YOLO: Mortality Beliefs andHousehold Finance Puzzles∗

Rawley Z. Heimer†

Boston CollegeKristian Ove R. Myrseth‡

Trinity College DublinRaphael S. Schoenle§

Brandeis University

June 2018

Abstract

We study the effect of subjective mortality beliefs on life-cycle behavior. With new surveyevidence, we document that survival is underestimated by the young and overestimated bythe old. We calibrate a canonical life-cycle model to elicited beliefs. Relative to calibrationsusing actuarial probabilities, the young under-save by 26%, and retirees draw down their as-sets 27% slower, while the model’s fit to consumption data improves by 88%. Cross-sectionalregressions support the model’s predictions: distorted mortality beliefs correlate with savingsbehavior while controlling for risk preferences, cognitive, and socioeconomic factors. Over-weighting the likelihood of rare events contributes to mortality belief distortions.

JEL Codes: D1, D9, E21

∗We are grateful for the assistance of Timothy Stehulak, we thank David Love for generously providing us with hisMatlab programs, and the Qualtrics Research Suite, Diane Mogren, and Kathy Popovich for helping obtain the surveydata. Any remaining errors or omissions are our own.†Boston College, Carroll School of Management. Phone: +1 (216) 774-2623, Email: heimer@bc.edu‡Trinity College Dublin, Trinity Business School. Phone: +353 1896 3462. Email: myrsethk@tcd.ie§Department of Economics and International Business School, Brandeis University. Phone: +1 (617) 680-0114,

Email: schoenle@brandeis.edu

Expectations about future events are crucial to inter-temporal decision-making. Yet, the economic

literature reveals that consumer expectations often fail to align with the correct probabilities. One

way in which individuals err in the formation of expectations is by systematically overweighting

rare events with salient attributes (Bordalo et al. (2012, 2016)).

Motivated by this observation, we consider how the formation of mortality beliefs influences

household financial decision making. Low probability events have the potential to distort individ-

uals’ mortality beliefs and consequently affect economic behavior. For example, while sharks on

average kill only one person per year in the United States (cows kill 20 on average), many people

are afraid of going to the beach during the summer.1 Similarly, during Super Bowl 47, Prudential

Financial Inc. aired a commercial in which 400 individuals were asked to post a blue sticker on

a billboard to indicate the age of the oldest person they know. The resulting distribution skewed

towards the age of 100 years, giving viewers the distinct impression that they would live to be very

old and prompting potential customers to contact Prudential. Indeed, financial practitioners often

use mortality beliefs in long-run financial planning (e.g., Appendix Figure A.1).

This paper presents new survey data on subjective mortality beliefs for approximately 4,500

respondents, administered by a professional survey provider. We find that individuals’ beliefs go

from pessimistic about survival, at young ages, to optimistic as individuals approach retirement

age.2 We attribute this flip from pessimism to optimism to salient, cohort-specific stereotypes of

cause-of-death. Our survey asks respondents to assess the weight placed on different mortality risk

factors during judgment of their own survival likelihood. Young people overweight near-term, rare

events (e.g., plane crashes or animal aggression), and higher weights on such events are associated

with greater survival pessimism. As people age, they place less weight on these rare events, but

more on thoughts of health and the ‘natural course of aging’.

1According to a headline in the August 29, 2015 edition of the L.A. Times, “La Jolla beach closed after sharksighting.”

2We can replicate this finding in canonical household surveys, namely the Survey of Consumer Finances and theHealth and Retirement Survey.

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We then consider the effect of mortality beliefs on lifetime savings by developing a canonical

life-cycle model with pre-cautionary savings. In this model, mortality beliefs s have direct bearing

on the inter-temporal trade-off between consumption today and the discounted present value of

future consumption streams,

V ∗t (·) = maxCt

{u(Ct) + βst+1Et[V∗t+1(·)]}.

Consumers decide throughout the life-cycle whether to save or consume. Thus, even small fi-

nancial mistakes, incurred by modest short-run mortality belief distortions, can by retirement ac-

cumulate into large financial shortfalls. We calibrate the model using a survival belief function,

estimated with elicited transition rates from our new survey. This simple, age-dependent survival

function captures changes in survival optimism over the life-cycle.

Our model simulations show that subjective mortality beliefs cause the average retiree to

undersave by approximately 26 percent relative to a benchmark model, calibrated to actuarial data

from the Social Security Administration (SSA). Owing to retirees’ overestimation of long-run sur-

vival rates, individuals consume about 27 percent less during retirement. These findings suggest

that a life-cycle model calibrated to subjective mortality beliefs gets closer to understanding two

notable puzzles in the household finance literature: many young people undersave towards retire-

ment (Skinner (2007)), and the dis-savings rate is too low for many retirees (Poterba et al. (2011,

2013)).3 Additionally, there is a sharp drop in consumption following retirement (as seen in the

data, e.g., Bernheim et al. (2001)), while consumption in the benchmark model with actuarial

rates continues to rise for several years post-retirement – further evidence that subjective mortality

beliefs improves the realism of the model.4

3For example, just 52 percent of households had assets in personal retirement accounts as of 2008 (Poterba et al.(2011)). And, there was a 4.3 percent annual increase in wealth among 70 to 75-year-olds between 1998 and 2006,even after controlling for personal incomes (Love et al. (2009)).

4The literature contains several compelling explanations for the drop in consumption at retirement, including thenon-separability between consumption and leisure, and home production (see Hurst (2008) for an overview).

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Moreover, we use the simulated method of moments (SMM) to test whether our life-cycle

model can match actual data series on consumption and net worth over the life-cycle. Calibrating

the model to subjective as opposed to objective mortality beliefs improves the model’s fit by be-

tween 50 to 90 percent. Finally, when we augment the model by adding realistic circumstances

that affect household decisions – namely, family formation and uncertain out-of-pocket medical

expenditures – we find that subjective mortality beliefs have independent effects on savings behav-

ior. These effects are qualitatively large relative to the aforementioned, alternative mechanisms.

Our model predictions are supported by cross-sectional regressions drawing on our survey

data, which include answers to off-the-shelf questions from commonly cited household surveys

(e.g., the Survey of Consumer Finances (SCF)): pessimistic survival beliefs are associated with

a greater propensity not to save or even to rely excessively on credit cards on a month-to-month

basis. Similarly, more (less) pessimistic beliefs are associated with an increase (decrease) in the

likelihood of expending savings more quickly, even after accounting for respondents’ age and risk

tolerance. To gauge economic significance, we find that the magnitude of the relationship between

survival beliefs and savings behavior is at least as large as that between savings behavior and

financial literacy – and as that between intended bequests and savings behavior.

Though we are cautious to interpret causality from the reduced-form regression results, we

provide evidence to limit concern over omitted variable bias. The most intuitive candidate alterna-

tive explanation is that these subjective mortality beliefs proxy for individual-level sophistication.

Contrary to this explanation, a strong correlation between mortality beliefs and savings persists

even after controlling for financial and numerical literacy, income, demographic, and educational

differences. We also statistically estimate the scope for omitted variable bias by applying the coeffi-

cient bounding procedure recently introduced by Altonji et al. (2005) and Oster (2016). According

to the procedure, the estimated coefficients are robust and stable to informative control variables,

thereby strengthening our interpretation of the results.

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In the absence of perfectly identified regressions, we construct a novel measure of survival

beliefs based on the relative weighting of salient risks. We use this measure to estimate savings

rates. The weight respondents place on salient risks is presumably orthogonal to other sensible

confounding variables, such as individuals’ health status or general optimism. In fact, we find that

the weight on salient risks explain at least twice as much variation (regression R2) in mortality

beliefs relative to socioeconomic factors, such as income or education. These salient risk factors

also prove externally valid. The number of deaths caused by natural disaster in a respondents’ ZIP

code predicts the respondents’ weight on ‘natural disasters’, but does not predict any of the other

potential risk factor weights. Male respondents place less weight on ‘traffic acidents’, consistent

with higher car insurance premiums for male drivers. Males also place less weight on subjective

health and diet, consistent with males being dismissive of the results of medical screening for

cholesterol and heart health. Indeed, we find that more weight placed on salient mortality risks

predicts lower savings rates.

This paper’s primary contribution is to furnish evidence for a mechanism by which the canon-

ical life-cycle framework becomes more realistic and thereby more effective in explaining empiri-

cal regularities in the literature on consumption and savings decisions. A secondary contribution is

to estimate a survival belief function, which can be applied readily to these and other quantitative

modeling efforts. And our approach is complementary, not exclusive, to mechanisms discussed

elsewhere in the literature. To understand pre-retirement savings, research has examined precau-

tionary savings (Lusardi (1998); Gourinchas and Parker (2002); Boar (2017)), financial literacy

(Anderson et al. (2017); Hubener et al. (2016)), self-control problems (O’Donoghue and Rabin

(1999)), hyperbolic discounting (Laibson (1997); Brown and Previtero (2014)), and stock market

participation (Gomes and Michaelides (2005)). To understand why many retirees do not consume

all of their assets during retirement, some study 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)).

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This paper is also among the first to connect the household finance literature to research

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. That many people purchase too much home

and life insurance (Sydnor (2010); Bhargava et al. (2015)), indicates that these beliefs affect eco-

nomic decisions. Probability weighting has also been applied to seminal theories, such as Cu-

mulative Prospect Theory (Tversky and Kahneman (1992)), which has important implications for

asset prices (Barberis and Huang (2008)) and portfolio choice (Polkovnichenko (2005)). Related

to these studies is a literature on tail events (Barberis (2013)), but few papers measure the ex ante

beliefs of such rare events (Goetzmann et al. (2016)).

Our research is motivated in part by Puri and Robinson (2007), who use longevity beliefs

from the SCF to create a proxy for individuals’ optimism. Puri and Robinson (2007) find that

optimistic mortality beliefs correlate with optimism about economic conditions, and that mortality

optimism predicts many important economic behaviors, such as stock market participation. Yet,

there is not much evidence that optimism, more generally, follows patterns over the life-cycle

that resemble those of subjective mortality beliefs. In documenting distinct patterns in subjective

mortality over the life-cycle and considering the effects thereof, our research thus departs from

Puri and Robinson (2007).

More broadly, we contribute to an emergent literature on the measurement and economic

implications of subjective expectations (Manski (2004)). The strand focusing on mortality beliefs,

specifically, hails back to Hamermesh (1985), and it offers mixed evidence from household in-

terview surveys on the economic consequences of mortality beliefs (Hurd and McGarry (2002);

Elder (2013); Post and Hanewald (2013); Jarnebrant and Myrseth (2013)). A related literature fea-

tures life-cycle models and calibrations to subjective mortality beliefs (Gan et al. (2005); van der

Klaauw and Wolpin (2008); Wu et al. (2015); Bissonnette et al. (2017)), longevity risk (Cocco and

Gomes (2012)), or survival ambiguity (Groneck et al. (2013); Caliendo et al. (2017)). However,

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these studies are mostly addressing the later years of life. Similar to our work, some studies inves-

tigate how individuals form their beliefs, but they tend to consider personal experiences (Kaustia

and Knupfer (2008); Choi et al. (2009); Malmendier and Nagel (2011, 2016); Kuchler and Zafar

(2015)) or limited attention (Carroll (2003); Gabaix (2014)). Our paper contributes to this liter-

ature by providing new evidence that mortality beliefs flip over the life-cycle from pessimism to

optimism, and we furnish evidence for a cognitive mechanism behind these belief distortions: the

salience of causes-of-death. And drawing on these beliefs, we show that the canonical life-cycle

model can achieve an improved fit to life-cycle consumption series by as much as 90 percent. We

thereby link two long-standing household finance puzzles, at opposite sides of the life-cycle, to a

specific cognitive mechanism.

