Are successive generations getting wealthier, and if so, why? Evidence from the 1990s.

Gale, William G. ; Pence, Karen M.

THE 1990S WERE a remarkable decade for saving and wealth accumulation. After averaging 3.4 times GDP between 1950 and 1990, aggregate net worth rose from 3.5 times GDP in 1990 to 4.2 times GDP in 2000, its highest *level since at least 1950. In nominal dollar terms, net worth rose from $20 trillion in 1990 to $42 trillion in 2000. Much of the increase in wealth was fueled by skyrocketing capital gains in the stock market, which helped boost the aggregate market value of equities from $3 trillion in 1990 to $15 trillion in 2000. The decade also saw widespread diffusion of stock ownership (directly and indirectly through mutual funds) and substantial increases in participation in and contributions to defined-contribution pension plans, typically 401(k)s. At the same time, however, the measured saving rate, excluding capital gains, fell over the decade, continuing a longer-term pattern. (1)

These patterns created a rich environment in which to examine household saving and wealth accumulation. Previous researchers have followed particular birth cohorts through the 1990s, separating the wealth changes that each cohort experienced into a component due to capital gains and a component due to active saving. These studies aimed to develop estimates of the age-wealth and age-saving profile, and to determine among which birth cohorts and among which types of assets wealth rose and active saving fell during the 1990s. Other studies have examined the extent to which households chose to use their accumulated capital gains in the 1990s to finance increased consumption expenditure or early retirement. (2)

This paper also focuses on the 1990s but addresses a different set of questions and thus takes a different approach to the data. Unlike previous studies, ours does not focus on tracking particular birth cohorts through time. Instead we examine the relative wealth status of different birth cohorts as they reach similar stages of the life cycle. Thus, for example, we compare (using data from the 1989-2001 Surveys of Consumer Finances) the 2001 wealth of households where the head was between the ages of 65 and 74 in 2001 with the 1989 wealth of households where the head was between 65 and 74 in 1989. The idea behind this type of comparison is to exploit the fact that households of a given age in 1989 had not experienced the 1990s, whereas households of the same age, observed in 2001, had. Thus, by controlling for other factors that may vary across generations-such as educational attainment, marital status, health status, and differing work norms for women--we can measure the effects of exposure to the 1990s on saving and wealth.

Our approach can provide insights regarding three questions: To what extent are successive generations of American households wealthier than their predecessors? What are the principal determinants of the trends in wealth across successive generations? And what are the implications? The answers to the first two questions turn out to be surprising and simple. The answer to the third is more complex.

We find that the rise in aggregate net worth over the 1990s (that is, the rise in net worth in 2001 relative to 1989) accrued almost entirely to older age groups. Older households (those with heads aged 55-64, 65-74, or 75-84 years) in 2001 had significantly more wealth than did similarly aged households in 1989. For example, real median wealth among 65- to 74-year-olds in 2001 was about $100,000 (60 percent) greater than among 65- to 74-year-olds in 1989. For these older households, economically and statistically significant increases in wealth occurred at almost all points in the wealth distribution and across all major wealth categories: retirement accounts, other financial assets, housing equity, and other real assets. In contrast, the typical younger household (aged 25-34, 35-44, or 45-54) in 2001 did not have more wealth than a typical younger household in 1989.

We also show that, despite the large capital gains, the rapid diffusion of stock ownership, and the significant increase in 401(k) participation and contributions in the 1990s, the principal factor determining changes in wealth across successive generations appears to be changes in household-level demographic characteristics, and not changes in the relationship between these characteristics and wealth. Informally, certain key demographic characteristics that affect wealth accumulation shifted substantially across age groups in a manner consistent with the differing trends in wealth. For example, compared with similarly aged households in 1989, older households in 2001 were more likely to be married, more likely to report their health as "excellent" or "good," and more likely to contain men who had completed postsecondary education. In contrast, for younger households in 2001, each of these trends was reversed relative to similarly aged households in 1989. Formal regression and decomposition analysis shows even more strongly that changes in demographic characteristics are closely tied to changes in median wealth, mean wealth, and the distribution of wealth between 1989 and 2001 for older generations. Indeed, information on households' 2001 demographic characteristics and the relationship between those characteristics and wealth that held in the 1989 sample predicts extremely accurately the distribution of wealth in 2001, without any reference to changes in capital gains, stock ownership, or participation in defined-contribution plans.

The rest of the paper is organized as follows. We begin by describing the data set. We then present trends across successive cohorts in wealth holdings and demographic characteristics. Next we describe the various tests and the econometric specifications we use to compare the wealth of successive cohorts. We then present our main empirical findings. Next we provide information on the role of capital gains, diffusion of stock ownership, and pension coverage across successive cohorts. We conclude by discussing alternative interpretations and implications of the results.

