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Financial risk taking by age and birth cohort.

1. Introduction

Conventional wisdom suggests that individuals prefer to take fewer financial risks as they age. Economic theory provides an explanation for such behavior, but empirical studies have yielded contradictory results. One of the key contributions of this study is to decompose the effects of chronological age, birth cohort, and calendar year on financial risk taking, which have been confounded in previous studies. In this study we are able to identify a "pure" age effect to obtain an age-risk profile. We are then able to identify a "pure" cohort effect that shows how age-risk profiles vary by birth cohort.

This research is important in light of the possible effects an aging population can have on securities markets. As the U.S. population ages, older people are accounting for a larger share of the total population. Estimates from the U.S. Census Bureau (2004) predict that between 2000 and 2030 the number of Americans ages 65 and over will double, eventually accounting for 27% of the adult population. This group also tends to hold a disproportionately large share of total personal wealth compared with their representation in the population (Bellante and Green 2004). If individuals are found to exhibit increasing relative risk aversion with age, then their behavior could put downward pressure on securities prices (Bakshi and Chen 1994). This in turn could affect defined-contribution pension investment returns and, if the Social Security System is privatized, could also affect investment returns for private retirement accounts. Understanding the relationship between age and financial risk taking is crucial for addressing the likely effects of an aging population on asset prices (Poterba 2004).

The research also has implications for financial management. With the trend to individual responsibility for investment management that is evident with the shift from defined-benefit to defined-contribution pensions, increased use of 401k and 403b tax-deferred investment accounts, and proposed changes to the Social Security system in the form of personal investment accounts, it is important to know how household portfolio allocations change as people age. Planning for age-related changes in risk tolerance is important for both financial planners and individual investors to ensure income security in old age.

The examination of the age profile of household risk taking is one aspect of the larger issue of understanding the allocation of household wealth over the life cycle. One part of an explanation of household life-cycle portfolio behavior must include an explanation of how household preferences for risk taking change as household members age. This "life-cycle" age effect is an attempt to answer the question: will a 35-year-old individual be taking more or less risk when s/he becomes 65 years old? Many studies have claimed to describe the life-cycle effects on the basis of a single cross-section. However, drawing life-cycle inferences on the basis of cross-sectional observations can be biased and misleading as documented in Jianakoplos, Menchik, and Irvine (1989) with regard to wealth, and in Thornton, Rodgers, and Brookshire (1997) with regard to earnings. The relationship between financial risk taking and age observed in a cross-section could be misleading for at least two reasons: a mortality effect and a cohort effect. Assume, for example, that financial risk taking was constant over the life cycle, but only the more risk-averse individuals survived into old age. Then it would appear from a cross-section that financial risk taking decreased with age when it is really the effect of mortality differences. Likewise, suppose that the members of the oldest cohort lived through a depression in their youth that resulted in a reduction in their willingness to take risk over their entire lives. In contrast, suppose that members of a younger cohort spent their youth in a period of prosperity that fostered more aggressive risk taking over their entire lives. Then it would appear from a cross-section that financial risk taking decreases with age when in fact the younger cohort might be willing to take greater risk in their old age than the current older individuals because of birth cohort differences.

Capturing life-cycle effects for individuals requires the use of longitudinal data. Existing panel data sets are problematic for this kind of research because they either do not provide comprehensive data on household wealth or focus on a subgroup of the population, such as those age 65 or older. Even the existence of ideal panel data would not remove the mortality effect, or the additional confounding influence of economy-wide changes over time, year effects, that appear in multiperiod data.

In this study we combine three cross-sectional surveys from the Federal Reserve-sponsored Surveys of Consumer Finances (SCF) spanning a 12-year period to compare the effects of chronological age with birth cohort on financial risk taking after making a normalizing assumption about the year effect. Although this approach does not allow us to make inferences about the relationship between age and financial risk taking of a single individual over the life cycle, it does permit us to examine this relationship for groups of households born in the same time interval, i.e., birth cohorts. Given the possibility of a mortality effect remaining in these data, the results only apply to the living members of the cohorts. A key contribution of this paper is the use of two specifications for risk taking, one based on observed portfolio allocations of wealth and another based on survey respondents' stated willingness to take financial risk. The results are robust across these two specifications. Our results reveal the age-risk profile to be downward sloping, supporting the conventional wisdom that risk taking decreases with age. They also reveal a cohort effect that shifts the age-risk profile down from older to younger cohorts. This suggests that successively younger cohorts are willing to take less financial risk than their older counterparts. Both of these results have important implications for securities markets and financial management.

2. Previous Studies

Why should financial risk taking vary with age? Samuelson (1969, p. 889) showed that in a model of rational portfolio selection, "in your prime of life you have the same relative risk-tolerance as toward the end of life!" Bodie, Merton, and Samuelson (1992) refined the Samuelson approach by including a flexible labor supply, that is, the ability to change how much and how long to work. If they assume that labor supply flexibility decreases over the life cycle in a model of rational decision making, then they can show that financial risk tolerance will decrease with age. It is not the remaining investment horizon that is important, but the ability to use labor income to cushion adverse investment returns that creates the age--risk relationship. Bodie, Merton, and Samuelson (1992) suggest that variables such as type of occupation, nearness to retirement, and two-earner households can provide evidence of labor supply flexibility.

Prospect theory (Kahneman and Tversky 1979) represents an alternative theoretical explanation to the explanation offered by life-cycle theory for how age may affect financial decision making. According to prospect theory, age may be a factor that alters the "objective" assessment of risk. In this vein, Harlow and Brown (1990) investigate the possibility of a biological explanation for the relationship between risk tolerance and age on the basis of changes in enzymes during the aging process. In both theories, it should be noted, the prediction is that risk taking will decrease with age.

Empirical investigations of the relationship between financial risk taking and age have used both subjective and objective measures of risk. The subjective measures depend on responses to survey questions to determine the degree of financial risk tolerance. On the basis of their surveys, Hallahan, Faff, and McKenzie (2003) and Chaulk, Johnson, and Bulcroft (2003) find that subjective measures of financial risk taking decrease with age. In contrast, Grable and Lytton (1999) find, on the basis of another survey, that their subjective measure of financial risk taking increases with age.

