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Understanding the factors behind the decision to purchase varying coverage amounts of long-term care insurance.

The debate continues as the body of research grows regarding the potential value of long-term care (LTC) insurance in reducing the out-of-pocket nursing home costs of policyholders and in affecting the overall level of Medicaid program expenditures (Cohen and Kumar 1993; Wilson and Weissert 1989; Rice, Thomas, and Weissert 1991; Rivlin et al. 1988; Kemper, Spillman, and Murtaugh 1991). Clearly, the potential benefits of LTC insurance to policyholders as well as to the Medicaid program depend on the type of coverage purchased as well as on the nursing home liabilities that policy-holders will incur. On this latter issue, the risk of needing LTC services, there is a great deal of knowledge. On the former issue, however, empirical data have only recently been available to assess the profile of LTC insurance purchasers, the type of coverage they buy and the reasons for their purchase (Cohen, Kumar, and Wallack 1993). What continue to remain unknown are the factors related to the purchase of specific levels of LTC insurance coverage.

Uncovering the factors related to the decision about how much LTC insurance to buy is important for a number of reasons. First, both the federal government and a number of state governments are implementing public policies designed to encourage the purchase of LTC insurance that provides meaningful coverage. Understanding the relationship between the amount of coverage people buy and their attitudes toward LTC and risk can assist in the development of strategies designed to encourage the purchase of comprehensive coverage. Potentially, this can result in savings to public programs that finance LTC services. Moreover, states may want to consider how changes in the Medicaid program affect the amount of insurance individuals purchase. This may be particularly important for states implementing public-private partnership programs in long-term care financing. Such partnerships are designed to encourage-individuals to purchase long-term care insurance in the hope that if policyholders require nursing home care, it will be paid for by their policy, and savings will accrue to the Medicaid program. Typically, the financial inducement provided by the states is in the form of an offer to exclude for the purposes of future Medicaid eligibility an amount of assets equal to the value of insurance benefits paid, or in some cases, when an approved policy is purchased, all assets are protected in the event that Medicaid is required in the future.(1)

In this article we examine this issue and assess the influence of demographic traits, attitudinal variables, risk premiums, availability of nursing home beds, and Medicaid program characteristics on the decision to buy policies that provide greater or lesser amounts of coverage. We address the following questions:

1. What are the factors related to an individual's decision to purchase a given amount of LTC insurance protection?

2. Are there variables important in explaining the initial decision to purchase a policy that no longer are important in explaining the amount of coverage an individual chooses to purchase?

3. What is the relationship between the risk premium that individuals are willing to pay for a policy and the amount of coverage that they purchase?

4. What is the relationship between the amount of insurance coverage purchased and Medicaid program characteristics?



Basic sample characteristics and sampling method have been described in detail elsewhere (Cohen, Kumar, and Wallack 1992). In brief, six companies that together represented 45 percent of total individual LTC insurance sales in 1990 contributed a sample of purchasers and nonpurchasers age 55 and over to the study of the individual market. Each company randomly selected a sample of individuals who had purchased policies in late 1990 or early 1991. An LTC insurance purchaser was defined as an individual who had purchased a policy, paid premiums, and not returned the policy within 30 days. A nonpurchaser was someone who had been approached by an agent and had received policy information, but had decided against buying a policy. These individuals typically had made an "active" decision not to buy either at the initial visit or within three months after the agent contact.

Each of 8,363 individual purchasers returned mail surveys containing information about their reasons for purchase, attitudes toward long-term care, and demographic characteristics. Through an identification code, information on the policy designs chosen by these individuals was linked to each of the returned surveys.(2) In this way it was possible to explore the relationship betWeen the policy designs purchased and the attitudes and profile of the roughly 60 percent of individual policyholders who responded to the survey.

For the roughly 50 percent of respondents who chose not to reveal their level of income and assets, fitted values were derived using discriminant analysis.(3) Age, sex, marital status, and level of education were the explanatory variables used to classify individuals into five income and asset categories. The vast majority of individuals answered all other questions. However, in that variables with missing values are excluded from the multivariate analysis, even a relatively small nonresponse rate for an item can greatly reduce overall sample size. The cumulative item nonresponse rate resulted in an estimation sample of 6,545 cases.


The insurance purchase decision can be conceptualized as a two-stage process. First, the consumer must decide whether or not to buy a policy. This decision will depend on a variety of factors related to the demographic profile of the individual, his or her attitudes toward risk, and knowledge about public and private coverages, insurance policy price, and the configuration of the Medicaid program in the state, as well as other factors. To model this first stage in the decision-making process-to buy or not to buy-data from the entire sample of purchasers and non-purchasers is used.

Once this decision is made, the individual then chooses the level of coverage desired from among a menu of choices. The coverage level is a function of the daily benefit amount, the number of years of coverage, and the deductible period. Daily nursing home benefit amounts can vary between $25 and $200, durations from between two years to lifetime coverage, and deductible periods from 0 to 100 days. Thus, there are thousands of possible policy design combinations. In the subsequent analysis, each policy design combination is captured by a single dollar value that represents the expected value of policy coverage, that is, the expected value of benefits to be derived from a policy of a given configuration.