Data

The Survey of Consumer Finances (SCF) is designed specifically to measure household wealth (net worth) and its components. (3) To capture how assets and debt are held broadly in the population, about two-thirds of the unweighted sample are drawn from a stratified, nationally representative random sample. To capture the concentration of assets and debt among high-wealth households, the remaining third are randomly selected from statistical records derived from tax returns, using a stratification technique that oversamples households likely to have substantial wealth. This sample design allows for more efficient and less biased estimates of wealth than are generally feasible through simpler designs.

Although the SCF has been conducted every three years since 1983, we focus on the data from 1989 to 2001, a period during which the survey has employed a consistent methodology. This period, of course, also brackets the sharp increase in the ratio of aggregate net worth to GDP described earlier. A key advantage of the SCF is that it covers all age groups and almost all household assets and liabilities, financial and real, including defined-benefit pension wealth. The only important exception is that households wealthy enough to be in the Forbes 400 are excluded. The main drawback of the SCF is its relatively small sample size of approximately 4,000 households in each survey year.

Our measures of net worth and its components follow the SCF definitions except for the treatment of pension wealth. Because the SCF defines net worth as resources that a household may access and control immediately, the survey's definition of wealth excludes defined-benefit pensions (which cannot be accessed until retirement) and includes only liquid defined-contribution plans: 401(k)s, thrift plans, defined-contribution plans from past jobs, and other plans that can be borrowed against or withdrawn from. These definitions understate pension wealth at any point in time and likely lead to systematic overstatements of the growth in pension benefits over time. Over the past twenty years, the employer pension system has moved dramatically toward defined-contribution plans and away from defined-benefit plans. Furthermore, among defined-contribution plans, firms have shifted from illiquid to liquid plans (as defined by the SCF). To address these issues, we include all defined-contribution balances, as well as estimates of defined-benefit wealth, in the wealth definition. (4)

Our definition of net worth, like the measure in the SCF, does not include expected future Social Security or Medicare benefits or taxes. Although Social Security benefits are a significant part of wealth for many lower- and middle-income households, their inclusion would not alter the results. There were no new legislated changes in Social Security over the sample period, although the retirement age did rise slightly as legislated by the 1983 Social Security reform. If anything, Social Security benefits increased over this time period for elderly households, accentuating rather than offsetting the trends in private wealth. Data from the Current Population Survey, for example, indicate that the median annual household Social Security benefit received by a household aged 65-74 was $9,935 in 1989 (expressed in 2001 dollars) and $11,330 in 2001. This increase likely reflects higher lifetime real wages and increased female labor force participation among the cohort aged 65-74 in 2001 compared with the cohort aged 65-74 in 1989 (as described below). Although legislated changes to Medicare over this period affected health care providers, it is not clear what net effect, if any, these changes had on household wealth. (5)

The SCF also includes information on household demographic characteristics, income, and current and past jobs held by the household head and spouse. We use these data to construct a series of variables described below.

Trends in Wealth and Demographics

In this section we explore the differences in total wealth between the 1989 and 2001 samples for each of the different age groups, on average, at the median and other selected points in the wealth distribution, and for the entire distribution for two of the age groups. We also look at differences across the same period for the different age groups with respect to each of several main categories of wealth. Among demographic variables, we examine trends in marital status, longevity, health, education, and labor force participation.

Wealth

Although the growth in equity markets and aggregate net worth over the 1990s is well documented, the distribution of these gains across age groups is not, and the differences in trends across age groups are striking. Older households, defined as those headed by a person aged 55 or older, had significantly more wealth in 2001 than did households in the same age range in 1989, whereas younger households in 2001 generally had the same amount of wealth as similarly aged households in 1989. (6)

The top panel of figure 1 shows that real median wealth for households with a head between the ages of 65 and 74 rose by almost 60 percent, from $169,000 in 1989 to $264,000 in 2001.7 The other two older age groups--those aged 55-64 and 75-84--also enjoyed substantial absolute and relative increases in wealth. In contrast, the median net worth of households with a head between the ages of 35 and 44 actually fell from $108,000 in 1989 to $99,000 in 2001. The other two younger age groups--those aged 25-34 and 45-54--fared similarly. The bottom panel of figure 1 shows similar trends for mean net worth. Mean wealth for each of the older three cohorts was roughly 50 percent higher in 2001 than for households of a similar age in 1989. For the three younger age groups, mean wealth grew by only about 10 to 20 percent.

[FIGURE 1 OMITTED]

Figure 2 shows similar trends for the 10th, 25th, 75th, and 90th percentiles of the wealth distribution for each age group. At each percentile the older cohorts in 2001 had substantially more wealth than did their counterparts in 1989. The younger cohorts in 2001 had about the same wealth as did their counterparts in 1989.