1 Mortality Beliefs Over the Life-cycle

1.1 Survey Description and Sample Characteristics

We contracted Qualtrics Panels to provide us with a survey of 4,500 respondents, screened ac-

cording to national residency and age. We required all respondents 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 age 40. 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 that in the median U.S. household. A little over half are female;

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68 percent have children; and just over half are married. Similar to U.S. population statistics, 29

percent have a bachelor’s degree, and about 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.

The survey starts by asking respondents to indicate their survival likelihood beliefs. Respon-

dents 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 respon-

dents 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 (see the Survey Appendix for an image of the belief elicitation

tool). The slider response mode helps respondents visualize a probability scale. This visualiza-

tion is thought to reduce focal answers relative to open-ended questions, for example, heuristic

responses at 50 percent (Firschhoff and Bruin (1999)).5

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 SCF. On the same pages on which 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)).

5Delavande and Rohwedder (2008) propose a visual ‘bins-and-balls’ elicitation procedure for subjective probabilitydistributions, shown to reduce the proportion of ‘unusable’ responses relative to that obtained from an open-endedresponse 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 estimatesof any probability, including very small probabilities and probabilities tending towards 100 percent.

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Following the elicitation of mortality beliefs, the survey gauges the cognitive factors under-

lying belief construction. First, the survey asks respondents to indicate the weight they place on

certain ‘causes of death’ when assessing their own chances of survival. The ‘causes of death’ can be

categorized as relating to one of three categories: ‘natural causes’ (aging), disastrous events (such

as car and plane crashes), or causes relating to health and diet.6 These questions were constructed

with an eye to the actuarial relative frequency of mortality events, across generations. Accordingly,

the questions reference leading medical causes of death (cancer and heart disease), leading non-

medical causes of death (traffic accidents and physical violence), in addition to much rarer salient

events, such as natural disasters and animal attacks. This allows us to ascertain whether individuals

place reasonable weights on the risk factors, whether weights vary systematically with mortality

belief errors, and whether these weights also predict savings behavior.

The survey elicits savings rates in two different ways, by asking about the share of income

saved, and by asking when respondents plan to expend their savings. 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 commonly referenced household surveys, such as the SCF and the Health

and Retirement Survey (HRS). 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)).

Though a few workhorse household surveys (e.g., the SCF and HRS) also elicit respondent

mortality beliefs, our survey differs principally in three ways. First, the survival beliefs elicited by

our survey are designed for the purpose of calibrating a canonical dynamic life-cycle model. Sec-

ond, by using a ‘slider-tool’ to help respondents visualize the distribution of potential responses,

6We also ask respondents to estimate the number of annual deaths by plane crash and the number of people struckby lightning. The former tends to be negatively related to survival optimism, while the latter is uncorrelated.

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our survey provides potentially more accurate measurement of beliefs by reducing cognitive biases

in numerical survey responses (e.g., respondents’ reliance on focal answers). Third, our survey is,

to the best of our knowledge, unique in that it attempts to diagnose how respondents form their

mortality beliefs. This allows us to better understand the theoretical mechanisms that underlie be-

lief formation. Yet, despite these differences from other household surveys, our survey respondents

tend to exhibit similar distributions of survival beliefs (see Appendix Figure A.2).

1.2 Mortality Beliefs Over the Life-cycle

Our analysis is motivated by Figure 1, which shows that respondents, as they grow older, go from

underestimating to overestimating their longevity. Specifically, both men and women underesti-

mate their expected longevity when they are part of the 58-year-old cohort, or younger. For exam-

ple, a 28-year-old female is projected to live to 86-years-old, but the average 28-year-old female

respondent expects she will live to be 84. For both genders, 68-year-olds are closely calibrated to

their expected longevity, while 78-year-olds overestimate how old they will become.

One reason to have confidence in our finding, that mortality beliefs flip from under- to over-

estimation over the life-cycle, is that we can replicate this result in other household surveys. The

SCF asks respondents how old they will be when they die. Our survey elicits longevity expectations

identically. Appendix Figure A.3, Panel A shows that respondents in the SCF exhibit mortality

beliefs similar to those elicited by our survey. The average SCF respondent who is younger than 50-

years-old underestimates longevity by two to three years (depending on gender), and the average

respondent post-retirement over-estimates longevity by as many years as five.

We also document a flip from under- to over-estimation of mortality beliefs in the HRS (see

Appendix Figure A.3, Panel B). The HRS is different from our survey in that it only includes re-

spondents over 50 years old, and it uses different questions to elicit respondents’ mortality beliefs.

The HRS asks how likely it is that respondents will live to reach a specific age – an age that tends to

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be between 10 and 15 years older than a respondent’s current age. The advantage of the HRS is that

the survey has excellent coverage of old-age cohorts, even respondents who could be in declining

health. Therefore, similar findings in the HRS shore up our confidence that the flip from under- to

over-estimation is not caused by potential selection biases among older survey participants (e.g.,

older respondents’ health status). Finally, our results could also be unique to U.S. respondents, but

Wu et al. (2015) document similar patterns in mortality beliefs in other countries.

For the purpose of parameterizing a life-cycle model in the following section, we estimate

survival beliefs to be a quadratic function of respondents’ age. We then use estimates of this

quadratic shape to test the robustness of mortality belief changes over the life-cycle to personal

characteristics and experimental treatments. The quadratic shape of these survival belief errors

over the life-cycle holds after accounting for respondents’ numerical literacy and treatments that

provide actuarial information, as well as for cigarette smoking and personal health assessments

(see Appendix, Table A.1). These results give us cause to be confident that individuals’ mortality

beliefs are robust to potential confounding factors.

Lastly, confidence in our survey results is shored up by evidence of a mechanism – salience

of cause-of-death – which causes distorted survival beliefs to change systematically over the life-

cycle. We describe evidence of this mechanism in the subsequent sections.

1.3 The Formation of Mortality Beliefs

Our analysis shows that mortality beliefs change systematically over the life-cycle. This is con-

sistent 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 individ-

uals 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, in particular, think they die because of unintended injury or other dis-

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astrous, unnatural causes. Disastrous, unnatural causes-of-death are thought to occur more often

than they do, because individuals overweight salient, but rare events. On the other hand, 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, or when their

own relative good health stands out over the inevitable consequences of aging.7

We provide evidence that the salience of rare events feature disproportionately in the forma-

tion of survival beliefs. Table 2, presents summary statistics on the weights placed on different

causes-of-death, on near-continuous slider scales, ranging from 1 to 100 (we do not require the

sum of the weights across risk factors to sum to 100). In addition to unconditional weights, the

table presents normalized weights that remove the individual fixed effect by dividing each response

by the sum of the weights the respondent places on all nine risk factors. To broadly characterize

the survey evidence, respondents place between a quarter and a half as much weight on dramatic,

non-medical causes, such as physical violence or rare natural disasters, as they do on medical con-

ditions or the survey’s benchmark, ‘the normal course of life and aging’. Even though, according

to the Centers for Disease Control and Prevention, dramatic, non-medical causes account only for

approximately a twentieth of all deaths.

Further, the relative weights on rare events versus natural causes-of-death change systemati-

cally over the life-cycle. The bar graph in Figure 2 shows how the unconditional and the normalized

weights vary by age. The weight on ‘the normal course of life and aging’ and ‘health conditions’

increases in respondent age. For example, the average normalized weight on ‘the normal course of

life and aging’ increases monotonically from 22, at age 28, to 27, at age 78. On the other hand, the

weight on all six rare-event causes-of-death is decreasing in respondent age. These results are con-

sistent with the recent finding that age is negatively related with subjective terrorism fatality risk

(Viscusi and Zeckhauser (2006)), and with the stylized fact that adolescents, compared to young

7It is also possible that older respondents display motivated beliefs (Benabou (2015)), although this explanationwould not account for the pattern obtained among younger respondents.

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adults, tend to overestimate dramatic risk factors (Millstein and Halpern-Felsher (2002); Reyna

and Farley (2006)).

Several features of these data lend credibility to the surveyed subjective weights on different

causes-of-death. Specifically, we regress the normalized risk factor weights on personal demo-

graphic factors – gender, age, income, and education – and geography.8 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 (coef = −0.75, s.e. = 0.16) and

medical conditions (coef = −0.42, s.e. = 0.40), consistent with findings in the medical profession

that men are 20 percent more likely than are women to dismiss results from medical screenings

on cholesterol and heart health (Agency for Healthcare Research and Quality). However, men

place greater weight on risky lifestyles (coef = 1.10, s.e. = 0.17), consistent with leading riskier

lifestyles (Rogers et al. (2010)). On the other hand, they place less weight on traffic accidents

(coef = −0.59, s.e. = 0.17), consistent with men attributing lower risks to driving and paying

higher car insurance premiums as a result.

Further, the relative weight placed on natural disasters corresponds to the actual likelihood

of experiencing a disaster, strengthening our confidence in the survey results.9 We regress the

normalized risk factor weights on the logarithm of one plus the number of natural disaster deaths

in the respondent’s ZIP code over the years 2001 to 2010.10 A one-percent increase in the number

of deaths by natural disaster in the area is associated with 0.93 (s.e. = 0.18) more weight placed

on natural disasters. The number of natural disaster deaths in the respondent’s vicinity does not

predict any of the other eight risk factors.

8For brevity, the paper does not include a table of these regression results.9Other research considers the effect of gun violence on mortality beliefs and finds results similar to ours (Balasub-

ramaniam (2016)).10The number of natural disaster deaths comes from the Spatial Hazard Events and Losses Database (SHELDUS).

The SHELDUS data is provided at the county level. We map counties to ZIP codes using the 2010 concordance fromthe Missouri Census Data Center.

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Having illustrated that these risk factor weights are sensible, we use the following regression

model to assess how they affect variation in mortality beliefs over the life cycle:

survival.optimismi = β0 + β1 · risk.factor.weighti +5∑

k=1

β2k ·Dagek + Γ ·Xi + εi. (1)

where survival.optimism equals P rit [surv(t+ l)] − Prit [surv (t+ l)], where t is respondent

i’s age and l = {1, 2, 5, 10} (P r indicates subjective probabilities, and Pr indicates actuarial prob-

abilities). Dagek is an indicator variable for ages {38, 48, 58, 68, 78}, with age 28 absorbed in the

intercept. The independent variable of interest, risk.factor.weight, is standardized so that a one

standard deviation increase equals a one unit increase. The regression also controls for age, gender,

income, education, and indicators for experimental treatments that provide some respondents with

actuarial information on longevity and survival probabilities. Standard errors, clustered by age,

are calculated using the Wild cluster-bootstrap percentile-t procedure from Cameron et al. (2008).

