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Three essays on the evaluation of long-term care insurance policies

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Three essays on the evaluation of long-term care insurance policies

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Content THREE ESSAYS ON THE EV ALUATION OF
LONG-TERM CARE INSURANCE POLICIES
by
Yinan Liu
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fullfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ECONOMICS)
August 2021
Copyright 2021 Yinan Liu
Dedication
This work is dedicated to my grandfather, the man who taught me to perform every
task, no matter how big or small, to the best of my ability. He is the kind of scholar who I
will always aspire to be.
ii
Acknowledgements
Throughout the writing of this dissertation, I have received a great deal of support
and assistance.
I would first like to thank my advisor, Professor John Strauss, whose expertise was
invaluable in formulating the research questions and methodology. His insightful feed-
back pushed me to sharpen my thinking and brought my work to a higher level. I have
benefited not only academically from his rigorous working attitude but also emotionally
from sharing fruits and donuts at his house.
I would like to thank my committee members, Professor Cheng Hsiao and Professor
Alice Chen, for their endless support and unwavering guidance. Those hour-long discus-
sions with them provided me with the tools that I needed to successfully complete my
dissertation and gave me the faith to continue work on my projects.
I would also like to thank Professor Geert Ridder and Professor Jeffrey Weaver for
their valuable guidance throughout my studies. They provided me with stimulating dis-
cussions that I needed to choose the right direction. I have no words to express my grati-
tude to my friend, and colleague, Qin Jiang, for listening to me and supporting me. I owe
special thanks to Young Miller and Alexander Karnazes. They have always been ready to
help and made my life pleasant and easier at USC.
Last but not least, I would like to thank my parents and my best friend, Hao Zhao, for
their wise counsel and unconditional love and support. They are always there for me.
iii
TABLE OF CONTENTS
Dedication ii
Acknowledgements iii
List of Tables viii
List of Figures ix
Abstract x
Chapter 1: Introduction 1
Chapter 2: The Value of Medicaid Long-Term Care: Evidence from the Deficit
Reduction Act of 2005 5
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Policy Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.1 Demographic Transition and Long-Term Care in United States . . . . 11
2.3.2 Medicaid Long-Term Care . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.3 The Home Equity Exemption Provision of the Deficit Reduction Act 13
2.4 Conceptual Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4.1 Conceptualizing Consumption Decisions . . . . . . . . . . . . . . . . 15
2.4.2 Expected Impacts of the DRA . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Empirical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5.1 Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5.2 Empirical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5.3 Robustness and Placebo Exercises . . . . . . . . . . . . . . . . . . . . 31
2.6 Welfare analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.6.1 Structural Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.6.2 Social Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.6.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.6.4 Results on Willingness to Pay . . . . . . . . . . . . . . . . . . . . . . . 44
2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Chapter 3: The Impact of Partnership Long-Term Care Program on Insurance
Coverage 69
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
iv
3.2 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.3 Policy Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.3.1 The Market for Private Long-Term Care Insurance . . . . . . . . . . . 76
3.3.2 Medicaid Long-Term Care . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.3.3 The Partnership for Long-Term Care . . . . . . . . . . . . . . . . . . . 78
3.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.5 Empirical Strategy and Results . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.5.1 Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.5.2 Robustness Checks and Placebo Tests . . . . . . . . . . . . . . . . . . 88
3.6 Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Chapter 4: The Unintended Consequence of Partnership Long-Term Care Pro-
gram on Labor Market 104
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.2 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.3 Policy Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.3.1 Medicaid Long-Term Care . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.3.2 The Partnership for Long-Term Care . . . . . . . . . . . . . . . . . . . 109
4.3.3 Labor Market Environment for Older Workers . . . . . . . . . . . . . 110
4.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.5 Empirical Strategy and Results . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.5.1 Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.5.3 Placebo Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.6 Discussion: The Bequest Motive . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Chapter 5: Conclusion 137
Bibliography 140
Appendix A: 146
Chapter 2 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
v
List of Tables
2.1 Pre-DRA Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.2 Testing the Parallel Trends Assumption - Home Equity . . . . . . . . . . . . 55
2.3 Triple-Difference (DDD) Estimate of the Impact of the DRA on Home Equity 56
2.4 Heterogeneous Triple-Difference (DDD) Estimate of the Impact of the DRA
on Home Equity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.5 Triple-Difference (DDD) Estimate of the Impact of the DRA on Home Value
and Home Loan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.6 Pre-DRA Summary Statistics: Consumption Details . . . . . . . . . . . . . . 59
2.7 Testing the Parallel Trends Assumption - Consumption . . . . . . . . . . . . 60
2.8 Triple-Difference (DDD) Estimate of the Impact of the DRA on Consumption 61
2.9 Testing the Parallel Trends Assumption - Consumption . . . . . . . . . . . . 62
2.10 Tripe-Difference (DDD) Estimate of the Impact of the DRA on Consump-
tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.11 Tripe-Difference (DDD) Estimate the DRA Effects on Different Categories
of Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.12 Tripe-Difference (DDD) Estimate the DRA Effects on Different Categories
of Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2.13 Heterogeneous Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.14 Overview of Empirical Objects . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2.15 Willingness to Pay (WTP) for Medicaid LTC . . . . . . . . . . . . . . . . . . . 68
3.1 Effective Date of the PLTC Program by State . . . . . . . . . . . . . . . . . . . 92
vi
3.2 Summary Statistics: Near-elderly (50-64 )and Elderly (70+) samples . . . . . 93
3.3 First-Stage Estimates: The Impact of the PLTC program on LTC Coverage
Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.4 DID Estimates of the PLTC Program’s Impact on LTC Coverage Rates (50-
64) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.5 DID Estimates of the PLTC Program’s Impact on LTC Coverage Rates (70+) 96
3.6 DID Estimates of the PLTC Program’s Impact on Medicaid Coverage Rates
(70+) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
3.7 Robustness Check: DID Estimates of the PLTC Program’s Impact on Medi-
caid Coverage Rates (75+) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
3.8 Robustness Check: DID Estimates of the PLTC Program’s Impact on LTC
Coverage Rates (75+) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.9 Robustness Check: DID Estimates of the PLTC Program’s Impact on Medi-
caid Coverage Rates (Asset> 5000) . . . . . . . . . . . . . . . . . . . . . . . . 100
3.10 Placebo Test: Event-Study Estimates of the PLTC Program’s Impact on Life
Insurance Coverage Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.11 Placebo Test: DID Estimates of the PLTC Program’s Impact on Life Insur-
ance Coverage Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
3.12 Mechanisms: Health Behavior Changes After the PLTC Program . . . . . . . 103
4.1 Effective Date of the PLTC Program by State . . . . . . . . . . . . . . . . . . . 123
4.2 Summary Statistics: Near-elderly (50-64 ) samples . . . . . . . . . . . . . . . 124
4.3 Test of Parallel Trends Assumption - Full-Time Job Status . . . . . . . . . . . 125
4.4 Test of Parallel Trends Assumption - Part-Time Job Status . . . . . . . . . . . 126
4.5 DID Estimates of the PLTC Program’s Impact on Full-Time Work Status . . 127
4.6 DID Estimates of the PLTC Program’s Impact on Part-Time Work Status . . 128
4.7 DID Estimates of the PLTC Program’s Impact on Work Status . . . . . . . . . 129
vii
4.8 Placebo Test: DID Estimates of the PLTC Program’s Impact on Work Status
(Age< 50) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.9 Placebo Test: DID Estimates of the PLTC Program’s Impact on Work Status
(Age> 70) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
4.10 Placebo Test: DID Estimates of the PLTC Program’s Impact on Work Status
(Asset6 2000) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.11 Test Hypothesis: DID Estimates of the PLTC Program’s Impact on Work
Status (Without Kids) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.12 Test Hypothesis: DID Estimates of the PLTC Program’s Impact on Work
Status (With Kids) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.13 Test Hypothesis: DID Estimates of the PLTC Program’s Impact on Work
Status (With Kids) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
4.14 Test Hypothesis: DID Estimates of the PLTC Program’s Impact on Work
Status (Without Kids) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
A.1.1Pre-DRA Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
A.1.2Robustness to Regression Sample . . . . . . . . . . . . . . . . . . . . . . . . . 148
A.1.3Robustness to Definition of the Middle-Aged . . . . . . . . . . . . . . . . . . 149
A.1.4Placebo Test to Alternative Definition of ”Above” Group . . . . . . . . . . . 150
A.1.5Robustness Checks of Key Estimates for Evaluation of Willingness to Pay . 151
viii
List of Figures
2.1 Total Long-Term Care Expenditures, 1996-2016 . . . . . . . . . . . . . . . . . 47
2.2 Long-Term Care Costs Can Exceed Seniors’ Income . . . . . . . . . . . . . . 48
2.3 The Utility Tree for A Two-Stage Budgeting Model . . . . . . . . . . . . . . . 49
2.4 Individuals’ Response to the DRA Under Different Demand for LTC . . . . 50
2.5 Evaluation of Willingness to Pay (WTP) With or Without Constrained Op-
timization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.6 Changes in Home Equity Across Years . . . . . . . . . . . . . . . . . . . . . . 52
2.7 Changes in Home Value and Home Loan Across Years . . . . . . . . . . . . . 53
A.1 Changes in Home Equity Across Consecutive Year Pairs . . . . . . . . . . . . 146
ix
Abstract
This dissertation evaluates various long-term care (LTC) insurance policies. Public
LTC insurance helps the elderly protect against financial risks, yet its value is hard to
measure. Chapter 2 provides a novel answer to this question by employing a quasi-
experiment from the Deficit Reduction Act (DRA) that restricts seniors’ Medicaid LTC
access. I find that in response to the DRA, single elderly individuals reduced their home
equity by $66.75K (12.1%), while increasing non-LTC consumption by $10.5K (22.5%).
Using these findings and a two-stage budgeting model, I then estimate that seniors’ will-
ingness to pay for Medicaid LTC is $1.2 per dollar of its net resource cost. This evidence
shows that the government’s intention to limit the provision of Medicaid LTC harms so-
cial welfare.
Chapter 3 focuses on the Partnership Long-Term Care (PLTC) Insurance program,
which aimed to encourage private LTC insurance coverage while alleviating the states’
burden to pay for this type of care. With the state-by-year variation in the adoption of the
PLTC program, I find that states adopting the program experienced an increase in LTC in-
surance coverage rates. The effects are most potent for the near-elderly population (aged
50-64), who experienced a rise in LTC insurance purchases by 3.4 percentage points after
their living states exposed to the PLTC program for four years. However, my results also
indicate that the PLTC program increases Medicaid insurance by 3 percentage points after
eight years of the program’s implementation. These findings suggest that the purchase
of private LTC insurance changed policyholders’ behavior, and these changes made them
x
more vulnerable when they needed LTC services.
Chapter 4 analyzes the efficiency of the PLTC program from a new perspective. In this
chapter, I explore the impact of the PLTC program on labor force participation among the
near-elderly population. The main finding is that this program increases full-time work
status by 2-7 percentage points for near-elderly individuals. Most of the effect is driven by
individuals whose assets are above $2000. These findings deviate from the program’s ini-
tial intention. To better understand this unintended consequence, I propose a theoretical
model based on the ”bequest motive” perspective. Empirical evidence confirms my the-
oretical prediction and shows that most of the program’s impact is driven by individuals
who have children and are in well-paid jobs.
xi
Chapter 1
Introduction
”A few conclusions become clear when we understand this: that our most cruel failure in how
we treat the sick and the aged is the failure to recognize that they have priorities beyond merely
being safe and living longer; that the chance to shape one’s story is essential to sustaining
meaning in life; that we have the opportunity to refashion our institutions, our culture, and
our conversations in ways that transform the possibilities for the last chapters of everyone’s
lives.”
— Atul Gawande, Being Mortal: Medicine and What Matters in the End
In many parts of the world, although the increase in people’s longevity and the im-
provement of the elderly’s health conditions represent the highest achievements of the
past decades, these trends have also brought tremendous challenges. As people age, they
become more and more likely to face difficulties with activities of daily living (ADL).
These ADL limitations created a demand for care that typically involves either significant
time commitments from family or expensive nursing services. Therefore, the aging issue
can affect economic growth, the patterns of work and retirement, the way that families
function, the ability of governments and communities to provide adequate resources for
the elderly, and most importantly, the prevalence of chronic diseases and disabilities.
In the United States, Norton (2000) concludes that long-term care (LTC) is the most
significant expenditure risk faced by older Americans. According to accounts compiled
by the Centers for Medicare and Medicaid Services, the United States’ total expenditure
1
on nursing homes and family health exceeded $270 billion in 2018. In the past 60 years,
both types of expenses have increased dramatically. In 2018, the actual nursing home
expenditure was more than 200 times its 1960 level, and the family health care spending
in 2018 was more than 1500 times the 1960 level. With the quantity and quality of care
remaining the same, CareScout (2011) reports that between 2005 and 2011, the nominal
cost of private nursing homes in the United States increased by 4.35% per year. While
during the same period, the annual growth rate of the US consumer price index was
2.5%.
Because of such tremendous expenditure of LTC services, the effectiveness of public
insurance and private insurance has become particularly important for the elderly. As a
supplement to the Social Security Act, Medicare and Medicaid enacted in 1965 provide
important resources that individuals can rely on in old age. Without these protections,
few Americans would be able to retire, given the costly health care services. However,
despite the large scale and continuous development of these plans, Medicare and Med-
icaid cannot meet all the health care needs of the population over 65, leaving gaps that
generate substantial risks to low- and middle-income retirees. Besides, the decline in the
health benefits of former employer retirees has also begun to put high-income retirees at
risk. These pressures indicate that the government needs to introduce appropriate poli-
cies to enable the elderly to spend their twilight years in peace.
In this dissertation, I focus on better understanding the essential determinants of suc-
cessful policies, which balance between meeting the needs of the elderly and allocating
limited social resources. Specifically, I mainly answer two questions: how elderly indi-
viduals evaluate public LTC insurance and whether it is possible to induce them to enroll
in private LTC insurance to reduce public expenditure.
Chapter 2 examines elderly individuals’ willingness to pay for public LTC insurance.
To investigate this question, I build my analysis in two steps. First, I make use of the
Deficit Reduction Act policy as a quasi-experiment. This policy sets a restriction rule in
2
2006 such that individuals with home equity above $500K are not eligible for public LTC
insurance. Using detailed panel data from the biennial survey of Health and Retirement
Study (HRS) and the Consumption and Activities Mail Survey (CAMS), I find that the
DRA policy reduces seniors’ home equity by $67K. Besides, I show that the DRA policy
increases seniors’ non-housing consumption by $10K. In my second step, I build a struc-
tural model to calibrate seniors’ willingness to pay for this public LTC insurance, using
parameters that I derived from my empirical analysis. I define the value of this LTC in-
surance as the amount of non-housing consumption seniors would be willing to give up
to be indifferent between receiving and not receiving LTC insurance. My calibration re-
sult shows that the seniors’ willingness to pay for this Medicaid is higher than the net
resource cost: for every dollar cost, they are willing to pay $1.2.
In Chapter 3, I look at the Partnership Long-term Care (PLTC) Insurance program,
which aimed to encourage people to purchase private LTC insurance to help cover LTC’s
cost while alleviating the states’ burden to pay for this type of care via Medicaid. This
program allows policyholders to protect a certain amount of additional assets from Med-
icaid’s asset limit. Specifically, I evaluate two questions related to this program: how does
the program affect private LTC insurance ownership rates and Medicaid coverage rates?
Using data from the HRS, I conduct the event-study analysis and find that states adopt-
ing the program experienced an increase in LTC insurance coverage rates. The effects are
most potent for the near-elderly population (aged 50-64). Then I examine whether the
presence of PLTC policies affects Medicaid coverage rates among the elderly (aged over
70). My results indicate that the PLTC program increases Medicaid insurance by 3 per-
centage points after eight years of its implementation, and the effect gets stronger as time
goes by. This finding suggests that the PLTC program induces more elderly individuals to
rely on Medicaid, which is contrary to the PLTC program’s intention to reduce the usage
of Medicaid. This finding echoes my hypothesis that the purchase of private LTC insur-
ance changed policyholders’ behavior, and these changes made them more vulnerable
3
when they needed LTC services.
Chapter 4 examines the efficiency of the PLTC program from a new perspective. Sup-
pose the PLTC program increases private LTC insurance coverage among the near-elderly
population, as shown in chapter 2. In that case, it is reasonable for us to infer that these
near-elderly individuals alter their decision on labor force participation. On the one hand,
they can save more than before the expansion of the PLTC program. Thus, they would
have more incentive to earn wages from the labor market. On the other hand, since they
would face less medical expense uncertainty and rely on private/public health insurance
to finance their health care, they will view earlier retirements as affordable and thus pro-
vide less effort on work. Using data spanning from 2000 to 2010, I find that the presence
of the PLTC program increases full-time work status by 2-7 percentage points for near-
elderly individuals. Most of the effect is driven by individuals whose assets are above
$2000. Besides, I supplement my analysis by proposing a theoretical model based on the
standpoint of the bequest motive. The model suggests that only when individuals whose
labor market conditions are favorable, the more assets they want to bequeath to their chil-
dren, the more likely they will join the labor market. My empirical evidence echoes my
hypothesis and shows that the effects are concentrated among individuals with kids who
are in well-paid jobs.
The remainder of this dissertation is organized as follows: Chapter 2 examines elderly
individuals’ willingness to pay for public LTC insurance; Chapter 3 evaluates the PLTC
program’s on private LTC insurance and Medicaid coverage rates; Chapter 4 explores the
unintended consequence of the PLTC program on labor force participation among near-
elderly individuals. Chapter 5 concludes and discusses several future strands of research.
4
Chapter 2
The Value of Medicaid Long-Term Care:
Evidence from the Deficit Reduction Act
of 2005
2.1 Introduction
In the last two decades, there has been a substantial increase in long-term care (LTC)
expenditures in the United States. As illustrated by Figure 2.1, total LTC expenditures
rose from $125 billion in 1996 to $350 billion by 2016. This rapid growth of LTC spend-
ing is due to two reasons: high demand and huge cost. About 42% of adults aged 65
and above have reported functional limitations in 2017 (CDC, 2017), suggesting that the
demand for LTC is extensive. Meanwhile, the cost of LTC is overwhelming compared to
seniors’ income. In 2019, the average annual cost of a private room in a nursing home
was around $102,200, which is almost four times larger than 200% of the Federal Poverty
Level (see in Figure 2.2). As the population ages and disabling health conditions become
increasingly common, these costs may keep rising.
This paper builds on the fact that LTC costs are one of the largest financial risks faced
5
by senior adults. Therefore, finding a way to pay for LTC becomes a big concern. Medi-
care does not cover most LTC expenses, and the private insurance market for LTC is
small. More than half of total costs are paid by the Medicaid LTC program, and indi-
viduals who are not eligible for Medicaid LTC mainly pay LTC costs out of pocket. As a
result, Medicaid LTC eligibility offers a valuable resource for senior adults to deal with
such unexpected financial risks. This leads to the research question of this paper: How
much are senior adults willing to pay for Medicaid LTC?
This question is challenging since Medicaid LTC, as public health insurance, is not
traded in a well-functioning market. This prevents us to implement welfare analysis
based on estimates of ex-ante willingness to pay derived from contract choices. To in-
vestigate this question, I build my analysis in two steps. First, I identify the impact of
Medicaid LTC eligibility on individuals’ consumption behavior using a quasi-experiment.
Second, I construct a two-stage budgeting model to evaluate the value of Medicaid LTC
to recipients in terms of the amount of non-housing, non-LTC consumption they would
need to give up to be indifferent between receiving and not receiving Medicaid LTC.
Specifically, for my first step, I make use of a policy change under the federally man-
dated Deficit Reduction Act (DRA). Before 2006, the primary residence was a non-countable
asset when determining eligibility for Medicaid LTC services, and therefore acts as a pop-
ular channel for sheltering assets. However, after the passage of the DRA in 2006, indi-
viduals with home equity above $500,000 were not able to receive payments for Medicaid
LTC services. This is the largest change to Medicaid LTC eligibility since its enactment in
1965. If individuals have little demand for LTC services, then a policy that influences the
eligibility for Medicaid LTC should barely affect their utility levels. On the other hand, if
individuals perceive that they will use a large amount of LTC services, then the same pol-
icy should significantly affect their well-being by distorting their consumption behavior.
Using detailed panel data from the biennial survey of Health and Retirement Study
(HRS) and the Consumption and Activities Mail Survey (CAMS), I test how the DRA af-
6
fects the consumption behavior of senior adults. The main challenge for identification of
the policy impact is that it was implemented across all states in the United States during
the housing market crash with the subsequent financial crisis. Thus a simple difference-
in-differences approach in estimating individuals’ consumption change during this pe-
riod could simply reflect broader trends and not be in any way caused by the provision
of the DRA.
I address this identification challenge by employing a triple-difference (DDD) frame-
work. I make use of the fact that seniors with home equity below the equity cap are not
influenced by the policy. I use these individuals as the control group and use those with
home equity above $500K as the treatment group. To account for the possible impact
of the housing market crash, I use a younger cohort aged 55-64 who are not eligible for
Medicaid LTC services as the second control group.
By dividing total non-LTC expenses into the consumption of housing services and the
consumption of non-housing goods and services, I establish two main empirical findings.
First, individuals with home equity above the DRA-imposed cap reduce their home eq-
uity by $66,750 to $97,950 depending on regression specification. Most of the impact of
this restriction policy is concentrated among individuals whose home equity is closer to
the cutoff point ($500,000), who have difficulties caring for themselves, and who have less
advantaged social-economic status. Further, with the evidence showing that home value
growth captures most of the movement pattern of home equity growth and that loan-
to-value ratio is stable, we can deduce that this restriction policy pushes the seniors to
sell their original house and move into a lower-value one without changing the mortgage
rate.
Second, I find that the DRA induces individuals to increase non-housing, non-LTC
consumption by $10,500. The increase in non-LTC consumption is mainly driven by the
increase in nondurables spending. Individuals affected by the DRA change their spend-
ing habits by investing $10,720 more on nondurables, while consumption changes in
7
other categories are insignificant. These results support a hypothesis of affected seniors
”burning up” money and distorting consumption to regain eligibility for Medicaid LTC.
Using these empirical findings, I then evaluate seniors’ willingness to pay for Medi-
caid LTC by applying a modified framework from Finkelstein et al. (2019). Specifically, an
individual’s willingness to pay for Medicaid LTC refers to the non-housing, non-LTC con-
sumption she would need to give up to be indifferent between receiving and not receiving
Medicaid LTC. In my model, I employ a two-stage budgeting framework that allocates
total expenditure in two stages: in the first stage, expenditure is allocated to LTC con-
sumption and non-LTC consumption, and in the second stage, non-LTC consumption is
further divided into housing and non-housing consumption. By assuming the separabil-
ity of components in the utility function, the optimizing individual’s first-order condition
allows me to value the marginal impacts of Medicaid LTC on any potential arguments
of the utility function through the marginal utility of that single argument. As a result,
I establish the link between non-housing, non-LTC consumption with Medicaid LTC sta-
tus. Total willingness to pay then can be divided into two parts: a transfer term and a
pure-insurance term. The transfer term captures the recipients’ expected valuation of the
transfer of resources from the rest part of the economy to them, and the pure-insurance
term captures the valuation of a budget-neutral reallocation of resources across different
states of the world. Lastly, I obtain the value of Medicaid LTC by combining the estimates
of these two parts.
The calibration result reveals that the willingness to pay for Medicaid LTC by seniors
is $1.2 per dollar of net cost, suggesting that seniors’ willingness to pay for Medicaid LTC
exceeds its net cost. This estimate is on par with existing measures of willingness to pay
in other health insurance contexts, such as general health insurance covered by Medicare
and Medicaid. This finding implies that the efficient allocation of Medicaid LTC services
has not been achieved yet, and the implementation of the DRA is not welfare-improving.
To my knowledge, the paper is one of the first studies to provide empirical evidence
8
on the importance of LTC expenses for multi-dimensional consumption behavior using a
quasi-experiment. It is also one of the first studies to evaluate seniors’ willingness to pay
for public long-term care insurance under a two-stage budgeting framework. Incorporat-
ing housing and non-housing consumption into the individual’s optimization problem
allows me to fix the distortion of consumption due to the DRA restriction and to obtain a
more accurate estimate of the value of Medicaid LTC.
The rest of this paper is organized as follows. Section 4.2 provides more details with
the relevant literature. Section 4.3 describes the background of long-term care in the
United States and the institutional details of Medicaid LTC. Section 4.6 proposes a sim-
ple conceptual framework to understand the link between the policy and consumption
arrangements among seniors. Section 4.5 describes the data and presents the empirical
strategy and the main results. Section 2.6 gives more details on the model and evaluates
the willingness to pay for Medicaid LTC. Finally, I conclude in Section 2.7.
2.2 Literature
The findings in this paper contribute to several strands of the economics literature.
First, this study contributes to a growing literature on the importance of LTC expenses
for consumption behavior. Theoretical work on savings response to old-age out-of-pocket
health expenses shows that uncertain medical expenses explain slow rates of dissaving
among elderly Americans after retirement (Kotlikoff, 1986; Hubbard et al., 1995; Palumbo,
1999; Scholz et al., 2006; De Nardi et al., 2010). Allowing for retirees to face both risky
medical expenses and risky nursing home expenses in a life-cycle framework, Kopecky
and Koreshkova (2014) show that over half of seniors’ savings are due to the presence of
nursing home expenses.
Empirical evidence on the importance of LTC expenses for consumption behavior,
however, is relatively less. One main reason for this scarcity is because it’s hard to find
9
an exogenous variation on LTC provision. This study is one of the first to utilize a quasi-
experiment to look at individuals’ multi-dimensional consumption responses to unex-
pected LTC expenses. The work most closely related to this study is Ricks (2018). Like
him, I also use the exogenous variation on LTC expenses from the DRA. The key differ-
ences between my work and his are twofold. First, I follow policy implementation as the
treated period, as opposed to relying on only anticipatory effects of the policy. Second, I
adopted a more rigorous empirical approach by using a triple-difference strategy that is
less impacted by self-reporting measurement errors and the potential violation of parallel
trends. Once these concerns are taken into account, I find that the effect of nursing home
expense risk on savings is substantial.
Second, this study is one of the first to estimate the value of public long-term care in-
surance with an empirical framework. Despite the challenges related to population aging
and the provision of long-term care, few previous studies have addressed willingness to
pay for long-term care services. Most of this literature has focused on European countries.
Those studies rely on the contingent valuation method by directly asking respondents to
report their WTP to evaluate various components for long-term care services (Amilon
et al., 2020; Callan and O’Shea, 2015; Nieboer et al., 2010). However, the main concern
of the contingent valuation method is that the respondents may not give a meaningful
answer to serve as the basis for an inference about the WTP of the entire population
(Haveman and Weimer (2001)). This paper, instead, uses a ”model-based” approach to
estimate WTP for public LTC services in the United States among senior adults with the
knowledge of their responsive consumption behavior.
This approach is methodologically related to Finkelstein et al. (2019), who develop a
model to estimate willingness to pay for Medicaid among working-age adults (19-64). My
research is different from their work in three dimensions. First, I extend their model to
explicitly incorporate housing consumption into decision making in which seniors bear
both LTC expenses and non-LTC expenses. This is very important since recent litera-
10
ture finds the important role of housing in retirees’ dissaving behavior (Nakajima and
Telyukova, 2020). Second, to calculate willingness to pay for Medicaid LTC, I modify
their definition of willingness to pay to take into account the equilibrium under the cor-
ner solution due to constrained optimization resulted from the policy intervention (see
more details in Section 2.6). Lastly, the main focus of this paper is senior adults whose
willingness to pay for public health insurance can be very different from working-age
adults.
Third, in a broad sense, this paper adds to the literature on the importance of exam-
ining how the public health insurance program affects seniors’ behavior. The focuses
of those studies range across assets reallocation, living arrangement decisions, and pri-
vate insurance takeup (Mommaerts (2018); Lin and Prince (2013); Greenhalgh-Stanley
(2012); Engelhardt and Greenhalgh-Stanley (2010); Coe (2007)). The key contribution of
this study is employing empirical findings from the policy change to deduce the value of
public health insurance.
2.3 Policy Background
This section provides details on the institutional environment of the long-term care
service in the United States and the details of the Medicaid LTC program.
2.3.1 Demographic Transition and Long-Term Care in United States
With the aging of the baby boom generation and the longer life expectancy of Ameri-
cans, the current population growth of 65 and over is unprecedented in the United States
history. It is estimated that by 2060, the number of Americans 65 and older will increase
from 52 million in 2018 to 95 million, and the proportion of the elderly in the total pop-
ulation will rise to 23% (Mather et al. (2015)). Due to the rapid increase in the overall
size of the elderly population, it is expected that the number of elderly Americans with
11
disabilities will also rise substantially.
Since most users of long-term care services are the elderly (Harris-Kojetin et al. (2019)),
the aging of the population and the increase in the prevalence of disability indicate that
the use of long-term care may surge. Long-term care includes a range of services and
supports that the elderly may need to meet their health or personal needs for a long
period of time. Specifically, it includes assistance in performing activities of daily living
(ADLs)
1
, instrumental activities of daily living (IADLs)
2
, and other health maintenance
tasks. According to the analysis of the U.S. Department of Health and Human Services
in 2018, approximately 70% of elderly individuals will depend on long-term care at some
stage in their lives. Though some of the long-term care received by seniors is provided
informally by the family at home, the availability of family caregivers declines over time
because of rising divorce rates (Kennedy and Ruggles (2014)), increasing childlessness
(Baudin et al. (2015)), and rising labor force participation of women (Greenwood et al.
(2016); Fern´ andez (2013)). The reduction in informal care has expanded the elderly’s
demand for paid services, such as formal home care or nursing home care. In 2018, formal
long-term care totaled US$379 billion, accounting for more than 10% of national health
expenditures (NHE, 2018).
Long-term care is generally not covered by Medicare or general private health insur-
ance. Medicare, the public health insurance for individuals aged 65 and over, provides
coverage for short-term post-acute care, but it does not cover long-term care over an ex-
tended period. In addition, less than 11% of Americans have a private LTC insurance
policy (Musumeci et al. (2019)). As a result, the lack of other insurance coverage makes
Medicaid the largest public payer for LTC.
1
ADLs are the basic self-care tasks. They include walking, eating, dressing, toileting, bathing, and trans-
ferring.
2
IADLs require more complex thinking skills, including organizational skills. They include managing
finances, managing transportation, shopping and meal preparation, housework, managing communication
and managing medications.
12
2.3.2 Medicaid Long-Term Care
Medicaid LTC is a means-tested, joint federal-state program that provides health in-
surance for the frail elderly population. In 2016, an estimated 62% of long-term care
users residing in nursing homes had Medicaid as a payer source (Harris-Kojetin et al.
(2019)). Medicaid LTC, therefore, acts as one major avenue through which seniors can
insure themselves against the uncertainty of long-term care costs. However, not all older
individuals are eligible. Eligibility for Medicaid LTC requires that an individual’s income
and assets fall below defined thresholds. Though eligibility tests vary by marital status
and by state, minimum eligibility requirements are determined at the federal level. Tradi-
tionally, a homeowner’s primary residence was not considered as a countable asset when
determining Medicaid LTC eligibility as long as the individual planned to return to the
home. This was true for both married and unmarried homeowners. For the former, com-
munity spouse provisions prevented the primary residence from becoming a countable
asset if the beneficiary’s spouse resided there. For the latter, the house was only countable
if the beneficiary left the home without intent to return.
2.3.3 The Home Equity Exemption Provision of the Deficit Reduction
Act
One major change to Medicaid LTC eligibility enacted by the DRA is on the program’s
home equity exemption. Previously, Medicaid LTC recipients could reserve a home of
unlimited value while receiving long-term care reimbursements. The DRA instead claims
that individuals shall not be eligible for long-term care assistance if the individual’s equity
interest
3
in the individual’s home exceeds $500K. This was and continues to be the only
mandatory federal change in the status of home equity with respect to Medicaid LTC
3
The equity interest is determined by dividing the total equity among all homeowners. For example, a
single homeowner with $500K in home equity would carry an equity interest of $500K (i.e., $500K divided
by one owner). In the case of two joint owners of a home, if the combined home equity is $500K, then each
owner would carry an equity interest of $250K (i.e., $500K divided by two owners).
13
eligibility.
The DRA was first introduced on October 27, 2005, and was signed into law on Febru-
ary 8, 2006. Since the DRA allows the new rules not to take effect immediately if state
legislation is required to implement them,
4
the full implementation date can be consid-
ered as of January 1, 2007, when all states were required to have the policies in place.
This restriction rule requires that all states deny payments for long-term care services
if an individual’s equity interest exceeds the threshold. Because of this, individuals with
LTC demand whose home equity is above the threshold would have to reduce their home
equity below the threshold in order to be eligible for Medicaid LTC coverage.
A critical note is that this new limit does not apply if a spouse remains living in the
home. Married households with one spouse remaining in the home should not be affected
by the DRA change in any state because the community spouse provision overrides the
equity limit provision. Thus, the target population affected by the restriction policy is un-
married homeowners with at least $500K in equity who do not share the house with other
individuals. This paper specifically exploits variations coming from this home equity ex-
emption of the DRA as a quasi-experiment. Such differences in the criterion of Medicaid
LTC eligibility could induce the targeted population’s response accordingly. Next, I will
use a two-stage budgeting model to illustrate how single seniors respond to the policy
change in greater detail in Section 4.6.
2.4 Conceptual Framework
This section provides a discussion of the theory-based predictions on how the impact
of the DRA on seniors’ consumption decisions will vary, depending on individuals’ de-
mand for long-term care. I present the baseline version of the model in this section to
4
Particularly, the DRA imposes a deadline on state legislation that the new rules take effect the first
day of the first calendar quarter beginning after the end of the state legislature’s next session. If a state’s
next legislative session begins in September 2006 and ends in December 2006, for example, the deadline is
January 1, 2007.
14
motivate empirical estimations. More details of the model for welfare analysis will be
described in Section 2.6.
2.4.1 Conceptualizing Consumption Decisions
In order to interpret the empirical findings and connect them to the predictions of
willingness to pay from the economic model, it is important to understand what changes
mechanically when an individual faces the shock with regard to the eligibility of Medicaid
LTC.
Consider a retired single individual, who belongs to the target population affected
by the DRA, seeking to maximize her expected utility. Her utility depends on the con-
sumption of LTC services, l, and the consumption of non-LTC goods, nl, which can be
separated as the consumption of housing,h, and the consumption of non-housing goods
and services, c. Under the assumption of weak separability of preferences, the utility
function is as follows:
u =v(l;c;h) =f[v
l
(l);v
nl
(c;h)] (2.1)
where f is an increasing function, and v
l
and v
nl
are the sub-utility functions associated
with LTC services and non-LTC goods, respectively. For the sake of brevity, I refer tol as
”LTC spending”, toh as ”home equity”, and toc as ”consumption”.
Figure 2.3 illustrates a two-stage budgeting model framework such that the individual
allocates total expenditure in two stages: at the first stage, total expenditure is allocated
to two broad groups of goods (LTC and non-LTC in Figure 2.3), while at the second stage,
group expenditures on non-LTC goods are allocated to the individual commodities (home
equity and consumption in Figure 2.3). At each of these two stages, only information
appropriate to that stage is required (Deaton and Muellbauer (1980)).
15
2.4.2 Expected Impacts of the DRA
As noted before, a distinguishing feature of the DRA is that only single seniors with
home equity above $500K are affected by this restriction policy. Therefore, we can ex-
pect that those individuals who used to enjoy Medicaid LTC with home equity above
the threshold would respond to this policy. While they are all affected by this policy, the
demand for long-term care varies from person to person. As a result, the budget share
spent on non-LTC goods and services could increase or remain the same depending on
the eligibility of Medicaid LTC. Based on the targeted population’s various demands for
long-term care, I formalize this insight into the following two propositions.
Proposition 1. After the introduction of Medicaid LTC restriction policy, for individuals with
home equity greater than the home equity cutoff point (H), if their demand for long-term care
services is small, they do not apply for Medicaid LTC, and only decrease home equity and con-
sumption on a small scale to compensate the cost for long-term care services.
This point is illustrated in Figure 2.4(a), where it shows a hypothetical individual’s
budget constraint and indifference curve for home equity and all other consumption.
Without the Medicaid LTC restriction policy, the individual can achieve maximal util-
ity level at U
0
with home equity H
0
(H
0
> H) and consumption C
0
at point A. After
the implementation of the new policy, the individual has to choose a new consumption-
home-equity bundle that satisfies a new budget constraint. When she chooses to give up
Medicaid LTC and allocates a small proportion of total expenditures on long-term care,
group expenditures on home equity and consumption falls on a small scale, as reflected
in the small inward shift fromI
1
toI
2
. At the new budget constraint, the individual could
afford less on home equity and consumption, and her new utility-maximizing bundle is
B, where the utility level is U
1
. In contrast, if the individual chooses to keep Medicaid
LTC by downsizing home equity to $500K, her budget constraint moves back toI
1
, and
the optimal utility level she can achieve isU at pointC. Note thatU
1
is greater thanU,
16
therefore, the individual decides not to apply for Medicaid LTC and to pay long-term care
out-of-pocket. In this case, as illustrated in Figure 2.4(a), the individual moves from her
initial optimal consumption bundle A to her new optimal consumption bundle B. Her
consumption of home equity and all other goods decrease from H
0
to H
1
and C
0
to C
1
,
respectively.
Proposition 2. After the introduction of Medicaid long-term care restriction, for individuals
with home equity greater than the home equity cutoff point (H), if their demand for long-term care
services is large, they apply for Medicaid LTC and decrease home equity to the level of the cutoff
point (H). As a result, their consumption level increases.
Figure 2.4(b) depicts the case when an individual’s demand for long-term care is large.
Similarly, the individual getsU
0
at pointA before the implementation of the Medicaid LTC
restriction policy. If the individual loses Medicaid LTC, she needs to allocate a large share
of total expenditures on long-term care. As a result, the budget constraint for home equity
and consumption shifts inward significantly from I
1
to I
2
. The new utility-maximizing
bundle is at pointB with utility levelU
1
. Note thatU
1
is smaller than the utility levelU
when the individual adjusts home equity to H and keeps relying on Medicaid LTC. As
a result, the individual decides to reduce home equity toH to gain back Medicaid LTC
eligibility and moves to a new consumption bundleC with consumption rising fromC
0
toC

