Misperception, self-reported probabilities and long-term care insurance take-up in the United States

Abstract

In the United States as in other developed countries, the take-up of Long-Term Care (LTC) insurance remains very low, suggesting that many individuals underestimate their future needs for professional LTC services. This paper examines the relationship between subjective expectations and LTC insurance demand, with a particular focus on miscalibration of survival beliefs. Using 12 waves of the Health and Retirement Study (1996–2018), we estimate various random effects linear probability models of LTC insurance take-up among individuals aged 50–75 years. We rely on two self-reported expectation measures: the probability of survival and the probability of nursing home entry. We then classify individuals into three groups – consistent, positive deviation, and negative deviation – based on the difference between subjective survival beliefs and life-table benchmarks. Robustness analyses are carried using alternative miscalibration measures, age groups and control variables. Our findings reveal strong heterogeneity. Individuals whose beliefs are consistent with life-table probabilities purchase more LTC insurance when they expect to live longer, in line with higher anticipated old-age expenditures. By contrast, individuals who substantially overestimate survival (“positive deviation” group) display no systematic response to either type of expectation, which could be related to cognitive difficulties in projecting future needs. Those who underestimate survival (“negative deviation” group) are responsive to nursing home expectations but less so to survival, indicating that they may anticipate short-term care needs but not long-term expenditures. Taken together, these results suggest that miscalibration of survival beliefs is an important determinant of insurance demand. They highlight that underestimation and overestimation reflect different mechanisms – potential private health information in the former case and cognitive limitations in the latter – ultimately contributing to the persistently low take-up of LTC insurance in the U.S.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10754-025-09408-4.

Introduction

The United States (US) population is aging rapidly. Between 1970 and 2021, and despite a recent inflection, the life expectancy of people aged 65 and older has increased by three years, and predictions show that by 2050, the 65 + population will represent over 20% of the overall population (OECD, 2023). This situation creates new needs. Over the past decades, the consumption of expensive long-term care (LTC) services, such as nursing home care, has increased due to the rise in the prevalence of aging-related conditions, such as dementia (OECD, 2023). Often, older parents receive assistance from family members and professional caregivers to perform basic daily activities at home or in institutions (Chari et al., 2015; Ornstein et al., 2017). A large share of the older population relies on help from informal caregivers: in the US, 7% of people aged 50 and over provide informal care to an older relative (OECD, 2023). However, 69% of informal care providers are women, and the supply of informal care providers will likely decrease primarily because of the increase in women’s labor force participation (OECD, 2023).

Prior work argues that most older people should purchase LTC insurance to cope with the increased expenditures associated with aging (Kessler, 2008). Indeed, Medicaid provides public financial support only for those below the poverty level, and Medicare covers spending on LTC services on a short-term basis (acute care). Therefore, older people in the US must seek additional financing sources for their LTC needs. Usual LTC insurance formulas provide reimbursements with daily limitations and fixed terms. Annuities depend on the cost of LTC services, and benefits can last longer if the actual cost of care is less than the daily benefit provided by the insurance policy.

The US LTC insurance market is by far the largest among OECD countries, with $11 billion in gross written premiums in 2017. The claims ratio has grown gradually since 2012 (OECD, 2020). Based on the 2022 American Association for Long-Term Care Insurance annual Price Index survey, the average yearly premium is equal to $2,220 for a single male aged 55 and equal to $3,700 for a single female aged 55 for an initial pool of benefits equal to $165,000 (each at age 55), and benefits grow at 3% yearly. The average annual premium for a couple over 55 equals $5,025 (American Association for Long-Term Care Insurance, 2023).

However, even though individuals face increased personal financial risk when they need LTC services, prior evidence suggests that the take-up rate for LTC insurance remains low. Indeed, it is estimated that between 10% and 13.8% of older people have LTC insurance in the US (Brown & Finkelstein, 2011; Gleckman, 2016) and that the different plans implemented to increase take-up rates have had modest impacts (Bergquist et al., 2016; Lin & Prince, 2013).

This study adds fresh evidence to the literature on the determinants of LTC insurance by examining how individuals’ expectations about longevity and potential nursing homes use shape their insurance choices. We exploit panel data from the Health and Retirement Study (HRS), spanning 1996–2018 (waves 3–14), and estimate random effects models that account for both observed and unobserved heterogeneity. Our contribution lies in differentiating three categories of respondents according to the extent of misalignment between their subjective and objective survival probabilities: individuals whose expectations are broadly consistent with actuarial predictions, those who underestimate their survival chances, and those who overestimate them.

Our findings highlight substantial heterogeneity. For respondents whose subjective life expectancy broadly matches statistical predictions, LTC insurance demand increases both with higher self-assessed probabilities of entering a nursing home within the next five years and greater confidence in surviving 10–15 years. This pattern is intuitive: perceiving a longer life horizon translates into anticipating higher LTC-related expenditures. Among those who underestimate their survival probability, however, higher take-up is observed only when they also anticipate entering a nursing home. This is consistent with the idea that such individuals may hold private information about poor health, which drives their demand independently of reported longevity expectations. In contrast, respondents who overestimate their survival appear less able to project their needs into the distant future. Their reported probabilities of long-term survival do not translate into higher insurance purchases, nor do expectations about nursing home use. This suggests difficulties in forming reliable forecasts, rather than private health information as the main mechanism.

The paper is organized as follows: Section 2 provides a literature review on the determinants of LTC insurance purchase, focusing on the impact of individual preferences. Section 3 presents the conceptual framework. Section 4 presents the data and our original identification strategy. Section 5 provides the results of the empirical estimations, which are discussed in Section 6.

Literature review

A large body of literature has explored the determinants of LTC insurance purchase from both theoretical and empirical perspectives (see Eling & Ghavibazoo, 2019; Cremer et al., 2012; Brown & Finkelstein, 2011). Theoretically, Pauly (1990) and Zweifel and Struwe (1998) argue that LTC insurance decisions are motivated by parents’ desire to protect their legacy from LTC expenditures. Using HRS data, Coe et al. (2015) provide evidence that prior experience with LTC use substantially increases the likelihood of purchasing LTC insurance: older individuals are more likely to seek coverage when they are aware of the financial consequences of nursing home care, even after controlling for expectations about family care and bequests. Similarly, using data from the RAND American Life Panel, Brown et al. (2012) confirm that bequest motives and beliefs about the future care need are the two main determinants of demand. Wealthier individuals are also likely to own LTC insurance (Mellor, 2001; Chatterjee & Fan, 2017). Davidoff (2010) suggests that committed home equity may substitute for LTC insurance; as it is rarely consumed before death, except when entering a nursing home. Public programs also matter: Medicaid reduces the incentive to insure privately. Brown and Finkelstein (2008) show that low and middle-wealth individuals may “spend down” their assets to qualify for Medicaid rather than purchase private coverage. More recently, Mommaerts (2023) shows that more generous Medicaid eligibility thresholds increase the likelihood of nursing home use relative to family care.

Other studies highlight the role of perceptions and knowledge. Higher cognitive capacity and financial literacy are associated with a greater propensity to purchase LTC insurance (McGarry et al., 2016, 2018; Lin & Prince, 2016). Misperceptions of risks also shape demand. Boyer et al. (2019), using Canadian survey data, find that misperceptions about needing help with ADLs, nursing home entry, and survival to age 85 significantly increase stated intentions to buy LTC insurance. Respondents were asked about their probability of purchasing one of five hypothetical contracts with varying benefits and premiums. However, misperceptions about ADLs and survival were uncorrelated with actual coverage, and misperceptions about nursing home use were negatively correlated with ownership. Zhou-Richter et al. (2010) argue that demand is low because individuals underestimate LTC costs; providing accurate information increases reported willingness to insure. Brown et al. (2012) show that beliefs about needing LTC are strongly correlated with coverage: 27% of individuals who agreed they were likely to lose independence purchased LTC insurance, compared with only 14% of those who disagreed. Consistently, De Donder and Leroux (2013) theoretically demonstrate that underestimating dependency risk leads to underinsurance.

Adverse selection has also been a central focus. According to economic theory, individuals who anticipate high LTC costs are more likely to purchase coverage and expect higher payouts. Sloan and Norton (1997) test this by using self-reported probabilities of nursing home entry within five years and survival over 10–15 years. They find no effect for survival expectations but a positive and significant effect for nursing home entry, concluding that adverse selection is present. Norton (2000) confirms that insured individuals anticipate nursing home use more than the uninsured. Oster et al. (2010) further show that individuals with genetic risk factors in their families are more likely to insure. However, selection may be multidimensional: Finkelstein and McGarry (2006) find that individuals who engage more in preventive health behaviors are also more likely to purchase LTC insurance, suggesting that private information about health may partly offset adverse selection.

