1. The 2018 ASSA Annual Meeting
January 6, 2018
Medicaid Crowd-Out of Long-Term Care Insurance With Endogenous Medicaid Enrollment
The 2018 ASSA Annual Meeting
Geena Kim
Health, Retirement, and Long-Term Analysis Division
The information in this presentation is preliminary and is being circulated to stimulate discussion and critical comment as developmental work for analysis for the Congress.

2. Introduction Long-Term Care Cost, Usage, and Private Insurance
Average annual cost of nursing home care was $82,128 in 2016
About half of Americans turning 65 were estimated to develop a disability that requires long-term care (ASPE, 2016)
Few (about 10 percent) have private long-term care insurance (LTCI)

3. Introduction (Continued)
Long-Term Care and Medicaid
In 2015, 62 percent of nursing home residents relied on Medicaid
Total nursing home care spending was $157 billion in 2015
Medicaid accounted for about a third of that spending
Long-term care costs accounted for about 30 percent of total Medicaid expenditures in 2015

4. Introduction (Continued)
Goals
To estimate the effect of lowering premiums of private long-term care insurance on LTCI demand
To estimate the Medicaid crowd-out effect

5. Introduction (Continued)
Approach
Develop and estimate a stochastic dynamic model of decisions on:
LTCI purchase
Medicaid enrollment
Nursing home use
Savings

6. Introduction (Continued)
Preview of Findings
Price elasticity of LTCI demand is small
Medicaid crowd-out of LTCI demand is small

7. Existing Literature Price Elasticities of LTCI Demand Goda (2011)
Coutemanche and He (2009)
Cramer and Jensen (2006)
Johnson, Schaner, Toohey, and Uccello (2007)
Medicaid Crowd-Out of LTCI Demand
Pauly (1989, 1990)
Brown and Finkelstein (2008)

8. Model Stochastic Dynamic Decision Model
Each period, shocks are realized (e.g., shocks to health, income, medical care cost, and preference)
Observing the shocks, individuals make decisions
Choices: On health insurance, nursing home use, and savings
State: Given their own state (realized at each period)
Objective: In order to maximize expected lifetime utility
Constraints: Subject to budget constraints, health transition functions, Medicaid eligibility rules, etc.

9. Model (Continued) Medicaid eligibility rules
Categorically needy (CN) and medically needy (MN)
CN: All states have a categorically needy program that specifies an income limit (Īs) and an asset limit (Ws) for Medicaid eligibility
MN: In some states, people may enroll in Medicaid even if their income/assets exceed categorical thresholds, provided that their income and wealth net of their total medical care cost are at or below certain limits
Post-eligibility rules: personal needs allowance
pnas: To maintain eligibility, a Medicaid beneficiary in a nursing home cannot have income exceeding the personal needs allowance

10. Model (Continued)
Individual’s Problem (*1 period = 2 years) where Ca is consumption, (Ws, Īs, pnaa) are determined by Medicaid rules, Ia is income, mca is medical care cost, pa is LTCI premium, k is type

11. Model (Continued) Choice Set Da = { hia, nha, sra }
hia ϵ { 0, 1, 2 }: health insurance
hia = 1: LTCI (long-term care insurance)
hia = 2: Medicaid
hia = 0: neither
nha ϵ { 0, 1 }: nursing home
nha = 1: nursing home use
nha = 0: no nursing home
sra : savings rate

12. Model (Continued) Dynamic Decisions
Buying private long-term care insurance enables usage of a nursing home sometime in the future at low cost
Nursing home use affects the probability of surviving to the next period
Current savings decision affects Medicaid eligibility in the next period

13. Model (Continued) State Space
Ωa = { s , a , e , Ha , Wa , hia-1, dra, nha-1 ; ϵa , k }
Ha ϵ {  0, 1, 2 }: health status (ADL: activities of daily living)
Ha = 1: #ADL < 3 (Good)
Ha = 2: #ADL ≥ 3 (Poor)
Ha = 0: (Dead)
s: state of residence
e: education
Wa: assets carried over to age a
dra: duration of LTCI ownership at age a
ϵa: vector of shocks
k: type (unobserved permanent heterogeneity)

14. Model (Continued)
Per-Period Utility

15. Model (Continued) Budget Constraints hia ≠ 2 (no Medicaid)
Wa+1 = (1 + r ) Wa + Ia − Ca − mca − pa · I ( hia = 1 )
hia = 2 & nha = 0 (Medicaid and no nursing home)
Wa+1 = (1 + r )  min{ Wa, Ws } + min{ Ia, Īs  } − Ca
hia = 2 & nha = 1 (Medicaid and nursing home)
Wa+1 = (1 + r )  min{ Wa, Ws  } + min{ Ia, pnas  } − Ca

16. Data and Estimation Data Health and retirement study (1998–2004)
Single elderly women living in CA, TX, MI, and FL
Estimation
Simulated maximum likelihood estimation

17. Solution Method
Dynamic Programming Estimation procedure Iterates between the solution of the dynamic programming and the calculation of the likelihood

18. Model Fit Health Insurance Choices by Age LTCI (%) Medicaid (%)
Neither (%)
Age
Actual
Pred.
73–74
15.9
13.8
18.2
11.7
65.9
74.5
75–76
15.7
13.2
18.1
12.9
66.2
73.9
77–78
12.0
12.1
17.7
14.2
70.3
73.7
79–80
11.6
10.2
17.3
16.1
71.1
81–82
7.5
8.2
15.5
16.4
77.0
75.4
83–84
6.5
8.3
17.0
78.0
74.7
85–86
9.4
7.1
23.0
20.0
67.6
72.9
87–88
27.4
22.3
66.1
69.4
Percentage holding private long-term care insurance, being on Medicaid, and having neither
Chi-square goodness-of-fit statistic: 4.31
Critical value of chi-square distribution with 2 degrees of freedom at 5 percent significant level: 5.99

19. Model Fit (Continued) Nursing Home (NH) Choice by Age NH (%) No NH (%)
Actual
Pred.
73–74
1.1
1.5
98.9
98.5
75–76
1.6
98.4
77–78
2.5
97.5
79–80
4.0
3.2
96.0
96.8
81–82
4.6
4.1
95.4
95.9
83–84
7.1
7.9
92.9
92.1
85–86
10.8
11.8
89.2
88.2
87–88
12.1
15.1
87.9
84.9
Percentage choosing nursing home and not choosing nursing home
Chi-square goodness-of-fit statistic: 1.17
Critical value of chi-square distribution with 1 degree of freedom at 5 percent significant level: 3.84

20. Model Fit (Continued)
Mean Assets by Age

21. Findings Price Elasticity of LTCI Demand
If the premium is reduced by half, the LTCI demand increases by 4.2 percent
Price elasticity of LTCI demand: -0.08
Medicaid Crowd-Out of LTCI Demand
In the absence of Medicaid:
LTCI demand would increase by 5.3 percent
Median assets would increase by 15.3 percent
Nursing home care use would decrease by 24.4 percent

22. Limitations
The findings from this study cannot be generalized to the entire U.S. population
Those findings are specific to unmarried elderly women living in four states: CA, TX, MI, and FL
Married couples’ incentives for LTCI needs are different from unmarried individuals’
Informal care is not explicitly modeled
Some individuals might prefer family-provided nursing care at home rather than in nursing home
Those people would be less price-sensitive

23. Conclusion Contributions
Provide a new estimate of price elasticity for a population at risk of future long-term care shock
Use a new approach where both price elasticity and Medicaid crowd-out are examined
Future work
Explicitly model informal care

24. Thank You