Lapses in Long-Term Care Insurance

Abstract

About a quarter of long-term care insurance (LTCI) policy holders aged 65 let their policies lapse prior to death, forfeiting all benefits. We find that lapse rates are substantially higher among the cognitively impaired in the Health and Retirement Study. This generates a pernicious form of dynamic advantageous selection, as the cognitively impaired are more likely to use care. Simulations show that an inappropriately optimistic asset drawdown path further increases the individual welfare cost of unanticipated lapses. Meanwhile, we find evidence of a significant but very small role for either strategic or financial motives for lapsing.

Long-term care, including both nursing home and home health care, represents a substantial financial risk for most retired households. Yet, few purchase long-term care insurance, and many purchasers let their policies lapse, even after holding them for years. Lapsing can be quite costly to individuals, as they forgo their aging reserves (that is, access to benefits that are backloaded relative to premiums) and face much higher premiums for a new policy. Extrapolating current lapse rates, over one-quarter of individuals who purchase long-term care insurance at age 65 will let their policies lapse before death, forfeiting all benefits.¹ We investigate whether the lapses might be strategic or unintended and whether lapsing leads to adverse or advantageous selection among remaining policyholders.

Researchers have sought evidence of adverse selection in the purchase or holding of many types of insurance, including for long-term care, by consumers with private information about their riskiness (Finkelstein and Einav 2011). While insurance lapsing is generally more difficult to observe than insurance purchases in the absence of industry data, dynamic adverse selection in long-term care insurance has received some previous attention (Finkelstein, McGarry, and Sufi 2005a, b). If some lapses are unintended, however, reflecting a lack of intertemporal consistency in decision-making, such lapses may induce dynamic adverse or advantageous selection.

We evaluate evidence for three possible explanations for lapsing. The first is the traditional one, involving new information about one’s need for care. Long-term care insurance contracts have very long duration – claims may occur 25 years or more after purchase. Individuals who learn during that period that their risk of needing care is less than previously expected may let policies lapse, generating strategic lapsing. The second explanation involves changes in financial status. This may take the form of negative information about household finances, which diminishes both the ability to pay premiums and the need to protect one’s wealth from Medicaid if care is needed. Alternatively, it may result from the planned drawdown of wealth; as time passes without needing care, then individuals with declining wealth to protect will find Medicaid increasingly attractive if care is needed. These events result in financial lapsing, and both the first and second explanations can be categorized as rational lapsing. The third explanation involves unanticipated lapses, for example due to time-inconsistent preferences or a loss of financial competence. Individuals who plan on future expenditure that is in their best interest may fail to follow through on that plan, inducing unintended lapsing.²

We evaluate these explanations for lapsing using both simulation and empirical methods. We begin by simulating a dynamic optimization model that quantifies the possible magnitude of rational lapsing, as well as the consequences of unintended lapsing by agents who initially purchase insurance optimally. We use a model of insurance, asset, and Medicaid choices that is standard in the literature (Brown and Finkelstein 2008, Friedberg, Hou, Sun, and Webb 2016). The analysis shows that changes in information would have to be large to motivate either strategic or financial lapsing for someone who optimally purchases a policy at age 65 that is described as typical in Brown and Finkelstein (2007). This is because individuals in our model continue to place a high value on insurance until very old age. Yet, models like this one cannot fully explain the low rate of insurance holding in the first place nor fully explain lapsing, so we test empirical explanations for observed lapses.

We analyze empirical lapsing from 2002–06 in the Health and Retirement Study (HRS). We use variables that plausibly capture the three explanations for lapsing enumerated above. We measure these variables at or around the time that lapsing is observed (during 2002–06 or alternately in 2002 alone).³ We find evidence of a significant but very small role for both strategic and financial lapsing, consistent with our model of rational decision-makers.⁴ However, we find that lapse rates are significantly and substantially higher among people with lower cognitive scores, demonstrating the importance of unintended lapsing. Our baseline estimates indicate that if everyone with low cognitive scores in the 2002–06 period had cognitive scores equal to the median value, lapsing would be 17% lower. We demonstrate the robustness of these estimates to different parameterizations of cognitive score and different approaches to measuring lapses.

We then use our dynamic optimization model to get an idea of the potential welfare cost of losing insurance due to unintended lapsing, by someone who purchased a policy optimally at age 65. Because policies remain valuable until extremely old ages in our model absent a drastic change in information, the cost of unintended lapsing is high. People who pay premiums and later lapse forgo their aging reserves (which can be thought of as the cost of an anticipated lapse), and also may have chosen a post-retirement wealth drawdown path based on the mistaken belief that they will retain coverage. We find, for example, that for people at the 80^th percentile of the wealth distribution at age 65, overconsuming their wealth makes the welfare cost of an unintended lapse over 30% higher for a single man and almost 10% higher for a single woman, in addition to the substantial cost of losing their aging reserves.⁵

Lastly, we consider whether lapsing induces adverse or advantageous selection among remaining policyholders. We do this by analyzing nursing home use in the HRS from 2006–12, a period immediately following our analysis of lapsing from 2002–06. If dynamic adverse selection occurs, it might help explain the small size and costly premiums observed in the long-term care insurance market. However, we find that cognitive impairment generates dynamic advantageous selection (from the point of view of insurers).⁶ These findings echo Fang, Keane, and Silverman (2008), who show that cognitive ability contributes to advantageous selection in the Medigap market, with individuals in the HRS who have higher cognitive ability being simultaneously healthier and more likely to hold a Medigap policy.⁷ This unintended lapsing is quite costly, both to individuals who end up in care and to Medicaid, which covers their costs when they cannot.⁸

The remainder of the paper is organized as follows. Section 1 presents industry data on lapse rates and an analysis of lapsing in a dynamic optimization model. Section 2 discusses the HRS data and summarizes previous research using the HRS. Section 3 presents our econometric models for lapsing and for dynamic selection based on subsequent nursing home entry. Section 4 reports descriptive statistics. Section 5 reports the evidence about lapsing and Section 6 about nursing home entry. Section 7 concludes.

1. Lapse Rates and the Cost of Lapsing

Lapse rates for long-term care insurance policies are substantial. Figure 1 shows cumulative retention rates for non-group policies issued from 1984–2007.⁹ Policies issued in the 1980s had especially high lapse rates, but lapses, though they have declined substantially remain relatively common.¹⁰ For policies issued in 1992–96 (corresponding roughly to the original HRS/AHEAD cohorts), 25.9% had lapsed after five years, and 41.1% had lapsed after fifteen years. At current lapse rates, though they are lower, we calculate that men and women who purchase a policy at age 65 have, approximately, a 27- and 29-percent chance of lapsing their policies before death, respectively.

Figure 1.

