Show Summary Details

Page of

date: 13 November 2018

# The Lifetime Dynamics of Health and Wealth

## Summary and Keywords

Life-cycle choices and outcomes over financial (e.g., savings, portfolio, work) and health-related variables (e.g., medical spending, habits, sickness, and mortality) are complex and intertwined. Indeed, labor/leisure choices can both affect and be conditioned by health outcomes, precautionary savings is determined by exposure to sickness and longevity risks, where the latter can both be altered through preventive medical and leisure decisions. Moreover, inevitable aging induces changes in the incentives and in the constraints for investing in one’s own health and saving resources for old age. Understanding these pathways poses numerous challenges for economic models.

The life-cycle data is indicative of continuous declines in health statuses and associated increases in exposure to morbidity, medical expenses, and mortality risks, with accelerating post-retirement dynamics. Theory suggests that risk-averse and forward-looking agents should rely on available instruments to insure against these risks. Indeed, market- and state-provided health insurance (e.g., Medicare) cover curative medical expenses. High end-of-life home and nursing-home expenses can be hedged through privately or publicly provided (e.g., Medicaid) long-term care insurance. The risk of outliving one’s financial resources can be hedged through annuities. The risk of not living long enough can be insured through life insurance.

In practice, however, the recourse to these hedging instruments remains less than predicted by theory. Slow-observed wealth drawdown after retirement is unexplained by bequest motives and suggests precautionary motives against health-related expenses. The excessive reliance on public pension (e.g., Social Security) and the post-retirement drop in consumption not related to work or health are both indicative of insufficient financial preparedness and run counter to consumption smoothing objectives. Moreover, the capacity to self-insure through preventive care and healthy habits is limited when aging is factored in. In conclusion, the observed health and financial life-cycle dynamics remain challenging for economic theory.

# Introduction

The interactions between financial decisions and outcomes (e.g., consumption, labor income, and wealth) and health-related ones (e.g., spending, leisure, status, morbidity, and mortality risks exposure) are complex and evolve over the life cycle. This article reviews the empirical regularities and modeling issues for the joint trajectories of health and wealth in the second half of the life cycle. It presents some of the main challenges for financial wealth accumulation and drawdown that are posed by deteriorating health and the consequent increases in both morbidity and mortality risks exposures. The market-provided instruments to insure, as well as the capacity to self-insure against these health-related risks through health expenditures and leisure choices, are also discussed.

Life-cycle data reveal a continuous decline in self-reported and objectively measured health statuses in adulthood that accelerates for elders (e.g., Smith, 2007). Because current health is a strong predictor of future onsets, its decline leads to continuous increases in exposure to morbidity (e.g., measured by limitations in daily activities or severe chronic conditions) and mortality risks (see Figure 1). This deterioration is conditional on both type and status of employment. Repetitive manual jobs lead to faster health declines (e.g., Schmitz, 2016), whereas retirement is associated with beneficial health effects (e.g., Coe & Zamarro, 2011). Moreover, decreases in longevity are not uniform across socioeconomic status, with agents in the highest income decile expecting to live 11 years longer than those in the lowest one (Bosworth et al., 2016).

A natural explanation for deteriorating health focuses on the biological effects associated with aging and that can be decomposed between pre-determined and induced factors (e.g., Jin, 2010). The former refer to a preestablished timeline with inevitable hormonal and immunological consequences. The latter is induced through wear and tear as well as basal metabolism. Due to complex interactions between the two elements, the relative contributions of predetermined and induced factors to health declines are difficult to establish.

The age-increasing exposure to sickness is conducive to an increase in health expenses. Indeed, total (i.e., all payers) expenses more than triple between youth (19 to 44) and old age (65 to 84) and are multiplied sevenfold afterward (see Table 1). Although the effects on household budget are mitigated by health insurance, out-of-pocket health expenses also increase sharply. Moreover the latter are highly skewed, with annual expenses reaching close to $27,000 in the top 95th percentile compared to less than$1,300 in the 50th to 70th percentile (De Nardi et al., 2015b). Furthermore, health expenditures change in composition toward the end of life with a stagnation in curative care such as doctor visits, hospital stays, drugs, and a substitution toward long-term care (e.g., nursing homes, home care) (De Nardi et al., 2015b). Since only the former expenses are covered by Medicare, and the latter are rarely insured against, spending on long-term care can cause a severe drain on financial resources. Indeed, wealth reserves fall sharply, as much as 50% in the last three years of life and 30% in the last year (De Nardi et al., 2015a).

Consumption expenses unrelated to health display the opposite pattern and tend to fall after retirement, even if we account for the predictable drop in work-related spending such as food away from home and transportation (see Figure 2). This consumption decline parallels the fall in total income (wage plus retirement) that is observed after age 65 (see Figure 3). The drawdown in financial (and especially housing) wealth is much slower, suggesting that net worth is set aside as precautionary reserves against large health-related spending (see Figure 4).

These stylized facts entail challenges for economic models. On the one hand, a pre-determined aging perspective suggests that health-related risks are age-increasing exogenous stochastic processes that condition the optimal life-cycle consumption, labor, portfolio, and insurance choices (e.g., French & Jones, 2011). On the other hand, an induced aging perspective assumes that the evolution of health-related outcomes and risks are at least partially controllable through medical spending and healthy leisure decisions. Modeling health-related expenses as deliberate choices is one of the main motivations of the seminal “health as capital” model of Grossman (1972) in which agents select investment (e.g., medical spending or costly healthy activities) in their depreciable health capital. Autonomous aging processes (e.g., increasing capital depreciation, sickness, or death risk exposures) can be appended in order to replicate observed life-cycle patterns in health statuses. Health-dependent morbidity and mortality distributions can also be added to replicate increasing exposure to health-related risks, although at the cost of significant complexity. In particular, (partially) endogenous mortality entails that financial and health-related decisions are intertwined and can no longer be separated from one another (Hugonnier et al., 2013). Endogenizing morbidity and mortality risks implies that some degree of self-insurance against sickness and death is possible. In particular, the agent can partially program the speed of the health decline and consequently the dynamic path of health-related risks over his remaining horizon. This approach helps rationalize the substitution away from curative care in favor of long-term care that is observed toward the end of life (Hugonnier et al., 2017).

Nonetheless, the possibility of self-insurance against health shocks through health decisions remains limited such that exposure to high health-related expenses cannot be fully hedged. Public safety nets for retirees, such as Social Security, Medicare, and Medicaid do offer some protection. However, social insurance also appears to crowd out insurance through precautionary reserves and therefore partially rationalizes insufficient financial preparedness for old age, especially among the poorer households (Hubbard et al., 1994). This is further evidenced by decisions on the timing of retirement, which tend to minimize the gap between employer-provided and state-provided health insurance, rather than rely on accumulated wealth to cover medical expenses until Medicare is operational.

Rationalizing the drop in post-retirement consumption is also a challenge to economic modeling. Indeed, the fall in income after 65 is predictable; consumption-smoothing objectives should aim at stabilizing non-health/work-related expenses over the life cycle. One potential explanation for the fall is related to non-separable preferences between health, consumption, and leisure. Slowly falling health would warrant slowly falling consumption if the two complement each other and if health declines more rapidly after 65 (Finkelstein et al., 2009). A drop in consumption could be explained by increased leisure after retirement if the two are substitutes.

The slow drawdown in post-retirement wealth is also a challenge for life-cycle theory (Love et al., 2009). The risk of outliving accumulated wealth is a potential rationale, yet that risk can be hedged through annuitization (Yaari, 1965). Paradoxically, the market for annuities remains underdeveloped relative to theoretical predictions (Peijnenburg et al., 2016). Intended bequests could provide another explanation for slow dissavings, but research finds that bequeathed wealth is rather limited in scope and more accidental than intended (Hurd & Smith, 2002). Furthermore, bequeathing wealth can be achieved through life insurance; any remaining wealth should be optimally lowered in accord with the remaining life horizon (e.g., Inkmann & Michaelides, 2012). Finally, large expected health expenses, especially those related to long-term care, could justify slow drawdowns (e.g., Kotlikoff, 1989). Again this risk could be optimally hedged through markets, yet insurance against home- and nursing-care expenditures remains marginal (see Table 2).

