Does Cognitive Aging Affect Portfolio Choice? (CMR17)

Does Cognitive Aging Affect Portfolio Choice?

Tae-Young Pak∗ Patryk Babiarz†

March 31, 2017

Abstract

Previous research has documented that cognitive decline is empirically associated

with portfolio reallocation towards riskless assets. While the literature suggests several

mechanisms such as the rising information costs and preference changes, these expla-

nations conflict with the evidence that some domains of cognitive functions (i.e., the

crystalized intelligence) rather improve with age, and individuals are often unaware of

their cognitive decline. This study adds to the literature by revisiting the link between

cognition and portfolio riskiness with a rigorous empirical framework. We argue that

the seasonal variation in mental health (i.e., the seasonal affective disorder) provides

a convenient way of isolating an exogenous variation in cognitive functioning. Our

findings show that the correlations between cognitive abilities and portfolio choice are

generally positive but statistically and quantitatively negligible when the endogeneity

is controlled for with an instrument. We conclude that the causality running from

cognitive aging to portfolio reallocation is not as strong as previously documented.

Keywords: Cognitive aging; Cognitive functioning; Portfolio choice; Stock market

participation; and Seasonal affective disorder

JEL Classification Codes: E2, D8, G1

∗Assistant Professor (corresponding author), Department of Consumer Sciences, University of Al-

abama, Address: 303A Adams Hall, Box 870158, Tuscaloosa, AL 35487, phone: +1-205-348-4068, e-mail:

[email protected].†Assistant Professor, Department of FHCE, University of Georgia, Address: 202 Consumer Re-

search Center (House C), 415 Sanford Dr., Athens, GA 30602, USA, phone: +1-706-542-4138, e-mail:

[email protected].

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1 Introduction

The association between cognitive abilities and financial decisions involving risky invest-

ments has been well documented. Studies have shown that cognitive decline is associated

with a lower propensity to hold stocks and adjustment of savings towards less information-

intensive assets such as bonds (Christelis et al., 2010; Grinblatt et al., 2011; Kezdi and Willis,

2003; McArdle et al., 2009). There are at least two pathways through which cognitive func-

tioning is likely to affect portfolio composition. First, cognitive decline discourages (direct)

stock market participation by increasing information costs. For individuals with declining

cognitive functions, it would be rational to invest through the professionally managed ac-

counts or rebalance their portfolios away from risky assets. Second, the loss of cognitive

abilities could lead to anomalous preferences such as impatience, myopic loss-aversion or

mood swings that distort expectations about risk-return trade-off. Cognitively impaired in-

vestors may view the continued stockholding as less favorable due to a lower willingness to

bear financial risk.

Although such narratives appear plausible, the mechanism through which cognitive de-

cline crowds out stockholding is theoretically ambiguous. Research has shown that cognitive

aging operates jointly with a learning process, implying that older investors often make better

investment choices relative to younger investors due to accumulated knowledge and experi-

ence (Korniotis and Kumar, 2011). According to the psychological literature, the ability to

solve novel problems declines progressively with age, while cognitive functions rooted in gen-

eral knowledge continue to improve throughout adulthood (Horn, 1968; Horn and Cattell,

1967; Christensen, 2001). Moreover, the self-assessment of intelligence (i.e., metacognition)

remains intact or gradually increases with age (Palmer et al., 2014). People generally do not

recognize or deny their weakening mental capability despite the consistent loss of memory

(Finke et al., 2016; Gamble et al., 2014). Those who overestimate their decision-making abil-

ity might not be able to identify the information barriers, and could act upon unwarranted

beliefs to take unwise risk (Jaccard et al., 2005). Consequently, such individuals would stay

invested in the equity market longer than people with the appropriate level of confidence

(Pak and Chatterjee, 2016).

Although cognition-stockholding correlation is inherently multi-faceted, the question of

whether or not cognitive aging affects the riskiness of portfolio has not been answered con-

vincingly. The difficulty of identifying the causal path arises because cognitive abilities vary

with unobserved factors that influence willingness to bear financial risk. For instance, poor

cardiovascular health and onsets of mental health conditions impair cognitive health (Barnes

et al., 2006; Jorm, 2001; Vogels et al., 2007; Wilson et al., 2002), and at the same time lower

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the riskiness of portfolio by increasing background health risks (Edwards, 2008; Fan and

Zhao, 2009). Retirement and pension income also induce a significant change in portfolio

makeup (Viciera, 2001; Vissing-Jorgensen, 2002) while simultaneously influencing cognitive

functions (Bonsang et al., 2012; Ayyagari and Frisvold, 2016). Unless these time-varying

confounders are explicitly controlled for, any correlation between cognition and portfolio

choice can be driven spuriously by unobserved third factors that move along the aging curve.

Additionally, the causality in this association could run from portfolio riskiness to cognitive

health. Richer individuals put more wealth in risky investments, enjoy a higher rate of return

in the long-run, and purchase additional medical services that help them maintain physical

and cognitive functioning (Ettner, 1996; Smith, 1999; Monticone, 2010). Moreover, healthier

individuals may be able to work for a prolonged period (McClellan, 1998; Wu, 2003) and

remain in social ties (Adams et al., 2011), which further delay the cognitive aging process.

This study contributes to the literature by revisiting the relationship between cognitive

functions and portfolio choice with a rigorous empirical framework. To account for the

unobserved heterogeneity and endogeneity of cognition, we estimate individual fixed effects

(FE) models with instrumental variable (IV) strategy. Our identification strategy relies on

the evidence that cognitive abilities exhibit a cyclical seasonal pattern, which peaks in spring

and summer and drops to a lower level in autumn and winter (Meyer et al., 2016; Sinclair et

al., 1994). Clinical studies have shown that limited sunlight exposure disrupts a circadian

cycle (internal body clock) that regulates metabolic processes such as sleeping, waking, and

eating (Germain and Kupfer, 2008). This change has been shown to disturb melatonin and

serotonin secretion, which impairs mental and cognitive health during a season with shorter

daytime (Kent et al., 2009; Partonen and Lonnqvist, 1998).1 Since the timing of interview

is unlikely to correlate with portfolio decisions in other ways than its effect on cognition,

the season-of-survey fixed effects offer a convenient way of isolating exogenous variation in

cognition. Our empirical analyses find the expected seasonal pattern in depressive symptoms

and cognitive functions over the year. The test statistics presented later in the paper also

confirm the exogeneity and excludability of these instruments.