Cumulative Retention Rates by Issue Year

Source: Authors’ calculations based on Society of Actuaries Experience Study (2011, 2015).

The cost of lapsing in terms of foregone “aging reserves” is substantial. Aging reserves accumulate because the premium on a newly issued policy is much more than the expected cost of that year’s care, since the risk of requiring care is dramatically lower at younger ages.¹¹ The excess premiums paid in the early years of the policy effectively form a reserve, which is drawn down in later years when the expected cost of care exceeds the premiums. An individual who lapses his policy forfeits this reserve and must face higher age-rated premiums if he wishes to purchase a new policy.

In order to evaluate the cost of lapsing, we compute both the financial and utility values of long-term care insurance. First, we compute the expected present value (EPV) at each age of remaining lifetime premiums and benefits, conditional on not currently needing care, for someone considering whether to hold onto a policy. Expected remaining premiums are based on policy characteristics described by Brown and Finkelstein (2007) as typical and updated to 2015. Expected benefits are based on the likelihood of needing different types of care as estimated in Friedberg, Hou, Sun, Webb, and Li (2016). These EPVs demonstrate the financial valuation of insurance. Second, we use a dynamic optimization model that is standard in the literature (Brown and Finkelstein 2008, Friedberg, Hou, Sun, and Webb 2016) to compute willingness-to-pay by age and wealth level for this typical policy. Single men and women in the model make monthly choices over insurance, assets, and the use of means-tested Medicaid, beginning at age 65. Willingness to pay depends not only on expected benefits relative to expected costs, as computed above, but also on factors including wealth, risk aversion, and the option to rely on Medicaid.¹² We use these calculations to consider the magnitude of changes in news or in financial status needed to justify strategic or financial lapsing.

The EPV calculations for remaining premiums and benefits at each age show that the value of continuing to hold a typical policy is large. At age 65, the EPV of lifetime premiums in Figures 2A and 2B are at their highest values and exceed the EPV of benefits, by a considerable amount for men (with EPVs of $55,196 and $21,857 for premiums and benefits) and by less for women (with EPVs of $60,851 and $46,307 for premiums and benefits). The EPV of premiums declines rapidly as people age and begins to exceed the slowly-declining EPV of benefits at around age 68 for women and at age 73 for men.

Figure 2.

Expected Present Value of Long-Term Care Insurance Premiums and Benefits

Meanwhile, willingness to pay for risk-averse single individuals who are relatively wealthy, in Figures 3A and 3B, is positive at age 65, and it grows until much older ages, absent a dramatic and unexpected change in beliefs or wealth.¹³ Lower-wealth individuals are not willing to purchase insurance at age 65 because they have the option to claim Medicaid. Valuations of insurance at age 65 become positive above the 70th wealth percentile for single men and women.

Figure 3.

Willingness to Pay for Long-Term Care Insurance, by Wealth Decile

Source: Authors’ calculations, based on a typical long-term care insurance policy. See text for more information.

After age 65, the same value of willingness to pay for age-65 prices, conditional on being in good health, also shows the value of holding the policy rather than lapsing. Consider a single man and a single woman at the 80^th percentile of their respective wealth distributions. Willingness to pay for a policy at age 65 is, respectively, $14,500 and $48,400, and then willingness to avoid lapsing that policy increases by a few thousand dollars per year for many years after. It is only then that the value of holding a policy starts to decline gradually, as individuals who have drawn down their wealth face an increasing implicit Medicaid tax. Willingness to pay remains even higher for those whose health deteriorates.

These results show that policy lapsing should not optimally occur for most people until extreme old age. Therefore, the results rule out one type of financial lapsing – arising because planned drawdown of wealth has left the typical policyholder willing to forgo insurance in favor of means-tested Medicaid. We can also quantify how big a negative wealth shock would have to occur to induce financial lapsing. If wealth suddenly fell below the 70^th percentile for men and the 80^th percentile for women at age 65, they would no longer want to hold a policy. At older ages, as policies continue to grow in value, the sudden and unexpected wealth drop would have to be greater.

Lastly, a change in one’s expectation of needing future care would also have to be large to generate strategic lapsing. In the optimization model, suppose people suddenly believed that they would never enter a nursing home before they died, but retained their expectation of needing home health care or assisted living. Given this major shift in beliefs, we calculate that a single woman at the 80^th percentile of wealth would still prefer to hold a policy at age 75, while a single man at the 80^th percentile would now have only a slight gain from lapsing, and single men with more wealth would still hold a policy. Consequently, major shifts in circumstances or beliefs are needed to generate strategic or financial lapsing in an optimizing model. Yet, optimizing models like this one cannot fully account for the low rate of insurance holding in the first place (Brown and Finkelstein 2008, Lockwood 2017) and may not fully explain lapsing. Therefore, we proceed to test empirical explanations for observed lapses.

2. Background and Literature

Studies of lapsing have typically used the HRS, a panel micro data set with detailed information about participants’ health and financial status.¹⁴ However, questions about long-term care insurance holdings in the HRS have changed in ways that substantively affect the measurement of lapsing, both by adding clarifying questions to confirm the type of policy and by shifting the focus to short-term lapsing, rather than lifetime lapsing. Using the most recent set of questions, we estimate short-term lapse rates that are in line with Society of Actuaries statistics. The capacity to measure short-term lapses allows us, further, to relate current lapsing to current variables that may account for lapsing, an approach that is difficult when the timing of lifetime lapsing cannot be pinpointed.

The HRS follows Americans aged 51 and older. It began in 1992 with people aged 51–61 (and their spouses of any age) and in 1993 with people aged 70 and over, and it re-interviews respondents every two years.¹⁵ As question sequences laid out in Table 1 show, from 1995 (AHEAD) and 1996 (HRS) on participants were asked whether they held long-term care insurance. Until 2002, participants were also asked, “Have you ever been covered by a policy that you cancelled or let lapse.”

Table 1:

Use of HRS Information about Long-term Care Insurance

HRS Wave	Questions about LTCI holding	Questions about lapsing
1992	(no separate question)
1993/94	(doesn’t ask about type of care that is covered)
1995/96	Do you hold long term care insurance	Have you ever been covered by any long-term care insurance that you cancelled or let lapse
1998	Do you hold long term care insurance	Have you ever been covered by any long-term care insurance that you cancelled or let lapse
2000	Do you hold long term care insurance	Have you ever been covered by any long-term care insurance that you cancelled or let lapse
2002	Do you hold long term care insurance Is it one of the plans you told me about previously	Have you ever been covered by any long-term care insurance that you cancelled or let lapse
2004	Do you hold long term care insurance Is it one of the plans you told me about previously
2006	Do you hold long term care insurance Is it one of the plans you told me about previously
2008	Do you hold long term care insurance Is it one of the plans you told me about previously
2010	Do you hold long term care insurance Is it one of the plans you told me about previously
	Papers about LTCI lapses	Data
	Finkelstein, McGarry, & Sufi (2005a,b)	Sample: people who report having LTCI in 1995/96 or 1998 or who report ever having lapsed in 1996, 1998, or 2000. Key variable: ever having lapsed.
	McNamara & Lee (2004)	Sample: people who report having LTCI 1996–2002. Key variable: number of consecutive waves covered by LTCI.
	Konetzka & Luo (2011)	Sample: people who report having LTCI 1996–2008. Key variable: lapse between waves. Do not mention how they made use of the clarifying question asked in 2002+.
	Cramer & Jensen (2007)	Sample: people who report having LTCI in 2002–2004. Key variable: lapse between waves.
	Li & Jensen (2012)	Sample: people who report having LTCI in 2002–2008. Key variable: lapse between waves.