As conceptualized in the foregoing section, the decision to purchase a certain level of coverage may be viewed as somewhat distinct from the initial decision to purchase insurance. A relatively simple method that can be used to model this process is the twin linear probability model first noted by Goldberg (1980). Under this specification a logistic regression is used to model the purchase-nonpurchase decision, and then a linear regression model is used to estimate the factors related to the amount of coverage purchased. However, a shortcoming of this approach is its failure to adjust for selectivity problems. For example, we wish to estimate a regression model to uncover a set of factors related to the amount of coverage individuals purchase. Given our sample, however, the observed data represent the amount of coverage purchased only for those who decided to buy policies. We do not know the factors that would be associated with chosen levels of coverage for individuals who decided not to purchase a policy. Thus, the observed data are not randomly sampled from the population of purchasers and nonpurchasers but only from the purchasers. In this respect, the sample is censored.

Another way to view this problem is in terms of a latent variable [Y.sup.*], which represents an index of an individual's propensity to buy insurance. When this index crosses a certain threshold, insurance is bought and we then observe the level of coverage chosen. Because the regression model treats observed data as being randomly sampled from the entire population rather than from the subpopulation of purchasers, estimated coefficients may be biased. This can result because the probability of purchasing insurance and the probability of purchasing a particular level of coverage are likely related; that is, it is likely that the disturbance terms for each equation are correlated. This problem often arises in situations of choice-based sampling, and it necessitates an approach that adjusts for selectivity.

To begin to address this problem, we use a two-stage estimation model that accounts for the fact that part of the sample is observed only when an underlying purchase index exceeds some threshold. In the first stage of the modeling process, the factors related to the purchase decision are estimated. In the second stage, factors related to the level of coverage are estimated. However, also included in the second-stage estimation model is a variable-referred to as Lambda-that represents the conditional expectation of the error term of the regression. This is derived from the first equation, and by including it in the second stage of the modeling, the correlated or nonrandom portion of the regression error term is removed and entered into the equation. What remains is a random error term, which theoretically solves the bias problem.

Such methods were first suggested by Heckman (1976), who used the technique in developing a labor supply model. Amemiya (1979) extended the use of these models to a wide range of situations. Lee (1983) provides an overview of a variety of two-stage estimation models that can be applied to help solve the problems inherent in choice-based sampling.

The choice-based sampling model that we use in the following analysis is a logit-OLS (ordinary least squares) two-stage model. Logistic regression is appropriate for the first-stage estimation because the decision to purchase can be represented as a dichotomous variable: purchase or no purchase. OLS regression is appropriate for the second-stage modeling as the dependent variable-the expected value of coverage-is continuous.


Tables 1 and 2 display the variables used in the analysis, the way they are coded, and their mean values and standard deviations.

The average age of individuals in the sample is about 70 years. Most (67 percent) are married, college educated (55 percent), and female (54 percent). About half the sample have incomes greater than $35,000 and assets in excess of $75,000. About 28 percent perceive the risk of nursing home use to be greater than 50 percent and few - less than 20 percent - believe that government programs or their Medigap policy will pay for significant LTC costs. Given the demographic profile of these individuals as well as trends in long-term care costs, the average expected future LTC liability for individuals in the sample is about $113,000. On almost all of these parameters, the sample differs from the profile of elderly individuals in the general population (age 55 and over).

The dependent variable, expected value of coverage, represents the average amount that will be paid out for a given policy design, that is, the amount that on average a policyholder will receive from the policy. This is different from the total amount of coverage purchased by an individual. For example, a two-year policy that pays a nursing home benefit of $100 per day provides total coverage of $73,000 ($100 x 2 x 365). Yet this is not the amount that will be paid out on average to all policyholders having a policy. The amount that each policy will pay out on average is a function of an individual's age at purchase as well as gender - variables that are related to services utilization and mortality; the level and duration of benefits chosen as well as the elimination period; underwriting and lapse assumptions assumed by companies as they price policies; and whether or not inflation protection was chosen. Thus, the expected value of coverage depends both on the characteristics of the policy purchased as well as on the characteristics of the purchasers themselves.