The existing literature faces several limitations. Evidence of adverse selection is mixed: Sloan and Norton (1997) and Norton (2000) provide no definitive proof, since demonstrating adverse selection would require showing a correlation between the level of coverage and realized LTC expenditures. Similarly, Boyer et al. (2019) report counterintuitive findings regarding risk misperceptions: while they shape intentions, misperceptions about ADLs, survival, and nursing home entry are uncorrelated – or even negatively correlated – with actual coverage. These limitations suggest the need for some additional frameworks that jointly consider expectations, miscalibration, and potential private health information to better understand LTC insurance demand.

For our conceptual framework, we build on Sloan and Norton (1997), whose variables allow us to distinguish between expectations of short-term and long-term LTC needs. However, the interpretation of self-reported probabilities is not straightforward: they may reflect genuine expectations, misperceptions of future risks, or private information about health status. To address this, we classify individuals into three groups based on their degree of life expectancy miscalibration. In contrast with Boyer et al. (2019), who directly use life expectancy miscalibration as a determinant of insurance demand in Canada, we argue that what matters is not the deviation itself from life tables, but rather how expectations of longevity translate into perceived needs for financing LTC.

Our contributions to this literature are threefold. First, we use self-reported probabilities as proxies for expectations of LTC needs in both the short and long term. Second, we classify individuals according to their life expectancy miscalibration to disentangle misperceptions from private health information. Third, we examine how these expectations shape LTC insurance take-up in the United States.

Conceptual framework

We use the two variables identified in prior work by Sloan and Norton (1997) to analyze the correlation between individuals’ expectations and LTC insurance take-up: the self-reported probability of being alive 10–15 years from the interview date and the self-reported probability of moving into a nursing home within the next five years. Each variable captures an expectation regarding the need to finance LTC expenses, either in the long or short term. The first variable reflects expectations associated with longevity and, therefore, a greater likelihood of facing long-term care costs over the life cycle. The second captures expectations related to short-term LTC expenditures.

The interpretation of these measures may differ depending on individual heterogeneity and the degree of understanding of self-reported probabilities. More broadly, why might individuals misestimate both their life expectancy and their future LTC expenditures? We identify three possible explanations. First, misestimation may reflect private information or self-assessment (Hypothesis 1). For example, individuals who underestimate their survival may do so because of family history, health behaviors, or medical monitoring, leading them to believe they will face fewer LTC costs. If this belief is correct, lower insurance demand is rational; if not, they risk underinsurance. Second, misestimation may reflect cognitive limitations or difficulties in projecting future needs, for instance, due to limited financial or health literacy (Hypothesis 2). In this case, mistakes can bias individuals toward lower demand for insurance, although the effect may be noisy if some purchase coverage anyway (e.g., through inertia or external advice). Third, misestimation may reflect psychological biases such as optimism or pessimism (Hypothesis 3). Optimists may underestimate adverse states (dependency, costly illness) and thus behave as if less risk-averse, reducing their incentive to purchase insurance. Yet optimism and pessimism can apply to two different domains: longevity (believing one will live longer than actuarial predictions) and expenditures (anticipating higher costs from living longer). As a result, “vital optimism” may coexist with “economic pessimism,” leading to distinct implications for LTC insurance demand.

Our empirical framework cannot directly test this third explanation, as it would require measures of individual risk preferences, which are not available. The reason is that optimism affects behavior in a way that is observationally equivalent to changes in risk aversion. Optimistic individuals underestimate the probability of adverse states and therefore behave as if they were less risk-averse, even if their utility function remains concave. Conversely, pessimists behave as if more risk-averse. Without direct measures of individual risk preferences, we cannot disentangle whether lower insurance take-up reflects distorted beliefs (optimism/pessimism) or genuine heterogeneity in risk aversion.

We therefore focus on the first two hypothesis. To account for these two possibilities, we construct a measure of miscalibration by comparing respondents’ self-reported life expectancy with actuarial predictions. Based on this comparison, we classify individuals into three groups. The first group includes those whose survival expectations are broadly consistent with actuarial tables (“consistent group”). The second includes those who substantially overestimate their survival probability (“positive deviation” group). The third includes those who substantially underestimate it (“negative deviation” group).

The purpose of introducing these three groups is to assess whether individuals are able to form reasonable expectations about future health events and thereby rule out Hypothesis 2. Specifically, we test whether miscalibration reflects private information about health or, alternatively, cognitive limitations in forming expectations. In other words, individuals in the “consistent” group are presumed capable of predicting their survival probabilities with reasonable accuracy. By contrast, individuals in the “negative deviation” and “positive deviation” groups may either possess private information about their health status (Hypothesis 1) or be unable to project themselves into the future and to provide meaningful estimates of survival probabilities (Hypothesis 2). To investigate the relationship between individuals’ expectations of financing future LTC needs and their insurance take-up, we use two panels, one of which allows us to exclude the possibility of private information, thus favoring Hypothesis 2 over Hypothesis 1.

Empirical methodology

Data

We use data from the Health and Retirement Survey (HRS), a longitudinal panel that surveys a representative sample of 20,000 Americans over the age of 50 every two years. The HRS explored the changes in labor force participation and the health transitions that individuals undergo toward the end of their working lives. We mobilize this panel, which also allows the exploration of LTC decisions in the US. To perform the empirical analyses, we use RAND HRS Longitudinal File data, a version that allows us to obtain cleaned and reprocessed variables. We use also the RAND HRS Family Data 2018 for have a proxy of parents’ altruism towards their children (i.e. the fact of having at least one child in the will). This second dataset is currently available up to 2018, hence we use 12 waves of the study, covering the period 1996–2018 (waves 3–14). We restrict our panels to individuals aged between 50 and 75 years (i.e., the age when the decision to buy LTC insurance becomes important) who were observed at least once during the period and have no missing values for our dependent and independent variables. Our sample is divided into two panels based on respondents’ age. Our first panel (panel A) consists of an unbalanced panel of 13,138 individuals aged between 65 and 75 years surveyed every two years, representing 37,523 observations (with 2.9 observation points per individual on average). Our second panel (panel B) consists of an unbalanced panel of 21,255 individuals aged between 50 and 65 years surveyed every two years, representing a total of 64,851 observations (with 3.1 observations point per individual on average).

Dependent variable

Our dependent variable measures the presence of LTC insurance coverage since the last interview (yes vs. no). It is obtained from the question, “Not including government programs, do you now have any insurance which specifically pays any part of LTC, such as, personal or medical care in the home or in a nursing home?”.

Independent variables of interest in panel A

As explained in the conceptual framework, we use the self-reported probability of being alive 10–15 years from the interview date and the self-reported probability of moving to a nursing home in the next five years. Each of these measures is used as a proxy for the individual’s expectation of the need to finance LTC expenses, in the short or long term.

For panel A, i.e. individuals aged between 65 and 75 years, we define a measure of life expectancy miscalibration in the same way as Puri and Robinson (2007) based on comparing respondents’ self-reported life expectancy and their life expectancy obtained from actuarial tables (i.e., VSLTs). Life expectancy miscalibration is the difference between two components: the individuals’ self-reported probability of living about another ten years (on a scale of 0 to 100) at time , denoted as , where  is a vector of personal characteristics, and the predicted probability of living about another ten years calculated from VSLTs using the individuals’ age and gender, denoted as . The self-reported probability is obtained from the question wording depends on the respondent’s age: “What is the percent chance that you will live to be (80, 85, 90, 95, or 100) or more?”.). The documentation specifies that, for respondents below age 70 at a given wave, the measure corresponds to the self-reported probability of living to age 80; for those aged 70 to 74, it corresponds to the probability of living to age 85; and so on. In other words, respondents under the age of 70 (e.g., 69 years and 11 months) are asked to estimate their self-reported probability of living to age 80, i.e., 10 more years. In contrast, respondents aged 70 are asked to estimate their self-reported probability of living to age 85, i.e., 15 more years. Life expectancy miscalibration is then defined as:

1

Then, three categories of life expectancy miscalibration are defined as in Roquebert et al. (2021): “consistent,” “negative deviation,” and “positive deviation.” Individuals are in the “consistent” group when the difference between their subjective and objective probabilities of living another 10–15 years is lower than one standard deviation in the absolute value of the life expectancy miscalibration measure. Individuals are in the “positive deviation” (resp. “negative deviation”) group when their life expectancy miscalibration is positive (resp. negative), i.e., when their self-reported probability is higher (resp. lower) than the probability obtained from VSLTs by more than one standard deviation.