Equation 1 is estimated separately for each of the nine risk factors.

Figure 3 presents the estimated relation between survival beliefs and respondent weighting

on different causes-of-death. Normal causes-of-death positively predict survival optimism, while

greater weight on rare causes-of-death predicts survival pessimism. For example, a one standard

deviation increase in ‘the normal course of life and aging’ predicts an increase in subjective sur-

vival probability of four percentage points. Meanwhile, all six of the rare event risk factors predict

statistically significant reductions in subjective survival beliefs, by between one and three percent-

age points for a one standard deviation increase in the rare event risk factor.

Furthermore, these salient risk factors better explain the variation in mortality beliefs than do

demographic and socioeconomic characteristics. A regression of survival.optimism on respon-

dent age has an R2 equal to 0.031. Including gender, income, and education raises the R2 to 0.067.

If, instead of the demographic characteristics, the regression includes the nine risk factor weights,

the R2 more than triples to 0.10. These results indicate that salient risk factors are a strong driver

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of life-cycle mortality belief distortions, thereby providing a deep foundation behind the empirical

relation between mortality beliefs and savings rates presented in Section 4.

To further evaluate whether life-cycle mortality belief changes are distinct from other factors

that affect life-cycle savings, we empirically evaluate a few possibly related individual attributes

(see Appendix Section A.7). First, related research (Puri and Robinson (2007)) connects general

economic optimism (measured by surveyed beliefs about future economic conditions) to financial

outcomes. Using the SCF, we do not find evidence that individuals become systematically more

optimistic about the economy as they get older, suggesting that our surveyed mortality beliefs are

a distinct mechanism. Similarly, we do not find that older individuals are more likely to believe

that interest rates and the stock market are going up in the following year (using data from the

Survey of Consumer Expectations). There are also no noticeable life-cycle patterns in individuals’

attitudes towards leaving inheritances (based on SCF data), which suggests that individuals are

not becoming more unselfish as they age. Individual risk tolerance is one important parameter

that changes over the life-cycle from more to less risk seeking (based on SCF data). However the

correlation coefficient between risk-tolerance and survival optimism (longevity optimism) in our

survey data is small and inconsistent across measures (-0.05 and 0.11, respectively). This suggests

that our measure of mortality beliefs is not merely picking up changes in risk tolerance.

Taken together, these findings emphasize the economically significant role of salience in dis-

tortions of subjective mortality beliefs. Generally, rare events receive too much weight. Pessimistic

mortality belief distortions relate positively to rare event risk weights, but negatively to natural risk

weights. The weight on rare events relative to natural causes changes over the life-cycle, thereby

contributing to life-cycle changes in mortality belief distortions .

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2 Modeling the Life Cycle and Subjective Beliefs

This section presents our modeling framework, a canonical dynamic life-cycle model. We high-

light how mortality beliefs impact the maximization problem as they enter the 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 survey-elicited survival transition probabilities.

2.1 Model Setup

Our framework is based on Love (2013). Agents make decisions in discrete time, where t =

0, 1, 2, 3, ...Tretire, ..., T , and Tretire denotes the age 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:

V ∗t (Xt, Pt) = maxCt,φt{u(Ct) + βst+1|tEt[V

∗t+1(Xt+1, Pt+1)] + ...

...β(1− st+1|t)Et[Bt+1(Rt+1(Xt − Ct))]} (2)

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 = φtRrt + (1 − φt)Rf . 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

15

transitory shock Θt. Thus, income evolves as follows,

Yt = Pt−1GtNtΘt (3)

and permanent income transitions according to,

Pt = Pt−1GtNt. (4)

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), where ρ is the curvature of the utility function. We use the

method of endogenous grid-points, described by Carroll (2011) and Love (2013), to numerically

solve the consumer’s problem.

Subjective beliefs play an important role in this framework: Individuals make their consump-

tion 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 ef-

fective period discount rate – that is, through βst+1. Clearly, any alternative explanation that also

leads to a lower discount factor early-in-life and a higher discount factor later-in-life will yield

results similar to ours. When the agent has a bequest motive, beliefs enter additionally through

β(1− st+1), which highlights that st+1 and β are not necessarily isomorphic.

2.2 Calibration

To show the effect of mortality beliefs on life-cycle decision-making, we compare the solutions 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 2010

Social Security Administration Period Life Tables. These transition rates give the likelihood of

16

surviving an additional year, based on population statistics, conditional on surviving to a given

age.

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+ γ2t2 (5)

where t denotes the current age in years. To capture the convexity of survival beliefs over the life-

cycle, we fit st+1|t to a quadratic approximation to the true underlying survival function, St(∆t) =

e−∫ t+∆tt λ(z)dz.11 According to OLS estimates of equation 5, γ0 equals 0.93, γ1 × 100 equals 0.15,

and γ2 × 1002 equals -0.32 (Table 3).

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. For the 2-, 5-, and 10-year survival beliefs, we

use a geometric mean to transform these responses into annual, conditional transition probabilities.

Finally, we normalize the data for age t by subtracting 28 years, the age of the youngest cohort in

our survey.12

Figure 4, 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 percent probability according to actu-

arial data, but believes this probability is 1.8 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

11The AIC criterion rejects higher order specifications of our survival function approximations.12For robustness, we estimate the survival probability function by using the component of the surveyed beliefs that

can be attributed to the salience of rare event risk. Specifically, we project the surveyed survival transition beliefs ontosalient.risk.weights, equal to the respondents’ weight on the ‘normal course of aging’ minus the average of the sixrare-event weights described in Table 2. We then use the predicted survival beliefs (s) to estimate equation 5, yieldingparameter values γ0 = 0.94, γ1 × 100 = 0.05, and γ2 × 1002 = −0.040. The estimates of the life-cycle model usingthis survival belief function are presented in Appendix Figure A.4.

17

percent chance of reaching 95, even though actuarial data predicts she has a 15 percent chance.

Similarly, males are cumulatively pessimistic until they reach 65 years, and optimistic thereafter.

To pin down the other parameters we follow the research on life-cycle behavior that attempts

to match the hump-shape in consumption over the life-cycle (e.g., Gourinchas and Parker (2002)).

As in this literature, we build a life-cycle consumption series from the Consumer Expenditure Sur-

vey (CEX;variable, TOTEXPPQ). Specifically, we follow the approach of Fernandez-Villaverde

and Krueger (2007) to construct consumption profiles that filter out business cycle fluctuations,

cohort effects, and heterogeneity in household size. We use CEX years 1996 to 2003, and convert

the series into 2010 dollars. We then use SMM to target the consumption series given the baseline

of objective beliefs (allowing β and ρ to be free parameters). Our baseline calibration does not

allow for bequests. We estimate the rate of time preference β to be 0.98, and the coefficient of

relative risk aversion ρ to be 6. We set 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. We refer readers to Love (2013)

for justification of these parameter choices. Table 3 summarizes our baseline parameter choice.

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. Appendix Section A.4 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.

18

3 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

less relative to individuals who make decisions based on actuarial statistics. Following retirement,

individuals consume their savings less quickly when acting on their subjective mortality beliefs.

This result holds even after allowing for similar levels of accumulated wealth at retirement. More-

over, heterogeneity in beliefs can exacerbate inequality in outcomes, as we show for heterogeneity

in educational attainment.

3.1 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 5). The following section discusses these results for our main calibration, an average

married U.S. person without dependents. The average person consumes approximately $557, or 2

percent, more of their income per year prior to retirement (Table 4). The difference corresponds

to consumption of 29.8 percent of cash-on-hand versus 22.3 percent in the benchmark case. As a

result of higher annual consumption, the representative individual has approximately a third less

saved upon retirement, $245,491, compared to the benchmark case using actuarial rates, $329,518.

Highlighting the importance of subjective mortality beliefs, the strongest effect on consump-

tion and savings occurs during segments of the life-cycle with larger discrepancies between these

beliefs and actuarial statistics. Sorting results by age, the largest underestimation of survival prob-

abilities occurs between ages 28 and 40. Correspondingly, the effect of subjective beliefs on con-

sumption is most pronounced early in the agent’s working life. Between ages 28 and 40, the

average person with subjective beliefs consumes 87.3 percent of their income versus 79.6 percent

under actuarial beliefs, or $1,914 more annually. Between ages 40 and 50, the effect of subjective

19

beliefs is less pronounced: the average person consumes 88.3 percent of their income, versus 85.3

percent, or $1,209 more.

Owing to the higher rate of consumption pre-retirement, individuals have less income to save

and thus have fewer accumulated assets upon retirement. The average pre-retirement savings rate

under subjective beliefs is 3.5 percent compared to 5.8 percent under the actuarial benchmark. The

difference is especially large early in the accumulation phase: for ages up to 40, the agent has a 7.7

percent lower savings rate. Between age 40 and 50, over-consumption corresponds to a 3 percent

lower savings rate. As a result, the agent with subjective beliefs has $245,491 dollars accumulated

upon retirement, whereas the agent using actuarial statistics has $329,518 dollars.

Subjective mortality beliefs also influence portfolio allocations through their effect on life-

cycle wealth accumulation. Under subjective beliefs, 78.1 percent of pre-retirement savings go into

the risky asset, but only 70.2 percent under actuarial beliefs. Approaching retirement, the share

of savings in the risky asset falls under both calibrations, but under subjective beliefs the level of

savings in the risky asset lags by approximately three to six years that under actuarial beliefs. For

example, it reaches less than 60 percent at age 54 under subjective beliefs, but at age 48 under

actuarial beliefs.

3.2 Model Results During Retirement

Subjective mortality beliefs also affect consumption and savings decisions during retirement. Start-

ing in the mid-fifties, and continuing throughout retirement, individuals consume less compared

to the benchmark-calibrated model. During retirement, the average person consumes $32,054 a

year under subjective beliefs, but $36,240 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.

20

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 $9749.16 a year, but only $7082.53 with subjective beliefs (the bottom left panel

of Figure 5). The slope on the right from the peak of wealth accumulation is steeper under actuarial

than under subjective beliefs, but approximately linear in both cases. At the same time, the lower

level of funds under subjective beliefs leads retirees to hold 70 percent of their assets in stocks.

Retirees under actuarial beliefs on average hold only 59.2 percent of their assets in stocks.

Our life-cycle model calibrated with survey-elicited survival beliefs also produces an im-

proved 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). 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, consump-

tion is smooth around retirement, increases by 0.2 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, 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.

3.3 Quantitative Importance of Mortality Beliefs

3.3.1 Model Estimates Compared to Life-Cycle Data

Here, we test in detail the ability of the model to match actual consumption and savings data series

over the life cycle. We run three estimation exercises. In all of them, the performance of the

basic life-cycle model improves substantially when we use our survey data to calibrate the agent’s

mortality beliefs.