[FIGURE 2 OMITTED]

The top panel of figure 3 shows the entire distribution of net worth in 1989 and 2001 for households with heads aged 65-74 in those years--the "middle" older cohort. For this group the cumulative distribution function (CDF) of net worth in 2001 lies to the right of the corresponding CDF in 1989, indicating that the 2001 sample was richer all across the distribution. The differences are statistically significant at a 95 percent confidence level at each decile break from the 30th to the 80th percentile. (8) The bottom panel of figure 3 shows the analogous results for households aged 35 to 44 in 1989 and 2001--the "middle" younger cohort. For these groups the distribution of wealth in 1989 approximately coincides with the distribution of wealth in 2001. No statistically significant differences occur at any decile of these distributions. (9)

[FIGURE 3 OMITTED]

Data for average holdings of particular components of wealth--retirement assets, other financial wealth, home equity, and other real assets--show patterns that are similar to those in the aggregate data but, not surprisingly, somewhat noisier, given that not all households hold all types of assets: some own their home but hold no financial wealth, for example, whereas others have pension wealth but do not own a home, and so on. In general, however, for each component of wealth, average holdings were higher in 2001 than in 1989 for older cohorts but not necessarily for younger cohorts.

The first panel of figure 4, for example, shows that average retirement wealth was $79,000 higher in 2001 for the 55-64 group, $37,000 higher for the 65-74 group, and $63,000 higher for the 75-84 group. Among the younger groups, the 45-54 group had a mean increase of $27,000, but the increases for the other two groups were $4,000 or less. Likewise, the average home equity of households in the 65-74 group rose from $95,000 in 1989 to $133,000 in 2001 (second panel of figure 4). In contrast, households in the 45-54 group had about the same average home equity ($104,000) as the 65-74 group in 1989, but by 2001 the home equity of households in this age group had not advanced beyond its 1989 level. (10) Mean financial assets rose for all age groups (third panel of figure 4). Although the absolute difference was larger for the older groups, the proportional increases were quite large for all groups. Other real assets, which include equity in vehicles, investment real estate, closely held businesses, and other miscellaneous assets, rose for the 55-64 and 65-74 groups and were roughly flat for the younger groups and the 75-84 group (last panel of figure 4).

[FIGURE 4 OMITTED]

Several aspects of the wealth trends noted above are significant. First, given the well-known trend toward greater income inequality over the sample period, (11) it is worth noting that the data do not simply show that wealthy age groups became wealthier. Median wealth for 45- to 54-year-olds in 1989 was $193,000, for example, substantially larger than that for households aged 65-74 ($169,000) or 75-84 ($131,000). Yet by 2001 median wealth for households aged 45-54 was virtually the same as in 1989 ($191,000), whereas median wealth had risen by about $100,000 for cohorts aged 65-74 and 75-84 relative to similarly aged counterparts in 1989 (figure 1).

Second, the results do not show that, within each age group, the rich got richer. The differences at the 75th and the 90th percentile occur only in the older groups, not in the younger groups (figure 3). Moreover, in the distribution of net worth for 65- to 74-year-olds, significant differences exist between the 1989 and 2001 distributions for the 30th to the 80th percentiles but not for the 90th percentile. These results are consistent with the finding by Arthur Kennickell that although the share of wealth held by households in the top 1 percent of the wealth distribution appears to have increased from 1989 to 2001, the change is not statistically significant. (12)

Third, the results are not consistent with the view that younger households (as defined here) simply do not save very much, so that they benefited little from the capital gains of the 1990s. In fact, median wealth for 45- to 54-year-olds in 1989 was the second highest of all groups (figure 1).

Fourth, the results show increases in all forms of wealth and increases in overall wealth across the entire wealth distribution for older households. This suggests that the determinants might be more than just capital gains or the spread of 401(k) plans, because both of these are distributed quite unequally across the wealth distribution.

Finally, it is worth noting that the facts documented here do indeed look like trends that have occurred over time, rather than simply two isolated sets of data points. Figure 5 shows median and mean wealth for successive cohorts for each SCF year in the sample period: 1989, 1992, 1995, 1998, and 2001. Because of the relatively small sample size within each age-year cell, and because economic conditions and asset returns naturally vary over time, the year-by-year data in these figures are necessarily noisier than the snapshots of the 1989 and the 2001 data.

[FIGURE 5 OMITTED]

Nonetheless, the figure shows that although macroeconomic conditions clearly affected all households, older households fared better than younger households regardless of the state of the economy. The median net worth of older households stayed level during the early-1990s recession and then skyrocketed in the booming second half of the decade (first panel of figure 5). In contrast, the median net worth of households aged 35-44 and 45-54 fell in the recession years and only came close to regaining its 1989 level in 2001 (second panel of figure 5). Likewise, older and younger households experienced comparable drops in average wealth between 1989 and 1992, but older households subsequently experienced much larger wealth gains (last two panels of figure 5). By focusing on 1989 and 2001--two years that were both preceded by several strong years in the stock and housing markets--we are able to abstract from some of this year-to-year macroeconomic variability.