In conclusion, the observed life-cycle decisions and outcomes on the health and wealth nexus remain challenging for economic models. The rest of this article is organized as follows. We first highlight the relevant evidence on the life cycles, starting with the trajectories for health and associated risks and expenses, followed by the life cycles for non-health expenses as well as for income and assets. We next look at the implications and challenges for economic modeling, starting with those for the demand for health, followed by those for wealth management and then concluding remarks.

# Evidence on the Health and Wealth Life Cycles

## Health, Risks, and Spending

### Health, Morbidity, and Mortality Risks

The observed life-cycle trajectories of both objective and subjective measures of health statuses are consistent with a steady deterioration throughout adulthood, picking up momentum around mid-life before accelerating in the last phase.1Banks et al. (2015) find that the percentage of agents reporting worse health doubles between ages 40 and 70 (see Figure 5, p. 12), whereas Heiss (2011) finds a doubling of the share of agents in “poor” health between ages 70 and 80 (see Figure 2, p. 124). Similar declines in self-reported health status are reported in Smith (2007) (see Figure 1, p. 740) as well as by Case and Deaton (2005), especially at lower income quartiles (see Figure 6.1, p. 186).

Indeed, the health decline is not uniform across socioeconomic and employment statuses. In particular, the type of work and the perceived degree of on-the-job control and influence have a strong incidence over the speed of health deteriorations: manual, repetitive occupations induce faster health declines compared to white-collar employment (Case & Deaton, 2005; Schmitz, 2016). The fall in health is also affected by the retirement decision. On the one hand, lower post-retirement income and loss of interaction with coworkers can induce a faster decline in early retirees. On the other hand, better sleep and physical activity and lower exposure to employment stress and hazards can improve the health trajectories. Although some ambiguity remains, recent literature points to positive effects of early retirement on health outcomes (e.g., see Coe & Zamarro, 2011; Eibich, 2015; Hallberg et al., 2015, for European evidence).

Since contemporary health is a key predictor of future major health onsets, this lifetime deterioration is accompanied by increases in exposures to sickness and death risks.2 Further evidence of these dynamics is provided in Figure 1, which relies on National Health Interview Survey (NHIS) data for 2015 to plot the life cycles for self-reported “poor/fair” statuses, the incidence of major chronic conditions (heart, stroke, hypertension/high blood pressure, diabetes, lung/breathing, cancer), as well as the self-reported limitations with daily activities. All variables are consistent with an uninterrupted decline in health and an increase in morbidity. Plotting the life cycle of survivorship obtained from U.S. life tables also indicates an accelerating exposure to mortality, particularly after middle age. Notwithstanding an initial fall from birth to puberty, the risk of dying increases exponentially from roughly age 28 onward (Harman, 1991).3

Click to view larger

Figure 1. Health, morbidity, and mortality trajectories, United States 2015 and 2017.

Sources: (1) Arias et al. (2017, Tab. B): survivors born alive, all races and origin, by age (normalized to 1 at age 20) and (2) National Health Interview Survey, 2015 and author’s calculations: fair/poor self-reported health status, reporting any limitations, reporting at least one severe chronic medical conditions (heart, stroke, hypertension/high blood pressure, diabetes, lung/breathing, cancer).

### Composition Effects

The recourse to cross-sectional rather than longitudinal data to chart the life-cycle evolution can distort the perceived dynamics of both health-related and financial variables. Since a person’s age is the current calendar year minus his or her birth year, the life cycles for the agents’ health, morbidity, and mortality levels measured in a given cross-section can confound those of a corresponding birth cohort with the evolution induced by aging. Indeed, these cohort effects can impact health outcomes via differential habits and preferences (e.g., smoking, eating, fitness, etc.), access to technology, or resources (income, wealth, education) across cohorts and be wrongfully attributed to age.4 For example, unhealthy habits, or less efficient medical technology for older cohorts compared to younger ones, would overstate the actual life-cycle deterioration associated with a given individual when illustrated from a cross-sectional perspective.

Moreover, the increased exposure to mortality as agents become older leads to another well-known composition effect that results in under-reporting the true decline in health. Indeed, a positive link between income and health, as well as between health and survivorship entails that the poorer and less healthy die earlier; the measured health status of survivors is consequently higher through an attrition effect (mortality selection). Indeed, Bosworth et al. (2016) report that agents in the 10th income decile expect to live on average 11.3 years longer than those in the 1st decile (84.6 versus 73.3). Moreover, recent research by Heiss et al. (2014) shows that failure to account for attrition leads to severe under-reporting in health decline. Hence, for a cohort aged 53 to 63 in 1994, they estimate that the composition bias is 7% by the time they reach age 69 to 79 in 2010 (i.e., the true decline in health should be 23%, instead of the observed change of 16%) (Heiss et al., 2014) (see Figure 2.5, p. 13).

### Aging Explanations to Declining Health

The medical literature explains the observed health decline through age-dependent natural/biological factors that play an accelerating role in health deteriorations (e.g., Jin, 2010; Robson & Kaplan, 2007; Harman, 1981, 1991). The human capital stock depreciates faster and is more exposed to morbidity at old age, thereby inducing future sickness and declines in health as well as higher exposure to death risk. These biological aging processes can be divided between programmed (i.e., predetermined), and damage/error (i.e., acquired) elements (Jin, 2010).

Predetermined health declines can be seen as a continuation of earlier-age development. Longevity is thus programmed to follow a preestablished timeline intervening at a genetic level (weaker natural selection of genes for elders), at an hormonal level (controlling the biological clock), or at an immunological level whereby antibodies gradually lose their effectiveness and agents become more subject to diseases. The damage and error processes associated with aging result from interaction with the environment. It involves elements such as wear and tear (i.e., living habits), basal metabolism (i.e., rate of living), as well as free radicals linked with cellular and organ malfunctions (Harman, 1981, 1991). The intricate interactions between these two components entail that no clear consensus emerges as to which is more determinant for the health dynamics.

## Health-Related and Other Expenditures

### Health-Related Spending

Continuous declines in health are associated with an age-increasing pattern in both total and out-of-pocket health expenses. This is reflected in Table 1 using US National Health Expenditures data for 2012, which presents total personal health care (PHC) per age group and payer source.5 Young adults (19 to 44) will see total PHC expenses increase 378% by the time they reach 65 to 84, and 727% afterward, while their out-of-pocket contribution to these expenses will increase by 449%, and 986% over the same periods. The accelerating spending in the last phase of life is also confirmed by De Nardi et al. (2015a) who report that average annual expenditures (all payers) are $25,000 between ages 70 and 90, and$43,000 in the last year of life alone.

Table 1. Per-Capita Total Personal Health-Care Spending, United States (in 2012 U.S. Dollars).

Age Group

Total

Medicare

Medicaid

Private Health Ins.

Out of Pocket

Other Payers and Progr.

Total

7,564

1,705

1,237

2,621

1,016

984

–18

3,552

2

1,266

1,237

384

663

–44

4,458

189

975

1,958

563

773

–64

9,513

1,031

1,162

4,759

1,213

1,348

–84

16,872

9,081

1,445

2,615

2,526

1,204

+

32,411

15,429

5,469

3,309

5,549

2,656

Sources: U.S. Center for Medicare and Medicaid Services (2017), and author’s calculations. Other payers are the Department of Defense, and Department of Veterans Affairs, private (e.g., charitable) funding, state, and local assistance and other programs.

Moreover, the average expenditures mask the catastrophic nature of certain health expenses whose distribution is highly skewed. Indeed, De Nardi et al. (2015b) rely on the 1996–2010 waves of the Medicare Current Beneficiary Survey (MCBS) data for U.S. elders (65 and over) to show that average total health expenses (all payers, including nursing homes) in the top 95th spending percentile is $97,880, compared to$7,750 in the 50th to 70th percentile (see Table 5 , p. 14). The share of these expenses borne by individuals can also be catastrophic, with OOPs averaging $26,930 for the top 95th, compared to$1,360 for the 50th to 70th percentiles.