.
The discussion above traced out two theoretical predictions on home equity and con-
sumption responses to the DRA. First, individuals with small demand for long-term care
will reduce both home equity and consumption to compensate for the expenditure of
long-term care that used to be covered by Medicaid. Second, individuals with substan-
tial demand for long-term care will decrease home equity to the cutoff point so that they
can continue to use Medicaid LTC. As a result, their consumption rises to absorb extra
funding released from the reduction of home equity.
Of course, people may have different responses to the DRA that depend on their indi-
17
vidual preferences or characteristics. Broadly speaking, the model I discussed here can be
the basis for an analysis of threshold effects in the evaluation of treatment effects under
endogeneity. While this is an ambitious and interesting exercise, it is beyond the scope of
this paper. Here, I consider how on average an individual is likely to be affected by the
DRA. Therefore, by observing the direction of the change of consumption, we can figure
out which case discussed above is dominant in the market.
2.5 Empirical Analysis
The theory suggests that seniors with considerable home equity may respond differ-
ently to the same policy change, depending on their demand for long-term care. In this
section, I develop an empirical framework for using the DRA policy to identify and esti-
mate the effect of Medicaid LTC eligibility on single seniors’ consumption behavior.
2.5.1 Data Sources
Data for the Estimation of Home Equity
To explore the hypotheses of the impact of the DRA on home equity proposed in Sec-
tion 2.4.2, I first make use of the data from the Health and Retirement Study (HRS) con-
ducted by the University of Michigan. The HRS dataset is a nationally representative
dataset that tracks households age 50 and above biennially. It provides detailed informa-
tion on basic demographic characteristics, health and functioning, health care and insur-
ance, medical expenses, and housing assets. The survey began in 1992. Since the early
data on assets were underreported (see De Nardi et al., 2010), and the large impacts of the
2008 Great Recession progressed into the early 2010s, this paper utilizes seven waves of
the HRS from 1996 to 2008.
In addition, I supplement these public-use files by adding state-of-residence informa-
tion from the restricted HRS data with permission from the HRS administration. Using
18
state information is crucial for my analysis because home market dynamics and Medicaid
LTC policies differ remarkably across states.
As most of the population affected by the restriction rule are single homeowners, the
main sample in my empirical analysis consists of single individuals aged 65 and above.
Moreover, since the DRA is considered fully implemented in 2007, I further restrict the
focus of the analysis to the elderly who held unmarried status from 2006 to 2008. This
leaves us with 4,126 individuals, of whom 403 seniors aged 65 and above in 2006 owned
houses with home equity larger than the cutoff point of the restriction rule ($500K).
Data for the Estimation of Consumption
To measure the impact of the DRA on consumption, I rely on the Consumption and
Activities Mail Survey (CAMS). The CAMS was first conducted in 2001 and mailed to
5,000 households selected at random from HRS 2000 core survey. For the later waves,
the CAMS followed the same households. The average response rate was 77.3 percent
(Hurd and Rohwedder, 2006). The design strategy adopted by CAMS was to choose
spending categories from the Consumer Expenditure Survey (CEX), which asks about
approximately 260 categories. However, to reduce the burden to respondents, the cate-
gories of the final questionnaire was aggregated further, which focused on six expensive
items (automobile; refrigerator; washer or dryer; dishwasher; television; computer) and
on 26 non-durable spending categories. The reference period for the expensive items is
“last 12 months,” and for the non-durables, it varied: the respondent could choose the ref-
erence period between “amount spent monthly” and “amount spent yearly” for regularly
occurring expenditures like mortgage and insurance where there is little or no variation
in amounts, and “amount spent last week,” ” amount spent last month,” and “amount
spent in last 12 months” for all other categories.
The fact that the sample in CAMS was drawn from the HRS population allows me
to link the spending data to the substantial amount of information collected in the HRS
19
core survey for the same individuals and households. For my analysis of the impact of
the DRA on consumption, I mainly follow RAND CAMS categories which divide total
household spending into four subsets: nondurables, durables, housing, and transporta-
tion.
2.5.2 Empirical Model
This section serves two purposes. First, it tests whether and how the seniors with
home equity above the cutoff point will change their home equity after the implemen-
tation of the DRA. Second, it examines how their consumption responds to the policy.
Combining these two results, I will be able to pin down which case discussed in Section
4.6 plays a key role in the data.
Effects on Home Equity
I investigate whether the change of home equity exemption rule led to changes in
seniors’ home equity. Before introducing the main identification strategy, I need to clarify
the main outcome of interest first. Consistent with the housing market literature (see
Garriga and Hedlund, 2020; Mian et al., 2013; Mian and Sufi, 2011), I use the changes of
home equity as the outcome variable. The main idea to use the home equity growth is
to control for individual-specific time trend since home equity may change over a steady
rate due to the changing pattern of home value and home loan. The feasibility of using
home equity growth is shown in Appendix A.
Identification Strategy: Triple-Difference Estimate
Specifically, I employ a triple-difference (DDD) framework to analyze the impact of
the DRA on home equity. The first difference compares home equity changes before
and after the provision of the DRA for single seniors with home equity above the cut-
off point ($500K) in 2006. I define those seniors meeting such criteria as the high-home-
20
equity (treatment) group. Since the first difference is likely to be confounded by other
changes taking place during the same period, I use single seniors with home equity be-
low $500K as the control group (low-home-equity group). This low-home-equity group
serves as a useful control to the treatment group because the group members would have
been exposed to all the changes that were taking place during the period of interest, but
were not affected by the restriction rule. However, during the same period, from 2006 to
2008, the housing market crashed and triggered the decline of housing prices until 2012
(see Butrica and Mudrazija, 2016; Mian and Sufi, 2011). If only using the difference-in-
difference framework, it is possible that the estimates reveal the individuals’ responses
to the housing market crash instead of the policy. I, therefore, construct the third vari-
ation by comparing the double-difference (as computed above) among single seniors in
the middle-aged population (aged 55-64). The use of the younger cohort as a comparison
group for seniors is credible since the two cohorts are of similar age and they all experi-
enced the same housing market crash during the period of interest. However, the younger
cohort is barely affected by the DRA due to the fact that the Medicaid LTC services are
generally restricted to people aged 65 or older (Harris-Kojetin et al., 2019).
Formally, the triple-difference framework for home equity and its deterministic factors
is as follows:
y
it
=g
i
+
0
Post
t
+
1
Senior
i
Post
t
+
2
Above
i
Post
t
+ Above
i
Senior
i
Post
t
+x
it
+"
it
(2.2)
wherey
it
is the change of home equity in two consecutive waves for individuali in year
t. Post
t
is an indicator that equals to one if the year is 2007 or later. Senior
i
is an indi-
cator that equals one if the individual is aged above 65 in 2006, and equals to zero if the
individual is aged 55-64 in 2008.
5
Above
i
is an indicator that equals to one if the individ-
5
Selecting middle-aged sample based on their ages in 2008 (the end of analysis period) avoids the over-
lapping of age groups during the analysis period.
21
ual’s home equity in 2006 belongs to the high-home-equity group.
6
One concern with
this crude categorization is that individuals with huge gaps in their home equity could
also have very different consumption behavior in response to the same policy. To ensure
that the estimation of home equity changes between the treatment group and the control
group only differs by the policy impact, I impose a restriction on regression samples to
home equity ranging from $300K to $700K in 2006. g
i
denotes individual fixed effects.
Additional time-varying controls are included in the vector x
it
, which mainly consists
of health status across the years. According to previous literature, physical ability, dia-
betes, and cancer diagnoses act as strong predictors of long-term care needs (Ricks (2018);
Davidoff (2010); Gaugler et al. (2007)), so I include indicators for diabetes status, cancer
status, having at least one ADLs/IADLs, and having memory problems. The main coeffi-
cient of interest is (the DDD estimator), and
0
through
2
are the estimates of the double
interaction terms and linear terms, respectively. Beyond the individual fixed effects, I also
include state fixed effects to ensure that when people move to different states, the impact
of geographical factors on home equity is captured. Robust standard errors are clustered
at the state level.
Summary Statistics of the HRS Data
Table 4.2 reports the summary statistics for the entire analysis sample described in
Section 2.5.2. An observation is an individual-year, and summary statistics are presented
6
There are three reasons why I choose home equity instead of equity interest as the criteria of the high-
home-equity group. First and most importantly, the law of equity interest for couples varies by state. In
community property states, such as CA, usually spouses own equally on the property. Therefore, it’s fine
to define that equity interest =
home equity
2
. However, if the couples are in common law states, then the
house belongs to whoever with name on the deed. For example, if only a husband’s name is on the deed,
the equity interest for the husband equals the home equity. For his wife, the equity interest is then zero.
Because of such difference across states and the lack of information on who’s name is on the deed from
the HRS, it could bring noises to my identification if using equity interest as the criteria. Second, middle-
aged couples with home equity larger than $1000K in the sample are rare. Therefore, if using $1000K as
the criteria instead, the total sample size shirks and the estimation would lose statistical power. Lastly, I
proved in Appendix A that using home equity as the criteria defining the high-home-equity group shows
no statistically significant difference as using equity interest.
22
for the balanced sample in a pre-DRA year.
Columns (1) - (4) corresponds to the sample of single seniors, who are the main popu-
lation affected by the DRA. As seen in Table 4.2, among single seniors with home equity
in the range $300K-$700K, the average home equity in 2006 is roughly $432.4K with 35%
of the sample holding equity larger than $500K. Individuals in the analysis sample have
experienced housing appreciation from 2004 to 2006 for about $118.9K (38%) and depreci-
ation from 2006 to 2008 for around $92.5 (21%). This fluctuation of home equity suggests
the possible impact of the housing market crash. If we fail to eliminate this housing mar-
ket effect, it is hard to argue that the estimates are the result of the restriction policy. Of
note, the analysis sample is mostly white and female, and the average annual personal
income is $61.6K in 2004. 14% of the sample reports diabetes, 20% has cancer, and 19%
has difficulty in at least one ADL or IADL.
7
Columns (5) - (8) corresponds to the sample of the middle-aged population with home
equity in the range $300K-$700K. Compared with single seniors, the distribution and the
appreciation of home equity before the DRA are similar, suggesting that using a middle-
aged sample as the comparison group is credible. Relative to single seniors, the group of
middle-aged consists of a more male, and well-educated population, who are less likely
to have Medicaid in 2004 and enjoy better health status.
Parallel Trends
Before presenting the main regression results, I test for parallel trends in the triple-
difference framework by comparing the periods 1996-1998, 1998-2000, 2000-2002, 2002-
2004 to 2004-2006. Table 2.2 shows the results. In odd-numbered columns, I run the
regressions without controlling for individual fixed effects but using individual charac-
teristics instead, and in even columns I additionally control for individual fixed effects.
7
The analysis sample lives in a better socio-economic status compared to the whole singe seniors sample
whose home equity range from -$115K to $5500K (seen in Table A.1.1). For example, the mean home equity
of the whole single seniors is $108.2K, which is far below the mean of the analysis sample.
23
All coefficients on the DDD term are insignificant so we can not reject the null hypothesis
of parallel trends.
Figure 2.6 shows different patterns of home equity changes across years between the
high-home-equity group and the low-home-equity group for single seniors and middle-
aged individuals, respectively. In the left panel of Figure 2.6, I show evidence on single
seniors. Overall, the changes in home equity rise for both the high-home-equity group
and the low-home-equity group from 1998 to 2006, and the gap between these two groups
grows slightly. In contrast, after 2006, the high-home-equity group suffers a bigger reduc-
tion in home equity compared to the low-home-equity group. To check if this jump is
fully due to the impact of the housing market crash, I conduct a similar comparison of
home equity growth among middle-aged people as presented in the right panel of Fig-
ure 2.6. Before 2006, the changes in home equity for both the high-home-equity group
and the low-home-equity group show a similar pattern to the single seniors. However,
after 2006, although home equity falls for both groups, the trend remains similar to the
previous years. Figure 2.6 and the estimates in Table 2.2 suggest that using middle-aged
people as the second control group is credible in eliminating the impact of the housing
market crash.
Homogeneous DDD Estimator
The triple-difference estimates based on equation (2.2) are presented in Table 2.3. The
results with only controls for individual characteristics and state fixed effects are shown
in column (1). The results with individual fixed effects are presented in column (2). Ad-
ditionally, columns (3) and (4) include weights. Robust standard errors are clustered at
the state level in each column. All DDD terms are significantly negative, suggesting that
the impact of the Medicaid LTC restriction policy deepens the decline of home equity by
$66.75K-$97.96K. Comparing with the mean equity value of the high-home-equity group
in 2006, these estimates suggest that the DRA intensifies the depreciation of home equity
24
by 12.1%-17.8%.
Heterogeneous DDD Estimator
One concern with the homogeneous DDD estimator is that it fails to capture different
levels of responses to the Medicaid LTC restriction policy. Specifically, single seniors in
the high-home-equity group whose home equity is closer to $500K would have a larger
incentive to lower their equity and be eligible for Medicaid LTC. Therefore, for single se-
niors with home equity far above $500k, assuming that their incentive to decrease home
equity is the same as those with home equity close to $500K is unrealistic. Another ad-
vantage of using a heterogeneous DDD identification strategy is that we can pin down
the targeted regression sample. For example, if we find that people with home equity
more than $700K stop responding to the policy, then it is rational to restrict the main re-
gression sample to people with home equity in the range $300K-$700K. Therefore, I adjust
equation (2.2) to capture the heterogeneous response as follows:
y
it
=g
i
+
0
Post
t
+
1
Senior
i
Post
t
+
2
Above
i
Post
t
+ (
1
+
2
H
i04
) Above
i
Senior
i
Post
t
+x
it
+"
it
(2.3)
where
2
is the parameter of interest, and indicates the extent to which the tripe-difference
estimate in equation (2.2) is differentially coming from individuals’ responses further
away from $500K. H
i04
denotes individual i’s home equity in 2004. Using the lagged
levelH
i04
can avoid any possible reverse causality since home equity itself is impacted by
the policy. The estimation controls and clustering are the same as in equation (2.2).
The heterogeneous DDD estimates based on equation (2.3) are presented in Table 2.4.
The regression sample of columns (1) and (2) expands to individuals with home equity in
2006 ranging from $200K to $800K. For columns (3) and (4), the range changes to $100K
to $900K. The first row shows that the DDD estimates presented in Table 2.3 is mainly
driven by seniors whose home equity is close to $500K. The estimates with heterogeneous
25
DDD impacts are presented in the second row. All estimates are positive and statistically
significant, suggesting that the more an individual’s home equity is above $500K, the
less likely that person would respond to the restriction rule and decrease home equity.
Additionally, I calculate the corresponding home equity level in 2006 where the impact of
restriction policy is zero, namely the turning point. The estimates of the turning point are
quite stable with different specifications. Individuals with home equity around $615K-
$660K stop responding to the DRA. This evidence supports the validity of using home
equity in the range $300K-$700K as the main regression sample.
Mechanisms for Changing Home Equity
After showing the negative impact of the DRA on home equity, it remains unclear
how seniors change home equity. Since home equity is the sum of home value and home
loan, two channels are available for adjusting home equity: decreasing home value or
increasing home loan. Figure 2.7 shows the changes in home value growth and home
loan growth across the years. As presented in the top panel of Figure 2.7, the changes in
home value growth are similar to the changes in home equity growth in Figure 2.6. For the
middle-aged population, the moving patterns are similar between the high-home-equity
group and the low-home-equity group, regardless of the timing. In contrast, for single
seniors, although the changes of home value growth between two groups are alike before
2006, the high-home-equity group suffers a bigger fall of home value changes thereafter.
At the same time, we do not observe many variations with home loan growth among
different comparison groups as shown in the bottom panel of Figure 2.7. This evidence
suggests that seniors move to lower-valued houses in order to decrease home equity as a
result of the DRA.
Table 2.5 presents the DDD estimates using home value changes and home loan changes
as dependent variables. For high-home-equity single seniors, being exposed to the Med-
icaid restriction policy aggravates the decline of home value by $112.64K. This decline
26
echoes the channel of lowering home equity by reducing home value. When it comes to
home loan changes, the result of the DDD estimation is negative and significant, which
contrasts to the channel of lowering home equity by increasing home loan. In column
(3), I also check whether the portfolio of home wealth changes after the restriction policy.
The result for the loan-to-value ratio is zero and insignificant, indicating that the impact
of the restriction policy is pushing seniors to sell their original houses and move into
lower-valued houses without changing the mortgage rate.
Effects on Consumption
With evidence on the negative impact of the DRA on home equity as shown in Sec-
tion 2.5.2, to what extent the DRA impacts the consumption of all other non-LTC goods
remains a key piece of the puzzle for understanding individuals’ distortion behavior. The
direction of the change of consumption determines which case predicted in Section 2.4.2
is likely to be the targeted population’s response to the DRA.
Same to the empirical exercise on home equity, I employ a triple-difference (DDD)
method to analyze the impact of the DRA on consumption. I follow equation (2.2) to esti-
mate a DDD estimator of policy impact by comparing the difference of consumption be-
tween the high-home-equity and the low-home-equity group among single seniors with
the difference among the middle-aged group. y
it
is the total non-LTC consumption that
includes non-LTC medical expenditures, transportation spending, durable goods spend-
ing, and non-durable goods spending. The controls and clustering are the same as in
equation (2.2).
Summary Statistics of the CAMS Data
I present additional summary statistics for consumption details in Table 2.6. Specifi-
cally, I divide total consumption into five categories: LTC expenditures, non-LTC medical
expenditures, transportation spending, durables spending, and nondurables spending.
27
As seen in Table 2.6, among single seniors, the mean total expenditures in 2006 is $41.41K.
The largest share of total expenditures goes to nondurables goods (78%), and the second-
largest share is on transportation (6%). Compared with singles seniors, the average of
total expenditures among the middle-aged group is higher ($54.36K), and the share on
nondurables reduces to 68% while the share on transportation goes up to 28%.
Estimation Results on Consumption
Following my empirical strategy in Section 2.5.2, I first test for parallel trends in the
triple-difference framework comparing the years 2002 and 2004 with 2006. Due to the
small sample size of the CAMS dataset, I expand the regression sample to individuals
with home equity in the range $200K-$800K.
8
As seen in Table 2.7, the coefficients on
the DDD term before the restriction policy are insignificant, so we can not reject the null
hypothesis of parallel trends.
Table 2.8 shows the main results of the impact of the DRA on non-LTC consumption.
The estimates without weights or individual fixed effects (columns (1)-(3)) suggest that
the DRA induces increased non-LTC consumption of $4.47K-$6.60K. Including controls
for both individual fixed effects and weights increases the estimate to $10.5K. Two points
are worth noting.
First, the estimates under all specifications are positive, though the coefficients for the
first three columns are not statistically significant. These stable signs of the estimates
support the hypothesis that the DRA causes individuals to consume more on non-LTC
goods and services. Again, these coefficients are based on a small sample size of the
CAMS, which might be the reason for the loss of statistical power of the estimates.
Second, the use of a younger cohort as the second control group may not provide
valid estimates for analyzing the impact on consumption. As seen from the Table 2.6,
the consumption behavior of the middle-aged could be very different from the seniors,
8
The results are similar if I restrict the regression sample to the range $300K-$700K. The tables are avail-
able upon request.
28
such as the total consumption is higher among the middle-aged and they spend more
on transportation goods and services. This difference has also been confirmed in the
literature (Drolet et al. (2007); Williams and Drolet (2005)). Therefore, to establish robust
empirical results, I use married seniors instead as the second control group to eliminate
the financial crisis impact on consumption.
I construct a DDD estimator of the DRA impact by comparing the difference of con-
sumption between the high-home-equity and the low-home-equity group among single
seniors with the difference among married seniors. Formally, the triple-difference equa-
tion for consumption and deterministic factors is as follows:
y
it
=g
i
+
0
Post
t
+
1
Single
i
Post
t
+
2
Above
i
Post
t
+ Above
i
Single
i
Post
t
+x
it
+"
it
(2.4)
where Single
i
is an indicator equal to one if the individual is single during 2006-2008.
Other independent variables are defined in the same way as in equation (2.2). The whole
regression sample consists of all individuals aged 65 and above in 2006. Standard errors
are clustered at the state level.
Before the DRA, the triple-difference estimates are insignificant. If anything, the es-
timates in Table 2.9 suggest that single seniors with home equity above $500K consume
less compared to married couples with similar housing assets. After showing the parallel
trends results in Table 2.9, the triple-difference estimates based on equation (2.4) are pre-
sented in Table 2.10. The results indicate that the DRA induces single seniors to increase
consumption by $6.49K-$12.03K. These significant signs of the DDD estimators suggest
the positive effects of the DRA on individual consumption.
Mechanisms for Changing Consumption
Since total non-LTC consumption is the sum of transportation spending, non-LTC
medical expenditures, durables spending, and nondurables spending, exploring which
29
mechanism results in the increment of total non-LTC consumption helps us to understand
seniors’ distortion behavior comprehensively. Table 2.11 reports the triple-difference es-
timators for the four different categories of non-LTC consumption by comparing seniors
with the middle-aged population. All columns include individual fixed effects and weights.
The estimates suggest that single seniors with equity above $500K increase consumption
in all categories, especially for nondurables, though the coefficients are not statistically
significant. If use the married couples as the second group instead, as seen in Table 2.12,
the channel through which individuals increase consumption becomes more clear. In-
dividuals affected by the DRA change their spending habits by investing $10.72K more
on nondurables, while consumption on other categories are insignificant. These results
strengthen the belief that affected seniors distort their consumption to gain Medicaid LTC
by ”burning up” money.
Heterogeneity in Responses by Individuals’ Characteristics
The results above display that the average impact of the DRA on seniors’ home eq-
uity is negative, and the average impact on consumption is positive. These two pieces
of evidence support the proposition 2 that due to the large demand for long-term care
services, on average individuals will manipulate their home equity to the cutoff point of
the DRA to gain Medicaid LTC, and therefore expand consumption on non-LTC goods
and services. However, exploring the cross-sectional heterogeneity in other variables of
interest is also important since it provides insights into the underlying motivation for in-
dividual distortion behavior. Table 2.13 shows other sources of heterogeneity, focusing
on the sample of individuals aged 55 and over. I first examine the effect of the restric-
tion policy by gender, under the hypothesis that female seniors have lower demand for
long-term care services in the short run because they are on average healthier. Columns
(1) and (2) show that the effects are stronger for male seniors though the difference is not
statistically significant. Columns (3) and (4) report the estimates by education in order
30
to explore the hypothesis that individuals with less advantaged social-economic status
are more likely to be on the margin of qualifying for Medicaid long-term care services.
The results show that the effects are concentrated in the less educated population. The
restriction policy induces a decrease in their home equity of almost $89.96K-$129.73K.
Columns (5) and (6) report estimates by whether individuals report difficulty caring for
themselves with at least one ADL/IADL, to examine the hypothesis that individuals who
need more long-term care are more likely to be hit by the restriction policy. The results
show that the effect of the restriction policy is concentrated among individuals who need
care (i.e., ”dependent”). The restriction policy induces a $141.11K-$158.79K decrease in
their home equity. Analogously, people with Medicaid two years before 2006 are more
likely to decrease home equity.
2.5.3 Robustness and Placebo Exercises
In this section, I address two potential concerns with my main identification strategy.
First, I present two tables showing robustness around my definition of the targeted popu-
lation and middle-aged population. At baseline, I define the targeted population as those
with home equity in the range $300K-$700K, and define the middle-aged population as
people aged 55-64 in 2008. In Appendix Table A.1.2 and Table A.1.3, I examine two alter-
native definitions. First, I present results including a broader group of individuals with
home equity in the range $200K-$800K. Second, maintaining my baseline definition of
the targeted population, I instead alter the definition of middle-aged to individuals aged
50-64. As seen from Table A.1.2 and Table A.1.3, broadening the regression sample and
the definition of the middle-aged population, the results are all significantly negative and
consistent with the baseline results.
Second, since the change of home equity closely relates to the absolute equity level
before the DRA, another potential concern might be that individuals with high-home-
equity may reduce their equity more due to other reasons that happened to take effect
31
in the period of 2006 to 2008. For example, the preference for living in a high-valued
house happened to vary during the financial crisis when people felt pessimistic about the
economy. To address this concern, I run a placebo test where I use a ”false” treatment
definition that treats those with home equity in 2006 above $600k (not the policy cutoff
point) as the ”Above” group. The results of this exercise are presented in Table A.1.4. All
specifications lead to insignificant results. Moreover, the signs of all estimates are positive,
which is opposite to our hypothesis that seniors would drop home equity in order to gain
Medicaid LTC services. This exercise supports the conclusion that the effects found in the
primary analysis are likely attributed to the DRA.
I also test the sensitivity of the baseline results by using alternative definitions of the
treatment period. The baseline analysis focuses on the period around the policy interven-
tion. One concern is that the treatment effect is an outcome of the natural home equity
movement across time. In order to test the validity of the treatment effects, I use consec-
utive HRS wave-pairs to re-examine equation (2.2) for 1998 through 2008. By examining
different ”post” periods, we can compare the results with the estimates presented in Table
2.3. If no effects are found across consecutive waves where no policy intervention took
place, then the effects found in the primary analysis are more likely due to the change of
Medicaid LTC policy. Specifically, I keep the definition of treatment status constant over
time such thatAbove
i
andSenior
i
are based on reported characteristics in the former of
the two years in each wave-pair. On the contrary,Post
t
is equal to one for the later of the
two years. For example, estimates for the period 1998 and 2000 would consider the post-
period as 2000 and define treatment status based on characteristics in 1998. The results of
this placebo test are presented in Figure A.1. Estimates of from equation (2.2) are plot-
ted on the y-axis with 90% confidence intervals. The x-axis reports the first year for any
consecutive year pair. For example, 1998 represents the change in home equity growth
for the period 1998 to 2000. The estimates for 2006 are exactly the same as the estimates
presented in column (4) of Table 2.3. I find no effects over the period 1998 through 2004.
32
In 2006, the point estimate is negative and significantly different from zero. This test pro-
vides evidence of little reduction in home equity among the treatment group relative to
the control group prior to the DRA. Thus, this finding reassures us that the results I find
in the main analysis are not driven by differential trends of home equity changes across
the different groups.
2.6 Welfare analysis
2.6.1 Structural Framework
Section 4.5 shows that the DRA drives individuals to reduce home equity and waste
money on nondurable goods and services. Although these results provide evidence that
individuals manipulate their home equity to gain Medicaid LTC, it is still not clear how
much would individuals value Medicaid LTC. The aggregate willingness to pay for Med-
icaid LTC is an important measurement of social benefits, which can help us assess the
economic efficiency of the DRA policy. This section expands the model in Section 4.6 to
calculate the willingness to pay for Medicaid LTC, defined as the maximum amount of
non-LTC consumption that the individual would need to give up in the world with Medi-
caid LTC that would leave her at the same level of expected utility as in the world without
Medicaid LTC.
Preferences
Following the setups in Section 4.6, a retired individual maximizes her utilityu as de-
scribed in equation (2.1). To make the model better fit with reality, I allow the individual
to reserve part of her assets,r, either to transfer to children or to deposit to funds. More
specifically, the utility function has the following form:
u =v(c;r;h;l) =f[v
nl
(c;r;h);v
l
(l)]: (2.5)
33
As in Section 4.6, for the sake of brevity, I refer to l as ”LTC spending”, to h as ”home
equity”, toc as ”consumption”, and tor as ”savings”.
Medicaid LTC
The presence of Medicaid LTC services is captured by the variable m, with m = 1
indicating that the individual is insured by Medicaid LTC and m = 0 representing not
being insured. To avoid fully specifying the utility function, following Finkelstein et al.
(2019), I assume that the individual is affected by Medicaid LTC services only through its
impact on her budget constraint, namely, the out-of-pocket price for LTC servicesp(m).
Other ways through which Medicaid LTC might affect c, h, r, or l, such as through an
effect on a nursing home’s willingness to treat a patient, are ruled out by this assumption.
For implementation purposes, I assume thatp(m) is constant inl. The function of out-of-
pocket spending on LTC takes the form:
s(m;l)p(m)l (2.6)
Note that I do not imposep(0) = 1 so that individuals without Medicaid LTC do not need
to pay total LTC spending out of pocket. This allows individuals who are not insured by
Medicaid LTC to have access to implicit insurance.
Individual Problem
An individual chooses optimal consumption,c, home equity,h, savings,r, and long-
term care spending,l, subject to her budget constraint. Note thath can be described as the
home equity level before the DRA implemented (h
0
) minus the shrinkage of home equity
after the DRA (h). The decline of home equity, h > 0, suggests that the individual
taps into her home equity to extract money for consumption. Additionally, I introduce a
parameter that denotes the underlying state of the world. I assume that each individual
34
is drawn from the population distribution of. Therefore, by observing the distribution
of outcomes across individuals, such asl() andy(), I am able to infer the distribution
of. Formally, the individual optimization problem is as follows:
max
fc;h;r;lg
u(c;h
0
h;r;l()) (2.7)
subject to
c +r +s(m;l) =y() + h: (2.8)
where y() represents state-contingent total resources. Consumption, c, home equity
decrements, h, reserved resources,r, and long-term care demand,l, therefore depend on
Medicaid LTC status,m, and the underlying state of the individual,. This dependence
is denoted byc(m;), h(m;),r(m;), andl(m;)respectively.
Willingness to pay
Following Finkelstein et al. (2019), the willingness to pay for Medicaid LTC (1) is
measured in terms of forgone consumption for keeping the same utility level with or
without Medicaid LTC. Specifically, (1) is defined as the amount of consumption that
the individual would need to give up in the world with Medicaid LTC that would leave
her at the same level of expected utility as in the world without Medicaid LTC:
E[u(c(1;)(1); h(1;);r(1;);l(1;))]
=E[u(c(0;); h(0;);r(0;);l(0;))]
(2.9)
where the expectations are taken with respect to the possible states of the world,. One
big difference between my paper and Finkelstein et al. (2019) is that I need to take into
account consumption distortion due to the home equity ceiling resulted from the new
policy. This point is illustrated in Figure 2.5, where the top figure illustrates the way to
calculate willingness to pay if individuals do not face the home equity restriction. The
35
figure shows both an individual’s choice of housing and other goods (point A) when she
has Medicaid LTC and the choice when she is not covered by Medicaid LTC (point B).
According to the definition in equation (2.9), the willingness to pay under this case is the
gap of C
0
C
0
0
as shown in Figure 2.5(a). However, this calculation method cannot be
directly employed by this paper. Model prediction and empirical results tell us that the
individual with home equity above $500K would decrease equity to the cutoff point to
gain Medicaid LTC and change her choice bundle over housing and consumption accord-
ingly. As a result, the proper calculation of the willingness to pay for Medicaid LTC for
the high-home-equity group is illustrated in Figure 2.5(b). Point B is still the individual’s
choice bundle if she is not covered by Medicaid LTC. Point C (instead of point A) shows
the choice bundle if the individual is covered by Medicaid LTC when she downsizes eq-
uity to the cutoff pointH. Therefore, the true willingness to pay for Medicaid LTC for the
high-home-equity group should be the gap ofC