Numerous studies have used the ratio of risky assets to household net worth as an objective or observed measure of financial risk taking. Morin and Suarez (1983) and Palsson (1996) find that such an objective measure of financial risk taking decreases with age. In contrast, Bellante and Saba (1986) and Wang and Hanna (1997) find that risk taking increases with age. The latter studies find that an important factor in determining the measured effect of age on financial risk taking is whether or not human capital is included in the analysis. In a recent study focusing exclusively on individuals 70 years of age and over, Bellante and Green (2004) find evidence of decreasing relative risk aversion among the elderly but a modest increase in relative risk aversion as the elderly grow older. All of the above-mentioned studies drew their conclusions about age and risk taking on the basis of single cross-sections of households. Some (Morin and Suarez 1983; Bellante and Saba 1986) incorrectly referred to their estimated relationships between age and risk aversion as "life-cycle" effects.

Several studies have used multiperiod data to examine the relationship between age and household portfolio allocation among various categories of assets. Many of these focused exclusively on the share of stock in household portfolios, rather than broader measures of risky assets. Poterba and Samwick (1997) pool the 1983, 1989, and 1992 SCF data assuming no time effects. They find evidence of cohort effects varying by asset category. Heaton and Lucas (2000) pool the 1989, 1992, and 1995 SCF excluding households with stock holdings of less than $500 or less than $10,000 in financial wealth. The focus of their regression analysis is exclusively on household stockholding by age, assuming no cohort or time effects. Bertaut and Starr-McClure (2002) assume no cohort effect in their analysis of the determinants of household portfolio allocation on the basis of the pooled 1989, 1992, 1995, and 1998 SCF data. Ameriks and Zeldes (2004) focus exclusively on stock ownership in their analysis of age, cohort, and year effects on the basis of data pooled from the 1989 through 1998 SCF. Our paper is distinguished from these previous studies by including the 2001 SCF, focusing on the age and cohort effects by making a normalizing assumption for the time effect, and most importantly, using a measure of stated as well as observed financial risk taking.

3. Data and Empirical Model

The underlying framework for estimating age--risk profiles is the theory of household portfolio allocation between risky and risk-free assets. Friend and Blume (1975) model this allocation decision in the following formulation:

(1) [[alpha].sub.k] = [E([r.sub.m] - [r.sub.f])/[[sigma].sup.2.sub.m](1/[C.sub.k]),

where [[alpha].sub.k] is the proportion of net worth that investor k places in risky assets, E([r.sub.m] - [r.sub.f]) is the expected difference between the return on the market portfolio of risky assets ([r.sub.m]) and the return on the risk-free asset ([r.sub.f]), [[sigma].sup.2.sub.m] is the variance of the return on the market portfolio of risky assets, [C.sub.k] is Pratt's (1964) measure of relative risk aversion ([C.sub.k] = [-U'([W.sub.k]/U"([W.sub.k])][W.sub.k]), and [W.sub.k] is investor k's wealth. The first term in brackets on the right-hand side of Equation 1 is the market price of risk, which is assumed to be the same for all households. Accordingly, household risk taking is proportional to household net worth. We augment this basic model to include age, cohort, and time variables as well as variables related to household labor supply flexibility as suggested by Bodie, Merton, and Samuelson (1992), while controlling for demographic characteristics and assets not included in the selected measure of household wealth.

To estimate the model we pool data from three independent cross-sectional surveys, the 1989, 1995, and 2001 Surveys of Consumer Finances (SCF89, SCF95, and SCF01). These surveys sampled 3143 households in 1989, 4299 households in 1995, and 4442 households in 2001. The households were chosen to provide a comprehensive picture of the financial situation of all U.S. households in those years. The surveys asked similar questions so that comparable variables could be constructed. More information about SCF89 can be obtained in Kennickell and Shack-Marquez (1992); Kennickell, Starr-McClure, and Sunden (1997) provide more details about SCF95; and more information concerning SCF01 is provided by Aizcorbe, Kennickell, and Moore (2003).

Risk Measures

From the survey data we construct two alternative measures of household risk taking. One measure, RATIO, is the observed ratio of risky assets to wealth. The other measure, RISKTAKER, is a stated (or subjective) measure based on each household's response to a survey question asking how much financial risk the household is willing to take. The proportion of household wealth held in risky assets is a frequently used measure of household financial risk. Shaw (1996), for example, used this measure as an explanatory variable, whereas Friend and Blume (1975), Morin and Suarez (1983), Jianakoplos and Bernasek (1998), and numerous others have used this measure as the focus of studies of financial risk taking. Previous research by Friend and Blume (1975) and Siegal and Hoban (1991) show that estimates are sensitive to the definition of wealth used. Economists are generally skeptical of statements made by households regarding their choices, preferring instead to use measures of the actual household behavior. Jianakoplos (2002) illustrates that although contradictions can be found in the stated versus observed financial risk taking of households, the measures are consistent at the ordinal level. Nevertheless, variables based on survey responses have been used as both the dependent variable (Chaulk, Johnson, and Bulcroft 2003) and independent variable (Haliassos and Bertaut 1995; Shaw 1996) in previous studies of financial risk taking.

The observed measure of financial risk taking (RATIO) is the ratio of risky assets (RISKY) to investment wealth (WEALTH) defined as the sum of RISKY and risk-free assets. Risk in this context refers to variable returns. Thus, risk-free assets are limited to those with fixed nominal values. Although important, we ignore the potential variability of return to nominally fixed assets that arises from inflation. The division of wealth into risky and risk-free assets is by nature arbitrary, but we have tried to be consistent with previous studies. Risk-free assets are defined to include dollar balances in checking, savings, money market, and brokerage call accounts, certificates of deposit (CD), U.S. savings bonds, individual retirement accounts (IRAs) invested in CDs, and the cash value of life insurance polices. RISKY (including mixed-risk assets) includes the value of balances in IRAs (not invested in CDs), bonds, stocks, mutual funds, balances in defined-contribution pensions less loans, trust and annuity assets, net value of businesses, net value of investment real estate, and the net value of other assets (oil and gas leases, futures contracts, etc.) less outstanding credit card balances, lines of credit, and other miscellaneous debts. Because we are concerned with financial risk taking rather than broader avenues of risk taking, we use a relatively narrow definition of wealth focusing on assets that households hold for investment purposes.

For a variety of reasons we exclude the value of residential housing, human capital, and expected defined-benefit pensions from the definition of investment wealth, although we control for these factors in the regression analysis reported in the next section. The value of defined-benefit pensions are excluded from the measure of investment wealth because households with this type of pension do not exercise any investment control over this asset. Unlike defined-contribution (401k type) pensions, where households typically manage the amounts contributed and the investment allocations, defined-benefit pensions provide definitely determined payments over a period of years (usually a lifetime) typically on the basis of a formula that combines the number of years of service and the average salary earned over the last few years of service. House values are excluded from the measure of investment wealth because the extent to which houses are owned for investment purposes in addition to consumption purposes is unclear. Human capital is excluded from the measure of investment wealth because it is not easily reallocated.