Two clear results stand out from our analyses. First, the FE estimates show that cogni-

tive functions are positively associated with stock ownership and the share of financial wealth

held in risky assets. Consistent with the previous findings, our baseline results show that

households exit the equity market roughly at the same time when their cognitive abilities

decline. Second, the correlation between cognition and portfolio allocation disappears with

the instrumentation of cognitive functions. The estimates are all positive of similar magni-

1Onsets of depressive symptoms are known to elevate the risk of mild cognitive impairment (MCI), andin turn, increase the risk of developing dementia and Alzheimer’s disease (Wilson et al., 2014).

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tude but no longer statistically significant in the IV models. This pattern remains robust to

the measurement of cognition and portfolio riskiness and whether or not the sample includes

proxy responses. Thus, we conclude that causality running from cognitive aging to a less

risky portfolio may not be as strong as first appears.

The rest of the paper is laid out as follows. In section 2, we provide a brief review of the

literature, with a focus on mechanisms linking cognition to portfolio choice, as well as the

counterevidence on the hypothesized relationship. Section 3 describes data, identification

strategies, and estimation methods. Section 4 presents the regression results. Section 5

concludes with a discussion of limitations.

2 Literature Review and Conceptual Framework

Literature suggests that cognitive abilities are related to the riskiness of financial port-

folio. In a study of the U.S. population, Kezdi and Willis (2003) found that risky asset

ownership increases with IQ score, with a disproportionately stronger association at the

higher-end of IQ distribution. McArdle et al. (2009) found that certain domains of cognitive

functions, such as the ability to perform numerical operations or to store and retrieve infor-

mation, are predictive of wealth accumulation and the share of risky assets. Another strand

of studies found that a deficiency in financial literacy - lack of understanding of financial

issues such as interest compounding, inflation, and the time value of money - is a significant

deterrent to stock market participation (van Rooij et al., 2011) and portfolio diversification

(Abreu and Mendes, 2010; von Gaudecker, 2015).

Cognitive functions are likely to affect portfolio choice through several pathways. First,

the costs of information acquisition and processing increase as the cognitive ability declines.

Coupled with growing complexity of financial instruments, it is becoming more challenging

for individual investors to gather all the relevant information and evaluate the profitability

of investment alternatives. The cost of keeping up with fast-changing financial market could

be particularly high for older and retired investors because retirement leads to a decline in

cognitive functions (Bonsang et al., 2012) and lower the social ties that provide investment

information through word-of-mouth (Hong et al., 2004). Christelis et al. (2010) found

that cognitive functioning is positively associated with stock market participation, but not

with the propensity to hold bonds, which are arguably a less information-intensive element

of the financial portfolio. Similarly, Grinblatt et al. (2011) demonstrated that mutual

funds ownership and portfolio diversification increase monotonically with IQ and that this

relationship holds even in the top decile of income distribution - a group for which the cost

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of participation is relatively small. To circumvent possible endogeneity issues, they used

brothers IQ score as an exclusion restriction but found no changes in portfolio composition

attributable to IQ. Calvet et al. (2007) found that financially knowledgeable investors are

not only more likely to participate in the equity market, but also invest in a highly efficient

manner.

Cognitive functions also vary with preferences and behavioral biases. In an experimental

study of German adults, Dohmen et al. (2010) found that cognitively smart respondents were

more likely to take risks in the lottery experiments. A recent study by Bonsang and Dohmen

(2015) reported that cognitive aging alone explains approximately 85% of the increase in risk

aversion at the end of life. Other studies such as Benjamin et al. (2013) and Burks et al.

(2009) also showed a positive association between cognitive functioning and risk tolerance in

the non-elderly sample. Findings on the connection between cognition and time preferences

are somewhat mixed. Studies on non-financial domains linked intelligence to discount rates

of cocaine addicts (Monterosso et al., 2001) or college students (Kirby et al., 2005) but found

no significant associations. In a study based on Chilean sample, Benjamin et al. (2013) found

that a one standard deviation increase in math score was linked to 8% higher engagement

in risk-neutral behaviors and about 10% greater patience involving short-term trade-offs.

Frederick (2005) also provided some evidence of impatience over short-term choices among

the cognitively limited individuals. In Oechssler et al. (2009), certain behavioral biases such

as conjunction fallacy and conservatism were more pronounced for the persons with lower

cognition scores.

Altogether, the evidence from past literature suggests that cognitive aging may crowd

out risky investments by raising information costs and amending preferences. However, such

inference could be simplistic and misleading because neurodegenerative changes may have

differential impacts on the various domains of cognitive functions. Psychologists differentiate

between a crystalized and a fluid form of intelligence. The crystalized intelligence refers to

the ability to use accumulated knowledge and experience, while the fluid intelligence refers

to the capacity to reason logically and solve new problems. Neuroscientists have found

that the crystallized intelligence remains quite stable or improves over the life cycle (Horn

and Cattell, 1967; Christensen, 2001). Intuitively, if knowledge regarding stock investing

grows with experience, the age-related rate of increase in information processing cost would

be lower. Korniotis and Kumar (2011) found that some domains of the investment skill

indeed improve with experience despite a significant decline in cognitive functions. Their

analysis showed that old investors score much less on the cognition test relative to younger

individuals, but display savvy investment practices in a number of domains involving stock

trading and portfolio diversification. It is not clear, however, whether this positive aspect

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of cognitive aging offsets the negative impact of declining fluid intelligence, which could still

yield an adverse effect on the investment decisions.

The age-related increase in overconfidence adds additional complexity to the understand-

ing of the impact of cognitive aging. Several studies recently found that individuals assess-

ment of cognition does not adjust downward even with a consistent drop in actual cognition.

