Mortality Beliefs and
Household Finance Puzzles
Rawley Z. Heimer, Kristian Ove R. Myrseth, and Raphael S. Schoenle∗
Abstract
Subjective mortality beliefs influence individual discount rates, affecting savings rates pre- and
post-retirement. New survey evidence indicates that the salience of cohort-specific causes-ofdeath causes younger individuals to overestimate mortality, and elderly individuals to overestimate survival probabilities. These distorted mortality beliefs correlate with savings behavior,
even controlling for cognitive and socioeconomic factors. We embed an estimated survival
belief function into a canonical life-cycle model. Relative to a benchmark model using actuarial transition probabilities, the young under-save (31% lower retirement savings), and retirees
draw down their assets more slowly (14% lower retirement consumption), reconciling contradictory savings puzzles at opposite ends of the life-cycle.
∗
Heimer is at the Federal Reserve Bank of Cleveland, Myrseth is at University of St Andrews, and Schoenle is at
Brandeis University. Heimer can be contacted at: [email protected], Myrseth at [email protected]
and Schoenle at [email protected]. The authors are grateful for the research assistance of Timothy Stehulak,
David Love for generously providing us with his Matlab programs, and the assistance of Diane Mogren and Kathy
Popovich for helping obtain the survey data. They thank Joseph Briggs, Stephen Cecchetti, Tony Cookson, Simon
Gilchrist, Daniel Hamermesh, Zoran Ivkovich, Paula Lopes-Cocco, Alex Michaelides, Olivia S. Mitchell, John Mondragon, Stefan Nagel, Jim Poterba, Andrei Shleifer, Klaus Schmidt, David Skeie, and participants at Brandeis, Fed Cleveland, Colorado - Boulder, Drexel, IIES, Sveriges Riksbank, Cesifo Area Conference in Behavioral Economics,
Cleveland Fed Household Finance Conference, IDC-Herzliya 13th Annual Conference in Financial Economics, London Business School - European Winter Finance Conference, NBER Summer Institute, Netspar International Pension
Conference, the Northern Finance Association, the Quadrant Asset Management Conference, and the Society for Economic Dynamics Annual Meeting for helpful comments and suggestions. The views in this article do not necessarily
reflect those of the Federal Reserve Bank of Cleveland or the Board of Governors.
Individuals hold distorted views of low-probability events and, for most of one’s life, few events
are less likely to occur than one’s death. Yet, visions of our own mortality can have important
economic consequences. For example, sharks are responsible for an average of just one U.S. death
per year (cows kill around 20 people on average), but according to a headline in the August 29,
2015 edition of the L.A. Times, “La Jolla beach closed after shark sighting.” And during Super
Bowl 47, Prudential Financial Inc. aired a commercial in which 400 individuals were asked to
indicate the age of the oldest person they know. The results indicated an average close to 100years-old, prompting viewers to believe we are living longer and potential customers to contact
Prudential today.
These examples illustrate how salient risk factors influence economic decision-making via
our beliefs. Motivated by recent efforts to use survey elicited beliefs to understand discrepancies
between classical economic models and real outcomes,1 we measure subjective mortality beliefs
and consider their effect on inter-temporal household decision-making and life-cycle implications.
We find that these elicited beliefs bring us closer to jointly understanding why some young people
undersave towards retirement (Skinner (2007)) and retirees do not fully draw down their assets
(Poterba et al. (2011)). Our reason for studying this mechanism is that subjective mortality beliefs
have direct bearing on what is among the equations most studied by the discipline: the intertemporal trade-off between consumption today and the discounted present value of future consumption
streams,
∗
Vt∗ (·) = max{u(Ct ) + β st+1 Et [Vt+1
(·)]}.
Ct
The discount factor (β ) and the utility function’s curvature (ρ) have been studied countless times.
However, despite no indication that subjective mortality beliefs (st+1 ) are any less meaningful, they
1 These
efforts have been applied to the recent housing boom (Soo (2015); Bricker et al. (2015)), historical asset
prices (Greenwood and Shleifer (2014)), consumption choices Christelis et al. (2015), or the difficulty implementing
monetary policy (Coibion et al. (2015)).
1
have received much less attention by the literature. The relative dearth of research is all the more
striking considering that practitioners widely use these beliefs to advertise financial products and
to develop long-run financial plans (e.g. Figure 1).
Using a new survey of nearly 5,000 respondents, administered by a professional survey panel
provider, we find that the distribution of subjective mortality beliefs is heavy-tailed in comparison
to actuarial tables provided by the Social Security Administration (SSA). That is, young individuals believe their chances of survival beyond the next few years are lower than that predicted by
actuarial data (as much as 7 ppt underestimation), while respondents beyond the age of retirement believe there is a reasonable chance of surviving to extreme old age (as much as 10 ppt
overestimation of surviving at least an additional ten years). These findings are robust across key
socioeconomic groups, and to experimental treatments that provide upfront some respondents with
longevity statistics and actuarial probabilities.
We provide evidence that salient, cohort-specific stereotypes of cause-of-death (Bordalo et al.
(2012, 2014)) constitute a unifying cognitive mechanism underlying the formation of distorted
mortality beliefs. Young people associate death with near-term, rare events (e.g. plane crashes or
animal aggression, such as shark attacks), the probability of which they overweight. As people
age, these rare events take a cognitive backseat to thoughts of health and the normal course of
aging. Because the average person who survives to old age has comparatively better health than
cohort members who have previously died, it is possible that long-term survival is perceived to be
more likely than it is on average.
Several empirical tests emphasize the importance of salient events for the formation of survival beliefs. We relate the weight respondents place on the number of natural disaster deaths to the
actual random number of deaths by natural disaster in respondents’ ZIP code, and we find that the
weight placed on natural disasters strongly correlates with the actual likelihood of experiencing a
disaster. The number of natural disaster deaths in the respondents’ vicinity does not predict any of
the other risk factors. Similarly, survival optimism is negatively correlated with the imaginability
2
of the cause-of-death. More pessimistic respondents believe that a greater number of people die in
plane crashes annually, but their mortality beliefs are uncorrelated with beliefs about the number
struck by lightning. These results further our confidence in the applicability of the survey elicited
mortality beliefs and our proposed mechanism.
These survival belief distortions matter for key aspects of financial decision-making. Using
off-the-shelf questions from commonly cited household surveys (e.g. the Survey of Consumer Finances), large survival belief errors are associated with a greater propensity to not save or even
to rely excessively on credit cards on a month-to-month basis. Similarly, increased (decreased)
expectation errors are associated with an increase (decrease) in the likelihood of using one’s savings more quickly, even after accounting for the respondent’s age. These same expectation errors
are associated with a reduced tendency to describe oneself as having investment experience. Our
findings hold after accounting for income, demographic, and educational differences, and with individuals randomly assigned to treatments presenting information on actuarial survival rates. To
gauge the economic significance, the magnitude of the relationship between survival beliefs and
savings behavior is at least as large as that between savings behavior and financial literacy or intended bequests.
We use our survey-elicited survival beliefs to estimate a survival beliefs function. This simple, age-dependent survival function incorporates the changes in survival optimism over the lifecycle. According to the estimated function, individuals go from being cumulatively pessimistic
about survival to cumulatively optimistic a few years prior to retirement age.
Next, we embed our survival beliefs function into the simplest form of a dynamic life-cycle
model with pre-cautionary savings, the solution to which advances our understanding of seemingly
disconnected empirical regularities. First, some argue that there is under-saving for retirement
that cannot fully be explained by income heterogeneity (Skinner (2007)). Our elicited subjective
beliefs suggest that individuals are too pessimistic about short-term survival rates, causing them
to undersave by about 31 percent relative to our benchmark model calibrated to actuarial data.
3
Second, a distinct body of research finds that retirees do not fully draw down their assets, even after
accounting for different bequest motives (Poterba et al. (2011)). Owing to retirees’ overestimation
of long-run survival rates, individuals consume 14 percent less during retirement. This mechanism
is independent from any income differences that may exist upon reaching retirement.
This paper’s primary modeling contribution is to expand the predictive power of the canonical life-cycle framework simply by feeding it new data on subjective survival beliefs. As such,
we follow a number of important approaches to explain empirical regularities in the literature on
consumption and savings decisions. To understand pre-retirement savings, research has considered
precautionary savings (Lusardi (1998); Gourinchas and Parker (2002)), financial literacy (Hubener
et al. (2016)), self-control problems (O’Donoghue and Rabin (1999)), and hyperbolic discounting
(Laibson (1997)). However, the existing empirical evidence suggests that there is room for further explanation of household balance sheets (Zinman (2014)). To better understand why many
retirees do not consume all of their assets during retirement, some have studied bequest motives
(Bernheim et al. (1985); Hurd (1989)) and public care aversion (Ameriks et al. (2011)), as well as
their interaction with wealth inequality (De Nardi and Yang (2015)) and health (Palumbo (1999);
Lockwood (2014)). Relative to this literature, an advantage of our approach is that we can jointly
describe savings behavior at opposite ends of the life-cycle that could otherwise be interpreted as
contradictory. Furthermore, our estimated survival belief function can easily be applied to these
and other quantitative modeling efforts.
Our paper also contributes to a literature on probability weighting. It is well-documented
that individuals place too much weight on low-likelihood events, a literature spurred in part by
Lichtenstein et al. (1979)’s findings that people overestimate the frequency of rare causes of death.
Probability weighting has been applied to seminal theories such as Cumulative Prospect Theory
(Tversky and Kahneman (1992)), which in turn has been shown to have important consequences
for asset prices (Barberis and Huang (2008)) and portfolio choice (Polkovnichenko (2005)). Related to these studies is a literature on tail events and their contribution to personal investing, but
4
only recently have scholars considered the ex ante beliefs of these rare events (Gao and Song
(2015); Goetzmann et al. (2016)). Perhaps the most striking market-based evidence that probability overweighting contributes to biased survival beliefs, and that these beliefs meaningfully
affect economic decisions, hails from research showing that many individuals purchase too much
insurance against unlikely events (Sydnor (2010); Bhargava et al. (2015)).
Finally, we contribute to an emergent literature on the measurement and implications of subjective expectations (Manski (2004)). Similar to our work, a nascent literature tries to understand
how individuals form their beliefs, but these studies consider personal experiences (Kuchler and
Zafar (2015); Malmendier and Nagel (2016)) or attention (Carroll (2003); Gabaix (2014)). There
is a longstanding literature measuring mortality beliefs (Hamermesh (1985)), as well as mixed evidence from household interview surveys on the economic outcomes affected by mortality beliefs
(Puri and Robinson (2007); Post and Hanewald (2013); Inkmann et al. (2011); Elder (2013); Bisetti
(2015)). A related literature using life-cycle models includes calibrations to subjective mortality
beliefs (Gan et al. (2005); van der Klaauw and Wolpin (2008); Wu et al. (2015)), longevity risk
(Cocco and Gomes (2012)), or survival ambiguity (Groneck et al. (2013)). However these studies
are mostly focused on the later years of life. Our contribution is to connect these areas of research by emphasizing that survival optimism flips over the life-cycle, and to furnish evidence for
a cognitive mechanism: the salience of cause-of-death. By validating a novel, deep mechanism, to
which any alternative interpretation of these elicited beliefs would have to be correlated, our paper
addresses a crucial gap in the literature, with broad implications for research involving discount
factors over the life-cycle.
This paper is organized as follows. Section 1 provides survey evidence on subjective mortality beliefs. Section 2 shows that these beliefs relate to household financial behavior. Section 3
describes our life-cycle model. Section 4 presents the solution to the model and describes its findings on consumption, savings, and investment over the life-cycle. Concluding thoughts are offered
in Section 5.
5
1
1.1
Mortality Beliefs Over the Life-cycle
Survey Description and Sample Characteristics
We contracted Qualtrics Panels to provide us with a survey of 5000 respondents, screened according to national residency and age. All respondents were required to be U.S. residents and have
English be their primary language. Respondents were drawn from the following six ages: 28, 38,
48, 58, 68, and 78, with the distribution roughly matching the relative proportion of the population
at each age. The survey specifically targets these ages to avoid respondents who are about to or
who have recently reached milestone ages, such as 40-years-old. We further requested an even
gender distribution sample-wide. The survey also includes additional filters to eliminate respondents who write-in gibberish for at least one response or who complete the survey in less (more)
than five (thirty) minutes.