For each individual in the sample, we calculated the expected value of policy benefits. For example, the expected value of coverage for a policy paying all nursing home costs, that is, a lifetime policy with full inflation protection and a 0-day elimination period, for a 75-year-old women, is given as:

E[V.sub.NH] [summation of] {[tpn (group) [multiplied by] [q.sub.n] (NH)] [multiplied by] [A[B.sub.n](NH) [multiplied by] [(1 + R).sup.n]]} [multiplied by] (1 - [L.sub.n]) [multiplied by] (1 - [U.sub.n]) where 110 to 75


EVnh = expected value of nursing home coverage

[q.sub.n](NH) = prevalence rate for nursing home care tpn(group) = cumulative survival function for group of 75 year old females

A[B.sub.n](NH) = annual nursing home policy payout [L.sub.n] = the annual lapse rate

[U.sub.n] = the annual impact of underwriting on utilization

R = annual inflation rate

The summation for this 75-year-old woman is over her remaining lifetime. Once the expected value of the lifetime policy is calculated, policies of differing benefit durations, benefit amounts, and elimination periods can be calculated. Adjustment factors based on the length of stay distribution for nursing home users as well as the fraction of future daily costs paid by a policy are used to estimate the expected value of coverage for each policy configuration. The expected value of coverage for individuals in the sample was slightly more than $32,000. (For additional information see Appendix A.)
Table 2: Means and Standard Deviations of Variables

Variables(*) Mean s.d.

1. Demographics

Age 69.8 years 6.4 years
Married 0.669 0.471
College educated 0.551 0.498
Males 0.460 0.498
Children within 25 miles 0.594 0.492
Caregiver experience 0.559 0.496
HMO member 0.092 0.289
Medigap policyholder 0.297 0.457
Expected LTC costs $112,760 $42,539

Report state 0.91 0.288

Income [less than] $10k 0.117 0.322
Income $10k-$14.9k 0.114 0.318
Income $15k-$19.9k 0.114 0.318
Income $20k-$24.9k 0.126 0.332
Income $25k-$34.9k 0.189 0.390
Income $35k-$49.9k 0.167 0.367
Income [greater than or equal to] $50,000 0.173 0.435

Assets [less than] $20k 0.249 0.433
Assets $20k-$29.9k 0.072 0.257
Assets $30k-$49.9k 0.082 0.273
Assets $50k-$74.9k 0.103 0.304
Assets $75k-$99.9k 0.095 0.293
Assets [greater than or equal to] $100,000 0.401 0.492


Perceived risk NH use 0.282 0.450
Perceived risk HH use 0.310 0.463
Medicaid will pay 0.038 0.191
Medicare will pay 0.196 0.397
Medigap will pay 0.179 0.384

Medicaid Variables

Medicaid per diem rate $55.65 $13.21
Medicaid estate recovery 0.451 0.497
Medicaid income limits 0.132 0.339
Nursing home beds per 1000 55.55 14.70

4. Company Variable

Exclusively use brokers for 0.242 0.429

* Based on a sample of 6545 purchasers and 1248 nonpurchasers.
Sample was re-weighted to adjust for oversampling of purchasers. The
income and asset variables include imputed values for missing cases.

Clearly, price influences the decision to buy varying amounts of coverage. A focus on policy premium as a proxy for price would not be appropriate, however, for the modeling exercise. Policies with more comprehensive benefit designs almost always cost more than those that provide fewer benefits. Thus, one would observe the relationship that the greater the price, the greater the level of coverage purchased. In the regression equation, we wish to uncover the variables that are related to an individual's decision to purchase a given level of coverage. Introducing the variable premium into the equation leads to the problem of endogeneity (simultaneity): an increase in coverage leads to an increase in the premium.

To begin to account for individual differences in willingness to pay, we focus on measuring how much an individual pays above and beyond the actuarially fair premium for the level of coverage purchased. The actuarially fair premium for each policy represents the amount of money that would have to be collected on an annual basis to fund the expected value of future policy benefits. In other words, one must solve for the value of level-funded premiums that would cover current risk and prefund future risk as defined by the policy configuration. For a cohort of individuals, actuarially fair premiums yield the result that all costs are paid for over the lifetime of the cohort and there is no excess of premiums over costs when the last individual of the cohort dies (see Appendix B).

The difference between the actual premium paid and the actuarially fair premium is accounted for by the expenses that the insurer must incur (for administration, marketing, taxes, etc.), the amount of profit to be earned, and an uncertainty premium. For example, the actuarially fair premium for a policy may be $1,000 per year whereas the policy premium may be $1,400. The $400 difference is often referred to as the risk premium or loading factor.

This factor, which is the ratio of actual premium paid to the actuarially fair premium, can be interpreted in two ways. First, it is a measure of the degree of risk aversion for an individual. The greater the risk premium paid by an individual, the greater the degree of risk aversion. Second, holding coverage constant, the risk premium can be viewed as a measure of the relative price charged by insurers for their product.(4)

In the subsequent analysis we focus our discussion on the factors related to the level of coverage chosen rather than on the factors related to the purchase decision itself. Where noteworthy, however, we do compare the coefficients in both equations to provide an understanding of ways in which considerations vary across each of the two decisions.


Table 3 summarizes the results of the two-stage logistic and regression analysis. Coefficients and standard errors (shown in parentheses) are presented for each variable.