In a study of American retirees, Finke et al. (2016) found a gradual decline in reasoning and

quantitative skills accompanied by a growing confidence in financial capability and literacy.

After reaching the age of 70, more than 25% of confidence in the financial decision-making

ability was not justified by actual financial acumen, and this disparity grew even larger

over time. In a similar vein, Gamble et al. (2014) reported high confidence in managing

own finances and poor understanding in the financial matter. Overconfident and unskilled

individuals are known to underestimate the risks involved in financial transactions while

displaying too much optimism about their ability to pick winning securities (Barber and

Odean, 2001; Puri and Robinson 2007). Individuals who become overconfident due to cog-

nitive aging may not recognize financial risks and allocate large fractions of their savings

to risky investments. A recent study by Pak and Chatterjee (2016) found that individuals

unaware of their cognitive decline are less likely to leave the equity market and hold more

savings in stocks and stock mutual funds. Along with the findings of Korniotis and Kumar

(2011), this result indicates that the direction of cognition effect depends on the relative

sizes of potentially offsetting mechanisms.

3 Methodology

3.1 Data

The data is drawn from 1998 through 2012 waves of the Health and Retirement Study

(HRS). The HRS is a nationally representative longitudinal survey of Americans aged 51 and

older that has been conducted every other year since 1992. The study collects information

on the various aspects of the aging process necessary to understand economic, social, and

health circumstances in late life. The HRS is particularly well suited to our study as cognitive

abilities are measured in a variety of domains including memory, vocabulary, orientation, and

metacognition (Ofstedal et al., 2005).

The sample is limited to the respondents older than 65 years of age and those who

responded to all the questions in the cognitive test module. We further exclude the obser-

vations with illogical reports on financial wealth or missing values on the covariates. Since

our empirical models use the estimation method exploiting within-individual variations, we

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also drop out the subjects who showed up only once during our study period. This leaves

us with an unbalanced panel of 73,381 observations from 15,610 individuals.

3.2 Cognitive Abilities

The cognitive performance battery in the HRS is adapted from the Telephone Inter-

view for Cognitive Status (TICS), a specialized test module developed for telephone survey

(Brandt et al., 1988).2 The cognition tasks are classified broadly into three groups: (a)

memory, (b) mental status, and (c) vocabulary (Herzog and Wallace, 1997). The survey be-

gins with a question about self-assessment of memory. Respondents are asked to rate their

memory by choosing one of the five response categories: excellent, very good, good, fair, or

poor. This response becomes our preferred measure of metacognition (or, perceived intelli-

gence). Next, the interviewer read a list of 10 specific words to respondents and asked them

to recall as many of those words as possible (immediate recall). After responding to other

survey questions for 5 minutes, the subjects were instructed to recall the phrase previously

presented in the immediate recall task (delayed recall). In each of the assessments, inter-

viewers count the number of words remembered correctly and summarize them with scores

ranging from 0 to 10. The responses for the two recall tasks combine for a 20-point episodic

memory score, which represents the ability to retrieve contextual information (McArdle et

al., 2007).

Working memory is assessed by serial 7 task in which respondents subtract 7 sequentially

from 100 up to five times. This yields a 5-point score showing the number of correct sub-

tractions for a total of five trials. Attention and processing speed are measured by counting

backward ten numbers from 20 to 1, which assigns 2 if successful on the first try, 1 if suc-

cessful on the second, and 0 if not successful on either try (Crimmins et al., 2011). Both

working memory and attention/processing speed are predictive of fluid intelligence and de-

cline significantly with age (Conway et al., 2005; Engle et al., 1999; Kyllonen and Christal,

1990; Salthouse and Pink, 2008). Scores from the serial 7 task and counting backward, along

with episodic memory, are combined to form a 27-point score of fluid intelligence (McArdle

et al., 2009; Yu et al., 2009).

Crystallized intelligence is measured by the vocabulary task and object naming task

(Ofstedal et al., 2005). In the vocabulary task, respondents are provided five words from one

of two sets and asked to define each in turns.3 Responses are coded 2 for a correct answer, 1

2Given the phone-based survey environment, the cognitive performance battery excluded non-verbalcognitive functioning measures such as visual and spatial processing, and focused on assessing memory,mental intactness, and premorbid intelligence.

3These two sets include, (a) repair, fabric, domestic, remorse, plagiarize, and (b) conceal, enormous,perimeter, compassion, audacious.

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for partially correct, and 0 for incorrect, yielding a score with a maximum of 10 and minimum

0. In the object naming task, respondents are provided a description of scissors and cactus

and asked to think of the name of the object. Responses are coded 0 for incorrect and 1

for correct, resulting in a score ranging from 0 to 2. Our preferred measure of crystallized

intelligence is a 12-point score adding up vocabulary score and object naming score.

The subsequent task asked month, day, year, and day of the week (date naming) and

the name of current president/vice president of the United States (president/vice-president

naming). These two tasks yield the 4-point and 2-point scores, respectively. We define a

composite mental status score by adding up backward counting from 20, object naming,

date naming, and president/vice-president naming scores (Ofstedal et al., 2005). This 15-

point score represents the extent of mental intactness to perform daily routines and activities

(Ashford et al., 1989). The total cognitive score is defined as the sum of episodic memory (0-

20) and mental status score (0-15), with higher scores indicating better cognitive functioning

(Rodgers et al., 2003). Figure 1 shows plausibly bell-shaped distribution of total cognitive

score, fluid intelligence, and crystallized intelligence.