### Changes in Type of Health Expenditures

Besides marked increases, end-of-life spending also changes in composition. Expenses associated with curative care such as doctor visits, hospital stays, drugs (among others) tend to stagnate while long-term care (LTC) such as home care, assisted living, and nursing home spending rises sharply (De Nardi et al., 2015b, p. 22) (see Figure 3). Two features of LTC spending are particularly relevant. First, certain long-term care characteristics are more similar to those found in luxury goods than in necessities consumption. In particular, income and wealth elasticities are higher than for other health expenses, warranting a comfort care interpretation to LTC in the end of life (De Nardi et al., 2015b; Tsai, 2015; Marshall et al., 2010). From that perspective, the shift away from curative in favor of more LTC is consistent with a predetermined biological perspective on aging. As the latter induces inevitable deteriorations in health, it justifies redirecting health spending toward more comfort and less curative care.

Second, formal long-term care expenditures are only partially covered through public programs such as Medicaid and Medicare, with limited scope for market-provided insurance (Brown & Finkelstein, 2011; Finkelstein & McGarry, 2006). This is evidenced in data reported in Table 2. The share of institutional, and community-based LTC expenses paid by private insurers was only 6.3% in 2011, compared to 20.1% for OOPs. The absence of private insurance for long-term care and the limitations imposed by public programs such as Medicare or Medicaid imply that LTC-related out-of-pocket expenses can cause severe stress on financial resources (De Nardi et al., 2015a, 2015b; Marshall et al., 2010; Love et al., 2009; French et al., 2006; Palumbo, 1999). Indeed, financial wealth falls by 50% in the last three years of life, with 30% occurring the last year alone, compared to only 2% per year for survivors (De Nardi et al., 2015a; French et al., 2006).

Table 2. Long-Term Care Total Annual Expenses, United States (in Billions of Dollars, 2011.

Type

Total

Medicare

Medicaid

OOP

Priv. Insur.

Other

Community based

57

31

20

3

2

1

Institutional

134

37

40

36

10

11

Total

191

68

60

39

12

12

Notes: Congressional Budget Office (2013, Ex. 4, p. 10) and author’s calculations. Other payers are the Department of Defense, and Department of Veterans Affairs, private (e.g., charitable) funding, state, and local assistance and other programs.

### Other Consumption

These life-cycle increases in health-related spending differ markedly from other components of total consumption. Figure 2 relies on Consumer Expenditure Survey (CEX) data to plot out-of-pocket health-care spending, as well as other expenses unrelated to health and work (where the latter are proxied by transportation and food away from home).6 Whereas non-health/work spending drops sharply after middle age, health care increases continuously. The share of out-of-pocket health in total consumption spending thus nearly triples from 5.5% at ages 25 to 34, to 15.4% after age 75.

Click to view larger

Figure 2. Consumption spending trajectories (in 2016 U.S. Dollars).

Sources: Tab. 1300, Consumer Expenditure Survey, U.S. Bureau of Labor Statistics, August 2017. Healthcare: Annual average expenditures on health insurance, medical services and supplies, drugs. Non-health/work: Annual average expenditures net of health care, food away from home, and transportation. Unit of analysis: household. Age: reference person.

The drop in non-health consumption at retirement is non-trivial, not fully explained by work-related items, and confirms other findings (e.g., Battistin et al., 2009). Key elements found in the literature are that the fall in consumption occurs primarily in food and work-related items, is robust across countries (e.g., Li et al., 2015, for data on China), or data sets, and is independent of whether retirement is expected or accidental (Banks et al., 1998; Hurst, 2008; Haider & Stephens, 2007). However, it is heterogenous across household characteristics, with married couples, those with large health expenses, low wealth, and previously unemployed individuals cutting back on post-retirement consumption more when compared to others (Lundberg et al., 2003; Banks et al., 2015; Hurst, 2008; Blundell et al., 1994).

## Income and Wealth

### Income

Figure 3 plots the life cycles for median total, wage, and retirement incomes using Survey of Consumer Finances (SCF) data. Wage income constitutes the bulk of total revenues in the first half, peaks at middle age, and falls thereafter under the combined influence of peaking wages at mid-life (e.g., Pelgrin & St-Amour, 2016), and a reduction in hours worked near and after retirement age (see Figure 2a, p. 81). Despite some evidence of increased elders’ participation on the labor market (Bosworth et al., 2016; Bureau of Labor Statistics, 2008; Toossi, 2015), post-retirement wage income is insufficient to compensate the fall in wage income and prevent a slow fall in total disposable revenues.

Click to view larger

Figure 3. Median annual income trajectories (in 2013 U.S. Dollars).

Sources: Survey of Consumer Finances (2013) and author’s calculations. Total income includes wages, retirement and Social Security, proprietary, transfers, and financial incomes net of taxes. Unit of analysis: household. Age: household head.

### Assets

Figure 4 plots the life cycles of median financial, housing assets, as well as net worth, again obtained through SCF data. It reveals the importance of housing wealth, relative to financial assets, which is observed throughout the agents’ life (Banks et al., 1998; Poterba, 2014). Indeed, financial wealth remains low, peaking at less than $65,000 at retirement and falling slowly afterward to$27,000 at age 85. Median housing peaks at $150,000 at 65 and falls more slowly to$98,000 at 85, indicating that unless they are faced with severe income or spending shocks, elders refrain from home downsizing at later stages of life (Poterba et al., 2011; Poterba, 2014).

Click to view larger

Figure 4. Median wealth trajectories (in 2013 U.S. Dollars).

Sources: Survey of Consumer Finances (2013) and author’s calculations. Net worth are total assets minus total debts. Financial assets are transactions and retirement accounts, value of life insurance, and managed and other financial assets. Housing is value of residential houses. Unit of analysis: household. Age: household head.

# Implications and Challenges for Economic Modeling

## Demand for Health

### Benchmark Model of Health as Capital

The deteriorating health conditions can be modeled as purely exogenous stochastic processes, or as resulting from deliberate decisions made by agents. In the latter case, the demand for health by agents has been represented as a demand for human capital since the seminal work of Grossman (1972). The basic setup is deterministic and assumes that individuals can adjust their health capital stock through a health production function that combines current health, health spending, and/or healthy time inputs to produce future health. In the absence of investment, health depreciates at a fixed rate. The demand for health is motivated by implicit services that are modeled through a utilitarian benefit and/or through other means (e.g., an improved capacity to work for the healthier agents). Variants of the Grossman (1972) framework include diminishing returns to investment (Ehrlich & Chuma, 1990), a morbidity-induced stochastic depreciation, and a stochastic horizon. More advanced versions endogenize morbidity and/or mortality risks exposure by making the likelihood of sickness and death a function of either the levels of input(s) or the health level.7 When morbidity and mortality exposures are declining in health status or spending, the demand for health is thus augmented by a demand for self-insurance against sickness and death risks.

Except in polar cases, the basic Grossman (1972) framework is unable to generate realistic time variation in health status, morbidity, or mortality risks. Indeed, in its simplest form with constant parameters, the model predicts constant rates of growth of the health capital. That rate of growth is negative only if depreciation is constantly above the net return on investment (e.g., Hugonnier et al., 2013, 2017). In particular, the non-monotonous and accelerating health-related patterns throughout the life cycle cannot be replicated using age-independent structural technological, preferences, or stochastic parameters. Put differently, aging must be resorted to for the model to generate realistic life cycles.

### Aging and the Life Cycle of Health

A first implementation of aging in life-cycle models is closely linked to the programmed approach of the biological aging literature. By specifying morbidity and mortality shocks as age increasing, this literature emphasizes the inevitability of more exposure to sickness and death as agents become older. Self-insurance against health shocks induced by aging is futile, and optimal decisions on consumption and wealth simply encompass the increasing health spending and increasing death risk at old age as exogenous time-varying stochastic processes.8

A second strand of the literature allows some degree of hedging against increasing morbidity and mortality risks. In the spirit of the damage and error theory of aging, the deterioration through aging results from interactions with the environment. To the extent that these interactions are in part decided by agents, they can somehow mitigate their exposure to aging-induced health risks and/or their consequences. This can be achieved by making the likelihood of sickness and death risks an inverse function of health spending (e.g., Picone et al., 1998; Blau & Gilleskie, 2008). Agents can thus partially postpone the occurrence of morbidity and/or mortality shocks by spending more. However, one criticism of this literature is that the mitigating effects of decisions are immediate. Put differently, there can be no inertia between health-related choices and consequences. In particular, these settings abstract from Long Reach of Childhood effects whereby early medical conditions and decisions have long-lasting effects on future outcomes.9

To address this concern, a third strand of the economic literature encompasses the effects of age within the context of the Grossman (1972) model, where spending and current health inputs produce future health. Improved health lowers the likelihood of future death and of sickness events. Realistic aging processes can then be appended, such as age-increasing health depreciation, consequences of sickness or likelihood of sickness and of death, and/or age-decreasing marginal returns to health spending or leisure. The latter all contribute to lower the desirability of investing in one’s health by augmenting costs and/or decreasing the returns throughout the life cycle (Hugonnier et al., 2013, pp. 702–703). The predicted trajectories of health (and consequently of morbidity and mortality risks exposure) are then much more flexible and can accommodate hump-shaped patterns and accelerating declines (Hugonnier et al., 2017). A non-negligible side benefit of age-dependent technological and stochastic parameters is that they prevent the agent from selecting an infinite lifespan when mortality risk exposure can be hedged and when life is strictly preferable to death.