C

0
.
Now consider a ”marginal” expansion in Medicaid LTC services. Under this expan-
sion,m denotes a linear coinsurance term between full Medicaid LTC coverage (m = 1)
and no Medicaid LTC coverage (m = 0) such that p(m) mp(1) + (1m)p(0). Then
out-of-pocket spending in equation (2.6) can be written as follows:
s(m;l) [mp(1) + (1m)p(0)]l (2.10)
Remember, I assume in Section (2.6.1) that the individual is affected by Medicaid LTC
services only throughp(m). Therefore, the marginal expansion of Medicaid LTC service
relaxes the individual’s budget constraint by
@s
@m
:

@s(m;l(m;))
@m
= (p(0)p(1))l(m;) (2.11)
Under this ”marginal” expansion of Medicaid LTC services, the amount of consump-
tion the individual would need to give up in a world withm insurance is(m), such that
36
she would achieve the same level of expected utility whenm = 0. Similarly as in equation
(2.9),(m) satisfies the following equation:
E[u(c(m;)(m); h(m;);r(m;);l(m;))]
=E[u(c(0;); h(0;);r(0;);l(0;))]:
(2.12)
After taking optimization of equation (2.12) overm and applying the envelope theo-
rem, the marginal impact of insurance on recipients’ willingness to pay takes the form:
d(m)
dm
=E[
u
c
E[u
c
]
((p(0)p(1))l(m;))] (2.13)
whereu
c
is the partial derivative of utility with respect to consumption.
uc
E[uc]
measures
the relative value of consumption in each state of the world to its average value, and
(p(0)p(1))l(m;) measures how much an increase in Medicaid LTC services releases
the individual’s budget constraint in each state.
The marginal value of Medicaid LTC services in equation (2.13) can be decomposed
into a transfer (T) term and a pure-insurance (PI) term. Specifically, the decomposition
has the following form:
d(m)
dm
= ((p(0)p(1))E[l(m;)]
| {z }
Transfer
+Cov[
u
c
E[u
c
]
; (p(0)p(1))l(m;)]
| {z }
Pure-Insurance
(2.14)
where the transfer term captures the recipients’ expected valuation of the transfer of re-
sources from the rest part of the economy to them. The pure-insurance term captures the
valuation of a budget-neutral reallocation of resource across different states of the world.
The pure-insurance term will be positive if resources are moved into states of the world
with higher marginal utilities of consumption.
To get the nonmarginal total willingness to pay for Medicaid LTC services, I integrated
37
d
dm
fromm = 0 tom = 1. With(0) = 0, we can get the following form:
(1) =
Z
1
0
d(m)
dm
dm
= (p(0)p(1))
Z
1
0
E[l(m;)]dm
| {z }
Transfer
+
Z
1
0
Cov[
u
c
E[u
c
]
; (p(0)p(1))l(m;)]dm
| {z }
Pure-Insurance
(2.15)
Implementation
To evaluate the total willingness to pay as in equation (2.15), first of all, we need infor-
mation onl(m;) to acquire the transfer term. Since we do not observe the path ofl(m;)
for interior values ofm, I follow Finkelstein et al. (2019) to make the statistical assumption
as follows:
Assumption 1. The integral expression for(1) in equation 2.15 is well approximated by:
(1)
1
2
(
d(0)
dm
+
d(1)
dm
): (2.16)
Though the evaluation of the transfer term does not need to specify about a utility
function, the evaluation of the pure-insurance term requires specification of the marginal
utility of consumption. Hence, I assume the utility function has the following form:
Assumption 2. The utility function is as follows:
u(c;h;r;a) =
(c

h
1
)
1
1
+w(r) +v(l); (2.17)
where consumption is aggregated by a Cobb-Douglas function, with determining the relative
importance of housing and consumption. The utility function applied to the aggregated goods
is a standard CRRA function with risk aversion parameter . w(:) and v(:) are the sub-utility
functions for reserved resources and the long-term care needs, respectively. These two functions
are left unspecified.
38
Utility thus has three additive components: a standard CRRA function in consump-
tion c and h with a coefficient of the relative risk aversion of and a coefficient of rel-
ative importance of housing , and two unspecified functions with respect to r and l.
The assumption that consumption, reserved resources, and LTC demand are additive is
commonly made in the aging and health literature (see De Nardi et al., 2016; Brown and
Finkelstein, 2008). It restricts the marginal utility of the consumption to be independent of
reserved resources and LTC demand. This assumption simplifies the implementation of
my estimates. The Cobb-Douglas function with respect to housing and all other consump-
tion follows Nakajima and Telyukova (2020). This utility function is common among the
literature that incorporates housing into a macroeconomic framework (D´ ıaz and Luengo-
Prado, 2010; Gervais, 2002).
Under this assumption, the pure-insurance term in equation (2.14) can be written as
Cov[
((h
0
+ h)
1
)
1
c(m;)
(1)1
E[ ((h
0
+ h)
1
)
1
c(m;)
(1)1
]
; (p(0)p(1))l(m;)] (2.18)
Using this equation, we can calculate the marginal value of
d(0)
dm
and
d(1)
dm
separately. After
applying the Assumption 1, we can use estimates of
d(0)
dm
and
d(1)
dm
to achieve the estimata-
tion of(1).
2.6.2 Social Costs
The provision of Medicaid LTC requires the use of economic inputs that could be used
to produce other things. With the knowledge of the individual’s willingness to pay for
Medicaid LTC, it is naturally to benchmark the estimates of willingness to pay against
social costs. To calculate Medicaid LTC social costs, I consider long-term care spending
only. This simplification allows me to abstract from potential administrative costs or any
other mechanisms that could impose fiscal externalities on the government. Under this
39
assumption, the net resource cost of Medicaid LTC per recipient,C, is given by:
C =E[l(1;)s(1;l(1;))]E[l(0;)s(0;l(0;))]: (2.19)
The net resource cost can be considered as how a change in Medicaid LTC coverage af-
fects social costs. Holding everything else constant, the total social costs whenm = 1 is
E[l(1;)s(1;l(1;))], and the total social costs whenm = 0 isE[l(0;)s(0;l(0;))],
so C captures the change when switching the Medicaid LTC coverage on and off. If I
rearrange equation (2.19),C can be described as follows:
C =E[l(1;)l(0;)] +E[s(0;l(0;))s(1;l(1;))]: (2.20)
Therefore, the net resource cost of Medicaid LTC is composed of two parts: the average
increase in long-term care spending induced by Medicaid LTC, denoted byl(1;)l(0;)
and the average decrease in out-of-pocket spending due to Medicaid LTC, denoted by
s(0;l(0;))s(1;l(1;)).
2.6.3 Estimation
With the welfare expressions in place, I now discuss how I measure the the key es-
timates empirically. The first section summarizes required empirical objects, while the
following sections discuss outcomes of interest.
Required Empirical Objects
Table (2.14) summarizes the empirical objects that I need for the evaluation of individ-
uals’ willingness to pay for Medicaid LTC, (1), and the net resource cost of providing
Medicaid LTC, C. Specifically, to calculate willingness to pay, first, I need information
on mean LTC spending for individuals, on the distribution of consumption, and on the
distribution of out-of-pocket spending, all with and without Medicaid. Second, the out-
40
of-pocket price of Medicaid LTC and home equity before the DRA are required. Since my
empirical results find that individuals with home equity above $500K would reduce their
home equity, the change of home equity after the DRA is also required. I use my empirical
findings to adjust individuals’ home equity in 2008 on the basis of their equity in 2006.
Moreover, calibration parameters,, and are necessary. Additionally, estimating the net
resource cost requires the information of mean out-of-pocket spending, with and without
Medicaid.
Importantly, since I need information on long-term care spending, I have to restrict
the sample to individuals who claim to have lived in a nursing home for positive days
between 2006 and 2008. This leaves us with the final sample of 460 individuals. Among
them, 39 individuals belong to the high-home-equity group and 83% are unmarried. Now
I discuss how I construct the aforementioned empirical objects.
Long-Term Care Spending
The HRS provides measure of utilization of nursing home. Specifically, the HRS asks
how many days respondents have stayed in a nursing home. With the average cost for
a private room in nursing home being $206 per day in 2006 (Houser (2007)), the average
annual long-term care spending in my sample for insured (m = 1) is $49,013 and $46,434
for uninsured (m = 0). Medicaid LTC increases total long-term care spending by about
$2579.
Out-of-Pocket Spending
I assume that the insured have zero out-of-pocket spending (s(1;l(1;)) = 0). This
assumption is reasonable because Medicaid LTC pays for stays in a nursing home from
the first day and for as long as the individual needs the care. To satisfy this assumption,
I further restrict the insured sample to those with zero out-of-pocket spending in nursing
41
homes.
9
This leaves us with 236 insured individuals.
The measurement of annual out-of-pocket spending for the uninsured (m = 0) is
based on self-reported out-of-pocket long-term care expenditures in the past 2 years, di-
vided by 2. Average annul out-of-pocket long-term care expenditures for uninsured is
E[s(0;l(0;))] = $15835.
Out-of-Pocket Prices
The estimation of willingness to pay for Medicaid LTC requires that we know the out-
of-pocket price of long-term care with Medicaid, p(1), and without Medicaid, p(0). For
those with Medicaid LTC, since they pay nothing out of pocket toward long-term care
services, p(1) = 0. Forp(0), I measure it as the ratio of mean out-of-pocket spending to
mean total long-term care spending for uninsured (p(0) =
E[s(0;l(0;))]
E[l(0;)]
). I estimatep(0) =
0:34, which implies that the uninsured pay $0.34 on the dollar for their long-term care
spending, with the remainder of the expenses being paid by external parties. This is
consistent with estimates from other contexts.
10
Consumption Inputs
For the evaluation of(1), I need information on the distribution of consumption. Be-
cause the final HRS sample for evaluating willingness to pay is small (460) and the CAMS
9
This paper uses zero-nursing-home cost as the measurement for Medicaid LTC status for two reasons.
First, the HRS does not include the question directly asking individuals’ status of Medicaid LTC. Instead,
the HRS asks about Medicaid status, which provides a wider range of services than Medicaid LTC. In my
sample, 69% of individuals with Medicaid reporting zero out-of-pocket spending for LTC. I define them
as Medicaid LTC insured people. Second, it could happen that in the middle of nursing home stays, the
individual qualified for Medicaid LTC. Since I assume that individuals’ willingness to pay are the same for
all qualified people when they make consumption decisions based on expected LTC demand. Individuals
should apply for Medicaid LTC before and enjoy Medicaid LTC from the first day in nursing facilities.
Therefore, full coverage of Medicaid LTC is considered as insured, and partial Medicaid LTC coverage is
considered as uninsured. Thus, p(0) could include the case when an individual receives partial coverage
from Medicaid LTC.
10
In the 2018 NHS, I estimate that non-Medicaid-LTC recipients pay about 33% of their LTC expenses out-
of-pocket per capita. The Kaiser Commission on Medicaid and Long-Term Care estimates that the average
non-Medicaid-LTC person in the United States pays about 39% of their total long-term care expenses out of
pocket in 2013 (fig.3 of Reaves and Musumeci (2015)).
42
data further reduce the sample size to a quarter of the initial sample, to preserve statistical
power of this analysis, I use consumption proxy approach to measure consumption. In
particular, I proxy for non-LTC consumptionc, using the individual’s out-of-pocket LTC
spending, s, combined with average values of non-LTC expenditure and out-of-pocket
LTC spending. This framework is consistent with the approach used in Finkelstein et al.
(2019). Specifically, the consumption proxy takes the following form:
c = c (s s); (2.21)
where c represents the average non-LTC expenditure and s denotes the average out-of-
pocket long-term care spending among the uninsured.
This consumption proxy approach is based on several assumptions. First, it assumes
that the only channel by which Medicaid LTC influences consumption is by decreasing
out-of-pocket spending. This rules out other channels by which Medicaid LTC affects
consumption such as by changing income. Considering that the subjects in this paper are
retired seniors, this assumption seems reasonable. Second, it assumes that consumption
would be the same for all seniors if they had the same out-of-pocket long-term care spend-
ing. This is an assumption made for convenience. However, it approximates the reality
to the extent that heterogeneity in non-LTC expenditure is limited since its magnitude
comparing with long-term care spending is relatively small.
For my baseline analysis, to acquire the estimate of(1) in equation (2.15), I also need
information on the coefficient of relative risk aversion,, and on the relative importance
of consumption,. Following the literature, I assume = 3 (see Finkelstein et al., 2019;
De Nardi et al., 2016) and = 0:83 (see Nakajima and Telyukova, 2020). In the stan-
dard life-cycle consumption-savings model, means-tested social insurance is typically
modeled as a government-provided consumption floor (e.g., De Nardi et al., 2016, 2010).
Therefore I also impose a consumption floorc
floor
= $1977 for my baseline results (as in
43
Finkelstein et al., 2019). The sensitivity analysis by varying,, andc
floor
is presented in
the section of robustness checks.
2.6.4 Results on Willingness to Pay
Table (2.15) shows the estimates of the key objects. Without any assumptions about
the utility function, the net cost of Medicaid LTC (C) is equivalent to the average increase
in long-term care spending induced by Medicaid LTC plus the average reduction in out-
of-pocket spending due to the insurance coverage (as shown in equation (2.19)). The
estimates forC is $9915 per recipient year.
The estimates of the transfer term in equation (2.15) is obtained by using only the
estimates of the impact of Medicaid LTC onl andp. The change in the out-of-pocket price
for long-term care because of insurance is 0.34. Applying linear approximation as shown
in Assumption 1 and the estimates of E[m(0;)] and E[m(0;)], I calculate the transfer
term of $8,314.
Then I calculate the pure-insurance term by incorporating the previous empirical find-
ings into a specific utility function as defined in equation (2.17). This requires an estimate
of the joint distribution of consumption and out-of-pocket spending for the uninsured,
which follows from equation (2.21). Following the finding that individuals with home
equity larger than $500K in 2006 decreased their home equity by $66.75K on average and
relaxed their budget constraint by $10.5K, the total pure-insurance component is therefore
calculated as $3,937. Adding this to the transfer term, the willingness to pay for Medicaid
LTC is $12,251.
For assessing the economic efficiency of the DRA, we need to measure the social bene-
fits against social costs. The last row of Table (2.15) provides the benchmark. It compares
willingness to pay to the net cost and the estimate of
(1)
C
is 1.2. This suggests that recip-
ients are willing to pay $1.2 of per dollar of providing Medicaid LTC. This is consistent
44
with the estimates from other contexts.
11
Of course, this baseline result is sensitive to the framework used and to the specific
implementation assumptions. To check on the sensitivity to a variety of alternative as-
sumptions, I conduct robustness checks in Appendix B. As shown in Table (A.1.5), across
different values on,, andc
floor
, willingness to pay is around the same magnitude as the
baseline estimation. And the estimates of the net cost value is also stable around $10K.
The smallest estimate of
(1)
C
is $1.15 when assuming the consumption floor is $2000, and
the largest estimate is $1.59 when the consumption floor is assumed to be $1500. When
adjusting the value of or, the estimates of
(1)
C
are stable and range from $1.21 to $1.36.
2.7 Conclusion
Welfare policies that affect health insurance eligibility may change individuals’ con-
sumption behavior, including housing assets and savings. Evaluating such policies re-
quires us to take these features into account, ultimately informing the design of policies
that are welfare-improving.
In this paper, I use the Deficit Reduction Act that ceases the eligibility of Medicaid LTC
for people with high home equity to establish that it causes changes in both the consump-
tion of housing services and the consumption of non-LTC goods. The triple-difference
analysis estimates a reduction of $66.75K in home equity and an increase of $10.5K in
non-LTC consumption among the high-home-equity single seniors. Combining these two
empirical results with a two-stage-budgeting model, I document that the majority of the
population affected by the DRA are individuals with a large demand for long-term care.
Using the model, I further estimate seniors’ willingness to pay for Medicaid LTC. After
correcting the distortion behavior of consumption, I show that seniors are willing to pay
$1.2 per dollar of the net cost of providing Medicaid LTC. This result is stable in the sense
11
Finkelstein et al. (2019) find that willingness to pay for Medicaid among 19-64 is $0.5-$1.2 per dollar of
net resource cost. Hendren and Sprung-Keyser (2020) show that willingness to pay for Medicare is $1.63
per dollar of net resource cost.
45
that the estimates of willingness to pay relative to net resource cost ranging from 1.2 to
1.6 across different specifications.
Crucially, my estimation of willingness to pay is specific to my setting. In particular,
the value of Medicaid LTC may well differ when it is expanded to cover individuals with
different social-economic status, or when it is mandatory rather than voluntary. Further
studies that extend the analysis regarding the aforementioned limitations can help us
understand the value of Medicaid LTC more comprehensively.
Policy implications from the findings in this paper are twofold. First, the findings on
the effects of the DRA on home equity and consumption re-emphasize the responsive
behavior among elderly households to gain eligibility for social insurance programs. Sec-
ond, as noted in Chetty and Finkelstein (2013), the kernel of analyzing social insurance
programs is answering whether the government intervention improves welfare. The mo-
tivation of the DRA is to improve America’s Medicaid LTC delivery and financing system
by limiting its eligibility. However, my evaluation shows that the current recipients’ will-
ingness to pay is larger than the net resource cost, suggesting that the efficient allocation
of Medicaid LTC services has not been achieved yet.
46
Figures
Figure 2.1: Total Long-Term Care Expenditures, 1996-2016
NOTES: This figure presents the yearly total national long-term care (LTC) expenditures for the
US. Total LTC expenditures includes spending on residential care facilities, nursing homes, home
health services, and home and community-based waiver services. This figure does not include
Medicare spending on post-acute care (e.g., $77.8 billion in 2016). This is consistent with the
estimates from Kaiser Family Foundation.
SOURCE: Estimates in this figure is based on 2018 National Health Expenditure Accounts from
CMS, Office of the Actuary
47
Figure 2.2: Long-Term Care Costs Can Exceed Seniors’ Income
NOTES: This figure presents median annual long-term care costs by type in 2019. In 2019, the
median annual cost of nursing home was $102,200. Home-based services are less expensive, but
still represent a major financial burden for individuals. In 2019, the median cost for one year of
home health aide was $52,624 and adult day care totaled almost $19,500. Accordingly, the 200%
of FPL in 2019 was $24,522, and 27% of seniors annual gross income was below it.
SOURCE: Estimates in this figure is based on Genworth 2019 cost of care survey,
https://www.genworth.com/aging-and-you/finances/cost-of-care.html; U.S. Department of
Health and Human Services, 2019 Poverty Guidelines.
48
Figure 2.3: The Utility Tree for A Two-Stage Budgeting Model
Total Consumption
LTC,l Non-LTC,nl
Non-housing,c Housing,h
NOTES: This figure describes the framework of a two-stage budgeting model. As illustrated in this
figure, the individual allocates total expenditure in two stages: at the first stage, total expenditure
is allocated to LTC and non-LTC, while at the second stage, total non-LTC expenditure is allocated
to consumption,c, and home equity,h.
49
Figure 2.4: Individuals’ Response to the DRA Under Different Demand for LTC
Home Equity ($K)
Non-LTC Consumption ($K)
H
0
C
0
A
I
1
H