The variable based on each household's stated financial risk-taking preference is the survey participants' responses to the following question: "Which of the statements on this (page/card) comes closest to the amount of financial risk that you (and your husband/wife) are willing to take when you save or make investments? (i) take substantial financial risk expecting substantial returns, (ii) take above-average financial risk expecting to earn above-average returns, (iii) take average financial risk expecting to earn average returns, or (iv) not willing to take any financial risks." RISKTAKER equals one for all respondents indicating that they are willing to take average, above average, or substantial financial risks and zero for those indicating that they are unwilling to take any financial risk.

Age, Generation/Cohort, and Year Measures

We include AGE, the age of the head of household in the analysis of RATIO and the age of the survey respondent in the analysis of RISKTAKER, to allow for systematic differences in financial risk taking by chronological age. (1) We also include AGE (2) to allow for nonlinearities in the impact of AGE. The estimated coefficients of these two variables represent a "pure" age effect. They help to answer the question: Do younger people take more financial risks than older people, holding other factors constant?

The upper left-hand quadrants of Figures 1 and 2 illustrate the risk-age profiles obtained from the three cross-sections of survey data. The profile of RATIO versus AGE in Figure 1 shows a hump-shaped pattern that peaks in the 40s and 50s. The profile of RISKTAKER and AGE in Figure 2 shows a generally downward-trending pattern over the entire age span. These cross-sectional profiles combine the effects of age, cohort, and time that we disentangle in the analysis below.

[FIGURES 1-2 OMITTED]

Individuals born in the same time period who share similar life experiences at each stage of the life cycle may be expected to view financial risk taking differently from individuals born in other periods. To capture the impact of aging on financial risk taking by households in different birth cohorts, we include dummy variables indicating birth cohort. Since the dividing line between cohorts is arbitrary, we use two different sets of birth cohort dummies. One set is based on popular categorization of cohorts, which we will refer to as generations. The other set is arbitrarily constructed as six successive 12-year groupings of households by year of birth.

The four-generation dummies roughly follow the division of birth cohorts used by Strauss and Howe (1991) to characterize the American population in their book Generations. The dummy variables created for the four generations are: GI equal to one for household heads born between 1898 and 1924, SILENT equal to one for heads born between 1925 and 1945, BOOMER equal to one for heads born between 1946 and 1964, and GENX for heads born between 1965 and 1983. Our cohorts differ from Strauss and Howe's generations in three ways. First, the beginning year of the GI cohort is extended back from Strauss and Howe's 1901 date to 1898 to accommodate the small number of the very oldest in our sample. Likewise, the ending year of GENX is extended from Strauss and Howe's choice of 1981 to 1983 to accommodate the small number of the very youngest in our sample. Strauss and Howe's definition of the baby boom generation to be individuals born between 1943 and 1960 differs from the more typical 1946 to 1964 dating (Crispell 1993; Gibson 1993; U.S. GPO 2004). The GI cohort is the omitted category when the equation is estimated.

We construct six arbitrary 12-year cohorts. COHORT1 includes the youngest respondents, those born between 1972 and 1983, whereas COHORT6 includes the oldest respondents, those born between 1898 and 1923. Because the surveys span a 12-year interval, the choice of 12-year cohorts conveniently allows us to view the financial risk-taking behaviors of several cohorts at the same age. For example, COHORT2 is ages between 18 and 29 in the 1989 survey, whereas COHORT1 spans the same age range in the 2001 survey. The estimated coefficients on the cohort dummies indicate how the age-risk profiles shift across cohorts, holding other factors constant. These estimated coefficients help to answer the question: Will current young people eventually have the risk preferences of current old people?

Table 1 provides the age span, number of observations, and the mean and standard error of RATIO for each generation/cohort in each of the three surveys. Table 2 provides the same information for RISKTAKER. Although the age spans are identical for generations and cohorts in the two tables, the number of observations in each cell differs because generations and cohorts were determined by the age of the household head in Table 1, but by the age of the survey respondent in Table 2. Reading across the final three columns of each table reveals how financial risk taking changes as members of the same cohort age. Financial risk taking, whether observed (RATIO) or stated (RISKTAKER), increases, on average, as each cohort ages in all but the oldest generation/cohort. It is important to remember that although we can observe the same cohort over the 12-year span, the individual households making up the cohort differ in each survey. Nevertheless, to the extent that the cohort average is representative of the typical household in a cohort, the change in cohort means/proportions over time provides a glimpse into the life-cycle profile of financial risk taking.

To allow for the impact of changes in the economy affecting all households between 1989 and 2001, such as financial deregulation, financial innovation, and stock market expansions, we include a dummy variable, TIME. As pointed out by Deaton (1997), because there is a linear relationship between age, birth-year cohort, and survey year, we must normalize one of these three factors. Following Deaton (1997), we use a time dummy that sums to zero and is orthogonal to a time trend. (2) As a result of this normalization, all aggregate macroeconomic effects on the age-risk profile are assumed to cancel out over the 12-year period. Because of the limited number of cross-sections, caution must be used in interpreting this estimated coefficient.

Labor Supply Flexibility Measures

Bodie, Merton, and Samuelson (1992) suggest that labor supply flexibility is responsible for the relationship between age and financial risk taking. To capture the impact of labor market flexibility, four dummy variables are included. Workers who are retired or in poor health can be expected to have very limited labor supply flexibility. The variable RETIRED equals one if the head of household was retired or disabled at the time of the survey. A dummy variable POORHEALTH equals one if either the household head or spouse (if any) reported himself/herself to be in poor health when asked in the survey. Households with two earners or who are self-employed are more likely to have labor supply flexibility than other households. Two dummy variables, TWOEARN, which equals one if both the household head and spouse report earnings in the year before the survey, and SELFEMPLOY, which equals one if either the household head or spouse is self-employed at the time of survey, are included.

Demographic Variables

Previous studies, including Jianakoplos and Bernasek (1998), have found financial risk taking to differ by gender, race, marital status, and the presence of children in the household. We include four dummy variables to control for such demographic factors. The variables SINGLEMALE and SINGLEFEMALE equal one for households headed by a single male or single female, respectively. Married couples are the omitted category. The variable NONWHITE equals one if the head of household classifies himself/herself in any racial category other than Caucasian. The variable KIDS equals one if there are children under the age of 18 living in the household.

