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Transcript of Long-term Care, Home Health Care, and Informal Care David Byrne, Michelle Goeree, Bridget Hiedemann,...
Long-term Care, Home Health Care, and Informal CareDavid Byrne, Michelle Goeree, Bridget Hiedemann, and Steven Stern
October 2005
Roadmap
• Introduction
• Medicaid Financing Rules
• Theoretical Model
• Data
• Econometrics
• Results
• Policy Experiments
Elderly Population Growth
• Increased by 28% between 1980 and 1993
• Will reach 20% of population by 2025
Long Term Care Arrangements
• Children are less likely to care for elderly parents
• Elderly parents are more likely to remain independent, move to a nursing home, or receive formal care
• Data from 84 NLTCS indicate that siblings often share LTC responsibilities.
Previous Literature
• Models with one child, one caregiver, or household utility function
• Joint modelling of care and labor force participation
• Intergenerational transfers and household formation
• Game theoretic• Nonstructural estimation vs structural
Models with one child
• Kotlikoff and Morris (1990)
• Pezzin and Schone (1997, 1999)
• Sloan, Picone, and Hoerger (1997)
Single household utility function
• Hoerger, Picone, and Sloan (1996)
• Kotlikoff and Morris (1990)
Joint modelling of care and labor force participation
• Ettner (1996)
• Pezzin and Schone (1997, 1999)
Intergenerational transfers and household formation
• Hoerger, Picone and Sloan (1996)
• Pezzin and Schone (1999)
Game theoretic
• Pezzin and Schone (1997, 1999)
• Sloan, Picone, and Hoerger (1997)
Nonstructural estimation
• Kotlikoff and coauthors (1988, 1990)• Wolf and Soldo (1988)• Lee, Dwyer, and Coward (1990)• Cutler and Sheiner (1993)• Ettner (1996)• Hoerger, Picone, and Sloan (1996, 1997)• Norgard and Rodgers (1997)• White-Means (1997)• Couch, Daly, and Wolf (1999)
Structural estimation
• Kotlikoff and Morris (1990)
• Pezzin and Schone (1997, 1999)
Focus on single caregiver
• Cantor (1983)
• Stoller and Earl (1983)
• Horowitz (1985)
• Barber (1989)
• Kotlikoff and Morris (1990)
• Miller and Montgomery (1990)
• Pezzin and Schone (1997, 1999)
My Work with Coauthors
• Stern 1994, 1995,1996
• Hiedemann and Stern 1999
• Engers and Stern 2001
• Neuharth and Stern 2002
Medicaid Rules
• Eligibility is linked to actual or potential receipt of cash assistance under SSI or former AFDC. Law generally requires states to cover these individuals. But states have some flexibility in determining their programs.
Coverage depends upon :• Categorically needy (12 states in 1993)
• Elderly who are not poor by SSI or SSP standards but need assistance with medical expenses (37 states in 1993)
• Individuals in medical care institutions or needing home care (over 40 states in 1993)
Home Health Care Coverage
State Individual Couple Program Individual Couple1915c Waiver
State Eligibility RuleAL $434 $652 No Yes SSIAR $434 $652 Yes $108 $217 No
CA $620 $1,140 Yes $575 $717 YesMedically Needy
LimitME $444 $667 Yes $416 $450 Yes SSI+SSPWV $434 $652 Yes $200 $275 Yes 300% SSIWY $444 $671 No No
SSI/SSP Categorical Coverage Medically Needy
Source: Green Book (1993); Medicaid Source Book (1993); State Profile Data (1992)
Eligibility Criteria for MedicaidSelected States
Income Standard
Theoretical Model
• I adult children and one or two elderly parents
• Assume that married couples act as a single player; therefore, there are I+1 players indexed by i=0,1,2,..,I
• When indexing married spouses, we use m (maternal) and p (paternal) for parents and c (child) and s (spouse) for children
Theoretical Model
• Each player makes decisions about consumption Xi, contributions to paid help for the parent Hi,
leisure Lik, time spent caring for each parent tipk
and tifk, and market work time k=c,s for children
and their spouses • Market work time is zero for both parents. For the
children and their spouses, market work time is 1-Lik-Σjtijk.