C

B
I
2
H = 500
C
C
U
0
U
1
U
(a) OptimalH

andC

for small LTC demand
Home Equity ($K)
Non-LTC Consumption ($K)
H
0
C
0
A
I
1
H
1
C
1
B
I
2
H

=H
C

C
U
0
U
1
U
(b) OptimalH

andC

for large LTC demand
NOTES: Both top and bottom figures show the change of utility curves and budget constraints
according to an individual’s LTC demand. Prior to the DRA, the individual chooses to consume at
pointA. The top figure shows how the constrained optimization between non-housing consump-
tion and home equity would change if the individual’s demand for LTC is small, while the bottom
figure shows how this optimization problem changes when the individual’s demand for LTC is
large.
50
Figure 2.5: Evaluation of Willingness to Pay (WTP) With or Without Constrained Opti-
mization
Home Equity ($K)
Non-LTC Consumption ($K)
H
0
C
0 C
0
0
A
I
1
B
A
0
I
2
U
0
U
1
WTP
(a) Willingness to pay with no constrained optimization
Home Equity ($K)
Non-LTC Consumption ($K)
A
I
1
B
I
2
H

=H
C

C
0
C

0
C
U
0
U
1
U
WTP
(b) Willingness to pay with constrained optimization
NOTES: Both top and bottom figures show the change of utility curves and budget constraints
when an individual’s LTC demand is large. Prior to the DRA, the individual chooses to consume
at point A. The top figure shows how to calculate willingness to pay when the individual faces
non-constrained optimization, while the bottom figure shows how the evaluation of willingness
to pay changes when the individual faces constrained optimization.
51
Figure 2.6: Changes in Home Equity Across Years
High−Home−Equity Group
Low−Home−Equity Group
Single Senior
−200 −100 0 100 200 300
ΔEquity ($K)
1998 2000 2002 2004 2006 2008
Year
High−Home−Equity Group
Low−Home−Equity Group
Middle−Aged
−200 −100 0 100 200 300
1998 2000 2002 2004 2006 2008
Year
NOTES: Dependent variable in both panels are the change of equity in consecutive two waves. The
left panel represents individuals who are single and aged above 65 and in 2006. The right panel
represents individuals aged 55-64 in 2008. Red dotted line (high-home-equity group) represents
individuals with home equity in 2006 greater than $500K. Blue dotted line represents individuals
with home equity in 2006 smaller than $500K. The average of Equity are plotted for each even-
numbered year from 1998 to 2008. Sample restricted to individuals with home equity in 2006
ranging from $300K to $700K.
52
Figure 2.7: Changes in Home Value and Home Loan Across Years
High−Home−Equity Group
Low−Home−Equity Group
Single Senior
−200 −100 0 100 200 300
ΔValue ($K)
1998 2000 2002 2004 2006 2008
Year
High−Home−Equity Group
Low−Home−Equity Group
Middle−Aged
−200 −100 0 100 200 300
1998 2000 2002 2004 2006 2008
Year
Changes in Home Value Across Years
High−Home−Equity Group
Low−Home−Equity Group
Single Senior
−200 −100 0 100 200 300
ΔLoan ($K)
1998 2000 2002 2004 2006 2008
Years
High−Home−Equity Group
Low−Home−Equity Group
Middle−Aged
−200 −100 0 100 200 300
1998 2000 2002 2004 2006 2008
Years
Changes in Home Loan Across Years
NOTES: Dependent variable in the top two panels are the change of home value in consecutive
two waves. Dependent variable in the bottom panels are the change of home loan in consecutive
two waves. The left figure in each panel represents individuals who are single and aged above
65 and in 2006. The right figure in each panel represents individuals aged 55-64 in 2008. Red
dotted line (high-home-equity group) represents individuals with home equity in 2006 greater
than $500K. Blue dotted line represents individuals with home equity in 2006 smaller than $500K.
The average of Value and of Loan are plotted for each even-number year from 1998 to 2008.
Sample restricted to individuals with home equity in 2006 ranging from $300K to $700K.
53
Tables
Table 2.1: Pre-DRA Summary Statistics
Single Seniors Middle Aged
Variables N Mean Median Std Dev N Mean Median Std Dev
(1) (2) (3) (4) (5) (6) (7) (8)
HRSdataset
Housing Asset
Home value, 2006 ($K) 335 460.59 450 120.10 628 531.75 500 183.93
Home debt, 2006 ($K) 335 28.19 0 65.34 628 106.25 50 142.31
Home equity, 2006 ($K) 335 432.40 400 102.26 628 425.50 400 107.75
Home equity> $500K 117 550.68 540 51.98 168 576.35 566.5 58.60
Change in home price, 2004-2006 ($K) 320 117.92 100 145.15 612 130.36 100 141.77
Change in home price, 2006-2008 ($K) 335 -90.89 -50 169.78 628 -31.83 -50 473.45
Change in home debt, 2004-2006 ($K) 320 -1.01 0 47.15 612 -0.21 0 103.83
Change in home debt, 2006-2008 ($K) 335 1.60 0 52.52 628 7.08 0 92.27
Change in home equity, 2004-2006 ($K) 320 118.93 103.5 140.74 612 130.57 120 135.33
Change in home equity, 2006-2008 ($K) 335 -92.49 -50 166.21 628 -38.91 -50 473.74
HealthStatus
Diabetes 334 0.14 0 0.35 627 0.10 0 0.29
Cancer 335 0.20 0 0.40 627 0.09 0 0.29
Difficulty w/ memory 335 0.03 0 0.18 628 0.02 0 0.13
Any ADLs /IADLs 335 0.19 0 0.39 628 0.08 0 0.27
HealthInsuranceandHealthServices
Medicaid, 2004 320 0.02 0 0.14 612 0.01 0 0.08
Ever had overnight stay in nursing home, 2004 320 0.03 0 0.17 612 0.00 0 0.04
Ever used home care services, 2004 320 0.07 0 0.25 612 0.01 0 0.11
BasicCharacteristics
Age, 2006 335 75.44 74 7.52 628 57.65 58 2.90
Male 335 0.29 0 0.45 628 0.44 0 0.50
White 335 0.90 1 0.29 628 0.89 1 0.32
Black 335 0.05 0 0.22 628 0.05 0 0.21
Native 335 0.90 1 0.30 628 0.86 1 0.35
Number of kids 335 2.96 3 2.15 628 2.64 2 1.56
Less than high school education 335 0.12 0 0.32 628 0.05 0 0.22
Income, 2004 ($K) 320 61.62 32.01 105.52 612 88.07 60 100.72
NOTES: Summary statistics are for individuals with home equity in 2006 in the range of $300K-
$700K. Diabetes, Cancer, Difficulty w/ memory, and Any ADLs/IADLs are indicators if the indi-
vidual reported having symptoms. Income is defined as personal income.
54
Table 2.2: Testing the Parallel Trends Assumption - Home Equity
Dependent Variable ($K) Equity
Treatment Years 06
Control Years 98 00 02 04
(1) (2) (3) (4) (5) (6) (7) (8)
Senior Above Post -54.90 -71.99 -25.80 -30.54 23.13 16.17 -37.51 -42.03
(53.948) (48.534) (41.532) (41.278) (32.662) (32.555) (69.310) (70.302)
Above Post 93.45 95.17 86.04** 83.00** 24.11 22.11 51.07 49.56
(64.196) (67.820) (33.166) (30.533) (32.800) (30.271) (49.107) (44.920)
Post 65.33*** 84.13 63.51*** 79.84 68.83*** 77.07 55.73*** 23.38
(17.929) (271.606) (15.579) (80.585) (19.105) (52.806) (16.151) (41.176)
Additional controls Yes Yes Yes Yes Yes Yes Yes Yes
State FE Yes Yes Yes Yes Yes Yes Yes Yes
Individual FE No Yes No Yes No Yes No Yes
Weights Yes Yes Yes Yes Yes Yes Yes Yes
Observations 516 516 1,256 1,256 1,274 1,274 1,324 1,324
R-squared 0.27 0.26 0.29 0.31 0.20 0.17 0.14 0.08
NOTES: The analysis uses individuals with home equity in the range of $300K-$700K in 2006,
prior to the launch of the DRA (1996-1998 through 2004-2006). Post = 1 indicates the year of
2008. Post = 0 indicates the year of 2006. Above = 1 when an individual’s home equity in 2006
is above $500K.Senior is an indicator variable denoting that an individual aged above 65 in 2006,
andSenior = 0 when an individual aged 55-64 in 2008. Each observation is an individual-year.
Odd-numbered columns do not include individual fixed effects, and even-numbered columns
additionally include individual fixed effects. All columns include weights and state FE (to control
the impact of geographical factors when people move to different states). Robust standard errors,
clustered by state, are in parentheses. (*** p<0.01, ** p<0.05, * p<0.1)
55
Table 2.3: Triple-Difference (DDD) Estimate of the Impact of the DRA on Home Equity
Dependent Variable ($K) Equity
Comparison Years 06-08
(1) (2) (3) (4)
Senior Above Post -97.96** -94.29** -75.12** -66.75*
(37.988) (38.569) (33.902) (34.452)
Above Post -41.98 -41.46 -49.76 -47.60
(55.014) (53.288) (38.175) (36.371)
Post -154.21*** -347.24*** -147.29*** -334.90***
(16.633) (89.131) (16.791) (83.633)
Specification =DDD
Mean home equity (Above = 1), 2006 550.68
Additional controls YES YES YES YES
State FE YES YES YES YES
Weights NO NO YES YES
Individual FE NO YES NO YES
Observations 1,828 1,828 1,828 1,828
R-squared 0.13 0.18 0.12 0.17
NOTES: Results presented are for individuals with home equity in the range of $300K-$700K in
2006. Post = 1 indicates the year of 2008. Post = 0 indicates the year of 2006. Above = 1 when
an individual’s home equity in 2006 is above $500K.Senior is an indicator variable denoting that
an individual aged above 65 in 2006, and Senior = 0 when an individual aged 55-64 in 2008.
Even-numbered columns include individual fixed effects, and columns (3)-(4) include weights.
All columns include state FE to control the impact of geographical factors on home equity when
people move to different states. Robust standard errors, clustered by state, are in parentheses. (***
p<0.01, ** p<0.05, * p<0.1)
56
Table 2.4: Heterogeneous Triple-Difference (DDD) Estimate of the Impact of the DRA on
Home Equity
Dependent Variable Equity
Comparison Years 06-08
(1) (2) (3) (4)
Senior Above Post -156.42*** -484.02*** -171.11*** -496.11***
(56.208) (39.529) (44.359) (45.619)
Senior Above PostH
i04
0.21** 0.97*** 0.27*** 1.02***
(0.095) (0.064) (0.081) (0.069)
Above Post -41.99 -41.19 -49.77 -47.48
(55.014) (53.387) (38.173) (36.384)
Post -154.33*** -335.44*** -147.29*** -327.33***
(16.705) (87.092) (16.836) (79.501)
Specification =
1
+
2
H
i04
Reg Sample H
i06
2 [200; 800) H
i06
2 [100; 900)
Turning point 659.99 615.42 641.98 636.65
Additional controls Yes Yes Yes Yes
State FE Yes Yes Yes Yes
Individual FE No Yes No Yes
Weights Yes Yes Yes Yes
Observations 3,400 3,400 6,658 6,658
R-squared 0.11 0.18 0.11 0.18
NOTES: Results presented in columns (1)-(2) are for individuals with home equity in the range of $200K-$800K in 2006. Results
presented in columns (3)-(4) are for individuals with home equity in the range of $100K-$900K in 2006. Post = 1 indicates the year
of 2008. Post = 0 indicates the year of 2006. Above = 1 when an individual’s home equity in 2006 is above $500K.Senior is an
indicator variable denoting that an individual aged above 65 in 2006, andSenior = 0 when an individual aged 55-64 in 2008. H
i04
denotes an individual’s home equity level in 2004. Turning point is the home equity level where the impact of the DRA is zero. Even-
numbered columns include individual fixed effects, and columns (3)-(4) include weights. All columns include state FE to control the
impact of geographical factors on home equity when people move to different states. Robust standard errors, clustered by state, are
in parentheses. (*** p<0.01, ** p<0.05, * p<0.1)
57
Table 2.5: Triple-Difference (DDD) Estimate of the Impact of the DRA on Home Value and
Home Loan
Dependent Variables Value Loan Loan/Value
Comparison Years 06-08
(1) (2) (3)
Senior Above Post -112.64** -37.51* -0.03
(43.995) (19.360) (0.027)
Above Post -15.34 34.42** 0.02
(39.627) (12.656) (0.017)
Post -145.98*** 1.31 0.05***
(14.729) (9.480) (0.008)
Additional controls Yes Yes Yes
State FE Yes Yes Yes
Individual FE Yes Yes Yes
Weights Yes Yes Yes
Observations 1,828 1,828 1,776
R-squared 0.12 0.08 0.21
NOTES: Results presented are for individuals with home equity in the range of $300K-$700K in
2006. Post = 1 indicates the year of 2008. Post = 0 indicates the year of 2006. Above = 1 when
an individual’s home equity in 2006 is above $500K. Senior is an indicator variable denoting
that an individual aged above 65 in 2006, and Senior = 0 when an individual aged 55-64 in
2008. The reduction of sample size in column (3) is due to the fact that the denominator of
loan
value
cannot equals to zero. All columns include individual FE and weights. All columns additionally
include state FE to control the impact of geographical factors on home equity when people move
to different states. Robust standard errors, clustered by state, are in parentheses. (*** p<0.01, **
p<0.05, * p<0.1)
58
Table 2.6: Pre-DRA Summary Statistics: Consumption Details
Single Seniors Middle-Aged
Variables N Mean Median Std Dev N Mean Median Std Dev
(1) (2) (3) (4) (5) (6) (7) (8)
PanelA:HRSdataset
Medical Consumption
LTC expenditures, 2006 ($K) 335 0.19 0 0.39 628 0.15 0 0.36
Non-LTC medical expenditures, 2006 ($K) 335 1.75 0.9 4.51 628 1.43 0.7 2.43
PanelB:CAMSdataset
Non-medical Consumption
Transportation spending, 2006 ($K) 104 6.76 3 12.91 111 15.27 8.04 15.73
Durables spending, 2006 ($K) 104 0.36 0 0.79 111 0.68 0 1.12
Nondurables spending, 2006 ($K) 104 32.35 23.77 28.38 111 36.83 32.33 21.12
NOTES: Summary statistics are for individuals with home equity in the range $300K-$700K in
2006. Since the CAMS randomly selects part of HRS households to measure spending, the total
sample size of the CAMS dataset is less than the HRS dataset. The measure of transportation
spending is the sum of all of the spending in the household on up to three automobile purchases,
vehicle insurance, vehicle maintenance, car payment of vehicle financing, and gasoline. The mea-
sure of durable spending is the sum of all of the household spending on durable goods excluding
autos. There are five durable categories: refrigerator, washer/dryer, dishwasher, television, and
computer. The measure of nondurable spending in general include: gifts, clothing, charitable
contributions, dining out, utilities, food and beverages, trips and vacations, sports, etc.
59
Table 2.7: Testing the Parallel Trends Assumption - Consumption
Dependent Variable ($K) Non-LTC Consumption
Comparison Years 02-06 04-06
(1) (2) (3) (4)
Senior Above Post -5.36 -10.14 2.20 -0.13
(9.959) (9.738) (7.090) (7.046)
Above Post -0.12 3.99 1.50 4.11
(6.990) (6.330) (6.683) (6.668)
Post 9.58*** -23.40 3.05 0.14
(2.545) (21.301) (2.091) (5.556)
Additional controls Yes Yes Yes Yes
State FE Yes Yes Yes Yes
Individual FE No Yes No Yes
Weights Yes Yes Yes Yes
Observations 464 464 454 454
R-squared 0.21 0.10 0.34 0.08
NOTES: The analysis uses individuals with home equity in the range of $200K-$800K in 2006, prior
to the launch of the DRA (2000-2002 through 2004-2006). Since the CAMS randomly selects part of
HRS households to measure spending, the total sample size of the CAMS dataset is less than the
HRS dataset. Post = 1 indicates the year of 2008. Post = 0 indicates the year of 2006. Above = 1
when an individual’s home equity in 2006 is above $500K.Senior is an indicator variable denoting
that an individual aged above 65 in 2006, andSenior = 0 if an individual aged 55-64 in 2008. Even-
numbered columns include individual fixed effects, and all columns include weights. Robust
standard errors, clustered by state, are in parentheses. (*** p<0.01, ** p<0.05, * p<0.1)
60
Table 2.8: Triple-Difference (DDD) Estimate of the Impact of the DRA on Consumption
Dependent Variable ($K) Non-LTC Consumption
Comparison Years 06-08
(1) (2) (3) (4)
Senior Above Post 4.47 6.44 6.60 10.50*
(4.770) (4.808) (5.514) (6.196)
Above Post 1.25 -0.08 0.77 -2.12
(3.267) (3.293) (3.308) (3.616)
Post -1.53 -7.00 -1.10 -10.12
(1.989) (7.520) (2.513) (8.187)
Mean (Above = 1), 2006 46.72
Additional controls YES YES YES YES
State FE YES YES YES YES
Weights NO NO YES YES
Individual FE NO YES NO YES
Observations 764 764 764 764
R-squared 0.23 0.07 0.20 0.07
NOTES: Results are presented for individuals with home equity in the range $200K-$800K in 2006.
Since the CAMS randomly selects part of HRS households to measure spending, the total sample
size of the CAMS dataset is less than the HRS dataset. Post = 1 indicates the year of 2008. Post =
0 indicates the year of 2006. Above = 1 when an individual’s home equity in 2006 is above $500K.
Senior is an indicator variable denoting that an individual aged above 65 in 2006. Even-numbered
columns include individual fixed effects, and columns (3)-(4) include weights. Robust standard
errors, clustered by state, are in parentheses. (*** p<0.01, ** p<0.05, * p<0.1)
61
Table 2.9: Testing the Parallel Trends Assumption - Consumption
Dependent Variable ($K) Non-LTC Consumption
Comparison Years 02-06 04-06
(1) (2) (3) (4)
Single Above Post -11.01 -13.72 -1.96 -1.14
(11.414) (11.702) (4.523) (4.073)
Above Post 3.36 1.99 5.44 4.22
(6.828) (5.927) (3.775) (2.915)
Post -1.33 -17.72** -4.33** -9.18**
(1.815) (8.522) (2.126) (3.507)
Additional controls Yes Yes Yes Yes
State FE Yes Yes Yes Yes
Individual FE No Yes No Yes
Weights Yes Yes Yes Yes
Observations 462 462 566 566
R-squared 0.24 0.08 0.22 0.12
NOTES: The analysis uses senior individuals aged 65 and above with home equity in the range
of $200K-$800K in 2006, prior to the launch of the DRA (2000-2002 through 2004-2006). Post = 1
indicates the year of 2008. Post = 0 indicates the year of 2006. Above = 1 when an individual’s
home equity in 2006 is above $500K. Single is an indicator variable denoting that an individual
were unmarried during 2006-2008. Even-numbered columns include individual fixed effects, and
all columns include weights. Robust standard errors, clustered by state, are in parentheses. (***
p<0.01, ** p<0.05, * p<0.1)
62
Table 2.10: Tripe-Difference (DDD) Estimate of the Impact of the DRA on Consumption
Dependent Variable ($K) Non-LTC Consumption
Comparison Years 06-08
(1) (2) (3) (4)
Senior Above Post 7.77** 6.49 12.03*** 10.43*
(3.211) (3.998) (4.089) (5.172)
Above Post 0.82 0.14 -0.26 -0.25
(3.080) (3.185) (2.902) (3.261)
Post -2.29* -6.52 -1.05 -8.78
(1.342) (9.047) (1.252) (12.327)
Additional controls YES YES YES YES
State FE YES YES YES YES
Weights NO NO YES YES
Individual FE NO YES NO YES
Observations 798 798 798 798
R-squared 0.29 0.16 0.27 0.13
NOTES: Results are presented for senior individuals aged 65 and above with home equity in the
range $200K-$800K in 2006. Post = 1 indicates the year of 2008. Post = 0 indicates the year of
2006. Above = 1 when an individual’s home equity in 2006 is above $500K.Single is an indicator
variable denoting that an individual were unmarried during 2006-2008. Even-numbered columns
include individual fixed effects, and columns (3)-(4) include weights. Robust standard errors,
clustered by state, are in parentheses. (*** p<0.01, ** p<0.05, * p<0.1)
63
Table 2.11: Tripe-Difference (DDD) Estimate the DRA Effects on Different Categories of
Consumption
Dependent Variable ($K) Transportation Non-LTC medicals Durables Nondurables
Comparison Years 06-08
(1) (2) (3) (4)
Senior Above Post 3.01 1.23 0.15 6.11
(3.090) (1.071) (0.372) (5.442)
Above Post -3.04 -0.05 -0.18 1.15
(2.711) (0.438) (0.232) (2.085)
Post 1.02 -0.61 0.13 -10.65
(3.358) (0.638) (0.148) (6.749)
Individual FE Yes Yes Yes Yes
State FE Yes Yes Yes Yes
Weights Yes Yes Yes Yes
Observations 764 764 764 764
R-squared 0.01 0.10 0.23 0.11
NOTES: Results are presented for individuals with home equity in the range $200K-$800K in 2006.
Post = 1 indicates the year of 2008. Post = 0 indicates the year of 2006. Above = 1 when an
individual’s home equity in 2006 is above $500K. Senior is an indicator variable denoting that
an individual aged above 65 in 2006. All columns include individual fixed effects and weights.
Robust standard errors, clustered by state, are in parentheses. (*** p<0.01, ** p<0.05, * p<0.1)
64
Table 2.12: Tripe-Difference (DDD) Estimate the DRA Effects on Different Categories of
Consumption
Dependent Variable ($K) Transportation Non-LTC medicals Durables Nondurables
Comparison Years 06-08
(1) (2) (3) (4)
Single Above Post -2.01 1.94 -0.21 10.72**
(2.898) (1.235) (0.288) (4.436)
Above Post 1.35 -0.83 0.16 -0.97
(1.673) (0.610) (0.177) (1.941)
Post -0.14 0.97 -0.23* -9.37
(3.195) (2.918) (0.134) (10.264)
Individual FE Yes Yes Yes Yes
State FE Yes Yes Yes Yes
Weights Yes Yes Yes Yes
Observations 798 798 798 798
R-squared 0.14 0.07 0.15 0.12
NOTES: Results are presented among senior individuals aged above 65 with home equity in the
range $200K-$800K in 2006. Post = 1 indicates the year of 2008. Post = 0 indicates the year of
2006. Above = 1 when an individual’s home equity in 2006 is above $500K.Single is an indicator
variable denoting that an individual were unmarried during 2006-2008. All columns include in-
dividual fixed effects and weights. Robust standard errors, clustered by state, are in parentheses.
(*** p<0.01, ** p<0.05, * p<0.1)
65
Table 2.13: Heterogeneous Effects
Left-hand-side variable ($K) Equity
(1) (2) (3) (4) (5) (6) (7) (8)
Less than Less than Any ADLs or Any ADLs or
Interaction variable Male Male high school high school IADLs, 06 IADLs, 06 Medicaid, 04 Medicaid, 04
Senior Above Post -91.30** -63.23* -80.47** -62.94* -76.91** -54.93 -90.58** -70.83**
(37.397) (34.298) (34.434) (32.771) (36.461) (32.882) (36.124) (33.121)
Senior Above Post -21.63 -35.38 -129.73** -89.96* -158.79*** -141.11*** -274.68* -198.44
Interaction Term (listed as top of column) (40.500) (35.147) (57.329) (46.609) (42.830) (35.245) (158.038) (167.875)
Above Post -45.03 -47.84 -44.99 -47.81 -42.28 -47.79 -42.27 -47.90
(53.994) (46.062) (53.980) (46.079) (53.974) (46.075) (53.969) (46.046)
Post -155.01*** -147.68*** -155.09*** -147.89*** -155.36*** -148.11*** -155.09*** -147.75***
(16.758) (14.795) (16.750) (14.914) (16.700) (14.836) (16.747) (14.822)
Additional controls Yes Yes Yes Yes Yes Yes Yes Yes
State FE Yes Yes Yes Yes Yes Yes Yes Yes
Weights No Yes No Yes No Yes No Yes
Observations 1,828 1,828 1,828 1,828 1,828 1,828 1,828 1,828
R-squared 0.13 0.12 0.13 0.12 0.13 0.12 0.13 0.12
NOTES: Results are presented among individuals with home equity in the range $200K-$800K in
2006. Post = 1 indicates the year of 2008. Post = 0 indicates the year of 2006. Above = 1 when an
individual’s home equity in 2006 is above $500K.Senior is an indicator variable denoting that an
individual aged above 65 in 2006. Even-numbered columns include individual fixed effects, and
all columns include weights. Robust standard errors, clustered by state, are in parentheses. (***
p<0.01, ** p<0.05, * p<0.1)
66
Table 2.14: Overview of Empirical Objects
Notation Meaning
(1) (2)
A.EmpiricalEstimatedObjects
A.1 Willingness to pay,
A.1.1 Transfer Term, (p(0)p(1))
R
1
0
E[l(m;)]dm
E[l(m;)] form = 0; 1 Mean LTC spending without and with Medicaid
p(m) form = 0; 1 Out-of-pocket price for LTC services without and with Medicaid
A.1.2 Pure-Insurance Term,
R
1
0
Cov[
uc
E[uc]
; (p(0)p(1))l(m;)]dm
c(m;) form = 0; 1 Distribution of non-LTC consumption without and with Medicaid
s(m;l(m;)) form = 0; 1 Distribution of out-of-pocket LTC spending without and with Medicaid
h
0
Home equity in 2006
h forAbove = 0; 1 The changes of home equity forh
0
> 500 group andh
0
< 500 group
A.2 Net resource cost,C =E[l(1;)l(0;)] +E[s(0;l(0;))s(1;l(1;))]
E[s(m;)] form = 0; 1 Mean out-of-pocket spending without and with Medicaid
B.ParametersoftheUtilityFunction
Coefficient of relative risk aversion
Relative importance of non-long-term-care consumption
67
Table 2.15: Willingness to Pay (WTP) for Medicaid LTC
Benefit
WTP ,(1) 12251
(standard eror) (3075.15)
Transfer term,T 8314.38
Pure-Insurance term,PI 3936.63
Cost
Net cost, C 9915
Benchmark
WTP as fraction of net cost,
(1)
C
1.24
NOTES: Estimates of willingness to pay and corresponding net cost are expresses in dollars per
year per Medicaid LTC recipient. Standard errors are bootstrapped.
68
Chapter 3
The Impact of Partnership Long-Term
Care Program on Insurance Coverage
3.1 Introduction
With the intensification of population aging, policymakers face an imperative: how to
optimize social resources to support the elderly who suffer the risk of becoming disabled
and needing long-term care (LTC). In the United States, particularly, the Department of
Health and Human Services’ estimation shows that adults who are 65-years-old have a
70% chance of needing some LTC services as they age.
1
Along with the considerable
demand, expenditures for LTC services can be a significant financial burden to families,
2
making Medicaid the largest payer and safety net for the fragile elderly. Due to the size of
LTC expenses, it has led to a growing concern among state governments and the federal
government to find ways to shift some of the financial burdens of paying for LTC away
from Medicaid.
Encouraging consumers to take personal responsibility and financing their own long-
1
Similarly, Brown and Finkelstein (2007) estimate that about 47% of the older Americans will require the
use of LTC after age 65
2
In 2019, the average annual cost of a private room in a nursing home was around $102,200, which is far
above the average income for Americans over 65 years old ($73,288).
69
term care is one of the approaches being promoted. One specific option that the fed-
eral and state governments have tried to address LTC expenses issues is the Partnership
Long-term Care (PLTC) Insurance program. This program aimed to encourage people to
purchase private LTC insurance to help cover LTC’s cost while also alleviating the states’
burden to pay for this type of care via Medicaid. Specifically, the PLTC program allows
policyholders to protect a certain amount of additional assets from Medicaid’s asset limit.
Medicaid applicants thus do not have to spend down on savings to qualify for Medicaid.
The exact amount protected from Medicaid is equal to that one’s partnership policy has
paid out for LTC services. Therefore, this asset protection provision seems most appealing
to people who have countable assets greater than Medicaid’s asset limit.
Two specific questions related to implementing the PLTC program arises: How does
the PLTC program affect private LTC insurance ownership rates? Even if we find that
the PLTC program does induce more widespread private LTC insurance ownership, will
government expenditures on Medicaid necessarily decline? Based on the concern on an
inefficient spend down of savings to qualify Medicaid, the PLTC program should have
increased the ownership of private LTC policies and lead to better allocation of social
resources by hitting its targeted population.
This paper focuses on these two questions by employing the state-by-year variation
in the adoption of the PLTC program. Specifically, the PLTC program was initially estab-
lished under the auspices of the Robert Wood Johnson Foundation and originated in four
states (California, Connecticut, Indiana, and New York) in the early/mid-1990s. In 1993,
the Omnibus Budget Reconciliation Act (OBRA) prevented the expansion of these pro-
grams to other states. However, with the Deficit Reduction Act (DRA) passage in 2005,
all remaining states can choose to create a PLTC plan. In 2010, 38 states adopted the PLTC
plan. Therefore, the variation in the adoption of PLTC program across states and over
time provides a quasi-experimental environment to examine the research questions.
First, to examine how the PLTC program affects private LTC insurance coverage rates,
70
I use the recent expansion of the PLTC program in a staggered difference-in-difference
(DID) framework. With data spanning from 2000 to 2010, I conduct the two-way fixed
effects (TWFE) regressions and find that the adoption of the partnership program has a
positive but insignificant impact on all age groups. These findings are consistent with
other evaluations of the PLTC program that draw upon the staggered DID design (Lin
and Prince (2013); Greenhalgh-Stanley (2014); Bergquist et al. (2018)). However, this stag-
gered DID design, in recent years, has been criticized since it can produce biased estima-
tor compared to the true treatment effects when treatment effects can evolve over time
(Goodman-Bacon, 2018; Sun and Abraham, 2020; Callaway and Sant’Anna, 2020; Baker
et al., 2021).
To account for the dynamic treatment effects, I then use an event-study specification
that stack and align states by their relative exposure time to the PLTC adoption (event
window) in treated states, and compare outcome changes in treated states with changes
in ”not-yet treated” states. By limiting my analysis to non-pilot states, this event-study
approach prevents using past treated units as effective comparison units, which may oc-
cur with a staggered DID design. The event study estimates trace out the timing of out-
come differences between treated states and ”not-yet treated” states. The results show
that treated states and ”not-yet treated” states do not trend differently for six years be-
fore the PLTC program. After the introduction of the PLTC program, I find that states
adopting the program experienced an increase in LTC insurance coverage rates. The ef-
fects are most potent for the near-elderly population (aged 50-64), who experienced a rise
in LTC insurance purchases by 3.4 percentage points after their living states exposed to
the PLTC program for four years. The results also demonstrate that the PLTC program’s
impact appears slowly but surely, which confirms that using staggered DID design is not
appropriate in this circumstance where treatment effects evolve over time. On the other
hand, the impacts of the program on the elderly population (aged over 70) are insignifi-
cant. This finding is consistent with the existence of insurance underwriting issues that
71
have been shown in the literature (Bergquist et al., 2018).
This study’s second question is whether the PLTC program is expected to reduce net
government expenditures. In other words, when individuals who purchased private LTC
insurance thanks to the PLTC program get into old age, will they reduce their reliance
on Medicaid? The question is not as apparent as it seems. On the one hand, individuals
who hold private LTC insurance would have private LTC insurance to first pay for their
LTC services. Medicaid benefits by having individuals take responsibility for the initial
phase of their LTC through private insurance. On the other hand, however, policyhold-
ers may change their health-related behavior after purchasing LTC insurance. They may
also change their attitude towards after-retirement savings since their assets got protected
through the PLTC program by which policyholders access to Medicaid under special el-
igibility rules. If policyholders consume savings meant for LTC services or take riskier
health-related behaviors, their demand for LTC services would rise. If that is the case, the
PLTC program will induce more demand for formal LTC services and increase the burden
on Medicaid.
Compared with the first question, the second question focuses more on examining
the long-term impact of the PLTC program since there is generally a lag between policy
purchase and benefits payout. To facilitate the purpose of studying the long-term effect,
I exploit the timing of the first implementation PLTC program conducted in 1993 when
only four states were allowed to have the program in place. Specifically, I take the orig-
inal four states as the treated states, while the remaining states as the control states, and
employ the standard DID design to estimate the PLTC program’s impact. To avoid the
influence of recent policy implementation, I draw upon data spanning from 1993 to 2004.
Similarly, as shown in the first part, I find that the PLTC program has impacts on LTC cov-
erage rates among the near-elderly population. At the same time, there are no impacts
among the elderly population.
Then I examine whether the presence of PLTC policies affects Medicaid coverage rates
72
among the elderly. Since Medicaid only provides to impoverished elderly individuals, I
limit my analysis to the sample of individuals whose assets are below the 50th percentile
each year. As the program mainly induces people under the age of 65 to purchase pri-
vate LTC insurance, it will take time for them to tap into LTC services or even exhaust
their private insurance benefits. We would expect that the longer time it takes from the
implementation date, the larger population would have been affected by the program.
Therefore, the more influential the program’s impact on Medicaid should be. My re-
sults indicate that the PLTC program increases Medicaid insurance by 3% points after
eight years of the program’s implementation, and the effect gets stronger as time goes
by. This finding suggests that the PLTC program induces more elderly individuals to rely
on Medicaid, which is contrary to the PLTC program’s intention to reduce the usage of
Medicaid. This finding echoes my hypothesis that the purchase of private LTC insurance
changed policyholders’ behavior, and these changes made them more vulnerable when
they needed LTC services.
Lastly, I explore various health care utilization measures and mechanisms to test my
hypothesis. The results show that the PLTC program leads to lower hospital/doctor vis-
its among the near-elderly population whose assets are below the 50th percentile. These
results indicate that private LTC insurance’s new purchasers alter their health behavior
by inducing them to take riskier behavior. Simultaneously, the near-elderly population
increases visits or stays in the nursing home while reducing usage on the home care ser-
vices, suggesting that the PLTC program results in an overuse of LTC insurance. These
findings are consistent with the ”moral hazard” problem shown in the health insurance
literature. This moral hazard issue helps us understand why and how the PLTC program
fails in its intention to shift the financial burden away from Medicaid.
To my knowledge, there have been limited evaluations of the PLTC that draw upon
the event-study methodology, which is less susceptible to the biases created by treatment
effect heterogeneity. Besides, this study is the first to look at the impact of the PLTC
73
program on Medicaid coverage rates with empirical identification. My findings suggest
that although the PLTC program generates new private LTC insurance purchases, the
states’ burden to pay for LTC services via Medicaid aggravates. The failure of the PLTC
program in alleviating state governments’ burden may arise due to the moral hazard that
changes the new purchasers’ saving patterns and health behavior.
The rest of this paper is organized as follows. Section 4.2 provides more details with
the relevant literature. Section 4.3 describes the background of long-term care in the
United States and the institutional details of the Partnership LTC program. Section 4.4
and Section 4.5 describe the data, the empirical strategy, and the main results. Section
4.5.3 explores mechanisms. Finally, I conclude in Section 4.7.
3.2 Literature
The findings in this paper contribute to several strands of the economics literature.
First, there have been limited evaluations of the PLTC program that draw upon proper
econometric techniques. Lin and Prince (2013), using the staggered DID design with
data from Health and Retirement Study (HRS), finds only modest effects of adopting
the PLTC program on total LTC insurance uptake. With the same methodology and data,
Greenhalgh-Stanley (2014) draws a similar conclusion that the impact of the PLTC pro-
gram is limited except when a sample of highly risk-averse and forward-looking individ-
uals is evaluated. Bergquist et al. (2018) draws upon data from the National Association
of Insurance Commissioners (NAIC) that collects information on PLTC contracts and ap-
plications explicitly. With the staggered DID design, they also suggest no significant effect
of the PLTC program on insurance uptake.
Note that all estimations mentioned above are based on the staggered DID design. Al-
though this estimation approach has become especially popular over the last two decades,
3
3
Baker et al. (2021) show that from 2000 to 2019, there were 49% of top finance and accounting journals
that employ the staggered DID design
74
recent advances in econometric theory suggest that the staggered DID design often do
not provide valid estimates of the causal estimands of interest (Athey and Imbens, 2018;
Goodman-Bacon, 2018; Sun and Abraham, 2020; Callaway and Sant’Anna, 2020; Baker
et al., 2021). The main reason for the pitfall of the staggered DID design is that such
design produce estimates of the variance-weighted average of many different treatment
effects. When treatment effects can evolve over time, the staggered DID estimates can
obtain the opposite sign to the true ATT or ATE. The intuition is that in the staggered DID
approach, already-treated units can act as effective comparison units. Changes in their
outcomes over time are subtracted from the changes of later-treated units. In our case,
therefore, the staggered DID design is problematic since the PLTC program’s impact is
expected to be emerging over time. Individuals living in the states that have adopted
the PLTC program need time to collect information regarding the benefits of the PLTC
program and adjust their decision or behavior about private LTC insurance. To address
this issue, in this paper, I instead employ event-study specification, and find the positive
effects of the PLTC program after states implemented the policy for four years.
Second, the previous PLTC literature has not studied the impact of the program be-
yond its scope on private LTC insurance. However, since the main purpose of the PLTC
program is to reduce the burden on the government, a direct estimate of how the program
affects Medicaid expenditures should be the core question that needs to be answered.
This paper is among the first to quantitatively evaluate the impact of the PLTC program
on Medicaid coverage using long-term panel data. Contrary to the program’s intention,
this paper finds that the program produces a larger proportion of Medicaid holders. This
finding is consistent with Goda (2011), which uses simulations and shows that state tax
subsidies are unlikely to significantly reduce government net expenditures, although they
will cause a reaction to private LTC insurance.
75
3.3 Policy Background
This section provides details on the market for private LTC insurance in the United
States and the details of the Partnership LTC program.
3.3.1 The Market for Private Long-Term Care Insurance
Since most users of long-term care services are older adults (Harris-Kojetin et al., 2019),
the aging population and increasing prevalence of disability indicate that the use of long-
term care may surge. Long-term care includes a range of services and supports that older
individuals may need to meet their health or personal needs over a long period. Specifi-
cally, it includes assistance in performing activities of daily living (ADLs)
4
, instrumental
activities of daily living (IADLs)
5
, and other health maintenance tasks. According to a
2018 analysis by the U.S. Department of Health and Human Services, approximately 70%
of elderly people will rely on long-term care at some stage in their lives. Although some of
the long-term care that older people receive is provided informally by their family mem-
bers, due to the rising divorce rate (Kennedy and Ruggles, 2014), increasing childlessness
(Baudin et al., 2015), and growing female labor force participation (Greenwood et al., 2016;
Fern´ andez, 2013), the reduction in informal care has expanded the elderly’s demand for
paid services, such as formal home care or nursing home care. In 2018, formal long-term
care totaled US$379 billion, accounting for more than 10% of national health expenditures
(NHE, 2018).
Long-term care is usually not covered by Medicare. One option for the elderly is LTC
insurance. LTC insurance pays or reimburses the policyholder’s LTC expenses. Private
LTC insurance was first provided in the United States in 1974. However, it was not un-
4
ADLs are the basic self-care tasks. They include walking, eating, dressing, toileting, bathing, and trans-
ferring.
5
IADLs require more complex thinking skills, including organizational skills. They include managing
finances, managing transportation, shopping and meal preparation, housework, managing communication
and managing medications.
76
til the 1980s that the National Association of Insurance Commissioners (NAIC) issued
the LTC insurance model act, which established minimum standards and practices for
companies selling LTC insurance. Since then, the demand for LTC insurance has been
sluggish. Still, in 2018, less than 11% of Americans had a private LTC insurance policy
(Musumeci et al., 2019).
The theoretical and empirical evidence indicates two main culprits of the small scale
of the private LTC insurance markets. First, price and affordability are essential factors
in an individual’s decision to purchase LTC insurance (Robert Wood Johnson Founda-
tion, 2014). Most notably, people buy LTC insurance when they are young, partly due to
lower premiums at younger ages (because premiums depend on the age at the time of
purchase). Second, many people believe that Medicaid can be used to cover LTC services.
Therefore, the private LTC insurance market has the potential to be squeezed out of the
market (Brown and Finkelstein, 2008, 2011). In addition, the LTC insurance market also
has problems such as personal uncertainty about the future cost of LTC services, high
management costs, insurance premiums that increase over time, and insurance lapses, as
well as insurance underwriting (Norton, 2000; Barr, 2010; Bergquist et al., 2018) and other
issues.
3.3.2 Medicaid Long-Term Care
Medicaid LTC is a means-tested, joint federal-state program that provides health in-
surance for the frail elderly population. In 2016, an estimated 62% of long-term care users
residing in nursing homes had Medicaid as a payer source (Harris-Kojetin et al., 2019).
Medicaid LTC, therefore, acts as one major avenue through which the elderly can insure
themselves against the uncertainty of long-term care costs. However, not all older indi-
viduals are eligible. Eligibility for Medicaid LTC requires that an individual’s income and
assets fall below defined thresholds. Though eligibility tests vary by marital status and
state, minimum eligibility requirements are determined at the federal level. Traditionally,
77
all states have an asset limit for Medicaid LTC, which, generally speaking, is $2,000. Med-
icaid applicants who have countable assets greater than $2,000 must ”spend down” the
extra assets to meet Medicaid’s asset limit, and hence, qualify for Medicaid LTC.
3.3.3 The Partnership for Long-Term Care
The Partnership LTC Program is a collaboration between private LTC insurance com-
panies and a state’s Medicaid program. The PLTC program was designed to attract con-
sumers who may not otherwise purchase LTC insurance. States provide guarantees that
if benefits under a PLTC policy are insufficient to cover the cost of care, the consumer
may be eligible for Medicaid under special eligibility rules while retaining a pre-specified
amount of asset (though income and functional eligibility rules still apply). For example,
suppose an individual has a PLTC policy that paid out $100,000 in LTC services for him.
Since his policy paid out $100,000, an equal amount ($100,000) is protected from Medi-
caid’s asset limit. Remember, Medicaid’s asset limit is $2,000, meaning that this individ-
ual is entitled to $2,000 in assets, plus the $100,000 that is protected, allowing him to retain
$102,000 total in assets. Thus, consumers are protected from having to become impover-
ished to qualify for Medicaid, and states avoid the full burden of LTC costs. Through the
PLTC program, if additional LTC coverage is required (beyond the scope provided by the
policy), states can provide consumers with Medicaid in accordance with special eligibil-
ity rules to promote the purchase of private LTC insurance. In turn, Medicaid benefits by
using private insurance to hold individuals accountable for the initial stages of their LTC.
This unique insurance model was developed in the 1980s with the support of the
Robert Wood Johnson Foundation (RWJF). The initial demonstration models have been
in California, Connecticut, Indiana, and New York since 1993. However, due to concerns
about the appropriateness of using Medicaid funds for this purpose, Congress imposed
restrictions on the further development of PLTC in the Omnibus Budget Reconciliation
Act (OBRA) of 1993. The four states with existing PLTC programs were allowed to con-
78
tinue, but the OBRA clause ended the replication of the partnership model in new states.
In 2005, the Deficit Reduction Act (DRA) removed the barriers imposed by Congress on
such programs and allowed the partnership program to be extended to other states across
the country. So far, all states except Alaska, Hawaii, and Mississippi now have PLTC pro-
grams.
6
The expansion of the PLTC program allows for empirical analysis of the program’s
effect on LTC insurance purchases and Medicaid coverage. The Department of Health
and Human Services (HHS) assumed that the program was at least budget neutral, with
opportunities for savings because it provides an alternative to transferring assets and be-
cause income from protected assets can be applied to the cost of care (Meiners, 2009). A
Government Accountability Office study (GAO, 2007) suggests that savings on Medicaid
were not likely because it assumed that many participants would still be too wealthy to
qualify for Medicaid. Because of the controversial conclusions from the previous litera-
ture, it is unclear what the program’s net effect on Medicaid spending will be.
3.4 Data
To explore the impact of the PLTC on private LTC insurance and Medicaid, I use the
data from the Health and Retirement Study (HRS) conducted by the University of Michi-
gan. The HRS dataset is a nationally representative dataset that tracks households age
50 and above biennially. It provides detailed information on basic demographic charac-
teristics, health and functioning, health care and insurance, medical expenses, and assets.
Most of the data come from the RAND HRS data files, which are derived from all waves
of HRS by the RAND Center with cleaned and consistent variables. Variables regarding
LTC coverage and other insurance-related variables, such as life insurance coverage, are
from the original HRS data. Besides, I supplement these public-use files by adding state-
of-residence information from the restricted HRS data with permission from the HRS
6
See https://www.medicaidplanningassistance.org/partnerships-for-long-term-care/
79
administration. Using state information is crucial for my analysis because PLTC policies
differ remarkably across states.
Based on the previous literature (Courtemanche and He, 2009; Lin and Prince, 2013),
individuals between 50 and 69 years of age are the primary age range for purchasing LTC
insurance. Therefore, from the overall sample of individuals, I split the sample into two
sub-groups based on their age: near-elderly, ages 50-65, and elderly, age 70 and older. I
narrow the age range of the first near-elderly group to rule out the possible Medicare’s
impact on individuals’ decisions for private LTC insurance. My second elderly group
then serves as the robustness check. Besides, since individuals with assets larger than
$2000 are most likely affected by the PLTC program, I focus on the sample of individuals
with assets of at least $2000 each year.
To answer the first empirical question, I limit my analysis to the 2000–2010 waves of
the HRS, which span the growth in adoptions from the DRA. Since all observable changes
in the adoption of the partnership program by the states occurred after 2006, with this
period, I am able to not only estimate the PLTC impact on LTC insurance coverage but
also show the trend of LTC insurance rates in adopted states and not-yet adopted states
before 2006. Notably, one would expect differences between those states that adopted the
program in the 1990s (original pilot states) and the states that did so after 2005. Therefore,
I further limit my analysis for the first empirical question on non-pilot states. Ultimately,
the sample I use for my first empirical questions results covers 21,042 unique individuals
with a total of 63,542 observations.
For the second empirical question, as HRS’s first survey on the elderly is in 1993,
which is included in the RAND HRS 1994 wave, I limit my analysis for this part to the
1994-2004 waves of the HRS. Comparing the original four pilot states with other non-
pilots states, I can show the long-run effects of the PLTC program on Medicaid cover-
age. Eventually, the sample I use for my second empirical questions results covers 25,967
unique individuals with a total of 83,790 observations.
80
I merged the HRS data with policy data regarding the implementation of the PLTC
program. For state PLTC programs, I collect state-level information from various sources
about whether the PLTC program has been implemented for a given state until 2021.
7
To construct a reliable measure for the implementation of the PLTC program, I take into
consideration that the HRS survey was conducted biannually throughout the survey year.
I acquire information about the month of the year when each survey was conducted for
each respondent. Together with the exact month and year of policy implementation, I can
pin down how long the individual was exposed to PLTC program in each specific state.
As illustrated in Table 4.1, four states had PLTC programs in place by 1994. In 2006, three
more states had PLTC programs in place; by 2008, 27 states had adopted them; by 2010,
38 states had PLTC programs.
Table 4.2 provides summary statistics of the key variables calculated using individual
sampling weights. Columns (1) and (2) correspond to the near-elderly group. 30% of
the sample lives in a state that has implemented a PLTC program. 9% of the sample
owns private LTC insurance, and 3% of the sample reports being enrolled in Medicaid.
The sample is mostly white and female, and 12% of the sample reports difficulty living
independently and caring for oneself (which I interpret as an indicator of LTC needs).
The third and fourth column of Table 4.2 reports similar statistics for the elderly sample.
Of note, 13% of the sample owns a private LTC insurance policy. 31% of the sample
reports being in poor health condition, 28% reports needing help with at least one ADLs
or IADLs. As has been noted by several prior studies, I find that private LTC coverage is
associated with higher education and more assets.
7
Most of the policy data during 1990-2014 were collected from https://www.aaltci.org/long-term-care-
insurance/learning-center/long-term-care-insurance-partnership-plans.php. This part is similar to the
database used by Greenhalgh-Stanley (2014). I also checked each state’s website to verify the implemented
date.
81
3.5 Empirical Strategy and Results
3.5.1 Empirical Strategy
Over the last 30 years, many states have adopted the PLTC program. This allows for
an analysis that exploits state-by-year variation to estimate the PLTC program’s effect on
various outcomes.
Effects on Private LTC Insurance
Staggered DID TWFE Estimate
To determine the impact of the PLTC program on private LTC insurance, I first fol-
low the literature and employ the staggered DID design. Specifically, I run the model
specification taking the following two-way fixed effect (TWFE) form:
Y
ist
=P
st
+
X
it
+
s
+
t
+
r
t +
ist
(3.1)
in whichi indexes the individual,s the state, andt the year.P
st
is an indicator for whether
the state has adopted the PLTC program, and is the main coefficient of interest. X
it
is a
set of individual control characteristics, which includes age, marital status, education sta-
tus, self-reported health status, any ADLS/IADLs, cancer status, diabetes status, number
of children, and assets. Besides, I also control for region-level time trends (
r
t) given that
the coefficient is likely to overestimate the effect in the presence of pre-trends. Individual
fixed effects are included as an alternative specification. The
ist
captures unobservables
at the individual-state-year level that impact the decision to purchase LTC insurance. I
use a linear probability model and cluster the standard errors at the state level in all spec-
ifications, and results are adjusted using person-level weights.
Panel A of Table 3.3 reports estimates of the effect of living in a state with the PLTC
82
program on private LTC insurance coverage. Columns (1) and (3) estimate the model
using the state fixed effects, year fixed effects, and region-level time trends, but no in-
dividual fixed effects. Therefore, they include the entire set of individual-level controls.
Columns (2) and (4) include individual fixed effects. The first two columns show that
the PLTC program has a slightly positive but insignificant overall effect on private LTC,
focusing on the near-elderly. Columns (3) and (4) report effects on the elderly, and they
show that the PLTC program has imprecisely overall effects.
However, recent work in econometric theory casts doubt on the validity and robust-
ness of the TWFE DID estimator when there are more than two treatment periods or
when there is variation in treatment timing. In particular, the main coefficient of interest
( of Eq., (3.1)) is not easily interpretable and is not consistent with the estimates of inter-
est. Numerous studies have shown that this coefficient is, in fact, a weighted average of
many different treatment effects and can yield estimates with the opposite sign compared
to the true ATT or ATE.
Event Study Estimate
To address the methodological challenge posed by TWFE estimation of DID with stag-
gered treatment timing, I instead provide an estimator that relies on event study DID,
which accommodates the possibility of dynamic treatment effects by modifying the set of
units that can act as effective comparison units in the estimation process. Specifically, I
run the event study specification in the following form:
Y
ist
=P
s
[
2
X
=6