Demographics

There is a long tradition in economics, dating at least as far back as Franco Modigliani's work in the 1950s, relating household demographic characteristics to wealth accumulation. Even after controlling for age, demographic factors such as marital status, health, education, and labor force participation can have significant effects on wealth and saving. Married households benefit from the economies of scale and household production associated with marriage and thus may save a larger fraction of their income than unmarried households. (13) Widowed households, in contrast, often face a negative income shock from decreased pension and Social Security benefits after a spouse's death, as well as a wealth shock from large out-of-pocket medical expenses incurred in the last year of the deceased spouse's life. (14) Advances in health affect wealth indirectly by reducing the number of widowed households. In addition, workers with better health may spend more years in the labor force and face lower out-of-pocket medical expenses. (15) Better-educated workers generally have higher lifetime earnings and are more likely to be invested in the stock market. (16) Education also appears to promote better health outcomes, even after controlling for income and wealth. (17) Finally, workers who spend more years in the labor force will have higher lifetime earnings, all else equal.

Notably, the trends in these key demographic characteristics across cohorts in the 1990s generally mirror the patterns shown in the wealth accumulation data. Specifically, demographic characteristics "improved" in a number of ways for older households in 2001 relative to those in 1989, and they either did not improve or actually deteriorated for younger households in 2001 relative to their 1989 counterparts. (18) For example, the share of married household heads rose among older households and decreased among younger households. In 2001, 58 percent of household heads between the ages of 65 and 74 were married, compared with 50 percent in 1989. In contrast, among 35- to 44-year-olds, the share fell from 64 percent to 58 percent (table 1). Data from the CPS (not shown) display a similar but more muted pattern, with the share of married households increasing from 53 percent to 55 percent for the 65-74 age group and decreasing from 65 percent to 61 percent for the 35-44 age group. (19)

The increase in the share of older married households may stem from increases in male longevity. Since 1975, male longevity at older ages has increased relative to female longevity, because smoking-related deaths have increased relatively more for women and because men have benefited disproportionately from decreases in cardiovascular disease. (20) Over the 1989-2001 period, for example, male life expectancy at age 65 increased by 12 months, whereas female life expectancy increased by only 2 months. (21) Perhaps reflecting these trends, the share of SCF households headed by a widow in the 65-74 age group fell from 31 percent in 1989 to 17 percent in 2001.

Among younger households, the decline in the married share appears to stem from delays in the age of first marriage. From 1989 to 2001 the share of households aged 35-44 with a never-married head (some of whom are living with a partner) increased from 16 percent to 22 percent. Although the share of married 35- to 44-year-olds fell, the share living with a partner or married held constant at 67 percent in both years.

Consistent with the increases in longevity noted above, the share of older households who reported their health as "excellent" or "good" increased over the 1989-2001 period (table 1). Among households in the 65-74 age group, that share rose from 57 percent in 1989 to 61 percent in 2001. Similarly, the share of CPS respondents aged 65-74 who described their health as "excellent," "very good," or "good" increased from 67 percent in 1995 to 70 percent in 2001 (not shown). (22) These self-reported health improvements are consistent with documented declines in chronic disabilities among older households. (23) The self-reported health of younger households, however, deteriorated: the share of households in the 35-44 age group who rated their health as "good" or "excellent" fell from 87 percent in 1989 to 83 percent in 2001. Although sampling fluctuations may account for this drop, there is some evidence that increased rates of asthma and diabetes have eroded the health of younger households. (24)

Educational attainment rose substantially for women in all age groups between 1989 and 2001 but rose more for successive older male cohorts than for younger male cohorts. The share of men in the 65-74 age group with postsecondary education increased from 31 percent in 1989 to 49 percent in 2001, whereas the share fell from 60 percent to 56 percent for men in the 35-44 age group (the other two younger age groups saw moderate increases in the share of men with postsecondary education; table 1). For women the corresponding increases were from 27 percent to 40 percent for the 65-74 group and from 49 percent to 59 percent for the 35-44 group. CPS data show similar trends. (25) These increases are consistent with the surge in college matriculation rates after World War II. Although college enrollment increased strongly throughout the twentieth century, the rise was especially pronounced after World War II, when the share of 18- to 24-year-olds enrolled in college rose from 10 percent in 1945 to nearly 30 percent in 1965. (26) The GI Bills for World War II and Korean War veterans, the democratization of the college application process, the rise in community colleges, and the advent of birth control account for some of this and later increases. (27)

Lifetime labor force participation increased for women in all age groups over this period but stayed constant for men. For example, on average, women in the 65-74 group had nineteen years of full-time work experience in 1989 and twenty-two years of experience in 2001 (table 1). Men in this age group had forty-two years of experience in both years. The forces underlying the increase in women's labor force participation include laborsaving devices that made housework less burdensome, the rise of the clerical sector, the growth of formal education, and decreased sex discrimination, as well as increased access to birth control. (28)

Modeling the Effects of Demographic Changes on Wealth

We use four different methods to provide perspectives on how changes in demographic characteristics affect the wealth accumulation of successive cohorts. The methods focus on differences in the median, mean, and distribution of wealth.

Median

We run least absolute deviation (LAD) regressions on the pooled 1989 and 2001 data. Initially, we specify wealth for household i as a function of just a constant and an indicator variable for being an observation in the 2001 sample:

(1) [w.sub.i] = [[alpha].sub.1] + [[beta].sub.1] [(year = 2001).sub.i] + [[epsilon].sub.1i].