Figure 1 presents the distribution of life expectancy miscalibration and the associated categories. In our panel, “consistent” reporting is majoritarian (68% of observations), “positive deviation” individuals represent 14% of observations, and “negative deviation” people represent 18% of observations. In the robustness checks, we use another threshold by taking the 10th and 90th percentiles of the distribution of life expectancy miscalibration. To facilitate the interpretation and comparison of point estimates, we re-scale (standardize) the self-reported probability for each category to have a mean of zero and unit variance.

Fig. 1.

Distribution of life expectancy miscalibration, panel A ()

Independent variables of interest in panel B

For panel B, we use only the self-reported probability of living to age 75, which is used as a proxy for the individual’s expectation of the need to finance LTC expenses in the long term. In fact, the self-reported probability of moving to a nursing home in the next five years is only asked of individuals over the age of 65.

For the second panel, i.e. individuals aged between 50 and 65 years, we create two empirical measures of life expectancy miscalibration, and , that differ in the way life expectancy miscalibration is calculated; we use data from actuarial tables and individual predictions from HRS data, respectively.

Our first measure for this panel is based on a comparison between respondents’ self-reported life expectancy and their life expectancy obtained from actuarial tables (i.e., VSLTs). Life expectancy miscalibration is defined as the difference between two components: the individuals’ self-reported probability of living to age 75 (on a scale of 0 to 100, note also that this question is only asked for individuals younger than 66 years old) at time , denoted as , where  is a vector of personal characteristics, and the predicted probability of living to age 75 calculated from VSLTs using the individuals’ age and gender, denoted as . Life expectancy miscalibration is then defined as:

2

Figure 2 presents the distribution of and the associated categories. In our panel B, “consistent” reporting is majoritarian (71% of observations), “positive deviation” individuals represent 4% of observations, and “negative deviation” individuals represent 25% of observations.

Fig. 2.

Distribution of life expectancy miscalibration, panel B ()

Our second measure for this panel is based upon the difference between individuals’ self-reported probability of living to age 75, denoted as , and their individual predicted probability of living to age 75, denoted as , where is a vector of the observed predictors. The predictors include information on age, gender, socio-economic characteristics, and health indicators (see Table 1). Life expectancy miscalibration is then defined as:

Table 1.

Models of survival expectations measurement. Individuals aged between 50 and 75 years old

Predictive models of individual life expectancy
Model	Predictorsof living up to 75 years old	Cross-validated AUC (95% CI)
Model 1	Age + gender	0.6210 (0.61613–0.62590)
Model 2	Age + gender + socio-economics + health indicators	0.8060 (0.80090–0.81104)
Model 3	Age + gender + socio-economics + health indicators in interaction	0.8089 (0.80381–0.81393)
Descriptive statistics of LEM
LEM variable	Mean (SD)	Range	Correlation with VSLT predictions
	-12.5 (30.0)	-92.7 to 39.9	-
	-7.0 (30.0)	-99.4 to 98.9	rho=0.7586

: difference between individuals’ 𝑖 self-reported probability of living to age 75 and predictions obtained from Vital Statistics Life Tables at time 𝑡

: difference between individuals’ 𝑖 self-reported probability of living to age 75 and individual predictions of living up to 75 years at time 𝑡 obtained from Model 2

AUC area under the ROC curve. The higher the AUC, the better the predictive validity. In bold: chosen model for individual predictions of life expectancy

Legend. Socio-economics variables include: marital status (married, widowed), level of education, white people or not, number of children, number of children in household, number of living siblings, number of future helpers, presence of living parents, informal care user, total wealth, children in will

Health indicators include: self-reported health, smoking status (smoker, ever smoked), dummy indicators of presence of any chronic disease (diabetes, cancer, arthritis, etc.), the CESD depression score, the number of ADL and IADLs, the bmi and bmi squared

In Model 3, all the dummy indicators of the presence of any chronic disease are interacted to reflect cumulative chronic conditions and the interaction of the number of ADL and IADLs

Source: Health and retirement study (HRS), waves 3 to 14 (1996-2018)

3

From Eq. (3), it is easy to see that our ability to predict individuals’ life expectancy increases the precision of ; i.e., it increases the likelihood that this variable captures the miscalibration of beliefs rather than private information.

To obtain the most accurate measure of , we use the informative predictors of living to 75 years in a four-step k-fold cross-validation strategy designed to optimize the out-sample predictive validity of our estimations. First, we randomly divide our sample into mutually exclusive subsets. Second, we estimate nested probability models (which vary according to the number of predictors) of living up to 75 years using subsets (training samples). Third, we predict the probability of living to age 75 for everyone in the omitted subset (validation sample). This process is repeated iteratively until predictions are made for everyone in the subsets. Fourth, we evaluate the out-of-sample predictive validity of our models using the area under the receiver operating characteristic (ROC) curve (AUC) statistic, and we choose the model with the highest AUC as our prediction model.

The various models tested and the resulting AUCs are displayed in Table 1. Our most parsimonious model of includes socioeconomics, health conditions and risky lifestyle measures (e.g., smoking), which are known predictors of mortality. The resulting model has strong out-of-sample predictive validity, with an AUC of 0.8060 (). Including interaction effects between health conditions does not improve the model fit in any significant manner. Note that our models are not estimated based on the entire 50–75 years of HRS data but only for individuals for whom it is possible to know whether they lived to 75 years. For some respondents, the follow-up in subsequent waves does not provide information on whether they survived to age 75; therefore, these individuals are excluded from the analysis. Restricting the sample in this way ensures that the dependent variable (survival to age 75) is accurately measured for all respondents included, while recognizing that those with incomplete follow-up cannot contribute to the estimate. Our two measures are strongly correlated (see Table 1). This suggests that they capture similar information, although may be more precise than .

Figure 3 presents the distribution of and the associated categories. In our panel B, “consistent” reporting is majoritarian (69% of observations), “positive deviation” individuals represent 9% of observations, and “negative deviation” individuals represent 22% of observations.

Fig. 3.

Distribution of life expectancy miscalibration, panel B ()

Control variables

We specify a model of LTC insurance demand that follows the framework provided by Coe et al. (2015). We first control for a vector of an individual’s health variables, which are the number of limitations on activities of daily living (ADLs) and instrumental activities of daily living (IADLs), the Center for Epidemiologic Studies Depression (CESD) score, the number of comorbidities (including high blood pressure, arthritis, diabetes, cancer, lung disease, heart disease, stroke, and psychiatric problems), the body mass index, an indicator of self-reported health as excellent or good/very good, and smoking habits. Thus, we control for the fact that the elderly and near-elderly populations are naturally more heterogeneous in health status than the younger population. Second, we include variables in our regressions that allow us to explore respondents’ access to informal care. These variables are the presence of informal care use, the number of children who will provide help in the future, the number of children living in the household, and the number of living siblings (brothers and sisters). We additionally control for a variable measuring prior home care use. Third, we control for a vector of economic and financial information: self-employment (yes vs. no), total financial wealth, including housing assets in a trust, total household income, and whether the respondent has a will that benefits his or her children (to test for parent’s altruism towards children). Fourth, we control for several socio-demographic variables: age, age squared, gender, race, education category, and marital status. Finally, all models control for time and census division effects (states and proportions of each census division are available online, Table S1).

Estimation model

We model the relationship between the self-reported probability of living about another 10 years for panel A or living to age 75 for panel B (, the self-reported probability of moving to a nursing home in the next 5 years for panel A ( and LTC insurance demand controlling for observed individual heterogeneity using random effects (RE) linear probability models. We estimate this relationship for the overall sample and then stratify the analysis according to each group of life expectancy miscalibration (“consistent”, “negative deviation”, “positive deviation”). We use time-varying and time-invariant observed variables for controlling observed individual heterogeneity:

4

RE linear probability models rely on between and within individual variations in the dependent and independent variables. Conversely, fixed effects (FE) linear probability models rely only on within individual variations. The latter model has the advantage of reducing omitted variable bias associated with unobserved individual characteristics not sufficiently captured by our independent variables. However, identification in FE models relies exclusively on within individual variation, which is limited in our data, particularly for the expectation variables. Additionally, only individuals who experience changes in the dependent variable contribute to identification, thereby reducing the number of observations and the sample size. For these reasons, we prefer to use RE linear probability models on the entire sample using many control variables to reduce omitted variable bias.