[Insert Figure 1 about here]

In case the survey could not continue with a primary respondent, the interviews were

conducted with a proxy informant (e.g., a family member). Functional limitations or cog-

nitive impairment could be a likely reason to switch to a proxy interview (Rodgers et al.,

2003). The proxy interview used a different survey instrument that is based on the subjective

assessment of cognitive impairment (Jorm, 1994; Jorm and Jacomb, 1989).4 The Informant

Questionnaire on Cognitive Decline in the Elderly (IQCODE) test asked the proxy respon-

dents 16 questions about recent changes in a primary respondent’s cognitive functioning such

as the ability to remember things, recall questions, run errands, handle financial matters,

and learn new things. The available responses range from 1 (=much improved) to 5 (=much

worse), with a higher score representing lower cognitive capacity relative to the previous

survey. The average score of these tests is called a Jorm score, and the score above 3.38 in-

dicates severe cognitive impairment (Jorm, 1994; Jorm et al., 1996). Using this information,

we define an alternative measure that merges the responses from proxy respondents with

self-reports. Following Ayyagari and Frisvold (2016), our indicator of cognitive impairment

is coded 1 for a total cognitive score between 0 and 8 or a Jorm score greater than 3.38, and

0 otherwise.

4Since the TICS-based cognitive tests were administered only to self-respondents, proxy responses couldnot be used for calculating cognition summary scores, leading to the underrepresentation of severe cognitiveimpairment in the sample.

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3.3 Measures of Portfolio Choice

A key measure of interest is the proportion of financial wealth held in equities, which

divides the amounts held in stocks, stock mutual funds, and investment trusts by financial

net worth (Rosen and Wu, 2004). Given that most of the life-cycle portfolio changes take

place on the extensive margin (Ameriks and Zeldes, 2004), we also utilize a binary indicator

of stock ownership. Financial net worth is defined as the sum of (a) checking, savings, or

money market accounts, (b) CDs, government savings bonds, and T-bills, (c) bonds and bond

funds, (d) stocks, mutual funds, and investment trusts, and (e) other savings, minus short-

term debt. This definition represents the value of financial assets held outside the retirement

account. While the nearly-retired and retirees hold a significant amount of wealth in their

retirement accounts, only the portions that individuals have a direct control and are likely

to be reported with minimum measurement error are considered (Love and Smith, 2010).

The alternative measure of equity share and equity ownership include both category (c) and

(d), given that bonds and bond funds are not entirely free of risk.

3.4 Covariates

Regression models include a set of covariates that explain household portfolio choice.

These include age, marital status, smoking, self-assessed physical health, insurance coverages,

labor force participation, income and total net worth, and S&P 500 index. Time-invariant

factors such as gender, race, and education, are not included as our empirical models exploit

within-individual variations. Age is obtained by subtracting year of birth from survey year,

given a high chance of an error in self-reports among the cognitively impaired. A dummy for

marital status is 1 for married and 0 for other relationships. Smoking is 1 for current smokers

and 0 for former or never smokers. We use smoking status to proxy for time preference and

risk aversion (Finke and Huston, 2013). The self-reported health and insurance coverage

account for the confounding impact of background risk (Edwards, 2008; Fan and Zhao,

2009). The HRS provides detailed information on doctor-diagnosed health problems, but as

in Love and Smith (2010), none of them were significantly associated with portfolio outcomes

in the preliminary analyses. Thus, our models include self-reported health, which is arguably

more predictive of the overall health (Bound, 1989). Insurance ownership is captured by the

binary indicators for health insurance coverage, long-term care insurance, and life insurance.

Total net worth and individual income from pension/annuity and Social Security are also

included to capture the possible income or wealth effect on cognitive functioning or portfolio

choice (Ayyagari and Frisvold, 2016; Mani et al., 2013).5 The monthly S&P 500 index nets

5Total net worth is log-transformed by log(wealth+.01) if wealth ≥ 0 or by −log(−wealth) if wealth < 0.

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out any confounding variation due to the changes in stock market performance.6 Census

region dummies account for any unobserved region-specific sentiments or policy changes

that may have an influence on risky investments.

3.5 Empirical Strategy

We estimate several variants of the following specification using individuals fixed effects

models.

yi,t = α + βci,t +Xi,tγ + νi + τt + εi,t (1)

In this equation, yi,t is individual i’s portfolio outcomes at time t represented by stock

ownership or the fraction of financial net worth held in stocks; ci,t is a measure of overall

cognitive ability, fluid intelligence, or crystallized intelligence; and Xi,t is a covariate matrix.7

The element νi represents individual heterogeneity that will be differenced out, and τt is a

time-specific effect captured by a set of year dummies. The fixed effects model accounts for

individual-specific and time-invariant factors that are unobserved, and that might be corre-

lated with the error term (represented by εi,t). If individual specific effects are uncorrelated

with the regressors, the random effects model yields more efficient estimates than the fixed

effects model. The results of Hausman specification tests based on the baseline estimates

indicate that the differences between the two are significant, and thus the fixed effects model

is preferred.

As discussed above, β does not allow for causal inference if there are omitted variables that

vary with cognitive decline and also with portfolio riskiness. Although the models include

time-varying covariates relevant to testing our hypothesis, there might still be some unob-

served factors left out of the model. More importantly, ci,t can be endogenously determined

within a model, which leads to the biased and inconsistent estimate of β. An appropriate

approach would then be to isolate the variation in ci,t by finding a suitable instrument that

affects portfolio riskiness only indirectly through the changes in cognitive functioning. Our

identification strategy is to exploit a seasonal pattern in cognitive functioning. It has been

shown that individuals suffering from the seasonal affective disorders (SAD) are more prone

to cognitive decline than people whose mood does not vary with the weather (O’Brien et al.,

1993; Partonen and Lonnqvist, 1998). A significant difference in sunlight exposure between

6The monthly S&P 500 index is obtained from the FRED Economic Data of Federal Reserve Bank of St.Louis and merged with the data according to the month-of-survey.

7We estimate linear probability models for modeling stock ownership. The marginal effect estimates fromthe probit models with correlated random effects are similar to the linear probability estimates. Details areavailable upon request.

9

seasons is believed to be a major risk factor for the SAD and cognitive decline in a gloomy

weather (Kent et al., 2009). The SAD sufferers tend to experience a progressive cognitive

decline over the long term, which leaves irreversible damage to the brain and intellectual

ability (Panza et al., 2010; Thomas and O’Brien, 2008; Vinkers et al., 2004).8 These findings

support the use of season-of-survey dummies for identifying the effect of cognition. Our

analyses reveal the expected seasonal patterns, with the intensity of depressive symptoms

being lower and the cognitive scores being higher in spring and early summer (Fig. 2).