In this specification the coefficient [[beta].sub.1] captures the change in median wealth between the 1989 and 2001 groups and is equal to the change in medians shown in figure 1.

In the second LAD specification, we incorporate demographic variables, denoted by X:

(2) [w.sub.i] = [[alpha].sub.2] + [[beta].sub.2] [(year = 2001).sub.i] + [[gamma].sub.2][X.sub.i] + [[epsilon].sub.2i].

If demographic changes explain most of the change in wealth between 1989 and 2001, [[beta].sub.2] should be close to zero, and the demographic variables should enter as economically and statistically significant. (29) This method assumes that the relationship between wealth and demographic characteristics is the same in both years (other than a shift in the intercept).

Mean

We use the familiar Blinder-Oaxaca decomposition to examine how much of the change in mean wealth for each age group comes from changes in the demographic characteristics over time and how much comes from all other factors, that is, from changes in the relationship between wealth and demographic characteristics over time. (30) Whereas the median regression imposes the same coefficients on the 1989 and 2001 data, this decomposition technique allows the relationship between demographics and wealth to differ in the two years.

Suppose that wealth w in a given year (say, 2001) is estimated as a linear combination of demographic characteristics X: [w.sub.01]= [X.sub.01] [[beta].sub.01] + [[epsilon].sub.01]. By the assumptions of ordinary least squares, E([w.sub.01]) = E([X.sub.01][[beta].sub.01]) = E([X.sub.01]) [[beta].sub.01]. We estimate E([X.sub.01]) with its sample analog [[bar.X].sub.01] and thus can express the difference between mean wealth in 2001 and mean wealth in 1989 as

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

In equation 3 the term in which X is constant shows the change in wealth attributable to changes in [beta], whereas the term in which [beta] is constant shows the change in wealth attributable to the change in X. The term in which [beta] is constant will be large if changes in demographic factors explain a substantial share of the change in wealth. Dividing each term in this equation by the change in expected wealth, E([w.sub.01]) - E([w.sub.89]), yields the share of the change in wealth due to demographic characteristics versus the share due to other factors.

Distribution

To examine the effects of demographic changes on the distribution of wealth, we ask the following counterfactual question: what would the distribution of wealth in 2001 look like if we took the distribution of demographic characteristics from 2001 but applied the relationship between demographics and wealth from 1989? Note that the latter relationship (loosely, [[beta].sub.89]) excludes all effects of the 1990s. Thus the counterfactual question allows us to calculate the share of the actual difference in wealth that can be explained by differences in demographic variables alone. If the relationship between demographics and wealth was approximately the same in 1989 and 2001, this counterfactual distribution should look quite similar to the actual 2001 distribution. If instead the demographics-wealth relationship was quite different in the two years, the counterfactual and the actual 2001 distributions should diverge.

We generate the counterfactual distribution in two ways. The first is a reweighting technique based on a paper by John DiNardo, Nicole Fortin, and Thomas Lemieux. (31) The idea is to reweight the households in the 1989 SCF so that they reflect the distribution of demographic characteristics in the 2001 SCF. The resulting distribution of household wealth thus reflects the 2001 demographic characteristics (due to the reweighting) and the 1989 relationship between demographics and wealth (since it still uses 1989 data). The second approach is a resampling technique based on a paper by Jose Machado and Jose Mata. (32) Here we create a predicted wealth value for 2001 by pairing the demographic characteristics from a randomly chosen household in the 2001 SCF with the coefficients from a quantile regression (using a randomly chosen quantile) of wealth on demographic characteristics from the 1989 SCF. Repeating this procedure over and over generates a counterfactual distribution.

More formally, we want to simulate the distribution of net worth as a function of demographic characteristics from 2001 and of the relationship between wealth and demographics from 1989. Borrowing notation and exposition from DiNardo, Fortin, and Lemieux, we write the density of wealth at a point in time, f(w), as the integral of the density of wealth conditional on a set of demographic characteristics X and on a date [t.sub.w], f(w|X, [t.sub.w]), over the distribution of individual attributes F(X|[t.sub.x]) at a date [t.sub.x]:

(4) f(w;[t.sub.w] = 1989, [t.sub.x] = 2001) = [integra]f(w|X, [t.sub.w] = 1989)dF(X|[t.sub.x] = 2001).

DiNardo, Fortin, and Lemieux note that equation 4 can be rewritten as

f (w;[t.sub.w] = 1989, [t.sub.x] = 2001) = [integral] f (w|X, [t.sub.w] = 1989)[[psi].sub.x]dF(X|[t.subx] = 1989),

where the weight [[psi].sub.x] = dF(X|[t.sub.x] = 2001)/dF(X|[t.sub.x] = 1989). (33) This term reweights the households in the 1989 SCF so that their distribution of demographic characteristics matches the distribution from the 2001 survey.

To estimate [[psi].sub.x], note that by Bayes' law,

dF(X|[t.sub.x] = 2001)/dF(X|[t.sub.x] = 1989 = prob(year=2001|X)prob(year=1989)/ prob(year=1989|X)prob(year=2001).