21

We start by following the research on life-cycle behavior that attempts to match the hump-

shape in consumption over the life-cycle (e.g., Gourinchas and Parker (2002)). We use SMM to

target the consumption series (allowing β and ρ to be free parameters), given either objective or

subjective beliefs.

The subjective beliefs calibration does a better job at matching the life-cycle consumption

data (see Figure 6, Panel A). Pre-retirement, the agent with subjective beliefs consumes at levels

significantly closer to the actual data. Furthermore, consumption in the actual data peaks at age

50. Consumption peaks at age 55 for the agent with subjective beliefs and closer to age 75 for the

agent with objective beliefs. Subjective beliefs improve the fit of the model relative to objective

beliefs by 91% as measured by the residual sum of squares (RSS).

We also test the performance of our subjective beliefs calibration of a life-cycle model by

comparing it to data on changes in net worth over the life-cycle. The model simulations compare

changes in net worth, which includes returns on the agent’s assets, to actual changes in net worth

over the life-cycle. Data on individuals’ net worth originates from the 1989 through 2004 waves of

the SCF (specifically, we use the variable “net worth” from the SCF summary extracts). We then

calculate a series of changes in net worth by subtracting age t net worth from age t+1 net worth. We

do so because changes in net worth are a good way to illustrate period-to-period levels of savings.

We also want our model to capture the notable feature of this life-cycle series that is difficult

for standard life-cycle models to explain: starting around the age of 70, wealth de-accumulation

reverses course and slows substantially.

Again, the subjective beliefs calibration does a better job of matching the data using SMM.

The RSS of the subjective beliefs calibration is approximately two thirds that of the objective

beliefs calibration. Though neither the subjective nor objective beliefs calibrations can match the

levels of savings pre-retirement, only the subjective beliefs calibration captures the post retirement

reversal in the pace of wealth de-accumulation. When the agent operates under objective mortality

22

beliefs, the amount of wealth she de-accumulates increases each year until the end of the life-cycle,

a result that significantly contrasts with the data.

Finally, we test the performance of the different mortality belief calibrations by using SMM

to jointly match the consumption and change-in-net-worth life-cycle series. The subjective beliefs

calibration yields a significant improvement to the life-cycle model – a 87 percent improvement in

the model’s fit (measured by the RSS) relative to the objective beliefs calibration (see Panel B of

Figure 6).

3.3.2 Importance of Mortality Beliefs Relative to Established Mechanisms

To further evaluate the quantitative importance of subjective mortality beliefs, we compare their

effect to that of other mechanisms proposed by the literature to make the life-cycle model more

realistic. First, we follow Love (2010) and augment the life-cycle model to allow for family for-

mation and the presence of children in the household. The intuition for why marriage and children

affects life-cycle decision making is that couples have competing preferences over future consump-

tion, and therefore solve a joint maximization problem. Solving this joint problem means that for

any individual, her/his current marginal utility does not necessarily equal the expected marginal

utility from future consumption streams. Also, the presence of children changes the household’s

bequest motive and causes increased out-of-pocket expenses, such as larger housing and college

tuition. We find that subjective beliefs significantly lower the amount of wealth accumulation,

whether or not the agent has formed a family (see Appendix Figure A.5). On the other hand, fam-

ily formation inhibits the agent from accumulating as much wealth early in life, but makes up for

it later in the life-cycle.

Second, we follow De Nardi et al. (2010) to allow for the effects on asset de-accumulation

during retirement of health uncertainty combined with uncertain out-of-pocket medical expendi-

tures (see Appendix Figure A.6). These factors make individuals more cautious about consuming

their retirement assets and, therefore, they maintain greater levels of assets during retirement. We

23

find that our survey-elicited subjective mortality beliefs have approximately as much of an effect

on asset de-accumulation as does medical uncertainty. For example, the agent with no medical

uncertainty completely draws down her assets by the end of the life-cycle. Adding medical uncer-

tainty to the model, and allowing the agent to operate under objective mortality beliefs, increases

the level of assets at the end of the life-cycle to around $40,000. When we make this agent operate

under subjective mortality beliefs, the assets at the end of the life-cycle increases to around $80,000

(these results refer to those in the top quartile of personal incomes). Because this exercise endows

agents with the same amount of wealth at retirement age, these results have the added benefit of

showing that Section 3.2’s results – on the slower pace of dis-savings during retirement when we

estimate the model over the whole life-cycle – do not merely arise from differences in retirement

wealth accumulated for agents operating under subjective versus objective beliefs.

Third, we consider the effect of subjective mortality beliefs on the demand for annuities.

Inkmann et al. (2011) shows that a life-cycle model with realistic frictions – liquidity constraints,

pension incomes, and investment opportunities in the stock market – can match the levels of an-

nuity market participation across households (between 3 and 10 percent). Because agents past

retirement with subjective mortality beliefs think they will live longer than the actuarial likelihood,

this would increase the demand for annuities. One concern is that this increase in demand would

be so large as to make the life-cycle model produce levels of annuity market participation that

no longer fit the data. Table A.2 of the Appendix replicates the model in Inkmann et al. (2011),

but includes a calibration to our survey’s subjective mortality beliefs. We find that subjective be-

liefs increase annuity market participation by a few percentage points, which in some calibrations

doubles the participation rate. However, the model’s frictions dampen the effect of subjective mor-

tality beliefs, such that the levels of annuity market participation in the model remain within a

range comparable to the data on annuity participation.

24

4 Do Mortality Beliefs Affect Household Finances?

4.1 Regression Model

We validate the predictions of the life-cycle model using regression analysis on the individual-level

survey data. Specifically, we estimate the following ordered logit model:

y∗i = β1k · survival.optimismi + Γ ·Xi + εi (6)

where y∗i is the unobserved dependent variable for individual i, and we observe the response

yi =

0 if y∗i ≤ µ1

1 if µ1 < y∗i ≤ µ2

...

k if µk < y∗i

over k categories. We estimate the ordered logit model for two different dependent variables, each

of which gives us a sense of personal savings rates. The first dependent variable is the fraction

of monthly income saved, ranging from ‘needing to rely on credit cards’ to ‘at least 50 percent

of income’. The second asks when respondents plan to use their savings. The independent vari-

able, survival.optimism, equals the difference between subjective and objective probabilities,

P rit [surv(t+ l)]−Prit [surv (t+ l)], where t is respondent i’s age and l = {1, 2, 5, 10}, and sur-

vival 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 respon-

dent’s age, age.category = {38, 48, 58, 68, 78}, while setting 28-year-olds as the omitted category.

The relationship between mortality beliefs and savings is potentially sensitive to other life-cycle

and demographic factors, so the vector Xi controls for many relevant personal characteristics, in-

25

cluding income, education, and marital status, as well as personal preferences, and abilities, such

as risk-tolerance and numerical literacy. We also include fixed effects for respondents’ age, which

control for factors that vary over the life-cycle and affect savings rates. 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 the model with robust standard errors clustered by respondent

age.

Before presenting the estimation results, we discuss the limitations of the regression es-

timates of equation 6 and the identification challenges. The ideal test using observational data

would exploit an exogenous shift in mortality beliefs that affects individual savings rates through

only that channel. In the real world, however, factors that affect subjective mortality beliefs with-

out also affecting other crucial variables are not easy to find. For example, a life-threatening event

could change mortality beliefs, but we would be unable to rule out concurrent changes to individ-

ual risk-tolerance. Because of this, even plausibly exogenous shocks to beliefs could have multiple

effects, leaving our estimates subject to broad concerns about interpretation and endogeneity.

Confronted with limited opportunity to conduct the ideal experiment and the resultant iden-

tification challenge, we gain confidence in our estimates by sensibly considering the sources of

endogeneity that would confound estimates of equation 6. The first source of endogeneity is re-

verse causality. This is an unlikely candidate; while lower (higher) savings rates could cause lower

(higher) mortality beliefs, other factors are certain to play a more significant role in determining

these beliefs. The second source of endogeneity is that some confounding factor that we do not

control for causes both savings rates and mortality beliefs. The most likely candidate factor is

unmeasured ‘individual sophistication’, which would simultaneously cause biased mortality belief

estimates and greater difficulties saving. To this end, all of our subsequent tests control for levels

of education and income. We also control for respondents’ numerical proficiency and financial

literacy to address concern that mortality belief errors are caused by difficulties in understanding

and calculating probabilities. Further, to complement our consideration of candidate omitted fac-

26

tors, we statistically evaluate how large selection on unobservables has to be to explain away our

results, using the approach described by Altonji et al. (2005) and Oster (2016).

Lastly, measurement error could also limit interpretation of the estimates of equation 6. For

example, recall bias could add error to our savings rates measures, and this error could correlate

with other important individual characteristics. For this reason, we show that our regression anal-

ysis is robust to using two different versions of the dependent variable, as well as two different

versions of our independent variable, namely survival and longevity beliefs.

4.2 Regression Estimates

4.2.1 Mortality Beliefs and Savings Rates

Table 5 presents estimates of equation 6. 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 determinants 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 sur-

vival beliefs and savings is brought about by differences in economic circumstances. Columns

4 through 6 are analogous to 1 through 3, except that the independent variable of interest is

longevity.optimism, the difference between the respondent’s subjective longevity beliefs and ex-

pected lifespan according to the SSA. These specifications test for robustness to different ways of

measuring subjective beliefs.

Across all measures, greater survival optimism robustly 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

27

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

of subjective beliefs, longevity.optimism, yields similar findings across the three specifications

(columns 4 through 6).

Next, we examine the effect of survival beliefs on the timing of savings draw-down. The

results are similar and robust (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 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.

To better illustrate the economic significance of the relation between survival optimism and

savings rates, Figure 7 presents fitted estimates of a multinomial logit model of savings choices,

analogous to equation 6. 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 hand-to-mouth consumption

– spending all of their current monthly income – falls from 40 to 24 percent. The likelihood of

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

28

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).

We statistically evaluate the scope for omitted variable bias by applying the coefficient

bounding procedure outlined by Oster (2016). Specifically, the procedure evaluates the potential

for selection on unobservables by testing the sensitivity of the coefficient estimate to the inclusion

of additional controls, while taking into account the change in R2 across regression models. The

key idea is that concern for omitted variable bias lessens as the model gets closer to explaining

all of the variation in the dependent variable – that is, as R2 increases towards its upper bound.

Oster (2016) uses this intuition to develop a test statistic for stability of the coefficient estimate

under reasonable assumptions about the maximum attainable R2.13 Indeed, all of our estimates

of β1k pass this test of coefficient stability (Appendix Table A.3), suggesting the relation between

our measures of savings and mortality beliefs is statistically unlikely to be confounded by omitted

variable bias.

To provide further evidence for our preferred interpretation of the positive statistical relation

between mortality beliefs and savings rates, we construct a novel measure of respondent sensitivity

to salient, rare event risks. The measure, salient.risk.weights, equals respondents’ weight on the

‘normal course of aging’ minus the average of the six rare-event weights described in Table 2.