It is important to note that not all variables included in the first stage of the analysis are included in the second stage. First, not all variables hypothesized to influence the purchase-nonpurchase decision were presumed to influence the decision regarding the amount of coverage to purchase. Moreover, among purchasers, responses to a number of questions did not vary. Finally, in a choice-based sampling model, there cannot be perfect overlap between the variables used in both equations.(5) Therefore, variables for which there was not a strong a priori hypothesis regarding impact on the dependent variable were excluded from the equation. (In most cases such variables were tested independently and found not to be significant.)


Age. Not only is age negatively associated with an individual's propensity to purchase insurance, but it is also negatively related to the level of coverage chosen. Holding other variables constant, each additional year of age reduces the expected value of coverage purchased by a minimal amount, $165. While somewhat counterintuitive, age is associated with decreasing risk aversion over the insurance versus self-insured state: persons considering purchase at older ages face a shorter time horizon and increasing probability of needing long-term care in the near future. As the probability of the need for care approaches certainty, the utility value of purchasing fair (or constant load) insurance to meet that needs falls, and self-insurance becomes relatively more attractive. An additional explanation is that for [TABULAR DATA FOR TABLE 3 OMITTED] the negative relationship, age is probably capturing some degree of price variation in these products, all of which are age-rated.

Gender and Marital Status. Gender affects both the purchase decision and the decision regarding level of coverage. While men in the sample were less likely to purchase insurance, once having bought a policy, they chose higher coverage amounts. Being male increased the expected value of coverage purchased by $4,081. Marital status affects the purchase decision as well as the decision regarding level of coverage. On the one hand, married individuals are more likely to purchase policies than are singles. On the other hand, having purchased a policy, the chosen level of coverage is typically lower. LTC insurance policies are not inexpensive. In 1990, the average premium paid for policies was about $1,000 per year. Thus, a household composed of a couple would, other things being equal, have to spend roughly twice this amount to obtain levels of coverage similar to that of single individuals. On average, policies purchased by individuals with spouses provide $2,188 less in expected benefits than policies bought by single individuals. However, this amount is not so great considering that the average expected value of policies in the sample is about $32,000. Even though a couple may face twice the price of an individual purchaser, the reduction in coverage per person is much less - only an 8 percent decline.

Education Level. A much higher proportion of LTC insurance policy-holders are college educated than is true for the population as a whole. Yet, among individuals approached by agents, those without college educations are more likely to purchase policies than are the college educated. Having purchased a policy, however, individuals without college educations buy policies with lower expected value: about $1,625 less than college-educated purchasers. This may reflect a better understanding among the more educated of the risks and costs of LTC use, the implications of choosing alternative policy designs, and the LTC environment in their particular geographic area.

Income Level. An individual's level of income is strongly associated with the decision to buy insurance and with the amount of insurance coverage purchased. On average, individuals with income in excess of $50,000 purchase between $3,300 and $7,800 more in coverage than do individuals with incomes less than this amount. It is not true, however, that as income rises, the amount of coverage purchased rises linearly. Compared to individuals with incomes over $50,000, individuals with incomes below $10,000 purchase policies with much lower - about $6,455 - expected benefits. However, individuals with incomes between $10,000 and $14,999 purchase $7,811 fewer benefits, whereas those with incomes between $25,000 and $34,999 purchase $5,670 fewer benefits (compared to those with incomes in excess of $50,000). Viewed in the context of other variables, income level has one of the largest effects on the expected value of coverage purchased by policyholders.

Assets. For the most part, asset levels do not affect the purchase decision nor the amount of coverage purchased by individuals. This finding is somewhat surprising given the fact that one of the reasons people purchase insurance is to protect their assets. One might have expected to observe a positive relationship between asset levels and coverage: the greater the level of assets the greater the level of coverage. On the other hand, Medicaid eligibility rules applicable at the time of the survey were such that an individual with significant assets only needed to pay for two years of care - during which time he could divest his assets - before becoming eligible for Medicaid reimbursement.(6) Given the fact that most estate planners do advise clients on the relationship between Medicaid eligibility rules and asset requirements, it is not unreasonable to assume that, armed with this knowledge, individuals with high asset levels purchase only enough coverage to finance two years of care in a nursing home. Thus, theoretically, one might also expect that individuals with greater asset levels purchase policies that have lower expected benefits. Results do not clarify which of these hypotheses, if either, is correct, since in no case was a particular asset category shown to be significantly related to the amount of coverage purchased. Further, individuals may be more willing to pay for nursing home care than is commonly assumed and are therefore not seeking complete asset protection.

Children Living within 25 Miles. Purchasers who have children living within 25 miles of their home are less likely to buy policies and also are less likely to purchase more comprehensive benefits than their counterparts without children nearby. For example, having children nearby reduces the expected value of coverage by $906. This is not surprising given the fact that most long-term care services are provided informally (unpaid) by adult daughters. If informal supports are nearby, then elders may perceive the risk of needing formal (paid) long-term care services to be lower, thereby decreasing the utility they would derive from insurance. Thus, they are less likely to purchase policies and when they do, to purchase less coverage.