### Preference for Life Over Death

A well-known methodological issue is the specification of preferences in endogenous mortality settings. The desirability of investing to prolong life is established by comparing the continuation utility of living to that of dying. In the standard setup, the latter is fixed to zero (Yaari, 1965; Hakansson, 1969). Positive utility is therefore required to prevent the counterintuitive case where the agent prefers death to life. Unfortunately, such polar cases occur using popular functionals for utility. For example, an Iso-Elastic (i.e., CRRA) function with curvature index larger than one yields a negative continuation utility; life is less valuable than death, and the agent will seek to invest negative sums to shorten his horizon (Shepard & Zeckhauser, 1984; Rosen, 1988; Hugonnier et al., 2013). Solutions to this problem include specifying death as imposing an infinite utility cost, adding an arbitrary constant to utility when alive, or resorting to the more generalized utility functions such as non-expected utility.10

A related issue is preference over the timing of death. If aging is inevitable, if there are biological upper bounds on the maximal lifespan, and if exposure to mortality risks can be partially controlled through health spending and healthy lifestyles, the question arises: what is the optimal path of health decline leading to high likelihood of death? These issues are addressed by Hugonnier et al. (2017). Relying on a demand for a health model with endogenous mortality risks, they first abstract from aging entirely to show that there exists a sufficient level of health depreciation where it becomes optimal to “close down the shop” (i.e., initiate a dynamic path of health declines eventually leading to high risk of dying), and gradually to indifference between life and death. Interestingly, the decline is optimally accelerated once a certain threshold of health is reached, consistent with the observed accelerating deteriorations and the substitution away from curative care in favor of comfort care. Importantly, allowing for autonomous effects of aging (e.g., age-increasing health depreciation rates and exposure to sickness) only reinforces the incidence of optimal closing-down dynamics.

### Non-Separable Health and Financial Decisions

In the standard Grossman (1972) setup with complete financial markets, health, and financial decisions can be separated from one another under specific conditions. In a first stage, a standard capital investment problem establishes the optimal spending on health. In the second, a claim to the proceeds from health (e.g., higher labor income), net of optimal spending costs, can be sold. The net value of this human capital is then simply added to financial wealth to obtain total (i.e., human plus financial) wealth. The agents then select the second set of controls involving financial decisions under the level and dynamics constraints for total wealth (Hugonnier et al., 2013).

This separation is convenient since it allows financial choices to be made independently, once health-related decisions have been made. Importantly, the modeling of consumption, savings, and portfolio decisions can therefore be performed taking as given the level of health and exposures to sickness or mortality. However, as shown by Hugonnier et al. (2013), such separation is only possible when mortality risk is exogenously set. If—as is more likely—the agent can influence his or her exposure to death risk through health status, the financial and health-related choices become intertwined and cannot be separated. Health spending is conditional on disposable resources and affects the evolution of morbidity and mortality risks that in turn determine how much to save for the future.

## Wealth and Spending

#### Private and Public Funding of Retirement

Savings adequacy for old age has been shown to be problematic, with low-income people tending to have insufficient levels of savings at retirement. This concern is evidenced by observing that near-universal public programs such as Social Security remain the key source of income for much of the population.11 The finding of insufficient accumulated wealth prior to retirement can in part be explained through a crowding-out argument. As emphasized by Hubbard et al. (1994, 1995), public insurance such as Social Security, Medicare, or Medicaid partially hedge downward risks for post-retirement disposable resources, thereby reducing the incentives for maintaining costly precautionary reserves.

#### Health Insurance and Labor Market Outcomes

It was earlier mentioned that the timing decision over retirement has a non-negligible impact on the post-retirement health status. This effect also runs in the opposite direction. Because most Americans are insured under private plans organized through, or sponsored by the employer (Henry J. Kaiser Family Foundation, 2011; Janicki, 2013), the timing of retirement must factor in the effect on out-of-pocket health expenses of losing private coverage, eventually replaced by public insurance such as Medicare after 65.12 Relying on a model with exogenous health spending and longevity shocks, French and Jones (2011) find that extending employer-provided insurance coverage for retirees hastens retirement by about six months, whereas delaying Medicare coverage by two years would delay retirement by about one month. Allowing for endogenous health expenses and mortality, Scholz and Seshadri (2013) find that availability of retiree insurance can hasten retirement by three months.

Health insurance effects on the labor market are not uniquely ascribed to those approaching retirement. Garthwaite et al. (2014) identify significant increases in labor supply when public insurance coverage (Medicaid) is curtailed. This increases occurs through an “employment lock” effect whereby agents try to retain or obtain employer-provided health insurance when access to public insurance is reduced. Similar adjustments through the intensive margin can also occur for different reasons. If health spending and leisure are substitutes in maintaining health, private coverage can also lead to adjustment in hours worked. This is evidenced by Pelgrin and St-Amour (2016) who find that health insurance lowers the effective cost of health care relative to that of leisure and consequently induces a substitution away from leisure and in favor of more spending that can lead to more hours worked over longer periods.

### Retirement Consumption Puzzle

The severe drop in post-retirement, work-unrelated consumption that is highlighted in Figure 2 cannot be rationalized through standard life-cycle models with separable consumption/leisure preferences. This decline is all the more puzzling in that, as mentioned earlier, it is also observed for those agents who retire at the date they elected to do so. The fall in consumption therefore cannot uniquely be attributed to an unexpected decline in disposable resources at retirement (Hurd & Rohwedder, 2005).

From a more general perspective, any variation in preferences, risks, returns, or income characteristics that occur through the life cycle will be matched by corresponding time variation in the propensities to consume, but without altering the underlying consumption smoothing objectives (e.g., Gourinchas & Parker, 2002). Equivalently, agents will optimally try to insulate consumption from stochastic income and spending shocks throughout their lifetime. To see this, consider the model of Heathcote et al. (2014) where heterogeneous agents aged $a$, have stochastic wages given by

$Display mathematics$

select optimal hours worked $hta$ and consumption $cta$, facing three sources of shocks:

• uninsurable macro income shocks (e.g., unemployment, income) $αt$,

• insurable (e.g., through retirement, family, . . .) individual income shocks $εt$,

• uninsurable individual labor disutility shocks (e.g., health shocks) $ψt$,

and income taxation at progressivity rate $τ$. Heathcote et al. (2014) show that log optimal hours $hta$ and consumption $cta$ jointly follow:

$Display mathematics$
(1)

$Display mathematics$
(2)

where $Hi$ and $Ci$ are constants that depend on the preferences (risk aversion, elasticity of inter-temporal substitution, work disutility) and tax parameters and $νhta,νcta$ are age- and time-dependent adjustments.