There are some useful advantages of this measure that may make it less sensitive to concern over

omitted variable bias relative to surveyed mortality beliefs, from our survey and from others in the

literature. First, it accounts for life-cycle changes in mortality beliefs, but is plausibly unrelated

to regular life-cycle patterns, such as earnings risk and human capital attainment. Second, this

measure is unlikely to reflect differences in individuals’ actual survival propensities, because few

people are likely to be killed by these rare events (e.g., plane crashes).

13According to Oster (2016), less than half of recently published papers in the leading economics journals that useobservational data pass this test of coefficient stability.

29

Our new measure of survival beliefs, salient.risk.weights, strongly predicts increased savings

rates. That is, the less concern that subjects have over rare event risks, the more they save or

delay the use of current savings. In Table 5, Panel A, the coefficient on salient.risk.weights is

between 0.06 and 0.11 and is statistically significant at the ten-percent level in columns 7 and 8.

This indicates that a one standard deviation increase in the measure predicts a 6 to 11 percent

increase in the log-odds of moving up a category of ‘share of income saved’. The measure is more

strongly positively related to ‘using savings at a later date’ (Panel B). The coefficient estimate

equals between 0.17 and 0.2 and is statistically significant at the one-percent level in all three

specifications.

In summation, we find that optimistic mortality beliefs strongly predict higher savings rates

even after controlling for sensible confounding factors, such as financial and numerical literacy.

We attribute much of this relationship to some individuals’ overestimation of the likelihood of

rare, but fatal events. However, because individuals’ actual survival odds are unobservable, our

tests are unable to discern how much of this relationship is caused by actual probabilities versus

mis-calibrated beliefs. Furthermore, though the coefficient estimates on subjective beliefs are ro-

bust and stable, our regression specifications can explain at most 12% of the variation in savings

rates (as measured by regression R2). This suggests that there is much scope for other factors to

contribute to people’s savings decisions.

4.2.2 Mortality Beliefs and Retirement Savings Draw-down

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 on retirement savings draw-down. The table uses ordered logit models to estimate equation

6, in which the dependent variable is the rate at which respondents draw down their savings. To test

the importance of bequests, these new specifications include an additional independent variable,

expected.bequests, equal to the chances from 0 to 100 that the respondent will leave an inheritance.

30

The variable is 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 in-

heritances 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 specifi-

cations and statistically significant at the five-percent level in five of six regressions. Consider-

ing estimates from the pooled samples, in column 3, the coefficients on survival.optimism and

expected.bequests equal 0.18 and 0.25, respectively. In column 6, the estimated coefficients on

longevity.optimism and expected.bequests equal 0.35 and 0.24, respectively. The similarly sized

coefficients suggest that mortality beliefs and bequest motives make similar contributions to sav-

ings 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.

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 suggested by actuarial data. Because mortality beliefs affect the individual’s subjective dis-

31

count 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 make the young save less and retirees dis-save 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. Speaking to this issue, 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 prob-

ability 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 (e.g., Poterba (2001)).

Another area to consider is the demand for life insurance and annuities (e.g., Hurwitz and Sade

(2017)). We leave these questions for future research.

32

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Table 1: Survey Respondent CharacteristicsDescription: This table presents data on the characteristics of participants in the survey administered by Qualtrics.

pct. pct.Personal characteristics Savings rates

age share monthly income saved28 12.1 ... rely on credit cards 0.0938 24.6 ... spend all income 0.3248 23.2 ... save ˜ 10% 0.4258 19.0 ... save ˜ 25% 0.1468 16.2 ... save ≥ 50% 0.0478 4.9

when plan to use savings?gender ... any time now 0.21

female 51.9 ... 2 - 5 years from now 0.29male 48.2 ... 6 - 10 years 0.16

... at least 10 years 0.34have children

no 32.2 Financial attributesyes 67.8 investing experience

... very inexperienced 0.39civil status ... somewhat inexperienced 0.25

single 21.9 ... somewhat experienced 0.25partner (not co-habitating) 1.2 ... experienced 0.07

partner (co-habiting) 7.7 ... very experienced 0.03married 50.4

divorced 13.7 risk tolerancewidowed 5.1 ... willing to take substantial financial risk 0.08

... above average 0.22education ... average 0.37

primary school 1.8 ... not willing to take financial risks 0.33high school 21.1

college, no degree 34.1 subjective likelihood of leaving bequest 0.51bachelor’s degree 29.3 financially literate ( = 1) 0.68

master’s degree 11.3 numerically literate ( = 1) 0.56doctorate 2.4

mean median std devgross household income Mortality beliefs (all ages, pooled)

less than $10k 7.0 survival optimism -8.12 -1.42 16.7$10k - $20k 10.1 longevity optimism -2.33 -2.20 14.8$20k - $35k 17.6$35k - $50k 17.2

$50k - $100k 33.2$100k - $200k 13.1

greater than $200k 1.8N = 4, 517

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Table 2: Risk Factors to Judge Subjective Survival ProbabilityDescription: This table presents data on the factors respondents use to judge their own survival probabilities. Respondents are asked to rate eachfactor on a scale of 0 to 100 (the weights do not have to sum to one across risk factors). For the normalized weights, we remove the individual fixedeffect in these responses by dividing the raw weight by the sum of the weights respondent 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?” (0 to 100 scale)raw weights normalized weights (w/in respondent)

variable mean median std dev mean median std dev

BenchmarkThe natural course of life and aging (“normal risk”) 73.69 80 23.79 23.44 20 14.73

Rare event risksTraffic accidents (e.g., car crash) 43.12 44 29.08 11.20 11 6.71Physical violence (e.g., murder) 31.22 20 30.04 7.04 7 5.28

Natural disasters (e.g., earth quakes) 31.72 20 29.68 7.32 7 5.49Animal attacks (e.g., shark attacks) 21.67 9 28.79 4.36 3 4.43Risky lifestyle (e.g., base jumping) 24.58 9 30.81 5.17 3 5.46

’Freak events’ (e.g., choking on your food) 29.75 19 29.37 6.94 6 5.86

Health risksMedical conditions (e.g., cancer and heart disease) 64.16 70 28.55 18.99 17 10.96

Dietary habits (e.g., unhealthy foods) 59.89 65 28.95 17.09 16 9.19

Salience measure of beliefsmean median std dev

Salient risk weights ≡ ...43.43 46 32.38

... The natural course of aging - 16·∑

Rare event risksN = 4, 517

39

Table 3: Life-Cycle Model Baseline ParametersDescription: This table presents the parameters used in the baseline version of the life-cycle model. The parameters γ0, γ1, and γ2 come fromestimates of st+1|t = γ0 + γ1t + γ2t2, where t is the survey respondent’s age minus 28 (28-years-old is the youngest age in our survey), andst+1|t is the predicted beliefs about survival at least one additional year.

Conventional Parameters Value Mortality Beliefs Parameters ValueRisk aversion (ρ) 6 γ0 0.933Bequest parameter (b) 2.5 γ1 × 100 0.149Discount factor (β) 0.98 γ2 × 1002 -0.320Risk-free rate (Rf ) 0.02Equity premium (Re

t −Rf ) 0.04Retirement age (TR) 65Maximum age (T ) 95Uncertain income in retirement? noBequest motive? no

40

Table 4: Life-Cycle Model ResultsDescription: This table presents results from solving the life-cycle model described in Section 2. The life-cycle begins at age 28, ends at 95,and retirement age is 65. Subjective mortality beliefs are our survey-elicited survival probabilities, and objective, actuarial mortality beliefs aretransition rates taken from the Social Security Administration life-tables. All other parameter choices are described in Table 3.

Pre-Retirement Post-RetirementMortality beliefs: Objective Subjective Objective Subjective

Average annual consumptiondollar amount 27,351 27,908 36,240 32,054

fraction of income 0.942 0.966 1.781 1.577fraction of cash-on-hand 0.223 0.298 0.282 0.315

Std. deviation consumptiondollar amount 6,675 5,422 3,079 2,613

fraction of income 0.188 0.142 0.160 0.130fraction of cash-on-hand 0.165 0.195 0.215 0.207

Wealth at retirementdollar amount 329,518 245,491

Investment behaviordollar amount saved 8,620.43 6,299.13 -9,749.16 -7,082.53

average share risky asset 0.702 0.781 0.592 0.700

41

Table 5: Mortality Beliefs and Savings Rates, Regression EvidenceDescription: 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. Theindependent 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 theSocial 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 longevityaccording to the SSA. Salient risk weights uses the risk factor weights in Table 2, and it equals respondents’ weight on the ‘normal course of aging’ minus the average of the six rare-eventweights. 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 beennormalized so that a one unit increase equals a one standard deviation increase. All regression also control for the survival horizon (experimental treatments for eliciting probability of livingat least x number of years, where x ∈ {1, 2, 5, 10}), and indicators for respondents treated with age-cohort-specific information about survival probabilities and expected longevity. Robuststandard 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 ordered logit dep var = frac. monthly income saved(1a) (2a) (3a) (4a) (5a) (6a) (7a) (8a) (9a)

survival optimism (Z) 0.191*** 0.187*** 0.139***(0.034) (0.035) (0.033)

longevity optimism (Z) 0.159** 0.159** 0.121**(0.069) (0.069) (0.059)

salient risk weights (Z) 0.104** 0.0977* 0.0687(0.053) (0.053) (0.056)

financially literate ( = 1) 0.130*** 0.00952 0.158*** 0.0278 0.122*** 0.00621(0.037) (0.049) (0.038) (0.052) (0.032) (0.041)

age FE x x x x x x x x xgender x x x x x x x x xrisk tolerance FE x x x x x x x x xnumerically literate x x x x x x x x xeducation FE x x xincome FE x x xbase category: rely on credit cards... spend all income -2.356*** -2.319*** -1.401*** -2.247*** -2.205*** -1.243*** -2.327*** -2.290*** -1.275***... save ˜ 10% -0.316 -0.278 0.732*** -0.215 -0.171 0.886*** -0.268 -0.230 0.851***... save ˜ 25% 1.704*** 1.743*** 2.885*** 1.802*** 1.848*** 3.039*** 1.772*** 1.811*** 3.000***... save ≥ 50% 3.378*** 3.417*** 4.620*** 3.479*** 3.524*** 4.776*** 3.464*** 3.504*** 4.733***

N = 4, 517

42

Table 5: ... continued, Mortality Beliefs and Savings Rates, Regression Evidence

Panel B ordered logit dep var = when do you plan to use savings?(1b) (2b) (3b) (4b) (5b) (6b) (7b) (8b) (9b)

survival optimism (Z) 0.231*** 0.223*** 0.201***(0.015) (0.017) (0.017)

longevity optimism (Z) 0.0897* 0.0924* 0.0795*(0.052) (0.050) (0.045)

salient risk weights (Z) 0.202*** 0.186*** 0.169***(0.058) (0.055) (0.051)

financially literate ( = 1) 0.345*** 0.275*** 0.374*** 0.297*** 0.295*** 0.251**(0.098) (0.10) (0.096) (0.10) (0.088) (0.099)

age FE x x x x x x x x xgender x x x x x x x x xrisk tolerance FE x x x x x x x x xnumerically literate x x x x x x x x xeducation FE x x xincome FE x x xbase category: any time now... 2 - 5 years from now -0.282* -0.192 0.111 -0.126 -0.0351 0.373 -0.234** -0.149 0.203... 6 - 10 years 1.179*** 1.275*** 1.591*** 1.320*** 1.418*** 1.841*** 1.217*** 1.307*** 1.677***... at least 10 years 1.865*** 1.966*** 2.298*** 1.999*** 2.103*** 2.543*** 1.908*** 2.001*** 2.382***