The first term on the right-hand side can be obtained by estimating a logit model on the pooled 1989 and 2001 SCF data in which the dependent variable is a dummy variable for "year = 2001" and the independent variables are demographic characteristics. (We use the sample weights in estimating this logit.) Exponentiating the predicted value for each observation gives the odds prob(year = 2001|X)/prob(year = 1989|X). We can ignore the second term because it is constant for all observations. We generate this weight for each household in the 1989 SCF, multiply it by the existing sample weight for the household, and then use standard methods to estimate the weighted quantiles of the distribution.

Whereas the DiNardo, Fortin, and Lemieux technique uses the actual relationship in the 1989 data to characterize the relationship between demographics and wealth, the Machado and Mata technique specifies this relationship parametrically. Machado and Mata note that the conditional distribution of wealth given demographics can be approximated at each quantile [theta] in [0,1] by quantile regressions of the form w = X[[beta].sub.[theta]] + [epsilon]. This specification imposes a linear relationship between wealth and demographic characteristics at each quantile. We estimate this specification at each percentile from the 1st to the 99th.

To obtain the distribution of wealth that would occur with the 2001 distribution of demographic characteristics and the 1989 relationship between wealth and demographics using the Machado and Mata technique, we employ the following procedure: In step 1 we randomly draw a quantile [theta] from a uniform [0,1] distribution and obtain the corresponding quantile regression coefficients [[beta].sub.[theta]] from the 1989 SCF. (We use the 1989 sampling weights when estimating these regressions.) In step 2 we randomly draw an observation from the 2001 SCF and obtain its set of demographic characteristics X. (34) Then we combine the coefficients [[beta].sub.[theta]] from step 1 and the characteristics X from step 2 to obtain an observation from the counterfactual wealth distribution. We repeat this procedure until a sample of the desired size is obtained, and we estimate weighted quantiles from this sample using the 2001 SCF sample weights. (35) In both decompositions, if changes in demographic characteristics explain much of the changes in the distribution in wealth, the counterfactual density based on 2001 demographic characteristics and the 1989 relationship between wealth and demographics should lie near the actual 2001 wealth distribution.

Specification of Demographic Characteristics

Each of the tests above requires the specification of demographic characteristics and wealth. Our specification of demographic variables balances three factors. First, we allow demographic trends to affect men and women differently. Second, our unit of observation is a household, not an individual. Third, our sample size is relatively small (about 500 households per age group per year), which places increased importance on having a relatively parsimonious specification.

To characterize marital status, we define indicator variables for "married couple or unmarried partners" (where the partners can be either of different sexes or of the same sex), for "second or subsequent marriage," and for "divorced or separated." (36) Single or widowed households are the omitted category. Since a divorce or death of a spouse can affect men and women differently, we include an indicator for female-headed households (which can include same-sex households). We also add variables for the number of years a married household has been married and the number of years an individual has been widowed or divorced.

We define variables for postsecondary education, years in the full-time workforce, and fair or poor health separately for men and women. (37) For a married couple the "male" variables correspond to the characteristics of the husband, and the "female" variables to those of the wife. For a household with only one head, the "male" or "female" variables are used and the others are set to zero. For a same-sex couple, the characteristics of the partner designated as the "head" are used, and the demographic characteristics of the other partner are ignored.

Under this specification, the effect of a marriage on wealth accumulation is not simply measured by the coefficient [[beta].sub.marriage], but also varies with the characteristics of the spouses. For example, the expected wealth of a married couple in which both spouses have postsecondary (post-HS) education is predicted by summing the coefficients [[beta].sub.marriage], [[beta].sub.male-post-HS], and [[beta].sub.female-post-HS], along with the appropriate male and female labor force and health coefficients, whereas the expected wealth of an otherwise observationally identical married couple without postsecondary education would differ by [[beta].sub.male-post-HS] + [[beta].sub.female-post-HS].

Wealth Transformations

To establish the robustness of our results, we use the above four techniques to analyze changes in both the level and the inverse hyperbolic sine of wealth. The level-of-wealth results explore the absolute changes in wealth over time, whereas the inverse hyperbolic sine results explore the proportionate changes in wealth over time. We use this transformation, rather than the traditional logarithmic transformation, because it approximates the logarithm but is defined for the zero and negative values that are common in wealth data.

More formally, if [theta] is a scaling parameter and w is a measure of wealth, the inverse hyperbolic sine of wealth can be written as [[theta].sup.-1][sinh.sup.-1]([theta]w) = [[theta].sup-1]ln[[theta]w + [([[theta].sup.2][w.sup.2] + 1).sup.1/2]]. This symmetric function is linear around the origin but approximates the logarithm for larger values of wealth. To see this, note that if w is large, ln[[theta]w + [([[theta].sup.2][w.sup.2] + 1).sup.1/2]] [approximately equal to] ln20 + lnw, which is simply a vertical displacement of the logarithm. Following previous research, we set [[theta] = 0.0001. (38) When multiplied by this scaling parameter, coefficients from an inverse hyperbolic sine specification, like coefficients from a logarithmic specification, can be interpreted as the effect of a change in a given demographic variable on the percentage change in wealth, for wealth values that are sufficiently large. (39)

Results

We report results for median regressions, Blinder-Oaxaca decompositions, and decompositions of the entire net worth distribution.

