contributing to a fall in net total wealth inequality. However, their

proportionate contribution to net wealth inequality remains at 25%. One may wonder

whether these conclusions on the importance of stockholding depend on using HSCV,

which is sensitive to the upper tail of the distribution. The next subsection examines

robustness with respect to using the Gini index.

21

4.2. Decomposition of the Gini Index by Source

Despite the fact that the Gini coefficient focuses on the middle of the

distribution and records increased inequality throughout the period under study, Gini

decompositions reinforce the conclusions based on HSCV. The commonly used

Lerman and Yitzhaki (1985) decomposition of the Gini index expresses the absolute

contribution of wealth factor f to overall inequality as:

f f f fWS G Rχ= (8)

where fG is the inequality of factor f measured by Gini, fχ is the share of factor f in

net total wealth, and fWR is the “rank correlation ratio” defined as the ratio of the

covariance of household’s amount of wealth factor f with its ranking in the cumulative

distribution of net total wealth, over the covariance of its amount of wealth factor f

with its ranking in the cumulative distribution of factor f.

Table 8 reports decompositions of inequality of net total wealth as

summarized by the Gini coefficient. Equity holdings display one of the highest rank

correlation ratios, which gets higher over time, highlighting the growing importance

of risky financial assets for households’ position in the overall net wealth distribution.

In the period 1989-98, only stock holdings exhibit an increase in absolute and

proportionate contributions to net wealth inequality. The main factor behind this

increased contribution is the rise in its share of net total wealth over this period.24

5. Concluding Remarks

In the past two decades, household participation in stockholding grew

dramatically in the face of a stock market upswing and subsequent downswing. In this

paper, we have employed high-quality household-level data from the Survey of

Consumer Finances to shed light on the important links between stockholding,

22

household characteristics, financial attitudes and practices, and net wealth inequality.

Counterfactual distributions of equity holdings, separating changes in the

influence of investor characteristics from changes in the distribution of characteristics

within the stockholder pool, imply that the booming stock market of the 1990s raised

the share of smaller stockholders, while the subsequent downturn are estimated to

have improved the tendency of the stockholder pool to exhibit large equity wealth. In

this sense, the US experience between 1989 and 2001 seems consistent with a

‘dilution effect’ arising from the stock market boom, followed by a ‘cleansing effect’

of the stock market downturn.

Results from two different approaches, based on counterfactual distributions

and on two-stage probits using responses on cumulative gains and losses from

stockholding, support the view that heterogeneity in household characteristics, as well

as financial attitudes and practices, matter for stockholding levels and outcomes.

Being given the incentives to invest in stocks - for retirement or for other purposes –

does not guarantee wealth generation, but presents a challenge to avoid investment

mistakes due to misguided attitudes and erroneous practices when handling risky and

information intensive investments. This is even true of mutual fund investments, even

though the latter are often thought of as straightforward.

We found inequality in equity holdings to be quite important for inequality in

overall net wealth, despite their limited share in net wealth. Reduced wealth inequality

is far from being an automatic outcome of the spread of stockholding opportunities. In

the absence of measures promoting financial education, transparency, and sound

portfolio practices, a shift of responsibility from Social Security to households could

well lead to a worsening of the distribution of wealth in the future, by challenging

disproportionately the small and less sophisticated investors.

23

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26

Appendix A: Simulated Average Marginal Effects Standard econometric packages automatically report marginal effects for each variable evaluated at mean remaining characteristics. Although it is standard practice to report such automatically generated marginal effects, this is often not economically relevant and sometimes even misleading. For example, it fails to distinguish among single dummy variables and groups of dummy variables that represent a given attribute; or properly evaluate effects of continuous variables entering with particular nonlinear forms.25. Deriving averages of marginal effects that have been first evaluated at each single observation can provide instead a more realistic and economically relevant interpretation. In this paper, we compute reported marginal effects in the following way. We start by estimating the relevant limited dependent variable model. We then simulate the model parameters (including ρ for probit models with selection) by making 1000 independent draws from the multivariate normal distribution, subject to the restrictions that the average of simulated values be equal to the respective estimated parameter and that the structure of the estimated robust variance covariance matrix be preserved. For each such set of simulated parameters, we calculate marginal effects for each individual household and then derive the weighted average marginal effect for the relevant population. We repeat the process for every set of simulated parameters, thus computing a series of average marginal effects. The mean of this series is the estimated marginal effect and the standard error is the simulated standard error of the marginal effect. In the cases of probit model with selection we compute conditional marginal effects, using the formulae described in Greene (2000, p.857 & 860) and calculating the average marginal effects over the selected sample. Finally it should be noted that SCF data have been constructed on the basis of repeated imputation, to eliminate missing values. Five different sets of imputed data are provided. We take into account this feature, by first applying the above procedure to each of the five implicates and then deriving marginal effects and standard errors that are corrected for multiple imputation according to Rubin (1987). Appendix B: The Machado-Mata Algorithm

