Actuarial Research Corporation’s Long Term Care Insurance Model
June 22, 2011
- No one can foresee how this program will operate, therefore premiums cannot be guaranteed to be adequate.
- Unknowns include level of participation, level of antiselection, and the effectiveness of procedures to determine earnings, “actively at work,” and qualifications for benefits, and the effect of providing advocacy services
- Level premiums cannot be determined for benefits linked to an index (CPI), because future benefits are unknown at the time that premiums are calculated.
- Adequacy of premium cannot be guaranteed when premium levels are unknown such as would be the case if premiums bounce up and down with income.
Actuarial Basis For Premium Formula
- For each issue age, projections of benefits, expenses, and premium income are made until age 100 (presumed to be the end of life for all individuals in the cohort).
- The Premium for each issue age is set so that the present value of benefits and expenses is equal to the present value of premium income.
- Premiums are calculated such that there is no subsidy across years of issue or age at issue, as is typical of social insurance.
- Premiums are based on a set of assumptions:
- Interest Rates
- Mortality Rates
- Lapse Rates
- Expense Levels
- Utilization Rates
Source for Assumptions
- All assumptions may be modified b the user.
- Interest rates and mortality rates are taken from the 2011 OASDI Trustees Reports.
- Lapse Rates are assumed to be 0.75% per year.
- Premium load for expenses is assumed to be 3%.
- Utilization comes from survey data with several adjustments.
- 2011 Trustees Report
- Mortality rates decline by roughly 0.8% per year
- Compared to 1994 GAM:
- Male GAM rates are about 99% of TR rates in 2011
- Male TR rates go below 1994 GAM in 2012
- Female GAM rates are about 83% of TR rates in 2011
- Female TR rates go below 1994 GAM in 2033
Utilization Assumptions: Data Sources for Nursing Home Rates
- For NH prevalence rates, incidence rates, average length of stay, and continuance table: 1985 National Nursing Home Surveys (NNHS), trended to 2004 NNHS (generally about 20% to 40% reduction depending on age and sex).
Utilization Assumptions: Data Sources for Home Care Rates
- For HC ages 65+, incidence rates, average length of episode, and continuance table: 1982-1989 National Long-Term Care Surveys (NLTCS) as analyzed by Eric Stallard and Bob Yee, trended to 2004 by change in prevalence rates from the 1989 to 2004 NLTCSs (generally about 20% to 50% increase depending on age and sex).
- For HC ages <65, home care prevalence rates from the 2009 National Health Interview Survey (NHIS). Average length of episode is extrapolated from the over 65 (increased by 1% for each age, which is from about 3 1/2 years at age 65 to about 5 3/4 years at age 18). Continuance table is from the over 65. Incidence rates are derived from the formula:
- PR = IR * ALOS, which is equivalent to IR = PR / ALOS
|Utilization Assumptions: Comparison of ARC Model Incidence Rates to SOA Data for 2+ ADLs|
|* Excluded adjustments are for selection, antiselection, trend, and ADL creep. Incidence rates are the sum of NH + HC incidence rates average of male and female.|
Utilization Assumptions: Adjustments
- Utilization data are tabulated by age, gender, and ADL.
- Utilization of the under 65 are also tabulated by income level and definition of cognitive impairment.
- We assume that 25% of those with one ADL less than the requirement will receive benefits.
- We calculate the number of new beneficiaries in the first year of benefit payments (2017) by using prevalence rates rather than incidence rates.
Utilization Assumptions: Selection and Antiselection
- Selection: Provisions that result in participants being healthier than average (average is based on survey data for the whole population).
- The 3-year work requirement
- NHIS data shows that ADL level of those that work ($1+ per year $1) have significantly lower utilization than the total population
- Antiselection: Those in need of services are the most likely to participate in an unsubsidized / voluntary program.
Utilization Assumptions: Selection
- Selection Factor: incidence rates in the last year of required work = 60% of ultimate
- Work is required for 3 out of the 5-year vesting period
- Selection wears off over 10-year period
Utilization Assumptions: Antiselection -- Two Methods
- Antiselectino Factor (AF) -- We model two different methods (and other methods are possible):
- Formula based on a comparison of participation rates and prevalence rates
- Estimate of additional 1st-year claims
- Additional First Year Claims
Formula Method of Antiselection
- A function of the participation rates and prevalence rates, assumed to diminish over a 20-year period.
- Starts by first calculating a factor that represents the maximum amount of antiselection and then dampens this factor.
- Maximum factor = 1/prevalence rate, if prevalence > participation.
- Maximum factor = 1/(prevalence / participation), if participation > prevalence.
- Different factor at each age and sex
Utilization Assumptions: Antiselection -- Examples
- Example 1 -- Male age 35 2+ ADLs: participation = 0.81% & prevalence rates = 0.13%
- AF = 1/.0081 = 124 (perfect antiselection)
- AF = 100^0.7 = 29.2 (imperfect antiselction)
- AF(5) = 12.8 (interpolated value at duration 5)
- Example 2 -- Male age 55: participation = 3.43%, prevalence = 0.24%
- AF = 1/.034 = 29.2 (perfect antiselection)
- AF = 29.2^0.7 = 10.6 (imperfect antiselection)
- AF(5) = 6.0 (interpolated value at duration 5)
Additional First Year Claims Method of Antiselection
- Tabulate NHIS number of individuals that meet criteria for participation and benefit eligibility.
- Assume that they all receive benefits in 2017 possible.
- * All = Dementia, developmental disabilities, mental retardation, ADD, schizophrenia, bipolar.
- ** SRD = 1st 3 in list above
|Income|| All* Cognitive or
2+ ADLs (000)
| All* Cognitive or
3+ ADLs (000)
| SRD** Cognitive or
2+ ADLs (000)
| SRD** Cognitive or
3+ ADLs (000)
Policy Options That Can Be Modeled
- Earnings requirement (parameter in law)
- Years of work required (3)
- Level for participation (quarter of coverage = $1,090 in 2009)
- Level for subsidy (poverty line = $10,830 in 2009)
- Benefit trigger (ADL requirement)
- Dollars per day of benefit including indexing options
- Indexing of premium
- Waiver of premium while in claim status
- While in nursing home
- And / or while in home care
- Deductible period
- Lifetime maximum
Assumptions That Can Be Modified
- Strength of antiselection
- Level of utilization
- Trend in utilization
- Expense load
- Level of mortality
- Trend in mortality
- Final Set of assumptions for calculating premiums have not yet been determined.
- Premiums are very sensitive to some assumptions.
- Low Income Subsidy / Income requirements
- Participation rates (1% to 4% decreases premiums by 13% to 18%)
- Indexing of premium (20+% reduction in initial premium)
- Interest (14% increase in premium for 4.7% interest vs 5.7% interest with no change in CPI)
- Lapse (8% increase in premium for 0% lapse from 0.75%)
- Trends in mortality (4.3% decrease in premium by changing annual trend from 0.75% to 0.25%) and morbidity
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