Median Regressions

Table 2 reports the results of the median regressions. The first column shows the coefficient [[beta].sub.1] from equation 1, that is, the effect of the 2001 indicator before adding demographic characteristics to the equation. The values are small and imprecisely estimated for the three younger age groups, indicating no economically or statistically significant differences in wealth over the course of the 1990s. In contrast, the estimated coefficients are large and significant for the three older age groups. These results, of course, mirror the results in figure 1.

The last column of table 2 shows the coefficient [[beta].sub.2] in equation 2, that is, the effect of the 2001 indicator after adding all of the demographic characteristics described above. The addition of demographic variables removes almost all of the 1989-2001 increase in wealth for the older cohorts. The difference in median wealth falls from $66,308 to $12,674 for the 55-64 group, from $94,996 to -$12,919 for the 65-74 group, and from $95,435 to $18,940 for the 75-84 group and is now statistically insignificant in all three groups. Controlling for demographic characteristics also changes the difference in median wealth for the younger households, but not in a systematic or statistically significant manner. Thus the [[beta].sub.2] coefficient in equation 2 indicates that once one controls for demographic characteristics, the increase in wealth observed in older cohorts disappears.

The middle four columns in table 2 show the effects of adding some but not all of the demographic variables to the right-hand side. These specifications are consistent with the demographic changes documented in table 1: when a demographic characteristic is added to the specification, the coefficient [[beta].sub.2] changes the most for those age groups in which that characteristic changed significantly from 1989 to 2001. The marital status variables, for example, have the largest effects on the two age groups--65-74 and 75-84--that saw large increases in the share of married households. The labor force variables affect only the 55-64 group, the group that saw the largest increase in female labor force participation. The health and education variables, which changed for all three older age groups, likewise contribute to a decrease in the [[beta].sub.2] coefficient across all three groups.

The pattern of coefficients from the inverse hyperbolic sine specification, shown in table 3, is similar. The first column shows that, when expressed in proportionate terms, the net worth of younger households was approximately the same in both 1989 and 2001. (40) Households in the 35-44 group, for example, had 8 percent less wealth in 2001 than 1989, whereas households in the 45-54 group had 1 percent less wealth. Older households, however, experienced substantial and statistically significant wealth gains: the 65-74 group had 56 percent more wealth in 2001 than in 1989, and the 75-84 group had 73 percent more wealth. These results follow the figure 1 numbers when expressed in percentage terms.

As with the levels specification, older households had about the same amount of wealth in 1989 as in 2001 once demographic variables are included. As shown in the final column of table 3, in the full specification, households in the 65-74 group had 4 percent less wealth in 2001 than in 1989; households in the 75-84 group had 12 percent more. These changes are not statistically different from zero. As before, adding the marital variables has a meaningful effect only on the 65-74 and 75-84 groups, whereas the education variables affect all three older age groups. The younger households have a near-zero change in wealth in almost all specifications, regardless of the control variables.

The coefficients on the demographic variables follow expected patterns across the various specifications (table 4). Wealth increases with educational attainment for both men and women; these coefficients are large and statistically significant at the 1 percent level. Households in which either men or women describe their health as "fair" or "poor" have lower wealth. Wealth increases with male labor force participation but not female labor force participation. Female labor force participation may have little effect on wealth accumulation because, historically, lower-income women have been more likely to work outside the home. Over the twentieth century this pattern changed somewhat, as the stigma attached to working outside the home decreased and the returns from market work for most women exceeded the returns from home production. Consistent with this pattern, our regressions indicate that female labor force participation is positively associated with wealth accumulation for the younger groups and negatively associated with it for the older age groups, although neither relationship is statistically significant. (41)

Married couples have more wealth than widowed or single households; divorced and separated households have about the same wealth as widowed or single households. Wealth increases with years of marriage for the 35-44 age group, but not the 65-74 age group. Since the coefficients are conditional on age group, the results suggest that the marginal returns to an extra year of marriage are high for younger households but not for older households, who may have been married for many years. The number of years since becoming widowed or divorced is associated with wealth decreases for the older group but not for the younger group.

Blinder-Oaxaca Decompositions

Turning next to average net worth, we focus on the Blinder-Oaxaca decompositions for age groups that had statistically and economically significant increases in mean wealth. This includes the three cohorts aged 55-64, 65-74, and 75-84. The bottom three rows of each panel in table 5 show that by far the greater part of the change in the average wealth of older households stems from demographic changes. In the levels-of-wealth decompositions, about half of the increase in net worth for the group aged 55-64 and almost all of the increase for the groups aged 65-74 and 75-84 can be attributed to changes in demographic variables. In the inverse hyperbolic sine decompositions, nearly all of the net worth increase in all three age groups can be attributed to changes in demographic variables. (42) Notably, these results are robust to whether the decomposition holds 2001 characteristics and 1989 [beta]s constant, or holds 1989 characteristics and 2001 [beta]s constant. In addition, at traditional significance levels, we can reject the hypothesis that the change stemming from changes in demographic variables is zero.