Table 1 demonstrates two important changes in the insurance questions that took place after 1996–2000, the time period that was the focus of previous research on lapsing. First, a new question was added in 2002 to clarify what type of plan was being discussed. The new question asked participants whether the policy that they had in mind when answering the long-term care insurance questions was one of the plans (referring to health insurance plans) that the participant had told the interviewer about earlier in the interview. The previous scope of respondent confusion appears to be high: 23% of respondents who said they had a long-term care insurance policy in 2002 then answered that this was one of the health insurance plans that they had mentioned earlier. This raises concern about the use of questions from before 2002 in the lapsing studies listed in Table 1.

Second, the question about ever lapsing was removed after 2002, so we use changes in reported policy holding across waves to measure recent lapses. The resulting lapse rates match up well with industry statistics. The two-year lapse rate that we compute for people aged 65 and over in the HRS between 2002–04 is 8.4%. The 2015 SOA study indicates a two-year lapse rate of 8.5% for those aged 60 and over and 9.7% for those aged 70 and over. This suggests that the new wording is critical in allowing us to measure cross-wave lapsing, in contrast to concerns raised by Finkelstein, McGarry, and Sufi (2005a) about the validity of short-term lapsing measures before 2002.¹⁶ Given both of the changes to the insurance questions – the addition of the clarifying question about the type of policy and the removal of the question about ever lapsing – we cannot replicate the earlier analysis (which shows dynamic adverse selection) using data from 2002 on or replicate our analysis (which shows dynamic advantageous selection) using data from before 2000.¹⁷ Neither can we replicate our analysis of possible explanations for lifetime lapsing, since the HRS does not report when many of those policies were either purchased or lapsed.

The papers most relevant to our analysis are those that study strategic lapsing and adverse selection. The long-term care insurance market is small and policies are expensive, with evidence of asymmetric information in who holds policies. Finkelstein and McGarry (2006) show that the self-reported likelihood of needing nursing home care is informative about future care use in the HRS even when conditioning on observable predictors of later care use. Yet, those who hold insurance are not more likely on average to use care in the future conditional on observables, in spite of their private information. They resolve this puzzle by showing that insurance holders are also more risk averse along various measures, and those who are risk averse are less likely to use care. This underlines two empirical points: a negative correlation between lapsing and care use can occur even in the absence of asymmetric information, if preferences rather than beliefs influence the lapsing decision; and conversely, the absence of a correlation does not prove that asymmetric information is irrelevant in the lapsing decision. Therefore, it is important to consider simultaneous motives for lapsing and then to control for them when analyzing the relationship between lapsing and subsequent nursing home use.

Meanwhile, Finkelstein, McGarry, and Sufi (2005a,b), focus on lapses rather than on holdings of long-term care insurance, in order to explore dynamic selection. They find that individuals in the HRS whose policies have ever lapsed are 2.4 percentage points less likely to be in a nursing home at any time between 1996 and 2000. As we have noted, this evidence of dynamic adverse selection is not confirmed with our use of data from 2002 and later. Still, they argue that strategic motives do not fully explain lapses, and nor do we find that the broader set of explanations we consider fully explain lapses. They point to the high early lapse rate as inconsistent with the immediate arrival of new information right after policy purchases, similar to our point above that considerable changes in information or circumstances would be needed to explain rational lapses.¹⁸

Table 1 lists other studies that also use the pre-2002 data on lapsing. McNamara and Lee (2004) find evidence consistent with financial lapsing. Konetzka and Luo (2011) use data from 1996 until 2010 to analyze the relationship between lapsing and later care use, combining information from before and after the HRS question that clarified insurance holding was included. Two recent studies of lapsing exploit the questions added in 2002, though neither considers dynamic selection, as we do. Li and Jensen (2012) find that the probability of a lapse increased with lack of knowledge about one’s policy benefit provisions, with prior encounters with the long-term care system, with less expensive policies, with less generous policies, and with low income and low wealth. Cramer and Jensen (2007) also find that inability to perform ADLs was positively correlated with lapsing.

3. Econometric Models of Lapsing and Dynamic Selection

In this section, we present our approach to testing explanations for lapsing and testing for dynamic selection. We regress lapsing on variables that capture various explanations for lapsing. Then, we observe nursing home use for a period of time after lapsing in order to analyze sources of dynamic selection, whether adverse or advantageous. We investigate whether any of the variables related to lapsing are also related to subsequent nursing home use. If so, that indicates a source of selection, either adverse or advantageous, out of policy holding. We focus on people aged 65 and over holding policies in 2002 (beginning when the HRS questions about long-term care insurance changed), then measure lapsing from 2002 to 2006, and then measure nursing home use from 2006 to 2012.

Testing explanations for lapsing

To test explanations for lapsing, we estimate the following as a probit model:

$$\mathrm{Pr}\left({LAPSE}_i=1\right)=\mathrm{f}\left({\beta }_s{strategic}_i+{\beta }_f{financial}_i+{\beta }_u{unintended}_i+{{\beta }_{x}X}_i+{\epsilon }_i^{\beta }\right)\mathrm{ }$$ (1)

in which the LAPSE takes the value one if the individual lapsed coverage between 2002 and 2006, or zero if he retained coverage. Right-hand side variables include characteristics that may result in strategic, financial, or unintended lapsing, plus controls for demographic characteristics and risk preferences.

We test three explanations for why individuals with long-term care insurance let their policies lapse. We do so by using variables from the HRS that plausibly capture these explanations. As these variables are not comprehensive, a null finding does not rule out an explanation, but a statistically significant finding suggests its presence. In evaluating each explanation, it is changes in conditions (wealth, need for care, cognitive ability) that should predict lapsing. However, it is not possible to measure changes in circumstances since a policy purchase, a potentially long period that is not well documented in the HRS.¹⁹ We instead rely on the observation by Hendren (2013) that policies are only offered to people in good physical and mental health and, similarly, only affordable to people with financial means.²⁰ This motivates our consideration of current circumstances as explanatory factors when we observe lapses. We view poor current circumstances as most likely reflecting changes for the worse since the policy was purchased.