The algorithm for constructing counterfactual distributions is a variant of Machado and Mata (2005), recently used by Albrecht et al. (2003) and Nguyen et al. (2007):

1. Draw m random numbers from a uniform distribution on (0, 1): 1 2, ,...... mθ θ θ ; here we set m=2000. 2. For each iθ where i = 1,2,…,m, use the 1998 data on stockholders to estimate the Quantile Regression coefficient, 98 ( )ib θ , from the model:

98 98 98 98[ | ] ( )i iQ y X Xθ β θ=

27

3. Make m random draws of characteristics and corresponding weights with replacement from the 1989 stockholder pool. Denote the outcomes of these draws by *89

ix for i = 1,2,….,m. 4. Generate counterfactual values (a random sample of size m from the desired distribution): * *89 98 ( )i i iy x b θ= , for i = 1,2,….,m. Use these values to generate

* 89 98( ; )f y X b . Then, for each of the three sequences of variables (log equity holdings in 1989 and 1998 and counterfactual values), we calculate percentiles using population weights. The difference between percentiles of the distributions of the endogenous variable in 1998 and 1989 can be decomposed into:

98 89 98 * 89 98 * 89 98 89( ) ( ) { ( ) ( ; )} { ( ; ) ( )}f y f y f y f y X b f y X b f y− = − + −

The term in the first curly brackets represents the contribution of the covariates to the overall difference between the 1998 and 1989 distributions, evaluated at each percentile. The term in the second curly brackets shows the contribution of the QR coefficients. The method is a generalization of Oaxaca (1973) to the whole distribution. We further decompose the covariate effects into the contribution made by household characteristics that can be seen as fundamentals and a remaining contribution that is due to particular attitudes and practices. We assess the contribution of three attitudes, namely financial alertness, willingness to take more than average risk, and intension to leave a bequest. To this end we use the following sequential decomposition:

98 89 98 ** 98 89 98

** 98 89 98 * 89 98

* 89 98 89

( ) ( ) { ( ) ( ; , , )}

{ ( ; , , ) ( ; )}

{ ( ; ) ( )}

f a

f a

f y f y f y f y X X b

f y X X b f y X b

f y X b f y

− = −

+ −

+ −

where the counterfactual **f represents the equity wealth distribution that would have prevailed in 1998 if the particular attitudes had been distributed as in 1989. The term in the first curly bracket shows the relative contribution of attitudes, while in the second the relative contribution of fundamentals. In order to construct the counterfactual **f we first divide each of the samples of equity owners in 1989 and 1998 into 8 cells representing all the possible combinations of the three attitudes. We follow steps 1 and 2 from above while in step 3 we make m random draws with replacement from 1998 sample, generating the 1998 equity wealth distribution implied by the model. Then we consider the subset of households in cell 1. We randomly draw with replacement observations from this subset to generate a relative sample size equal to the fraction of households in cell 1 in 1989. We repeat the last two steps for cells 2 to 8. A similar approach is followed for the period 1998-2001.

28

Appendix C: Data Appendix US SCF data regard cross sections of households and are collected on a triennial basis since 1983. High quality and highly comparable data are available since 1989. They offer disaggregated information on a range of assets and liabilities as well as details on households’ various financial attitudes and practices. An additional reason that makes them appropriate for the purposes of this paper is that the survey over-samples rich households, offering reliable information for the top of the wealth distribution. This is important given that the main bulk of stockholding is concentrated among the rich, the top 10 percent of households posses 2/3 of total household wealth, and the main developments in the US wealth distribution over the last years have taken place in its upper part. To make our figures representative for the whole US population we adjust all our measures using survey weights. The survey uses a multiple imputation procedure to impute missing values and we take this into account in our statistical and regression analysis. I. Asset Categories for Financial Wealth Directly held stocks: [1] [1] publicly traded stocks Indirectly held equity: [2] + [3] + [4] + [5] [2] stock mutual funds (full value if described as stock mutual fund, 1/2 value of combination mutual funds) [3] IRAs/Keoghs invested in stock (full value if mostly invested in stock, 1/2 value if split between stocks/bonds or stocks/money market, 1/3 value if split between stocks/bonds/money market). [4] Other managed assets w/equity interest: annuities, trusts, MIAs (full value if mostly invested in stock, 1/2 value if split between stocks/MFs & bonds/CDs, or "mixed/diversified", 1/3 value if "other") [5] thrift-type retirement accounts invested in stock (full value if mostly invested in stock, 1/2 value if split between stocks and interest earning assets). Safe Assets: Total Financial Assets – Directly held stocks – Indirectly held equity II. Asset and Debt Categories for Net Total Wealth (Tables 2&3) Risky Financial Assets: Directly held stocks + Indirectly held equity Safe Financial Assets: Total Financial – Risky Financial Net Wealth in Risky Real Assets & Business Equity: [1] + [2] + [3] – [4] − [5] [1] Other Residential Real Estate (includes land contracts/notes household has made, properties - other than the principal residence - classified under certain codes for family residences, time shares and vacations homes) [2] Gross equity in Non-residential Real Estate (real estate - other than the principal residence, properties classified under certain codes for family residences, time shares, and vacation homes) [3] Business Equity (for businesses where the HH has an active interest, value is net equity if business were sold today, plus loans from HH to business, minus loans from