HMO Member. Being a member of an HMO is negatively related to the probability of purchase but has no significant effect on the expected value of coverage. The vast majority of HMOs do not provide any LTC coverage. Thus, it is somewhat surprising that HMO membership reduces the probability of purchase. This may reflect a selection issue in that individuals who join HMOs may perceive their health status to be superior, and hence they may have a lower perceived risk of incurring catastrophic LTC costs. The reduced probability of purchase also may reflect the belief that membership in an HMO will provide greater possibilities for service substitutions within the HMO framework, or even more ease in gaining access to LTC services outside of the HMO.

Caregiving Experience. The fact that an individual has had experience caring for a disabled eider living in the community has a negative impact on the initial decision to purchase insurance, but it does not influence the amount of coverage purchased. Because most of the LTC policies selling at the time of the survey did not include significant home health care coverages, they were likely viewed as primarily policies for nursing home coverage. Therefore, for the most part, the expected value of the coverage reflected the amount of institutional coverage rather than community coverage. Because caregiving experience typically occurs in the community setting, it is not surprising that such experience does not influence the amount of primarily nursing home coverage purchased by individuals.

Expected Lifetime Costs. Individuals with higher expected future LTC costs may be somewhat less likely to purchase a policy, but among purchasers they appears to seek greater coverage. For each additional $10,000 in expected lifetime costs, the expected value of benefits purchased increases by $3,879.(7) Insurers underwrite individuals to assure that they are not "selected against" by individuals who have a higher-than-average risk of needing services. Many insurers assume that individuals who assess their risk for needing services to be high will be more likely to purchase policies and will also more likely purchase comprehensive coverage. The fact that this is not occurring at the point of purchase suggests that insurers may be successful in screening out individuals with higher-than-average risk. Yet, because few companies do additional underwriting on individuals once they are deemed as acceptable risks for the purchase of insurance, there may be antiselection occurring at the time that individuals decide how much insurance coverage to purchase. This may be reflected in the positive coefficient on this variable.


Risk for Needing LTC: Nursing Home and Home Care. Individuals were asked how likely they thought it might be that they would require nursing home care for more than six months. Unlike the insurance purchase decision, where individuals who believed that their risk was greater than 50 percent were also more likely to purchase policies, no such relationship is found for the coverage decision. One might have expected that individuals who perceived a greater likelihood of nursing home use would purchase greater amounts of insurance coverage. It may be that the previous variable, expected lifetime costs, is capturing this effect.

Regarding perceived home health care risk, however, a somewhat different picture emerges. Individuals who view the risk as high (greater than 50 percent) are less likely to purchase policies. Yet, among those who do purchase policies, a perceived high risk of needing home care leads to a purchase of $1,777 more in insurance protection. The additional coverage is typically reflected in the form of home care benefits, which the policyholder can choose to include in his coverage plan. Such a purchase reflects a desire of individuals to remain in the community for as long as possible by using a combination of formal and informal supports.


Two of the three Medicaid variables are significantly related to the expected value of policy coverage. We find that as the Medicaid reimbursement rate in a state increases, so too does the expected value of benefits chosen by individuals in a particular state. Each additional dollar of Medicaid reimbursement leads individuals to purchase policies providing an additional $315 in expected benefits.(8)

This may reflect the fact that higher reimbursement rates are generally found in states with higher nursing home costs. Therefore, this variable could be a proxy for the average costs of nursing home care in each state. To support this hypothesis further, we tested the correlation between the daily benefit amounts that individuals chose and the Medicaid reimbursement rate in their particular state. We found the correlation coefficient between these two variables to be .48 and significant at the .001 level.

Individuals living in states that have general estate recovery programs do purchase more coverage than individuals in states with more limited or no programs.(9) (Again, this may be related to the fact that estate planners have provided information to these individuals; it is difficult to believe that most individuals are aware, on their own, of the extent to which their state engages in estate recovery.) Holding other variables constant, these individuals purchase policies that provide an additional $2,382 in expected benefits. The presence of income limits for Medicaid eligibility does not affect the amount of coverage purchased by individuals.(10)

Nursing Home Bed Supply. One of the perceived benefits of LTC insurance is that it increases one's access to nursing home care. Again, we posited that in states with low nursing home bed ratios, other things being equal, individuals would purchase higher coverage amounts to further ensure their access to care as private pay patients. However, contrary to expectations, the variable is neither related to the insurance purchase decision nor to the decision about the amount of coverage to buy.