The first explanation we consider in our analysis is that policyholders may acquire new information about their risk of requiring care. If they learn that the risk is lower than they originally expected, they have less need for insurance and may let their policies lapse, which we term strategic lapsing. We use HRS variables on both the self-assessed probability of needing care, as in Finkelstein and McGarry (2006) and other objective and subjective measures of well-being: self-reported health, the log of last year’s medical expenditures, and having any difficulties in performing Activities of Daily Living (ADLs).²¹ We also consider whether the individual has a spouse, any children, or any daughters, which may prompt a reassessment of care options. Relatives provide the bulk of informal care (Hiedemann et al 2016), possibly including financial management, and may offset the effects of cognitive impairment.²²

A second explanation for lapses is that some purchasers may come to view the insurance premium as a financial burden over time. This could occur if they suffer a negative wealth or income shock or because a policy they were willing to purchase becomes less valuable after gradual (and planned) wealth drawdown increases the Medicaid implicit tax on retaining a private policy, inducing financial lapsing. We examine whether wealth or income (measured in logs) are associated with observed lapses.

A third explanation for lapses is that they are unintended, for example due to time-inconsistent preferences or inattention. We cannot test comprehensively for sources of unintended lapses, so we try two sets of variables to capture particular explanations. First, we consider whether proxies for a propensity to plan and undertake precautionary actions (getting a flu shot, cholesterol test, pap smear, or breast or prostate cancer screening, as suggested by Finkelstein and McGarry 2006), affect lapsing. Second, we consider whether having difficulty handling money or experiencing cognitive impairment increases lapsing (while also showing that these variables do not increase misreporting about policies in other ways). For example, individuals might forget to pay their premiums or no longer understand the value of their policies. In this case, individuals may be more likely to lapse even though their impairment makes them more likely to need care, making these unintended lapsers the opposite of strategic lapsers.²³ Several questions in the HRS are designed to reveal a respondent’s cognitive state. We form an index of those answers that are found in Hurd et al (2013) to significantly predict dementia.²⁴

Finally, we include socioeconomic variables (age, education, and gender) that may affect demand for insurance and also reflect other variables that influence insurance offer and pricing decisions (Hendren 2013). We follow the baseline approach from Hendren of using a minimal set of controls. Other health-related variables that may influence purchases and that he uses in an extended set of controls are not observable at the time that many policies were issued.²⁵ In papers studying other old-age financial decision using the HRS, Fang and Kung (2012) and Gottlieb and Mitchell (2020) use similar sets of control variables to ours.²⁶

Dynamic selection due to lapsing

Dynamic adverse selection due to strategic lapsing might help explain the small size and costly premiums observed in the long-term care insurance market. One approach to test for selection due to asymmetric information involves estimating whether holding insurance coverage against a risk and subsequent realization of the risk are positively correlated (Chiappori and Salanie, 2000). A similar test for dynamic selection involves estimating a bivariate model of lapsing and nursing home entry, conditional on a vector of risk classification variables that are observable to insurers when the policy was issued, and then testing whether the error terms are positively correlated (indicating adverse selection) or negatively correlated (indicating advantageous selection).

However, these tests do not distinguish between asymmetric information and preference-based selection. As mentioned above, Finkelstein and McGarry (2006) show that preference-based selection (the risk averse like to buy insurance although their risk is low) offsets risk-based selection in the decision to purchase long-term care insurance. Similarly, the absence of a negative correlation between lapsing and care use does not prove that the market is free of dynamical selection. As an alternative, we consider the following relationship, estimated as a probit model and adapted from Finkelstein and McGarry:

$$\mathrm{Pr}\left({CARE}_i=1\right)=\mathrm{f}\left(\gamma \mathrm{ }{LAPSE}_i+{\gamma }_s{strategic}_i+{\gamma }_f{financial}_i+{\gamma }_u{unintended}_i+{{\gamma }_{x}X}_i+{\epsilon }_i^{\gamma }\right)\mathrm{ }\mathrm{ }\left(2\right)\mathrm{ }$$ (2)

CARE indicates whether a person entered a nursing home between 2006–12. The other variables are the ones from above. X includes the variables that may explain lapsing from 2002–06. If any control variable explains care use as well as lapsing, then this suggests a source of dynamic selection. LAPSE indicates whether the individual lapsed the policy before entering care, and if it remains significant conditional on X, then it indicates further unobservable sources of dynamic selection. In this approach, lapsing does not cause care use but instead captures private information about likely care use that is not reflected in X and that affects insurance demand.

4. Data

We use HRS questions about long-term care insurance holdings that were first asked in 2002 in order to define our sample of policyholders. As we noted earlier, 2002 was the first year in which survey questions about long-term care insurance fully distinguished them from health insurance plans that an individual might also hold. We use changes in reported insurance holding across waves to define lapsing. We focus on lapsing between 2002–06 and care use between 2006–12.²⁷ Among people aged 65 or older in 2002, 1,048 had long-term care insurance, and among them, 966 had known insurance status in 2006. We drop people who are missing answers to questions about anticipated care use and about cognitive ability, because these are critical to our analysis; this leaves us with an insured sample of 891. For this group with insurance in 2002, based on our preferred definition, 13.0% lapsed their policy between 2002–06.²⁸ As we showed in Section 2, this lapse rate is quite similar to national statistics for aged policyholders. Table 2 reports sample statistics at the outset of this period, using sample weights in order to make the sample nationally representative, for this group with long-term care insurance in 2002.²⁹ Sample members have an average age of 74 and are quite likely to be married. They are relatively well off (as predicted by our earlier simulations), with median financial wealth of $125,000 and median annual income of $44,380.³⁰ Their health is good; 17.0% report fair or poor health (as opposed to excellent, very good, or good), and 4.0% have limitations on activities of daily living (ADLs). Interestingly, a relatively high share – 31.3% – reports having difficulty handling money.