29

business to HH not previously reported, plus value of personal assets used as collateral for business loans that were reported earlier; for businesses where the HH does not have an active interest, market value of the interest) [4] Debt for Other Residential Property (includes land contracts, residential property other than the principal residence, misc. vacation, and installment debt reported for cottage/vacation home) [5] Debt for non-residential real estate mortgages and other loans taken out for investment real estate Other Wealth: value of vehicles + other non-financial miscellaneous assets Wealth in Primary Residence: Gross value of primary residence Principal Residence Debt: [6] [6] Principal Residence Debt (mortgage, home equity loans and HELOCs --mopup LOCs divided between HE and other) Consumer Debt: [7]+[8]+[9]+[10] [7] Other lines of credit [8] Credit Card Debt [9] Installment loans [10] Other Debt (loans against pensions, loans against life insurance, margin loans, miscellaneous) Note: All monetary values have been deflated using the CPI-U-Research Series index and expressed into constant 2004 prices. III. Variable Definitions No high school diploma (omitted variable): Highest grade completed (X5901)<12 & No high school diploma or passed equivalent test (X5902=5) High school graduate: Highest grade completed (X5901)<12 & Has got high school diploma (X5902=1) or passed equivalent test (X5902=2) OR Highest grade completed (X5901)=12 OR Highest grade completed (X5901)>12 & No college degree (X5904=5) College graduate: Highest grade completed (X5901)>12 & Has got a college degree (X5904)=1 Save for “rainy days”: The survey question is “Now I'd like to ask a few questions about your (family's) savings. People have different reasons for saving. What are your (family's) most important reasons for saving?” The dummy refers to those reporting one of the following reasons: Emergencies; “rainy days”; other unexpected needs; for "security"/independence (X3006=25 or X3007=25). Financial alertness: The survey question is “When making major decisions about borrowing and saving, some people shop around for the very best terms while others don't. What number would you be on the scale?” The 10-number scale ranges from 1-“almost no shopping” to 10-“a great deal of shopping”. Since 1995 the above question has been replaced by two separate ones – one for borrowing and one for saving – with

30

responses coded on a 1 to 5 scale. We have standardized these measures by averaging the two questions asked in post 1995 surveys and express them in 1-10 scale. The dummy represents those declaring that they do a great deal of shopping (values 9, 10 in the scale). Credit constrained: Indicates household response that it has been turned down for credit in the past five years or did not receive amount originally requested or did not apply for credit because it thought it might be turned down. Willingness to take above average financial risk: The survey question is “Which of the following statements comes closest to the amount of financial risk that you and your (spouse/partner) are willing to take when you save or make investments? 1. take substantial financial risks expecting to earn substantial returns 2. take above average financial risks expecting to earn above average returns 3. take average financial risks expecting to earn average returns 4. not willing to take any financial risks” The dummy represents those answering 1 or 2. (X3014=1 or X3014=2). Health poor: The survey question is “Would you say your health is excellent, good, fair, or poor?” Those describing their health as being poor are represented by the dummy (X6030=4). non equity net total Wealth: Total Assets – (Directly held stocks + Indirectly held equity) – Other lines of credit - Credit Card Debt - Installment loans - Other Debt (loans against pensions, loans against life insurance, margin loans, miscellaneous) Income: income from wages, salaries, professional practice or business unemployment compensation, social security, annuity, or other pensions. Intension to leave a bequest: Yes to “Do you expect to leave a sizable estate to others?” (X5825=1). Has received inheritance: Yes to “Have you ever received an inheritance, or been given substantial assets in a trust or in some other form?” (X5801=1). Cumulative gains/losses in direct holdings of stocks: The survey asks stock holders if there is a gain or loss in the value of the currently held stocks since they obtained them (X3916). The same information is available for mutual fund holders (X3831) Number of stocks held: The survey asks stock holders in how many different companies they own stocks (X3914) and mutual fund holders in how many mutual funds they own shares (X3820) Investment Horizon>10 years: The dummy represents those declaring that a period longer than 10 years is important when making their family’s saving and spending plan (X3008) Access to professional advice: “How do you make decisions about savings and investments?” (X7112-X7121 & X6865-X6869) The dummy comprises those asking advice from at least one of the following: accountant, banker, broker, financial planner

31

Appendix D: Formulae for inequality indices Mean logarithmic deviation (MLD) of variable y with mean μ and n observations is defined as:

1

1(0) logn

i iMLD GE

n yμ

=

≡ = ∑

The Theil index is given by

1

1(1) logn

i i

i

yyTheil GEn μ μ=

≡ = ∑

Half of the square of the coefficient of variation (HSCV) is given by

2 21

1 var( )(2) ( )2 2

n

i ii

yHSCV GE y yn

μμ μ=

≡ = − =∑

It can be shown that the more positive a is, the more sensitive GE(a) is to inequality at the top of the distribution. The Gini coefficient, is of the form:

21

2 1( )2

n

ii

nGini i yn μ =

+= −∑

where yi’s are in ascending order

32

Table 1: Probit Regressions for Ownership of Equity Holdings

1989 1998 2001 Marginal

Effect t-

valueMarginal

Effect t-

valueMarginal

Effect t-

value Age 0.0031 *** 4.62 0.0027 *** 4.60 0.0006 0.91 Male 0.0097 0.33 0.0041 0.17 0.0346 1.41 Married 0.0720 *** 2.81 0.0985 *** 4.25 0.0645 *** 3.15 Has children -0.0395 ** -2.23 -0.0255 * -1.69 -0.0086 -0.57 White 0.1244 *** 5.89 0.1412 *** 7.73 0.1166 *** 6.47 Health poor -0.1287 *** -4.06 -0.0796 ** -2.25 -0.1849 *** -5.55 High school graduate 0.1556 *** 6.86 0.1918 *** 8.03 0.1969 *** 8.25 College graduate 0.2867 *** 11.27 0.3437 *** 13.11 0.3638 *** 14.05 Save for “rainy days” -0.0050 -0.32 -0.0026 -0.18 -0.0049 -0.32 Credit constrained -0.0407 * -1.68 -0.0086 -0.49 -0.0476 ** -2.44 Non-investment Income 0.0076 *** 5.99 0.0086 *** 6.92 0.0071 *** 7.00 Non-equity net total Wealth 0.0116 *** 7.11 0.0088 *** 7.54 0.0087 *** 7.68 Intension to leave a bequest 0.0784 *** 4.65 0.1144 *** 7.84 0.1128 *** 7.98 Has received inheritance 0.0292 * 1.77 0.0697 *** 4.17 0.0489 *** 2.64 Financial alertness -0.0197 -1.20 0.0239 1.21 0.0177 1.06 Willingness to take above average financial risk 0.0809 *** 3.89 0.1871 *** 11.75 0.1701 *** 10.34 Investment horizon > 10yrs 0.0481 ** 2.44 0.1076 *** 4.96 0.0486 *** 2.65 observations 3,143 4,305 4,442 log likelihood -1530.8 -1982.8 -1970.2

Data from Surveys of Consumer Finances. The specification accounts for age through a 2nd order polynomial, and for labor status. It controls for income, and non equity net total wealth using the inverse hyperbolic sine transformation: log(x+(x2+1)1/2). Marginal effects are averaged across households (using survey weights). The marginal effects for income and non equity net total wealth are based on a $5000 increase in the underlying variables and for age on a one year increase. Numbers in italics report t-values, derived from simulated standard errors (details can be found in appendix A). ***,** and * denote significance at 1%, 5% and 10% level, respectively. Reported estimates are corrected for multiple imputation.

33

Table 2: Educational Attainment, Income and net Wealth in the Population and among Equity Owners

Weighted data from Surveys of Consumer Finances. The reported statistics are corrected for multiple imputation. The sample of equity owners includes households who own directly or indirectly stocks. Money values refer to 2004 Dollars.

1989 1998 2001 Population Education (%) Less than high school education 23.3 15.4 15.2 High school graduates 48.8 51.4 50.9 College degree or more 27.9 33.2 33.9 Mean (Median) non-investment Income

51,203 (35,168)

56,538 (37,245)

64,102 (38,691)

Mean (Median) non-equity Net total Wealth

249,749 (66,469)

244,506 (68,579)

308,318 (76,679)

Equity Owners (%) 31.8 48.9 51.9 Equity Owners Education (%) Less than high school education 7.3 5.4 4.7 High school graduates 45.5 47.8 45.7 College degree or more 47.2 46.8 49.6 Mean (Median) non-investment Income

87,145 (61,161)

82,825 (58,783)

93,731 (61,091)

Mean (Median) non-equity net total Wealth 513,993 (181,918)

390,595 (127,400)

486,494 (154,720)

34

Table 3: Incidence of Cumulative Gains or Losses in Stockholding since Purchased, by Education Group (%)

Holders by Educational Attainment All

Holders Less than High School Education

High School Graduates

College Degree or More

1998 Direct Stockholding Cumulative Gains 79.2 73.3 78.1 80.4 No Gains or Losses 8.4 15.3 9.6 7.0 Cumulative Losses 12.4 11.5 12.3 12.6 Mutual Funds Cumulative Gains 85.8 66.7 84.3 87.7 No Gains or Losses 8.0 21.2 8.0 7.3 Cumulative Losses 6.2 12.2 7.8 4.9

2001 Direct Stockholding Cumulative Gains 52.4 43.0 48.5 55.5 No Gains or Losses 12.3 15.8 13.4 11.3 Cumulative Losses 35.3 41.2 38.1 33.2 Mutual Funds Cumulative Gains 53.2 27.8 49.1 56.5 No Gains or Losses 11.5 20.1 13.8 9.7 Cumulative Losses 35.4 52.1 37.1 33.7

Weighted data from Surveys of Consumer Finances. The reported statistics are corrected for multiple imputation.