Investment Wealth and Other Assets

The theoretical framework makes risk taking depend on household wealth. Household wealth is included in the estimating equation as the logarithm of WEALTH, a measure of the household's investment wealth. Several other components of household wealth, not part of investment wealth, may affect risk taking and are included in the regressions. These include a proxy for the household's human capital, HUMAN, a dummy variable, HOMEOWN, taking the value of one for homeowners and zero for all others, and a dummy variable, DBPENSION, equal to one if the household head or spouse has a defined-benefit pension. Using a method similar to that used by Friend and Blume (1975) and Heaton and Lucas (2000) we construct a measure of human capital by assuming that the current annual wage, salary, and self-employment earnings of each household would continue until the household head retires at age 65 for household heads ages 65 and younger, for an additional 4 years for household heads between the ages of 66 and 69, for an additional 3 years for household heads between the ages of 70 and 74, for an additional 2 years for heads between the ages of 75 and 79, and for an additional year for heads age 80 and over. Human capital is the present discounted value of this earnings stream using a 2% discount rate. The assumption of a constant growth rate of the age-earnings profile is consistent with the findings of Thornton, Rodgers, and Brookshire (1997), who examine these profiles using longitudinal data, rather than making inferences on the basis of cross-sectional data.

Estimation Issues

We estimate the model for two measures of financial risk taking and two definitions of generation/cohort. Since the first measure of financial risk taking, RATIO, can take values between zero and one inclusive, a maximum likelihood tobit procedure that allows for both left- and right-censored dependent variables is used to estimate the following equation:

(2) RATIO = [[beta].sub.0] + [[beta].sub.1] AGE + [[beta].sub.2] [AGE.sup.2] + [summation][[gamma].sub.i] [COHORT.sub.i] + [[beta].sub.3] TIME + [[beta].sub.4] ln WEALTH + [[beta].sub.5] HUMAN + [[beta].sub.6] HOMEOWNER + [[beta].sub.7] DBPENSION + [[beta].sub.8] RETIRED + [[beta].sub.9] POORHEALTH + [[beta].sub.10] TWOEARN + [[beta].sub.11] SELFEMPLOY + [[beta].sub.12] TWOEARNER + [[beta].sub.13] SINGLEMALE + [[beta].sub.14] SINGLEFEMALE + [[beta].sub.15] KIDS + [[beta].sub.16] NONWHITE + [epsilon],

where [epsilon] is a random disturbance term.

In the analysis of the other measure of financial risk taking, RISKTAKER, a maximum likelihood probit model is estimated for the following equation:

PR(RISKTAKER = 1) = [PHI]([[beta].sub.0] + [[beta].sub.1] AGE + [[beta].sub.2] [AGE.sup.2] + [summation][[gamma].sub.i] [COHORT.sub.i] + [[beta].sub.3] TIME + [[beta].sub.4] ln WEALTH + [[beta].sub.5] HUMAN + [[beta].sub.6] HOMEOWNER + [[beta].sub.7] DBPENSION + [[beta].sub.8] RETIRED + [[beta].sub.9] POORHEALTH + [[beta].sub.10] TWOEARN + [[beta].sub.11] SELFEMPLOY + [[beta].sub.12] TWOEARNER + [[beta].sub.13] SINGLEMALE + [[beta].sub.14] SINGLEFEMALE + [[beta].sub.15] KIDS + [[beta].sub.16] NONWHITE + [epsilon].

Table 3 reports the mean values and standard errors of the variables used in the regression estimations. Following other research we exclude those households from the sample with less than $1000 (2001 dollars) in investment wealth and those households with risky assets having a net value less than zero. These restrictions reduce the pooled sample size to 9189 households. Dollar values from the 1989 and 1995 surveys were adjusted to 2001 purchasing power using the consumer price index. Because wealth is highly skewed, the surveys oversampled high-income households. Accordingly, all summary statistics and regressions reported in this paper are sample weighted to adjust for the effect of this oversampling and other aspects of the sample design. We make use of the versions of these surveys that use the imputed values of missing data produced by researchers at the Board of Governors of the Federal Reserve System. Appropriate regression estimates and robust standard errors are obtained using software procedures in Stata Release 8 (StataCorp 2003) for survey data that adjust for observations not sampled independently.

4. Results and Discussion

Table 4 reports the estimated coefficients and summary statistics for three variations of the Equation 2 estimated with RATIO as the dependent variable. Table 5 reports estimated coefficients and the marginal effects for two variations of Equation 3 when RISKTAKER is the dependent variable. Because the estimated coefficients are similar for both measures of risk taking, we interpret the results for both equations concurrently in the discussion that follows.

Pure Age Effect

Estimates from all three specifications reported in Table 4 and both specifications in Table 5 suggest a downward-sloping age-risk profile over most age spans, holding other factors constant. The specification reported in columns (A) and (B) of Table 4 are identical except that the generation dummies are used for specification (A) while the 12-year cohort dummies are used for specification (B). In specification (A) the coefficients of both AGE and [AGE.sup.2] are statistically different from zero at conventional levels. These coefficients indicate a quadratic (hump-shaped) relationship between chronological age and financial risk taking with a peak at age 22.5 years, so that risk taking is declining over almost all adult ages. The coefficients from specification (B) in Table 4 and both specifications in Table 5 indicate a risk profile that declines continuously over all ages. The top right quadrant of Figures 1 and 2 graphically illustrates this "pure" age effect based on the coefficients from specification (B) in Table 4 and specification (B) in Table 5. The estimated age effect is consistent with the conventional wisdom that risk declines with age. However, the pattern of age coefficients does not correspond to the observed increase in risk taking as members of the same cohort age shown in Tables 1 and 2, at least for the short time interval over which we can observe these cohorts.

Cohort Effects

The coefficients of the generation dummies and the 12-year cohort dummies estimated for both observed and stated risk taking indicate that older cohorts take more financial risks than younger ones, holding other factors constant. The coefficients indicate how the age-risk profile shifts up or down, while maintaining its shape, for households with identical characteristics but from different cohorts. The oldest generation or cohort is omitted in both specifications, so the coefficients indicate shifts in the age-risk profile relative to the profile of the oldest generation/cohort. In all specifications the estimates indicate that the profiles shift down successively from the oldest to the youngest generation/cohort. The "pure" cohort effect based on coefficients from specification (B) in Table 4 and specification (B) in Table 5 are graphed in the bottom left quadrants of Figures 1 and 2, respectively. It is worth noting that none of the specifications constrained the generation/cohort dummies to follow this smooth, continuously increasing pattern. The estimated cohort effect is determined by the data.