Results

Results for panel A: Individuals aged between 65 and 75 years old

Table 2 describes our panel A. On average, 14.9% of individuals aged between 65 and 75 are covered by LTC insurance. The average number of functional limitations is low (0.10 ADLs and 0.04 IADLs), 79.1% of individuals report being in good health, and the average number of comorbidities is 2.09. The mean age is 69.8. The average number of children is 3.5 (99% of the panel have at least one child), and 67.3% of individuals are married. The average net wealth is $550,324, and 52.4% of respondents include their children in their will. We find that individuals classified in the “negative deviation” group are less likely to buy LTC insurance, be married, be white, be in good health, be self-employed, and have children in their will. They are significantly more likely to have ADLs/IADLs, have depression or comorbidities, have a higher body mass index, be smokers, use formal care and informal care, be female, and have a higher education degree than individuals in the “consistent” group. They also have lower levels of income and wealth than individuals in the “consistent” group. In reverse, individuals in the “positive deviation” group are likelier to be in good health, use informal care and be self-employed. They are significantly less likely to have children in their will, have depression or comorbidities, be female, be white, and have a higher education degree than individuals in the “consistent” group. They also have lower levels wealth than individuals in the “consistent” group.

Table 2.

Descriptive statistics and comparison by life expectancy miscalibration. Panel of individuals aged between 65 and 75 years old

	Overall	Negative deviation (N)	Positive deviation (P)	Consistent (C)	Differences between samples a
Variables					C/N	C/P
LTC insurance purchase (%)	14.84	10.47	15.04	15.95	***	NS
Number of ADLs (mean SD)	0.10 (0.40)	0.18 (0.55)	0.08 (0.36)	0.08 (0.36)	***	NS
Number of IADLs (mean SD)	0.04 (0.23)	0.07 (0.32)	0.03 (0.21)	0.03 (0.20)	***	NS
Depression score (mean SD)	1.11 (1.69)	1.73 (2.07)	0.88 (1.44)	1.00 (1.59)	***	***
Comorbidity score (mean SD)	2.09 (1.35)	2.52 (1.44)	1.84 (1.31)	2.03 (1.32)	***	***
Body mass index (mean SD)	28.06 (5.33)	28.49 (5.83)	27.98 (4.96)	27.96 (5.25)	***	NS
Self-reported health (%)	79.05	57.59	86.07	83.31	***	***
Smoker (%)	11.20	16.76	10.07	9.96	***	NS
Children living in household (mean SD)	2.13 (1.01)	2.16 (1.15)	2.15 (1.01)	2.11 (0.97)	***	***
Number of children (mean SD)	3.46 (1.93)	3.57 (2.00)	3.70 (2.09)	3.39 (1.86)	***	***
Number of living siblings (mean SD)	2.74 (2.38)	2.97 (2.51)	2.84 (2.54)	2.66 (2.30)	***	***
Number of future helpers (mean SD)	1.16 (1.59)	1.08 (1.60)	1.34 (1.83)	1.14 (1.54)	***	***
Home care user (%)	5.14	6.90	4.63	4.78	***	NS
Informal care user (%)	0.43	0.78	0.56	0.32	***	***
Age (mean SD)	69.75 (3.14)	69.43 (3.14)	71.06 (2.94)	69.56 (3.11)	***	***
Female (%)	57.45	62.47	39.71	59.73	***	***
White (%)	82.18	79.19	73.51	84.74	***	***
General educational development (%)	4.69	6.25	4.65	4.28	***	NS
High-school graduate (%)	33.02	34.97	29.97	33.12	***	***
Some college (%)	22.64	18.62	22.23	23.79	***	NS
College and above (%)	22.37	12.16	22.00	25.15	***	***
Married (%)	67.32	60.62	67.61	69.05	***	NS
No living parents (%)	79.18	81.88	79.54	78.39	***	NS
Self-employed (%)	8.76	5.44	11.59	9.07	***	***
Total household income (mean SD)	64675.76 (327775.6)	45141.49 (70260.75)	64164.72 (148030.6)	69967.95 (389827.1)	***	NS
Total household wealth (mean SD)	550324.5 (1235589.0)	330032.2 (841198.3)	530821.5 (1233365)	612806.4 (1314746.0)	***	***
Children in will (%)	52.39	43.00	50.36	55.31	***	***
Observations	37,523	6,782	5,205	25,536

^a Statistical significance of the difference between the two samples. Results of student test for continuous variables, andtest for categorical variables. ***; ns non significant

Positive deviation (resp. negative): Individuals for whom the self-reported probability is much higher (resp. lower) than the probability obtained from VSLTs by more than one standard deviation

Consistent: Individuals for whom the difference between self-reported probability and the probability obtained from VSLTs is lower than one standard deviation in absolute value

Source: Health and retirement study (HRS), waves 3 to 14 (1996–2018)

Table 3 confirms that overall, an increase in the self-reported probability of being alive 10–15 years after the interview date and an increase in the self-reported probability of moving to a nursing home significantly increase the probability of having LTC insurance. We find that a one-point increase in the probability of being alive 10–15 years is associated with a 0.46 pp increase in LTC insurance purchases. Moreover, a one-point increase in the probability of moving to a nursing home in the next five years is associated with a 0.33 pp increase in LTC insurance purchase (Model 1).

Table 3.

Impact of self-reported probabilities on the probability of being covered by LTC insurance. Panel of individuals aged between 65 and 75 years old

Variables	Overall (1)	Negative deviation (2)	Positive deviation (3)	Consistent (4)
Probability of being alive in 10–15 years (standardized)	0.00463*** (0.00157)	0.00089 (0.00338)	−0.00521 (0.00487)	0.00434** (0.00195)
Probability of moving to nursing home in 5 years (standardized)	0.00325** (0.00134)	0.00697** (0.00321)	0.00206 (0.00432)	0.00444*** (0.00166)
Age	0.01161 (0.01731)	0.02071 (0.04476)	−0.05126 (0.05802)	0.00640 (0.02209)
Age squared	−0.00006 (0.00012)	−0.00014 (0.00032)	0.00036 (0.00041)	−0.00002 (0.00016)
Female	0.01555*** (0.00554)	0.01189 (0.00962)	0.02503** (0.01269)	0.02194*** (0.00652)
White	0.02825*** (0.00722)	0.01036 (0.01158)	0.03561** (0.01509)	0.02752*** (0.00862)
Education GED	0.01061 (0.01365)	−0.00518 (0.02014)	−0.00614 (0.02998)	0.01672 (0.01644)
High-school graduate	0.03877*** (0.00800)	0.00795 (0.01192)	0.03395** (0.01700)	0.04258*** (0.00968)
Some college	0.05841*** (0.00866)	0.03140** (0.01395)	0.04134** (0.01866)	0.06182*** (0.01034)
College and above	0.13825*** (0.00913)	0.07526*** (0.01640)	0.13261*** (0.01964)	0.14512*** (0.01081)
No living parents	0.01384*** (0.00440)	0.01857* (0.01012)	0.01760 (0.01276)	0.00762 (0.00528)
Married	0.02866*** (0.00485)	0.01506 (0.00926)	0.03878*** (0.01312)	0.03411*** (0.00586)
Self-employed	−0.01842*** (0.00584)	−0.02697* (0.01549)	−0.00219 (0.01530)	−0.02400*** (0.00705)
Total income (standardized)	0.00098 (0.00109)	0.01161*** (0.00379)	0.00149 (0.00376)	0.00093 (0.00139)
Total wealth (standardized)	0.00557*** (0.00172)	0.01192*** (0.00432)	0.00514 (0.00446)	0.00629*** (0.00209)
Children in will	0.03195*** (0.00346)	0.04569*** (0.00783)	0.04261*** (0.01030)	0.03510*** (0.00421)
Number of ADLs	0.00189 (0.00370)	0.00051 (0.00633)	−0.01376 (0.01324)	0.00455 (0.00510)
Number of IADLs	0.00185 (0.00639)	−0.01169 (0.01109)	0.00814 (0.02269)	0.00592 (0.00883)
Depression score	−0.00044 (0.00093)	−0.00301* (0.00176)	0.00066 (0.00333)	−0.00011 (0.00119)
Comorbidity score	−0.00329* (0.00171)	−0.00065 (0.00311)	0.00180 (0.00448)	−0.00446** (0.00207)
Body mass index	−0.00124*** (0.00042)	−0.00076 (0.00073)	−0.00285** (0.00115)	−0.00126** (0.00052)
Self-reported health OK	0.00839** (0.00395)	0.00506 (0.00743)	0.00419 (0.01390)	0.01044** (0.00519)
Smoker	−0.02031*** (0.00627)	−0.01614 (0.01094)	−0.02149 (0.01748)	−0.02255*** (0.00791)
Children living in household	−0.00152 (0.00177)	−0.00221 (0.00342)	0.00112 (0.00515)	−0.00311 (0.00225)
Number of children	−0.00234* (0.00132)	−0.00105 (0.00231)	−0.00362 (0.00291)	−0.00243 (0.00160)
Number of living siblings	−0.00147 (0.00108)	−0.00393** (0.00182)	−0.00376 (0.00236)	−0.00053 (0.00130)
Number of future helpers	−0.00194** (0.00096)	0.00142 (0.00226)	−0.00314 (0.00260)	−0.00163 (0.00123)
Home care user	0.01245** (0.00553)	0.00863 (0.01170)	−0.01156 (0.01956)	0.01224* (0.00711)
Informal care user	−0.01910 (0.02247)	0.02271 (0.03941)	−0.02827 (0.06566)	−0.01937 (0.03350)
Wave dummies	Yes	Yes	Yes	Yes
Census division dummies	Yes	Yes	Yes	Yes
Constant	−0.38353 (0.60430)	−0.62497 (1.55640)	2.01441 (2.03746)	−0.22844 (0.76991)
Observation	37,523	6,782	5,205	25,536