Table 2:

Summary Statistics of LTCI Policy Holders

	Full sample	Non-lapsers	Lapsers	p-value, T-test
Characteristics, lapse sample:
Variables which may reflect strategic lapsing (averaged over 2002–2006)
Self-assessed probability of moving to a nursing home in next 5 years (1–100)	19.464	19.580	18.686	0.433
Fair or poor health	0.170	0.157	0.260	0.007 ***
Has limitations on Activities of Daily Living	0.040	0.036	0.070	0.125
Log medical expenditure	7.130	7.140	7.064	0.382
Has children	0.926	0.931	0.895	0.199
Has daughters	0.763	0.781	0.643	0.007 ***
Variables which may reflect financial lapsing (2002)
Log financial wealth	10.969	11.110	10.024	0.002 ***
Log household income	10.731	10.768	10.480	0.000 ***
Variables which may reflect unintended lapsing (averaged over 2002–2006)
Cognitive score	2.983	3.017	2.759	0.000 ***
Cognitive score, if < 50th percentile	0.499	0.471	0.689	0.000 ***
Cognitive score, if < 25th percentile	0.250	0.225	0.416	0.000 ***
Has difficulty handling money	0.313	0.310	0.336	0.553
Demographic characteristics (2002)
Male	0.402	0.403	0.396	0.811
Age	73.554	73.238	75.675	0.001 ***
Less than high school education	0.084	0.079	0.114	0.175
Some college	0.574	0.585	0.503	0.191
Married or partnered	0.690	0.708	0.566	0.012 **
N	891
Lapse occurs, 2002–2006	0.130	0	1
In a nursing home, 2006–2012	0.323	0.310	0.416	0.015**
N	823

Notes: The lapse sample consists of people who are aged 65 and over in the 2002 HRS; who have long-term care insurance in 2002; who have known insurance status in 2006; and who answer questions about the expected likelihood of needing care and who answer questions about cognitive ability. Lapsers are those who no longer have a LTCI policy in 2006.

The nursing home sample consists of those in the lapse sample who have known nursing home status between 2006–12.

Cognitive score is the weighted sum of answers to several questions that test cognitive ability, where the weights are the inverse of the standard deviation of the answers.

^***p<0.01

^**p<0.05

^*p<0.1 for T test of equality of mean values of non-lapsers, lapsers.

Lapsers are in significantly poorer shape on many dimensions than are non-lapsers – an indication that lapsing may yield advantageous selection among remaining policyholders. Lapsers are less likely to be married (56.7% versus 70.8%) and have somewhat lower income and financial wealth. They are in poorer health (26.0% versus 15.7% in fair or poor health) and have lower cognitive scores (2.7 versus 3.0).³¹ On the other hand, they have similar rates of difficulty in handling money (31.0% versus 33.6%, difference not statistically significant) and similar beliefs about the likelihood of moving into a nursing home in the next five years (19.6% versus 18.7% chance).

For the 2002–06 insurance sample, we then consider whether they used nursing home care between 2006–12. We do not observe subsequent nursing home use for 68 individuals, leaving a nursing home sample of 823.³² Table 2 shows that lapsers have much higher subsequent care use, at 41.6%, compared to non-lapsers, at 31.0%. This statistically significant difference suggests the possibility of dynamic advantageous selection in the long-term care insurance market. As noted earlier, it stands in contrast to the evidence from Finkelstein, McGarry, and Sufi (2005a,b) using earlier HRS data.

5. Evidence about Explanations for Lapsing

We estimate a probit model of lapsing between 2002–06 in order to test for the presence of strategic, financial, and unintended lapsing. As we noted earlier, we use variables from the HRS that plausibly capture these explanations for lapsing /we are not able to measure and control for all possible factors, though. Therefore, a null finding does not rule out an explanation, but a statistically significant estimate suggests its presence.

Baseline results

The lapsing model controls for characteristics that may result in financial, strategic, or unintended lapsing, as well as demographic characteristics and risk preferences. Variables intended to capture financial lapsing are log financial wealth and log income. Variables intended to capture strategic lapsing are the self-assessed probability of using nursing home care within the next five years, limitations on ADLs, the log of last year’s medical expenditures, and whether the individual has a spouse, children, or daughters in particular. Variables intended to capture unintended lapsing are cognitive score and having difficulty handling money. As we noted earlier, we cannot reliably determine when a policy was purchased or measure changes in these variables over the entire time since purchase. Instead, we rely on the recognition that policies are only purchased by people with financial means and in good physical and mental health (Hendren 2013), and we use variables measuring current circumstances when we observe lapses.³³

Table 3 reports probit marginal effects. The results show that lower income and lower financial wealth are associated with higher probabilities of lapsing, but the estimated magnitudes are small. A 10% lower level of financial wealth is associated with a statistically significant 0.1 percentage point reduction in the probability of lapsing, and a 10% lower level of income is associated with a 0.3 percentage point reduction, which falls short of statistical significance.³⁴ This finding provides limited support for the hypothesis of financial lapsing.

Table 3:

Probit Estimates for Lapsing, Nursing Home Use

	Dependent variable:
	LTCI policy lapsed 2002–2006	Entered nursing home 2006–2012
	Estimated marginal effect (standard error)
Lapse 2002–2006		−0.0302 (0.0567)
Variables which may reflect strategic lapsing (averaged over 2002–2006)
Self-assessed probability of moving to nursing home in next 5 years (0–100)	−0.0013** (0.0006)	0.0009 (0.0010)
Fair or poor health	0.0761** (0.0356)	0.1650** (0.0659)
Has limitations on Activities of Daily Living	0.0161 (0.0646)	0.1560 (0.1430)
Log medical expenditure	−0.0018 (0.0053)	−0.0021 (0.0103)
Have children	0.0253 (0.0389)	−0.1790* (0.0950)
Have daughters	−0.0994*** (0.0358)	0.0493 (0.0508)
Variables which may reflect financial lapsing (2002)
Log financial wealth	−0.0091*** (0.0034)	0.0020 (0.0070)
Log household income	−0.0277 (0.0178)	0.0020 (0.0289)
Variables which may reflect unintended lapsing (averaged over 2002–2006)
Cognitive score	−0.0879*** (0.0263)	−0.2470*** (0.0564)
Has difficulty handling money	−0.0014 (0.0086)	0.0416** (0.0163)
Demographic characteristics (2002)
Male	0.0193 (0.0243)	−0.0271 (0.0397)
Age	0.0040** (0.0019)	0.0223*** (0.0037)
Less than high school education	−0.0228 (0.0335)	−0.0423 (0.0681)
Some college	−0.0022 (0.0244)	0.0691* (0.0410)
Married or partnered	−0.0203 (0.0280)	−0.0625 (0.0474)
N	891	823

Notes: This table reports probit estimates. The left-hand side variable is defined as letting a LTCI lapse between 2002–2006; and being in a nursing home at some point between 2006–2012.

The sample consists of people who are aged 65 and over in the 2002 HRS, and who have long-term care insurance in 2002. Lapsers are those who no longer have a LTCI policy in 2006. Other details about sample construction and variable definition appear in the Table 2 notes.