N = 4, 517

43

Table 6: Dis-savings During Retirement: The Effect of Mortality Beliefs and BequestsDescription: This table presents results from estimating ordered logistic models. Coefficients give the ordered log-odds of moving to a highercategory of the dependent variable. The independent variable survival optimism equals respondent i’s belief in the probability they survive at leastx number of years minus the statistical probability of survival according to the Social Security Administration (SSA) actuarial tables. Longevityoptimism 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 normalizedso that a one unit increase equals a one standard deviation increase. All regression also control for the survival horizon (experimental treatments foreliciting probability of living at least x number of years, where x ∈ {1, 2, 5, 10}), and indicators for respondents treated with age-cohort-specificinformation about survival probabilities and expected longevity. The sample includes respondents age 58 and older. Robust standard errors clusteredby respondent age are in parentheses, and *, **, *** denote statistical significance at the p < 0.10, p < 0.05, p < 0.01 levels, respectively.

ordered logit dep var = when do you plan to use savings?sample: age 58 and older, has children no children pooled has children no children pooled

(1) (2) (3) (4) (5) (6)survival optimism (Z) 0.251*** 0.0113 0.182***

(0.047) (0.084) (0.030)longevity optimism (Z) 0.348** 0.385*** 0.346***

(0.14) (0.061) (0.065)expected bequests (Z) 0.255*** 0.230*** 0.248*** 0.263*** 0.193*** 0.240***

(0.098) (0.038) (0.055) (0.087) (0.028) (0.057)age = 58, omittedage = 68 -0.641*** -0.875*** -0.688*** -0.619*** -0.903*** -0.682***

(0.059) (0.029) (0.031) (0.040) (0.017) (0.021)age = 78 -0.836*** -1.204*** -0.892*** -0.795*** -1.235*** -0.877***

(0.063) (0.079) (0.0044) (0.018) (0.053) (0.025)has children ( = 1) -0.0820 -0.0379

(0.13) (0.14)age FE x x x x x xgender x x x x x xrisk tolerance FE x x x x x xnumerically literate x x x x x xeducation FE x x x x x xincome FE x x x x x xbase category: any time now... 2 - 5 years from now -2.099*** -1.594*** -2.094*** -1.772*** -1.641*** -1.848***... 6 - 10 years -0.658* -0.343 -0.727** -0.342 -0.376** -0.481... at least 10 years 0.435 0.530* 0.290 0.753*** 0.511*** 0.541**N 1,301 489 1,790 1,301 489 1,790

44

Figure 1: Subjective Longevity Beliefs vs. Actuarial DataDescription: The figure compares subjective longevity beliefs to the Social Security Administration’s projected longevity estimated from actuarialprobabilities. Our sample (HMS Survey) includes respondents age 28, 38, 48, 58, 68, and 78, and the survey asks, “About how long do you thinkyou will live? Please indicate the age that you expect to reach.”

Figure 2: Salient Risk Factors Over the Life-CycleDescription: The figure shows how salient risk factors change over the life-cycle, using the data described in Table 2.

46

Figure 3: Salience and Mortality BeliefsDescription: The figure presents estimates of the coefficient β1 from the following OLS regression: survival.optimismi = β0 + β1 ·risk.factor.weighti +

∑5k=1 β2k · Dage

k + Γ · Xi + εi. Survival optimism equals the difference between elicited survival beliefs (“sub-jective survival prob.”) and actuarial probabilities from statistical life tables provided by the Social Security Administration, P rit [surv(t+ l)]−Prit [surv (t+ l)], where l is the probability the respondent survives beyond l ∈ {1, 2, 5, 10} years. Dage

k is an indicator variable for ages38, 48, 58, 68, 78, with intercept absorbing age 28 as a base category. Risk factor weight is equal to the subjective weight respondent i assignsto each of the nine risk factors described in Table 2, elicited using the following survey question: “When you assessed your survival likelihood,to what extent did you place weight on the following risk factors?” We de-mean risk factor weight by dividing the raw weight by the sum of theweights on the nine risk factors. We then convert risk factor weight to a Z-score, with a one unit increase equal to a standard deviation increase. Theregressions also control for age categories, and the vector Xi contains income, education, gender, survival horizon, and indicators for experimentaltreatments that present survival and longevity statistics to respondents. The regressions are estimated separately for each of the nine risk factors.Ninety-five percent confidence intervals are estimated using the Wild cluster-bootstrap percentile-t procedure from Cameron et al. (2008), allowingfor clustering by respondent age.

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Figure 4: Estimated Subjective Survival FunctionDescription: The figure presents the cumulative density of the subjective survival function, st+1|t, for survival up to 95 years, given age t. Weestimate st+1|t = γ0 + γ1t+ γ2t2 using OLS and our survey’s 1-, 2-, 5-, and 10-year elicited survival beliefs. The survey responses on survivalbeliefs 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 transformthese responses into annual, conditional transition probabilities. The data is normalized by subtracting 28 (the age of the youngest respondent cohortin our survey) from age t. The solid black line shows the cumulative probability of surviving to age 95 at age t, given actuarial data from the SocialSecurity Administration.

0%

20%

40%

60%

80%

age: 30 40 50 60 70 80 90

Cumulative prob. of surviving to end of lifecyclefemale

0%

20%

40%

60%

80%

age: 30 40 50 60 70 80 90

male

Objective prob. Subjective prob. 95% Prediction Interval

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Figure 5: Life-Cycle Results: Subjective vs. Objective BeliefsDescription: This figure presents the paths of consumption, savings, cash-on-hand, and the portfolio share of the risky asset obtained from thesolution to the life-cycle model outlined in Section 2. ‘Objective beliefs’ indicates that the model calibration uses year-to-year actuarial survivalrates from the Social Security Administration. ‘Subjective beliefs’ indicates that the model uses the subjective beliefs survival function describedin Figure 4.

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age: 30 40 50 60 70 80 90

consumption (1000s of 2010 dollars)

0

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−10

age: 30 40 50 60 70 80 90

change in net worth (1000s of 2010 dollars)

0

1

2

3

age: 30 40 50 60 70 80 90

cash on hand (100,000s of 2010 dollars)

.4

.6

.8

1

age: 30 40 50 60 70 80 90

share of risky assets

obj. beliefs subj. beliefs

49

Figure 6: Life-Cycle Results: Matching the DataDescription: This figure presents life-cycle paths of consumption and year-to-year changes in net worth. The data series on consumption is fromthe 1997 to 2003 waves of the Consumer Expenditure Survey (CEX), and is filtered to remove business cycle fluctuations, cohort effects, andheterogeneity in household size. The net worth series comes from the 1989 to 2004 waves of the Survey of Consumer Finances (SCF). Both seriesare converted to 2010 dollars. The figures also show the paths of consumption and net worth from the life-cycle model. For the two calibrationsof the life-cycle model, with objective mortality beliefs or with subjective mortality beliefs, we use the simulated method of moments to target thedata series (we allow the subjective discount factor and the curvature of the utility function to be free parameters, while the other parameters arethe same as in the baseline model). In Panel A, we let the model target the consumption series or the change-in-net-worth series independently. InPanel B, we ask the model to jointly target both data series.

15

20

25

30

35

age: 30 40 50 60 70 80

Panel A: independent targetsconsumption (1000s of 2010 dollars)

−6

−3

0

3

6

age: 30 40 50 60 70 80

change in net worth (1000s of 2010 dollars)

15

20

25

30

35

age: 30 40 50 60 70 80

Panel B: joint targeting cons. & ∆ net worthconsumption (1000s of 2010 dollars)

−6

−3

0

3

6

age: 30 40 50 60 70 80

change in net worth (1000s of 2010 dollars)

obj. beliefs subj. beliefs cons. (CEX) or ∆ net worth (SCF)

50

Figure 7: Mortality Beliefs and Savings Rates, Regression EstimatesDescription: The figure presents the predictions from the following multinomial logistic model: f (k, i) = β0k + β1ksurvival.optimismi +βkXi, where f (k, i) is a prediction of the probability that observation i has outcome k. The dependent variable in Figure A is the surveyquestion: “How much of your monthly income do you save? (choose the closest answer from the following)”, with the following set of possibleresponses: 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% ofmy monthly income.” In Figure B the dependent variable is the survey question: “When do you expect to use most of the money you are nowaccumulating 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.” The coefficient β1k capturesthe effect of survival.optimism on the the likelihood of choosing k. Survival.optimism equals P rit [surv(t+ l)] − Prit [surv (t+ l)], andit is standardized so that a one standard deviation increase equals a one unit increase. The vector Xi includes i’s age, gender, income, education,numerical literacy, and risk-tolerance. It also controls for the survival horizon (experimental treatments for the probability of living at least xnumber of years, where x ∈ {1, 2, 5, 10}), and indicators for respondents treated with age-cohort-specific information about survival probabilitiesand expected longevity.

.05

.1

.15

−2 −1 0 1 2survival optimism

Pr(spend > earn, rely on credit)

.2

.25

.3

.35

.4

.45

−2 −1 0 1 2survival optimism

Pr(spend all of my income)

.3

.35

.4

.45

.5

.55

−2 −1 0 1 2survival optimism

Pr(save ~10% of monthly income)

.05

.1

.15

.2

−2 −1 0 1 2survival optimism

Pr(save ~25% of monthly income)

.03

.035

.04

.045

.05

−2 −1 0 1 2survival optimism

Pr(save at least 50%)

Panel A: How much of your monthly income do you save?

.1

.15

.2

.25

.3

−2 −1 0 1 2survival optimism

Pr(use savings any time now)

.2

.25

.3

.35

.4

−2 −1 0 1 2survival optimism

Pr(use savings in 2 − 5 years)

.1

.15

.2

−2 −1 0 1 2survival optimism

Pr(use savings in 6 − 10 years)

.2

.3

.4

.5

−2 −1 0 1 2survival optimism

Pr(use savings > 10 years from now)

Panel B : When do you expect to use your savings?

Online Appendix:

Mortality Beliefs and Household Finance Puzzles

Intended for online publication

A.1: Mortality Beliefs and Financial Planning

Figure A.1 displays the inputs into a personal financial plan used by the online investment service,Betterment.

Figure A.1: Mortality Beliefs and Financial Planning

i

A.2: Subjective Mortality Beliefs in Other Surveys

Figure A.2 compares the distribution of subjective longevity beliefs in the 2010 wave of the Surveyof Consumer Finances to those in our survey (HMS Survey).