The survey collects demographic information on the respondents (Table 1). The typical
survey respondent looks similar to those in the median U.S. household. A little over half are female,
68 percent have children, and just over half are married. Similar to U.S. population statistics, 29
percent have a bachelor’s degree, and around 13 percent have an advanced degree, although the
fraction of respondents without high school degrees appears underrepresented. Furthermore, the
income distribution is reasonable, with the largest group of respondents reporting between 50,000
and 100,000 dollars in household income.
Table 2 presents summary statistics on other variables of interest. The survey starts by asking
respondents to indicate their survival likelihood beliefs. Respondents are asked the likelihood
that they live at least an additional y = {1, 2, 5, 10} years. We randomly assigned respondents
to one of these four survival horizons, while one-fifth of respondents were asked all four horizons
sequentially. To elicit survival beliefs, the survey uses a slider response mode, ranging from zero to
one hundred, on which respondents indicate their answer by pointing and clicking their mouse. The
slider response mode helps respondents visualize a probability scale. This visualization is thought
6
to reduce focal answers—in particular, heuristic responses at 50-percent—relative to open-ended
questions (Firschhoff and Bruin (1999)).2
To provide a comparison to more widely-used surveys, respondents are asked on a separate
page to indicate their expected longevity (the age to which they will survive), a question also
included in the Survey of Consumer Finances (SCF). On the same pages that respondents report
their survival likelihood and expected longevity, respectively, they are asked to indicate their degree
of confidence in their answers. These confidence questions presumably prompt respondents to
carefully consider their answers about mortality beliefs. The survey’s main questions on mortality
beliefs ask about the chances of survival, rather than the chances of dying, because the latter could
inflate beliefs about the likelihood of death (Payne et al. (2013)).
Following the elicitation of mortality beliefs, the survey gauges the cognitive factors that
respondents use to construct their beliefs, as well as their personal assessment of the frequency of
rare deaths. First, we ask respondents to indicate the weight they place on certain causes-of-death
when assessing their own chances of survival. The causes-of-death can roughly be categorized as
relating either to natural causes, such as aging and health related, or unnatural events, such as car
and plane crashes. We also ask respondents to estimate the number of annual deaths by plane crash
and the number of people struck by lightning.
The survey elicits savings rates in a few different ways, by asking about the share of income
saved, when respondents plan to use their savings, and alternatively, the respondent’s investing
experience. The set of potential responses to these questions are divided into broad categories
to lessen the scope for recall bias. For example, the survey asks for the approximate share of
monthly income saved (e.g., “I save around 10% of my monthly income”). The remainder of the
survey, including the aforementioned savings questions, is designed to resemble more commonly
2 Delavande and Rohwedder (2008) propose a visual “bins-and-balls” elicitation procedure for subjective probability distributions, shown to reduce the proportion of “unusable” responses relative to that obtained from an open-ended
response mode. However, the bins-and-balls procedure, by which respondents move illustrations of balls into bins,
would appear less applicable to our context, where respondents must be given opportunity to indicate precise estimates
of any probability, including very small probabilities and probabilities tending towards 100 percent.
7
referenced household surveys, such as the SCF and the Health and Retirement Survey. Other
questions gauge risk tolerance, income expectations, and personal health assessments. The survey
also includes off-the-shelf questions on financial and numerical literacy (Lusardi and Mitchell
(2011); Cokely et al. (2012)).
1.2
Mortality Beliefs Over the Life cycle
Our analysis is motivated by Figure 2, which shows that, as respondents get older, they go from
underestimating to overestimating their subjective longevity. Specifically, both men and women
underestimate their expected longevity when they are part of the 58-years-old cohort or younger.
For example, a 28-year-old female is projected to live to 86-years-old, but the average 28-yearold female respondent expects she will live to be 84. For both genders, 68-year-olds are better
calibrated to their expected longevity, while 78-year-olds overestimate how old they will live.
Moreover, the flip from underestimation to overestimation of longevity as respondents get older is
corroborated by in-person interview survey data. According to the 2010 wave of the SCF, women
(men) underestimate their longevity until they are in their 70s (50s) (Appendix Figure A.1).
To connect mortality beliefs to our subsequent efforts to model the life-cycle, we also measure subjective year-to-year transition rates. Figure 3 plots the average respondent’s subjective
survival beliefs by current age and survival horizon. The figure shows respondents’ forecasts 1-, 2, 5-, and 10-year ahead, across the complete set of ages: 28, 38, 48, 58, 68, and 78. For illustrative
purposes, we include a fitted line through the ten-year forecast errors.
Similar to our findings on longevity beliefs, we also find that subjective transition rates
change over the life-cycle. On average, younger (older) individuals substantially underestimate
(overestimate) their survival chances relative to actuarial statistics from the Social Security administration. For example, the average respondent who is 38 years old underestimates the probability
of surviving an additional year by as many as ten percentage points. Only when respondents turn
8
68 years old are their subjective survival beliefs equal to the actuarial statistics, although their
10-year ahead forecast are overly optimistic by about five percentage points.
1.2.1
Robustness
The finding is robust across demographic characteristics and to different experimental treatments
(Appendix, Table A.1). Among our more convincing tests, we gave half of all respondents precise
information upfront on the actuarial likelihood of survival and expected longevity for a male or
female around their age. There are no strong differences in subjective mortality beliefs between
respondents who did and did not receive this information. Additionally, the quadratic shape of
these survival belief errors over the life-cycle holds after accounting for respondent’s numerical
literacy and treatments for asking about all four survival horizons, as well as cigarette smoking
and personal health assessments. Thus, there are many reasons to be confident that, as the average
respondent gets older, survival beliefs indeed flip from underestimation to overestimation.
Yet another reason to have confidence in the result is that previous literature has hinted at
life-cycle survival belief changes across a variety of settings and sample populations, even though
few data sets provide as comprehensive a look at survival beliefs over the life-cycle. An argument
could be made that our online survey is not of the same quality as the interview surveys frequently
employed throughout the household finance literature. However, a similar inflection in survival
belief errors across ages is found in the University of Michigan’s Health and Retirement Survey
(Groneck et al. (2013)). Another possibility is that the average person has difficulty working with
probabilities. However, Jarnebrant and Myrseth (2013) survey German engineering students at a
technical university and find that even this mathematically capable sample underestimates survival
probabilities at short horizons and overestimates it at long horizons. Furthermore, our results could
be unique to U.S. respondents, but the survival belief findings are similar in other countries (Wu
et al. (2015)).
9
Lastly, confidence in our survey results comes not only from the fact that the inclusion of
these beliefs into a life-cycle model aligns better with actual savings and consumption behavior at
opposite ends of the life-cycle than using actuarial data. We also describe a mechanism that causes
distorted survival beliefs to change systematically over the life-cycle. In the following section, we
discuss evidence of such a mechanism: salience of cause-of-death.
1.3
How do Mortality Beliefs Form?
Our analysis shows that mortality beliefs change systematically over the life-cycle, and it is consistent with recent studies demonstrating that survival beliefs are constructed at the moment of
judgment, based on the information immediately accessible (Payne et al. (2013)). When individuals think about death, they appear to draw on an availability heuristic (Tversky and Kahneman
(1973, 1974)) and follow certain stereotypes about the cause-of-death at different ages over the
life-cycle. Young people are thought to die because of unintended injury or other unnatural causes.
Unnatural causes-of-death are thought to occur more often than they do, because individuals overweight salient unlikely events. Meanwhile, failing health causes death among the elderly. Older
respondents may be optimistic about their survival when examples of individuals who have reached
very old age easily come to mind. Because ‘natural deaths’ tend to be less imaginable than dramatic deaths, caused by rare events, individuals under-weight the likelihood of occurrence of the
former.3
We provide evidence that rare events play a disproportionate role in the formation of survival
beliefs. Table 3, Panel A, presents summary statistics on the weights placed on different causesof-death, on near-continuous slider scales, ranging from one to one hundred (we do not require the
sum of the weights across risk factors to sum to 100). Respondents place roughly half as much
weight on unnatural causes, such as physical violence, as they do on medical conditions or ‘the
3 It
is also possible that older respondents are displaying motivated beliefs (Bénabou (2015)), although this explanation would not account for the pattern obtained among younger respondents.
10
normal course of aging’. However, according to the Centers for Disease Control and Prevention,
unnatural causes account for approximately a twentieth of all deaths.
To test how different individual attributes contribute to these risk factors, Table 3, Panel B
presents estimates of the following regression model:
5
risk. f actor.weighti = β0 + β1 · survival.optimismi + ∑ β2l · age.categoryi + Γ · Xi + εi .
(1)
l=0
The dependent variable, risk. f actor.weight, is equal to the weight that respondent i places on the
corresponding risk factor, divided by the sum of the weights that i places on all nine risk factors.
The independent variable, survival.optimism, equals Eit [surv(t + l)] − Prit [surv (t + l)], where t is
respondent i’s age and l = {1, 2, 5, 10}, and survival probabilities are from the SSA. We normalize
survival.optimism so that a one unit increase equals a standard deviation increase. The regression
uses a set of indicator variables for the respondent’s age, age.category = {38, 48, 58, 68, 78}, while
setting 28-years-old as the omitted category. The matrix X includes other control variables, such as
gender and the assignment to different experimental treatments. Standard errors, clustered by age,
are calculated using the Wild cluster-bootstrap percentile-t procedure from Cameron et al. (2008).
The relative weighting on these different risk factors correlates with differences in survival
beliefs. The coefficient on survival.optimism is positive and statistically significant for natural
aging (coe f = 3.46, s.e. = 0.10) and diet (coe f = 1.11, s.e. = 0.18). However, it is not statistically
different from zero when the dependent variable is the weight on medical factors. Meanwhile, the
coefficient estimate is negative and statistically significant for all six of the unnatural causes-ofdeath, with the estimate ranging from -0.30 to -0.93. To convey the potential economic significance
of these results (column 9), the average normalized weight on ‘freak events’ is roughly 7, and a
one standard deviation increase in survival optimism reduces the weight to 6, roughly a 13 percent
reduction.
11
Likewise, respondent age plays a prominent and distinct role in determining the relative
weighting. The relative weight placed on natural, medical, and lifestyle causes-of-death is monotonically increasing in respondent age. For example, the share of the weight on the ‘natural course
of aging’ increases by 4.8 (or 20 percent of the average share) when comparing 78-year-olds to
28-year-olds. Similarly, the share of the weight on all six of the unnatural causes-of-death decreases monotonically in respondent age. Taken together, these findings suggest that mortality
beliefs change over the life-cycle, and how respondents think about death does, as well.
Several additional results in Table 3, Panel B, lend credence to the elicited beliefs about
different causes-of-death. First, the differences in risk factor weighting across genders corresponds
to well-known differences between men and women. On average, men in our survey place less
weight on diet (column 3, coe f = −0.75, s.e. = 0.16) and medical conditions (column 2, coe f =
−0.42, s.e. = 0.40), a result that accords with findings in the medical profession – that men are
20 percent more likely than women to dismiss results from medical screenings on cholesterol and
heart health (Agency for Healthcare Research and Quality). However, men place a greater weight
on risky lifestyles (column 8, coe f = 1.10, s.e. = 0.17). On the other hand, they place less weight
on traffic accidents (column 4, coe f = −0.59, s.e. = 0.17), consistent with men attributing lower
risks to driving and paying higher car insurance premiums as a result.
Secondly, the relative weight placed on natural disasters corresponds to the actual likelihood
of experiencing a disaster, strengthening our confidence in the survey results.4 We include as
an independent variable the logarithm of one plus the number of natural disaster deaths in the
respondent’s ZIP code. The number of deaths by natural disaster is taken from the Spatial Hazard
Events and Losses Database (SHELDUS) and is the sum over the years 2001 to 2010.5 The
regression estimate implies that a one percent increase in the number of deaths by natural disaster
4 Other research considers the effect of gun violence on mortality beliefs and finds results similar to ours (Balasubramaniam (2016)).