35

Table 4: Determinants of Cumulative Gains or Losses in Direct Holdings of Stocks, since Purchased

1998 2001 Pr(Gains) Pr(Losses) Pr(Gains) Pr(Losses)

Marginal Effect

t- value

Marginal Effect

t-value

Marginal Effect

t- value

Marginal Effect

t-value

Age -0.0004 -0.31 -0.0005 -0.52 0.0043*** 3.39 -0.0022 * -1.82Male -0.0805 ** -1.98 0.0460 1.46 0.0189 0.32 -0.0254 -0.45Married 0.0826 ** 2.15 -0.0728 ** -2.25 -0.0069 -0.15 0.0022 0.05Has children -0.0171 -0.65 -0.0022 -0.11 0.0370 1.21 -0.0365 -1.28White 0.0678 1.39 -0.0036 -0.09 0.0839* 1.67 -0.0697 -1.39Health Poor 0.1206 ** 2.10 -0.0812 * -1.72 -0.0622 -0.59 0.0252 0.25High school graduate 0.0571 0.64 -0.0325 -0.41 0.0914 1.17 -0.0129 -0.16College graduate 0.1176 1.33 -0.0361 -0.46 0.1463** 1.96 -0.0688 -0.86Credit constrained -0.0155 -0.37 0.0143 0.40 -0.0412 -0.73 0.0639 1.15Non-investment Income -0.0001 -0.04 0.0009 0.90 0.0015 1.42 -0.0021 * -1.86Non-equity net total Wealth 0.0006 1.00 -0.0004 -0.77 0.0013 1.36 -0.0003 -0.30Has received inheritance 0.0476 ** 2.08 -0.0294 -1.46 0.0922*** 3.49 -0.0777 *** -3.08Financial alertness 0.0654 ** 2.57 -0.0221 -0.91 -0.0083 -0.26 -0.0222 -0.68Willingness to take above average financial risk -0.0296 -1.31 0.0291 1.44 0.0428* 1.66 -0.0043 -0.16Investment horizon > 10yrs 0.0120 0.45 -0.0304 -1.49 0.0567* 1.93 -0.0588 ** -2.12Use of professional advice 0.0336 1.34 -0.0279 -1.34 -0.0470 -1.63 0.0189 0.68Number of Stocks held 0.0018 ** 2.26 -0.0012 * -1.78 0.0016** 2.29 -0.0015 ** -2.16ρ̂ -.11 .004 -.32 .37* observations / uncensored obs. 4,305 / 1,390 4,305 / 1,390 4,442 / 1,515 4,442 / 1,515 log likelihood -603.9 -449.6 -970.8 -2975.7

Data from Surveys of Consumer Finances. Second-stage probit regressions, correcting for selectivity bias among owners of directly held stocks (each ρ̂ is estimated from a two stage probit model and when it is insignificant the estimation is reduced to a probit regression over the uncensored observations). The specification accounts for age through a 2nd order polynomial, and for labor status. It controls for income, and non equity net total wealth using the inverse hyperbolic sine transformation: log(x+(x2+1)1/2). Conditional marginal effects are averaged across households who directly own stocks (using survey weights). The marginal effects for income and non equity net total wealth are based on a $5000 increase in the underlying variables and for age on a one year increase. Numbers in italics report t-values, derived from simulated standard errors (details can be found in appendix A). ***,** and * denote significance at 1%, 5% and 10% level, respectively. Reported estimates are corrected for multiple imputation.

36

Table 5: Determinants of Cumulative Gains or Losses in Stockholding through Mutual Funds, since Purchased

1998 2001 Pr(Gains) Pr(Losses) Pr(Gains) Pr(Losses)

Marginal Effect

t- value

Marginal Effect

t-value

Marginal Effect

t- value

Marginal Effect

t-value

Age 0.0009 0.74 -0.0018 * -1.89 0.0048*** 3.22 -0.0030 ** -2.05 Male 0.0290 0.64 -0.0347 -0.95 0.1559** 2.46 -0.1662 ** -2.50 Married -0.0258 -0.74 0.0224 0.97 -0.0588 -1.10 0.0938 * 1.84 Has children -0.0040 -0.15 -0.0302 * -1.75 0.0454 1.36 -0.0406 -1.26 White 0.0425 0.92 0.0072 0.23 0.2332*** 4.03 -0.1334 ** -2.23 Health Poor 0.0492 0.68 - - 0.1838 1.56 -0.0549 -0.47 High school graduate 0.1429 1.46 0.0088 0.15 0.1699* 1.68 -0.1680 -1.56 College graduate 0.1418 1.46 0.0022 0.04 0.2779*** 2.81 -0.2262 ** -2.15 Credit constrained -0.0050 -0.11 -0.0329 -1.26 -0.0170 -0.24 0.0161 0.24 Non-investment Income 0.0008 0.58 -0.0012 -1.07 0.0003 0.23 -0.0016 -1.43 Non-equity net total Wealth 0.0000