^***p<0.01

^**p<0.05

^*p<0.1

The self-assessed probability of requiring care is statistically significant but the effects are quite small. A 10% higher probability is associated with a 0.3 percentage point reduction in the likelihood of lapsing. On the other hand, people with fair or poor health or experiencing ADL limitations do not have a significantly higher likelihood of lapsing (and these variables do not gain in significance if we omit the self-assessed probability of requiring care). A potential concern is that the absence of a substantial negative correlation between lapsing and the self-assessed probability of using care might reflect the offsetting effect of a correlation between lapsing and risk preferences, similar to the results for coverage reported by Finkelstein and McGarry (2006). In results that are not reported, we find no evidence of such an offsetting effect, using the variables that they employ.³⁵ In short, we find only slight evidence in favor of strategic lapsing.

Importantly, we find that having a lower cognitive score is associated with significantly higher lapse rates, even after controlling for other plausible factors including health. The effect is large – someone with a 10% lower cognitive score has a 3.0 percentage point higher risk of lapsing, and someone with a one-standard deviation lower score has a 4.6 percentage point higher risk, relative to an overall lapse rate of 13.0%. We interpret this as reflecting unanticipated or unintended lapsing.³⁶ To provide further context, suppose that everyone with low cognitive scores in our sample actually had cognitive scores equal to the 50^th percentile value. Our estimates suggest that lapsing would decline by 2.2 percentage points, or 17% of total lapses. Interestingly, though, we do not find a statistically significant or meaningful effect of having difficulty handling money.

Lastly, having a daughter is associated with a substantial lower likelihood of lapsing, of 10.0 percentage points (though having a spouse or son is not similarly protective). On the one hand, family members are relatively likely to provide informal care, potentially leading to strategic lapsing. On the other hand, Ko (2021) shows that, while having adult children reduces the likelihood of purchasing insurance, it also increases care use among those who purchase; our results suggest that this form of moral hazard in care use may help explain reduced lapsing.

Robustness analysis

Because of the importance of our results about cognitive score, we explore which parts of the distribution of cognitive score matter most; whether the timing matters for when we measure cognitive score and other possible explanations for lapsing; and the robustness of the baseline estimates to different definitions of key variables.

As can be seen in Figure 4, the distribution of cognitive score has a long left tail of low cognitive scores, while most people are massed with high scores. Table 4 explores different ways to control for cognitive score. In the first column, we repeat our baseline results from above, with a linear control for cognitive score. In other columns, we explore the impact of being in the lower part of the cognitive score distribution. The second and third columns control for having a cognitive score below the median or the 25^th percentile values of the distribution; both these values are illustrated with vertical lines in Figure 4.

Figure 4.

Cognitive Score Density Function

Notes: The sample consists of people who are aged 65 and over in the 2002 HRS; who have long-term care insurance in 2002; who have known insurance status in 2006; and who answer questions about the expected likelihood of needing care and who answer questions about cognitive ability. We compute the cognitive score reported in this Figure by forming an index of answers to cognitive questions that have a statistically significant association with dementia, based on Hurd et al (2013); we use the weighted sum of correct answers, where the weights are the inverse of the standard deviation of the correct answers.

Table 4:

Probit Estimates for Lapsing, by Cognitive Score Percentiles

	Dependent variable: LTCI policy lapsed 2002–2006
	Cognitive score
	Baseline	Dummy = 1 if < 50th percentile	Dummy = 1 if < 25th percentile
	Estimated marginal effect (standard error)
Variables which may reflect strategic lapsing (averaged over 2002–2006)
Self-assessed probability of moving to nursing home n next 5 years (0–100)	−0.0013 **	−0.0013 **	−0.0013 **
	(0.0006)	(0.0006)	(0.0006)
Fair or poor health	0.0761 **	0.0694 *	0.0766 **
	(0.0356)	(0.0360)	(0.0362)
Has limitations on Activities of Daily Living	0.0161	0.0221	0.0244
	(0.0646)	(0.0639)	(0.0657)
Log medical expenditure	−0.0018	−0.0233	−0.0034
	(0.0053)	(0.0284)	(0.0053)
Have children	0.0253	0.0279	0.0264
	(0.0389)	(0.0387)	(0.0389)
Have daughters	−0.0994 ***	−0.0954 ***	−0.0970 ***
	(0.0358)	(0.0359)	(0.0356)
Variables which may reflect financial lapsing (2002)
Log financial wealth	−0.0091 ***	−0.0102 ***	−0.0099 ***
	(0.0034)	(0.0034)	(0.0034)
Log household income	−0.0277	−0.0267	−0.0300
	(0.0178)	(0.0179)	(0.0200)
Variables which may reflect unintended lapsing (averaged over 2002–2006)
Cognitive score	−0.0879	0.0503 **	0.0613 **
	(0.0263)	(0.0240)	(0.0305)
Has difficulty handling money	−0.0014	0.0007	0.0002
	(0.0086)	(0.0087)	(0.0087)
Demographic characteristics (2002)
Male	0.0193	0.0216	0.0256
	(0.0243)	(0.0248)	(0.0246)
Age	0.004 **	0.0054 ***	0.0054 ***
	(0.0019)	(0.0020)	(0.0020)
	−0.0228	−0.0116	−0.0172
Less than high school education	(0.0335)	(0.0354)	(0.0353)
	−0.0022	−0.0062	−0.0054
Some college	(0.0244)	(0.0244)	(0.0247)
	−0.0203	−0.0233	−0.0191
Married or partnered	(0.0280)	(0.0240)	(0.0820)
N	891	891	891

Notes: This table reports probit estimates. The left-hand side variable is defined as letting a LTCI lapse between 2002–2006. The first column replicates our previous estimates, in which cognitive score enters linearly. In the second and third columns, cognitive score enters as a binary variable, taking a value of one if cognitive score is below the median or 25^th percentile values, respectively. The sample consists of people who are aged 65 and over in the 2002 HRS, and who have long-term care insurance in 2002. Lapsers are those who no longer have a LTCI policy in 2006. Other details about sample construction and variable definition appear in the Table 2 notes. Statistical significance is denoted by

^***p<0.01

^**p<0.05

^*p<0.1.

We find that the effect of cognitive score on lapsing becomes quite severe in the lower part of the cognitive score distribution. In both specifications, the effect of having a low value of cognitive score is large and significant (and is positive-signed as expected, given that a value of one for this binary variable indicates a very low cognitive score). Someone with a value below the median of the cognitive score distribution is 10.0 percentage points more likely to lapse than someone with a value above, and someone with a value below the 25^th percentile is 11.1 percentage points more likely to lapse.