5 The SHELDUS data is provided at the county level. We map counties to ZIP codes using the 2010 concordance
from the Missouri Census Data Center.
12
in the area is associated with 0.93 (s.e. = 0.18) more weight placed on natural disasters, when
respondents develop their mortality beliefs (column 6). Moreover, the number of natural disaster
deaths in the respondent’s vicinity does not predict any of the other eight risk factors.
We provide additional evidence that imaginability, or salience, plays a critical role in developing survival beliefs: we test the relation between the respondent’s survival beliefs and the
respondent’s estimates of the number of people to die annually, either in plane crashes or by lightning strike. Even though the odds of falling victim to these two unnatural deaths are not very
different, plane crashes are presumably more easily visualized, and awareness of the event is even
reinforced through media coverage.
To test the relation between survival beliefs and imaginability, Table 4 presents estimates of
the following Poisson regression model:
5
log (E (#deaths|Xi )) = β0 + β1 · survival.optimismi + ∑ β2l · age.categoryi + Γ · Xi + εi .
(2)
l=0
The dependent variable equals respondents’ beliefs about either the number of Americans to die
in plane crashes (columns 1 and 2) or the number struck by lightning (columns 3 and 4).6 We use
a Poisson regression because the dependent variable is truncated at zero, and we calculate robust
standard errors that allow for correlated residuals by respondent age.
In support of our hypothesis, survival optimism is negatively correlated with beliefs about
the number of people to die in plane crashes, but does not relate to beliefs about death by lightning
strikes. In columns 1 and 2, the coefficient estimate on survival.optimism is about equal to -0.093
and statistically significant at the one percent level. This implies that a one standard deviation
increase in subjective survival likelihood is associated with a difference in the logs of expected
counts of number of deaths that decreases by about nine percent. In contrast, the relation between
6 The
right tail of these variables are Winsorized at 2.5 percent.
13
survival.optimism and subjective assessments of the number of people struck by lightning is not
statistically different from zero (columns 3 and 4).
2
Do Mortality Beliefs Affect Household Finances?
Before studying the aggregate implications of subjective mortality beliefs, we provide evidence
that these beliefs correlate with household balance sheets in ways that are consistent with lifecycle theory. Our evidence comes from estimates of the following ordered logit model:
y∗i = β1k · survival.optimismi + Γ · Xi + εi
(3)
where y∗i is the unobserved dependent variable for individual i, and we observe the response
yi =




0







1

..


.







k
i f y∗i ≤ µ1
i f µ1 < y∗i ≤ µ2
i f µk < y∗i
over k categories. The coefficient β1k captures the ordered log-odds estimate of moving up a
category of yi for a one standard deviation increase in survival.optimism. We estimate this model
for three different dependent variables, each of which gives us a sense of personal savings rates.
The first measure is the fraction of monthly income saved, ranging from “needing to rely on credit
cards” to “at least 50 percent of income”. The second measures asks when respondents plan
to use their savings. To add further robustness, because respondents may experience different
income shocks at difference times, thereby adding noise to individual estimates of savings rates, we
measure respondents’ accumulated financial knowledge by asking about their experience investing.
14
The relationship between mortality beliefs and savings is potentially sensitive to other life-cycle
and demographic factors, so the matrix Xi controls for many relevant personal characteristics,
including age, income, education, and marital status, as well as personal preferences, and abilities,
such as risk-tolerance and numerical literacy. We estimate the model with robust standard errors
clustered by respondent age.
Table 5 presents estimates of equation 3. Column 1 estimates the effect of survival optimism
on savings rates, while including a large set of control variables. To offer a comparison to another
important determinate of personal finances, Column 2 adds to the right-hand side an indicator
variable for the respondent’s financial literacy. The regression in Column 3 adds the respondent’s
income and education, in order to give a sense of how much of the relationship between survival
beliefs and savings is brought about by differences in economic circumstances. Columns 4 through
6 are analogous to 1 through 3, except the independent variable of interest is longevity.optimism,
the difference between the respondent’s subjective longevity beliefs and expected lifespan according to the SSA. These regressions suggest robustness to different ways of measuring subjective
beliefs.
Across all measures, greater survival optimism correlates with higher savings rates. The
regressions in Panel A use the share of monthly income saved as a dependent variable. In column
1, the coefficient on survival.optimism, β1k , equals 0.19 and is statistically significant at the one
percent level. The coefficient estimate implies that a one standard deviation increase in survival
optimism is associated with a 19 percent increase in the ordered log-odds of moving to a higher
savings category. In column 2, the coefficient estimate on survival.optimism is not much changed,
and the coefficient on the financially literate indicator variable equals 0.13 (s.e. = 0.037). These
estimates suggest that the effect of survival optimism on savings rates is at least as large as that
of financial literacy. After controlling for income and education in column 3, the estimate of β1k
equals 0.14 (s.e. = 0.033), suggesting that most of the effect of survival beliefs on savings goes
above and beyond any individual differences in economic circumstances. Our alternative measure
15
of subjective beliefs, longevity.optimism, yields similar findings across the three specifications
(columns 4 through 6).
The results are similar when we examine survival beliefs and savings draw-down (Panel
B). The coefficient on survival.optimism is between 0.20 and 0.23 across the three specifications
and statistically significant at the one percent error level (columns 1 - 3). This implies that a
one standard deviation increase in survival optimism is associated with a 20 percent increase in
the log odds of delaying the use of savings (e.g. from 6 - 10 years to at least 10 years from
today). Similarly, the coefficient on longevity.optimism is around 0.09 and statistically significant
significant at the ten percent level across columns 4 through 6. Lastly, more optimistic survival
beliefs even correlate positively with self-identified investing experience (Panel C).
To better illustrate the economic significance of the relation between survival optimism and
savings rates, Figure 4 presents fitted estimates of a multinomial logit model, analogous to equation
3. Moving from two standard deviations below to two standard deviations above the mean survival
optimism reduces the respondents’ likelihood of spending more than they earn from about 13 to
5 percent (Panel A). The likelihood of spending all of their monthly income falls from 40 to 24
percent. Saving around ten percent increases from 33 to 50 percent, and saving around twenty-five
percent increases from 11 to 17 percent. Likewise, for the same increase in survival optimism,
respondents’ likelihood of using their savings any time now decreases from 30 to 13 percent. The
likelihood of using their savings in two to five years decreases from 35 to 23 percent, and the
likelihood of using their savings in six to ten years increases from 13 to 17 percent. The likelihood
of using savings at least ten years from now increases from 22 to 44 percent (Panel B).
Retirees may benefit from leaving bequests, offering an alternative explanation for why many
do not fully draw down their savings. Table 6 tests the relative contribution of bequests versus
survival beliefs by estimating ordered logit estimates of equation 3, in which the dependent variable
is the rate at which respondents draw down their savings. Specifically, these new tests include an
additional independent variable, expected.bequests, equal to the chances from 0 to 100 that the
16
respondent will leave an inheritance, normalized so that a one standard deviation increase equals
a one unit increase. Furthermore, we focus these tests on the sample of respondents near and
beyond retirement (58, 68, and 78-year-olds). Columns 1 and 4 include the sample of respondents
with children, columns 2 and 5 those without children, and columns 3 and 6 pool these samples.
The variable of interest is survival.optimism in columns 1 through 3, and longevity.optimism in
columns 4 through 6.
Survival beliefs are at least as important as bequest motives in determining the rate at which
retirees draw down their savings. Across all specifications, the expected likelihood of leaving inheritances correlates positively with delayed use of one’s savings (coefficient estimates equal to
between 0.24 and 0.25 for the pooled sample), and the relationship is stronger for respondents
with children (coefficient estimates equal to 0.26 for those with children and between 0.19 and
0.23 for those without). Bolstering our confidence that mortality beliefs have a distinct effect on
savings rates, the coefficients on our measures of mortality optimism are positive in all specifications and statistically significant at the five percent error level in five of six regressions. Considering estimates from the pooled samples, in column 3, the coefficients on survival.optimism
and expected.bequests equal 0.18 and 0.25. In column 6, the coefficients on longevity.optimism
and expected.bequests equal 0.35 and 0.24. The similarly sized coefficients suggest that mortality
beliefs and bequest motives make similar contributions to savings rates. A final notable feature
of Table 6 is that the expected likelihood of delaying the use of personal savings declines in respondent age, confirming that the dependent variable serves as a reasonable measure of savings
drawn-down during retirement.
3
Modeling the Life Cycle and Subjective Beliefs
This section presents our modeling framework, a canonical dynamic life-cycle model. We highlight in this framework how mortality beliefs impact the maximization problem as they enter the
17
effective discount rate: while the first component of the effective discount rate is given by the
constant rate of time preference, the second component is a function of subjective transition probabilities. This connects the model directly to our empirical analysis, where we measure survival
transition probabilities. The next section shows the dramatic effect that calibration to subjective
transition probabilities can have for consumption, savings, and portfolio choice.
3.1
Model Setup
Our framework is based on Love (2013). Agents live in discrete time, where t = 0, 1, 2, 3, ...Tretire , ..., T
, and Tretire denotes the date of retirement. Agents maximize their expected discounted stream of
utility by choosing current period consumption, as well as what share of income to allocate either
to a risky or risk-free asset. Recursively, their problem can be written as follows:
∗
Vt∗ (Xt , Pt ) = max{u(Ct ) + β st+1|t Et [Vt+1
(Xt+1 , Pt+1 )] + ...
Ct ,φt
...β (1 − st+1|t )Et [Bt+1 (Rt+1 (Xt −Ct) )]} (4)
where Ct denotes consumption in period t, and φt is the share of wealth allocated to the risky asset.
Pt is permanent income, Xt is cash on hand, and a bequest motive is given by Bt (Xt ). Cash on
hand evolves as Xt = Rt (Xt−1 − Ct−1 ) + Yt , where the gross rate of return on the portfolio is the
weighted return of the risky and the risk free asset, Rt = φt Rtr + (1 − φt )R f . Our primary focus is on
β , the rate of time preference and st+1|t , the subjective survival probability that individuals attach
to transitioning to period t + 1, conditional on having reached current age t.
Following Carroll (2011), the process for income Yt is given by permanent income Pt−1 , an
adjustment for the age-earnings profile Gt , a shock Nt following a log-normal distribution, and a
18
transitory shock Θt . Thus, income evolves as follows,
Yt = Pt−1 Gt Nt Θt
(5)
and permanent income transitions according to,
Pt = Pt−1 Gt Nt .
(6)
We parameterize the utility function by choosing u(C) = C1−ρ /(1 − ρ), and the bequest function
by choosing B(X) = b(X/b)(1−ρ) /(1 − ρ). The curvature of the utility function is ρ. We use the
method of endogenous grid-points, described by Carroll (2011) and Love (2013), to numerically
solve the consumer’s problem.
We emphasize that subjective beliefs play an important role in this framework. Individuals make their consumption and portfolio choices today using their subjective beliefs about their
likelihood of transitioning to the next period. These beliefs enter the maximization problem multiplicatively, through the effective period discount rate, that is, through β st+1 (and additionally,
β (1 − st+1 ) when the agent has a bequest motive).
3.2
Calibration
To show the effect of mortality beliefs on life-cycle decision-making, we compare the solution to
the life-cycle model when agents make decisions based on actuarial probabilities versus our elicited
survival beliefs. Doing so involves the comparison of two calibrations of the model’s survival
probabilities, st+1|t . The first calibration draws on actuarial transition rates obtained from the 2007
Social Security Administration Period Life Tables. These transition rates give the likelihood of
surviving an additional year, based on population statistics, conditional on surviving to a given
age.