-0.02 0.0011

** 2.42 0.0003

0.58 -0.0004

-0.90

Has received inheritance 0.0339 1.40 0.0011 0.06 -0.0065 -0.23 -0.0195 -0.68 Financial alertness 0.0249 0.94 -0.0108 -0.55 0.0334 0.98 -0.0707 ** -2.19 Willingness to take above average financial risk 0.0532

** 2.38 -0.0260

* -1.76 0.0487

* 1.65 -0.0408

-1.36

Investment horizon > 10yrs 0.0251 1.02 -0.0044 -0.26 0.0670** 2.20 -0.0744 ** -2.50 Use of professional advice 0.0366 1.40 -0.0107 -0.60 -0.0343 -1.08 0.0121 0.40 Number of shares in different mutual funds 0.0053

* 1.65 -0.0066

** -2.45 0.0119

*** 3.56 -0.0117

*** -3.30

ρ̂ -.92 .47 .01 .19 observations / uncensored obs. 4,305 / 1,086 4,305 / 1,086 4,442 / 1,155 4,442 / 1,155 log likelihood -395.6 -226.3 -732.7 -687.4

Data from Surveys of Consumer Finances. Second-stage probit regressions, correcting for selectivity bias among owners of mutual funds (each ρ̂ is estimated from a two stage probit model and when it is insignificant the estimation is reduced to a probit regression over the uncensored observations). The specification accounts for age through a 2nd order polynomial, and for labor status. It controls for income, and non equity net total wealth using the inverse hyperbolic sine transformation: log(x+(x2+1)1/2). Conditional marginal effects are averaged across households who own mutual funds (using survey weights). The marginal effects for income and non equity net total wealth are based on a $5000 increase in the underlying variables and for age on a one year increase. Numbers in italics report t-values, derived from simulated standard errors (details can be found in appendix A). ***,** and * denote significance at 1%, 5% and 10% level, respectively. Reported estimates are corrected for multiple imputation.

37

Table 6: Net Wealth Inequality Indices Generalized Entropy Class

Year GE(0)

MLD

GE(1)

Theil

GE(2)

HSCV

Gini

1989 2.022 1.523 14.037 0.769

1998 1.860 1.646 19.156 0.776

2001 1.966 1.622 12.847 0.788

Weighted data from Surveys of Consumer Finances. The reported statistics are corrected for multiple imputation. The sample excludes households with negative net worth.

38

Table 7: Net Wealth Inequality Decomposition by Sources using HSCV

Weighted data from Surveys of Consumer Finances. The reported statistics are corrected for multiple imputation. The sample excludes households with negative net worth.

Year Net Total Wealth

Wealth in Safe Financial Assets

Wealth in Equity Holdings

Net Wealth in Risky Real Assets & Bus. Equity

Other Wealth

Wealth in Primary Residence

Principal Residence Debt

Consumer Debts

Percentage with positive factor wealth (nf

+ )

1989 1998 2001

0.957 0.973 0.971

0.907 0.936 0.937

0.339 0.512 0.537

0.289 0.271 0.259

0.857 0.850 0.870

0.681 0.703 0.714

0.418 0.454 0.468

0.615 0.607 0.616

Factor Share (χƒ)

1989 1998 2001

1.000 1.000 1.000

0.251 0.219 0.212

0.100 0.254 0.268

0.353 0.296 0.287

0.061 0.054 0.048

0.356 0.320 0.307

-0.093 -0.115 -0.102

-0.029 -0.029 -0.022

Correlation with net total wealth (ρfW)

1989 1998 2001

1.000 1.000 1.000

0.542 0.559 0.639

0.446 0.647 0.682

0.905 0.863 0.825

0.267 0.358 0.370

0.401 0.401 0.507

-0.174 -0.160 -0.183

-0.264 -0.358 -0.203

Factor Inequalities (Iƒ)

1989 1998 2001

14.037 19.156 12.847

16.831 14.592 18.211

37.110 46.750 24.825

72.197 108.032

63.960

31.696 7.909 8.038

1.362 1.376 1.561

2.351 1.696 1.836

11.891 26.424 22.817

Within Factor Inequality (If

+ )

1989 1998 2001

13.409 18.628 12.462

15.226 13.631 17.036

12.257 23.695 13.106

20.257 28.881 16.178

27.318 6.649 6.932

0.767 0.819 0.971

0.692 0.498 0.592

7.126 15.851 13.857

Proportionate Factors contributions (sƒ)