An indication of the magnitude of the difference in risk taking by cohort can be obtained by using the estimated coefficients to predict the level of risk taking for each generation holding other factors constant at the sample averages. The estimated coefficients from specification (A) of Table 4 imply that baby boomers at age 50 are predicted to hold 83% of their investment wealth in risky assets, compared to 69% of the investment portfolios held in risky assets by members of Gen X at age 50. Likewise, with all other factors held constant at the sample averages, the coefficients of specification (A) in Table 5 predict that 86% of baby boomers would be financial risk takers at age 50, compared to 81% of Gen X at age 50. Figure 3 illustrates the shift in the age-risk profile between the BOOMER and GENX generations across the entire life span that is implied by the estimated generation coefficients from specification (A) in Table 4 when the other variables in the equation are held constant at the sample means.

[FIGURE 3 OMITTED]

The estimated cohort effect is puzzling. In previous research where authors decomposed age-earnings or age-wealth relationships, Deaton (1997) and Jappelli (1999), for example, the age-earnings and age-wealth profiles are estimated to shift up from oldest to youngest cohort. These shifts are attributed to a secular increase in productivity. This explanation is based on the idea that older cohorts had less access to productivity-enhancing opportunities than younger cohorts at the same age and thus the cohort effect serves to reduce the age-earnings or age-wealth profile for older cohorts compared to younger cohorts. In contrast, the estimates presented here suggest that age-risk profile shifts down from older to younger cohorts.

There are several possible explanations for the estimated cohort effects. Our preferred explanation for this cohort effect is that overall household financial security has been decreasing over time. Examples of this decreased security include declining expectations of receiving Social Security benefits among younger cohorts, less likelihood of receiving defined benefit pensions, and reduced job security. In this scenario younger cohorts have responded by reducing the amount of financial risk they are willing to undertake. (3) Other explanations revolve around some type of measurement error. Deaton (1997) suggests that the inverse relationship between cohort age and risk preferences could be the result of selection bias as a consequence of using the household as the unit of observation. Older individuals with relatively low preferences for risk taking may have become part of households headed by younger individuals (for example, an elderly parent goes to live with an adult child who is head of household). According to this scenario members of older cohorts remaining as heads of household may have greater risk tolerance than those in younger cohorts. Of course the cohort effect could be the result of only observing cohorts for a very limited 12-year time span. Over this interval the younger cohorts may face greater borrowing constraints than the older cohorts, although this argument does not easily explain the cohort effect found in the analysis of stated risk taking.

The finding of a pure cohort effect indicating greater risk taking for older cohorts is robust across both stated and observed financial risk taking and for the two alternative definitions of cohorts. To further test the robustness of this result, the regressions were re-estimated excluding the very youngest and very oldest cohorts. The results (not presented here, but available on request) exhibit the same pattern, showing younger cohorts taking relatively less risk than older cohorts. Additionally, when the sample is divided by education level (whether or not the household head or spouse, if present, has a college degree), the estimated pattern of cohort effects (not shown here, but available on request) persists.

Year Effect

The estimated coefficients of the time dummies for both stated and observed measures of financial risk taking indicate that economy-wide factors shift age-risk profiles upward in 1995 compared to 1989 and 2001. Although only one time dummy is included in each regression, the coefficients associated with each of the three survey years can be recovered because of the restriction that the dummies sum to zero and are orthogonal to a time trend. The graphs in the bottom right quadrants of Figures 1 and 2 graphically illustrate the estimated year effect. This is consistent with the stock market boom of the 1990s that attracted more investors to financial risk taking before the steep market decline beginning in 2001. Because there are only three surveys, the estimated time pattern must be treated with extreme caution, recognizing that the year effects are constrained to sum to zero over the 12-year survey span.

Labor Flexibility

Several of the variables included to capture labor supply flexibility are found to be statistically significant with the hypothesized signs. Being retired or in poor health, variables hypothesized to reduce labor supply flexibility and reduce financial risk taking, are estimated to significantly reduce financial risk taking in all of the estimated specifications. Being self-employed or part of a two-earner household was hypothesized to increase labor force flexibility and financial risk taking. Self-employment is statistically significant, with the appropriate sign only in specifications explaining observed financial risk taking, whereas the two-earner variable is not statistically significant in any of the specifications. On balance, however, these results support the hypothesis that labor force flexibility increases household financial risk taking, holding other factors constant.

Demographics

Among the variables used to control for demographic differences in financial risk taking we find that single females take significantly less risk than married couples, in all of the specifications estimated. This result is consistent with previous research (Jianakoplos and Bernasek 1998) that found that single women were more risk averse than married couples, and is consistent with the idea that the lack of labor supply flexibility of single women relative to married couples would reduce financial risk taking. In contrast, the SINGLEMALE dummy is estimated to significantly increase financial risk taking, but only in the stated risk-taking specifications, not in the observed risk-taking specifications. This result could be an example of the divergence between stated and observed risk-taking behavior where single males verbally indicate that they are willing to take financial risks, but their balance sheets do not reflect their statements.

Households with children are estimated to take significantly less risk than households without children in specifications estimated for stated risk taking, but children do not have a significant impact on observed financial risk taking. Across all specifications and for both measures of financial risk taking, we do find evidence that nonwhite households take significantly less financial risk than white households, controlling for other factors.

Asset Ownership

The inverse of the coefficient of ln WEALTH is proportional to the coefficient of relative risk aversion. The estimated coefficient of ln WEALTH is positive and statistically significant in every specification, indicating decreasing relative risk aversion. This is consistent with previous findings by Friend and Blume (1975) and Jianakoplos and Bernasek (1998), for example. Measures of three components of household wealth not included in the construction of the RATIO variable (human capital, home ownership, and defined benefit pension ownership) were included in specifications (A) and (B) of Table 4 to control for the possible impact of these assets on financial risk taking. Only home ownership is estimated to have a significant impact on financial risk taking and only when the generation dummies are used. Because of the possible endogeneity of these variables, they were excluded from specification (C) in Table 4. None of the magnitudes or statistical significance of the remaining variables was altered much by this exclusion. In contrast, all three of these asset variables are estimated to have a statistically positive influence on stated financial risk taking as shown in Table 5.