19
The second calibration of st+1|t uses our survey-elicited survival beliefs. We estimate the
following survival probability function st+1|t :
st+1|t = γ0 + γ1t + γ2t 2
(7)
where t denotes the current age in years. To capture the convexity of survival beliefs over the lifecycle, we fit st+1|t to a quadratic approximation to the true underlying survival function, St (∆t) =
e−
R t+∆t
t
λ (z)dz .7
According to OLS estimates of equation 7, γ0 equals 0.933, γ1 equals 0.149, and γ2
equals -0.00432 (Table 7).
To obtain these estimates of the agent’s subjective survival function, we use our survey’s
1, 2, 5, and 10-year elicited survival beliefs. We start by winsorizing the bottom one percent of
survey responses, to soften the influence of outliers (with an upper-bound of 100 percent survival,
there is no need to winsorize the upper tail of data). For the 2, 5, and 10-year survival beliefs, we
use a geometric mean to transform these responses into annual, condition transition probabilities.
Finally, we normalize the data for age t by subtracting 28 years, the age of the youngest cohort in
our survey.
Figure 5, illustrates the effect of st+1|t on the agent’s discount rate over the life-cycle. The
figure plots the cumulative probability – based on our estimates of st+1|t – of surviving to target age
T =95. For females, a 28-year-old survives to T with 11.0 percent probability according to actuarial
data, but believes this probability is 1.81 percent according to st+1|t . Her survival pessimism
switches to optimism at age 65. For example, when she is 75-years-old she believes she has a
24.0 percent chance of reaching 95, even though actuarial data predicts she has a 14.7 percent
chance. Similarly, males are cumulatively pessimistic until they reach 65 years, and optimistic
thereafter.
7 The
AIC criterion rejects higher order specifications of our survival function approximations.
20
Although we use the estimated survival beliefs of the average individual to calibrate our
baseline life-cycle model, we estimate equation 7 for different segments of the population to assess
the heterogeneity in these beliefs. The associated parameter estimates are presented in Table A.2, in
the Appendix. These subjective survival functions segment the population by gender and income,
as well as differences in educational attainment. Notably, all of the estimates of equation 7 are
downwards-sloping parabolas, with peaks in the mid-50s.
The other parameters we use to calibrate the model reflect standard values chosen by the
life-cycle literature (Table 7). We set the rate of time preference β equal to 0.98, the risk-free rate
equal to 2 percent, the excess return to 4 percent, and the standard deviation of the risky asset to
18 percent. The excess return is somewhat lower than that found by Campbell and Viceira (2002),
which is needed so that households do not end up at a corner solution of investing 100 percent into
the risky asset. Having a risk aversion parameter as high as 5 helps the model obtain an interior
solution. We refer readers to Love (2013) for justification of these parameter choices.
Following Love (2013) and Carroll and Samwick (1997), we use 1970 - 2007 PSID data to
calibrate the agent’s income process. While many potentially interesting aspects to the life cycle
arise from family composition and marital status (e.g. Love (2010); Hubener et al. (2016)), our
baseline model is calibrated to the life cycle income of the average U.S. person who lives in a
married household without dependents. The appendix describes how we construct the income
process for the average individual, as well as for other demographic groups. Further, we allow for
a non-zero correlation between permanent income and excess returns during the working life, but
set the correlation to zero during retirement.
4
Life-cycle Model with Mortality Beliefs, Results
Introducing subjective beliefs into a conventional life-cycle model with precautionary savings has
a dramatic effect on household behavior. Prior to retirement, individuals consume more and save
21
less relative to individuals who make decisions based on actuarial statistics. Following retirement,
individuals consume their savings less quickly when they act according to their subjective mortality
beliefs. This result holds even after allowing for similar levels of accumulated wealth at retirement.
Third, heterogeneity in beliefs can exacerbate inequality in outcomes, as we show for heterogeneity
in educational attainment.
4.1
Model Results During Working Life
During their working life, individuals who act on their subjective survival beliefs consume more
than predicted by the benchmark specification based on actuarial probabilities (the top left panel
of Figure 6). The following discusses these results for our main calibration for an average married
U.S. person without dependents, while Section 4.3 examines heterogeneity in more detail. The
average person consumes approximately $644, or 2 percent, more of their income per year prior
to retirement (Table 8). The difference corresponds to a consumption of 34.5 percent of cash-onhand versus 24.4 percent in the benchmark case. As a result of higher annual consumption, the
representative individual has approximately a third less saved upon retirement, $219,921, than in
the benchmark case using actuarial rates, $319,688.
Highlighting the importance of subjective mortality beliefs, the strongest effect on consumption and savings occurs during segments of the life-cycle when there are larger discrepancies between these beliefs and actuarial statistics. Sorting results by age, the largest underestimation of
survival probabilities occurs between ages 28 and 40. Correspondingly, the effect of subjective
beliefs on consumption is most pronounced early in the agent’s working life. Between ages 28
and 40, the average person with subjective beliefs consumes 90.7 percent of their income versus
82.4 percent under actuarial beliefs, or $2122 more annually. Between ages 40 and 50, the effect of subjective beliefs is less pronounced: the average person consumes 90.1 percent of their
22
income, versus 86.8 percent, or $1209 more. Starting at age 55 and continuing until retirement,
consumption under actuarial beliefs exceeds consumption under subjective beliefs.
Owing to the higher rate of consumption pre-retirement, individuals have less income to
save and thus have fewer accumulated assets upon retirement. The pre-retirement savings rate
under subjective beliefs is 2 percent compared to 3.9 percent under the actuarial benchmark. The
difference is especially large early in the accumulation phase: for ages up to 40, the agent has an
8.3 percent lower savings rate. Between age 40 and 50, over-consumption corresponds to a 3.3
percent lower savings rate. As a result of these savings rates, the agent with subjective beliefs
has $219,921 dollars accumulated upon retirement, whereas the agent using actuarial statistics has
$319,688 dollars.
Subjective mortality beliefs also influence portfolio allocations through their effect on lifecycle wealth accumulation. Under subjective beliefs, 89.2 percent of pre-retirement savings go into
the risky asset, but only 80.9 percent under actuarial beliefs. Approaching retirement, the share of
savings in the risky asset falls under both calibrations, but falls to comparable levels approximately
only 6 years later under subjective beliefs. For example, it reaches less than 90 percent at age 50
under subjective beliefs, but at age 44 under actuarial beliefs.
4.2
Model Results During Retirement
Subjective mortality beliefs also affect consumption and savings decisions during retirement. Starting in the mid-fifties, and continuing throughout retirement, individuals consume less compared
to the benchmark calibrated model. During retirement, the average person consumes $31,077 a
year under subjective beliefs, but $36,109 under actuarial beliefs. This difference in consumption
is due, in part, to the lower level of wealth accumulated during the working life, and to optimistic
survival beliefs during old age, as discussed further below.
23
Importantly, subjective mortality beliefs cause retirees to run down their assets at a slower
pace, consistent with empirical evidence (Poterba et al. (2011)). On average, a retiree with actuarial
beliefs dis-saves $15,848 a year, but only $10,627 if he holds subjective beliefs (the bottom left
panel of Figure 6). The slope on the right from the peak of wealth accumulation is steeper under
actuarial than under subjective beliefs, but practically linear in both cases. At the same time, the
lower level of funds under subjective beliefs leads retirees to hold 82 percent of their assets in
stocks. Retirees only hold 70 percent of their assets in stocks under actuarial beliefs.
Our life-cycle model calibrated with survey-elicited survival beliefs also produces an improved description of consumption behavior around the age of retirement. Household surveys
indicate approximately a 35 percent reduction in consumption following retirement according to
Bernheim et al. (2001) and Aguiar and Hurst (2005).8 Yet, previous attempts to model the complete life-cycle often generate smooth consumption before and immediately after retirement (e.g.
Love (2010); Cocco and Gomes (2012)). In the benchmark version of our life-cycle model, consumption is smooth around retirement, increases by 0.3 percent annually, and does not peak until
age 72. On the other hand, our model with subjective mortality beliefs produces peak consumption
at the age of retirement, 64, followed by a sharp drop in the rate of consumption. Consumption
falls by 0.6 percent per year in the five years that follow retirement.
Moreover, the slower pace of dis-savings is caused by the mortality beliefs of the old, an
effect that goes above and beyond the savings decisions made by the agent at a younger age. We
separate the effect of old-age survival optimism from the consumer’s past savings decisions by
giving both agents exactly the same amount of assets – 300,000 dollars, approximately equal to
the average savings of the agent who uses actuarial statistics – at retirement age 65. We then
compare the decisions made post-retirement, either under subjective or actuarial transition probabilities. Because solving the life-cycle model requires backward induction, we let both agents
plan as though they will live to be T = T + s (we set T + s = 119) and have agents die at age
8 The
drop in post-work life consumption is often attributed to increased home production.
24
T . This modification allows the model solution to have differences in terminal wealth and we can
compare financial decisions in the run-up to the agent’s “accidental” demise. We find that subjective transition probabilities still generate a pattern of slow dis-saving and under-consumption at the
beginning of retirement, relative to a benchmark of actuarial transition probabilities (Figure 7).
4.3
Effects of Subjective Beliefs for Inequality in Outcomes
There is much variation in survival beliefs across individuals, and this variation exacerbates inequality in household outcomes. We focus our analysis on differences in respondent educations,
because educational attainment is a natural jumping-off point for different lifetime income paths.
There are large differences in outcomes across educational groups (Table A.3 summarizes
our findings and Figure A.2 illustrates the paths of consumption, savings and assets over the lifecycle). Pre-retirement, college graduates consume $32,237 under subjective versus $32,661 under
actuarial beliefs, high-school graduates $25,340 versus $25,783, and the less-than-high-school
educated consume $24,488 versus $25,806. Those with a college degree save the most of their
annual income, on average 4.15 percent, or $1,236, under subjective and 6.33 percent, or $1,823,
under actuarial beliefs. Those with no more than a high-school degree save less of their income
(0.75 percent, or $235, under subjective and 2.88 percent, or $752, under actuarial beliefs, average
annually), while those with less than a high-school degree save the least (on average -3.45 percent,
or -$872, under subjective and 1.73 percent, or $482, under actuarial beliefs, average annually).
These different savings trajectories caused by subjective survival beliefs better align with
actual retirement savings estimates across different educational groups. Most interestingly, when
using actuarial statistics, the college educated enter retirement with $405,899, and the less-thanhigh-school educated have $281,587, a difference of around 45 percent. Under subjective beliefs,
the college educated save $312,774 and the less-than-high-school educated save more than five
times less, $55,338. The disparity better accords with findings, such as those in Poterba et al.
25
(2011), that many households have no financial savings at retirement, whereas those at the top of
the distribution have accumulated substantial wealth. For example, households in the bottom 20
percent of the distribution have less than $1,000 in financial wealth at retirement, whereas the top
ten percent has several hundred thousand, a figure that grows once other retirement benefits are
included.
4.4
Robustness
Our results are robust to a number of alternative parameterizations. The over-consumption of the
young increases and wealth accumulation falls when β is increased (Figure A.3), implying an
interaction between the discount factor and survival beliefs. Furthermore, when the coefficient of
relative risk-aversion is changed from our preferred parametrization (ρ = 5), the model produces
additional over-consumption for both increases and decreases in ρ (Figure A.4). These differences
arise from changes in how individuals allocate their savings between the risky and risk-less asset.
Our quantitative findings are also robust to allowing agents to have a bequest motive. When
agents have a bequest motive, they gain utility from giving to subsequent generations. Consequently, they save more during their working life and run down assets more slowly at the beginning
of retirement, which could undo our finding that there is over-consumption prior to retirement.
We show that mortality beliefs generate large over-consumption even when agents have a
bequest motive. Appendix Figure A.5 presents the life-cycle results under subjective beliefs, and
compares the model solution when agents have a bequest motive to when they do not.9 Bequest
motives decrease consumption by about nine percent during the first ten years. Agents maintain
a higher level of cash-on-hand during retirement when they have a bequest motive, which leads
to about two percent lower levels of consumption. However, even these differences are not large
9 Because
the bequest motive and mortality beliefs are non-separable (β (1 − st+1|t )Et [Bt+1 (Rt+1 (Xt − Ct) )]), we
calibrate the bequest motive by minimizing the sum of squared deviations from cash-on-hand when agents have no
bequest motive and objective survival beliefs. This yields a bequest parameter equal to 2.94, which is slightly higher
than the value often chosen by previous literature, 2.5.