Results of random effects linear probability models. *, **, ***

Source: Health and retirement study (HRS), waves 3 to 14 (1996–2018)

Factors associated with a greater probability of LTC coverage are the use of formal care (+ 1.2 pp), self-reported health (+ 0.8 pp), presence of a bequest (+ 3.2 pp), female (+ 1.6 pp), white (+ 2.8 pp), marriage (+ 2.9 pp), and no living parents (+ 1.4 pp) and wealth. Factors correlated with a lower probability of being insured are self-employment (−1.8 pp), comorbidity score (−0.3 pp), body mass index (−0.1 pp), smoking status (−2.0 pp), access to informal care, and level of education.

Table 3 also shows the results for the three categories of life expectancy miscalibration. In the “negative deviation” group, a one-point increase in the probability of moving to a nursing home is associated with a 0.70 pp increase in LTC insurance purchase (Model 2). On the other hand, for this same group, the LTC insurance take-up is not correlated with the probability of being alive for 10–15 years. In the “positive deviation” group, LTC insurance take-up is not correlated with the probability of being alive for 10–15 years or moving to a nursing home (Model 3). In the “consistent” group, a 1-point increase in the probability of being alive 10–15 years is associated with a 0.43 pp increase in LTC insurance purchase. Moreover, a 1-point increase in the probability of moving to a nursing home in the next five years is associated with a 0.44 pp increase in LTC insurance purchase (Model 4).

In the supplementary materials, we modify the thresholds for creating the three groups of individuals by taking the 10th and 90th percentiles of the distribution of life expectancy miscalibration. Table S2 describes the sample and each group with these thresholds. Table S3 confirms all the results obtained with different thresholds. In the “consistent” group, a one-point increase in the probability of moving to a nursing home and a one-point increase in the probability of being alive for 10–15 years are associated with an increase in LTC insurance purchase (Model 4). Table S3 also confirms that in the “negative deviation” group, a one-point increase in the probability of moving to a nursing home is associated with an increase in LTC insurance purchase, and that the LTC insurance take-up is not correlated with the probability of being alive for 10–15 years (Model 2). In the “positive deviation” group, LTC insurance take-up is not correlated with the probability of being alive for 10–15 years or moving to a nursing home (Model 3).

Finally, for the overall sample (Table S4) and for each group (Tables S5-S7), we gradually add the different control variables: the first model includes individuals’ expectations (Model 1), the second model adds socio-demographic variables (Model 2), the third model adds individual’s health variables and control variables for economic and financial information (Model 3). Finally, the fourth model presents the full model including respondents’ access to informal care (Model 4). The results show that the addition of individual’s health variables, control variables for economic and financial information and respondents’ access to informal care do not change either the sign or the intensity of the estimated coefficients of Model 2 including only the socio-demographic variables. Our results are thus robust to different specifications, and are unlikely affected by unobserved heterogeneity.

Results for panel B: Individuals aged between 50 and 65 years old

Table 4 describes panel B and groups defined according to the distribution of . On average, 9.3% of individuals aged between 50 and 65 years are covered by LTC insurance. The average number of functional limitations is low (0.10 ADLs and 0.05 IADLs), 79.7% of individuals report being in good health, and the average number of comorbidities is 1.43. The mean age is 58.1. The average number of children is 3.2, and 69.9% of individuals are married. The average net wealth is $396,516, and 34.8% of respondents include their children in their will. We find that individuals classified in the “negative deviation” group are less likely to buy LTC insurance, be married, be white, be in good health, be self-employed, and have children in their will. They are significantly more likely to have ADLs/IADLs, have depression or comorbidities, have a higher body mass index, be smokers, use formal care and informal care, be female, and have a higher education degree than individuals in the “consistent” group. They also have lower levels of income and wealth than individuals in the “consistent” group. In reverse, individuals in the “positive deviation” group are likelier to be married and self-employed. They are significantly less likely to have children in their will, have depression or comorbidities, be female, and be white than individuals in the “consistent” group.

Table 4.

Descriptive statistics and comparison by life expectancy miscalibration. Panel of individuals aged between 50 and 65 years old (creating groups according to the distribution of )

	Overall	Negative deviation (N)	Positive deviation (P)	Consistent (C)	Differences between samples a
Variables					C/N	C/P
LTC insurance purchase (%)	9.34	6.57	8.71	10.34	***	***
Number of ADLs (mean SD)	0.10 (0.43)	0.18 (0.59)	0.08 (0.41)	0.07 (0.36)	***	NS
Number of IADLs (mean SD)	0.05 (0.27)	0.09 (0.38)	0.04 (0.25)	0.03 (0.22)	***	NS
Depression score (mean SD)	1.32 (1.88)	1.96 (2.27)	1.02 (1.53)	1.12 (1.69)	***	***
Comorbidity score (mean SD)	1.43 (1.26)	1.86 (1.41)	0.99 (1.05)	1.30 (1.18)	***	***
Body mass index (mean SD)	28.68 (5.85)	29.43 (6.42)	28.45 (4.74)	28.43 (5.68)	***	NS
Self-reported health (%)	79.67	61.60	87.22	85.51	***	NS
Smoker (%)	19.43	26.72	20.59	16.84	***	***
Children living in household (mean SD)	2.56 (1.31)	2.59 (1.43)	2.72 (1.37)	2.53 (1.26)	***	***
Number of children (mean SD)	3.19 (1.79)	3.30 (1.88)	3.37 (1.90)	3.15 (1.75)	***	***
Number of living siblings (mean SD)	3.31 (2.56)	3.66 (2.74)	3.32 (2.62)	3.19 (2.49)	***	***
Number of future helpers (mean SD)	1.06 (1.51)	1.00 (1.47)	1.14 (1.77)	1.07 (1.51)	***	NS
Home care user (%)	2.47	3.62	2.22	2.09	***	NS
Informal care user (%)	0.41	0.66	0.38	0.32	***	NS
Age (mean SD)	58.08 (4.04)	58.39 (4.02)	56.92 (3.72)	58.04 (4.05)	***	***
Female (%)	58.95	70.21	0.00	58.43	***	***
White (%)	72.97	68.32	70.32	74.73	***	***
General educational development (%)	5.19	7.16	5.96	4.47	***	***
High-school graduate (%)	29.25	31.84	28.36	28.40	***	NS
Some college (%)	26.64	24.00	26.62	27.56	***	NS
College and above (%)	24.29	13.61	21.34	28.17	***	***
Married (%)	69.94	62.34	76.92	72.18	***	***
No living parents (%)	37.01	45.77	27.38	34.53	***	***
Self-employed (%)	11.71	8.22	17.65	12.58	***	***
Total household income (mean SD)	82684.57 (194530.8)	58104.37 (92388.78)	86550.70 (279904.7)	90983.98 (213071.1)	***	NS
Total household wealth (mean SD)	396515.7 (1015272.0)	254085.3 (785676.2)	390909.2 (1075344.0)	446215.0 (1075848.0)	***	NS
Children in will (%)	34.75	24.78	32.88	38.31	***	***
Observations	64,851	16,012	2,652	46,187