5. Summary and Conclusions

The relationship between age and financial risk taking has important implications for the effects of an aging population on securities prices and the effects of increasing individual responsibility for income security in older age. The main contribution of this paper is to decompose the effects of chronological age, birth cohort, and calendar year on two alternative measures of financial risk taking. We use data from the Federal Reserve's Survey of Consumer Finances for three representative samples of U.S. households surveyed in 1989, 1995, and 2001, spanning a 12-year period. Two specifications are used for risk taking; one is the observed portfolio allocation of household wealth and the second is the stated willingness to take financial risks of survey respondents. The results obtained are robust across both specifications.

The result obtained for the "pure" age effect confirms the conventional wisdom that risk taking decreases with age (the age-risk profile is downward sloping). Holding other factors constant, older people are found to take fewer risks than younger people, both in terms of their observed and stated willingness to take risk. The result obtained for the "pure" cohort effect reveals that successively younger cohorts are less willing to take risks than their older counterparts (age-risk profiles shift down from older to younger cohorts). This result is perhaps surprising since a priori it could be hypothesized that productivity differences over time might be expected to shift age-risk profiles up from older to younger generations. Our results are consistent with the idea that preferences for financial risk taking decreased in conjunction with decreases in household financial security over time as people experienced less job security and greater uncertainty surrounding expected public and private pension benefits.

This study is distinguished from previous studies by the inclusion of measures of labor supply flexibility, which were hypothesized by Bodie, Merton, and Samuelson (1992) to affect financial risk tolerance. The results confirm the hypothesis that less labor supply flexibility is associated with less willingness to take risks. To the extent that less labor supply flexibility is associated with aging we will see the two effects reinforce one another.

How one allocates assets among risky and less risky options has taken on increasing importance with the proposed privatization of Social Security and increased reliance on defined-contribution pensions and 401(k) retirement plans. The degree of financial risk taking exhibited by households is a fundamental element of these allocation decisions. Taking into account any systematic differences in financial risk taking should be an important part in assessing the impact of retirement policy changes. It is also an important element in the performance of financial advisers. The results obtained in this study provide important information to individuals and financial planners. If people are willing to take fewer financial risks as they age, they must adjust their investment plans accordingly to prepare themselves adequately for retirement. Furthermore, to the extent that younger cohorts are less willing to take risks than their older counterparts, a different strategy for ensuring their income adequacy in retirement will be required. Past experience will not necessarily be a good guide to the future. The results suggest caution in estimating the potential returns from private investment accounts that are being proposed as part of the reform of the Social Security system.

In terms of predicting the effects of an aging population on stock prices our results suggest that a dampening effect is likely. Although we cannot predict the magnitude of such an effect, both the age and cohort effects reinforce one another and suggest that there will be less risk taking over time. As the proportion of older people in the population increases, the result that older people are less willing to take financial risks than younger people creates downward pressure on stock prices. Furthermore, since the Gen X cohort is less willing to take risks than the baby boom generation, not only is there no offsetting of this tendency, it is actually reinforced. One of the issues for future research will be estimating the magnitude of this dampening effect.

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(1) The husband was arbitrarily classified as the head of household for married households. However, the husband was not necessarily the household member who answered the survey questions. Since the RATIO variable refers to household wealth, which is not easily divided between household members, we choose to continue the arbitrary practice of associating household characteristics of the head of household in analysis based on this variable. However, only one household member responded to the survey question about financial risk preferences. Thus, we have associated the age of that respondent with the RISKTAKER variable.

(2) We thank an anonymous referee for suggesting this specification.

(3) We thank Ron Phillips for suggesting this possibility.

Nancy Ammon Jianakoplos * and Alexandra Bernasek ([dagger])

* Department of Economics, 1771 Campus Delivery, Colorado State University, Fort Collins, CO 80523, USA; E-mail Nancy.Jianakoplos@ColoState.edu: corresponding author.

([dagger]) Department of Economics, 1771 Campus Delivery, Colorado State University, Fort Collins, CO 80523, USA; E-mail Alexandra.Bernasek@ColoState.edu.

We thank two anonymous referees and Julie Hotchkiss (the co-editor) for their helpful and constructive comments.

Received October 2004; accepted August 2005.
Table 1. Cell Size and Mean Ratio of Risky
Assets By Generation and Cohort of Household Head

 Cell Cell Cell
 Age in Age in Age in Size Size Size
Year of Birth 1989 1995 2001 1989 1995 2001

Generations:
 Silent: 1925-1945 18-24 18-30 18-36 37 301 544
 Boomer: 1946-1964 25-43 31-49 37-55 758 1274 1586
 Silent: 1925-1945 44-64 50-70 56-76 1042 1265 1052
 GI: 1898-1924 65-95 71-95 77-95 590 483 257
Cohorts:
 (1): 1972-1983 -- 18-23 18-29 -- 51 235
 (2): 1960-1971 18-29 24-35 30-41 141 502 663
 (3): 1948-1959 30-41 36-47 42-53 522 881 1047
 (4): 1936-1947 42-53 48-59 54-65 650 793 763
 (5): 1924-1935 54-65 60-71 66-77 563 647 514
 (6): 1898-1923 66-95 72-95 78-95 551 449 217
Total: 18-95 18-95 18-95 2427 3323 3439

 Mean Ratio Mean Ratio Mean Ratio
 1989 1995 2001
Year of Birth (Std. Error) (Std. Error) (Std. Error)

Generations:
 Silent: 1925-1945 0.51 (0.08) 0.57 (0.02) 0.60 (0.02)
 Boomer: 1946-1964 0.58 (0.02) 0.67 (0.01) 0.70 (0.01)
 Silent: 1925-1945 0.62 (0.01) 0.65 (0.01) 0.61 (0.02)
 GI: 1898-1924 0.39 (0.02) 0.38 (0.02) 0.38 (0.03)
Cohorts:
 (1): 1972-1983 -- 0.46 (0.06) 0.52 (0.03)
 (2): 1960-1971 0.49 (0.04) 0.62 (0.02) 0.69 (0.01)
 (3): 1948-1959 0.59 (0.02) 0.67 (0.01) 0.69 (0.01)
 (4): 1936-1947 0.63 (0.02) 0.69 (0.02) 0.69 (0.02)
 (5): 1924-1935 0.61 (0.02) 0.59 (0.02) 0.51 (0.02)
 (6): 1898-1923 0.38 (0.02) 0.38 (0.02) 0.38 (0.03)
Total: 0.54 (0.01) 0.61 (0.01) 0.63 (0.01)