k

1ftt

s
=g +
4
X
=0

k

1ftt

s
=g] +
X
it
+
s
+
t
+
r
t +
ist
(3.2)
in which the pre/post treatment of demographic groupk is defined by dummy variables
that measure the time relative to the PLTC implementation year in states, 1ftt

s
=g.
Treatment and control groups are defined by the dummy variableP
s
such thatP
s
= 1 if
83
the state has implemented the PLTC program by 2010.
The coefficients of interest,
k

and
k

, measure the relationship between LTC insurance
coverage and whether the state has adopted the PLTC program in the six years leading
up to the PLTC program’s introduction and the four years later. Since the HRS dataset is
biannual, I bundle odd event time with even event time in the same demographic group,
so
4
represents four or five years before adoption, and
2
represents one or two years
after adoption.
2
that represents two or three years before the PLTC program is omitted.
The
k

are from falsification tests that capture the relationship between treatment status
and outcomes before the PLTC program existed. Their pattern and statistical significance
are a direct test of the common trends assumption. The
k

are estimates of the PLTC
program’s impact on LTC insurance coverage. This specification identifies heterogeneity
in the PLTC program’s effect.
Panel B of Table 3.3 reports estimates of the PLTC program’s impact on private LTC
insurance coverage with this event-study specification. In all specifications, estimates in
the six years before the PLTC program are small and insignificant, supporting the com-
ment trend assumption. The size of estimates increases slowly after the PLTC program
implementation. After three or four years of exposure to the program, the near-elderly
LTC insurance coverage rises by 3.4 percentage points. This evidence supports our belief
that the treatment effect of the PLTC program is not constant across time. On the other
hand, columns (3) and (4) show estimates for the elderly group. The results are all in-
significant, suggesting no impact of the PLTC program on the elderly purchasing LTC
insurance. This finding is consistent with the presence of insurance underwriting issues.
Effects on Medicaid Coverage
The stated objective of implementing the PLTC program is to shift LTC costs away
from Medicaid. Then the second question arises: to what extent will the increase in
private LTC insurance be converted into a decline in Medicaid expenditure. Previous
84
literature has argued that if the PLTC program generates new private LTC insurance pur-
chases, more consumers who purchased private insurance will cover LTC needs with pri-
vate insurance. This possibility will lead to savings in Medicaid spending. However, the
increase in private LTC insurance is neither a sufficient condition nor a necessary condi-
tion for the decrease in Medicaid expenditure. These two statements are equal only when
consumers’ total demand for LTC services would not change with or without private LTC
insurance.
On the one hand, the PLTC program should reduce the number of potential Medi-
caid recipients since it transfers Medicaid’s responsibility to private insurance, especially
at individuals’ initial phase of LTC. On the other hand, since the PLTC program can be
thought of as an asset protection technique, it may induce more relative healthier and
wealthier seniors who do not have an immediate need for LTC stepping into LTC ser-
vices earlier. Besides, health insurance literature has shown the reverse impact of health
insurance on healthcare spending (the “moral hazard” problem). If that is the case, we
have a good reason to believe that individuals who purchase LTC insurance will overuse
LTC services and rely more on Medicaid.
These countervailing directions produce unpredictable effects of the PLTC program
on Medicaid coverage. To facilitate the study of the PLTC program’s impact on Medicaid,
I use the point of use of Medicaid as the measurement of consumers’ demand for Medi-
caid. Because the population purchasing insurance during their 60s will make most of
their LTC claims when they at least get into 70s, we need panel data with an extensive pe-
riod to observe individuals’ responses after many years of adopting the PLTC program.
Therefore, in this section, I limit my analysis to the 1994-2004 waves of the HRS. During
this period, all observable changes in adoption of the PLTC program by the four original
PLTC states (pilot states) occurred by 1994, which helps us examine the program’s long-
term effect. Besides, I focus on the elderly group during my study period, as this is the
primary age range for enrolling in Medicaid. One would expect that the later the survey
85
is conducted, the larger proportion of the elderly population would have been exposed
to the PLTC program, and the impact of the program on Medicaid would be more salient.
DID Estimate
The PLTC program was originally implemented in four states by 1994, and the other
remaining states were not allowed to adopt the PLTC program until 2005. This allows me
to use standard DID design to examine the effect of the PLTC program on the usage of
Medicaid. I run the following model specification:
Y
ist
=Pilot
s
Post
t
+
X
it
+
s
+
t
+
r
t +
ist
(3.3)
in which Pilot
s
is an indicator for whether the state is the original four states adopting
the program. Post
t
is an indicator if the year is after 1994. As in Equation (3.1), I control
for state fixed effects and year fixed effects. All estimates are adjusted by personal-level
weights, and standard errors are clustered at the state level.
Due to the time limitation of the HRS dataset, I only have one period before the policy,
making it impossible to test the parallel trends assumption. To make my estimation on
Medicaid reasonable, I first recheck the PLTC program’s impact on LTC insurance within
this new study period. If the new estimators are comparable to those in section 3.5.1,
we will have more confidence to estimate the program’s effect on Medicaid. As in sec-
tion 3.5.1, I exploit the program’s impact separately for the near-elderly and the elderly
population.
Table 3.4 reports estimates of the impact on the near-elderly population. Considering
the importance of dynamic treatment effects, as shown in columns (1) to (5), I split the
post-period into five separate groups by the survey year and compare each survey year
with 1994. The homogeneous DID estimator is reported in the last column. The findings
are very similar to what I have found in section 3.5.1. Estimates increase slowly after
86
the implementation of the PLTC program. After four years of exposure to the program,
the near-elderly LTC insurance coverage rises by 4.1 percentage points, and the positive
effects persist even after ten years (2.7 percentage points). These estimates’ consistency
strengthens our belief that this new specification does not suffer from differential trends
between pilot states and non-pilot states. Besides, these findings show the long-term
positive effects of the PLTC program on the purchase of LTC insurance and, therefore,
complements the earlier evidence that only reports the program’s short-term effects.
Similarly, the PLTC program’s impact on LTC purchases among the elderly contin-
ues to be insignificant. As shown in Table 3.5, the effects of the PLTC program on LTC
purchases are all insignificant, with or without considering dynamic treatment effects.
This evidence is consistent with earlier estimation. It also suggests that the PLTC pro-
gram does not change the preferences of the elderly regarding the LTC services. If we
find any effects of the PLTC program on Medicaid coverage, it should work only through
the mechanism that the program influences the near-elderly population in treated states.
When these near-elderly grow old, their behavior concerning Medicaid, therefore, could
be different from their peers living in control states.
The critical evidence of the PLTC program on the usage of Medicaid is presented in
Table 3.6. The homogeneous DID estimator is reported in the last column. The overall
DID estimate is positive and significant, suggesting that the PLTC program leads to an
increase in the usage of Medicaid. If we look at dynamic treatment effects that are pre-
sented in columns (1) to (5), I still find that the PLTC program’s impact on Medicaid is
positive and evolves over time. The usage of Medicaid rises by 3% percentage point in
both 2002 and 2004, during which we would expect a larger proportion of the elderly
population has been exposed to the PLTC program.
Contrary to the policy intention to reduce individuals’ reliance on Medicaid, this ev-
idence is consistent with the previous hypothesis that the PLTC program induces more
seniors to step into LTC services earlier or the use of LTC insurance presents a significant
87
”moral hazard” problem. Under both hypotheses, individuals who purchased LTC insur-
ance when they were young are more likely to use LTC services. When they used up their
private LTC insurance benefits, they have to rely on Medicaid.
3.5.2 Robustness Checks and Placebo Tests
In this section, I address two potential concerns with my main identification strategy.
First, to check if my analysis is sensitive to the choice of regression sample, I present two
robustness tests. The first table confirms robustness around my definition of the elderly
population. In the primary analysis, I define the elderly population as those aged 70 and
above. In Table 3.7, I instead alter the definition of the elderly to individuals aged 75
and above. As seen from Table 3.7, narrowing the regression sample and the definition
of the elderly population, the results of the PLTC program’s impact on Medicaid are all
positive. Although the sample size is much smaller, which may result in less statistical
power, I still found that in 2004, after ten years of adopting the PLTC program, the usage
of Medicaid increases by 3.1 percentage points significantly. On the other hand, I did not
find that the PLTC program brings any changes to LTC insurance coverage (as shown
in Table 3.8). These findings are consistent with the baseline results. Second, keeping
my baseline definition of the targeted elderly population, I instead alter the regression
sample to individuals with assets larger than $5000. As seen from Table 3.9, the results
are consistent with the baseline results with a narrower regression sample.
Besides, one may be concerned that positive effects on private LTC insurance coverage
among the near-elderly population are due to other reasons instead of the PLTC program.
For example, these near-elderly individuals happen to have increased interest in the in-
surance industry. To address this concern, I use whether the individual is covered by life
insurance as the outcome. I run both the event-study specification spanning 2000-2010
and DID estimation through 1994-2004. As shown in Table 4.8 and Table 4.9, the effects of
the PLTC program on life insurance are insignificant in all specifications.
88
3.6 Mechanism
Section 4.5 shows that the PLTC program drives individuals aged 50-65 to purchase
private LTC insurance. However, when this near-elderly population grows old, they rely
more on Medicaid. These findings are contrary to our intuition since Medicaid only reim-
burses LTC expenditures when the individual runs out of his insurance benefits. Hence,
one would expect less proportion of the elderly population enrolling in Medicaid after the
adoption of the PLTC program. Moreover, these findings are also against the intention of
the PLTC program for alleviating the burden on Medicaid.
To better understand the deviation of empirical findings from the PLTC program’s
intention, in this section, I will propose one hypothesis and use empirical findings to
support it. Specifically, one possible mechanism that incurs this inconsistency is the moral
hazard problem in LTC insurance.
While limited, empirical evidence on the extent of moral hazard in the health insur-
ance context has shown that the gain of health insurance could result in changes in health
behavior that increases the risk or severity of illness.
8
There are theoretical reasons to
believe that LTC insurance coverage, as one type of health insurance, may cause a change
of health behavior among policyholders.
Specifically, I explore this hypothesis by comparing the health behavior of new pur-
chasers (the near-elderly population) living in treated states with their peers living in
control states. Focusing on the near-elderly population is useful because the benefits of
better health behavior may be more salient.
Table 3.12 explores the effect of the PLTC program on different health behaviors, which
may influence the future need for LTC services, focusing on the sample of individu-
8
For example, Klick and Stratmann (2007) find that state-mandated health insurance coverage for the
treatment of diabetes, which is linked to obesity, was associated with higher body mass index among dia-
betics. Empirical evidence in other insurance contexts is more supportive of the existence of a substantial
amount of moral hazard. In the case of automobile insurance, there appears to be a significant reduction
in prevention and an increase in accidents when the generosity of insurance is increased (Chiappori (2000);
Cohen and Dehejia (2004)).
89
als aged 50-65 whose assets above $2000 but below 50th percentile of the population.
Columns (1) and (2) show that the PLTC program reduces a 3.9 percentage points visits in
hospital or 3.8 percentage points in doctor visits. Though the usage of medicines and den-
tist services does not see a significant reduction, through column (5), I find that the PLTC
program also reduces 2.4 percentage points in the usage of home care services. These re-
ductions in health care utilization suggest that the PLTC program may result in changes
in health behavior that increases the risk or severity of illness among these private LTC
insurance purchasers. In the meantime, columns (6) and (7) show that the adoption of the
PLTC program induces 0.17 more nights spending in the nursing home, indicating that
the PLTC program induces more individuals to experience LTC services. This evidence is
consistent with my hypothesis that since the PLTC program can be thought of as an asset
protection technique, it may induce more relative healthier and richer seniors who do not
have an immediate need for LTC to step into LTC services earlier.
3.7 Conclusion
As the number of elderly Americans increases, LTC needs and costs are likely to grow.
Many believe that private LTC insurance can and should play a more significant role in
financing LTC services. Wider use of such insurance is expected to shift the burden away
from state Medicaid programs, which often serve as a default financier of LTC services.
This paper exploits variation in adopting the Partnership LTC program across states and
over time to determine whether encouraging consumers to invest in LTC insurance can
alleviate state governments’ financial burden.
By analyzing data from the Health and Retirement Study over 16 years, my study
indicates that, to date, implementation of the Partnership LTC program has a positive
impact on private LTC insurance rates on the near-elderly population. With the event-
study specification, I find dynamic treatment effects, suggesting that the PLTC program’s
90
impact evolves over time. However, the effects on the elderly population are insignificant.
These findings indicate that the design of PLTC did not change the traditional barriers in
the access to LTC in the United States, especially affordability and underwriting.
Moreover, when I examine the PLTC program’s long-term effects using pilot states,
I find that the increase in LTC insurance does not guarantee reduced Medicaid spend-
ing. On the contrary, my findings indicate that the PLTC program induces more elderly
individuals to rely on Medicaid. These effects are possibly driven by the moral hazard
problem in LTC insurance: individuals protected from LTC insurance are more likely to
undertake riskier health behavior and overuse LTC services.
Overall, these findings suggest that the success of one policy in reducing state LTC
expenditures depends on the policy’s ability to encourage people with moderate assets,
who would otherwise rely on Medicaid for potential LTC needs, to purchase private in-
surance and not to change their health behavior. Suppose the policy serves primarily to
provide asset insurance for wealthier individuals who could otherwise afford to pay out-
of-pocket or purchase other private LTC insurance. In that case, savings of government
funds will not be realized.
91
Tables
Table 3.1: Effective Date of the PLTC Program by State
State Effective Date State Effective Date
Alabama March 2009 Montana July 2009
Alaska Not Filed Nebraska July 2006
Arizona July 2008 Nevada January 2007
Arkansas July 2008 New Hampshire February 2010
California Pilot State New Jersey July 2008
Colorado January 2008 New Mexico August 2019
Connecticut Pilot State New York Pilot
Delaware November 2011 North Carolina March 2011
Florida January 2007 North Dakota January 2007
Georgia January 2007 Ohio September 2007
Hawaii Not Filed Oklahoma July 2008
Idaho November 2006 Oregon January 2008
Illinois 2019 Pennsylvania September 2007
Indiana Pilot State Rhode Island July 2008
Iowa January 2010 South Carolina January 2009
Kansas April 2007 South Dakota July 2007
Kentucky June 2008 Tennessee October 2008
Louisiana October 2009 Texas March 2008
Maine July 2009 Utah October 2014
Maryland January 2009 Vermont 2020
Massachusetts 2020 Virginia September 2007
Michigan February 2016 Washington January 2012
Minnesota July 2006 West Virginia July 2010
Mississippi Not Filed Wisconsin January 2009
Missouri August 2008 Wyoming July 2009
NOTES: Illinois, Massachusetts, and Vermont are three states that I can only collect adopted year informa-
tion
92
Table 3.2: Summary Statistics: Near-elderly (50-64 )and Elderly (70+) samples
Near-Elderly Elderly
Variable Mean Std.dev. Mean Std.dev.
PLTC state 0.291 0.454 0.265 0.441
LTC insurance 0.089 0.285 0.13 0.336
Medicaid 0.025 0.157 0.047 0.211
Age 57.638 3.729 78.467 5.69
Unmarried 0.26 0.439 0.461 0.498
Male 0.483 0.5 0.423 0.494
White 0.866 0.34 0.916 0.277
Less than high school 0.124 0.33 0.272 0.445
Poor health status 0.194 0.396 0.313 0.464
Cancer 0.073 0.259 0.185 0.388
Diabetes 0.124 0.33 0.167 0.373
And ADLs/IADLs 0.118 0.322 0.284 0.451
Number of children 2.842 1.86 3.083 2.174
Assets ($K) 453.782 1131.663 430.542 985.896
93
Table 3.3: First-Stage Estimates: The Impact of the PLTC program on LTC Coverage Rates
Dependent Variable Private LTC Insurance Coverage Rates
Near-Elderly Elderly
(1) (2) (3) (4)
A. Two-way Fixed Effect (TWFE) Estimates
PLTC 0.008 0.001 0.005 -0.001
(0.009) (0.013) (0.009) (0.006)
B. Grouped Event Study Estimates
Pre-PLTC:
(Years -6) Treat -0.015 -0.011 -0.008 0.003
(0.012) (0.019) (0.011) (0.008)
(Years -4) Treat -0.008 -0.012 -0.002 0.000
(0.007) (0.010) (0.007) (0.005)
Post-PLTC:
(Years -0) Treat 0.004 0.002 0.004 -0.002
(0.010) (0.014) (0.007) (0.006)
(Years -2) Treat 0.009 0.011 0.007 -0.001
(0.011) (0.018) (0.011) (0.009)
(Years -4) Treat 0.034** 0.065** 0.014 -0.014
(0.016) (0.024) (0.021) (0.018)
Post utilization in PLTC
states
0.112 0.169
Year FE Yes Yes Yes Yes
State FE Yes Yes Yes Yes
Region Trend Yes Yes Yes Yes
Individual FE No Yes No Yes
Additional controls Yes No Yes Yes
Weights Yes Yes Yes Yes
Observations 29677 29677 29471 29471
R-squared 0.040 0.692 0.079 0.850
NOTES: This table only reports comparison between non-pilot states during the recent adoption
of the PLTC program. All regression reported controls for: age, gender, marital status, years of ed-
ucation, White, self-reported health, cancer, diabetes, any ADLs/IADLs, and number of children.
When fixed effects are included, controls that not time varying are dropped. Individual weighting
is used to represent the whole population. Results with no weighting are very similar. Robust
standard errors, clustered at the state level, are in parentheses. (*** p<0.01, ** p<0.05, * p<0.1)
94
Table 3.4: DID Estimates of the PLTC Program’s Impact on LTC Coverage Rates (50-64)
Dependent Variable LTC Insurance Coverage (Near-Elderly)
Post Years 1996 1998 2000 2002 2004 Overall
(1) (2) (3) (4) (5) (6)
Pilot Post 0.014 0.014 0.041** 0.001 0.027** 0.021
(0.014) (0.019) (0.019) (0.016) (0.013) (0.013)
Post utilization in PLTC states 0.118 0.090 0.104 0.096 0.122 0.106
Additional controls Yes Yes Yes Yes Yes Yes
Year FE Yes Yes Yes Yes Yes Yes
State FE Yes Yes Yes Yes Yes Yes
Region Trend Yes Yes Yes Yes Yes Yes
Weights Yes Yes Yes Yes Yes Yes
Observations 14943 16250 14887 13505 14961 42822
R-squared 0.049 0.051 0.058 0.048 0.049 0.033
NOTES: This table reports comparison between pilot and non-pilots states during the first adop-
tion of the PLTC program (1994). All regression reported controls for: age, gender, marital status,
years of education, White, self-reported health, cancer, diabetes, any ADLs/IADLs, and number
of children. When fixed effects are included, controls that not time varying are dropped. Indi-
vidual weighting is used to represent the whole population. Results with no weighting are very
similar. Robust standard errors, clustered at the state level, are in parentheses. (*** p<0.01, **
p<0.05, * p<0.1)
95
Table 3.5: DID Estimates of the PLTC Program’s Impact on LTC Coverage Rates (70+)
Dependent Variable LTC Insurance Coverage (Elderly)
Post Years 1996 1998 2000 2002 2004 Overall
(1) (2) (3) (4) (5) (6)
Pilot Post -0.024 -0.011 -0.018 -0.020 -0.015 -0.017
(0.022) (0.022) (0.023) (0.023) (0.020) (0.020)
Post utilization in PLTC states 0.100 0.119 0.118 0.136 0.139 0.056
Additional controls Yes Yes Yes Yes Yes Yes
Year FE Yes Yes Yes Yes Yes Yes
State FE Yes Yes Yes Yes Yes Yes
Region Trend Yes Yes Yes Yes Yes Yes
Weights Yes Yes Yes Yes Yes Yes
Observations 10862 11530 11415 11470 11607 34448
R-squared 0.041 0.042 0.047 0.047 0.051 0.056
NOTES: This table reports comparison between pilot and non-pilots states during the first adop-
tion of the PLTC program (1994). All regression reported controls for: age, gender, marital status,
years of education, White, self-reported health, cancer, diabetes, any ADLs/IADLs, and number
of children. When fixed effects are included, controls that not time varying are dropped. Indi-
vidual weighting is used to represent the whole population. Results with no weighting are very
similar. Robust standard errors, clustered at the state level, are in parentheses. (*** p<0.01, **
p<0.05, * p<0.1)
96
Table 3.6: DID Estimates of the PLTC Program’s Impact on Medicaid Coverage Rates
(70+)
Dependent Variable Medicaid Coverage (Elderly)
Post Years 1996 1998 2000 2002 2004 Overall
(1) (2) (3) (4) (5) (6)
Pilot Post 0.004 0.016 0.014 0.032* 0.030** 0.020**
(0.008) (0.013) (0.019) (0.016) (0.013) (0.009)
Post utilization in PLTC states 0.091 0.094 0.097 0.097 0.101 0.096
Additional controls Yes Yes Yes Yes Yes Yes
Year FE Yes Yes Yes Yes Yes Yes
State FE Yes Yes Yes Yes Yes Yes
Region Trend Yes Yes Yes Yes Yes Yes
Weights Yes Yes Yes Yes Yes Yes
Observations 5152 5255 5152 5173 5128 14900
R-squared 0.121 0.127 0.117 0.118 0.141 0.131
NOTES: This table reports comparison between pilot and non-pilots states during the first adop-
tion of the PLTC program (1994). All regression reported controls for: age, gender, marital status,
years of education, White, self-reported health, cancer, diabetes, any ADLs/IADLs, and number
of children. When fixed effects are included, controls that not time varying are dropped. Indi-
vidual weighting is used to represent the whole population. Results with no weighting are very
similar. Robust standard errors, clustered at the state level, are in parentheses. (*** p<0.01, **
p<0.05, * p<0.1)
97
Table 3.7: Robustness Check: DID Estimates of the PLTC Program’s Impact on Medicaid
Coverage Rates (75+)
Dependent Variable Medicaid Coverage (75+)
Post Years 1996 1998 2000 2002 2004
(1) (2) (3) (4) (5)
Pilot Post 0.016 0.015 0.007 0.020 0.031*
(0.013) (0.014) (0.023) (0.021) (0.018)
Additional controls Yes Yes Yes Yes Yes
Year FE Yes Yes Yes Yes Yes
State FE Yes Yes Yes Yes Yes
Region Trend Yes Yes Yes Yes Yes
Weights Yes Yes Yes Yes Yes
Observations 3811 3752 3744 3696 3611
R-squared 0.131 0.141 0.127 0.121 0.138
NOTES: This table reports comparison between pilot and non-pilots states during the first adop-
tion of the PLTC program (1994). All regression reported controls for: age, gender, marital status,
years of education, White, self-reported health, cancer, diabetes, any ADLs/IADLs, and number
of children. When fixed effects are included, controls that not time varying are dropped. Indi-
vidual weighting is used to represent the whole population. Results with no weighting are very
similar. Robust standard errors, clustered at the state level, are in parentheses. (*** p<0.01, **
p<0.05, * p<0.1)
98
Table 3.8: Robustness Check: DID Estimates of the PLTC Program’s Impact on LTC Cov-
erage Rates (75+)
Dependent Variable LTC Insurance Coverage (75+)
Post Years 1996 1998 2000 2002 2004
(1) (2) (3) (4) (5)
Pilot Post -0.042 -0.020 -0.033 -0.006 -0.052
(0.029) (0.034) (0.031) (0.035) (0.037)
Additional controls Yes Yes Yes Yes Yes
Year FE Yes Yes Yes Yes Yes
State FE Yes Yes Yes Yes Yes
Region Trend Yes Yes Yes Yes Yes
Weights Yes Yes Yes Yes Yes
Observations 3672 3606 3620 3578 3500
R-squared 0.056 0.054 0.062 0.051 0.047
NOTES: This table reports comparison between pilot and non-pilots states during the first adop-
tion of the PLTC program (1994). All regression reported controls for: age, gender, marital status,
years of education, White, self-reported health, cancer, diabetes, any ADLs/IADLs, and number
of children. When fixed effects are included, controls that not time varying are dropped. Indi-
vidual weighting is used to represent the whole population. Results with no weighting are very
similar. Robust standard errors, clustered at the state level, are in parentheses. (*** p<0.01, **
p<0.05, * p<0.1)
99
Table 3.9: Robustness Check: DID Estimates of the PLTC Program’s Impact on Medicaid
Coverage Rates (Asset> 5000)
Dependent Variable Medicaid Coverage (Higher Asset)
Post Years 1996 1998 2000 2002 2004
(1) (2) (3) (4) (5)
Pilot Post 0.000 0.017 0.022 0.030** 0.027*
(0.012) (0.012) (0.017) (0.014) (0.016)
Additional controls Yes Yes Yes Yes Yes
Year FE Yes Yes Yes Yes Yes
State FE Yes Yes Yes Yes Yes
Region Trend Yes Yes Yes Yes Yes
Weights Yes Yes Yes Yes Yes
Observations 4770 4917 4843 4862 4801
R-squared 0.121 0.128 0.118 0.123 0.148
NOTES: This table reports comparison between pilot and non-pilots states during the first adop-
tion of the PLTC program (1994). All regression reported controls for: age, gender, marital status,
years of education, White, self-reported health, cancer, diabetes, any ADLs/IADLs, and number
of children. When fixed effects are included, controls that not time varying are dropped. Indi-
vidual weighting is used to represent the whole population. Results with no weighting are very
similar. Robust standard errors, clustered at the state level, are in parentheses. (*** p<0.01, **
p<0.05, * p<0.1)
100
Table 3.10: Placebo Test: Event-Study Estimates of the PLTC Program’s Impact on Life
Insurance Coverage Rates
Dependent Variable Life Insurance Coverage
Near-Elderly
(1) (2)
Grouped Event Study Estimates
Pre-PLTC:
(Years -6) Treat 0.027 0.003
(0.018) (0.025)
(Years -4) Treat 0.003 -0.005
(0.012) (0.015)
Post-PLTC:
(Years -0) Treat -0.005 -0.008
(0.013) (0.018)
(Years -2) Treat -0.015 -0.015
(0.017) (0.020)
(Years -4) Treat -0.020 -0.004
(0.026) (0.043)
Year FE Yes Yes
State FE Yes Yes
Region Trend Yes Yes
Individual FE No Yes
Additional controls Yes No
Weights Yes Yes
Observations 29926 29926
R-squared 0.086 0.750
NOTES: This table only reports comparison between non-pilot states during the recent adoption
of the PLTC program. All regression reported controls for: age, gender, marital status, years of ed-
ucation, White, self-reported health, cancer, diabetes, any ADLs/IADLs, and number of children.
When fixed effects are included, controls that not time varying are dropped. Individual weighting
is used to represent the whole population. Results with no weighting are very similar. Robust
standard errors, clustered at the state level, are in parentheses. (*** p<0.01, ** p<0.05, * p<0.1)
101
Table 3.11: Placebo Test: DID Estimates of the PLTC Program’s Impact on Life Insurance
Coverage Rates
Dependent Variable Life Insurance Coverage
Post Years 1996 1998 2000 2002 2004
(1) (2) (3) (4) (5)
Pilot Post 0.004 -0.003 0.010 -0.006 0.021
(0.013) (0.010) (0.012) (0.017) (0.018)
Additional controls Yes Yes Yes Yes Yes
Year FE Yes Yes Yes Yes Yes
State FE Yes Yes Yes Yes Yes
Region Trend Yes Yes Yes Yes Yes
Weights Yes Yes Yes Yes Yes
Observations 15042 16495 14997 13541 15000
R-squared 0.082 0.081 0.084 0.085 0.091
NOTES: This table reports comparison between pilot and non-pilots states during the first adop-
tion of the PLTC program (1994). All regression reported controls for: age, gender, marital status,
years of education, White, self-reported health, cancer, diabetes, any ADLs/IADLs, and number
of children. When fixed effects are included, controls that not time varying are dropped. Indi-
vidual weighting is used to represent the whole population. Results with no weighting are very
similar. Robust standard errors, clustered at the state level, are in parentheses. (*** p<0.01, **
p<0.05, * p<0.1)
102
Table 3.12: Mechanisms: Health Behavior Changes After the PLTC Program
Dependent Variable
All Post Years Hospital Stays Doctor Visit Drugs Dentist Home Health Care Nursing Home Stay # Nursing Home Nights
(1) (2) (3) (4) (5) (6) (7)
Pilot Post -0.039*** -0.038* -0.038 -0.227 -0.024*** 0.001 0.170**
(0.012) (0.021) (0.027) (0.217) (0.006) (0.002) (0.082)
Additional controls Yes Yes Yes Yes Yes Yes Yes
Year FE Yes Yes Yes Yes Yes Yes Yes
State FE Yes Yes Yes Yes Yes Yes Yes
Region Trend Yes Yes Yes Yes Yes Yes Yes
Weights Yes Yes Yes Yes Yes Yes Yes
Observations 18071 17943 18086 14974 18086 18086 18085
R-squared 0.108 0.065 0.174 0.117 0.062 0.026 0.014
NOTES: This table reports comparison between pilot and non-pilots states during the first adop-
tion of the PLTC program (1994). Each column reports estimates based on the pooled post years.
Results with separate post years are very similar. All regression reported controls for: age, gender,