26
enough to diminish our findings. Relative to the baseline calibration to objective mortality beliefs,
agents consume far more pre-retirement and far less post-retirement when they have subjective
beliefs, regardless of whether they do or do not have bequest motives.
5
Conclusion
This paper presents new findings on subjective survival beliefs over the life-cycle. Young people
tend to overestimate their mortality risk, while older individuals believe they will survive longer
than actuarial data imply. Because mortality beliefs affect the individual’s subjective discount factor, they have important theoretical implications for savings rates over the life-cycle. We provide
evidence – using both a novel survey and a canonical life-cycle model – that mortality belief distortions cause the young to save less and those beyond retirement age to consume their accumulated
savings at a slower pace. Our evidence suggests that mortality beliefs are quantitatively as important as commonly cited explanations for variation in savings rates, such as financial literacy and
bequest motives.
Diagnosing the source of mortality belief distortions is crucial for policy prescriptions, as
well as to practitioners. As such, we find that mortality beliefs change over the life-cycle in conjunction with the salience of age-cohort specific causes-of-death. When younger individuals consider their mortality, they think of salient rare events such as plane crashes, the probability of
which they overweight. Older individuals place more weight on natural aging, leading to higher
subjective survival estimates.
Finally, subjective mortality beliefs can have important implications for other areas in the
literature of financial economics. They may extend beyond the partial equilibrium setting of our
life-cycle model to a general equilibrium effect on market prices. For example, some research has
considered the role of aging and demographics on equilibrium asset prices (Poterba (2001)). In a
related working paper, Heimer et al. (2015) examines the asset pricing implications of mortality
27
beliefs that vary by generation. Using an over-lapping generations model, the increased (decreased)
patience of the older (younger) generation lowers (raises) the rate of return on bonds (equities),
which gives rise to an equity premium. Another potential area to consider is the demand for life
insurance and annuities. We leave for future work a thorough investigation into these areas of
research.
28
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32
Table 1: Survey Respondent Characteristics
Description: This table presents data on the characteristics of participants in the survey administered by Qualtrics.
pct.
age
pct.
civil status
28
38
48
58
68
78
12.1
24.6
23.2
19.0
16.2
4.9
gender
female
male
51.9
48.2
have children
no
yes
32.2
67.8
single
partner (not co-habitating)
partner (co-habiting)
married
divorced
widowed
21.9
1.2
7.7
50.4
13.7
5.1
pct.
gross hh income
less than $10k
$10k - $20k
$20k - $35k
$35k - $50k
$50k - $100k
$100k - $200k
greater than $200k
7.0
10.1
17.6
17.2
33.2
13.1
1.8
education
primary school
high school
college, no degree
bachelor’s degree
master’s degree
doctorate
1.8
21.1
34.1
29.3
11.3
2.4
N = 4, 517
33
Table 2: Summary Statistics of Regression Variables
Description: This table presents summary statistics of variable used in the regression analysis. The data comes from a survey administered by
Qualtrics. Survival optimism equals the difference between the respondent’s subjective belief about surviving at least l = {1, 2, 5, 10} years and the
˜ it [surv(t + l)] − Prit [surv (t + l)], where t is respondent i’s age. Longevity
actuarial probability according to the Social Security Administration, Pr
optimism equals the difference between the respondent’s subjective longevity and the projected age of death according to the Social Security
Administration.
mean
std dev
p25
median
p75
-9.12
-2.16
19.76
13.09
-13.46
-8.30
-0.80
-2.10
0.96
4.50
0.34
0.18
0.50
0.81
mortality beliefs
survival optimism (ppt)
longevity optimism (years)
savings rates
share monthly income saved
... rely on credit cards
... spend all income
... save ~ 10%
... save ~ 25%
... save ≥ 50%
when plan to use savings?
... any time now
... 2 - 5 years from now
... 6 - 10 years
... at least 10 years
investing experience
... very inexperienced
... somewhat inexperienced
... somewhat experienced
... experienced
... very experienced
personal attributes
risk tolerance
... willing to take substantial financial risk
... above average
... average
... not willing to take financial risks
subjective likelihood of leaving bequest
financially literate ( = 1)
numerically literate ( = 1)
0.09
0.32
0.42
0.14
0.04
0.21
0.29
0.16
0.34
0.39
0.25
0.25
0.07
0.03
0.08
0.22
0.37
0.33
0.51
0.68
0.56
N = 4, 517
34
Table 3: Risk Factors and the Formation of Mortality Beliefs
Panel I, Description: This table presents data on the factors respondents use to judge their own survival probabilities. They are asked to rate each
factor on a scale of 0 to 100 (the weights do not have to sum to one). For the normalized weights, we remove the individual fixed effect in these
responses by dividing the raw weight by the sum of the weights i places on all nine risk factors.
“When you assessed your survival likelihood, to what extent did you place weight on the following risk factors?”
variable
The natural course of life and aging (“normal risk”)
Medical conditions (e.g., cancer and heart disease)
Dietary habits (e.g. unhealthy foods)
Traffic accidents (e.g., car crash)
Physical violence (e.g., murder)
Natural disasters (e.g., earth quakes)
Animal attacks (e.g., shark attacks)
Risky lifestyle (e.g., base jumping)
“Freak events” (e.g., choking on your food)
mean
73.69
64.16
59.89
43.12
31.22
31.72
21.67
24.58
29.75
raw weights
median
std dev
80
23.79
70
28.55
65
28.95
44
29.08
20
30.04
20
29.68
9
28.79
9
30.81
19
29.37
normalized weights (w/in respondent)
mean
median
std dev
23.44
20
14.73
18.99
17
10.96
17.09
16
9.19
11.20
11
6.71
7.04
7
5.28
7.32
7
5.49
4.36
3
4.43
5.17
3
5.46
6.94
6
5.86
N = 4, 517
Panel II, Description: This table presents estimates of the following regression estimated using OLS: risk. f actor.weighti = β0 + β1 ·
survival.optimismi + ∑5l=0 β2l age.categoryi + Γ · Xi + εi . The dependent variable, risk. f actor.weight, is equal to the weight respondent i places
on the corresponding risk factor divided by the sum of the weights i places on all nine risk factors, for which summary statistics are presented in
˜ it [surv (t + l)] − Prit [surv (t + l)], where t is respondent i’s age and l = {1, 2, 5, 10}
Panel I. The independent variable survival optimism equals Pr
(normalized so that a one unit increase equals a standard deviation increase), and survival probabilities are from the Social Security Administration.
Log num natural disaster deaths in ZIP code equals the natural logarithm of one plus the number of deaths by natural disaster in a a respondent’s
ZIP code between 2001 and 2010 according to the Spatial Hazard Events and Losses Database (SHELDUS). We map the counties in SHELDUS
to ZIP codes using the 2010 concordance from the Missouri Census Data Center. Standard errors (in parentheses), clustered by age, are calculated
using the Wild cluster-bootstrap percentile-t procedure from Cameron et al. (2008), and *, **, *** denote statistical significance at the p < 0.10,
p < 0.05, p < 0.01 levels, respectively.
risk factor normalized weight
survival optimism (Z)
age = 28, omitted
age = 38
age = 48
age = 58
age = 68
age = 78
male ( = 1)
log num natural disaster deaths in ZIP code
survival horizon FE
survival & longevity information treatments
mean of dependent variable
N
R2
(1)
natural aging
3.458***
(0.10)
(2)
medical
-0.180
(0.27)
(3)
diet
1.114***
(0.18)
(4)
traffic accident
-0.303**
(0.094)
(5)
violence
-0.772***
(0.17)
(6)
natur. disaster
-0.812***
(0.058)
(7)
animal attack
-0.705**
(0.19)
(8)
risky lifestyle
-0.615**
(0.19)
(9)
freak events
-0.932***
(0.073)
-0.261**
(0.082)
0.302**
(0.089)
1.300***
(0.057)
1.576***
(0.095)
4.709***
(0.080)
-1.020**
(0.39)
0.509
(0.65)
x
x
23.47
4,517
0.056
1.900***
(0.12)
3.009***
(0.13)
4.784***
(0.081)
8.327***
(0.13)
9.604***
(0.018)
-0.424
(0.40)
-0.577
(0.40)
x
x
18.97
4,517
0.065
1.601***
(0.050)
1.536***
(0.048)
3.678***
(0.044)
5.894***
(0.054)
7.299***
(0.031)
-0.754***
(0.16)
-0.285
(0.56)
x
x
17.09
4,517
0.065
-0.220***
(0.025)
-0.322***
(0.032)
-0.573***
(0.018)
0.281***
(0.027)
-0.447***
(0.029)
-0.585**
(0.17)
-0.173
(0.17)
x
x
11.22
4,517
0.0052
-0.648***
(0.056)
-0.492***
(0.059)
-1.332***
(0.043)
-1.297***
(0.066)
-2.492***
(0.021)
0.371
(0.19)
-0.0326
(0.30)
x
x
7.03
4,517
0.036
-0.581***
(0.044)
-0.784***
(0.049)
-1.654***
(0.022)
-1.141***
(0.042)
-2.206***
(0.036)
0.118
(0.24)
0.925***
(0.18)
x
x
7.32
4,517
0.033
-0.487***
(0.073)
-0.903***
(0.075)
-1.819***
(0.056)
-1.584***
(0.083)
-2.252***
(0.013)
0.476*
(0.21)
0.0719
(0.13)
x
x
4.35
4,517
0.055
-0.445***
(0.062)
-1.086***
(0.063)
-2.257***
(0.050)
-2.622***
(0.069)
-3.274***
(0.021)
1.095***
(0.17)
-0.188
(0.14)
x
x
5.15
4,517
0.059
-0.923***
(0.034)
-1.323***
(0.038)
-2.182***
(0.025)
-1.630***
(0.037)
-3.402***
(0.023)
0.571**
(0.16)
0.167
(0.28)
x
x
6.95
4,517
0.042
35
Table 4: Rare Event Deaths and Mortality Beliefs
Description: This table presents estimates of a Poisson regression. The dependent variables are respondents’ estimates of the number of Americans
who die in plane crashes annually or the number of people struck by lightning in a given year. The independent variable survival optimism equals
˜ it [surv(t + l)] − Prit [surv (t + l)], where t is respondent i’s age and l = {1, 2, 5, 10} (normalized so that a one unit increase equals a standard
Pr
deviation increase), and survival probabilities are from the Social Security Administration. Numerical literacy equals one if the respondent can
correctly calculate probabilities (the exact questions are described in the Appendix). (Z) indicates that a variable is normalized such that a one unit
increase equals a one standard deviation increase. Robust standard errors clustered by respondent age are in parentheses, and ***, **, * denote
statistical significance at the p < 0.10, p < 0.05, p < 0.01 levels, respectively.