Table 2. Cell Size and Proportion of Financial Risk
Takers by Generation and Cohort of Survey Respondent

 Cell Cell Cell
 Age in Age in Age in Size Size Size
Year of Birth 1989 1995 2001 1989 1995 2001

Generations:
 GenX: 1965-1983 18-24 18-30 18-36 43 347 577
 Boomer: 1946-1964 25-43 31-49 37-55 802 1295 1617
 Silent: 1925-1945 44-64 50-70 56-76 1016 1220 1015
 GI: 1898-1924 65-95 71-95 77-95 566 461 230
Cohorts:
 (1): 1972-1983 -- 18-23 18-29 -- 51 235
 (2): 1960-1971 18-29 24-35 30-41 141 502 663
 (3): 1948-1959 30-41 36-47 42-53 522 881 1047
 (4): 1936-1947 42-53 48-59 54-65 650 793 763
 (5): 1924-1935 54-65 60-71 66-77 563 647 514
 (6): 1898-1923 66-95 72-95 78-95 551 449 217
Total: 18-95 18-95 18-95 2427 3323 3439

 Proportion Proportion Proportion
 Risk Taker Risk Taker Risk Taker
 1989 1995 2001
Year of Birth (Std. Error) (Std. Error) (Std. Error)

Generations:
 GenX: 1965-1983 0.70 (0.07) 0.71 (0.03) 0.80 (0.02)
 Boomer: 1946-1964 0.68 (0.02) 0.72 (0.01) 0.74 (0.01)
 Silent: 1925-1945 0.59 (0.02) 0.59 (0.02) 0.62 (0.02)
 GI: 1898-1924 0.38 (0.03) 0.34 (0.03) 0.33 (0.04)
Cohorts:
 (1): 1972-1983 -- 0.65 (0.07) 0.80 (0.03)
 (2): 1960-1971 0.67 (0.04) 0.73 (0.02) 0.77 (0.02)
 (3): 1948-1959 0.69 (0.03) 0.71 (0.02) 0.76 (0.02)
 (4): 1936-1947 0.65 (0.03) 0.69 (0.02) 0.74 (0.02)
 (5): 1924-1935 0.54 (0.03) 0.49 (3.00) 0.51 (0.03)
 (6): 1898-1923 0.38 (0.03) 0.34 (0.03) 0.33 (0.04)
Total: 0.58 (0.01) 0.62 (0.01) 0.69 (0.01)

Table 3. Variable Means and Standard Errors (Sample Weighted)

 1989 1995

 Mean S.E. Mean S.E.

Age: head (years) 49.9 0.49 50.2 0.39
Age: respondent (years) 49.3 0.49 49.4 0.39
Generation head:
 GenX (%) 4 0.65 12 0.69
 Boomer (%) 39 1.37 42 1.08
 Silent (%) 33 1.25 30 1.01
 GI (%) 24 1.25 16 0.88
Generation respondent:
 GenX (%) 4 0.67 14 0.73
 Boomer (%) 40 1.37 42 1.08
 Silent (%) 33 1.26 29 1.00
 GI (%) 23 1.12 15 0.86
Cohort head:
 1972-1983 (%) -- -- 2 0.27
 1960-1971 (%) 12 1.04 20 0.87
 1948-1959 (%) 26 1.24 29 0.98
 1936-1947 (%) 22 1.10 18 0.84
 1924-1935 (%) 17 0.97 16 0.83
 1898-1923 (%) 22 1.11 15 0.86
Cohort respondent:
 1972-1983 (%) -- -- 2 0.27
 1960-1971 (%) 12 1.04 20 0.87
 1948-1959 (%) 26 1.24 29 0.98
 1936-1947 (%) 22 1.10 18 0.84
 1924-1935 (%) 17 0.97 16 0.83
 1898-1923 (%) 22 1.12 15 0.86
Wealth:
 Investment wealth ($000) 287 13.89 271 9.47
 Risk-free assets ($000) 55 3.00 47 2.15
 Risky assets ($000) 232 12.70 224 8.62
 Human capital ($000) 873 29.48 867 24.08
 Homeowner (%) 75 1.29 74 0.96
 Defined benefit pension (%) 33 1.27 25 0.92
Labor supply Flexibility:
 Retired (%) 23 1.14 22 0.97
 Poor health (%) 7 0.74 6 0.55
 Self-employed (%) 18 0.98 16 0.75
 Two earners (%) 35 1.29 36 1.04
Demographics:
 Single male (%) 14 1.05 13 0.74
 Single female (%) 21 1.17 24 0.98
 Married couple (%) 65 1.36 64 1.08
 Children (%) 36 1.33 34 1.03
 Nonwhite (%) 15 1.01 16 0.83
N 2427 3323

 2001 Pooled Surveys

 Mean S.E. Mean S.E.

Age: head (years) 50.7 0.36 50.3 0.24
Age: respondent (years) 50.0 0.36 49.6 0.24
Generation head:
 GenX (%) 21 0.86 13 0.44
 Boomer (%) 43 1.00 42 0.67
 Silent (%) 27 0.95 30 0.61
 GI (%) 9 0.62 15 0.51
Generation respondent:
 GenX (%) 22 0.88 14 0.45
 Boomer (%) 44 1.05 42 0.67
 Silent (%) 26 0.94 29 0.61
 GI (%) 8 0.60 15 0.49
Cohort head:
 1972-1983 (%) 10 0.61 4 0.24
 1960-1971 (%) 24 0.90 19 0.54
 1948-1959 (%) 27 0.93 27 0.60
 1936-1947 (%) 17 0.79 19 0.52
 1924-1935 (%) 15 0.79 16 0.49
 1898-1923 (%) 7 0.57 14 0.49
Cohort respondent:
 1972-1983 (%) 10 0.61 4 0.24
 1960-1971 (%) 24 0.90 19 0.54
 1948-1959 (%) 27 0.93 27 0.60
 1936-1947 (%) 17 0.79 19 0.52
 1924-1935 (%) 15 0.79 16 0.49
 1898-1923 (%) 7 0.57 14 0.49
Wealth:
 Investment wealth ($000) 432 14.48 335 7.46
 Risk-free assets ($000) 59 2.52 54 1.48
 Risky assets ($000) 373 13.42 281 6.86
 Human capital ($000) 1044 29.69 934 16.19
 Homeowner (%) 79 0.81 76 0.59
 Defined benefit pension (%) 22 0.86 26 0.59
Labor supply Flexibility:
 Retired (%) 21 0.90 22 0.58
 Poor health (%) 5 0.47 6 0.34
 Self-employed (%) 17 0.75 17 0.48
 Two earners (%) 40 1.03 37 0.65
Demographics:
 Single male (%) 13 0.71 13 0.48
 Single female (%) 20 0.86 22 0.57
 Married couple (%) 67 1.00 65 0.66
 Children (%) 35 1.01 35 0.64
 Nonwhite (%) 16 0.79 16 0.50
N 3439 9189