^a Statistical significance of the difference between the two samples. Results of student test for continuous variables, andtest for categorical variables. ***; ns non significant

Positive deviation (resp. negative): individuals for whom the self-reported probability is much higher (resp. lower) than the probability obtained from VSLTs by more than one standard deviation

Consistent: individuals for whom the difference between self-reported probability and the probability obtained from VSLTs is lower than one standard deviation in absolute value

Source: Health and retirement study (HRS), waves 3 to 14 (1996–2018)

Table 5 confirms that overall, an increase in the self-reported probability of living to age 75 increases the probability of having LTC insurance. We find that a one-point increase in the probability of living to age 75 is associated with a 0.60 pp increase in LTC insurance purchases (Model 1). Factors associated with a greater probability of LTC coverage are the use of formal care (+ 1.9 pp), self-reported health (+ 0.7 pp), presence of a bequest (+ 3.6 pp), female (+ 0.8 pp), marriage (+ 1.5 pp), total income and wealth. Factors correlated with a lower probability of being insured are self-employment (−2.4 pp), white (−1.1 pp), depression score (−0.3 pp), access to informal care, and level of education.

Table 5.

Impact of life expectancy on the probability of being covered with LTC insurance. Panel of individuals aged between 50 and 65 years old (creating groups according to the distribution of )

Variables	Overall (1)	Negative deviation (2)	Positive deviation (3)	Consistent (4)
Probability of living to age 75 (standardized)	0.00602*** (0.00124)	0.00023 (0.00228)	−0.00147 (0.00561)	0.00610*** (0.00153)
Age	−0.00780 (0.00729)	−0.01253 (0.01331)	0.06490 (0.04611)	−0.01023 (0.00904)
Age squared	0.00009 (0.00006)	0.00011 (0.00011)	−0.00057 (0.00040)	0.00011 (0.00008)
Female	0.00772** (0.00311)	0.00807 (0.00562)	0.00000 (.)	0.00743* (0.00381)
White	−0.01140*** (0.00368)	−0.01771*** (0.00559)	−0.00642 (0.01472)	−0.01098** (0.00444)
Education GED	0.01670** (0.00751)	0.02108** (0.01044)	0.02794 (0.02771)	0.01126 (0.00943)
High-school graduate	0.02363*** (0.00485)	0.01711** (0.00687)	0.05007*** (0.01833)	0.02384*** (0.00606)
Some college	0.04371*** (0.00505)	0.03346*** (0.00745)	0.06490*** (0.01925)	0.04434*** (0.00624)
College and above	0.07262*** (0.00546)	0.04954*** (0.00905)	0.08465*** (0.02099)	0.07355*** (0.00660)
No living parents	0.00273 (0.00286)	0.00715 (0.00472)	0.03156** (0.01361)	0.00040 (0.00348)
Married	0.01527*** (0.00328)	0.01753*** (0.00526)	0.03214** (0.01548)	0.01310*** (0.00400)
Self-employed	−0.02402*** (0.00398)	−0.01534** (0.00762)	−0.02488 (0.01538)	−0.02642*** (0.00471)
Total income (standardized)	0.00424*** (0.00117)	0.00616*** (0.00237)	0.02437*** (0.00582)	0.00347** (0.00144)
Total wealth (standardized)	0.00469*** (0.00135)	0.00374 (0.00261)	−0.00859 (0.00652)	0.00600*** (0.00163)
Children in will	0.03616*** (0.00288)	0.03762*** (0.00531)	0.00241 (0.01341)	0.04052*** (0.00341)
Number of ADLs	−0.00085 (0.00287)	0.00020 (0.00375)	0.01426 (0.01437)	−0.00383 (0.00416)
Number of IADLs	0.00352 (0.00445)	0.00413 (0.00564)	−0.02249 (0.02440)	0.00156 (0.00670)
Depression score	−0.00276*** (0.00067)	−0.00294*** (0.00098)	−0.00501 (0.00392)	−0.00310*** (0.00089)
Comorbidity score	0.00104 (0.00122)	0.00210 (0.00183)	0.00569 (0.00609)	0.00065 (0.00153)
Body mass index	0.00021 (0.00025)	−0.00028 (0.00038)	0.00153 (0.00129)	0.00062** (0.00031)
Self-reported health OK	0.00681** (0.00327)	0.00476 (0.00469)	0.01048 (0.01887)	0.00826* (0.00441)
Smoker	−0.00130 (0.00352)	−0.00307 (0.00531)	−0.00521 (0.01480)	−0.00174 (0.00441)
Children living in household	−0.00316*** (0.00102)	−0.00279* (0.00160)	−0.00608 (0.00476)	−0.00351*** (0.00128)
Number of children	−0.00246*** (0.00086)	−0.00227* (0.00135)	−0.00585* (0.00342)	−0.00265** (0.00104)
Number of living siblings	−0.00148** (0.00060)	−0.00147 (0.00092)	0.00082 (0.00239)	−0.00159** (0.00073)
Number of future helpers	0.00113 (0.00080)	0.00241* (0.00140)	0.01072*** (0.00338)	−0.00016 (0.00099)
Home care user	0.01910*** (0.00671)	0.01469 (0.00992)	0.05520 (0.03754)	0.02073** (0.00904)
Informal care user	−0.00872 (0.01680)	−0.03203 (0.02325)	−0.03427 (0.09353)	−0.00512 (0.02389)
Wave dummies	Yes	Yes	Yes	Yes
Census division dummies	Yes	Yes	Yes	Yes
Constant	0.24249 (0.21095)	0.43948 (0.38549)	−1.82144 (1.32189)	0.29170 (0.26160)
Observation	64,851	16,012	2,652	46,187

Results of random effects linear probability models. *, **, ***

Source: Health and retirement study (HRS), waves 3 to 14 (1996–2018)

Table 5 also shows the results for the three categories of . In the “negative deviation” group and in the “positive deviation” group, LTC insurance take-up is not correlated with the self-reported probability of living to age 75 (Models 2 and 3). In the “consistent” group, a 1-point increase in the probability of living to age 75 is associated with a 0.61 pp increase in LTC insurance purchase (Model 4).

Table 6 describes groups defined according to the distribution of . We find that individuals classified in the “negative deviation” group are less likely to buy LTC insurance, be white, be in good health, be smoker, be self-employed, and have children in their will. They are significantly more likely to have ADLs, have depression, have a higher body mass index, be female, and have a higher education degree than individuals in the “consistent” group. They also have lower income levels than individuals in the “consistent” group. We find that individuals classified in the “positive deviation” group are less likely to buy LTC insurance, be female, be white, be in good health, be self-employed, and have children in their will. They are significantly more likely to have ADLs/IADLs, have depression or comorbidities, have a higher body mass index, be smoker, use formal and informal care. They also have lower levels of income and wealth than individuals in the “consistent” group.

Table 6.

Descriptive statistics and comparison by life expectancy miscalibration. Panel of individuals aged between 50 and 65 years old (creating groups according to the distribution of )