This finding suggests that assuring access to nursing home beds in markets with "tight" bed supplies may not be an important motivation behind the initial purchase decision or the decision regarding the amount of coverage to purchase. Individuals who must rely solely on Medicaid often have difficulty gaining access to a nursing home of their choice. Because most LTC insurance purchasers are unlikely in any event to have to rely on Medicaid to pay for their care, they are also not very likely to view the insurance as a means for assuring them access to a nursing home bed in a tight market. For this reason, the variable is not significant.(11)

Risk Premium. As mentioned, the purpose for creating the risk premium variable was to deal with the problem of endogeneity that would be introduced if "actual premium" had been used in the equation. The negative coefficient on this highly significant variable indicates that as the relative price increases, that is, as the difference between the premium charged and the actuarially fair premium increases, individuals purchase less coverage. The average loading charge (risk premium) for policies in the sample is 1.5. This means that for every dollar of premium collected, 67 cents will be paid out in benefits and the other 33 cents will be retained by the insurer for expenses, profits, and risk charges. A 0.1 unit increase (e.g., 1.5 to 1.6) in the ratio leads to a decline in the expected value of benefits of $814. At the actuarially fair premium (i.e. where, risk premium equals 1), an additional $4,070 of coverage would be purchased. Put another way, the greater the risk premium (loading factor), the lower the expected value one derives from the policy.


Clearly, the way in which agents present information and deal with prospective LTC insurance purchasers influences both the purchasers' decisions to buy policies and their decisions to buy certain levels of coverage. In general, companies. in the sample employed one of two sales strategies: (1) using captive agents who sold only a single company product, or (2) using brokers who represented a variety of products from different companies. Individuals approached by brokers rather than captive agents were far more likely to purchase a policy. In fact, an individual was 73 percent less likely to purchase a policy when contacted by a captive agent than when a broker initiated the contact. This may be explained in part by the fact that a broker may be viewed by a prospective client as more objective if he or she is representing many different products that can be tailored to meet the client's needs. Brokers not only had a positive impact on the purchase decision, but also on the amount of coverage purchased: a broker-initiated sale led to the purchase of $6,346 more in coverage than a captive agent-initiated sale.


Lambda-the conditional expectation of the error term given that a linear index representing the propensity to purchase a policy has been exceeded - was not significant. This suggests that selection bias is not present in the model. To test this finding further, the model was estimated without the adjustment for sample selection. Results did not change, thus indicating that differences between the subsample of purchasers and nonpurchasers did not have a significant impact on the estimation process.

This finding is not too surprising. Insurance agents target individuals who are identified as "potential LTC insurance purchasers." For the most part, agents do not solicit persons whose incomes and assets would either qualify them for Medicaid or would place them only slightly above the Medicaid threshold. Hence, agents approach only a very specific subgroup of the population sharing relatively similar demographic characteristics.


The two-stage model explains about 47 percent of the variance in the expected value of policy coverage. Clearly, many of the variables that are important to the purchase decision are also related to the amount of coverage that individuals buy. Yet some important differences do exist, relating to the impact of marital status, education level, self-perception of risk, and other such variables. The analysis suggests that even after accounting for demographic and attitudinal variables, the risk premium charged by insurers has a significant influence on the amount of purchased coverage.

An important finding with implications for policymakers is that changes in Medicaid policy can affect the decisions of consumers regarding the acquisition of private LTC policies as well as the level of protection they choose. The presence of Medicaid does dampen the demand for insurance, even among individuals who, based on their income and asset profile, would not likely qualify for benefits. This supports other evidence that suggests that such individuals have alternative means of potential access to Medicaid benefits, such as divesting themselves of assets (Burwell 1991). Clearly, what occurs in the public LTC protection market (Medicaid) influences developments in the private LTC protection market (LTC insurance).

As mentioned, a number of states like Connecticut, New York, and California have implemented or are considering implementing public-private partnerships in LTC financing. These partnerships are designed to encourage LTC insurance purchase and, by so doing, also to reduce potential Medicaid expenditures. This is done by disregarding for Medicaid eligibility purposes a level of assets that reflects the value of long-term care insurance benefits spent on care or, in some cases, all assets. Such programs are likely to meet with success when structured in a way that minimizes the ability to transfer assets in the context of serious state efforts to take steps toward estate recovery. However, insofar as income is highly correlated with the amount of coverage purchased, it remains to be seen how much Medicaid savings will accrue to states implementing such programs. Unless significant asset transfer is occurring, purchasers with high incomes are not likely to have access to Medicaid benefits in any event.

Clearly, the risk premium charged by insurers for their products affects the amount of insurance people ultimately choose to buy. As insurers gain more experience in the market, risk premiums are likely to decline. Evidence already exists that more comprehensive benefit packages are being provided at lower prices than just a few years ago. A reduction in risk premiums should lead to an increase in demand for more comprehensive coverages, and this, in turn, should result in a more meaningful share of LTC expenses financed by private insurance.


The Expected Value of Policy Purchased

The expected value of the policy purchased refers to the amount the policy will pay on average. This is a function of demographic characteristics of the purchaser; the prevalence rates of nursing home and community-based care use; the length of stay in nursing homes and in the community as a disabled individual; mortality rate assumptions; the nature of the policy purchased; and company pricing, underwriting, and lapse assumptions.