Table 5 explores whether the results are sensitive to the timing of when we measure the variables that we use to capture explanations for lapsing. As we have discussed, we cannot reliably determine when a long-term care insurance policy was purchased or, therefore, measure changes in someone’s conditions since that time. Instead, we assume that individuals were in good financial, physical, and mental health when they purchased their policies (Hendren 2013). This justifies our approach of measuring current circumstances when we observe lapses. In the baseline estimates from above, we measure variables reflecting strategic or unintended lapsing, which include measures of physical and cognitive health, over the 2002–06 period, the same time period over which we measure lapsing; with this approach, we make sure not to miss any onset of decline; while we measure income and wealth in 2002, since nonpayment of insurance can affect financial status.³⁷ To explore sensitivity to these choices, in Table 5 we consider using the same variables measured only in 2002, or averaged over 1998–2002, and therefore strictly before the period over which we observe lapsing. The disadvantages of doing this are that we might fail to observe recent changes in conditions that influence lapsing, and for the latter, that we lose additional observations due to non-response when adding more waves of the HRS.

Table 5:

Probit Estimates of Lapsing, with Alternate Timing of Key Right-Hand Side Variables

	Dependent variable: LTCI policy lapsed 2002–2006
	Timing of key variables reflecting strategic, unintended lapsing
	Baseline (Average, 2002–2006)	2002 only	Average, 1998–2002
	Estimated marginal effect (standard error)
Variables which may reflect strategic lapsing (averaged over 2002–2006)
Self-assessed probability of moving to nursing home in next 5 years (0–100)	−0.0013** (0.0006)	−0.0006 (0.0005)	−0.0011* (0.0006)
Fair or poor health	0.0761** (0.0356)	0.0258 (0.0376)	−0.0257 (0.0315)
Has limitations on Activities of Daily Living	0.0161 (0.0646)	0.0719 (0.0896)	−0.0007 (0.0260)
Log medical expenditure	−0.0018 (0.0053)	−0.0045 (0.0054)	0.0029 (0.0055)
Have children	0.0253 (0.0389)	0.0299 (0.0386)	0.0238 (0.0391)
Have daughters	−0.0994*** (0.0358)	−0.0869** (0.0367)	−0.1050*** (0.0362)
Variables which may reflect financial lapsing (2002)
Log financial wealth	−0.0091*** (0.0034)	−0.0088** (0.0037)	−0.0017 (0.0043)
Log household income	−0.0277 (0.0178)	−0.0340* (0.0185)	0.0083 (0.0097)
Variables which may reflect unintended lapsing (averaged over 2002–2006)
Cognitive score	−0.0879*** (0.0263)	−0.0564** (0.0243)	−0.0937*** (0.0329)
Has difficulty handling money	−0.0014 (0.0086)	0.0018 (0.0063)	−0.0009 (0.0472)
Demographic characteristics (2002)
(omitted to save space, same as in previous tables)
N	891	891	873

Notes: This table reports probit estimates. The left-hand side variable is defined as letting a LTCI lapse between 2002–2006; and being in a nursing home at some point between 2006–2012. The first column replicates our previous estimates, with variables reflecting strategic and cognitive explanations for lapsing averaged between 2002–2006. The second column uses those variables only measured in 2002; the third column averages those variables between 1998–2002, which reduces the sample slightly due to nonresponse.

The sample consists of people who are aged 65 and over in the 2002 HRS, and who have long-term care insurance in 2002. Lapsers are those who no longer have a LTCI policy in 2006. Other details about sample construction and variable definition appear in the Table 2 notes.

^***p<0.01

^**p<0.05

^*p<0.1

As before, the first column of Table 5 repeats our baseline estimates. The second column measures variables in 2002 only, and the third column measures them over 1998–2002. Some of the variables that capture financial or strategic motives for lapsing have similar coefficients and significance as in the baseline specification, including cognitive score, while others are closer to zero. Overall, this suggests that controlling for circumstances close in timing to lapsing is important. Doing so seems to matter particularly for some of the variables reflecting strategic and financial motives for lapsing. Coefficients that become smaller when using the 2002-only or the average 1998–2002 information include the self-assessed probability of needing care (which already had a quite small effect), being in fair or poor health, and log wealth and income (which also had small effects). Meanwhile, compared to our baseline estimated marginal effect for 2002–06 (of −0.0879), the impact of cognitive score is somewhat smaller when measured only in 2002 (with an estimated marginal effect of −0.0560) and a little larger when averaged over 1998–02 (with an estimated marginal effect of −0.0937). Thus, adjusting the time period used to measure contemporaneous or recent cognitive ability (or other relevant variables) does not have a consequential effect on our conclusions about lapsing, suggesting it may take some time for lapsing to occur following the onset of cognitive decline.

Lastly, Table 6 shows that our results about cognitive score and other key variables are unchanged when we alter their specification further. With the left column again showing the baseline estimates, the middle column reports estimates when using the answers to all the cognitive score questions, instead of limiting it to those answers that are statistically significant in the predictions of dementia from Hurd et al (2013). The impact of cognitive score remains statistically significant, and the impact of a 10% lower cognitive score remains similar, at a 2.7% increase in the likelihood of a lapse.

Table 6:

Probit Estimates of Lapsing, Robustness to Alternate Control Variables

	Dependent variable: LTCI policy lapsed 2002–2006
	Baseline	Cognitive score, raw sum	Cognitive score x have daughters
	Estimated marginal effect (standard error)
Variables which may reflect strategic lapsing (averaged over 2002–2006)
Self-assessed probability of moving to nursing home in next 5 years (0–100)	−0.0013** (0.0006)	−0.0013** (0.0006)	−0.0013** (0.0006)
Fair or poor health	0.0761** (0.0356)	0.0705** (0.0357)	0.0761** (0.0356)
Has limitations on Activities of Daily Living	0.0161 (0.0646)	0.0189 (0.0643)	0.0160 (0.0646)
Log medical expenditure	−0.0018 (0.0053)	−0.0025 (0.0053)	−0.0018 (0.0053)
Have children	0.0253 (0.0389)	0.0253 (0.0392)	0.0252 (0.0390)
Have daughters	−0.0994*** (0.0358)	−0.0966*** (0.0356)	−0.1180 (0.2530)
Variables which may reflect financial lapsing (2002)
Log financial wealth	−0.0091*** (0.0034)	−0.0091*** (0.0034)	−0.0090*** (0.0034)
Log household income	−0.0277 (0.0178)	−0.0277 (0.0177)	−0.0277 (0.0178)
Variables which may reflect unintended lapsing (averaged over 2002–2006)
Cognitive score	−0.0879*** (0.0263)		−0.0920 (0.0598)
Cognitive score, raw total		−0.0102*** (0.0032)
Cognitive score x have daughters			0.0049 (0.0625)
Has difficulty handling money	−0.0014 (0.0086)	−0.0014 (0.0086)	−0.0013 (0.0086)
Demographic characteristics (2002)
(omitted to save space, same as in previous tables)
N	891	891	891

Notes: This table reports probit estimates. The left-hand side variable is defined as letting a LTCI lapse between 2002–2006; and being in a nursing home at some point between 2006–2012. The first column replicates our previous estimates. The second column controls for the raw value of cognitive score, entering all correct answers together; the third column interacts cognitive score with a dummy for having daughters.