The optimal life cycles for hours (1) and consumption (2) reveal the fundamental principles of consumption smoothing against income shocks. First, the agents will continuously adjust to any predictable age and time variation in income via the terms $νhta,νcta$. Second, consumption is fully insulated from insurable income shocks $εt$, such as the predictable drop in post-retirement income; rather the adjustment is coming through the hours worked. The insurance mechanism can be formal (e.g., via annuities, savings, retirement plans) or informal (through family arrangements). Third, the uninsurable shocks $(ψt,αt)$ are partially passed through both hours and consumption, with the degree of pass-through depending on preferences parameters implicit in $H1,H2$, and $C1,C2$. Fourth tax progressivity $τ$ also plays a key role in how much of these shocks affect the optimal rules. For example, an unfavorable health shock increasing the disutility of work (high $ψt$) is fully absorbed by hours but not by consumption. Indeed, a high progressivity $τ$ insulates consumption by shifting the burden of the adjustment through hours worked. Similar consumption insulation occur with respect to uninsurable macro income shocks $αt$. Adding death risk does not fundamentally alter the result. Indeed, an agent facing age-independent death risk behaves equivalently to one who is more impatient (see Blanchard, 1985). The consumption smoothing result is also robust to incorporating a finite maximal horizon (e.g., Merton, 1971, p. 390), or age-increasing exposure to death risk (e.g., Hugonnier et al., 2013, pp. 702–703).

### Health-Dependent Utility

State-dependent preferences do not rationalize the abrupt drop in post-retirement consumption, but may explain its slow decline. More precisely, how the marginal utility of consumption is affected by health status has strong consequences for optimal insurance and savings. In particular, positive cross derivatives entail that the marginal utility of consumption is lower in bad health. This reduces the demand for health insurance against detrimental health shocks and also affects the life cycle profile of consumption. Since health falls more rapidly in the second half of life, so does the desirability of future consumption (Finkelstein et al., 2009; Domeij & Johannesson, 2006). Forward-looking agents fully anticipate the drop in marginal utility, and optimally lower savings for old age in favor of more consumption when young and healthier. Using HRS data, Finkelstein et al. (2013) test, and reject the null of health-independence in favor of positive cross derivatives. They estimate that savings are lowered by 4% compared to state-independent alternatives. Note that a similar result obtains under endogenous mortality. Unhealthy individuals facing high death risks behave as more impatient agents and discount more heavily the next-period utility procured by future consumption (Hugonnier et al., 2013).

### Post-Retirement Slow Drawdown

In addition to problematic financial preparedness for old age, the management of wealth during the retirement period is deemed to be sub-optimal. Indeed, whereas pre-retirement resources are often considered to be insufficient, the post-retirement level of dissaving is too slow to accord with standard life-cycle theory. Moreover, allowing for more comprehensive measures of wealth than financial net worth does not alleviate the inadequate dissavings problem; post-retirement wealth depletion remains insufficient given expected lifespan, regardless of how wealth is measured (Love et al., 2009). The main elements put forward to justify slow drawdowns are intended bequests, uncertain lifespan, and age-increasing risks of catastrophic medical expenses.

### Intended Bequests

A slow trajectory of dissaving could be justified through the desire to leave bequests. However the literature finds that most bequests appear to be accidental, rather than intended (Hurd, 1987, 1989; Benartzi et al., 2011). Moreover, the bequeathed amount appears to be relatively small. For example, Hurd and Smith (2002) find that elders aged 70 to 74 consume more than 60% of their wealth before dying and bequeathing residual net worth.

An alternative form of bequest is captured by life insurance which provides hedging against “living too short,” and not leaving enough resources for survivors (Hong & Rios-Rull, 2012; Inkmann & Michaelides, 2012). However, life insurance goes against the evidence of slow dissavings by providing a credible commitment to set aside bequeathed wealth ex-ante, and to free up other resources for consumption purposes.

### Longevity Risks

A natural justification for slow dissavings is lifespan uncertainty. Agents may elect to maintain high levels of assets to accommodate a potentially long post-retirement period. Conditional on low pension wealth and income, a slow drawdown policy can be justified as precautionary savings against the risk of outliving and out-consuming accumulated wealth (e.g., De Nardi et al., 2009).

However, this longevity risk rationale is more difficult to invoke under complete financial markets. Indeed, for actuarially fair contracts, the optimal response is to hedge the risk of “living too long” by fully annuitizing accumulated net worth and therefore guarantee a steady income flow until death (Yaari, 1965). This argument in favor of annuities is all the more valid for healthy agents with a long expected lifespan who are being cross-subsidized by unhealthy ones with a shorter longevity (Mortality Premium). Nonetheless, the rate of annuitization remains too low compared to optimal levels, suggesting an under-valuation of annuities by households (Brown, 2007; Inkmann et al., 2011).

Peijnenburg et al. (2016) review four potential explanations for under-participation in the annuity market. First, market incompleteness entails that exposure to inflation risks remains detrimental in the absence of real annuities. Second, uncertain income or health spending creates background risks that warrant partial annuitization and maintaining precautionary reserves. Third, incomplete annuitization is also justified when the agent intends to leave large bequests (Jousten, 2001; Lockwood, 2012). Finally, potential default of market provider is a strong disincentive against annuities. Despite these elements, Peijnenburg et al. (2016) show that full annuities remain potentially optimal in a life-cycle model where all four caveats are included.

Other explanations focus on the differences between subjective and objective life expectations in explaining low participation in annuities (Gan & Gong, 2007). Individuals are presumably better informed than markets on their true health status and therefore on their actual survival probabilities (Hurd et al., 2001; Hurd & McGarry, 2002). Annuity contracts relying on actuarial tables may over-estimate longevity, and therefore be less attractive for those expecting a shorter lifespan, through a Mortality Premium effect.

### Health-Care Expenses

As is well known, income or spending uncertainty that cannot be hedged through markets induces precautionary savings under standard risk aversion assumptions (Kimball, 1990; Caballero, 1990; Carroll, 1997, 2009). The anticipation of high and potentially catastrophic health-related out-of-pocket expenses justifies maintaining high precautionary reserves after retirement (e.g., Kotlikoff, 1989; Levin, 1995; Palumbo, 1999; Marshall et al., 2010; De Nardi et al., 2015a). Indeed, Dalton and LaFave (2017) use PSID data to show that the onset of severe health-related limitations leads to substantial decreases in income and increases in health expenses. Non-health consumption is imperfectly hedged against these negative income and spending shocks (see also Gertler & Gruber, 2002), particularly for singles who cannot rely on risk-sharing through co-insurance and home production involving their partner.

Finally, Table 2 showed that market-provided insurance against long-term care expenses remains very limited. Research by Finkelstein and McGarry (2006); Ameriks et al. (2016) shows that adverse selection and insurance product flaws are partially at stake to explain low participation in private LTC insurance. Incomplete LTC insurance could explain the insufficient drawdown of financial assets as an optimal response to high anticipated long-term care spending.

# Concluding Remarks

This survey of the life cycle literature has highlighted the complex interactions between financial- and health-related decisions and outcomes. In particular, the uninterrupted deterioration in health that is observed in adulthood increases the exposure to death and sickness risks that in turn accelerate the fall. From an individual perspective, these dynamics create particular challenges for wealth management if an objective of consumption smoothing is required. From a society perspective, they are also challenging in a context of aging population, changing medical technology, and limited public funding of health and retirement expenses (e.g., see Dormont et al., 2010).

Despite a flourishing literature, many research areas remain uncharted. One of the main points of this review is that consumption savings, labor leisure, and retirement decisions cannot be separated from health expenditures and insurance choices. A non-separable analysis of these choices is both warranted and more complicated than when financial and health decisions are treated separately. Incorporating biological processes related to aging complicates the analysis even further. Aging may be inevitable, but the speed and extent of its ravages are partially controllable through spending and healthy habits. The resulting effects on sickness and death risk exposure have profound life-cycle consequences for their financial choices.