Poisson regression dep var =
survival optimism (Z)
age = 28, omitted
age = 38
age = 48
age = 58
age = 68
age = 78
male ( = 1)
subjective assessment of
annual plane crash deaths
(1)
-0.0936***
(0.014)
(2)
-0.0934***
(0.015)
(3)
0.0463
(0.045)
(4)
0.0374
(0.047)
-0.0807***
(0.014)
-0.0497***
(0.013)
-0.279***
(0.012)
-0.411***
(0.013)
-0.658***
(0.032)
-0.301***
(0.088)
-0.0807***
(0.014)
-0.0497***
(0.013)
-0.279***
(0.014)
-0.411***
(0.013)
-0.658***
(0.031)
-0.301***
(0.085)
-0.00327
(0.049)
x
x
x
626.0
4,515
0.026
0.262***
(0.016)
0.245***
(0.017)
0.253***
(0.026)
0.231***
(0.018)
-0.0765**
(0.032)
0.0486
(0.043)
0.260***
(0.017)
0.247***
(0.016)
0.238***
(0.032)
0.217***
(0.023)
-0.0823**
(0.034)
0.0327
(0.038)
0.159*
(0.095)
x
x
x
670.6
4,187
0.019
numerical literacy ( = 1)
survival horizon FE
education FE
income FE
mean of dependent variable
N
pseudo R2
subjective assessment of
num. struck by lightning
x
x
x
626.0
4,515
0.026
36
x
x
x
670.6
4,187
0.018
Table 5: Mortality Beliefs and Savings Rates
Description: This table presents results from estimating ordered logistic models. Coefficients give the ordered log-odds of moving to a higher
category of the dependent variable. The independent variable survival optimism equals respondent i’s belief in the probability they survive at least
x number of years minus the statistical probability of survival according to the Social Security Administration (SSA) actuarial tables. Longevity
optimism is the respondent’s beliefs about the age at which they will die minus the age-gender-conditional expected longevity according to the
SSA. Financially literate equals one if i correctly answers at least 2 out of 3 of the financial literacy survey questions from Lusardi and Mitchell
(2011). (Z) indicates that a variable has been normalized so that a one unit increase equals a one standard deviation increase. All regression include
controls for the respondent’s gender, age, survival horizon (experimental treatments for the probability of living at least x number of years, where
x ∈ {1, 2, 5, 10}), indicators for respondents treated with age-cohort-specific information about survival probabilities and expected longevity, an
indicator for numerical literacy, and the respondents’ risk-tolerance. Robust standard errors clustered by respondent age are in parentheses, and
***, **, * denote statistical significance at the p < 0.10, p < 0.05, p < 0.01 levels, respectively.
Panel A
survival optimism (Z)
ordered logit dep var = frac. monthly income saved
(1a)
0.191***
(0.034)
(2a)
0.187***
(0.035)
(3a)
0.139***
(0.033)
longevity optimism (Z)
financially literate ( = 1)
education FE
income FE
base category: rely on credit cards
... spend all income
... save ~ 10%
... save ~ 25%
... save ≥ 50%
-2.356***
-0.316
1.704***
3.378***
Panel B
survival optimism (Z)
0.130***
(0.037)
0.00952
(0.049)
x
x
-2.319***
-0.278
1.743***
3.417***
-1.401***
0.732***
2.885***
4.620***
financially literate ( = 1)
(2b)
0.223***
(0.017)
(3b)
0.201***
(0.017)
0.345***
(0.098)
0.275***
(0.10)
x
x
-0.282*
1.179***
1.865***
-0.192
1.275***
1.966***
0.111
1.591***
2.298***
(1c)
0.0796***
(0.031)
(2c)
0.0724**
(0.030)
Panel C
survival optimism (Z)
(6a)
0.159**
(0.069)
0.159**
(0.069)
0.158***
(0.038)
0.121**
(0.059)
0.0278
(0.052)
x
x
-2.247***
-0.215
1.802***
3.479***
-2.205***
-0.171
1.848***
3.524***
-1.243***
0.886***
3.039***
4.776***
(4b)
(5b)
(6b)
0.0897*
(0.052)
0.0924*
(0.050)
0.374***
(0.096)
0.0795*
(0.045)
0.297***
(0.10)
x
x
-0.126
1.320***
1.999***
-0.0351
1.418***
2.103***
0.373
1.841***
2.543***
ordered logit dep var = experience investing
(3c)
0.0203
(0.032)
longevity optimism (Z)
financially literate ( = 1)
education FE
income FE
base category: very inexperienced
... somewhat inexperienced
... somewhat experienced
... experienced
... very experienced
N
(5a)
ordered logit dep var = when do you plan to use savings?
(1b)
0.231***
(0.015)
longevity optimism (Z)
education FE
income FE
base category: any time now
... 2 - 5 years from now
... 6 - 10 years
... at least 10 years
(4a)
-0.950***
0.297**
2.033***
3.227***
4,517
0.316***
(0.098)
0.169**
(0.080)
x
x
-0.842***
0.411**
2.150***
3.344***
37
4,517
0.0229
1.334***
3.166***
4.424***
4,517
(4c)
(5c)
(6c)
0.0945***
(0.031)
0.100***
(0.030)
0.331***
(0.097)
0.0479*
(0.027)
0.175**
(0.080)
x
x
-0.891***
0.357**
2.093***
3.288***
4,517
-0.783***
0.471**
2.211***
3.407***
4,517
0.0459
1.357***
3.190***
4.448***
4,517
Table 6: The Effect of Mortality Beliefs and Bequests on Savings Draw Down
Description: This table presents results from estimating ordered logistic models. Coefficients give the ordered log-odds of moving to a higher
category of the dependent variable. The independent variable year-to-year survival rate beliefs equals respondent i’s belief in the probability they
survive at least x number of years minus the statistical probability of survival according to the Social Security Administration (SSA) actuarial tables.
Longevity beliefs is the respondent’s beliefs about the age at which they will die minus the age-gender-conditional expected longevity according to
the SSA. Expected bequests is equal to the subjective probability that the individual will leave an inheritance. (Z) indicates that a variable has been
normalized so that a one unit increase equals a one standard deviation increase. All regression include controls for the respondent’s gender, survival
horizon (experimental treatments for the probability of living at least x number of years, where x ∈ {1, 2, 5, 10}), indicators for respondents treated
with age-cohort-specific information about survival probabilities and expected longevity, indicators for numerical literacy and financial literacy, and
the respondents’ risk-tolerance. Robust standard errors clustered by respondent age are in parentheses, and ***, **, * denote statistical significance
at the p < 0.10, p < 0.05, p < 0.01 levels, respectively.
sample:
survival optimism (Z)
has children
(1)
0.251***
(0.047)
ordered logit dep var = when do you plan to use savings?
no children
pooled
has children
no children
(2)
0.0113
(0.084)
(3)
0.182***
(0.030)
longevity optimism (Z)
expected bequests (Z)
age = 58, omitted
age = 68
age = 78
(5)
(6)
0.348**
(0.14)
0.263***
(0.087)
0.385***
(0.061)
0.193***
(0.028)
0.346***
(0.065)
0.240***
(0.057)
0.255***
(0.098)
0.230***
(0.038)
0.248***
(0.055)
-0.641***
(0.059)
-0.836***
(0.063)
-0.875***
(0.029)
-1.204***
(0.079)
-0.688***
(0.031)
-0.892***
(0.0044)
-0.0820
(0.13)
-0.619***
(0.040)
-0.795***
(0.018)
-0.903***
(0.017)
-1.235***
(0.053)
-0.682***
(0.021)
-0.877***
(0.025)
-0.0379
(0.14)
-2.099***
-0.658*
0.435
1,301
0.057
-1.594***
-0.343
0.530*
489
0.056
-2.094***
-0.727**
0.290
1,790
0.050
-1.772***
-0.342
0.753***
1,301
0.056
-1.641***
-0.376**
0.511***
489
0.063
-1.848***
-0.481
0.541**
1,790
0.051
has children ( = 1)
base category: any time now
... 2 - 5 years from now
... 6 - 10 years
... at least 10 years
N
pseudo R2
pooled
(4)
38
Table 7: Life-cycle Model Baseline Parameters
Description: This table presents the parameters used in the baselines version of the life-cycle model. The parameters γ0 , γ1 , and γ2 come from
estimates of st+1 = γ0 + γ1 t + γ2 t 2 where t is the survey respondent’s age (normalized to 28-years-old) and st+1 is the predicted beliefs about survival
at least one additional year.
Conventional Parameters
Risk aversion (ρ)
Bequest parameter (b)
Discount factor (β )
Risk-free rate (R f )
Equity premium (Rte − R f )
Retirement age (T R )
Maximum age (T )
Uncertain income in retirement?
Bequest motive?
Value
5
2.5
0.98
0.2
0.4
65
95
no
no
Mortality Beliefs Parameters
γ0
γ1
γ2
39
Value
0.9329
0.149
-0.00432
Table 8: Life-Cycle Model Results
Description: This table presents results from solving the life-cycle model described in Section 3. The life-cycle begins at 28-years-old, ends at
95-years-old, and retirement age is 65. Subjective mortality beliefs are our survey-elicited survival probabilities and objective mortality beliefs are
transition rates taken from the Social Security administration life-tables. All other parameter choices are described in Table 7.
Mortality beliefs:
Pre-Retirement
Objective
Subjective
Post-Retirement
Objective
Subjective
Average annual consumption
dollar amount
fraction of income
fraction of cash-on-hand
27,791
0.961
0.244
28,435
0.980
0.345
36,109
1.785
0.291
31,077
1.521
0.342
Std. deviation consumption
dollar amount
fraction of income
fraction of cash-on-hand
6,457
0.184
0.177
5,061
0.125
0.208
3,524
0.182
0.218
2,952
0.143
0.211
Wealth at retirement
dollar amount
319,688
219,921
Investment behavior
average fraction income saved
dollar amount saved
average share risky asset
0.039
1,031
0.810
0.020
566
0.892
-0.785
-15,848
0.700
-0.521
-10,627
0.824
40
Figure 1: Mortality Beliefs and Financial Planning
Description: This figure displays the inputs into a personal financial plan used by the online investment service Betterment.
41
Figure 2: Longevity Beliefs vs. Actuarial Data
Description: The figure compares subjective longevity beliefs to the Social Security Administration’s projected longevity estimated calculated
using actuarial probabilities. Our sample includes respondents age 28, 38, 48, 58, 68, and 78 and asks them, “About how long do you think you will
live? Please indicate the age that you expect to reach.”
d
ol
d
78
yr
ol
d
68
yr
ol
d
58
yr
ol
d
yr
48
yr
ol
d
Female
38
28
yr
ol
d
ol
d
78
yr
ol
d
68
yr
ol
d
58
yr
ol
d
yr
ol
48
yr
38
28
yr
ol
d
60
longevity (age)
70
80
90
100
Longevity beliefs
Male
Subjective longevity
Objective longevity
Source of expected longevity estimates: Social Security Administration, 2016
42
Figure 3: Survival Beliefs vs. Actuarial Data
The figure shows survival optimism, equal to the difference between elicited survival beliefs (“subjective
survival prob.”) and actuarial probabilities from statistical life tables provided by the Social Security Administration,
˜ it [surv(t + l)] − Prit [surv (t + l)]. We sample respondents age 28, 38, 48, 58, 68, and 78 ask them the probability
Pr
that they will survive beyond l ∈ {1, 2, 5, and10} years. We ask an equal number of respondents (one-fifth each) about
survival beyond 1 year, 2 year, 5 year, 10 years, and all horizons jointly. We include a fitted line for the 10-year
survival estimates.
Subjective minus objective pr(survival)
−20%
0%
20%
40%
Description:
Errors in subjective survival beliefs
30
40
50
60
70
survive at least to age
95% Prediction Interval
1 year
5 years
43
80
Fitted line, 10 years
2 years
10 years
90
Figure 4: Mortality Beliefs and Savings Rates
Figure A, Description: The figure presents the predictions from the following multinomial logistic model: f (k, i) = β0k +β1k survival.optimism1i +
βk Xi , where f (k, i) is a prediction of the probability that observation i has outcome k. The dependent variable is the survey question: “How much
of your monthly income do you save? (choose the closest answer from the following)”, with the following set of possible responses: 1) “I spend
more money than I earn. I often use credit cards or other loans to supplement my monthly income”, 2) “I save around 25% of my monthly income”,
3) “I save around 10% of my monthly income”, 4) “I spend all of my income each month”, or 5) “I save at least 50% of my monthly income.”
The coefficient β1k captures the effect of survival.optimism on the the likelihood of choosing k, and it equals P̃it [surv(t + l)] − Prit [surv (t + l)],
standardized so that a one standard deviation increase equals a one unit increase. The matrix Xi includes i’s age, gender, income, education, a
categorical adjustment for the survival horizon, an indicator if i was asked to consecutively provide her subjective beliefs about the four different
survival horizons, and an indicator if i correctly answers our numeracy test.