marital status, years of education, White, self-reported health, cancer, diabetes, any ADLs/IADLs,
and number of children. When fixed effects are included, controls that not time varying are
dropped. Individual weighting is used to represent the whole population. Results with no weight-
ing are very similar. Robust standard errors, clustered at the state level, are in parentheses. (***
p<0.01, ** p<0.05, * p<0.1)
103
Chapter 4
The Unintended Consequence of
Partnership Long-Term Care Program on
Labor Market
4.1 Introduction
The Partnership Long-term Care Insurance (PLTC) program is one of the strategies
that attempt to shift long-term care (LTC) costs away from Medicaid, which often serves
as a default financier of LTC services. The PLTC program brings states and private insur-
ers together to create a new insurance product that allows people to sequester a portion
of their assets (equivalent to the value of the LTC insurance policy) from Medicaid as-
set requirements. The elderly are thus protected from having to become impoverished
before becoming eligible for Medicaid. In the meantime, by encouraging consumers to
invest in LTC insurance, this program is expected to shift the burden from state Medicaid
programs by having individuals take responsibility for the initial phase of their long-term
care through the use of private insurance.
While the PLTC program was designed to expand private LTC insurance coverage and
104
alleviating states’ burden to pay for LTC services, the program’s asset protection feature
may have unintended effects on the labor force. Specifically, as I have shown in my sec-
ond chapter, the PLTC program successfully increases private LTC insurance purchases
among individuals aged between 50 and 64 (defined as the near-elderly population). If,
as suggested by Ameriks et al. (2020), older Americans have a strong willingness to work,
then it is reasonable for us to infer that those near-elderly individuals who purchased LTC
insurance may increase labor force participation. They can save more than before the ex-
pansion of the PLTC program and remain eligible for Medicaid due to the higher asset el-
igibility threshold. On the other hand, since the near-elderly individuals who purchased
LTC insurance would face less medical expense uncertainty and rely on private/public
health insurance to finance their health care, their real lifetime income increases. Under
this circumstance, they will view earlier retirements as both desirable and affordable.
These countervailing directions produce unpredictable effects of the PLTC program on
older worker’s labor force participation. In this paper, I use data spanning the recent state
adoptions of the PLTC program to examine the consequences of the PLTC program on
labor market outcomes among the near-elderly population. With the passing of the 2005
Deficit Reduction Act (DRA), all states were given the option of creating PLTC programs.
At the time of 2010, 38 states adopted PLTC programs. Thus, the variation in the adoption
of the PLTC program across states and over time provides us a quasi-experiment setting
to examine this research question.
Earlier evidence of the PLTC program has mainly focused on its short-term impact on
private LTC coverage, which is essential for the optimal design of such programs whose
main purpose is to reduce Medicaid expenditures by incentivizing LTC insurance pur-
chases. However, this is not the whole story. As the PLTC program raises the qualification
threshold of Medicaid assets and reduces the uncertainty of future medical expenses, it
would affect labor supply decisions based on the preventive savings model (Gruber and
Yelowitz, 1999; Maynard and Qiu, 2009; Gallagher et al., 2020). Therefore, I expand the lit-
105
erature and consider how welfare benefits affect the career of older workers through this
channel, beyond the gradual changes in private LTC insurance coverage. As far as I know,
this study is the first to use empirical identification to study the unintended consequences
of the PLTC program on labor force participation.
Using data from the Health and Retirement Study (HRS) from 2000 to 2010, I test
whether the presence of the PLTC program affects labor force participation among older
workers. I find that the presence of the PLTC program increases full-time work status
by 2-7 percentage points for individuals aged between 50 to 65. Most of this effect is
driven by individuals whose assets are above $2000. I find no impact on individuals
aged above 70 or below 50. These findings are consistent with the fact that most of the
PLTC program’s effects on LTC insurance purchasing are concentrated on the near-elderly
population. The relevant margin for this PLTC program is those with relatively higher
assets than traditional Medicaid asset cut-offs.
To understand the reason behind these findings, I supplement my analysis by propos-
ing a theoretical model based on the standpoint of the bequest motive. The model sug-
gests that only when individuals whose labor market conditions are favorable, the more
assets they want to bequeath to their children, the more likely they will join the labor
market. On the contrary, if the individual is in low-paid jobs, he would prefer to receive
government transfers and enjoy leisure. The results from the sub-population analysis
suggest that the mechanism through which the PLTC program affects labor force partic-
ipation is through the bequest motive: the effects are concentrated among individuals
with kids who are in well-paid jobs. This finding is consistent with previous literature
studying saving behavior among the elderly (De Nardi, 2004; Kopczuk and Lupton, 2007;
De Nardi et al., 2010).
The rest of this paper is organized as follows. Section 4.2 provides more details with
the relevant literature. Section 4.3 provides the institutional details of the Partnership LTC
program and the labor market among older workers. Section 4.4 and Section 4.5 describes
106
the data and presents the empirical strategy and the main results. Section 4.6 proposes a
theoretical model explaining the reason behinds the empirical results. Finally, I conclude
in Section 4.7.
4.2 Literature
The findings in this paper contribute to several strands of the economics literature.
First, there have been limited evaluations of the Partnership programs’ budgetary impact.
The Department of Health and Human Services (HHS) assumed that the program was at
least budget neutral, with opportunities for savings. It provides an alternative way for
policyholders to transfer assets and apply their income from protected assets to the cost of
care (Meiners, 2009). A Government Accountability Office study (GAO, 2007) finds that
Medicaid savings were not likely but that costs to Medicaid would be minimal because
it assumed that many participants would still be too wealthy to qualify for Medicaid.
The GAO study also assumed that policyholders do not over-insure their assets, which
constitute a significant source of potential savings. It also took that people do not often
transfer their assets to qualify for Medicaid (GAO, 2007; Meiners, 2009).
In comparison, more cost-benefit studies have been conducted on tax incentive pro-
grams. In 1996, Congress passed the Health Insurance Portability and Accountability Act
(HIPAA), which allows federal tax relief for the cost of LTC insurance. Courtemanche and
He (2009) found that the plan represents a net loss to the federal government’s budget.
Since HIPAA, many states have allowed state tax deductions for LTC insurance expenses.
Goda (2011) analyzed the impact of these subsidies and found that they represent the net
loss of the state government.
This paper adds to this strand of the literature by considering the second-order effects
of the PLTC program. With evidence showing that the PLTC program increases the labor
force participation among older workers without affecting job opportunities for other age
107
groups, it could be the potential channel to improve government’s finance. On the one
hand, encouraging more people to work can boost fiscal revenue for the government. On
the other hand, more older workers on the labor market means that fewer people are
receiving social security and thus reduce the government’s spending. In sum, this study
sheds new light on this problem from a new perspective and shows that the second-order
effects should be taken into account for designing optimized government spending for
LTC services.
Second, a substantial body of empirical work examines the link between health in-
surance and household savings. From the precautionary savings view, there should be a
positive association between insurance and savings. In an influential paper, Gruber and
Yelowitz (1999) find evidence supporting a precautionary savings effect. They analyze
the 1984–93 period, when several states expanded Medicaid to children and pregnant
women, and find that Medicaid eligibility for children reduces household net worth and
increases consumption. According to their analysis, asset tests for Medicaid eligibility
more than double the negative impact of Medicaid on net worth. Gallagher et al. (2020)
explores variation in Medicaid eligibility across income and state from the Affordable
Care Act (ACA) and shows that households that are not experiencing financial hardship
behave in a manner consistent with a precautionary savings model, meaning they save
less under Medicaid. This paper takes advantage of these points of view and discusses
another important dimension of household financial well-being, labor force participation,
and tries to provide empirical evidence for the dispute about relaxing public health in-
surance asset restrictions for older workers.
4.3 Policy Background
This section provides details on Medicaid in the United States, the details of the Part-
nership LTC program, and the labor market environment for older workers.
108
4.3.1 Medicaid Long-Term Care
Medicaid LTC is a means-tested, joint federal-state program that provides health in-
surance for the frail elderly population. In 2016, an estimated 62% of long-term care users
residing in nursing homes had Medicaid as a payer source (Harris-Kojetin et al., 2019).
Medicaid LTC, therefore, acts as one major avenue through which the elderly can insure
themselves against the uncertainty of long-term care costs. However, not all older indi-
viduals are eligible. Eligibility for Medicaid LTC requires that an individual’s income and
assets fall below defined thresholds. Though eligibility tests vary by marital status and
state, minimum eligibility requirements are determined at the federal level. Traditionally,
all states have an asset limit for Medicaid LTC, which, generally speaking, is $2,000. Med-
icaid applicants who have countable assets greater than $2,000 must ”spend down” the
extra holdings to meet Medicaid’s asset limit, and hence, qualify for Medicaid LTC.
4.3.2 The Partnership for Long-Term Care
The Partnership LTC Program is a collaboration between private LTC insurance com-
panies and a state’s Medicaid program. The PLTC program was designed to attract con-
sumers who may not otherwise purchase LTC insurance. States provide guarantees that
if benefits under a PLTC policy are insufficient to cover the cost of care, the consumer
may be eligible for Medicaid under special eligibility rules while retaining a pre-specified
amount of asset (though income and functional eligibility rules still apply). For example,
suppose an individual has a PLTC policy that paid out $100,000 in LTC services for him.
Since his policy paid out $100,000, an equal amount ($100,000) is protected from Medi-
caid’s asset limit. Remember, Medicaid’s asset limit is $2,000, meaning that this individ-
ual is entitled to $2,000 in assets, plus the $100,000 that is protected, allowing him to retain
$102,000 total in assets. Thus, consumers are protected from having to become impover-
ished to qualify for Medicaid, and states avoid the full burden of LTC costs. Through the
109
PLTC program, if additional LTC coverage is required (beyond the scope provided by the
policy), states can provide consumers with Medicaid in accordance with special eligibil-
ity rules to promote the purchase of private LTC insurance. In turn, Medicaid benefits by
using private insurance to hold individuals accountable for the initial stages of their LTC.
This unique insurance model was developed in the 1980s with the support of the
Robert Wood Johnson Foundation (RWJF). The initial demonstration models have been
in California, Connecticut, Indiana, and New York since 1993. However, due to concerns
about the appropriateness of using Medicaid funds for this purpose, Congress imposed
restrictions on the further development of PLTC in the Omnibus Budget Reconciliation
Act (OBRA) of 1993. The four states with existing PLTC programs were allowed to con-
tinue, but the OBRA clause ended the replication of the partnership model in new states.
In 2005, the Deficit Reduction Act (DRA) removed the barriers imposed by Congress on
such programs and allowed the partnership program to be extended to other states across
the country. So far, all states except Alaska, Hawaii, and Mississippi now have PLTC pro-
grams.
1
4.3.3 Labor Market Environment for Older Workers
The labor force participation rates of older Americans fell for nearly four decades after
World War II. Many factors contributed to that decline, including the provision of Social
Security retirement benefits, the provision of employer-provided pension plans, the emer-
gence of Medicare in 1965 to finance health care for the aged, and continued economic
growth that has increased real lifetime income. Therefore, Therefore, the combination of
longer lifespan and early retirement has greatly increased policymakers’ concerns about
the affordability of government expenditures. The aging of the population implies that
the ratio of workers to retirees is declining. The Social Security Board of Trustees (2011)
predicts that assets of the combined Social Security trust funds will be fully exhausted in
1
See https://www.medicaidplanningassistance.org/partnerships-for-long-term-care/
110
2036.
Consequently, the government is considering pension reforms to reduce retirement
benefits and raise the statutory retirement age. As the Social Security full retirement age
increases, the benefit reduction for retirement at earlier ages increases, reducing the bene-
fit amount payable each month. Besides, in recent years, about half of the workforce does
not have an employer-provided pension since rapidly rising costs of health insurance.
Lastly but not the least, many workers have not saved adequate resources for retirement
as the consequence of the low personal saving rate. Therefore, it is unsurprising that re-
cent surveys show that large numbers of younger workers and near-retirees appear to
have inadequate retirement resources and lack confidence about their long-range finan-
cial status (Helman et al., 2011).
Due to these factors, many public officials and financial planners encourage people to
work longer and delay applying for social security benefits. This strategy shortens the
retirement period that needs to be funded and can generate additional savings. How-
ever, the policy reform to increase the statutory retirement age is difficult to implement
for two main reasons. The first concern is that raising the statutory retirement age is
not an effective policy tool because the employment opportunities for older workers are
weak. Therefore, raising the retirement age is unlikely to increase the employment of
older workers. On the contrary, it will increase unemployment benefits and disability
benefits wages. Second, raising the statutory retirement age is unfair because it limits
the opportunity set of workers with the weakest labor market position and does not re-
strict unaffected workers whose labor market conditions are more favorable (Staubli and
Zweim ¨ uller, 2013).
111
4.4 Data
For the empirical analysis, I merge two types of data: (1) survey data on labor force
outcomes, and (2) state policies and state time-varying variables over time.
To explore the impact of the PLTC program on labor force participation among older
workers, I use the data from the Health and Retirement Study (HRS) conducted by the
University of Michigan. The HRS dataset is a nationally representative dataset that tracks
households age 50 and above biennially. It provides detailed information on basic de-
mographic characteristics, health and functioning, health care and insurance, medical
expenses, and assets. Most of the data come from the RAND HRS data files, which are
derived from all waves of HRS by the RAND Center with cleaned and consistent vari-
ables. Variables regarding LTC coverage and other insurance-related variables, such as
life insurance coverage, are from the original HRS data. Besides, I supplement these
public-use files by adding state-of-residence information from the restricted HRS data
with permission from the HRS administration. Using state information is crucial for my
analysis because PLTC policies differ remarkably across states.
Based on my findings in the second chapter, individuals between 50 and 65 years of
age is the primary subjects purchasing LTC insurance because of the PLTC policy. They
are also active in the labor market. Therefore, I focus on the sample of individuals be-
tween 50 and 65 years of age during my study period. I use individuals aged over 70
or below 50 only as robustness checks. Besides, since individuals with assets larger than
$2000 are most likely affected by the PLTC program, I focus on the sample of individuals
with assets of at least $2000 each year.
I limit my analysis to the 2000-2010 waves of the HRS mainly for two reasons. First,
since all observable changes in the adoption of the PLTC program by the states occurred
after 2005, using data spanning before and after the growth in adoptions from the DRA
can help me test the parallel trends assumption and look at longer-term effects. Second,
112
recent expansions in Medicaid from the Affordable Care Act (ACA) were implemented
starting from 2010. Their effects on reducing ”employment lock” among childless adults
who were previously ineligible for public coverage may also impact the work motivation
of the near-elderly population. Therefore, using the data period before the ACA helps
me capture the policy effects only from the PLTC program. Notably, one would expect
differences between those states that adopted the program in the 1990s (original pilot
states) and the states that did so after 2005. Therefore, I further limit my analysis to
non-pilot states. Ultimately, the main sample (the near-elderly population) I use for my
empirical results covers 24,892 unique individuals with a total of 32,086 observations.
I merged the HRS data with policy data regarding the implementation of the PLTC
program. For state PLTC programs, I collect policy data regarding the implementation
of the PLTC program. For state PLTC programs, I collect state-level information from
various sources about whether the PLTC program has been implemented for a given state
until 2021.
2
To construct a reliable measure for the implementation of the PLTC program,
I take into account that the HRS survey was conducted biannually throughout the survey
year. I acquire information about the month of the year when each survey was conducted
for each respondent. Together with the exact month and year of policy implementation,
I can pin down how long the individual was exposed to PLTC program in each specific
state. As illustrated in Table 4.1, four states had PLTC programs in place by 1994. In 2006,
three more states had PLTC programs in place; by 2008, 27 states had adopted them; by
2010, 38 states had PLTC programs.
To control state-specific time-varying variables that may affect labor force outcomes,
I collect data about state characteristics in 2000, including the log of the population and
the percentage of the population identified as black, aged greater than 65, and in poverty
from Census Bureau and Bureau of Labor Statistics.
2
Most of the policy data during 1990-2014 were collected from https://www.aaltci.org/long-term-care-
insurance/learning-center/long-term-care-insurance-partnership-plans.php. This part is similar to the
database used by Greenhalgh-Stanley (2014) Each state’s website was also visited to verify the implemented
date.
113
Table 4.2 provides summary statistics of the key variables for the near-elderly group
calculated using individual sampling weights. 60% of the sample lives in a state that has
implemented a PLTC program. 53% of the sample is full-time workers, and 9% of the
sample reports having a part-time job. The sample is mostly white and female. 20% of
the sample reports in poor health status, and 11% reports with LTC insurance.
4.5 Empirical Strategy and Results
4.5.1 Empirical Strategy
In 2005, the Deficit Reduction Act (DRA) lifted the barriers Congress had imposed on
the PLTC program, allowing for the expansion of the Partnership to other states across
the country. Since then (post-DRA), many states have adopted the PLTC policies. This
allows for an analysis that exploits within-state variation to examine the effect of the PLTC
program on various outcomes.
Previous studies of the PLTC program primarily employ the staggered difference-in-
difference (DID) methodology to examine its effects. However, recent work in economet-
ric theory casts doubt on the validity and robustness of staggered DID estimator. The
main reason for the pitfall of the staggered DID design is that such design produces esti-
mates of the variance-weighted average of many different treatment effects. When treat-
ment effects can evolve over time, in the staggered DID approach, already-treated units
can act as effective comparison units. Changes in their outcomes over time are subtracted
from the changes of later-treated units. Therefore, the staggered DID estimates can obtain
the opposite sign compared to the true ATT or ATE (Athey and Imbens, 2018; Goodman-
Bacon, 2018; Sun and Abraham, 2020; Callaway and Sant’Anna, 2020; Baker et al., 2021).
To address this concern and to better adapt the model specification to fluctuations in
the labor market, I run standard DID by comparing post-DRA periods with 2004 when
114
no states adopted the program yet. Specifically, I run the following model specification:
Y
ist
=Treat
s
Post
t
+
X
it
+
s
+
t
+Z
s00
t +
r
t +
ist
(4.1)
in whichi indexes the individual,s the state, andt the year. Treat
s
is an indicator if the
state has adopted the PLTC program. Post
t
is an indicator if the year is after 2004. X
it
is a set of individual characteristics, including age, marital status, education status, self-
reported health status, cancer status, diabetes status, number of children, and assets.Z
s00
is a set of 2000 state characteristics, including the log of the population, the percent of the
population black, the percent of population aged greater than 65, and the percent of the
population in poverty. Besides, I control for state fixed effects and year fixed effects. In
addition, given that the coefficient is likely to overestimate the effect in the presence of
pre-trends, I control for region-level time trends (
r
t) as an alternative specification. All
estimates are adjusted by personal-level weights, and standard errors are clustered at the
state level.
4.5.2 Results
Before presenting the main regression results, I tested for the parallel trends assump-
tion in the DID framework by comparing 2000 and 2002 to 2004. Table 4.3 shows the
results for full-time work status, and Table 4.4 for part-time work status. In both tables, I
run the regressions without controlling for region trends in odd-numbered columns, and
in even-numbered columns, I additionally control for region trends. All coefficients on
the DID term are insignificant, so we can not reject the null hypothesis of parallel trends.
The DID estimates based on equation (4.1) for the full-time work status are presented
in Table 4.5. Except for 2008, DID terms in all post years are significantly positive under
both specifications, suggesting that the PLTC program induces a 2.5-6.9 percentage points
increase in the number of older workers holding a full-time job. Table 4.6 reports effects
115
on the part-time status. Contrary to the full-time job, the results show that the PLTC
program negatively affects part-time job rates, especially in 2006. The coefficients imply
the adoption of the PLTC program induces a 1.2-2.1 percentage point decrease in the
number of individuals working part-time.
These findings indicate that the PLTC program induces more people to work as full-
time workers, with fewer people doing part-time jobs. To check whether these changes
mean that older workers shift from part-time jobs to full-time jobs, I also run specifications
in which the outcome variable equals one if the individual either holds a full-time job
or a part-time job as in Table 4.7. With controlling region trends, the coefficients imply
that the adoption of the PLTC program raises the total labor force participation by 3.0-
5.2 percentage points among older workers. The rise of labor force participation among
older workers suggests that this program encourages individuals to work more, which is
consistent with the hypothesis that an increase in Medicaid asset eligibility threshold and
the reduction of future medical expense uncertainty would affect labor supply decisions.
4.5.3 Placebo Tests
One may be concerned that the positive effects of the PLTC program on labor force
participation are mainly due to the macro environment. For example, states that adopted
the PLTC program happened to have increased demand in the labor market, resulting in
the increment in labor force participation among older workers. To address this concern, I
examine two alternative age groups. First, I present results among a group of individuals
aged below 50 who would experience the same demand change in the labor market. As
seen from Table 4.8, altering the regression sample to the younger cohorts, the results
are all insignificant, suggesting that the changes in labor force participation among older
workers are due to the PLTC program. As a placebo test, I also conduct similar regressions
among individuals aged over 70 during my study period. Since most elderly individuals
should have been retired after 65, we would expect that the coefficients among this age
116
group should be insignificant. As shown in Table 4.9, the results are consistent with this
prediction, suggesting that my empirical specification are valid to examine the impact of
the PLTC program.
Another concern is that though labor demand was similar between treated states and
”not-yet” treated states during the study period, the states that adopted the program
could differ on other policies that push older workers to work, regardless of the PLTC
program’ impacts. To address this concern, I use near-elderly individuals whose assets
below $2000 as a placebo test. These low-asset individuals are at the same age as the main
group, so they should experience a similar job market or macroeconomic background.
However, since their asset level is below $2000, they are not affected before or after the
adoption of the PLTC program because they are always qualified to enroll in Medicaid.
Table 4.10 reports estimates of the effect of living in a state with the PLTC program on la-
bor force participation among the near-elderly population with assets lower than $2000.
None of the estimates are significant, indicating that the changes in labor force participa-
tion among the higher-asset group are not due to the macroeconomic background com-
mon to all older workers.
In sum, the results in this section show that the PLTC program affects the job arrange-
ments of near-elderly individuals, particularly those who have assets larger than $2000
(who are less likely to be qualified to Medicaid without the PLTC policy). The following
section hypothesizes that these effects might be associated with the bequest motives.
4.6 Discussion: The Bequest Motive
Though I find that near-elderly individuals increase labor force participation due to
the PLTC program, it is still unclear why they do that. After all, the near-elderly indi-
viduals who purchased LTC insurance would face less medical expense uncertainty and
easily rely on private/public health insurance to finance their health care. To better un-
117
derstand the benefits of the PLTC program and how it may differ across individuals, this
section first outlines one hypothesis - the bequest motive - describing why older work-
ers may respond to the PLTC program. Then with theoretical analysis, I confirm that the
bequest motive is the reason driving near-elderly individuals to work more.
As mentioned in previous studies, one fundamental reason for explaining the saving
behavior among the elderly is the bequest motive (De Nardi, 2004; Kopczuk and Lup-
ton, 2007; De Nardi et al., 2010). If this is the case, one would expect that near-elderly
individuals without any children should not respond to the PLTC program. Table 4.11
reports estimates of the PLTC program’s impact on labor force participation among child-
less near-elderly individuals. As we predicted, I find no effects of the PLTC program on
childless individual’s labor market outcomes, either for full-time work status or part-time
work status. On the contrary, when I limit my analysis to near-elderly individuals with
children, the results show a different story. Though these individuals who have children
did not change their part-time job status, they increase full-time jobs significantly by 1.8-
7.2 percentage points (as shown in Table 4.12).
These findings show significantly different patterns between individuals with or with-
out children, suggesting that individuals with children are the major group to respond to
the PLTC program. However, one may be concerned about other policies rather than the
PLTC program driving this difference. To address this concern, I illustrate a theoretical
framework to explore why the changes in labor force participation are made due to the
PLTC program.
Consider in a static model where an individual aged 50-64 seeking to maximize his
utility. The individual derives utility from consumption,C, and hours of leisure,L. His
utility function is in the form
U(C;L) =
1
1
(C