## References

Ameriks, J., Briggs, J., Caplin, A., Shapiro, M. D., & Tonetti, C. (2016). Late-in-life risks and the under-insurance puzzle. Working Paper 22726. Washington, DC: National Bureau of Economic Research.Find this resource:

Arias, E., Heron, M., & Xu, J. (2017). United States life tables, 2013. National Vital Statistics Report, 66(3), 1–63.Find this resource:

Asakawa, K., Senthilselvan, A., Feeny, D., Johnson, J., & Rolfson, D. (2012). Trajectories of health-related quality of life differ by age among adults: Results from an eight-year longitudinal study. Journal of Health Economics, 31(1), 207–218.Find this resource:

Banks, J., Blundell, R., Levell, P., & Smith, J. P. (2015). Life-cycle consumption patterns at older ages in the US and the UK: Can medical expenditures explain the difference? IFS Working Papers W15/12. Institute for Fiscal Studies, London.Find this resource:

Banks, J., Blundell, R., & Tanner, S. (1998). Is there a retirement-savings puzzle? American Economic Review, 88(4), 769–788.Find this resource:

Battistin, E., Brugiavini, A., Rettore, E., and Weber, G. (2009). The retirement consumption puzzle: Evidence from a regression discontinuity approach. American Economic Review, 99(5), 2209–2226.Find this resource:

Bell, A., & Jones, K. (2015). Age, period and cohort processes in longitudinal and life course analysis: A multilevel perspective. In C. Burton-Jeangros, S. Cullati, A. Sacker, & David Blane (Eds.), A life course perspective on health trajectories and transitions (chapter 10, pp. 197–213). London: SpringerOpen.Find this resource:

Benartzi, S., Previtero, A., & Thaler, R. H. (2011). Annuitization puzzles. Journal of Economic Perspectives, 25(4), 143–164.Find this resource:

Benjamins, M. R., Hummer, R. A., Eberstein, I. W., & Nam, C. B. (2004). Self-reported health and adult mortality risk: An analysis of cause-specific mortality. Social Science & Medicine, 59(6), 1297–1306.Find this resource:

Blanchard, O. J. (1985). Debt, deficits and finite horizons. Journal of Political Economy, 93(2), 223–247.Find this resource:

Blau, D. M., & Gilleskie, D. B. (2008). The role of employee health insurance in the employment behavior of older men. International Economic Review, 49(2), 475–514.Find this resource:

Blundell, R., Browning, M., & Meghir, C. (1994). Consumer demand and the life-cycle allocation of household expenditures. Review of Economic Studies, 61(1), 57–80.Find this resource:

Bosworth, B. P., Burtless, G., & Zhang, K. (2016). Later retirement, inequality in old age, and the growing gap in longevity between rich and poor. Economic Studies at Brookings, Brookings Institute, https://www.brookings.edu/wp-content/uploads/2016/02/BosworthBurtlessZhang_retirementinequalitylongevity_012815.pdf.Find this resource:

Brown, J. R. (2007, October). Rational and behavioral perspectives on the role of annuities in retirement planning. Working Paper 13537. Washington, DC: National Bureau of Economic Research.Find this resource:

Brown, J. R., & Finkelstein, A. (2011). Insuring long-term care in the United States. Journal of Economic Perspectives, 25(4), 119–142.Find this resource:

Bureau of Labor Statistics. (2008, July). Older workers. In BLS Spotlight on statistics. U.S. Department of Labor.Find this resource:

Caballero, R. J. (1990). Consumption puzzles and precautionary savings. Journal of Monetary Economics, 25, 113–136.Find this resource:

Campbell, D., & Weinberg, J. A. (2015). Are we saving enough? Households and retirement. Federal Reserve Bank of Richmond Economic Quarterly, 101(2), 99–123.Find this resource:

Capatina, E. (2015). Life-cycle effects of health risk. Journal of Monetary Economics, 74, 67–88.Find this resource:

Carroll, C. D. (1997). Buffer-stock saving and the life cycle/permanent income hypothesis. Quarterly Journal of Economics, 112(1), 1–55.Find this resource:

Carroll, C. D. (2009). Precautionary saving and the marginal propensity to consume out of permanent income. Journal of Monetary Economics, 56(6), 780–790.Find this resource:

Case, A., & Deaton, A. (2005). Broken down by work and sex: How our health declines. In D. A. Wise (Ed.), Analyses in the economics of aging (pp. 185–205). Chicago: University of Chicago Press.Find this resource:

Case, A., Fertig, A., & Paxson. C. (2005). The lasting impact of childhood health and circumstance. Journal of Health Economics, 24(2), 365–389.Find this resource:

Case, A., & Paxson, C. (2011). The long reach of childhood health and circumstance: Evidence from the Whitehall II study. Economic Journal, 121(554), F183–204.Find this resource:

Coe, N. B., & Zamarro, G. (2011). Retirement effects on health in Europe. Journal of Health Economics, 30(1), 77–86.Find this resource:

Congressional Budget Office. (2013, June). Rising demand for long-term services and supports for elderly people. Washington, DC: Congress of the United States.Find this resource:

Córdoba, J. C., & Ripoll, M. (2017). Risk aversion and the value of life. Review of Economic Studies, 84(4), 1472–1509.Find this resource:

Cropper, M. L. (1977). Health, investment in health, and occupational choice. Journal of Political Economy, 85(6), 1273–1294.Find this resource:

Currie, J., & Madrian, B. C. (1999). Health, health insurance and the labor market. In O. Ashenfelter & D. Card (Eds.), Handbook of labor economics (vol. 3, pp. 3310–3416). Amsterdam: Elsevier Science, North-Holland.Find this resource:

Cutler, D., Deaton, A., & Lleras-Muney, A. (2006). The determinants of mortality. Journal of Economic Perspectives, 20(3), 97.Find this resource:

Cutler, D. M., Lleras-Muney, A., & Vogl, T. (2008). Socioeconomic status and health: Dimensions and mechanisms. NBER Working Paper 14333. Cambridge, MA: National Bureau of Economic Research.Find this resource:

Dalton, M., & LaFave, D. (2017). Mitigating the consequences of a health condition: The role of intra- and interhousehold assistance. Journal of Health Economics, 53, 38–52.Find this resource:

De Nardi, M., French, E., & Bailey Jones, J. B. (2009). Life expectancy and old age savings. American Economic Review, 99(2), 110–115.Find this resource:

De Nardi, M., French, E., & Bailey Jones, J. B. (2010). Why do the elderly save? The role of medical expenses. Journal of Political Economy, 118(1), 39–75.Find this resource:

De Nardi, M., French, E., & Bailey Jones, J. B. (2015a, June). Savings after retirement: A survey. Working Paper 21268. Cambridge, MA: National Bureau of Economic Research.Find this resource:

De Nardi, M., French, E., Jones, J. B., & McCauley, J. (2015b, June). Medical spending of the U.S. elderly. Working Paper 21270. Cambridge, MA: National Bureau of Economic Research.Find this resource:

Deaton, A., & Paxston, C. (1998). Aging and inequality in health and income. American Economic Review, 88(2), 248–253.Find this resource:

Domeij, D., & Johannesson, M. (2006). Consumption and health. B.E. Journal of Macroeconomics: Contributions to Macroeconomics, 6(1), 1–30.Find this resource:

Dormont, B., Martins, J. O., Pelgrin, F., & Suhrcke, M. (2010). Health, expenditure, longevity and growth. In P. Garibaldi, J. O. Martins, & J. van Ours (Eds.), Ageing, health, and productivity: The economics of increased life expectancy (pp. 1–98). Oxford: Oxford University Press.Find this resource:

Ehrlich, I., & Chuma, H. (1990). A model of the demand for longevity and the value of life extension. Journal of Political Economy, 98(4), 761–782.Find this resource:

Eibich, P. (2015). Understanding the effect of retirement on health: Mechanisms and heterogeneity. Journal of Health Economics, 43, 1–12.Find this resource:

Finkelstein, A., Erzo F., Luttmer, P., & Notowidigdo, M. J. (2009). Approaches to estimating the health state dependence of the utility function. American Economic Review, 99(2), 116–121.Find this resource:

Finkelstein, A., Erzo F., Luttmer, P., & Notowidigdo, M. J. (2013). What good is wealth without health? The effect of health on the marginal utility of consumption. Journal of the European Economic Association, 11(Suppl.), 221–258.Find this resource:

Finkelstein, A., & McGarry, K. (2006). Multiple dimensions of private information: Evidence from the long-term care insurance market. American Economic Review, 96(4), 938–958.Find this resource:

Fonseca, R., Michaud, P.-C., Galama, T., & Kapteyn, A. (2013, September). Accounting for the rise of health spending and longevity. Discussion Paper 7622, IZA. Bonn, Germany: Institute for the Study of Labor.Find this resource:

Foster, A. C. (2010, February). Out-of-pocket health care expenditures: a comparison. Technical Report. Monthly Labor Review. Washington, DC: U.S. Department of Labor, Bureau of Labor Statistics.Find this resource:

French, E. (2005). The effects of health, wealth, and wages on labour supply and retirement behaviour. Review of Economic Studies, 72(2), 395–427.Find this resource:

French, E., De Nardi, M., Jones, J. B., Baker, O., & Doctor, P. (2006). Right before the end: Asset decumulation at the end of life. Federal Reserve Bank of Chicago Economic Perspectives, 30(3), 2–13.Find this resource:

French, E., & Jones, J. B. (2011). The effects of health insurance and self-insurance on retirement behavior. Econometrica, 79(3), 693–732.Find this resource:

Gan, Li, & Gong, G. (2007). Estimating interdependence between health and education in a dynamic model. Working Paper 12830. Cambridge, MA: National Bureau of Economic Research.Find this resource:

Garthwaite, C., Gross, T., & Notowidigdo, M. J. (2014) Public health insurance, labor supply, and employment lock. Quarterly Journal of Economics, 129(2), 653–696.Find this resource:

Gertler, P., & Gruber, J. (2002). Insuring consumption against illness. American Economic Review, 92(1), 51–76.Find this resource:

Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society, 115, 513–585.Find this resource:

Gourinchas, P.-O., & Parker, J. A. (2002). Consumption over the life cycle. Econometrica, 70(1), 47–89.Find this resource:

Grossman, M. (1972). On the concept of health capital and the demand for health. Journal of Political Economy, 80(2), 223–255.Find this resource:

Haider, S. J., & Stephens, M. (2007). Is there a retirement-consumption puzzle? Evidence using subjective retirement expectations.” Review of Economics and Statistics, 89(2), 247–264.Find this resource:

Hakansson, N. H. (1969). Optimal investment and consumption strategies under risk, an uncertain lifetime, and insurance. International Economic Review, 10(3), 443–466.Find this resource:

Hall, R. E., & Jones, C. I. (2007). The value of life and the rise in health spending. Quarterly Journal of Economics, 122(1), 39–72.Find this resource:

Hallberg, D., Johansson, P., & Josephson, M. (2015). Is an early retirement offer good for your health? Quasi-experimental evidence from the army. Journal of Health Economics, 44, 274–285.Find this resource:

Harman, D. (1981). The aging process. Proceedings of the National Academy of Sciences of the United States of America, 78(11), 7124–7128.Find this resource:

Harman, D. (1991). The aging process: Major risk factor for disease and death. Proceedings of the National Academy of Sciences of the United States of America, 88(12), 5360–5363.Find this resource:

Heathcote, J., Storesletten, K., & Violante, G. L. (2014). Consumption and labor supply with partial insurance: An analytical framework. American Economic Review, 104(7), 2075–2126.Find this resource:

Heckman, J., & Robb, R. (1985). Using longitudinal data to estimate age, period and cohort effects in earnings equations. In W. M. Mason & S. E. Fienberg (Eds.), Cohort analysis in social research: Beyond the identification problem (pp. 137–150). New York: Springer-Verlag.Find this resource:

Heiss, F. (2011). Dynamics of self-rated health and selective mortality. Empirical Economics, 40(1), 119–140.Find this resource:

Heiss, F., Venti, S. F., & Wise, D. A. (2014, July). The persistence and heterogeneity of health among older Americans. Working Paper 20306. Cambridge, MA: National Bureau of Economic Research.Find this resource:

Henry J. Kaiser Family Foundation. (2011). Employer health benefits: 2011 annual survey. Menlo Park CA: Henry J. Kaiser Family Foundation.Find this resource:

Hong, J. H., & Rios-Rull, J.-V. (2012). Life insurance and household consumption. American Economic Review, 102(7), 3701–3730.Find this resource:

Hubbard, R. G., Skinner, J., & Zeldes, S. P. (1994). Expanding the life-cycle model: Precautionary saving and public policy. American Economic Review, 84(2), 174–179.Find this resource:

Hubbard, R. G., Skinner, J., & Zeldes, S. P. (1995). Precautionary saving and social insurance. Journal of Political Economy, 103(2), 360–399.Find this resource:

Hugonnier, J., Pelgrin, F., & St-Amour, P. (2013). Health and (other) asset holdings. The Review of Economic Studies, 80(2), 663–710.Find this resource:

Hugonnier, J., Pelgrin, F., & St-Amour, P. (2017, February). Closing down the shop: Optimal health and wealth dynamics near the end of life. Research Paper 17–11. Geneva, Switzerland: Swiss Finance Institute.Find this resource:

Hurd, M. D. (1987). Savings of the elderly and desired bequests. American Economic Review, 77(3), 298–312.Find this resource:

Hurd, M. D. (1989). Mortality risk and bequests. Econometrica, 57(4), 779–813.Find this resource:

Hurd, M. D. (2002). Portfolio holdings of the elderly. In L. Guiso, M. Haliassos, & T. Jappelli (Eds.), Household portfolios (pp. 431–472). Cambridge MA: MIT Press.Find this resource:

Hurd, M. D., McFadden, D., & Merrill, A. (2001). Predictors of mortality among the elderly. In D. A. Wise (Ed.), Themes in the economics of aging (pp. 171–197). NBER Conference Report series. Chicago and London: University of Chicago Press.Find this resource:

Hurd, M. D., & McGarry, K. (2002). The predictive validity of subjective probabilities of survival. Economic Journal, 112(482), 966–985.Find this resource:

Hurd, M. D., & Rohwedder, S. (2005, February). The retirement-consumption puzzle: Anticipated and actual declines in spending at retirement. Working Paper Series WR-242. RAND, Santa Monica (CA).Find this resource:

Hurd, M. D., & Smith, J. P. (2002, July). Expected bequests and their distribution. Working Paper Series DRU-3007. RAND, Santa Monica (CA).Find this resource:

Hurst, E. (2008, February). The retirement of a consumption puzzle. Working Paper 13789. Cambridge, MA: National Bureau of Economic Research.Find this resource:

Inkmann, J., Lopes, P., & Michaelides, A. (2011). How deep is the annuity market participation puzzle? Review of Financial Studies, 24(1), 279–319.Find this resource:

Inkmann, J., & Michaelides, A. (2012). Can the life insurance market provide evidence for a bequest motive? Journal of Risk and Insurance, 79(3), 671–695.Find this resource:

Janicki, H. (2013, February). Employment-based health insurance: 2010. Household Economic Studies, Census Bureau. Washington, DC: U.S. Department of Commerce.Find this resource:

Jin, K. (2010). Modern biological theories of aging. Aging and Diseases, 1(2), 72–74.Find this resource:

Jousten, A. (2001). Life-cycle modeling of bequests and their impact on annuity valuation. Journal of Public Economics, 79(1), 149–177.Find this resource:

Kimball, M. S. (1990). Precautionary saving in the small and in the large. Econometrica, 58(1), 53–73.Find this resource:

Kotlikoff, L. J. (1989). Health expenditures and precautionary savings. In L. J. Kotlikoff (Ed.), What determines savings? (pp. 141–162). Cambridge, MA: MIT Press.Find this resource:

Kuhn, M., Wrzaczek, S., Prskawetz, A., & Feichtinger, G. (2015). Optimal choice of health and retirement in a life-cycle model. Journal of Economic Theory, 158 (Part A), 186–212.Find this resource:

Levin, L. (1995). Demand for health insurance and precautionary motives for savings among the elderly. Journal of Public Economics, 57(3), 337–367.Find this resource:

Li, H., Shi, X., & Wu, B. (2015). The retirement consumption puzzle in China. American Economic Review, 105(5), 437–441.Find this resource:

Lockwood, L. M. (2012). Bequest motives and the annuity puzzle. Review of Economic Dynamics, 15(2), 226–243.Find this resource:

Love, D. A., Palumbo, M. G., & Smith, P. A. (2009). The trajectory of wealth in retirement. Journal of Public Economics, 93(1–2), 191–208.Find this resource:

Love, D. A., Smith, P. A., & McNair, L. C. (2008). A new look at the wealth adequacy of older U.S. households. Review of Income and Wealth, 54(4), 616–642.Find this resource:

Lubitz, J., Cai, L., Kramarow, E., & Lentzner, H. (2003). Health, life expectancy, and health care spending among the elderly. New England Journal of Medicine, 349(11), 1048–1055.Find this resource:

Lundberg, S., Startz, R., & Stillman, S. (2003). The retirement-consumption puzzle: A marital bargaining approach. Journal of Public Economics, 87(5–6), 1199–1218.Find this resource:

Makeham, W. (1860). On the law of mortality and the construction of annuity tables. Journal of the Institute of Actuaries and Assurance Magazine, 8, 301–310.Find this resource:

Marshall, S., McGarry, K. M., & Skinner, J. S. (2010). The risk of out-of-pocket health care expenditure at end of life. Working Paper 16170. Cambridge, MA: National Bureau of Economic Research.Find this resource:

Meer, J., Miller, D. L., & Rosen, H. S. (2003). Exploring the health-wealth nexus. Journal of Health Economics, 22(5), 713–730.Find this resource:

Merton, R. C. (1971). Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3(4), 373–413.Find this resource:

Ozkan, S. (2011). Income inequality and health care expenditures over the life cycle. Washington, DC: Federal Reserve Board.Find this resource:

Palumbo, M. G. (1999). Uncertain medical expenses and precautionary saving near the end of the life cycle. Review of Economic Studies, 66(2), 395–421.Find this resource:

Pang, G., & Warshawsky, M. J. (2013). Retirement savings adequacy of US workers. Working Paper 2263379. SSRN, https://ssrn.com/abstract=2263379.Find this resource:

Peijnenburg, K., Nijman, T., & Werker, B. J. M. (2016). The annuity puzzle remains a puzzle. Journal of Economic Dynamics and Control, 70, 18–35.Find this resource:

Pelgrin, F., & St-Amour, P. (2016). Life cycle responses to health insurance status. Journal of Health Economics, 49, 79–96.Find this resource:

Picone, G., Uribe, M., & Wilson, R. M. (1998). The effect of uncertainty on the demand for medical care, health capital and wealth. Journal of Health Economics, 17(2), 171–185.Find this resource:

Portrait, F., Lindeboom, M., & Deeg, D. (2001). Life expectancies in specific health states: Results from a joint model of health status and mortality of older persons. Demography, 38(4), 525–536.Find this resource:

Poterba, J. M. (2014). Retirement security in an aging population. American Economic Review, 104(5), 1–30.Find this resource:

Poterba, J. M., Venti, S. F., & Wise, D. A. (2012, December). The nexus of social security benefits, health, and wealth at death. Working Paper 18658. Cambridge, MA: National Bureau of Economic Research.Find this resource:

Poterba, J., Venti, S., & Wise, D. (2011). The composition and drawdown of wealth in retirement. Journal of Economic Perspectives, 25(4), 95–118.Find this resource:

Rhee, N., & Boivie, I. (2015, March). The continuing retirement savings crisis. NIRS Research Report. National Institute on Retirement Security, Washington, DC.Find this resource:

Robson, A. J., & Kaplan, H. (2007). Why do we die? Economics, biology, and aging. American Economic Review, 97(2), 492–495.Find this resource:

Rosen, S. (1988). The value of changes in life expectancy. Journal of Risk and Uncertainty, 1(3), 285–304.Find this resource:

Rust, J., & Phelan, C. (1997). How Social Security and Medicare affect retirement behavior in a world of incomplete markets. Econometrica, 65(4), 781–831.Find this resource:

Schmitz, L. L. (2016). Do working conditions at older ages shape the health gradient? Journal of Health Economics, 50, 183–197.Find this resource:

Scholz, J. K., & Seshadri, A. (2012, August). Health and wealth in a life cycle model. Department of Economics. University of Wisconsin-Madison.Find this resource:

Scholz, J. K., & Seshadri, A. (2013, September). Health insurance and retirement decisions. Working Paper WP 2013–292. Ann Arbor: Michigan Retirement Research Center, University of Michigan.Find this resource:

Shepard, D. S., & Richard J. Zeckhauser (1984). Survival versus consumption. Management Science, 30(4), 423–439.Find this resource:

Skinner, J. (2007) Are you sure you’re saving enough for retirement? Journal of Economic Perspectives, 21(3), 59–80.Find this resource:

Smith, James P. (1999). Healthy bodies and thick wallets: The dual relation between health and economic status. Journal of Economic Perspective, 13(2), 145–166.Find this resource:

Smith, J. P. (2005). Consequences and predictors of new health events. In D. A. Wise (Ed.), Analyses in the economics of aging (pp. 213–237). Chicago: University of Chicago Press.Find this resource:

Smith, J. P. (2007). The impact of socioeconomic status on health over the life-course. Journal of Human Resources, 42(4), 739–764.Find this resource:

Smith, J. P. (2009). The impact of childhood health on adult labor market outcomes. Review of Economic and Statistics, 91(3), 478–489.Find this resource:

Toossi, M. (2015). Labor force projections to 2024: The labor force is growing, but slowly. Monthly Labor Review.Find this resource:

Tsai, Y. (2015). Social security income and the utilization of home care: Evidence from the social security notch. Journal of Health Economics, 43, 45–55.Find this resource:

U.S. Center for Medicare and Medicaid Services (2017). Health expenditures by age and by gender.

Van Kippersluis, H., Van Ourti, T., O’Donnell, O., & van Doorslaer, E. (2009). Health and income across the life cycle and generations in Europe. Journal of Health Economics, 28, 818–830.Find this resource:

Yaari, M. (1965). Uncertain lifetime, life insurance and the theory of the consumer. Review of Economic Studies, 52, 137–150.Find this resource:

Yogo, M. (2016). Portfolio choice in retirement: Health risk and the demand for annuities, housing, and risky assets. Journal of Monetary Economics, 80, 17–34.Find this resource:

## Notes:

(1.) Among others, see Asakawa et al. (2012, p. 210) for Canadian health dynamics, or Van Kippersluis et al. (2009, pp. 820, 823, 824), for international data.

(2.) See in particular Smith (2007, pp. 747–752), as well as Benjamins et al. (2004); Heiss (2011); Hurd et al. (2001); Hurd (2002); Portrait et al. (2001); Lubitz et al. (2003); Cutler et al. (2006) for further evidence and discussion.

(3.) The life-cycle path in mortality is referred to as Gompertz-Makeham law (Gompertz, 1825; Makeham, 1860).

(4.) See Bell and Jones (2015) for a general discussion of age-period-cohort effects, Heckman and Robb (1985) for identification issues, and Deaton and Paxston (1998) for empirical analysis of age and cohort effects on health outcomes.

(5.) Note that the cross-sectional evidence on age trajectories such as those presented in Figures 14, or in Table 1 provides an incomplete view of the underlying life-cycle profiles (better captured via longitudinal data) to the extent that key elements such as prices, technology, cohort effects, etc., are abstracted from.

(6.) Foster (2010) provides evidence that the CEX data correlates well with other out-of-pocket survey data. For total health expenses, the CEX/MEPS ratio was 0.71, and the CEX/NHEA ratio was 0.74 in 2006.

(7.) See Cropper (1977) for a health capital model with endogenous morbidity. Examples with endogenous mortality only include Hall and Jones (2007); Scholz and Seshadri (2012); Fonseca et al. (2013). Examples with both endogenous morbidity and mortality include Ozkan (2011); Hugonnier et al. (2013); Kuhn et al. (2015); Pelgrin and St-Amour (2016).

(8.) Examples of life-cycle models with exogenous age-related stochastic processes for health spending, mortality, and morbidity include French (2005); De Nardi et al. (2009, 2010); French and Jones (2011); Capatina (2015).

(9.) Prolonged impact of early health conditions is referred to as Long Reach of Childhood. See Case et al. (2005); Cutler et al. (2006); Smith (2009); Case and Paxson (2011) for evidence and discussion.

(10.) Hall and Jones (2007) add a positive constant to utility to guarantee positiveness. See Scholz and Seshadri (2012); Hugonnier et al. (2013); Yogo (2016); and Córdoba and Ripoll (2017) for applications with non-separable preferences that guarantee preference for life irrespective of parametric values.

(11.) See Skinner (2007); Love et al. (2008); Poterba et al. (2012); Pang and Warshawsky (2013); Poterba (2014); Rhee and Boivie (2015); Campbell and Weinberg (2015). for evidence and discussions of savings inadequacy.

(12.) Currie and Madrian (1999) provides a thorough review of the links between health status, and insurance with labor market outcomes. See also Rust and Phelan (1997) for discussion. See also Kuhn et al. (2015) for additional morbidity and work disutility links between health and retirement decisions.