Figure B, Description: The dependent variable is the survey question: “When do you expect to use most of the money you are now accumulating
in your investments or savings?” The set of possible answers are: 1) “At any time now...so a high level of liquidity is important”, 2) “Probably in
the future...2-5 years from now”, 3) “In 6-10 years”, and 4) “Probably at least 10 years from now.”
Figure 5: Estimated Subjective Survival Function
Cumulative survival probability
Male
20%
40%
60%
80%
100%
Female
0%
Cumulative survival probability to end of lifecycle
Description: The figure presents the cumulative density of the subjective survival function, st+1|t , for survival up to 95 years, given age t. We
estimate st+1|t = γ0 + γ1 t + γ2 t 2 using OLS and our survey’s 1, 2, 5, and 10-year elicited survival beliefs. The survey responses on survival beliefs
are winsorized at the bottom one percent of the distribution. For the 2, 5, and 10-year survival beliefs, we use a geometric mean to transform these
responses into annual, condition transition probabilities. The data is normalized by age t by subtracting 28 years, the age of the youngest cohort in
our survey. The solid black line shows the cumulative probability of surviving to age 95 at age t, given actuarial data from the SSA.
20
40
60
80
100 20
40
60
80
Respondent age
Objective probability
95% Prediction Interval
45
Subjective probability
100
Figure 6: Life-Cycle Results: Subjective vs. Actual Life-Expectancies
Description: This figure presents the paths of consumption, savings, cash-on-hand, and the portfolio share of the risky asset obtained from the
solution to the life-cycle model outlined in Section 3. “Objective beliefs” indicates that the model calibration uses year-to-year survival rates from
the Social Security Administration. “Subjective Beliefs” indicates that the model uses the subjective beliefs survival function described in Figure 5.
4
Consumption
#10 4
1
Objective Beliefs
Subjective Beliefs
Savings
#10 4
0.5
3.5
0
$
$
3
-0.5
2.5
-1
2
-1.5
1.5
20
40
60
80
-2
20
100
Objective Beliefs
Subjective Beliefs
40
Age
3.5
Cash on hand
#10 5
3
60
80
100
Age
1
Objective Beliefs
Subjective Beliefs
Share of risky assets
0.95
0.9
Portfolio weight
2.5
$
2
1.5
1
0.85
0.8
0.75
0.7
0.65
0.6
0.5
0
20
0.55
40
60
80
0.5
20
100
Age
Objective Beliefs
Subjective Beliefs
40
60
Age
46
80
100
Figure 7: Savings and Consumption During Retirement: Subjective vs.
Expectancies
Actual Life-
Description: This figure presents the paths of consumption, savings, cash-on-hand, and the portfolio share of the risky asset obtained from the
solution to the life-cycle model outlined in Section 3. “Objective Beliefs” indicates that the model calibration uses year-to-year survival rates from
the Social Security Administration. “Subjective Beliefs” indicates that the model uses the subjective beliefs survival function described in Figure 5.
The representative consumer is endowed with $300,000 of accumulated wealth at retirement (age 65) , which (excluding housing equity and social
security income) is close to the median household net worth in 2008 according to Poterba et al. (2011). The model is solved with agents dying at
age 95, but we allow consumers to plan as though they will live until 120.
3.6
#10 4
Consumption, Bequest = 0
-0.6
Savings, Bequest = 0
#10 4
3.5
#10 5
Cash on hand, Bequest = 0
Objective Beliefs
Subjective Beliefs
3
3.2
-1
2.5
3
-1.2
2
$
$
-0.8
$
3.4
2.8
-1.4
1.5
2.6
-1.6
1
-1.8
0.5
2.4
Objective Beliefs
Subjective Beliefs
2.2
65
70
75
Objective Beliefs
Subjective Beliefs
80
85
90
-2
65
95
70
75
Age
3.4
#10 4
80
85
90
0
65
95
70
75
Age
Consumption, Bequest = 1
-0.6
Savings, Bequest = 1
#10 4
80
85
90
95
Age
3.5
#10 5
Cash on hand, Bequest = 1
-0.8
3
3
-1
2.5
2.8
-1.2
2
2.6
2.4
$
3.2
$
$
Objective Beliefs
Subjective Beliefs
-1.4
1.5
-1.6
1
Objective Beliefs
Subjective Beliefs
2.2
65
70
75
Objective Beliefs
Subjective Beliefs
80
85
90
95
-1.8
65
70
75
Age
80
Age
47
85
90
95
0.5
65
70
75
80
Age
85
90
95
Online Appendix:
YOLO: Mortality Beliefs and Household Finance Puzzles
Not intended for publication
A1: Robustness of Survival Beliefs:
Table A.1: Robustness of Mortality Belief Errors Over the Life-cycle
Description: This table presents OLS regression results. In Panel A, target age is the respondent’s current age plus survival target years, x ∈
{1, 2, 5, 10}. In Panel B, age is the respondent’s current age. Standard errors are in parentheses, and ***, **, * denote statistical significance at the
p < 0.10, p < 0.05, p < 0.01 levels, respectively.
Panel A
target age squared
target age
(1a)
0.00511***
(0.0014)
-0.354**
(0.16)
actuarial probabilities info treatment ( = 1)
(2a)
0.00512***
(0.0014)
-0.355**
(0.16)
-0.408
(0.59)
dep var = survival optimism (ppt)
(3a)
(4a)
(5a)
0.00517***
0.00509***
0.00493***
(0.0014)
(0.0014)
(0.0014)
-0.360**
-0.362**
-0.339**
(0.16)
(0.15)
(0.16)
all survival horizons treatment ( = 1)
1.614**
(0.65)
numerical literacy ( = 1)
4.414***
(0.58)
smoker ( = 1)
-1.128
(0.70)
subjective health assessment (Z)
gender
education FE
income FE
N
R2
x
x
x
4,517
0.066
x
x
x
4,517
0.066
(1b)
0.00275**
(0.0011)
-0.307***
(0.12)
(2b)
0.00278***
(0.0011)
-0.311***
(0.12)
-1.290***
(0.45)
Panel B
respondent age squared
respondent age
actuarial probabilities info treatment ( = 1)
x
x
x
4,517
0.067
x
x
x
4,517
0.078
x
x
x
4,515
0.067
dep var = longevity optimism (years)
(3b)
(4b)
(5b)
0.00275**
0.00275**
0.00213*
(0.0011)
(0.0011)
(0.0011)
-0.308***
-0.307***
-0.259**
(0.12)
(0.12)
(0.12)
all survival horizons treatments ( = 1)
5.877***
(0.34)
x
x
x
4,510
0.15
(6b)
0.00188*
(0.0010)
-0.215*
(0.11)
0.861
(0.57)
numerical literacy ( = 1)
-0.0160
(0.47)
smoker ( = 1)
-3.029***
(0.56)
subjective health assessment (Z)
gender
education FE
income FE
N
R2
(6a)
0.00422***
(0.0013)
-0.255*
(0.15)
x
x
x
4,517
0.036
x
x
x
4,517
0.037
x
x
x
4,517
0.036
i
x
x
x
4,517
0.036
x
x
x
4,515
0.043
4.154***
(0.24)
x
x
x
4,510
0.11
(7a)
0.00430***
(0.0013)
-0.272*
(0.15)
-0.374
(0.56)
1.326**
(0.62)
4.393***
(0.56)
0.0684
(0.66)
5.869***
(0.34)
x
x
x
4,508
0.17
(7b)
0.00147
(0.0011)
-0.185
(0.11)
-1.247***
(0.43)
0.715
(0.54)
-0.134
(0.45)
-2.347***
(0.55)
4.078***
(0.24)
x
x
x
4,508
0.12
A2: Subjective Survival Probability Estimates
Table A.2: Subjective Survival Probability Function
Description: This table presents parameter estimates of the subjective survival probability function for various subsets of the data. The estimated
equation in each column is st,t+1 = γ0 + γ1 t + γ2 t 2 where st,t+1 denote our surveyed beliefs at age t minus 28 years. To estimate this equation, we
use our survey’s 1, 2, 5, and 10-year elicited survival beliefs. The survey responses on survival beliefs are winsorized at the bottom one percent of
the distribution. For the 2, 5, and 10-year survival beliefs, we use a geometric mean to transform these responses into annual, condition transition
probabilities. Standard errors are in parentheses, and ***, **, * denote statistical significance at the p < 0.10, p < 0.05, p < 0.01 levels, respectively.
age2
age
constant
N
R2
age2
age
constant
N
R2
All
-0.0032***
(0.0006)
0.149***
(0.031)
93.28***
(0.32)
7,160
0.0033
<10k
-0.0101***
(0.0044)
-0.492***
(0.18)
86.09***
(1.67)
518
0.028
gender:
Male
Female
-0.0051***
-0.0007
(0.0009)
(0.0009)
0.256***
0.0059
(0.044)
(0.044)
91.89***
95.01***
(0.44)
(0.47)
3,417
3,743
0.0093
0.046
College Grad
-0.0031***
(0.0008)
0.150***
(0.039)
94.21***
(0.39)
3,080
0.0041
income buckets:
<50k
>50k
-0.0017*
-0.0044***
(0.0015)
(0.0008)
0.075**
0.206***
(0.071)
(0.036)
91.83***
93.65***
(0.75)
(0.37)
2,496
4,664
0.0005
0.0071
>100k
-0.0063***
(0.0016)
0.359***
(0.078)
92.04***
(1.83)
1,050
0.051
ii
education:
High School
Less than High School
-0.0041***
-0.0160
(0.0009)
(0.013)
0.191***
0.396
(0.046)
(0.52)
92.35***
86.57***
(0.50)
(4.71)
3,942
138
0.0043
0.012
A3: Mortality tables by education, and aggregate income process
We construct mortality tables by education in several steps. First, we use Tables 2 and 3 from
the U.S. Census Bureau American Community Survey to compute the shares of “White alone, not
Hispanic or Latino”, “Hispanic or Latino (of any race)” and “Black or African American”, a well
as shares of males and females. These shares are provided in 5-year age-interval and we use linear
interpolation to annualize the shares. Second, we use Tables 10A.1 and 10A.2 in Brown et al.
(2002) and the demographic weights we construct in the previous step to compute educational
shares for categories LTHS, HS+, and COL. Because not all combinations of race and educational
attainment are provided in these tables, we use the next lowest educational category if no category
is available. For “Black,” we use HS+ instead of college. For “Hispanics,” we use "All" in all
three cases. Fourth, we aggregate categories LTHS, HS+, and COL across gender, using weights
from the second step. Finally, we use the educational series as described in Brown et al. (2002) to
generate education-specific mortality series.
We construct the aggregate income path using our estimates for the polynomial fit in each
educational category to compute income at each given age. Then, we average these income paths
based on weights that we construct from Table H-13 of the Current Population Survey by the U.S.
Census Bureau for the year 2014. Moreover, we set the variance for the transitory and permanent
aggregate income shocks as the sum of the variances and covariances of LTHS, HS+ and COL,
assuming correlations of 0.85.
iii
A4: Life-cycle Model Robustness to Alternative Parameter Choices
Table A.3: Model Results for Different Income Paths
Description: This table presents results from solving the life-cycle model described in Section 3. The life-cycle begins at 28-years-old, ends at
95-years-old, and retirement age is 65. Subjective mortality beliefs are our survey-elicited survival probabilities and objective mortality beliefs
are transition rates taken from the Social Security administration life-tables. We use Table A.2’s estimates to parametrize the subjective survival
functions across education groups. All other parameter choices are presented in Table 7.