Consistent with our finding that changes in demographic variables explain most of the change in average wealth for these age groups, almost none of the 1989 [beta]s are statistically significantly different from the 2001 [beta]s (not shown). Only two coefficients change in a consistent and statistically significant manner across specifications and age groups: One is the "female, postsecondary education" coefficient, which is larger in 2001 than in 1989 for the 45-54 group in both specifications, and smaller in 2001 than in 1989 for the 75-84 group in the levels specification and for the 65-74 and 75-84 groups in the inverse hyperbolic sine specification; the other is the "years since divorce or death of spouse" coefficient, which is smaller in 2001 than in 1989 in the levels specification for all three younger age groups and in the inverse hyperbolic sine specification for the 25-34 group.

For purposes of completeness, table 5 also reports Blinder-Oaxaca decompositions for groups that did not have statistically significant changes in wealth. In principle, these regressions are more difficult to interpret, because there is no statistically significant change in wealth to explain in the first place and because many of the changes in means are small in economic terms as well. In practice, the results of the decomposition are significantly less stable for the younger groups than for the older groups. Although some of these decompositions indicate that demographic characteristics explain part of the change in average wealth, our main finding for these groups is that the results are not consistent across X and [beta] combinations or across the levels and inverse hyperbolic sine specifications. Some of the results are also not statistically significant. The jumbled and inconsistent pattern of results that emerges for the younger groups (where there were no significant changes in wealth) is, at the very least, quite different from the very clear and dominant role for demographic factors that emerges for the older groups (where the changes in wealth are large in economic terms and precisely estimated).

Distribution of Net Worth

The decompositions of the entire net worth distribution provide perhaps the most powerful evidence that demographic characteristics are a significant determinant of the greater wealth of older households in 2001. Figure 6 shows the 1989 and 2001 distributions of net worth and a counterfactual distribution of net worth based on the 2001 characteristics and the 1989 coefficients (that is, the 1989 relationship between demographics and wealth) for the three older age groups and for both the DiNardo-Fortin-Lemieux decomposition and the Machado-Mata decomposition. For expositional ease, net worth is shown on a logarithmic scale on the vertical axis; these decompositions are estimated only for the inverse hyperbolic sine specification. If the change in demographic variables explains the change in wealth, the counterfactual and the actual 2001 distributions should largely coincide. If instead other factors (such as historically unique capital gains) explain the changes in wealth, the counterfactual and the actual 2001 distributions should diverge.

[FIGURE 6 OMITTED]

The figure presents the striking result that the counterfactual distributions of net worth (as defined above) nearly exactly coincide with the actual distribution of net worth in 2001 for the 55-64 and 65-74 age groups. This implies that almost all of the change in wealth for those successive cohorts can be explained by changes in demographic status, without appealing at all to any special factors in the 1990s; those special factors would show up as changes in the relationship between demographic characteristics and wealth. Likewise, changes in demographic characteristics can explain about half of the wealth increase for the 75-84 group. The deciles of the counterfactual distribution are statistically significantly different from the deciles of the actual 1989 distribution except at the tails. (43) This result is robust to the choice of decomposition technique, although the Machado-Mata technique appears to behave erratically in the tails of the distribution.

For the younger age groups (figure 7), the 2001 distribution of net worth is almost the same as the 1989 distribution. Thus the decomposition has very little difference in wealth to explain, and the counterfactual distribution lies close to the actual distribution. The deciles of the counterfactual distributions are not statistically significantly different from the 1989 distribution for any of the younger age groups.

[FIGURE 7 OMITTED]

To explore the robustness of our results for the older age groups, we repeat the exercise but attempt to backcast 1989 wealth based on 1989 demographic characteristics and the 2001 relationship between demographics and wealth. Note that the latter relationship includes any impact of the 1990s. If the change in demographic characteristics is a major factor in the change in wealth, and if the relationship between demographics and wealth was the same in 1989 and in 2001, we should find that this counterfactual 1989 distribution is similar to the actual 1989 distribution. Indeed, as shown in figure 8, for the three older age groups this counterfactual distribution lies almost on top of the actual 1989 distribution.

[FIGURE 8 OMITTED]

The fact that the results from both these decompositions and the earlier Blinder-Oaxaca decompositions are robust to which year is used for the distribution of demographic characteristics, and to which year is used for the relationship between demographics and wealth, is notable evidence of a robust relationship. In some empirical literatures the results are sensitive to this choice. Barsky and his coauthors, for example, note that the role that the black-white earnings gap plays in explaining the black-white wealth gap appears to depend on whether the decomposition is based on the black or the white earnings distribution. (44)