L
1
)
1
: (4.2)
118
Individuals with higher values of
place less weight on leisure.
The quality of leisure is
L =THP (4.3)
whereT is the individual’s total time endowment. P denotes participation in the labor
market. I allowP to be a continuous variable, which equals one if the individual takes a
full-time job. WhenP is a fraction number, it means that the individual takes a part-time
job.H is the total working hours if he chooses a full-time job.
The individual decides his optimal consumption with the following form:
C = (TL)wP + (1P )Y
b
MA (4.4)
where w denotes the total wages for a full-time job, Y
b
denotes the benefits or transfers
from the government. M denotes his total medical spending, whileA denotes the asset
he is willing to save for children. IfA equals zero, it means that the individual consumes
every penny.
The research question now is whether individuals who prefer to leave more assets
to their children would be more likely to join the labor market. Based on the implicit
function theory, this question is equivalent to test whether
dP
dA
=
@U
@A
@U
@P
> 0. To test it, we
examine the inequality,
@U
@A
@U
@P
< 0. The nominator can be described as the following:
@U
@A
=
[HwP
2
+ (1P )Y
b
MA]

(1)1
(THP )
(1
)(1)
; (4.5)
and the denominator is as follows:
@U
@P
=
[HwP
2
+ (1P )Y
b
MA]

(1)1
(THP )
(1
)(1)
(2HwPY
b
)
(1
) [HwP
2
+ (1P )Y
b
MA]