Lifetime incomes:
Mortality beliefs:
Average annual consumption
dollar amount
fraction of income
fraction of cash-on-hand
Less-than High School Degree
Pre-Retirement
Post-Retirement
Objective
Subjective
Objective
Subjective
High School Degree
Pre-Retirement
Post-Retirement
Objective
Subjective
Objective
Subjective
24,488
0.983
0.204
25,806
1.035
0.473
31,125
1.810
0.291
18,593
1.077
0.907
25,340
0.971
0.219
25,783
0.993
0.323
32,283
1.841
0.283
26,460
1.517
0.357
Std. deviation consumption
dollar amount
fraction of income
fraction of cash-on-hand
5,628
0.235
0.141
3,437
0.103
0.114
3,253
0.190
0.218
2,544
0.131
0.162
5,575
0.207
0.159
3,947
0.139
0.190
3,216
0.190
0.217
3,072
0.172
0.217
Wealth at retirement
dollar amount
281,587
55,338
299,720
117,676
Investment behavior
average fraction income saved
dollar amount saved
average share risky asset
0.017
483
0.762
-0.035
-872
0.945
0.030
777
0.786
-0.0053
-104
0.937
-0.839
-14,791
0.678
-0.257
-4,507
0.958
Lifetime incomes:
Mortality beliefs:
Average annual consumption
dollar amount
fraction of income
fraction of cash-on-hand
-0.808
-13,899
0.691
-0.077
-1,340
0.994
College Degree
Pre-Retirement
Post-Retirement
Objective
Subjective
Objective
Subjective
32,237
0.937
0.239
32,661
0.959
0.308
45,534
1.800
0.287
40,716
1.618
0.303
Std. deviation consumption
dollar amount
fraction of income
fraction of cash-on-hand
9,274
0.181
0.178
7,948
0.140
0.204
4,256
0.178
0.218
2,961
0.122
0.205
Wealth at retirement
dollar amount
405,899
312,774
Investment behavior
average fraction income saved
Dollar Amount Saved
Dollar Amount Saved
0.063
1,823
0.780
0.042
1,236
0.814
-0.796
-20,136
0.680
-0.618
-15,523
0.755
iv
Figure A.1: Subjective Longevity Beliefs from the Survey of Consumer Finances
Description: The figure compares, a) subjective longevity beliefs drawn from the 2010 wave of the Survey of Consumer Finances (SCF) to b) the
Social Security Administration’s projected longevity estimated calculated using actuarial probabilities. For the purposes of illustration, the figure
bins respondents in the SCF into their respective age decile and we calculate and present the mean response (actuarial longevity estimate) of these
groups.
Female
90
80
70
60
50
40
30
20
90
80
70
60
50
40
30
20
60
70
longevity (age)
80
90
100
Longevity beliefs in the Survey of Consumer Finances (2010)
Male
Subjective longevity
Objective longevity
Data sources: Social Security Administration, 2010, and Survey of Consumer Finances, 2010
v
Figure A.2: Subjective Survival Beliefs For Different Levels of Education
Description: This figure presents the paths of consumption, savings, cash-on-hand, and the portfolio share of the risky asset obtained from the
solution to the life-cycle outlined in Section 3. “Objective beliefs” indicates that the model calibration uses year-to-year survival rates from the
Social Security Administration. “Subjective Beliefs” indicates that the model uses the subjective beliefs survival function described in Figure 5.
We use the estimates provided in Table A.2 to parametrize the subjective survival functions across education groups. Income paths for different
educational groups are constructed by Love (2013) using the 1970 - 2007 data from the PSID.
Less-than-high-school
#10 4
5
High-school
#10 4
5
4
4
3
3
3
$
4
$
$
Consumption
5
2
2
2
1
1
1
30
40
50
60
70
80
90
30
40
50
Age
1
1
90
30
1
0
-0.5
-1
-1
-1.5
-1.5
-1.5
-2
-2
60
70
80
90
40
50
Age
80
90
30
3
3
$
3
2
1
60
70
80
90
30
40
50
60
70
80
90
30
0.8
0.8
0.8
0.7
0.7
0.7
$
1
0.9
$
1
0.6
0.6
0.6
0.5
0.5
0.5
0.4
0.4
70
80
90
80
90
50
60
70
80
90
70
80
90
Age
0.9
60
40
Age
1
50
70
2
0.9
40
60
1
Age
30
50
Age
4
50
90
#10 5
4
40
40
Age
$
$
70
#10 5
1
$
60
4
30
80
-2.5
30
#10 5
2
70
-2
-2.5
50
60
$
0
-0.5
$
0
40
50
#10 4
0.5
-1
30
40
Age
-0.5
$
Savings
80
#10 4
0.5
-2.5
Cash-on-hand
70
Objective Beliefs
Subjective Beliefs
Age
#10 4
0.5
Share of risky asset
60
College
#10 4
0.4
30
40
50
Age
60
Age
vi
70
80
90
30
40
50
60
Age
Figure A.3: Subjective Survival Beliefs and Different Discount Factors
Description: This figure presents the paths of consumption, savings, cash-on-hand, and the portfolio share of the risky asset obtained from the
solution to the life-cycle outlined in Section 3. The model is calibrated using model uses the subjective beliefs survival function described in Figure
5. The different lines indicate variation in the rate of time preference, β .
5.5
Consumption
#10 4
1
5
Savings
#10 4
0.5
4.5
0
4
$
$
-0.5
3.5
-1
3
-1.5
2.5
Beta =1
Beta =0.99
Beta =0.98
Beta =0.97
Beta =0.9
2
1.5
20
30
40
50
60
70
80
90
-2
-2.5
20
100
Beta =1
Beta =0.99
Beta =0.98
Beta =0.97
Beta =0.9
30
40
50
Age
Cash on hand
#10 5
3.5
3
$
90
100
80
90
100
0.9
2
1.5
0.85
0.8
0.75
1
0.7
0.5
0.65
30
80
0.95
2.5
0
20
70
Share of risky assets
1
Beta =1
Beta =0.99
Beta =0.98
Beta =0.97
Beta =0.9
Portfolio weight
4
60
Age
40
50
60
70
80
90
0.6
20
100
Age
Beta =1
Beta =0.99
Beta =0.98
Beta =0.97
Beta =0.9
30
40
50
60
Age
vii
70
Figure A.4: Subjective Survival Beliefs and Different Levels of Risk-tolerance
Description: This figure presents the paths of consumption, savings, cash-on-hand, and the portfolio share of the risky asset obtained from the
solution to the life-cycle outlined in Section 3. The model is calibrated using model uses the subjective beliefs survival function described in Figure
5, while varying the coefficient of relative risk aversion ρ.
5.5
Consumption
#10 4
1
CRRA =1
CRRA =3
CRRA =5
CRRA =10
5
Savings
#10 4
0.5
4.5
0
4
-0.5
$
$
3.5
3
-1
2.5
-1.5
2
-2
1.5
1
20
30
40
50
60
70
80
90
-2.5
20
100
CRRA =1
CRRA =3
CRRA =5
CRRA =10
30
40
50
Age
4.5
Cash on hand
#10 5
4
70
80
90
100
80
90
100
Share of risky assets
1
CRRA =1
CRRA =3
CRRA =5
CRRA =10
0.9
3.5
0.8
Portfolio weight
3
$
2.5
2
1.5
0.7
0.6
0.5
0.4
1
0.3
0.5
0
20
60
Age
30
40
50
60
70
80
90
0.2
20
100
Age
CRRA =1
CRRA =3
CRRA =5
CRRA =10
30
40
50
60
Age
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70
Figure A.5: Consumption: Subjective Mortality Beliefs and Bequest Motives
Description: This figure presents the paths of consumption obtained from the solution to the life-cycle outlined in Section 3. “Objective beliefs”
indicates that the model calibration uses year-to-year survival rates from the Social Security Administration. “Subjective Beliefs” indicates that the
model uses the subjective beliefs survival function described in Figure 5. We allow for a bequest motive with a bequest parameter b=2.94 that is
chosen to minimize the sum of squared deviations of cash-on-hand under subjective beliefs relative to objective beliefs and no bequest motive.
4
Consumption
#104
3.5
$
3
2.5
2
1.5
1
Objective Beliefs, no Bequest
Subjective Beliefs, Bequest (b=2.94)
Subjective Beliefs, no Bequest
0
10
20
30
40
Age
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50
60
70
Survey Description:
YOLO: Mortality Beliefs and Household Finance Puzzles
Not intended for publication
1. Survey overview
The survey was administered on the Qualtrics Research Suite, and Qualtrics Panels provided the
responses. Respondents were randomly assigned to treatments that, principally, varied (i) information provided and (ii) the questions posed. Following mortality judgments, participants were
randomly assigned to one of three treatments in which they rated the risk factors considered in
their own mortality judgments. Subsequently, participants reported judgments of inflation and financial preferences. They were then tested for financial literacy, and finally reported health status
and other demographic information.
2. Sample
Invitations went out to residents of the U.S. Respondents were pre-screened for residence-status,
English language fluency, and age. All respondents who failed to meet the screening criteria were
discontinued from the survey. Only respondents who confirmed residence in the U.S., who professed English language fluency, and who reported to be of ages 28, 38, 48, 58, 68, and 78, were
brought on to the survey proper. Upon meetings these criteria, we screened responses by removing any participants who took less than five minutes to complete the survey or had at least one
gibberish response (e.g. sd#$2).
3. Mortality belief treatments
The treatments to which participants were randomly assigned depended on the participants’ age.
Participants of age x = {28, 38, 48, 58, 68, 78} were randomly assigned to one of the following 21
treatments [3(information treatments) x 6(transition horizons) + 1(full life horizon) + 1(HRS80) +
1(HRS90)]:10
10 For both information treatments (2 and 3), respondents were asked to estimate their own expected longevity before
reporting judgments of their transition probabilities. However, in the no-information treatments (1), respondents
reported judgments of their transition probabilities before estimating their expected longevity. In both cases, each
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1. No information, questions about. . .
(a) one-year transition horizon
(b) two-year transition horizon
(c) three-year transition horizon
(d) five-year transition horizon
(e) ten-year transition horizon
(f) all transition horizons
2. Information about life expectancy for y = {30, 40, 50, 60, 70, 80}-year-olds, questions about. . .
(a) one-year transition horizon
(b) two-year transition horizon
(c) three-year transition horizon
(d) five-year transition horizon
(e) ten-year transition horizon
(f) all transition horizons
3. Information about life expectancy and transition probability for y-year-olds
(a) one-year transition horizon
(b) two-year transition horizon
(c) three-year transition horizon
(d) five-year transition horizon
(e) ten-year transition horizon
of the estimates was followed by a confidence judgment in the estimate (e.g., “How confident are you in the answer
provided above?”).
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(f) all transition horizons
4. Questions about plausibility of survival for entire life horizon (28-year olds only)
5. One question, mirroring the Health and Retirement Survey, asking participants about the
likelihood that they reach 80 (90) for the 68-year (78-year) old sample
Questions on transition probabilities were given as follows:
4. Risk Factor Treatments
Participants were randomly assigned to one of three risk factor treatments. The risk factor treatments asked participants to indicate the relative weight placed on the risk factors in the prior
mortality judgments. Common for all three conditions were the following risk-actors:
the natural course of life and aging (“normal risk”)
medical conditions (e.g., cancer and heart disease)
dietary habits (e.g., unhealthy foods)
traffic accidents (e.g., car crash)
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physical violence (e.g., murder)
a freak events (e.g., choking on your food)
In addition, each of the three treatments presented three risk factors of the same categories—natural
disasters, animal attacks, and risky lifestyle—but with different examples, tailored to different
regions of the United States:
West Coast
Natural disasters (e.g., earthquakes)
Animal attacks (e.g., shark attacks)
Risky lifestyle (e.g., scuba diving)
East Coast
Natural disasters (e.g., hurricanes)
Animal attacks (e.g., shark attacks)
Risky lifestyle (e.g., scuba diving)
Heartland
Natural disasters (e.g., tornadoes)
Animal attacks (e.g., bear attacks)
Risky lifestyle (e.g., skiing)
After each of the treatments, participants were asked to select one of two possible cognitive strategies that best described their prior mortality judgments. Participants had to pick one of the following three options:
1. I used analytic reasoning (e.g., “I might have considered background statistics or done some
mental calculations”)
2. I used imagined scenarios (e.g,. “I imagined events that might happen to me”)
3. Other
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Thereafter, participants were asked to produce their best numerical estimates for the following two
rare events:
1. Annually, how many Americans are struck by lightning? (Please indicate a whole number.)
2. Annually, how many Americans are killed in plane crashes? (Please indicate a whole number.)
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