The sample consists of people who are aged 65 and over in the 2002 HRS, and who have long-term care insurance in 2002. Lapsers are those who no longer have a LTCI policy in 2006. Other details about sample construction and variable definition appear in the Table 2 notes.

^***p<0.01

^**p<0.05

^*p<0.1

The final column analyzes whether family relationships help mitigate the impact of cognitive score. We try interacting cognitive score with whether the respondent has daughters (as daughters, more commonly than sons, help provide informal care to elderly parents). The coefficient on the term that interacts having daughters with cognitive score is very small and statistically insignificant, while the coefficient on cognitive score has a similar magnitude as in the baseline specification, although its statistical significance is somewhat diminished. Thus, we find little support for the possibility that family relationships alleviate the impact of cognitive decline on lapsing. In further results that appear in the Technical Appendix, we demonstrate that the estimates are not sensitive to different ways to measure lapsing over time. This is important, given possible measurement error arising because our measure of lapsing depends on individual answers about LTCI holding across multiple waves.

Welfare effects for unintended lapsing

Our earlier simulations in Section 1 yield insights into the welfare loss faced by someone who purchases a policy optimally and then lapses for some unintended reason. Recall that Figures 3A and 3B show the willingness to pay by age and wealth for an age-65 long-term care insurance policy – which is also the willingness to continue holding and avoid an unintended lapse of a policy that one purchased at age 65. The only thing that changes as people age in these figures is the optimal drawdown of wealth and predictable age-related changes in the likelihood of needing care (since we assume away shocks to both wealth and care expectations). As noted earlier, holding onto a policy becomes more valuable for many years after age 65. For someone in the 80^th wealth percentile who purchases at age 65 and lapses at age 75, the individual welfare loss of lapsing, measured at age 65, is $56,978 for a single man and $98,247 for a single woman. Thus, unintended lapses are extremely costly in this optimization framework.

The willingness to avoid unintended lapses has two components – the loss which people would have suffered had they foreseen giving up their policy at a later age and chosen a wealth drawdown path accordingly, and the additional loss resulting from the choice of what was, with the benefit of hindsight, an inappropriately optimistic drawdown path. Considering someone again in the 80^th wealth percentile, an anticipated lapse at age 75 would cause somewhat smaller welfare losses than an unanticipated lapse, equivalent to $41,516 for single men and $90,708 for single women. So, the additional welfare loss for unintended lapsers arising because of excessive consumption is almost 10% for single women and 37% for single men.

Thus, unintended lapsing among those who purchased a policy optimally is extremely costly. While much of the substantial welfare loss to lapsers may be transferred to non-lapsing policy holders in the form of lower premiums, net of administrative and marketing costs, the additional welfare cost to lapsers of consuming too much of their wealth is also substantial.

6. Evidence about Dynamic Selection

We finish by estimating a probit model of later long-term care use, as shown in equation (2), for the sample of policyholders in 2002. The model for care use between 2006–12 includes the same 2002–06 variables that we used to account for lapsing, along with the lapse variable itself. If a control variable is statistically significant in both the care use and lapsing regressions, then this suggests a source of (potentially observable) dynamic selection. If lapsing itself is statistically significant in the care use regression conditional on these control variables, it captures other unobservable sources of dynamic selection.

The raw data showed that people whose insurance policies lapse between 2002–06 are more likely to use care later on, between 2006–12. Our probit estimates in the second column of Table 3 demonstrate, however, that, once we control for the same variables as in our lapsing model, lapsing itself does not have a statistically significant association with care use, with a coefficient of −0.0302 (standard error of 0.0567). Unsurprisingly, being older, being in fair or poor health, or having ADL limitations is also associated with more care use, as is having difficulty handling money, while having children is associated with less care use; yet, none of these variables that have a statistically significant association with care use were significantly associated with lapsing. Also, most of the variables that were significantly associated with lapsing in our earlier results (notably, wealth and the self-assessed probability of needing care) do not have a statistically significant relationship with the use of care.

The exception is cognitive impairment, which is associated with significantly and substantially higher use of later care. Someone with a cognitive score that is one standard deviation lower has a 10.3 percentage point higher likelihood of using care, relative to a mean of 32.3%. Because cognitive impairment also causes lapses, we can see that cognitive impairment generates dynamic advantageous selection, echoing evidence from Fang, Keane, and Silverman (2008), who show that HRS individuals with higher cognitive ability are both healthier and more likely to hold a Medigap policy.³⁸ While this potentially benefits insurers and those who hold onto their policies, this unintended lapsing is extremely costly outside of the insurance pool: annual nursing home costs are $79,800 on average, and Medicaid currently pays about $130 billion per year for long-term care on behalf of individuals who are not insured and cannot afford care (Friedberg, Hou, Sun, and Webb 2016).

7. Conclusion

Individuals with long-term care insurance policies exhibit very high lapse rates, with people aged 65 having over a one-quarter chance of lapsing prior to death and forfeiting all benefits. Our optimization model shows both a high cost of lapsing absent a change in information, and also that changes in information would have to be large to explain lapsing. We investigate what factors account for observed lapses and whether those factors lead to adverse or advantageous selection among remaining policyholders.

Our analysis yields three main findings. First, lapse rates are significantly and substantially higher among the cognitively impaired, demonstrating the importance of unintended lapsing. Yet, we find limited evidence of either strategic or financial motives for lapsing, which are the explanations that follow naturally from a model of optimizing decision-makers. Second, we show that unintended lapsing is an important source of dynamic advantageous selection. This selection takes an especially pernicious form, as policyholders who are at imminent risk of needing care are also more likely to stop paying for insurance.

Lastly, we calculate the welfare cost to those who optimally purchase insurance but then lapse unexpectedly. Our model assumes that people insure themselves at age 65 if their willingness-to-pay is positive, given their care expectations, wealth, and the Medicaid program. Lapsing is quite costly to individuals, as policies continue to grow in value far into old age, and it is made costlier when people who do not anticipate lapsing consume too much of their wealth.

One way of eliminating lapses would be to pay premiums in a lump sum. While this is difficult for people who are liquidity-constrained, long-term care insurance is generally purchased by people who are relatively wealthy because crowd-out by means-tested Medicaid reduces demand by others (Brown and Finkelstein, 2008). Some wealthy households could afford to pre-pay much of their premium early on, and might prefer to do this. Not only would it reduce the risk of periodic increases in premiums, but it would also serve to insulate against the risk of unintended lapses. On the supply side, prepayment would help insurers hedge the risk of a decline in interest rates, which increases the present value of future claims, but it would prevent them from increasing premiums should their risk model prove to be incorrect.

Data availability statement:

The data sets used in this paper are all publicly available.