(1)
(THP )
(1
)(1)1
H
(4.6)
From (4.5), we know
@U
@A
< 0.
@U
@A
@U
@P
< 0 if and only if
@U
@P
> 0. This inequality holds ifw is
119
big enough. The intuition is that only when the individual whose labor market conditions
are favorable, the more assets they want to leave to their children, they are more likely
to join the labor market. On the contrary, if the individual is in low-paid jobs, he would
prefer to receive government transfers and enjoy leisure.
Table 4.13 reports the DID estimates among near-elderly individuals with children to
test this theory. Columns (1) and (2) show that if individuals’ assets are below 50% of
the population, they will not change their work status after the PLTC program. Columns
(3) and (4) instead report the estimates when individuals’ wage rates are above 50% of
the population. The results indicate that the PLTC program has a positive and significant
effect on labor-force participation among them. Especially in 2010, the effect increases to
8.9-10.3 percentage points.
To avoid the concern that individuals with higher wage rates increase their labor force
participation regardless of the PLTC program, I conduct a test among childless near-
elderly individuals in well-paid jobs. Since childless individuals are less likely to have
the bequest motive, one would expect that we cannot observe the program’s effect on
them. As we have seen from Table 4.14, among childless near-elderly individuals, the re-
sults of the PLTC program on labor force participation are small and insignificant under
all specifications. This evidence is consistent with our expectation, suggesting that the
significant increase in labor force participation among well-paid individuals is due to the
bequest motive and the PLTC program.
4.7 Conclusion
Cost-effectiveness is a key rationale behind the Partnership program. Proponents of
the program believe it can reduce Medicaid spending in the future by creating an incen-
tive for individuals to assume responsibility through LTC insurance for at least the initial
phase of their need for LTC services. With attracting individuals who might not otherwise
120
purchase private LTC insurance, the government expects to save spending on Medicaid
by shifting the responsibilities to private companies and individuals. However, previ-
ous literature casts doubt about the efficiency of this program because many participants
would still be too wealthy to qualify for Medicaid (GAO, 2007).
In this paper, I shed light on this problem from a new perspective. I use data from the
Health and Retirement Study spanning the recent state adoptions of the PLTC program
to examine the responsiveness of work status to changes in the existence of the programs
across states and over time. I find that near-elderly individuals increase their labor force
participation, and more of the effects coming from individuals with assets above $2000. To
explore the reason behind this responsiveness, based on the bequest motive hypothesis, I
propose a theoretical model that suggests that only when individuals are in well-paid jobs
would they be more motivated by the PLTC program by taking full-time jobs. Empirical
evidence confirms my theoretical model, showing that most of the program’s impact is
driven by individuals who have children and are in well-paid jobs. Overall, these findings
suggest that changes in the PLTC program could have unintended (second-order) effects.
Besides, this paper also provides a new direction for thinking about the aging issues.
As aging populations and decreasing labor force participation rates among older workers
create a financial strain on public pension and health care programs,
3
encouraging em-
ployment among older workers becomes an important factor in helping society to deal
with the ongoing demographic transition toward an older population. In response, many
countries are starting to enact or at least consider policies that cut retirement benefits and
increase the statutory retirement age. However, these policy reforms are not considered
as effective policy instruments because it mainly restricts the opportunity set of the less
healthy workers in low-paid jobs (with the highest incentive to retire), who are the main
recipients of social security and health care programs. Finding an efficient way to pro-
mote the labor force participation of older workers is a topic that should have attracted
3
Between 1980 and 2020, the old-age to working-age ratio has increased from 20 to 31. (OECD (2020)).
121
significant attention from policymakers and researchers. This paper, therefore, provides
empirical evidence on the unintended positive effects of an LTC insurance program on
employment among older workers. I interpret the results as suggestive that PLTC pro-
gram can be the potential way to promote labor force participation of older workers.
122
Tables
Table 4.1: Effective Date of the PLTC Program by State
State Effective Date State Effective Date
Alabama March 2009 Montana July 2009
Alaska Not Filed Nebraska July 2006
Arizona July 2008 Nevada January 2007
Arkansas July 2008 New Hampshire February 2010
California Pilot State New Jersey July 2008
Colorado January 2008 New Mexico August 2019
Connecticut Pilot State New York Pilot
Delaware November 2011 North Carolina March 2011
Florida January 2007 North Dakota January 2007
Georgia January 2007 Ohio September 2007
Hawaii Not Filed Oklahoma July 2008
Idaho November 2006 Oregon January 2008
Illinois 2019 Pennsylvania September 2007
Indiana Pilot State Rhode Island July 2008
Iowa January 2010 South Carolina January 2009
Kansas April 2007 South Dakota July 2007
Kentucky June 2008 Tennessee October 2008
Louisiana October 2009 Texas March 2008
Maine July 2009 Utah October 2014
Maryland January 2009 Vermont 2020
Massachusetts 2020 Virginia September 2007
Michigan February 2016 Washington January 2012
Minnesota July 2006 West Virginia July 2010
Mississippi Not Filed Wisconsin January 2009
Missouri August 2008 Wyoming July 2009
NOTES: Illinois, Massachusetts, and Vermont are three states that I can only collect adopted year
information
123
Table 4.2: Summary Statistics: Near-elderly (50-64 ) samples
Near-Elderly (50-65)
Variable Mean Std.dev.
PLTC state 0.597 0.302
Full-time work 0.529 0.499
Part-time work 0.087 0.282
Age 57.716 3.71
Unmarried 0.270 0.444
Male 0.482 0.500
White 0.863 0.344
Less than high school 0.107 0.309
Poor health status 0.199 0.399
Private LTC insurance 0.105 0.306
Cancer 0.077 0.266
Diabetes 0.136 0.343
And ADLs/IADLs 0.126 0.332
Number of children 2.769 1.812
Assets ($K) 460.236 1044.951
124
Table 4.3: Test of Parallel Trends Assumption - Full-Time Job Status
Dependent Variable: Full-Time Work
Post Years 2000 2002
(1) (2) (3) (4)
Treat Post 0.010 0.007 0.026 0.042
(0.017) (0.018) (0.025) (0.033)
Additional controls Yes Yes Yes Yes
Year FE Yes Yes Yes Yes
State FE Yes Yes Yes Yes
2000 state vars trend Yes Yes Yes Yes
Region trend No Yes No Yes
Weights Yes Yes Yes Yes
Observations 11668 11668 10439 10439
R-squared 0.170 0.171 0.163 0.164
NOTES: This table reports comparison spanning the recent adoption of the PLTC program. All re-
gression include controls for: age, gender, marital status, years of education, White, self-reported
health, cancer, diabetes, any ADLs/IADLs, and number of children. State variables for 2000 in-
clude log of population, percent of population black, age > 65, and in poverty, each interacted
with a linear time trend. Individual weighting is used to represent the whole population. Results
with no weighting are very similar. Robust standard errors, clustered at the state level, are in
parentheses. (*** p<0.01, ** p<0.05, * p<0.1)
125
Table 4.4: Test of Parallel Trends Assumption - Part-Time Job Status
Dependent Variable: Part-Time Work
Post Years 2000 2002
(1) (2) (3) (4)
Treat Post 0.013 0.013 0.002 0.008
(0.019) (0.019) (0.011) (0.014)
Additional controls Yes Yes Yes Yes
Year FE Yes Yes Yes Yes
State FE Yes Yes Yes Yes
2000 state vars trend Yes Yes Yes Yes
Region trend No Yes No Yes
Weights Yes Yes Yes Yes
Observations 11668 11668 10439 10439
R-squared 0.043 0.043 0.037 0.038
NOTES: This table reports comparison spanning the recent adoption of the PLTC program. All re-
gression include controls for: age, gender, marital status, years of education, White, self-reported
health, cancer, diabetes, any ADLs/IADLs, and number of children. State variables for 2000 in-
clude log of population, percent of population black, age > 65, and in poverty, each interacted
with a linear time trend. Individual weighting is used to represent the whole population. Results
with no weighting are very similar. Robust standard errors, clustered at the state level, are in
parentheses. (*** p<0.01, ** p<0.05, * p<0.1)
126
Table 4.5: DID Estimates of the PLTC Program’s Impact on Full-Time Work Status
Dependent Variable: Full-time work
Post Years 2006 2008 2010
(1) (2) (3) (4) (5) (6)
Treat Post 0.029** 0.050*** 0.025 0.039 0.050** 0.069***
(0.014) (0.014) (0.019) (0.025) (0.023) (0.022)
Additional controls Yes Yes Yes Yes Yes Yes
Year FE Yes Yes Yes Yes Yes Yes
State FE Yes Yes Yes Yes Yes Yes
2000 state vars trend Yes Yes Yes Yes Yes Yes
Region trend No Yes No Yes No Yes
Weights Yes Yes Yes Yes Yes Yes
Observations 10260 10260 9361 9361 11787 11787
R-squared 0.164 0.164 0.148 0.148 0.160 0.160
NOTES: This table reports comparison spanning the recent adoption of the PLTC program. All re-
gression include controls for: age, gender, marital status, years of education, White, self-reported
health, cancer, diabetes, any ADLs/IADLs, and number of children. State variables for 2000 in-
clude log of population, percent of population black, age > 65, and in poverty, each interacted
with a linear time trend. Individual weighting is used to represent the whole population. Results
with no weighting are very similar. Robust standard errors, clustered at the state level, are in
parentheses. (*** p<0.01, ** p<0.05, * p<0.1)
127
Table 4.6: DID Estimates of the PLTC Program’s Impact on Part-Time Work Status
Dependent Variable: Part-Time Work
Post Years 2006 2008 2010
(1) (2) (3) (4) (5) (6)
Treat Post -0.021** -0.020** -0.012 -0.016 -0.015 -0.017
(0.009) (0.009) (0.013) (0.015) (0.016) (0.021)
Additional controls Yes Yes Yes Yes Yes Yes
Year FE Yes Yes Yes Yes Yes Yes
State FE Yes Yes Yes Yes Yes Yes
2000 state vars trend Yes Yes Yes Yes Yes Yes
Region trend No Yes No Yes No Yes
Weights Yes Yes Yes Yes Yes Yes
Observations 10260 10260 9361 9361 11787 11787
R-squared 0.039 0.039 0.042 0.042 0.032 0.032
NOTES: This table reports comparison spanning the recent adoption of the PLTC program. All re-
gression include controls for: age, gender, marital status, years of education, White, self-reported
health, cancer, diabetes, any ADLs/IADLs, and number of children. State variables for 2000 in-
clude log of population, percent of population black, age > 65, and in poverty, each interacted
with a linear time trend. Individual weighting is used to represent the whole population. Results
with no weighting are very similar. Robust standard errors, clustered at the state level, are in
parentheses. (*** p<0.01, ** p<0.05, * p<0.1)
128
Table 4.7: DID Estimates of the PLTC Program’s Impact on Work Status
Dependent Variable: Full/Part-Time Work
Post Years 2006 2008 2010
(1) (2) (3) (4) (5) (6)
Treat Post 0.008 0.030** 0.012 0.022 0.035 0.052**
(0.012) (0.01) (0.017) (0.020) (0.022) (0.020)
Additional controls Yes Yes Yes Yes Yes Yes
Year FE Yes Yes Yes Yes Yes Yes
State FE Yes Yes Yes Yes Yes Yes
2000 state vars trend Yes Yes Yes Yes Yes Yes
Region Trend No Yes No Yes No Yes
Weights Yes Yes Yes Yes Yes Yes
Observations 10260 10260 9361 9361 11787 11787
R-squared 0.039 0.039 0.042 0.042 0.032 0.032
NOTES: This table reports comparison spanning the recent adoption of the PLTC program, and
pooled full-time/part-time work status together. All regression include controls for: age, gender,
marital status, years of education, White, self-reported health, cancer, diabetes, any ADLs/IADLs,
and number of children. State variables for 2000 include log of population, percent of population
black, age > 65, and in poverty, each interacted with a linear time trend. Individual weighting
is used to represent the whole population. Results with no weighting are very similar. Robust
standard errors, clustered at the state level, are in parentheses. (*** p<0.01, ** p<0.05, * p<0.1)
129
Table 4.8: Placebo Test: DID Estimates of the PLTC Program’s Impact on Work Status
(Age< 50)
Dependent Variable
Full-Time Work Part-Time Work
Comparison Years (1) (2) (3) (4)
2000 -0.014 -0.023 0.014 0.012
(0.071) (0.063) (0.072) (0.065)
2002 0.055 0.053 -0.079 -0.075
(0.056) (0.052) (0.066) (0.064)
2006 0.034 0.029 -0.020 -0.020
(0.079) (0.080) (0.054) (0.056)
2008 0.118 0.116 -0.046 -0.052
(0.093) (0.079) (0.051) (0.049)
2010 0.079 0.070 0.020 0.016
(0.057) (0.053) (0.051) (0.044)
Additional individual controls Yes Yes Yes Yes
Year FE Yes Yes Yes Yes
State FE Yes Yes Yes Yes
2000 state vars trend Yes Yes Yes Yes
Region trend No Yes No Yes
Weights Yes Yes Yes Yes
Observations 2401 2401 2401 2401
R-squared 0.124 0.050 0.127 0.056
NOTES: This table reports results comparing 2004 (as the benchmark year) with all other years,
and pooled all years in one regression. All regression include controls for: age, gender, marital
status, years of education, White, self-reported health, cancer, diabetes, any ADLs/IADLs, and
number of children. State variables for 2000 include log of population, percent of population
black, age > 65, and in poverty, each interacted with a linear time trend. Individual weighting
is used to represent the whole population. Results with no weighting are very similar. Robust
standard errors, clustered at the state level, are in parentheses. (*** p<0.01, ** p<0.05, * p<0.1)
130
Table 4.9: Placebo Test: DID Estimates of the PLTC Program’s Impact on Work Status
(Age> 70)
Dependent Variable
Full-Time Work Part-Time Work
Comparison Years (1) (2) (3) (4)
2000 -0.012 -0.012 0.016 0.016
(0.010) (0.010) (0.017) (0.017)
2002 -0.008 -0.007 -0.001 -0.001
(0.008) (0.007) (0.006) (0.006)
2006 -0.012 -0.012 -0.002 -0.001
(0.008) (0.008) (0.003) (0.004)
2008 -0.013 -0.012 0.005 -0.005
(0.009) (0.009) (0.006) (0.006)
2010 -0.005 -0.006 0.004 0.005
(0.008) (0.009) (0.007) (0.007)
Additional individual controls Yes Yes Yes Yes
Year FE Yes Yes Yes Yes
2000 state vars trend Yes Yes Yes Yes
Region trend No Yes No Yes
Weights Yes Yes Yes Yes
Observations 47698 47698 47698 47698
R-squared 0.064 0.064 0.015 0.015
NOTES: This table reports results comparing 2004 (as the benchmark year) with all other years,
and pooled all years in one regression. All regression include controls for: age, gender, marital
status, years of education, White, self-reported health, cancer, diabetes, any ADLs/IADLs, and
number of children. State variables for 2000 include log of population, percent of population
black, age > 65, and in poverty, each interacted with a linear time trend. Individual weighting
is used to represent the whole population. Results with no weighting are very similar. Robust
standard errors, clustered at the state level, are in parentheses. (*** p<0.01, ** p<0.05, * p<0.1)
131
Table 4.10: Placebo Test: DID Estimates of the PLTC Program’s Impact on Work Status
(Asset6 2000)
Dependent Variable
Full-Time Work Part-Time Work
Comparison Years (1) (2) (3) (4)
2000 0.034 0.035 0.044 0.047
(0.057) (0.055) (0.046) (0.045)
2002 0.001 0.002 0.028 0.036
(0.066) (0.064) (0.028) (0.028)
2006 -0.017 -0.003 -0.028 -0.018
(0.038) (0.035) (0.034) (0.032)
2008 0.031 0.038 -0.032 -0.034
(0.070) (0.067) (0.066) (0.065)
2010 0.010 0.010 0.015 0.023
(0.053) (0.053) (0.028) (0.027)
Additional individual controls Yes Yes Yes Yes
Year FE Yes Yes Yes Yes
State FE Yes Yes Yes Yes
2000 state vars trend Yes Yes Yes Yes
Region trend No Yes No Yes
Weights Yes Yes Yes Yes
Observations 4222 4222 4222 4222
R-squared 0.221 0.223 0.052 0.054
NOTES: This table reports results among individuals aged 50-64 by comparing 2004 (as the bench-
mark year) with all other years, and pooled all years in one regression. All regression include
controls for: age, gender, marital status, years of education, White, self-reported health, cancer,
diabetes, any ADLs/IADLs, and number of children. State variables for 2000 include log of pop-
ulation, percent of population black, age> 65, and in poverty, each interacted with a linear time
trend. Individual weighting is used to represent the whole population. Results with no weight-
ing are very similar. Robust standard errors, clustered at the state level, are in parentheses. (***
p<0.01, ** p<0.05, * p<0.1)
132
Table 4.11: Test Hypothesis: DID Estimates of the PLTC Program’s Impact on Work Status
(Without Kids)
Dependent Variable
Full-Time Work Part-Time Work
Comparison Years (1) (2) (3) (4)
2000 -0.113 -0.075 0.038 0.071
(0.079) (0.069) (0.081) (0.087)
2002 -0.053 -0.055 0.050 0.074
(0.114) (0.108) (0.074) (0.069)
2006 -0.015 -0.027 -0.041 -0.006
(0.062) (0.079) (0.073) (0.060)
2008 -0.001 -0.067 0.056 0.078*
(0.075) (0.095) (0.067) (0.042)
2010 0.078 0.082 0.011 0.020
(0.065) (0.072) (0.049) (0.038)
Additional individual controls Yes Yes Yes Yes
Year FE Yes Yes Yes Yes
State FE Yes Yes Yes Yes
2000 state vars trend Yes Yes Yes Yes
Region trend No Yes No Yes
Weights Yes Yes Yes Yes
Observations 2101 2101 2101 2101
R-squared 0.157 0.164 0.058 0.065
NOTES: This table reports results among childless individuals aged 50-64 by comparing 2004 (as
the benchmark year) with all other years, and pooled all years in one regression. All regression
include controls for: age, gender, marital status, years of education, White, self-reported health,
cancer, diabetes, any ADLs/IADLs, and number of children. State variables for 2000 include log
of population, percent of population black, age> 65, and in poverty, each interacted with a linear
time trend. Individual weighting is used to represent the whole population. Results with no
weighting are very similar. Robust standard errors, clustered at the state level, are in parentheses.
(*** p<0.01, ** p<0.05, * p<0.1)
133
Table 4.12: Test Hypothesis: DID Estimates of the PLTC Program’s Impact on Work Status
(With Kids)
Dependent Variable
Full-Time Work Part-Time Work
Comparison Years (1) (2) (3) (4)
2000 -0.006 -0.010 -0.012 -0.006
(0.017) (0.016) (0.019) (0.015)
2002 -0.002 -0.031 -0.003 -0.003
(0.018) (0.022) (0.015) (0.015)
2006 0.029* 0.043*** -0.017 -0.012
(0.017) (0.015) (0.012) (0.011)
2008 0.018 0.031 -0.014 -0.009
(0.021) (0.024) (0.015) (0.016)
2010 0.048* 0.072*** -0.015 -0.013
(0.025) (0.025) (0.018) (0.018)
Additional individual controls Yes Yes Yes Yes
Year FE Yes Yes Yes Yes
State FE Yes Yes Yes Yes
2000 state vars trend Yes Yes Yes Yes
Region trend No Yes No Yes
Weights Yes Yes Yes Yes
Observations 28206 28206 28206 28206
R-squared 0.167 0.168 0.036 0.036
NOTES: This table reports results among individuals aged 50-64 with kids by comparing 2004 (as
the benchmark year) with all other years, and pooled all years in one regression. All regression
include controls for: age, gender, marital status, years of education, White, self-reported health,
cancer, diabetes, any ADLs/IADLs, and number of children. State variables for 2000 include log
of population, percent of population black, age> 65, and in poverty, each interacted with a linear
time trend. Individual weighting is used to represent the whole population. Results with no
weighting are very similar. Robust standard errors, clustered at the state level, are in parentheses.
(*** p<0.01, ** p<0.05, * p<0.1)
134
Table 4.13: Test Hypothesis: DID Estimates of the PLTC Program’s Impact on Work Status
(With Kids)
Dependent Variable: Full-Time Work
Wage Rate Below 50% Wage Rate Above 50%
Comparison Years (1) (2) (3) (4)
2000 -0.046 -0.029 0.001 -0.017
(0.054) (0.047) (0.025) (0.025)
2002 -0.040 -0.030 -0.013 -0.022
(0.045) (0.054) (0.020) (0.021)
2006 -0.007 -0.015 0.037** 0.046***
(0.047) (0.048) (0.017) (0.013)
2008 -0.023 -0.028 0.034* 0.049**
(0.045) (0.050) (0.018) (0.022)
2010 -0.056 -0.032 0.089*** 0.103***
(0.045) (0.057) (0.023) (0.026)
Additional individual controls Yes Yes Yes Yes
Year FE Yes Yes Yes Yes
State FE Yes Yes Yes Yes
2000 state vars trend Yes Yes Yes Yes
Region trend No Yes No Yes
Weights Yes Yes Yes Yes
Observations 6908 6908 21298 21298
R-squared 0.082 0.086 0.231 0.232
NOTES: This table reports results among individuals aged 50-64 with kids by comparing 2004 (as
the benchmark year) with all other years, and pooled all years in one regression. All regression
include controls for: age, gender, marital status, years of education, White, self-reported health,
cancer, diabetes, any ADLs/IADLs, and number of children. State variables for 2000 include log
of population, percent of population black, age> 65, and in poverty, each interacted with a linear
time trend. Individual weighting is used to represent the whole population. Results with no
weighting are very similar. Robust standard errors, clustered at the state level, are in parentheses.
(*** p<0.01, ** p<0.05, * p<0.1)
135
Table 4.14: Test Hypothesis: DID Estimates of the PLTC Program’s Impact on Work Status
(Without Kids)
Dependent Variable: Full-Time Work
Wage Rate Above 50%
Comparison Years (1) (2)
2000 -0.049 -0.067
(0.067) (0.068)
2002 -0.023 -0.008
(0.128) (0.106)
2006 -0.072 -0.126
(0.072) (0.093)
2008 -0.064 -0.073
(0.077) (0.091)
2010 0.042 0.022
(0.084) (0.067)
Additional individual controls Yes Yes
Year FE Yes Yes
State FE Yes Yes
2000 state vars trend No Yes
Region trend No Yes
Weights Yes Yes
Observations 1605 1605
R-squared 0.194 0.206
NOTES: This table reports results among childless individuals aged 50-64 by comparing 2004 (as
the benchmark year) with all other years, and pooled all years in one regression. All regression
include controls for: age, gender, marital status, years of education, White, self-reported health,
cancer, diabetes, any ADLs/IADLs, and number of children. State variables for 2000 include log
of population, percent of population black, age> 65, and in poverty, each interacted with a linear
time trend. Individual weighting is used to represent the whole population. Results with no
weighting are very similar. Robust standard errors, clustered at the state level, are in parentheses.
(*** p<0.01, ** p<0.05, * p<0.1)
136
Chapter 5
Conclusion
Long-term care is an important source of risk for the elderly. Thus, LTC insurance
is undoubtedly the most effective means for the elderly to fight for financial risks. De-
spite its importance, only about 10 percent of elderly individuals purchase private LTC
insurance, with many of the remainder relying on Medicaid. Facing rising Medicaid ex-
penditures on LTC services, it is crucial for policymakers to propose effective strategies to
provide Medicaid to the population in real need while shifting the demand of relatively
wealthier individuals to private insurance.
To facilitate such purpose, this dissertation focuses on a better understanding of how
elderly individuals value public LTC insurance and how they behave under various cur-
rent LTC policies. These two aspects are of great interest since, in the course of developing
estimates of the fiscal impact of LTC policies, it appears that policymakers generally as-
sumed no behavioral responses. However, this assumption is proved as ill-suited in my
studies. Specifically, Chapter 2 exploits the Deficit Reduction Act that ceases the eligibility
of Medicaid LTC for people with high home equity. With a triple-difference methodology,
My results suggest that this policy causes individuals to change consumption behavior,
with a reduction in housing equity and a rise in the consumption of non-LTC goods. Be-
sides, I further estimate elderly individuals’ willingness to pay for Medicaid LTC with
137
a structural model. I find that they are willing to pay $1.2 per dollar of the net cost of
providing Medicaid LTC. Combining these empirical results with the structural model, I
document that the majority of the population affected by the DRA are individuals with a
great demand for long-term care.
Chapter 3 also provides evidence to show that the assumption of no behavioral re-
sponses among consumers is inappropriate. With the state variation in the adoption of
the Partnership Long-Term Care insurance program, I can examine the impact of the pro-
gram on individuals’ private and public LTC insurance ownership. Though I find evi-
dence that this program induces new purchases of private LTC insurance, I also notice
that more elderly individuals rely on Medicaid in the end. This finding is contrary to the
program’s intention precisely because consumers have changed their health behaviors
after purchasing private LTC insurance. The results report that the PLTC program leads
to lower hospital/doctor visits among the individuals aged between 50 and 64 (called
”near-elderly”), indicating that private LTC insurance induces its new purchasers to take
riskier health behaviors. Simultaneously, the same population increase visits or stays in
the nursing home, suggesting that the program results in an overuse of LTC insurance.
These findings are consistent with the ”moral hazard” problem in the insurance literature.
On the other hand, consumers’ behavioral responses may also bring unexpected bene-
fits to the policy. In Chapter 4, using data spanning from the recent adoption of the PTLC
program, I find that near-elderly individuals increase their labor force participation, and
most of the effects come from individuals with relatively higher assets. These findings
deviate from the program’s initial intention. To better understand this unintended con-
sequence, I propose a theoretical model based on the ”bequest motive” perspective. Em-
pirical evidence confirms my theoretical prediction and shows that most of the program’s
impact is driven by individuals who have children and are in well-paid jobs.
Overall, this dissertation contributes to the literature by providing empirical evidence
on individuals’ behavioral changes due to various LTC policies. Therefore, considering
138
consumers’ behavioral responses should be essential for policy designs aiming to reduce
their wasteful spend-down of savings to be qualified for public LTC insurance. This new
policy design perspective benefits the whole society by improving the allocative efficiency
of limited government resources. Further research is needed to determine the causes
of such behavioral changes and provide more accurate estimations of cost-effectiveness
analysis under various LTC policies.
139
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Appendix A
Chapter 2 Appendix
Figures
Figure A.1: Changes in Home Equity Across Consecutive Year Pairs
DDD Estimate: −66.75 (s.e. = 34.452)
−500 −300 −100 100 300 500
ΔEquity ($K)
1998 2000 2002 2004 2006
Year
NOTES: This figure uses consecutive HRS wave-pairs to re-examine equation (2.2) over the period
1996 to 2008. Specifically, the y-axis corresponds to the estimate of the tripe-difference term, and
is measured in $K. The x-axis denotes the pre-period year within the consecutive year pair. I
keep the definition of treatment status constant over time such thatAbove
i
andSenior
i
are based
on reported characteristics in the former of the two years in each wave-pair. On the contrary,
Post
t
equals to one for the later of the two years. For example, in the x-axis , ”1998” represents
the estimate for the period 1998 and 2000, where the outcome in 1998 equals to the home equity
growth from 1996 to 1998. Within this wave-pairs, the post-period is 2000 and I define treatment
status based on characteristics in 1998.
146
Tables
Table A.1.1: Pre-DRA Summary Statistics
Single Seniors
Variables N Mean Median Std Dev
(1) (2) (3) (4)
HRSdataset
Housing Asset
Home value, 2006 ($K) 4126 120.32 60 224.81
Home debt, 2006 ($K) 4126 12.10 0 39.03
Home equity, 2006 ($K) 4126 108.23 49.5 214.17
Change in home price, 2004-2006 ($K) 3983 17.67 0 152.12
Change in home price, 2006-2008 ($K) 4126 -4.89 0 267.44
Change in home debt, 2004-2006 ($K) 3983 1.09 0 27.65
Change in home debt, 2006-2008 ($K) 4126 -0.23 0 30.11
Change in home equity, 2004-2006 ($K) 3983 16.58 0 152.47
Change in home equity, 2006-2008 ($K) 4126 -4.65 0 266.87
HealthStatus
Diabetes 4116 0.21 0 0.41
Cancer 4111 0.17 0 0.37
Difficulty w/ memory 4126 0.06 0 0.25
Any ADLs or IADLs 4123 0.32 0 0.47
HealthInsuranceandHealthServices
Medicaid, 2004 3958 0.15 0 0.36
Ever had overnight stay in nursing home, 2004 3982 0.05 0 0.21
Ever used home care services, 2004 3980 0.09 0 0.28
BasicCharacteristics
Age, 2006 4126 76.27 75 7.98
Male 4126 0.23 0 0.43
White 4126 0.78 1 0.41
Black 4126 0.19 0 0.39
Native 4124 0.90 1 0.30
Less than high school education 4126 0.31 0 0.47
Number of kids 4035 3.16 3 2.32
Income, 2004 ($K) 3983 30.17 18.30 58.73
NOTES: Summary statistics are for individuals with all home equity values. Diabetes, Cancer,
Difficulty w/ memory, and Any ADLs/IADLs are indicators if the individual reported having
symptoms. Income is defined as personal income.
147
Table A.1.2: Robustness to Regression Sample
Dependent Variable ($K) Equity
Comparison Years 06-08
(1) (2) (3) (4)
Senior Above Post -81.75*** -80.98*** -64.01** -58.64*
(29.186) (29.633) (31.669) (32.293)
Above Post -91.49** -88.37** -89.22** -89.48**
(41.387) (40.352) (38.330) (37.814)
Post -117.79*** -216.45*** -113.45*** -224.66***
(15.030) (61.883) (14.481) (66.679)
Additional controls Yes Yes Yes Yes
State FE Yes Yes Yes Yes
Individual FE No Yes No Yes
Weights No No Yes Yes
Observations 3,400 3,400 3,400 3,400
R-squared 0.12 0.19 0.11 0.17
NOTES: Results presented are for individuals with home equity in the range of $200K-$800K in
2006. Post = 1 indicates the year of 2008. Post = 0 indicates the year of 2006. Above = 1 when an
individual’s home equity in 2006 is above $500K.Senior is an indicator variable denoting that an
individual aged above 65 in 2006. Even-numbered columns include individual fixed effects, and
columns (3)-(4) include weights. Robust standard errors, clustered by state, are in parentheses.
(*** p<0.01, ** p<0.05, * p<0.1)
148
Table A.1.3: Robustness to Definition of the Middle-Aged
Dependent Variable ($K) Equity
Comparison Years 06-08
(1) (2) (3) (4)
Senior Above Post -97.06*** -90.57*** -76.19** -63.93*
(37.286) (37.309) (33.202) (33.189)
Above Post -45.78 -40.15 -46.44 -43.15
(52.556) (53.299) (43.218) (45.206)
Post -160.85*** -349.72*** -153.58*** -356.12***
(14.016) (92.533) (14.625) (98.326)
Additional controls Yes Yes Yes Yes
State FE Yes Yes Yes Yes
Individual FE No Yes No Yes
Weights No No Yes Yes
Observations 1,876 1,876 1,876 1,876
R-squared 0.13 0.19 0.12 0.17
NOTES: Results presented are comparing individuals aged above 65 in 2006 with individuals aged
50-64 in 2008. Sample is restricted to individuals whose home equity in the range of $300K-$700K
in 2006. Post = 1 indicates the year of 2008. Post = 0 indicates the year of 2006. Above = 1 when
an individual’s home equity in 2006 is above $500K.Senior is an indicator variable denoting that
an individual aged above 65 in 2006. Even-numbered columns include individual fixed effects,
and columns (3)-(4) include weights. Robust standard errors, clustered by state, are in parentheses.
(*** p<0.01, ** p<0.05, * p<0.1)
149
Table A.1.4: Placebo Test to Alternative Definition of ”Above” Group
Dependent Variable Equity
Comparison Years 06-08
(1) (2) (3) (4)
Senior Above Post 42.00 48.08 57.07 61.86
(78.743) (81.148) (79.304) (83.105)
Above Post -70.88 -70.68 -74.88 -74.53
(54.899) (55.429) (53.315) (56.978)
Post -177.35*** -481.99*** -165.56*** -480.20***
(36.861) (91.656) (36.956) (109.143)
Additional controls YES YES YES YES
State FE YES YES YES YES
Weights NO NO YES YES
Individual FE NO YES NO YES
Observations 1,116 1,116 1,116 1,116
R-squared 0.13 0.18 0.13 0.17
NOTES: Results presented are comparing individuals aged above 65 in 2006 with individuals aged
55-64 in 2008. Sample is restricted to individuals whose home equity in the range of $400K-$800K
in 2006. Post = 1 indicates the year of 2008. Post = 0 indicates the year of 2006. Above = 1 when
an individual’s home equity in 2006 is above $600K.Senior is an indicator variable denoting that
an individual aged above 65 in 2006. Even-numbered columns include individual fixed effects,
and columns (3)-(4) include weights. Robust standard errors, clustered by state, are in parentheses.
(*** p<0.01, ** p<0.05, * p<0.1)
150
Table A.1.5: Robustness Checks of Key Estimates for Evaluation of Willingness to Pay
c
floor
Baseline 2 4 5 0.6 0.7 0.9 1500 2000 2500
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
WTP for Medicaid LTC 12251 11980 13114 13512 11951 12225 12206 15990 11396 11960
Net Costs, C 9915 9915 9915 9915 9915 9915 9915 10080 9907 9734
WTP Relative to Net Cost 1.24 1.21 1.32 1.36 1.21 1.23 1.23 1.59 1.15 1.23
NOTES: This table presents the sensitivity of my baseline results of willingness to pay to alterna-
tive assumptions related to consumption. Column (1) reports the baseline specification. Columns
(2)-(10) report the estimates under alternative assumptions about risk aversion (columns (2)-(4)),
relative importance of consumption (columns (5)-(7)), and the consumption floor (columns (8)-
(10)).
151
Home Equity Growth as the Outcome Variable
To show the feasibility of using home equity growth as the outcome variable in my
empirical analysis, let us consider a two-way fixed effects regression model with time
trends as follows:
Y
it
=
i
+
t
+g
i
t +P
it
+X
it
+
it
(A.1)
whereY
it
is the absolute level of home equity for seniori during yeart.
i
and
t
denote
individual fixed effects and year fixed effects respectively. g
i
captures the impact of time
trend which varies across individuals. P
it
is an indicator variable which equals to 1 if
the individual is affected by the DRA policy. I useX
it
to control for other time-varying
individual characteristics which have effects on home equity.
it
is an idiosyncratic error
term.
The repeated observations of the same individual make it possible to remove
i
via
differencing. By taking the difference of two consecutive years, we can get rid of
i
as
follows:
y
it
=
t
+g
i
+ P
it
+ X
it
+"
it
(A.2)
where
t
is equal to (
t

t1
) and"
it
is equivalent to
t

t1
. Now the main outcome
of interest is home equity changes in consecutive two years, i.e.,y
it
is equal to Y
it
. Then
using panel data techniques, we can estimate, the policy effect.
Triple-Difference Cutoff Standard
Set Up
To show the feasibility of using home equity as the criterion defining the treated group
in my empirical analysis, let us consider the triple-difference estimator either based on
home equity interest (HI) or home equity (HE). Consider two groups of population that
will be compared within the triple-difference framework: single seniors (ss) and middle-
152
aged (m), where middle-aged can be further divided into married middle-aged (m) and
single middle-aged (sm). Known that the outcome is home equity, the triple-difference
(DDD) estimator can be described as follows:
DDD =fE(HEjss = 1; HI>= 500k;T > 06)E(HEjss = 1; HI>= 500k;T < 06)g
fE(HEjss = 1; HI< 500k;T > 06)E(HEjss = 1; HI< 500k;T < 06)g
fE(HEjm = 1; HI>= 500k;T > 06)E(HEjm = 1; HI>= 500k;T < 06)g
+fE(HEjm = 1; HI< 500k;T > 06)E(HEjm = 1; HI< 500k;T < 06)g
To make the equation look simpler, the above equation can be written as
DDD =fE(HE
ss
jHI
ss
>= 500k;T > 06)E(HE
ss
jHI
ss
>= 500k;T < 06)g
fE(HE
ss
jHI
ss
< 500k;T > 06)E(HE
ss
jHI
ss
< 500k;T < 06)g
fE(HE
m
jHI
m
>= 500k;T > 06)E(HE
m
jHI
m
>= 500k;T < 06)g
+fE(HE
m
jHI
m
< 500k;T > 06)E(HE
m
jHI
m
< 500k;T < 06)g
For singles, HI=HE; for couples, HI=HE/2. If we divide middle-aged group into mar-
ried middle-aged and single middle-aged, then we can get the following:
153
DDD =fE(HE
ss
jHE
ss
>= 500k;T > 06)E(HE
ss
jHE
ss
>= 500k;T < 06)g
fE(HE
ss
jHE
ss
< 500k;T > 06)E(HE
ss
jHE
ss
< 500k;T < 06)g
f[
n
mm
n
m
E(HE
mm
jHE
mm
>= 1000k;T > 06) +
n
sm
n
m
E(HE
sm
jHE
sm
>= 500k;T > 06)]
[
n
mm
n
m
E(HE
mm
jHE
mm
>= 1000k;T < 06) +
n
sm
n
m
E(HE
sm
jHE
sm
>= 500k;T < 06)]g
+f[
n
mm
n
m
E(HE
mm
jHE
mm
< 1000k;T > 06) +
n
sm
n
m
E(HE
sm
jHE
sm
< 500k;T > 06)]
[
n
mm
n
m
E(HE
mm
jHE
mm
< 1000k;T < 06) +
n
sm
n
m
E(HE
sm
jHE
sm
< 500k;T < 06)]g
wheren
a
denotes the total number of observations amonga group.
Research Question
The key question is whether the DDD coefficient would be the same with using ei-
ther home interest or home equity as the cutoff criterion. For singles, both cutoff criteria
would give the same results. Therefore, the difference mainly comes from married mid-
dle age group. Thus, the key question now changes to whether the average difference of
married middle age group before and after the policy based on home interest cutoff cri-
terion would be the same as the difference based on home equity criterion. In this sense,
we need to proof the following equation:
E(HE
mm
jHE
mm
>= 1000k;T > 06)E(HE
mm
jHE
mm
>= 1000k;T < 06)
E(HE
mm
jHE
mm
< 1000k;T > 06 +E(HE
mm
jHE
mm
< 1000k;T < 06)
=E(HE
mm
jHE
mm
>= 500k;T > 06)E(HE
mm
jHE
mm
>= 500k;T < 06)
E(HE
mm
jHE
mm
< 500k;T > 06 +E(HE
mm
jHE
mm
< 500k;T < 06)
154
Since the main regression is focus on individuals with home equity2 [300,700), the
above equation should be modified as the following (with abbreviation):
E(HE
mm
jHE
mm
2 [1000; 1400);T > 06)E(HE
mm
jHE
mm
2 [1000; 1400);T < 06)
E(HE
mm
jHE
mm
2 [600; 1000);T > 06 +E(HE
mm
jHE
mm
2 [600; 1000);T < 06)
=E(HE
mm
jHE
mm
2 [500; 700);T > 06)E(HE
mm
jHE
mm
2 [500; 700);T < 06)
E(HE
mm
jHE
mm
2 [300; 500);T > 06 +E(HE
mm
jHE
mm
2 [300; 500);T < 06)
To make the equation looks simpler, let
F (1000; 1400) =E(HE
mm
jHE
mm
2 [1000; 1400);T > 06)E(HE
mm
jHE
mm
2 [1000; 1400);T < 06)
In other words,F (a;b) meaning the before and after average difference for those whose
home equity belong to [a$k;b$k) before the policy implemented. Therefore, the key ques-
tion is to proof the following,
F (500; 700)F (300; 500) =F (1000; 1400)F (600; 1000)
,
n
[500;600)
n
[500;700)
F (500; 600) +
n
[600;700)
n
[500;700)
F (600; 700)F (300; 500)
=F (1000; 1400) [
n
[600;700)
n
[600;1000)
F (600; 700) +
n
[700;1000)
n
[600;1000)
F (700; 1000)
155
,
n
[500;600)
n
[500;700)
F (500; 600) + (
n
[600;700)
n
[500;700)
+
n
[600;700)
n
[600;1000)
)F (600; 700)
F (300; 500)F (1000; 1400) +
n
[700;1000)
n
[600;1000)
F (700; 1000)
= 0
where
n
[a;b)
n
[c;d)
is the fraction of observations with home equity belong to [a,b) among [c,d)
group.
This can be tested by regression, where F (a;b) is the interaction term D
(a;b)
Post
among married middle age group. The F-statistic is 0.94, so that we cannot reject the null
hypothesis, which says that using home equity as the criterion is same as using home
interest.
156

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Asset Metadata

Creator Liu, Yinan (author)

Core Title Three essays on the evaluation of long-term care insurance policies

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Degree Conferral Date 2021-08

Publication Date 06/30/2021

Defense Date 04/23/2021

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag fiscal impact,long-term care insurance,Medicaid,OAI-PMH Harvest

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Strauss, John (committee chair), Chen, Alice (committee member), Hsiao, Cheng (committee member)

Creator Email lyn613gogo@hotmail.com,yinanliu@usc.edu

Permanent Link (DOI) http://doi.org/10.25549/usctheses-c89-473373

Unique identifier UC13012711

Identifier etd-LiuYinan-9678.pdf (filename), usctheses-c89-473373 (legacy record id)

Legacy Identifier etd-LiuYinan-9678

Dmrecord 473373

Document Type Dissertation

Rights Liu, Yinan

Internet Media Type application/pdf

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

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