	Overall	Negative deviation (N)	Positive deviation (P)	Consistent (C)	Differences between samples a
Variables					C/N	C/P
LTC insurance purchase (%)	9.34	7.79	7.39	10.10	***	***
Number of ADLs (mean SD)	0.10 (0.43)	0.10 (0.42)	0.21 (0.64)	0.09 (0.40)	***	***
Number of IADLs (mean SD)	0.05 (0.27)	0.04 (0.25)	0.10 (0.39)	0.04 (0.25)	NS	***
Depression score (mean SD)	1.32 (1.88)	1.41 (1.95)	1.93 (2.13)	1.21 (1.80)	***	***
Comorbidity score (mean SD)	1.43 (1.26)	1.38 (1.16)	2.01 (1.52)	1.36 (1.23)	NS	***
Body mass index (mean SD)	28.68 (5.85)	28.94 (5.39)	29.28 (7.45)	28.51 (5.73)	***	***
Self-reported health (%)	79.67	78.94	58.07	82.92	***	***
Smoker (%)	19.43	9.45	55.66	17.53	***	***
Children living in household (mean SD)	2.56 (1.31)	2.61 (1.35)	2.59 (1.45)	2.53 (1.27)	***	***
Number of children (mean SD)	3.19 (1.79)	3.27 (1.83)	3.39 (1.97)	3.14 (1.75)	***	***
Number of living siblings (mean SD)	3.31 (2.56)	3.76 (2.83)	3.32 (2.50)	3.17 (2.47)	***	***
Number of future helpers (mean SD)	1.06 (1.51)	1.03 (1.49)	1.11 (1.64)	1.06 (1.50)	NS	NS
Home care user (%)	2.47	2.04	4.46	2.34	NS	***
Informal care user (%)	0.41	0.32	1.29	0.31	NS	***
Age (mean SD)	58.08 (4.04)	58.62 (3.95)	56.83 (4.00)	58.08 (4.04)	***	***
Female (%)	58.95	65.54	44.22	58.92	***	***
White (%)	72.97	70.94	57.35	75.79	***	***
General educational development (%)	5.19	6.03	6.89	4.69	***	***
High-school graduate (%)	29.25	32.78	28.70	28.21	***	NS
Some college (%)	26.64	23.55	26.92	27.58	***	NS
College and above (%)	24.29	20.11	10.22	27.58	***	***
Married (%)	69.94	73.53	52.89	71.18	***	***
No living parents (%)	37.01	39.98	42.53	35.30	***	***
Self-employed (%)	11.71	11.13	9.04	12.26	***	***
Total household income (mean SD)	82684.57 (194530.8)	80583.07 (331943.0)	48387.89 (51278.65)	88136.17 (140203.8)	***	***
Total household wealth (mean SD)	396515.7 (1015272.0)	421721.6 (1133900.0)	124115.5 (297831.4)	426549.1 (1034453.0)	NS	***
Children in will (%)	34.75	33.44	17.81	37.53	***	***
Observations	64,851	14,101	6,215	44,535

^a Statistical significance of the difference between the two samples. Results of Student test for continuous variables, andtest for categorical variables. ***; ns non significant

Positive deviation (resp. negative): individuals for whom the self-reported probability is much higher (resp. lower) than the probability obtained from individual predictions by more than one standard deviation

Consistent: individuals for whom the difference between self-reported probability and the probability obtained from individual predictions is lower than one standard deviation in absolute value

Source: Health and retirement study (HRS), waves 3 to 14 (1996–2018)

Table 7 also shows the results for the three categories of . In contrast to other estimates, in the “negative deviation” group, a 1-point increase in the probability of living to age 75 is associated with a 0.51 pp increase in LTC insurance purchase (Model 2). However, this effect is only significant at the 10% threshold. In the “positive deviation” group, LTC insurance take-up is not correlated with the self-reported probability of living to age 75 (Model 3). In the “consistent” group, a 1-point increase in the probability of living to age 75 is associated with a 0.44 pp increase in LTC insurance purchase (Model 4).

Table 7.

Impact of life expectancy on the probability of being covered with LTC insurance. Panel of individuals aged between 50 and 65 years old (creating groups according to the distribution of )

Variables	Overall (1)	Negative deviation (2)	Positive deviation (3)	Consistent (4)
Probability of living to age 75 (standardized)	0.00602*** (0.00124)	0.00509* (0.00281)	0.00270 (0.00397)	0.00435** (0.00192)
Age	−0.00780 (0.00729)	−0.01836 (0.01509)	0.02045 (0.02359)	−0.00661 (0.00922)
Age squared	0.00009 (0.00006)	0.00018 (0.00013)	−0.00017 (0.00021)	0.00008 (0.00008)
Female	0.00772** (0.00311)	0.00929 (0.00597)	0.00196 (0.00786)	0.00900** (0.00371)
White	−0.01140*** (0.00368)	−0.01210* (0.00663)	−0.02421*** (0.00813)	−0.01031** (0.00441)
Education GED	0.01670** (0.00751)	0.01287 (0.01300)	0.01051 (0.01537)	0.01384 (0.00917)
High-school graduate	0.02363*** (0.00485)	0.01724** (0.00855)	0.02153** (0.00981)	0.02302*** (0.00597)
Some college	0.04371*** (0.00505)	0.03839*** (0.00922)	0.05185*** (0.01034)	0.04106*** (0.00615)
College and above	0.07262*** (0.00546)	0.05481*** (0.01015)	0.03413** (0.01408)	0.07158*** (0.00657)
No living parents	0.00273 (0.00286)	0.00096 (0.00545)	−0.01154 (0.00753)	0.00576* (0.00349)
Married	0.01527*** (0.00328)	0.01835*** (0.00639)	0.01919** (0.00819)	0.01007** (0.00396)
Self-employed	−0.02402*** (0.00398)	−0.01389* (0.00784)	−0.02642** (0.01206)	−0.03079*** (0.00476)
Total income (standardized)	0.00424*** (0.00117)	0.00020 (0.00224)	0.02100*** (0.00394)	0.00946*** (0.00155)
Total wealth (standardized)	0.00469*** (0.00135)	0.00625** (0.00278)	−0.00188 (0.00369)	0.00477*** (0.00167)
Children in will	0.03616*** (0.00288)	0.04130*** (0.00565)	0.02877*** (0.00950)	0.03817*** (0.00344)
Number of ADLs	−0.00085 (0.00287)	0.00080 (0.00583)	−0.00691 (0.00581)	0.00150 (0.00391)
Number of IADLs	0.00352 (0.00445)	0.00866 (0.00912)	0.01316 (0.00967)	−0.00199 (0.00599)
Depression score	−0.00276*** (0.00067)	−0.00173 (0.00127)	−0.00310* (0.00174)	−0.00358*** (0.00087)
Comorbidity score	0.00104 (0.00122)	0.00284 (0.00248)	0.00361 (0.00282)	0.00110 (0.00153)
Body mass index	0.00021 (0.00025)	−0.00014 (0.00051)	0.00024 (0.00052)	0.00034 (0.00031)
Self-reported health OK	0.00681** (0.00327)	0.00258 (0.00639)	0.01522* (0.00780)	0.00808* (0.00445)
Smoker	−0.00130 (0.00352)	0.00863 (0.00879)	0.00138 (0.00794)	−0.00549 (0.00462)
Children living in household	−0.00316*** (0.00102)	−0.00299 (0.00195)	−0.00445* (0.00256)	−0.00330*** (0.00127)
Number of children	−0.00246*** (0.00086)	−0.00366** (0.00158)	−0.00141 (0.00197)	−0.00250** (0.00104)
Number of living siblings	−0.00148** (0.00060)	−0.00163 (0.00104)	0.00041 (0.00149)	−0.00118 (0.00073)
Number of future helpers	0.00113 (0.00080)	0.00131 (0.00157)	0.00440** (0.00220)	0.00021 (0.00100)
Home care user	0.01910*** (0.00671)	0.00155 (0.01482)	0.02015 (0.01602)	0.02698*** (0.00871)
Informal care user	−0.00872 (0.01680)	−0.02133 (0.03803)	−0.01915 (0.03165)	−0.00730 (0.02433)
Wave dummies	Yes	Yes	Yes	Yes
Census division dummies	Yes	Yes	Yes	Yes
Constant	0.24249 (0.21095)	0.56230 (0.43864)	−0.52309 (0.67580)	0.19990 (0.26691)
Observation	64,851	14,101	6,215	44,535

Results of random effects linear probability models. *, **, ***

Source: Health and retirement study (HRS), waves 3 to 14 (1996–2018)

Finally, for the overall sample of individuals aged between 50 and 65 years (Table S8) and for each group created according to the distribution of (Tables S9-S11), and created according to the distribution of (Tables S12-S14), we gradually add the different control variables. The first model includes individuals’ expectations (Model 1), the second model adds socio-demographic variables (Model 2), the third model adds individual’s health variables and control variables for economic and financial information (Model 3). Finally, the fourth model presents the full model including respondents’ access to informal care (Model 4). Our results are thus robust to different specifications, and are unlikely affected by unobserved heterogeneity.

Robustness tests: Individuals not covered by medicaid

In the supplementary materials, we reproduce all estimates for individuals who report not being covered by Medicaid. The aim of these robustness checks is to verify that our results hold when excluding individuals who meet Medicaid eligibility requirements.