[Insert Figure 2 about here]

4 Results

4.1 Descriptive Analysis

Table 1 presents the summary statistics for the full sample and by stock ownership.

Females make up 59% of the sample; the mean age is about 75 years; and 58% of respondents

are married. Stock ownership is more pronounced among males, non-Hispanic Whites, and

better-educated respondents. Married couples are more likely to hold stocks than singles,

and this difference is significant at the 1% level. The ownership of health insurance and

long-term care insurance is observed more frequently among the stock owners. On average,

almost 70.2% of financial net worth is held in assets that carry little or no investment risks

such as checking, savings, and money market accounts (56.8%), and CD, government savings

bonds, and T-bills (13.4%). Stocks, mutual funds, or investment trusts combine for 18.6%

of financial net worth. Bonds and bond funds are the least favored investment vehicle and

comprise only 2.6% of financial net worth. Consistent with the previous studies, all three

measures of cognition vary considerably across stock ownership status. The mean fluid

intelligence score is 15.9, which is 15.2% higher than that of non-stock owners. Crystallized

intelligence is approximately 13.9% greater for stock investors relative to non-investors. The

overall proportion of respondents classified as cognitively impaired is 1.4%, and it is smaller

in a group owning stocks.

[Insert Table 1 about here]

8The clinical evidence also suggests that symptomatic relief from depression is not accompanied by com-plete recovery of cognitive health (see, Hammar and Ardal, 2009; Marvel and Paradiso, 2004).

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4.2 Regression Results

Table 2 presents the results from the OLS regressions for the full sample. The dependent

variables are the proportion of financial net worth held in stocks (models in the first three

columns) and the stock ownership dummy (the next three columns). Regression models

include a full set of covariates including the S&P 500 index, year dummies, and the Census

region fixed effects. In analyses not shown, we estimated a model including both age and

age squared to capture nonlinear age effects. The coefficients on age squared are negative

but insignificant at the 10% level, perhaps because of the selection of sample above age 65.

Thus, our models include only a linear age term. Across all six models, intraclass correlation

is consistently large, and Hausman specification tests reject the null hypothesis that the

random effects (RE) specification is more appropriate. The estimates on the covariates

carry the expected signs. The riskiness of portfolio is greater for the married and wealthy,

and smaller for the older respondents. As in Love and Smith (2010), the effect of self-reported

health is positive but insignificant at the 10% level. Health insurance ownership is positively

associated with equity ownership, showing a possible substitution between background health

risk and financial risk.

The OLS coefficient estimates on cognition suggest that conditional on time-varying

covariates, the riskiness of portfolio decreases with cognitive decline. Column (1) and (2)

show that a 10 percentage point decline in overall cognitive functioning and fluid intelligence

are associated with 0.19, and 0.21 percentage point decreases in stock share, respectively.

Evaluated at the sample mean, these represent approximately 1% and 1.1% drop in stock

share, which is small but certainly not negligible. When the transition across extensive

margin is modeled, the probability of holding stocks is estimated to decrease by 0.37 and

0.36 percentage point, respectively, with a 10 percentage point decline in overall cognitive

functioning and fluid intelligence. In all models, the coefficient estimates on crystallized

intelligence are not statistically significant, indicating that portfolio choice is associated

primarily with problem-solving abilities rather than acquired knowledge.


If better-educated individuals face lower stock market entry barrier, the increase in infor-

mation costs due to cognitive aging ought to be greater in a better-educated group. To test

this hypothesis, we estimate the FE models separately in subsamples defined by educational

attainment. Panel A in Table 3 shows results for the college-educated sample of respondents

(including completion of a 2-year college) and panel B shows results for the sample of respon-

dents with no prior exposure to college education. The estimates support our hypothesis. In

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panel A, all three cognitive measures are positively associated with equity ownership at the

5% level. The impact on the intensive margin of asset allocation is positive but no longer

significant at the 10% level. Results in the bottom panel generally show no significant as-

sociation between cognitive functioning and portfolio choice. These uneducated individuals

should have already faced high participation costs, which attenuated the cost-raising impact

of cognitive aging.


The first three columns in Table 4 present the first-stage regression results for the IV

models. The estimates in columns (1) and (2) support the evidence from clinical literature

that cognitive functions are higher in spring and summer.9 Relative to the sample mean in

winter, the total cognitive score is 0.45% and 0.24% greater in spring and summer, respec-

tively. The improvement in fluid intelligence is even greater, with 0.71% and 0.44% increases

in spring and summer, respectively. The estimates in column (3) suggest that crystallized

intelligence does not exhibit a similar seasonal pattern. Rather surprisingly, respondents do

not self-report better memory when their cognitive functions improve. This finding is broadly

in line with Finke et al. (2016), who documented a stable metacognition coupled with declin-

ing cognitive abilities. Column (5) and (6) present the results from regressions of portfolio

outcomes on seasonal dummies. The coefficients on season fixed effects are not significantly

different from zero in both models. Therefore, it is plausible to assume that season-of-survey

affects portfolio choice only indirectly through the changes in cognitive functions.


Table 5 presents estimates from the second-stage regressions for risky asset ownership.

In addition to the estimates from models of stockholding reported in columns (1) and (2),

columns (3) and (4) report the results from equivalent estimations for bond ownership. The

models in panel A use season dummies as instrumental variables. The test statistics indi-

cate that the first-stage equations are neither underidentified nor weakly identified, and the

instruments are plausibly uncorrelated with the error term. Instrumenting the endogenous

cognition variables inflates the coefficient estimates and their standard errors, rendering these

estimates statistically insignificant. Similarly, there is no evidence of a significant impact of

cognitive functioning on bond ownership, possibly because only a small fraction of respon-

dents hold bonds. Overall, the associations between cognitive functioning and risky asset

9Cognitive abilities are significantly better from February through June relative to December. Whenmonth-of-survey dummies are used as instruments, the null hypotheses could be over-rejected with a smallerdifference across the estimates. Thus, our preferred instruments are seasonal dummies that better identifyfirst-stage regressions.