Demographic Variables. The expected value of coverage depends in part on the expected lifetime costs of care for individuals with different characteristics. We calculated expected lifetime costs as a function of age and gender. The nursing home prevalence rates that describe the number of persons in a nursing home on any given day of the year and are used to calculate lifetime costs are based on the 1985 National Nursing Home Survey (Hing 1987). The length of stay distribution, which refers to the distribution of the time spent by an admissions cohort in a nursing home, is based on the work of Spence and Wiener (1990). Length of stay in disability in the community is derived from the 1982-1984 National Long-Term Care Surveys (NLTCs).

Mortality Rates. The group annuitant mortality rates are used instead of standard mortality rates. These are the mortality tables insurance companies use when pricing their policies or calculating the expected liability on a policy. The group annuitant mortality tables assume lower mortality rates than the standard mortality tables. The assumption here is that since individuals purchasing a long-term care insurance policy have passed underwriting, they are in better health than the general population and consequently can be expected to have lower mortality rates. Mortality rates are modeled as constant over the period in question.

Policy Specific Variables. The following policy-specific variables are used: the daily nursing home benefit that will be paid when an individual goes on claim-roughly $70 per day; the elimination period, which is the period for which the individual will have to pay for care before the insurance policy begins to pay benefits; the policy duration, which refers to the length of time the policy will pay benefits-on average, slightly more than four years; and inflation protection, which increases the value of the daily benefit purchased by the rate of inflation chosen, typically by 3 percent to 5 percent.

Underwriting Assumptions. Everyone who is eventually issued a long-term care insurance policy has to undergo some form of underwriting. The underwriting techniques used vary by insurer as well as by the age of the purchaser. However, all insurance companies assume that underwriting will, in effect, reduce claims or prevalence in the initial years. The standard assumption used by insurance companies is that the effect of underwriting will wear off in five years. In other words, with respect to service utilization, the cohort of purchasers will resemble the general population at the end of five years. Underwriting is assumed to have the following impact on claims:
Year Reduction in Expected Claims

1 600%
2 40%
3 30%
4 15%
5 0%

These represent standard assumptions used by many long-term care insurance companies.

Lapse Rate. Lapses refer to the phenomenon of individuals. dropping their policies before they go into benefit. For example, if a hundred persons purchased a policy in the first year, ten of them might drop their policies within one year of purchase. People drop their policies for various reasons, including a change of mind, the fact that they might purchase a different policy, or their inability to pay the premiums. When an individual lapses a policy before he or she goes into benefit it means that the insurer does not face any claims liability for that individual. Lapses have the effect of reducing the overall premium charged by the insurer. While assumptions about lapse rates vary across companies, the following rates are used by many of the large carriers:
Year Lapse Rates

1 10%
2 9%
3 8%
4 6%
5 and thereafter 5%

No adjustment is made to account for possible induced demand effects. This is because experience to date suggests that even after individuals have had their policies for more than five years, utilization-incidence and duration - is less than what is observed in the general population. Clearly, induced demand would lead to greater expected long-term care costs. Moreover, if known and taken into account by insurers, the expected value of coverage would also increase since this represents the average amount that a policyholder will receive from the policy, which is in part a function of the expected utilization of services. It should not, however, materially affect results unless some groups exhibit significantly different levels of induced demand than others.


As mentioned, the actuarially fair premium for each policy represents the amount of money that would have to be collected on an annual basis to fund the expected value of future policy benefits. Suppose ten individuals purchase LTC insurance policies of a particular configuration. For the purposes of illustration, assume further that all of these individuals die over a ten-year period. The expected hypothetical stream of discounted claims payments for the group of individuals is shown in Table B1. For the premium to be actuarially fair, the present value of premium payments must equal the present value of claims costs. As shown, the present value of claims is equal to $22,505. To solve for premium payments, one must multiply the number of survivors by the estimated premium and then sum the present value of premiums. If the sum of the present value of premiums is greater than the sum of the present value of costs, the premium is too high. In the example, the premium that yields equality between discounted claims costs and discounted premium payments is $513.

As shown, in early years, the amount of money collected on an annual basis is greater than the amount spent on claims. These monies both pay for current claims and prefund payments for future claims. However, as more individuals use benefits or die, the amount collected on an annual basis is less than the amount paid out. Thus, later claims are paid by premiums collected in earlier years.
Table B1: Example of Discounted Claims and Premium Payments

 Discounted Discounted Premiums (at
Year Survivors Claims Costs Annual Premium of $513)

1 10 $ 400 $ 4,794
2 10 $ 800 $ 4,481
3 9 $ 1,171 $ 3,769
4 8 $ 2,016 $ 3,131
5 7 $ 3,072 $ 2,560
6 5 $ 3,746 $ 1,709
7 3 $ 4,000 $ 958
8 2 $ 3,500 $ 597
9 1 $ 2,300 $ 279
10 1 $ 1,500 $ 261

Total 56 premium $22,505 $22,504


The authors gratefully acknowledge the advice and guidance of Tom McGuire, Ph.D. and Randy Ellis, Ph.D. of the Boston University Department of Economics. We would also like to thank the reviewers of this article for their insightful comments.