Medicaid eligibility varies across States according to financial rules, which can be more generous than the Federal threshold. Moreover, there are significant differences in state-level spending on LTC across the US. Prior work (Yang et al., 2024a, b) identified that higher levels of LTC spending were linked to fewer unmet care needs among adults with disabilities, particularly for specific ethnic groups (non-Hispanic white respondents). Moreover, those living alone-especially with cognitive impairment-continue to face a significantly higher risk of unmet care needs compared to those living with others. LTC insurance programs are designed for populations who can afford complementary insurance, and therefore do not target people eligible for Medicaid, who face important financial constraints.

Table S15 describes the sample of individuals aged 65 to 75 across the three groups (“consistent,” “positive deviation,” and “negative deviation”). Table S16 shows that an increase in the self-reported probability of being alive 10–15 years after the interview and an increase in the self-reported probability of moving to a nursing home both significantly raise the likelihood of having LTC insurance, for the overall subsample of non-Medicaid-covered individuals (Model 1) as well as for the “consistent” group (Model 4). Within the “negative deviation” group, we also find that a higher self-reported probability of moving to a nursing home significantly increases LTC insurance take-up, while survival expectations (10–15 years) are not correlated with coverage (Model 2). Finally, for the “positive deviation” group, LTC insurance take-up is not correlated with either survival or nursing home expectations (Model 3).

Table S17 describes the sample of individuals aged 50 to 65 across the groups defined by the distribution of . Table S18 shows that a higher self-reported probability of living to age 75 is associated with a 0.66 pp increase in LTC insurance purchase overall (Model 1) and a 0.57 pp increase within the “consistent” group (Model 4). By contrast, no significant relationship is found for either the “negative deviation” group (Model 2) or the “positive deviation” group (Model 3).

Table S19 then describes the same age group, this time classified according to the distribution of . Table S20 confirms that a higher probability of living to 75 is associated with a 0.66 pp increase in LTC insurance take-up overall (Model 1) and a 0.45 pp increase in the “consistent” group (Model 4). Within the “negative deviation” group, a one-point increase in survival probability raises the likelihood of purchase by 0.49 pp (Model 2), although this effect is only significant at the 10% level. Finally, no significant association is found for the “positive deviation” group (Model 3).

Taken together, these supplementary analyses confirm that our main results are robust to the exclusion of individuals covered by Medicaid, across both panels and all group classifications.

Discussion

Our results show that, overall, older adults are more likely to purchase private LTC insurance when they anticipate both living longer and entering a nursing home. The self-reported life expectancy probability reflects an expectation associated with the perception of longevity and, therefore, a greater likelihood of incurring LTC expenses over the life cycle. In addition, the self-reported probability of moving to a nursing home in the next five years reflects an expectation associated with LTC expenditures in the short term.

In panel A, composed of individuals aged between 65 and 75, our results suggest that individuals in the “negative deviation” group are responsive to expectations of nursing home entry but not to survival expectations. These individuals thus appear capable of projecting themselves into the future to identify their short-term old-age related expenditure needs, even though their demand for LTC insurance is not sensitive to their self-reported probability of living a long life. This pattern suggests that it is more plausible that these individuals possess private information about their health status – likely poor in this case – consistent with Hypothesis 1, and less plausible that they are simply unable to project themselves into the future and to provide consistent estimates, as suggested by Hypothesis 2 (The hypotheses are explained in Section 3, Conceptual framework). Still within panel A, individuals in the “positive deviation” group do not respond systematically to either type of expectation. This finding is more consistent with Hypothesis 2, as these individuals seem unable to report coherent survival probabilities over a 10–15 year horizon, likely reflecting difficulties in projecting themselves into the future. Overall, however, the evidence from panel A does not allow us to fully disentangle Hypotheses 1 and 2.

Panel B, composed of individuals aged between 50 and 65, helps to reduce the uncertainty surrounding these results, as we have here an additional measure of misperception of the probability of long living. By construction, this measure (i.e., ) captures more directly a miscalibration of beliefs consistent with Hypothesis 2, making it possible to exclude Hypothesis 1 – that miscalibration stems from private information about health status. In the “positive deviation” group, LTC insurance take-up remains uncorrelated with the self-reported probability of living to age 75, again confirming the prevalence of Hypothesis 2 over Hypothesis 1 for these individuals: their cognitive limitations or difficulties in projecting future needs lead them to base insurance decisions on other, possibly exogenous, criteria. For those classified in the “negative deviation” group, our results are once again more nuanced. Unlike in panel A, we now find that an increase in the probability of living to age 75 is associated with an increase in LTC insurance purchase – consistent with the idea that a longer life mechanically entails higher old-age expenditures. Because panel B provides a sharper test of Hypothesis 2 relative to Hypothesis 1, this suggests that it is primarily those who substantially overestimate their survival probability, rather than those who underestimate it, who struggle to form accurate expectations about longevity and thus about future needs. This misperception hinders their LTC insurance purchase. This finding is consistent with our results in panel A, which indicated that individuals in the “negative deviation” group are nevertheless responsive to their expectations of nursing home entry, thereby better anticipating short-term rather than long-term needs.

Finally, across both panels A and B, individuals in the “consistent” group – those presumed capable of predicting their survival probabilities with reasonable accuracy – purchase more LTC insurance when they expect to live longer, consistent with the idea that longer life spans imply greater old-age related expenditures.

These findings highlight the importance of improving individuals’ awareness of their LTC risks, especially among those who substantially overestimate their probability of survival. A better understanding of future age-related expenditures could lead to higher and more appropriate LTC insurance coverage.

The results obtained with the control variables are consistent with prior research (Van Houtven et al., 2015; Costa-Font & Courbage, 2015; Coe et al., 2015). In line with previous evidence, we find that indicators of potential future informal care provision, such as the expected number of future helpers, are negatively correlated with the propensity to purchase LTC insurance. We also show that higher total wealth is positively associated with insurance coverage, supporting the interpretation of LTC insurance as a normal good. Finally, our findings confirm that parents are more likely to purchase coverage when they wish to protect their bequests from potential LTC expenditures, consistent with altruistic motives towards children.

Despite these strengths, several limitations should be noted. First, our empirical analyses do not provide causal estimates of the relationship between self-reported expectations and LTC insurance take-up. Second, the HRS relies on self-reported information; misreporting may occur, for instance if some individuals incorrectly state that they do not hold LTC insurance. Replication using alternative data sources would strengthen the robustness of our results. Third, we are unable to fully account for state-level variation, even though LTC decisions are likely influenced by substantial heterogeneity in the organization and availability of care across states (Reinhard et al., 2014). While we include census division dummies to partially capture such differences, further research using state-level data would be necessary to better account for this dimension.

Finally, we must keep in mind how previous research has emphasized the importance of rethinking LTC insurance contract design to increase coverage (Cremer et al., 2016; Cornell et al., 2016). Tax-qualified LTC insurance premiums and benefits can now be deducted if certain conditions are met to encourage the purchase of LTC insurance. Despite this incentive, the private LTC insurance market is worth $11 billion, and less than 14% of Americans have purchased LTC insurance, raising the need to redesign contracts. Current insurance contracts reimburse LTC expenses, but a daily limit and a fixed term limit them. The longer the term and the higher the daily limit, the higher the premium. The scheme is characterized by high load charges, as policyholders’ needs are highly individual, limiting the performance of LTC insurance. In theory, this scheme is preferred to the flat-rate benefit scheme for risk-averse individuals because the insurance covers a part of the LTC expenses. In contrast, the flat-rate formula pays an annuity independent of the costs. Cremer et al. (2016) and Klimaviciute (2017) show that if children can help their parents, and if parents prefer helping their children, a flat-benefit scheme will be preferred. Coe et al. (2023) find that LTC insurance coverage reduces parents’ perceptions of the willingness of their children to care for them in the future and that the behavior of adult children changes, especially for cohabitation and participation in the labor market. Klimaviciute and Pestieau (2019) recommend the creation of LTC insurance contracts based on Arrow’s theorem of the deductible (Arrow, 1963), which is defined as a period beyond which the total cost of LTC would be covered. Before this period, LTC needs are paid by the dependent person. In 2011, the Dilnot Commission in the United Kingdom recommended the introduction of such a scheme for social LTC insurance programs (Dilnot Commission, 2011). When the maximum deductible is reached, the individual becomes eligible for full state assistance. Under such a scheme, individuals developing a need for LTC would immediately benefit from public assistance with no deductible.

Supplementary Information

Below is the link to the electronic supplementary material.

Funding sources

This study was sponsored by the AgingUP! grant, funded by Mécénat des Mutuelles AXA and Caisse des Dépôts et Consignations.

Declarations

Conflict of interest

The authors declare no conflicts.