1989 1998 2001

1.000 1.000 1.000

0.149 0.107 0.162

0.073 0.258 0.254

0.722 0.606 0.529

0.025 0.012 0.014

0.045 0.034 0.054

-0.007 -0.005 -0.007

-0.007 -0.012 -0.006

Absolute Factors contributions (Sƒ)

1989 1998 2001

14.037 19.156 12.847

2.082 2.045 2.074

1.013 4.918 3.262

10.163 11.634 6.797

0.346 0.237 0.182

0.622 0.657 0.698

-0.093 -0.104 -0.090

-0.098 -0.230 -0.076

Percentage change in source contributions (sƒ%ΔSƒ)

1998-1989

2001-1998

0.365

-0.318

-0.003

0.002

0.280

-0.087

0.105

-0.252

-0.008

-0.003

0.003

0.002

-0.001

0.001

-0.009

0.008

39

Table 8: Net Wealth Inequality Decomposition by Sources using Gini

Weighted data from Surveys of Consumer Finances. The reported statistics are corrected for multiple imputation. The sample excludes households with negative net worth.

Year Net Total Wealth

Wealth in Safe Financial Assets

Wealth in Equity Holdings

Net Wealth in Risky Real Assets & Bus. Equity

Other Wealth

Wealth in Primary Residence

Principal Residence Debt

Consumer Debts

Factor Share (χƒ)

1989 1998 2001

1.000 1.000 1.000

0.251 0.219 0.212

0.100 0.254 0.268

0.353 0.296 0.287

0.061 0.054 0.048

0.356 0.320 0.307

-0.093 -0.115 -0.102

-0.029 -0.029 -0.022

Rank correlation ratio (RfW)

1989 1998 2001

1.000 1.000 1.000

0.913 0.902 0.914

0.909 0.932 0.939

0.942 0.945 0.948

0.729 0.654 0.692

0.821 0.812 0.841

0.445 0.443 0.473

0.385 0.329 0.299

Gini Index (Gf)

1989 1998 2001

0.769 0.776 0.788

0.823 0.809 0.831

0.939 0.908 0.898

0.957 0.955 0.955

0.664 0.618 0.601

0.645 0.605 0.624

0.795 0.749 0.750

0.784 0.794 0.776

Proportionate Factors contributions (sƒ)

1989 1998 2001

1.000 1.000 1.000

0.245 0.206 0.205

0.111 0.277 0.287

0.414 0.345 0.330

0.039 0.028 0.026

0.245 0.202 0.205

-0.043 -0.049 -0.046

-0.011 -0.010 -0.006

Absolute Factors contributions (Sƒ)

1989 1998 2001

0.769 0.776 0.788

0.189 0.160 0.161

0.085 0.215 0.226

0.318 0.267 0.260

0.030 0.022 0.020

0.189 0.157 0.162

-0.033 -0.038 -0.036

-0.009 -0.007 -0.005

40

Figure 1A. Quantile Regression Decomposition 1998-1989: Coefficient and Covariate effects

-2-1

.5-1

-.50

.51

1.5

2D

iffer

ence

in lo

g E

quity

0 20 40 60 80 100Percentile

coefficient effects covariate effectsactual difference

Figure 1B. Quantile Regression Decomposition 1998-1989:Contributions of Fundamentals to Covariate effects

-2-1

.5-1

-.50

.51

1.5

2D

iffer

ence

in lo

g E

quity

0 20 40 60 80 100Percentile

fundamentals as in 1989 covariate effects

41

Figure 2A. Quantile Regression Decomposition 2001-1998: Coefficient and Covariate effects

-1.5

-1-.5

0.5

11.

5D

iffer

ence

in lo

g E

quity

0 20 40 60 80 100Percentile

coefficient effets covariate effetsactual difference

Figure 2B: Quantile Regression Decomposition 2001-1998: Contributions of Fundamentals to Covariate effects

-1.5

-1-.5

0.5

11.