12

ownership disappear after the endogeneity of cognition is accounted for. In panel B of Table

5, we enhance our identification strategy by adding the Center for Epidemiological Studies

Depression (CES-D) score as an additional exclusion restriction. As argued in Bogan and

Fertig (2012), mental health may affect portfolio choice indirectly through changing cogni-

tive abilities or risk aversion. While the pathway through risk aversion was often suggested

in the literature, our analyses show no correlation between depression and risk aversion even

in univariate tests. Moreover, depression appears to have no influence on portfolio choice

other than through its effect on cognitive ability, supporting its potential use as an instru-

ment.10 Both the Kleibergen-Paap rank LM-statistics and Cragg-Donald Wald F statistics

are greater in panel B than in panel A, while the instruments remain uncorrelated with the

error term. However, although this IV specification appears stronger, the estimates on the

total cognitive score and fluid intelligence remain insignificant at the 10% level.


In Table 6, we provide the second-stage regression results for the share of stocks in

respondents financial net worth (columns 1 and 2) and financial net worth that additionally

includes the amounts held in IRA and Keogh accounts (columns 3 and 4). The expanded

measure of financial net worth is intended to tests the robustness of findings considering that

some individuals could include equities in retirement accounts when reporting the value of

stocks. No estimates of the impact of cognition are significantly different from zero in panel

A or in panel B that relies on the enhanced identification strategy. We implement a further

improvement in panel C by using heteroskedasticity-based instruments of Lewbel (2012).

This method exploits heteroskedasticity in the first-stage regression for identification. If Z

is a vector of exogenous variables in X and ǫ is the error term in the first-stage equation, β̂

can be consistently estimated using (Z− Z̄)ǫ̂ as an identifying information. In this exclusion

restriction, ǫ̂ is the estimated residual from a model for cognition, and Z̄ is the mean of

Z. Identification requires the errors in a model of the mismeasured regressor on the other

regressors be heteroskedastic, which is the case in our models for cognitions. As season-of-

survey dummies are plausibly uncorrelated with portfolio choice, we include both external

and generated instruments in the first-stage regressions. Including the generated instruments

indeed improves the identification but leaves the point estimates and test results quite similar.

Overall, we find convincing evidence that the cognitive decline has only a negligible impact

on portfolio choice.


10These results are not reported for brevity but available upon request.

13

Finally, we examine whether the lack of impact of cognitive aging on stockholding is an

artifact of the underrepresentation of cognitively impaired respondents (Table 7). As dis-

cussed above, of particular interest is whether or not the coefficient on cognitive impairment

dummy is robust to the inclusion of proxy responses. Relative to the continuous measures of

cognition, the within-variation in cognitive impairment status is small, suggesting the pooled

OLS as a more appropriate estimation method. In column (1) and (4), we report results

obtained from a sample of respondents that excludes proxy interviews. In column (2) and

(5), we employ the alternative measure of cognitive impairment, one that includes the proxy

reports on seven Jorm symptoms. Finally, the models in column (3) and (6) rest only on

proxy responses, given that cognitively dysfunctional respondents may differ substantially

from main respondents in unobserved ways. The first two models of each panel show that

risky asset ownership is smaller in a group with severe cognitive impairment. However, the

absolute value of this association becomes weaker in column (2) and (5) when the sample is

expanded to include proxy responses. Jorm score also appears to be uncorrelated with risky

asset ownership, suggesting that the extent of cognitive impairment does not matter with

stock investment decision among the severely impaired. This could be due to the shift of

financial decision-making responsibility within a household (Hsu and Willis, 2013) or a lack

of cognitive resources to adjust portfolio allocation. In either case, these findings support the

narrative that the underrepresentation of severe cognitive impairment does not drive away

the significance of correlations in the IV models.


5 Conclusion

This study revisited the association between cognitive abilities and the riskiness of house-

hold portfolio composition. The results from fixed effects models suggest that the depletion

of cognitive functions is associated with late-life portfolio reallocation towards less risky as-

sets - an outcome both predicted by underlying theory and documented by prior literature.

To identify the direction of causality of the relationship between cognition and portfolio

choice, we employed an instrumental variable approach isolating the exogenous variation

in cognition triggered the by seasonal affective disorder. Results from the IV models sug-

gest that the correlations of interest are much smaller and generally negligible in terms of

both the quantitative and statistical significance. This finding was robust to the alternative

identification strategies using depression score and heteroskedasticity-based instruments as

additional exclusion restrictions. Furthermore, we established that the findings of no-effect

14

are not driven by the underrepresentation of subjects with cognitive impairment. We con-

clude that the mental health-related cognitive decline does not affect equity ownership or

the riskiness of household portfolio allocations.

It is important to note that the associations between cognitive resources and portfolio

riskiness, although lacking statistical significance, are consistently positive in the estimated

models. It appears that a small amount of variations in portfolio reallocations could be

influenced by the cognitive decline, although most of the causal impact is offset by the

feedback effect of stockholding or the lack of awareness of cognitive aging. Considering the

dominant impact of life-cycle factors at the end of life, we conclude that the causality running

from cognitive decline to portfolio reallocation towards safer financial assets is not as strong

as documented in the extant literature.

While this study adds to the literature on cognitive aging and financial decisions by

advancing methodological rigor, the following limitations should be acknowledged. First,

the measure of equity ownership in this study does not differentiate between cases of direct

stock market participation and investments professionally-managed accounts. As argued

in Christelis et al. (2010), stocks owned through mutual funds or retirement accounts are

arguably less information-intensive, and hence cognitively impaired investors can lower the

risk by reallocating savings from stocks to mutual funds. Unavailability of data on mutual

fund holdings prevented us from investigating this aspect of cognitive aging. Second, the

data does not allow us to account for numeracy and financial literacy, both of which could

determine a sizeable portion of variation in equity ownership. While numeracy and financial

literacy are included in the special modules of the HRS, such questions are not asked regularly

in the survey. In general, financial literacy is believed to be a specialized cognitive skill that

is more relevant to explaining investment behaviors, while cognitive decline is indicative

of memory-related diseases and general economic well-being (Lusardi and Mitchell, 2014).