1. The Omnibus Reconciliation Act of 1993 (OBRA) made Medicaid eligibility requirements more stringent by increasing the look-back period for assets from two to three years. This change was designed to make it more difficult for individuals to transfer assets in order to obtain Medicaid eligibility. Most importantly, perhaps, is that with the exception of assets in California, Connecticut, Indiana, and Iowa, assets protected by LTC insurance will be considered part of the person's estate, and the act requires the states to attempt to recover the cost of institutional care from the estates of Medicaid patients.

2. Policy design information includes details on daily nursing home benefit amounts, elimination periods, benefit duration, the presence of inflation protection, and premium levels.

3. We tested the subsequent equations with and without the imputed income and asset variables and found signs and coefficients to remain relatively unchanged. This provides a degree of confidence that results for these two variables are reliable even in the presence of substantial imputation. Not shown in subsequent tables is a variable indicating whether or not someone reported state of residence. We found that individuals who did not report income and asset levels also did not report state of residence, in part because this question followed the income and asset questions and was the final question on the survey. Because it is not possible to impute state of residence, we included in the equation a variable indicating whether or not an individual reported state of residence. This enabled us to ensure that imputed values on income and assets were included in the analysis. This variable was not significantly related to purchased coverage amounts.

4. Typically price is defined in terms of an absolute value, say $100 or $200. The measure used in this analysis should not be interpreted as price in the traditional sense because it is operationalized as a ratio. In this analysis, we interpret the ratio level variable as relative price, that is, relative to the coverage offered, the proportion of premium attributable to non-claims costs or the "cost" of the insurance policy exclusive of costs attributable to claims.

5. Too great an overlap between the independent variables used in the first and second stages of the equation can lead to multicollinearity and an unstable Lambda (inverse Mills ratio). Lambda is the conditional expectation of the error term from the first-stage equation introduced into the second stage to adjust for selectivity problems (see Maddala 1983).

6. Given recent changes in Medicaid eligibility rules - OBRA, 1993 - the look-back period for Medicaid asset transfers has increased to three years.

7. The variable that measures the expected future LTC costs faced by individuals is in part a function of age and sex. Because estimates of lifetime costs can alternatively be interpreted as various combinations of age and sex, there is a high degree of correlation between the gender variable and the expected lifetime cost variable. When gender is excluded from the equation, the coefficient and sign for the expected LTC cost variable change with respect to the purchase-nonpurchase decision. This indicates instability in the first-stage equation, suggesting that results for this variable should be interpreted with caution.

8. Medicaid reimbursement rates are taken from Swan, Harrington, Grant, et al. (1991).

9. Two types of general estate recovery programs are found in the states: (1) comprehensive programs where everything paid out of Medicaid can be recovered from an individual's estate and (2) programs where payments are collected from estates in cases where errors were made, or programs that exist in statute only but are not really enforced. About 24 states have general recovery programs where the rest of minimal or no programs (U.S. Congress, Office of the Inspector General 1988).

10. In his 1990 article, Pauly argues that in the presence of Medicaid and intra-family moral hazard, a rational, risk averse utility maximizing individual may opt against the purchase of LTC insurance. He argues that the presence of insurance merely enhances the value of one's estate, something that many individuals may not want to do. However, in his article, Medicaid is not explicitly modeled and ignored is the fact that people purchase policies for a variety of reasons and not merely to assure the provision of an estate.

11. We focused our analysis on the number of beds per person over age 65. Perhaps a more precise measure would be the number of beds per person over age 75.


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Data collection for this research was funded by a contract with the Health Insurance Association of America. Preparation of this article was funded from a grant from the Robert Wood Johnson Foundation.

Address correspondence and requests for reprints to Nanda Kumar, Ph.D., Research Associate, LifePlans, Inc., Two University Office Park, 51 Sawyer Road, Suite 340, Waltham, MA 02154. Dr. Kumar is also Assistant Professor, School of Public Health, Harvard University. Marc A. Cohen, Ph.D., is Principal, LifePlans, Inc. and Researcher, JDC-Brookdale Institute, Jerusalem, Israel; Christine E. Bishop, Ph.D., is Research Professor, Institute for Health Policy, Heller Graduate School, Brandeis University; and Stanley S. Wallack, Ph.D., is Director, Institute for Health Policy, Heller Graduate School, Brandeis University and Chairman of the Board, LifePlans, Inc. This article, submitted to Health Services Research on September 27, 1993, was revised and accepted for publication on August 23, 1994.
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Author:Kumar, Nanda; Cohen, Marc A.; Bishop, Christine E.; Wallack, Stanley S.
Publication:Health Services Research
Date:Feb 1, 1995
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