5D

iffer

ence

in lo

g E

quity

0 20 40 60 80 100Percentile

fundamentals as in 2001 covariate effets

42

Endnotes 1 For participation trends in the United States since the 1980s, see Bertaut and Starr-McCluer (2001). International comparisons can be found in the volume edited by Guiso, Haliassos, and Jappelli (2001). 2 Limited stockholding participation in the early to mid 1980s was documented in US data by King and Leape (1984), Mankiw and Zeldes (1991), and Haliassos and Bertaut (1995). A number of authors have recently explored determinants of participation in stockholding. See, for example, Haliassos and Bertaut (1995), Cocco, Gomes and Maenhout (2005), Heaton and Lucas (2000), Gollier (2001), Campbell and Viceira (2002), Haliassos and Michaelides (2003), and Gomes and Michaelides (2004). 3 Hurst and Lusardi (2004) have recently documented that a positive relationship between wealth and entry into entrepreneurship can be found only at the top five percentiles of the wealth distribution. Carroll (2001) showed that the portfolio behavior of rich households is quite different from that of households lower in the distribution of wealth, and richer households are not simply blown-up versions of poorer households. Wolff (1998) shows that only the top 20 percent of households enjoys higher mean net worth and financial wealth levels between 1983 and 1995, while the other groups undergo real wealth or income losses with the shortfall being more severe for the poor. 4 For effects of stock market participation regarding market volatility and stock market trading, see Pagano (1989), Allen and Gale (1994), Herrera (2001), and Bilias, Georgarakos, and Haliassos (2007). For effects on the equity premium, see for example Heaton and Lucas (1999) and Calvet et al. (2004). 5 In this paper, we try to avoid some pitfalls involved in automatic computation of marginal effects by standard econometric software, which have recently been emphasized. We explain how we overcome these problems in Appendix A. 6 Regressors are the same as for the participation probits, presented in Table 1. 7 Coefficient and covariate effects deviate across higher percentiles, and both are significant in most percentiles, according to bootstrapped standard errors not reported here. 8 The current analysis, based on different cross sections, cannot directly reveal whether significant entries and exits took place during that time. Using panel data for the same period, Bilias, Georgarakos, and Haliassos (2007) confirm such a conjecture by showing that a non-trivial number of US households (over 20%) have changed stock ownership status. 9 Another approach would be to construct realized stockholding returns by household and then compare them to some stock market index over the relevant period. Whatever the merits of such an approach, it cannot be implemented in population-wide survey data, because realized rates of return over specific periods cannot be computed. 10 We have also experimented with specifications without the use of any exclusion restriction (where the functional form contributes to the model identification) and the results are similar to those we present. 11 The SCF reports also unrealized capital gains, but we do not use those to measure relative success, as there is no information on the length of the holding period to which they correspond. 12Under ‘professionals’, we include accountants, bankers, brokers, and financial planners. The proportion of stockholders who report using professional advice in making decisions about savings and investments is 59% in 1998 and drops slightly to 57% in 2001, following the stock market downturn. 13 They would be weakened by strong evidence that use of financial advice is actually due to the absence of cumulative gains, suggesting endogeneity. We doubt that such factors are dominant here, as the use of financial advisors is typically observed among households with limited knowledge of the market or by financially successful households who do not have the time to monitor their own portfolios. 14 In view of the tremendous upswing of the stock market in the 1990s and the downswing around the end of the century, the earlier households have bought stocks, the more likely they are to report cumulative gains. This can provide an important channel through which characteristics that correlate with financial sophistication lead to cumulative gains, namely by inducing households to enter the market earlier. Still, there is no reason to suppose that the influence of these characteristics is exhausted in the timing of initial entry and that it does not extend to subsequent entries and exits and to other aspects of portfolio behavior contributing to gains. 15 The measurement part of our analysis of wealth distribution is complementary to the careful work by Kennickell (2003), which is based on the same set of SCF surveys. Kopczyk and Saez (2003) use estate tax returns to study shares of wealth held by the very rich and they find, consistent with Kennickell, that top wealth shares have not increased since 1995, and that the share of stock market wealth held by the richest (relative to the total stock market wealth held by the whole population) fell in the past 20 years. They attribute the latter finding partly to increased stock market participation.

43

16 The presence of the rich is very important in studying the distribution of wealth since the richest 1% of households possesses roughly the 1/3 of the total wealth. The Survey excludes only households that belong to the Forbes 400. See also Kennickell (2003). 17 As Atkinson (1983) points out, “[inequality indices] embody implicit judgments about the weight to be attached to the inequality at different points in the […] scale”. Details on the asset definitions and the formulae for inequality indices are provided in Appendices C and D, respectively. 18 Inequality indices for gross total wealth over the full sample of households produce a similar picture. 19 See Jenkins (1995) for a similar argument in favor of using HSCV for analysis of income inequality. 20 Decompositions presented in tables 2 and 3 have been also applied to gross total wealth using the full sample of households and excluding the two categories that represent debt. In all cases they suggest similar patterns to those we present. 21 The result mainly comes from the increasing factor correlation, implying a stronger association between housing value and total net wealth over time, which outweighs the decreasing factor shares. Factor shares decrease presumably due to movements in housing prices, since ownership rates move in the opposite direction. 22 This is because the dropping factor share and correlation with net total wealth moderate the effects from the increase in this factor’s inequality. 23 Stock holdings exhibit a high increase in factor share, increased correlation with net total wealth, and increased inequality (coming from the increase in within inequality that almost doubles, outweighing the effect from the increase in the percentage of stock owners), all leading to a more than quadruple increase in their absolute factor contribution between 1989 and 1998. 24 The higher risky shares result from increasing ownership rates and sizeable stock gains in a decade marked by a spread of equity culture and a stock market boom. 25 There is growing discussion of these issues and an effort to provide codes that circumvent some inefficiencies of standard software packages (see, for instance, King et al., 2003).