Thus, stronger inferences could be drawn by tracking financial literacy and its association

with late-life changes in equity ownership.

15

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21

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Figure 1: Histograms of Cognition Scores

Figure 2: Seasonal Pattern in Cognitive Functions and Depressive Symptoms

22

Table 1: Descriptive Statistics

Hold NoStocks

Hold Stocks Full Sample

Portfolio composition (%)Cash equivalents / financial wealth 56.8Low-risk assets / financial wealth 13.4Bonds / financial wealth 2.6Stocks / financial wealth 18.6Hold stock 32.9Hold stock or bond 35.0

Cognitive functionsTotal cognitive score (0-35) 21.1 23.4 21.9Fluid intelligence (0-27) 13.8 15.9 14.5Crystallized intelligence (0-12) 7.2 8.2 7.6Cognitively impaired (0,1) 0.019 0.006 0.014

Socioeconomic covariatesAge of respondent 75.2 75.2 75.2Female (0,1) 0.61 0.55 0.59Non-Hispanic Black (0,1) 0.11 0.02 0.08Hispanic (0,1) 0.30 0.20 0.29Some college or college graduate (0,1) 0.31 0.58 0.40Married (0,1) 0.53 0.68 0.58SR health: good or better (0,1) 0.67 0.82 0.72Health insurance (0,1) 0.42 0.58 0.47Long-term care insurance (0,1) 0.10 0.23 0.14Life insurance (0,1) 0.60 0.65 0.62Employed (0,1) 0.18 0.21 0.19Pension income $6,851 $8,745 $7,475Social Security income $10,027 $10,993 $10,345Total net worth§ $141,000 $638,091 $245,733

Observations 50,767 22,614 73,381

Notes: Figures are calculated using the individual and household weights provided in theHRS. Cash equivalents include checking, savings, and money market accounts, and low-riskassets include CD, government savings bonds, and T-bills. Bonds include bonds and bondfunds. Stocks represent stocks, mutual funds, and investment trusts. Financial wealth isdefined as the sum of cash equivalents, liquid savings, bonds and bond funds, stocks, andall other savings. Total net worth is defined as the sum of financial and housing wealthless short-term debts, mortgages, and home loans. Total cognitive score is based on theimmediate/delayed recall, serial 7, backwards counting, object naming, date naming, andpresident/vice-president naming. Fluid intelligence is composed of immediate/delayed recall,serial 7, and backwards counting test. Crystallized intelligence sums vocabulary and objectnaming. Cognitive impairment is 1 for the subjects with a total cognitive score less than orequal to 8, and 0 for the rest. All dollar figures are adjusted to 2012 dollars using the ConsumerPrice Index for all urban consumers (CPI-U). § denotes the median value.

23

Table 2: Models for Portfolio Choice

Response: Stocks / FW [0,1] Hold stock (0,1)(1) (2) (3) (4) (5) (6)

Total cognitive score 0.0019* 0.0037***(0.0010) (0.0014)

Fluid intelligence 0.0021** 0.0036***(0.0009) (0.0012)

Crystallized intelligence 0.0006 0.0011(0.0010) (0.0014)

Age -0.0034 -0.0034 -0.0118* -0.0005 -0.0005 -0.0026(0.0049) (0.0049) (0.0071) (0.0066) (0.0066) (0.0097)

Married 0.0062 0.0062 0.0010 0.0150** 0.0151** 0.0134(0.0051) (0.0051) (0.0065) (0.0066) (0.0066) (0.0084)

Smoking -0.0091 -0.0091 -0.0039 -0.0112 -0.0113 -0.0143(0.0061) (0.0061) (0.0087) (0.0087) (0.0087) (0.0117)

SR health: fair 0.0019 0.0019 -0.0005 -0.0009 -0.0009 -0.0027(0.0037) (0.0037) (0.0051) (0.0051) (0.0051) (0.0070)

SR health: good 0.0045 0.0045 0.0037 0.0003 0.0004 0.0021(0.0042) (0.0042) (0.0056) (0.0058) (0.0058) (0.0077)

SR health: very good 0.0085* 0.0085* 0.0065 0.0065 0.0064 0.0064(0.0046) (0.0046) (0.0062) (0.0063) (0.0063) (0.0085)

SR health: excellent 0.0077 0.0075 -0.0050 0.0072 0.0072 -0.0049(0.0059) (0.0059) (0.0079) (0.0081) (0.0081) (0.0109)

Health insurance 0.0044 0.0044 0.0072* 0.0077** 0.0077** 0.0083*(0.0028) (0.0028) (0.0037) (0.0037) (0.0037) (0.0050)

LTC insurance -0.0030 -0.0030 -0.0072 0.0068 0.0068 0.0011(0.0051) (0.0051) (0.0067) (0.0069) (0.0069) (0.0089)

Life insurance 0.0037 0.0037 0.0013 0.0138*** 0.0139*** 0.0146**(0.0032) (0.0032) (0.0044) (0.0044) (0.0044) (0.0060)

Employed -0.0017 -0.0017 -0.0076 -0.0035 -0.0035 -0.0108(0.0040) (0.0040) (0.0052) (0.0055) (0.0055) (0.0073)

Log(pension income) 0.0003 0.0003 0.0003 0.0007** 0.0007** 0.0011**(0.0002) (0.0002) (0.0003) (0.0003) (0.0003) (0.0004)

Log(SS income) -0.0001 -0.0001 -0.0001 -0.0000 -0.0000 0.0001(0.0003) (0.0003) (0.0005) (0.0004) (0.0004) (0.0006)

Log(total net worth) 0.0028*** 0.0028*** 0.0029*** 0.0041*** 0.0041*** 0.0044***(0.0002) (0.0002) (0.0003) (0.0003) (0.0003) (0.0004)

Observations 73,381 73,381 45,524 73,381 73,381 45,524Rho 0.59 0.59 0.63 0.64 0.64 0.65Hausman test (p-value) 0.00 0.00 0.00 0.00 0.00 0.00

Notes: Regression models include S&P 500 index, year fixed effects, and Census region fixed effects.Cognition scores are re-scaled on a 0-10 scale. ‘Rho’ is the variance share of unobserved heterogeneityfrom a corresponding random effects model. Hausman test tests the null hypothesis that the differencesin coefficients of fixed and random effects model are not systematic. Robust standard errors arein parentheses. Significance levels are indicated by *, **, and *** for 10, 5, and 1 percent level,respectively.