Table 4. Censored Regression Results. Dependent Variable: Ratio of
Risky Assets to Investment Wealth (Robust Standard Errors)

Variables (A) (B)

Age 0.009 ** (0.003) -0.002 (0.004)
Age squared -0.0002 *** (0.00003) -0.0002 *** (0.00004)
Generation:
 GenX -0.423 *** (0.052)
 Boomer -0.275 *** (0.042)
 Silent -0.105 *** (0.031)
Cohort:
 1972-1983 -0.886 *** (0.077)
 1960-1971 -0.636 *** (0.061)
 1948-1959 -0.482 *** (0.052)
 1936-1947 -0.297 *** (0.043)
 1924-1935 -0.137 *** (0.032)
Time Dummy -0.064 *** (0.005) -0.071 *** (0.005)
In Wealth 0.042 *** (0.002) 0.050 *** (0.002)
Human capital (000) -3.54e-08 (3.32e-07) -5.57e-07 (5.09e-07)
Homeowner 0.025 * (0.015) 0.018 (0.015)
Defined benefit
 pension 0.006 (0.011) 0.004 (0.011)
Retired -0.059 *** (0.021) -0.066 *** (0.021)
Poor health -0.069 ** (0.030) -0.064 ** (0.029)
Self-employed 0.111 *** (0.012) 0.102 *** (0.012)
Two earners -0.020 (0.014) -0.017 (0.014)
Single male -0.001 (0.020) 0.005 (0.020)
Single female -0.045 ** (0.017) -0.038 ** (0.017)
Children 0.005 (0.013) 0.007 (0.013)
Nonwhite -0.034 ** (0.016) -0.027 * (0.016)
Constant 0.594 *** (0.095) 1.126 *** (0.122)
F-statistic 73.25 *** 67.51 ***
Number of observations
 Total 9189 9189
 Left-censored 805 805
 Right-censored 108 108

Variables (C)

Age 0.010 *** (0.003)
Age squared -0.0002 *** (0.00003)
Generation:
 GenX -.428 *** (.052)
 Boomer -.278 *** (.042)
 Silent -0.106 *** (0.031)
Cohort:
 1972-1983
 1960-1971
 1948-1959
 1936-1947
 1924-1935
Time Dummy -0.064 *** (0.005)
In Wealth 0.042 *** (0.002)
Human capital (000)
Homeowner
Defined benefit
 pension
Retired -0.059 *** (0.021)
Poor health -0.070 ** (0.030)
Self-employed 0.110 *** (0.012
Two earners -0.018 (0.014)
Single male -0.006 (0.020)
Single female -0.049 *** (0.017)
Children 0.007 (0.013)
Nonwhite -0.036 ** (0.016)
Constant 0.591 *** (0.094)
F-statistic 82.87 ***
Number of observations
 Total 9189
 Left-censored 805
 Right-censored 108

*, **, *** Significantly different from zero at the 10, 5, and 1%
levels, respectively.

Table 5. Probit Estimates. Dependent Variable: Willing to Take
Financial Risks

 (A)

 Coefficient (Robust Std.
Variables Error) Marginal (a)

Age -0.013 (0.011) -0.005
Age squared -0.0002 * (0.0001) -0.00007
Generation:
 GenX -0.849 *** (0.181) -0.327
 Boomer -0.641 *** (0.136) -0.237
 Silent -0.293 *** (0.095) -0.110
Cohort:
 Birth year
 1972-1983
 1960-1971
 1948-1959
 1936-1947
 1924-1935
Time dummy -0.114 *** (0.016) -0.042
ln Wealth 0.104 *** (0.007) 0.038
Human capital (000s) 0.0001 *** (0.00003) 0.00005
Homeowner 0.095 * (0.050) 0.035
Defined benefit pension 0.139 *** (0.046) 0.051
Retired -0.122 * (0.065) -0.046
Poor health -0.396 *** (0.087) -0.153
Self-employed 0.041 (0.052) 0.015
Two earners -0.044 (0.053) -0.016
Single male 0.144 ** (0.069) 0.052
Single female -0.179 *** (0.056) -0.067
Children -0.141 *** (0.049) -0.052
Nonwhite -0.292 *** (0.052) -0.111
Constant 1.329 *** (0.341)
F-statistic 42.22 ***
Number of observations 9189 9189

 (B)

 Coefficient (Robust Std.
Variables Error) Marginal (a)

Age -0.023 * (0.012) -0.008
Age squared -0.0001 (0.0001) -0.00004
Generation:
 GenX
 Boomer
 Silent
Cohort:
 Birth year
 1972-1983 -0.928 *** (0.232) -0.357
 1960-1971 -0.779 *** (0.187) -0.299
 1948-1959 -0.543 *** (0.153) -0.206
 1936-1947 -0.306 ** (0.126) -0.116
 1924-1935 -0.244 *** (0.091) -0.092
Time dummy -0.111 *** (0.016) -0.041
ln Wealth 0.104 *** (0.007) 0.038
Human capital (000s) 0.0001 *** (0.00003) 0.00005
Homeowner 0.090 * (0.049) 0.033
Defined benefit pension 0.127 *** (0.046) 0.046
Retired -0.123 * (0.066) -0.046
Poor health -0.407 *** (0.086) -0.158
Self-employed 0.040 (0.053) 0.015
Two earners -0.044 (0.53) -0.016
Single male 0.155 ** (0.069) 0.056
Single female -0.170 *** (0.057) -0.064
Children -0.156 *** (0.048) -0.058
Nonwhite -0.286 *** (0.052) -0.108
Constant 1.510 *** (0.367)
F-statistic 38.85
Number of observations 9189 9189

(a) Marginal effects are evaluated at the sample mean for continuous
variables and for discrete changes of dummy variables from 0 to 1.

*, **, *** Significantly different from zero at the 10, 5, and 1%
levels, respectively.
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