Figure A.2: Subjective Longevity Beliefs vs. Actuarial Data

ii

Figure A.3: Subjective Longevity Beliefs vs. Actuarial DataPanel A, Description: The figure compares subjective longevity beliefs in the 2010 wave of the Survey of Consumer Finances (SCF) to the SocialSecurity Administration’s (SSA) projected longevity estimates calculated using actuarial probabilities. For the purposes of illustration, the figurebins respondents in the SCF into their respective age decile, and we calculate and present the mean response (actuarial longevity estimate) of thesegroups. Panel B, Description: This figure comes from the 2014 wave of the Health and Retirement Survey (HRS). It displays the differencebetween individual’s subjective probabilities of survival to objective measures from the SSA. The HRS asks respondents 55 – 64-years-old thechances they will live to 75; 65 – 69-years old the chances they will live to 80; 70 – 74-years old the chances they will live to 85; 75 – 79-years oldthe chances they will live to 90; 80 – 84-years old the chances they will live to 95; and 85 – 89-years old the chances they will live to 100.

Panel A: Survey of Consumer Finances

Panel B: Health and Retirement Survey

−.2

0.2

.4

55 60 65 70 75 80 85 90age

all respondents respondents w/out proxy help

Health and Retirement Survey, 2014

Subjective prob of survival to age ##minus objective survival probability

Female

−.2

0.2

.4

55 60 65 70 75 80 85 90age

all respondents respondents w/out proxy help

Health and Retirement Survey, 2014

Subjective prob of survival to age ##minus objective survival probability

Male

A.3: Survival Beliefs Over the Life-cycle, Robustness

Section 1 demonstrates that average subjective mortality beliefs exhibit over the life-cycle a quadraticshaped flip from underestimation to overestimation. Table A.1 regresses subjective survival prob-ability errors (Panel A) and longevity errors (Panel B) on respondent age. It shows that the flip inmortality beliefs is robust to numerous explanatory variables. These potential confounders oftencause a level-shift in mortality beliefs, but do not negate the quadratic shape of belief errors.

Table A.1: Robustness of Mortality Belief Errors Over the Life-cycleDescription: 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 thep < 0.10, p < 0.05, p < 0.01 levels, respectively.

Panel A dep var = survival optimism (ppt)(1a) (2a) (3a) (4a) (5a) (6a) (7a)

target age of survival horizon squared 0.00511*** 0.00512*** 0.00517*** 0.00509*** 0.00493*** 0.00422*** 0.00508***(0.0014) (0.0014) (0.0014) (0.0014) (0.0014) (0.0013) (0.0014)

target age of survival horizon -0.354** -0.355** -0.360** -0.362** -0.339** -0.255* -0.348**(0.16) (0.16) (0.16) (0.15) (0.16) (0.15) (0.16)

actuarial probabilities info treatment ( = 1) -0.408(0.59)

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) 5.877***(0.34)

children ( = 1) -0.360(0.63)

gender x x x x x x xeducation FE x x x x x x xincome FE x x x x x x xN 4,517 4,517 4,517 4,517 4,515 4,510 4,517R2 0.066 0.066 0.067 0.078 0.067 0.15 0.066

Panel B dep var = longevity optimism (years)(1b) (2b) (3b) (4b) (5b) (6b) (7b)

respondent age squared 0.00275** 0.00278*** 0.00275** 0.00275** 0.00213* 0.00188* 0.00267**(0.0011) (0.0011) (0.0011) (0.0011) (0.0011) (0.0010) (0.0011)

respondent age -0.307*** -0.311*** -0.308*** -0.307*** -0.259** -0.215* -0.295**(0.12) (0.12) (0.12) (0.12) (0.12) (0.11) (0.12)

actuarial probabilities info treatment ( = 1) -1.290***(0.45)

all survival horizons treatments ( = 1) 0.861(0.57)

numerical literacy ( = 1) -0.0160(0.47)

smoker ( = 1) -3.029***(0.56)

subjective health assessment (Z) 4.154***(0.24)

children ( = 1) -0.826*(0.50)

gender x x x x x x xeducation FE x x x x x x xincome FE x x x x x x xN 4,517 4,517 4,517 4,517 4,515 4,510 4,517R2 0.036 0.037 0.036 0.036 0.043 0.11 0.036

iv

A.4: Mortality Tables by Education, and Aggregate Income Process

We construct mortality tables by education in several steps. First, we use Tables 2 and 3 fromthe U.S. Census Bureau American Community Survey to compute the shares of ‘White alone, notHispanic or Latino’, ‘Hispanic or Latino (of any race)’ and ‘Black or African American’, as wellas shares of males and females. These shares are provided in 5-year age-interval, and we use linearinterpolation 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 educationalshares for categories LTHS, HS+, and COL. Because not all combinations of race and educationalattainment are provided in these tables, we use the next lowest educational category if no categoryis available. For ‘Black’, we use HS+ instead of college. For ‘Hispanics’, we use ‘All’ in allthree cases. Fourth, we aggregate categories LTHS, HS+, and COL across gender, using weightsfrom the second step. Finally, we use the educational series as described in Brown et al. (2002) togenerate education-specific mortality series.

We construct the aggregate income path using our estimates for the polynomial fit in eacheducational category to compute income at each given age. Then, we average these income pathsbased 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 permanentaggregate income shocks as the sum of the variances and covariances of LTHS, HS+, and COL,assuming correlations of 0.85.

v

A.5: The Effect of Salience of Mortality Beliefs

This section presents robustness of the life-cycle model described in Section 2 and estimated inSection 3 to an alternative calibration of survival beliefs. Figure A.4 present the results of thelife-cycle model when the survival function is parameterized using the component of survival be-liefs that can be explained by salient rare event risk factors. Specifically, Figure A.4 presentsthe paths of consumption, savings, cash-on-hand, and the portfolio share of the risky asset. ‘Ob-jective beliefs’ indicates that the model calibration uses year-to-year actuarial survival rates fromthe Social Security Administration. ‘Subjective beliefs’ indicates that the model uses the subjec-tive beliefs survival function. Specifically, we calibrate the subjective beliefs survival functionst|t+1 = γ0 + γ1t+ γ2t

2 by projecting salient risk weights (the weight on ‘normal course of aging’minus the average of the six rare event weights) onto our survey-elicited survival probabilities.Then, the predicted survival probabilities s are used to parameterize the survival function via OLSestimates of st|t+1 = γ0+γ1t+γ2t

2. The resulting parameter values are γ0 = 0.94, γ1×100 = 0.05,and γ2 × 1002 = −0.040.

Figure A.4: Life-Cycle Results: Using Salience of Mortality Beliefs

15

20

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30

35

40

age: 30 40 50 60 70 80 90

consumption (1000s of 2010 dollars)

0

5

10

−5

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age: 30 40 50 60 70 80 90

change in net worth (1000s of 2010 dollars)

0

1

2

3

age: 30 40 50 60 70 80 90

cash on hand (100,000s of 2010 dollars)

.4

.6

.8

1

age: 30 40 50 60 70 80 90

share of risky assets

obj. beliefs subj. beliefs

vi

A.6: Model Extensions

This section considers several extensions of the life-cycle model. Figure A.5 presents simulatedlevels of cash-on-hand for the life-cycle model that corresponds to Figure 4 of Love (2010). Thefigure on the left is for married high school graduates, and the right figure is for married collegegraduates. We include simulated paths for households with and without children, and with andwithout subjective mortality beliefs. In accordance with Love (2010), we use a correlation betweenstocks and permanent income equal to 0.15 and a coefficient of relative risk aversion equal to 6.The discount factor for high school graduates is 0.9215, and 0.9050 for college graduates. Thebequest parameter is 3.25 for high school graduates, and 4.00 for college graduates.

Figure A.6 considers the role of health status and medical expenses in determining wealthde-accumulation post-retirement. Specifically, we follow the work of De Nardi et al. (2010) andadd medical expenditure shocks to life expectancy, and bequest motives to the conventional life-cycle model. We also use their calibration of these shocks, which come from the HRS. The onlydifference between our work and theirs is that we estimate a version of the model that is calibratedusing our survey-elicited survival beliefs. Figure A.6 presents the path of household wealth duringretirement. Both graphs have two pairs of lines: (i) individuals hold subjective survival beliefsand are, or are not, subject to out-of-pocket medical expenses, and (ii) individuals hold objectivebeliefs and are, or are not, subject to out-of-pocket medical expenses. These figures mirror Figure9 in De Nardi et al. (2010).

Finally, we study the relation between subjective mortality beliefs and the demand for an-nuities. To do so, we replicate the life-cycle model of Inkmann et al. (2011) and use our esti-mated survival function to calibrate their model. Inkmann et al. (2011) finds that a reasonablycalibrated life-cycle model can achieve levels of annuity market participation that are consistentwith the data (close to a 10% participation rate for stockholders, and a 3% participation rate fornon-stockholders). Contrary to frictionless theoretical models, there are several reasons why manyhouseholds should not purchase annuities. These include pension incomes, better opportunities inthe stock market, liquidity constraints, and because many cannot afford them. Indeed, these find-ings suggest that viewed through the lens of a realistic life-cycle model, the rate of annuity marketparticipation is not so puzzling.

We find that the over-estimation of survival rates for post-retirement individuals makes themodel predict increased levels of annuity market participation (for most calibrations). However,the magnitude of this increase is not so large. As presented in Table A.2, we tend to find thatusing our survey-elicited survival beliefs to calibrate this life-cycle model increases annuity marketparticipation by just a few percentage points. This suggests that our subjective mortality beliefscalibration is not so extreme as to re-introduce the annuity market participation puzzle.

Specifically, we replicate the model’s comparative statics presented in Table 5 of Inkmann,Inkmann et al. (2011). We compare their original calibration to our calibration with subjectivemortality beliefs. The model also features a bequest motive, relative risk aversion ranging from 2to 6, an elasticity of intertemporal substitution ranging from 0.1 to 0.5, a discount factor rangingfrom 0.89 to 0.98, and division between stockholders and non-stockholders. In order to provide asense of how these parameter choices affect annuity market participation rates, Table A.2 presents

vii

model estimates across the range of these parameters (note: to make our results easy to compare,we present model estimates for the parameters choices in Table 5 of Inkmann et al. (2011)).