24

Table 3: Models for Portfolio Choice

Response: Stocks / FW [0,1] Hold stock (0,1)(1) (2) (3) (4) (5) (6)

Panel A: Subjects with college degreeTotal cognitive score 0.0030 0.0088***

(0.0021) (0.0027)Fluid intelligence 0.0022 0.0068***

(0.0017) (0.0022)Crystallized intelligence 0.0028 0.0063**

(0.0021) (0.0028)Observations 27,627 27,627 16,767 27,627 27,627 16,767

Panel B: Subjects without college degreeTotal cognitive score 0.0013 0.0009

(0.0011) (0.0016)Fluid intelligence 0.0020** 0.0015

(0.0009) (0.0013)Crystallized intelligence -0.0005 -0.0016

(0.0011) (0.0016)Observations 45,754 45,754 28,757 45,754 45,754 28,757

Notes: Regression models control for all covariates including S&P 500 index, year fixed effects,and Census region fixed effects. Cognition scores are re-scaled on a 0-10 scale. Robust standarderrors are in parentheses. Significance levels are indicated by *, **, and *** for 10, 5, and 1 percentlevel, respectively.

Table 4: Seasonal Pattern in Cognitive Abilities: First-Stage Regressions

Response:Total cognitive

scoreFluid

intelligenceCrystallizedintelligence

Self-ratedmemory

Hold Stock Stocks / FA

(1) (2) (3) (4) (5) (6)

Spring 0.094*** 0.099*** -0.050** -0.0025 -0.0016 -0.0006(0.016) (0.019) (0.024) (0.0063) (0.0051) (0.0037)

Summer 0.051*** 0.062*** -0.035 0.0044 -0.0058 0.0000(0.016) (0.018) (0.024) (0.0061) (0.0050) (0.0037)

Autumn -0.007 0.000 0.010 0.0005 -0.0053 -0.0034(0.017) (0.019) (0.025) (0.0064) (0.0054) (0.0039)

Observations 73,381 73,381 73,357 73,381 73,381 73,381

Notes: Regression models control for all covariates including S&P 500 index, year fixed effects, and Censusregion fixed effects. The omitted base category of season fixed effects is winter, which include November, De-cember, and January. Spring and summer includes February through April and May through July, respectively.Autumn includes August, September and October. Robust standard errors are in parentheses. Significancelevels are indicated by *, **, and *** for 10, 5, and 1 percent level, respectively.

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Table 5: Second-Stage Regressions for Stock Ownership

Response: Hold stock (0,1) Hold stock or bond (0,1)(1) (2) (3) (4)

Panel A: IVs include season dummiesTotal cognitive score 0.020 0.018

(0.035) (0.036)Fluid intelligence 0.015 0.013

(0.035) (0.036)Underidentificationa 80.5 58.7 80.5 58.7Overidentification (p-value)b 0.29 0.27 0.21 0.20Weak instrumentsc 28.4 20.6 28.4 20.6Observations 73,381 73,381 73,381 73,381

Panel B: IVs include season dummies and CES-D scoreTotal cognitive score 0.014 0.024



Notes: Regression models control for all covariates including S&P 500 index, year fixed effects,and Census region fixed effects. Cognition scores are re-scaled on a 0-10 scale. aKleibergen-Paaprank LM-statistic tests the null hypothesis of underidentification. bHansen J statistic tests thenull hypothesis that the instruments are uncorrelated with the error term and correctly excludedfrom the estimated equation. cCragg-Donald Wald F statistic tests the null hypothesis of weakinstruments. Robust standard errors are in parentheses. Significance levels are indicated by *, **,and *** for 10, 5, and 1 percent level, respectively.

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Table 6: Second-Stage Regressions for the Share of Stocks

Response: Stocks / FW [0,1] Stocks / FW including retirement accts. [0,1](1) (2) (3) (4)

Panel A: IVs include season dummiesTotal cognitive score 0.021 0.011



Panel B: IVs include season dummies and CES-D scoreTotal cognitive score 0.021 0.003



Panel C: IVs include season dummies and generated instrumentsTotal cognitive score 0.009 0.007



Notes: Regression models control for all covariates including S&P 500 index, year fixed effects, and Census regionfixed effects. Cognition scores are re-scaled on a 0-10 scale. aKleibergen-Paap rank LM-statistic tests the nullhypothesis of underidentification. bHansen J statistic tests the null hypothesis that the instruments are uncorrelatedwith the error term and correctly excluded from the estimated equation. cCragg-Donald Wald F statistic tests thenull hypothesis of weak instruments. Robust standard errors are in parentheses. Significance levels are indicatedby *, **, and *** for 10, 5, and 1 percent level, respectively.

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Table 7: Robustness Checks with Proxy Responses

Response: Hold stock (0,1) Hold stock or bond (0,1)(1) (2) (3) (4) (5) (6)

Cognitively impaired -0.026*** -0.026***(0.007) (0.007)

Cognitively impaired (w/ proxy) -0.016*** -0.017***(0.006) (0.006)

Jorm score 0.0004 -0.0025(0.0077) (0.0079)

Observations 88,703 94,333 5,633 88,703 94,333 5,633

Notes: Regression models control for all covariates including S&P 500 index, year fixed effects, and Censusregion fixed effects. Robust standard errors are in parentheses. Significance levels are indicated by *, **,and *** for 10, 5, and 1 percent level, respectively.

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Appendix A

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Documents

Does Cognitive Aging Affect Portfolio Choice? (CMR17)