Figure A.5: Life-Cycle Results: Family Formation

025

050

0

20 40 60 80 100Age

High SchoolAssets (1000s of dollars)

025

050

075

0

20 40 60 80 100Age

CollegeAssets (1000s of dollars)

obj. beliefs, no kids obj. beliefs, has kids subj. beliefs, no kids subj. beliefs, has kids

Figure A.6: Life-Cycle Results: Health Status and Out-of-Pocket Medical Expenses

5010

015

020

0

75 80 85 90 95 100age

obj. beliefs, no medical uncertainty obj. beliefs, medical uncertainty subj. beliefs, no medical uncertainty subj. beliefs, medical uncertainty

Top income quintileAssets (000s of 1998 dollars)

2040

6080

100

75 80 85 90 95 100age

obj. beliefs, no medical uncertainty obj. beliefs, medical uncertainty subj. beliefs, no medical uncertainty subj. beliefs, medical uncertainty

4th income quintileAssets (000s of 1998 dollars)

viii

Table A.2: Subjective Mortality Beliefs and Annuity Market ParticipationPanel A: stockholdersmortality beliefs objective subjectiveBequest parameter, b 6Relative risk aversion, γ 2 2 6 6 2 2 6 6Elast. intertemp. subs, ψ 0.2 0.5 0.2 0.5 0.2 0.5 0.2 0.5With life insurance β = 0.99Annuity m. participation 0.01 0.01 0.29 0.26 0.00 0.00 0.37 0.30Cond. annuity demand 2.52 2.56 5.20 5.16 0.00 0.00 6.58 6.66Cond. sh. of wealth in ann. 0.10 0.11 0.41 0.43 0.00 0.00 0.48 0.51Life insu. m. participation 0.15 0.07 0.36 0.35 0.40 0.40 0.36 0.39Condit. life insu. payout 16.24 12.54 25.30 51.38 44.28 61.80 24.91 48.98Sh. of wealth in life insu. 0.06 0.03 0.20 0.26 0.33 0.31 0.23 0.33Share of wealth in bonds 0.02 0.09 0.16 0.28 0.02 0.08 0.16 0.27Share of wealth in stocks 0.92 0.88 0.64 0.46 0.65 0.61 0.60 0.39Without life insurance β = 0.89Annuity m. participation 0.00 0.00 0.18 0.13 0.00 0.00 0.32 0.28Cond. annuity demand 0.00 0.00 4.67 4.07 0.00 0.00 6.12 6.12Cond. sh. of wealth in ann. 0.00 0.00 0.37 0.37 0.00 0.00 0.44 0.47Share of wealth in stocks 0.77 0.79 0.68 0.70 0.66 0.66 0.62 0.68

Panel B: non-stockholdersmortality beliefs objective subjectiveBequest parameter, b 0.2Relative risk aversion, γ 2 2 3 3 2 2 3 3Elast. intertemp. subs, ψ 0.1 0.5 0.1 0.5 0.1 0.5 0.1 0.5With life insurance β = 0.94Annuity m. participation 0.04 0.04 0.07 0.23 0.05 0.09 0.14 0.17Cond. annuity demand 3.87 5.97 6.16 2.14 8.00 6.34 4.52 4.13Cond. sh. of wealth in ann. 0.43 0.64 0.49 0.32 0.60 0.65 0.45 0.55Life insu. m. participation 0.78 0.85 0.76 0.82 0.89 0.84 0.87 0.79Condit. life insu. payout 7.45 16.25 10.02 15.39 5.91 11.67 7.85 11.62Sh. of wealth in life insu. 0.66 0.65 0.60 0.36 0.73 0.62 0.66 0.39Share of wealth in bonds 0.34 0.35 0.40 0.63 0.27 0.38 0.34 0.60Share of wealth in stocks . . . . . . . .Without life insurance β = 0.88Annuity m. participation 0.03 0.03 0.05 0.04 0.05 0.05 0.10 0.10Cond. annuity demand 3.17 2.89 6.18 4.96 7.83 7.59 5.88 6.33Cond. sh. of wealth in ann. 0.39 0.46 0.49 0.52 0.58 0.66 0.52 0.59Share of wealth in stocks . . . . . . . .

ix

A.7: Variation Over the Life-Cycle of Other Important Variables

To further evaluate whether life-cycle mortality belief changes are distinct from other factors thataffect life-cycle savings, we empirically evaluate a few possibly related individual attributes. Theseindividual attributes include: beliefs about future economic conditions, beliefs about future interestrates and stock markets, attitudes toward leaving inheritances, and general tolerance towards risk.Beliefs about future interest rates and stock markets come from the June 2013 to August 2018editions of the FRBNY Survey of Consumer Expectations. To avoid repeat entries by respondents,we only include individuals’ third-wave responses. The other three data series come from the 2013Survey of Consumer Finances.

Figure A.7: Subjective Beliefs and Attitudes Over the Life-Cycle

x

A.8: Regression Evidence, Selection on Unobservables

We evaluate the robustness to omitted variable bias of the relation between savings rates and mor-tality beliefs (presented in Table 5) by applying the approach described by Altonji et al. (2005)and Oster (2016). The main idea in these papers is to evaluate the scope for omitted variable biasby observing changes in the regression coefficient of interest after including controls, taking intoaccount changes in R2. Moreover, what matters is to take into account the variance of the outcomeand treatment, and information on the share of the treatment variation explained by the observedexplanatory variables.

Using this intuition, Oster (2016) develops a test statistic, δ, for stability of the coefficientestimate with respect to potential unobserved controls. In particular, we follow Proposition 3 inOster (2016), and calculate δ∗ such that we get a treatment effect for our variables of interest that iszero (β = 0). This δ∗ denotes the degree of selection on unobservables relative to observables thatwould be necessary to explain away the estimated coefficient. If for example, unobservables aretwice as important as the observables to produce a treatment effect of zero, this would imply a δ∗

of 2. The calculation of δ∗ requires assumptions about the maximum attainable R2, R2max. Based

on a meta-analysis of published empirical research, Oster (2016) suggests that R2max be set equal

to 1.3 times the R2 of the regression model that includes the full set of available and reasonablecontrols. Values of δ greater than one indicate that it is unlikely for the coefficient estimates to beconfounded by selection on unobservables.

One difference between the test in Oster (2016) and our regression evidence is that an or-dered logit is the appropriate regression specification for the relation between savings and mortalitybeliefs in our survey, while δ is calculated using OLS. Because the ordered logit model does nothave an associated R2, we use OLS to estimate equation 6 and to calculate δ. However, Table A.3also presents the coefficient of interest from the corresponding ordered logit estimator. Clearly, theOLS and ordered logit coefficients change similarly between the regression with and without con-trols (Baseline and Controlled effect), which suggests that the results of Oster (2016)’s test wouldbe similar if we could apply the procedure to the maximum likelihood estimator of the orderedlogit model. The value δ is greater than one in all six combinations of savings rate dependentvariables and mortality belief independent variables. This result provides statistical evidence thatthe reduced form regressions in Table 5 are unlikely to suffer from concern over omitted variablebias.

xi

Table A.3: Selection on Unobservables in Regression EstimatesDescription: This table presents results from estimating δ∗ (calculated in Proposition 3 of Oster (2016)). Estimates of δ > 1 suggest that selectionon unobservables has to be really large to explain away any regression results due to omitted variable bias (drive the coefficient to 0 if it werepossible to include all relevant control variables in the model). The table presents coefficients that correspond to OLS and ordered logit estimatesof equation 6, presented in Table 5. The independent and dependent variables are described in Table 5. The column “Controlled effect” includes allof the control variables described in Table 5. To calculate δ∗, we set R2

max equal to 1.3*R2, where R2 denotes the R-squared from the regressionwith all controls (Controlled effect).

Addendum to Table 5Panel A: Dependent variable: Fraction monthly income savedindep. var. survival optimism (Z) longevity optimism (Z) salient risk weights (Z)

Baseline Controlled effect Baseline Controlled effect Baseline Controlled effectOLS coef. 0.109 0.060 0.102 0.049 0.057 0.029Ologit coef. 0.256 0.201 0.256 0.201 0.127 0.069δ 3.08 2.61 2.63R2 0.013 0.117 0.011 0.116 0.004 0.114

Panel B: Dependent variable: When do you plan to use savings?indep. var. survival optimism (Z) longevity optimism (Z) salient risk weights (Z)

Baseline Controlled effect Baseline Controlled effect Baseline Controlled effectOLS coef. 0.163 0.118 0.057 0.047 0.151 0.098Ologit coef. 0.238 0.139 0.093 0.080 0.240 0.169δ 4.57 9.12 3.35R2 0.019 0.115 0.002 0.107 0.017 0.112

xii

Survey Description:

Mortality Beliefs and Household Finance Puzzles

Intended for online 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) infor-

mation 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 fi-

nancial 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 pro-

fessed 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 remov-

ing 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 28 were randomly assigned to one of the following 16 treatments [3(information

treatments) x 5(transition horizons) + 1(full life horizon) ]. Participants of age x = {38, 48, 58}

were randomly assigned to one of the following 15 treatments: [3(information treatments) x 5(tran-

sition horizons)]. Participants of age 68 were randomly assigned to one of the following 16 treat-

ments: [3(information treatments) x 5(transition horizons) + 1(HRS80)]. Participants of age 78

A

were randomly assigned to one of the following 16 treatments: [3(information treatments) x 5(tran-

sition horizons) + 1(HRS90)]. An overview of the treatments is given below:

14

1. No information, questions about. . .

(a) one-year transition horizon

(b) two-year transition horizon

(c) five-year transition horizon

(d) ten-year transition horizon

(e) 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) five-year transition horizon

(d) ten-year transition horizon

(e) all transition horizons

3. Information about life expectancy and transition probability for y-year-olds

(a) one-year transition horizon

(b) two-year transition horizon14For 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), respondentsreported judgments of their transition probabilities before estimating their expected longevity. In both cases, eachof the estimates was followed by a confidence judgment in the estimate (e.g., “How confident are you in the answerprovided above?”).

B

(c) five-year transition horizon

(d) ten-year transition horizon

(e) 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 treat-

ments 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-factors:

the natural course of life and aging (“normal risk”)

medical conditions (e.g., cancer and heart disease)

C

dietary habits (e.g., unhealthy foods)

traffic accidents (e.g., car crash)

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 strate-

gies that best described their prior mortality judgments. Participants had to pick one of the follow-

ing 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”)

D

3. Other

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 num-

ber.)

5. Numerical and Financial Literacy, and Risk Preferences

These questions are used to assess numerical and financial literacy, as well as financial risk prefer-

ences.

Numerical Literacy:

1. Imagine that we roll a fair, six-sided die 1,000 times. Out of 1,000 rolls, how many times

do you think the die would come up even (2, 4, or 6)?

2. In the Big Bucks Lottery, the chances of winning a $10 prize is 1%. What is your best

guess about how many people would win a $10 prize if 1,000 people each buy a single ticket to

Big Bucks Lottery?

3. In the Acme Publishing Sweepstakes, the chance of winning a car is 1 in 1,000. What

percent of tickets to Acme Publishing Sweepstakes win a car?

Financial Literacy:

1. Suppose you had $100 in a savings account and the interest rate was 2% per year. After

5 years, how much do you think you would have in the account if you left the money to grow? (a)

More than $102, (b) Less than $102, (c) Do not know, (d) Refuse to answer.

2. Imagine that the interest rate on your savings account was 1% per year and inflation was

2% per year. After 1 year, how much would you be able to buy with the money in this account? (a)

More than today, (b) Less than today, (c) Exactly the same, (d) Do not know, (e) Refuse to answer.

E

3. Please tell us whether this statement is true or false. “Buying a single company’s stock

usually provides a safer return than a stock mutual fund.” (a) True, (b) False, (c) Do not know, (d)

Refuse to answer.

Risk Preferences:

Which of the following statements on this page comes closest to the amount of financial risk

that you are willing to take when you save to make investments? (a) Take substantial financial

risk expecting to earn substantial returns, (b) Take above average financial risks expecting to earn

above average returns, (c) Take average financial risks expecting to earn average returns, (d) Not

willing to take any financial risks.

F