m
I
oi
i
I
i sck
mikmikmikik
pmpmpmpm
ZH
tta
ttaQ
)(
)(
1 ,
2
02
000
p
I
oi
i
I
i sck
pikpikpikik
mpmpmpmp
ZH
tta
ttaQ
)(
)(
1 ,
2
02
000
• The coefficients β1i, β2i, β3ik, and β4jik are deterministic functions of observed child characteristics
• The errors εXi, εLik, and εtijk are functions of unobserved child characteristics
• It is assumed that β1i≥0, β2i≥0, β3ik≥0, εXi ≥0, and εLik ≥0,
uijiktijkjik
sck pmj
jik
ikLikik
sck
ik
iXij
pmj
ji
taa
La
XQU ii
)(
ln
lnln
4
, ,
0
3
,
2
,
010
Budget Constraint
• For each child,
iiXiii qHXpYY ***,max
***
1*, ,
iii
sck pmj
jikikikiki
sYYY
tLwaY
Budget Constraint
• We estimate Yi and s using CPS data and allow it to vary across states
• For the parent, the budget constraint is Y0+G0≥pX0X0+qH0 if she is not eligible for Medicaid reimbursement of home health care expenses. If she is eligible, the budget constraint is equal to Ψ-max(qH0-qH) ≥ pX0X0
• 1 ≥L0k+t0jk
Consumption
• For each child and parent, we can solve for Xi using the budget constraint to get
Xi
iiii
p
qHYYX
***,max
0
000
Xp
qHYX
Formal Care Payments
• For each player other than the parent, the set of FOCs for Hi is
0 ,0 ,0
ii
ii
i
iH
H
UH
H
U
Formal Care Payments
• If ∂Ui/ ∂Hi<0, then FOC implies
pmj j
j
i
iXiiXi
Q
aQ
q
QXp
,
0
2
1
where
Formal Care Payments
• If ∂Ui/ ∂Hi=0, then FOC implies
q
QXp
i
iXiiXi
2
1
Informal Care Hours• The FOCs for tijk depend on Hi. If Hi>0,
0 if
*
as and 0 if
*** if
*** if1*
where
21*
41
41
jik
jikj
jikikiitijk
jik
ii
iii
jikjikj
jikikiitijk
t
Qws
t
YYs
YYs
tQq
Qws
Informal Care Hours• If Hi=0,
0 if
*
and 0if
21*
412
412
jik
jikjikj
i
iXi
ikiXiitijk
jik
jikjikjikj
i
iXi
ikiXiitijk
t
QXp
ws
t
tQXp
ws
Leisure
1Lik if3
*2
1Lik if3
*2
i
1Lik if3
*1
1Lik if3
*1
iiik
,0H If
,0H If .Hon depend also Lfor FOCs The
ikq
wikLikXisiiikq
wikLikXisii
Lik
ikq
QwikLikisiikq
QwikLikisi
Lik
Data
• Asset and Health Dynamics Among the Oldest Old (AHEAD) data set.
• AHEAD is a nationally representative longitudinal data set designed to facilitate study of Americans 70 or older.
• Emphasis on the joint dynamics of health, family characteristics, income, and wealth
• Response rates are over 80%. • Blacks, Hispanics, and Florida residents are
oversampled.
Selection criteria
• We use 2,876 households out of approximately 6,000
• We use the first wave of data collected in 1993
• 1,822 were dropped because their records were missing data on the respondent, the respondent's spouse, or the respondent's children.
Selection criteria
• Households with working respondents (270) or two respondents each of whom helped the other (25) were dropped
• Only the black and white non-Hispanic groups were sufficiently large to be included once households were dropped for the reasons listed above
Selection criteria
• Households included in AHEAD contain at least one respondent 70 years old or older.
• Many households also include spouses, some of whom are less then 70 years old.
• Spouses of respondents are, themselves, respondents
Descriptive Statistics
• Among 65% of 2876 households reporting receipt of paid help in their homes, average payment was $31/week and maximum was $570/week
• 58% of households reported receiving some help from kids (avg: 22 hours/week)
• Men (37% of sample) are, on average, 77 years old, have 11.7 years of education, have 2 living children; 72% are married, and 93% are white
Descriptive statistics• Women (63% of sample) are, on average, 77 years
old, have 11.8 years of education, have 2 living children; 42% are married, and 90% are white
• 19% of men and 24% of women have an ADL• 49% of children are male, 71% are married; avg
kid is 47 years old with 2 children• Imputed wages using CPS: avg imputed wage is
$510/week• Other state-specific variables: price level (BEA);
cost of home health care; avg home health care state subsidy (HCFA)
Empirical Specification
sticscharacteri child of
vector a is and spouse, theof vector a is
stics,characteri -parent of vector a is where
exp
0 ifexp
0 ifexp
0
0
0
****0
**0*0
ikk
j
Zjj
ikj
kjjik
WW
jW
WZ
iWW
iWW
Empirical Specification
0 ifW
0 if****
4***4jik
**4
0*4
0
4iW
iWW
ik
kjkjik
Empirical specification
• β30k and β4j0k can not be identified separately because the parents’ leisure time is determined jointly with their caregiving time. Thus, we set β30k=0 with no loss in generality.
• Increasing all of the β terms by the same proportion has no effect on choices. Thus, we set β2i=1.
Empirical Specification
2
20
2
2
2
,0~
,for ,0~
1
1,0~
1
1,0~ ;exp
,0~ ;exp
uui
tktj
t
t
ttjis
tjic
L
L
lLis
LicLikLik
XXiXiXi
iidN
pmkjiidN
iidN
iidN
iidN
Identification• Inclusion of “happy” variable allows us to
decompose informal care effects into burden and quality of care effects.
• For example, if we were to observe that the provision of informal care by children has a very small empirical effect on the parent's happiness relative to the effect of variables affecting Z, we would conclude that α is very small and β4i >0.
• Alternatively, if we were to observe that very little informal care is provided but those parents who receive it are usually happier, we would conclude that α is large and β4i <0.
Estimates with Variation in log α and β4
(Parent Characteristics)Variable Estimate on
log αEstimate on logZ
Estimate on β4
Estimate on log β1
Constant -5.089** -3.203** -4.186** -0.722**
Age/100 -0.864** -3.121** 0.913
Education -0.020**
White 0.115 -0.009 -0.236
Married 0.331**
#ADLs -0.165** -0.287** -0.280**
Mother 0.353** 0.184 0.116
Spouse Characteristics
Age/100 2.599**
#ADLs -0.095**
Estimates with Variation in log α and β4
(Child Characteristics)Variable Estimate on
log αEstimate on β4
Estimate on log β1
Estimate on log β3
Constant -0.752** -5.333** 1.113** 0.346**
Age/100 -0.918** 9.933**
Male 0.389** -1.262
Biological 0.110 -0.376
Biological*Male
-0.449** 0.851
Education 0.002 -0.178**
Married 0.401* -11.539**
#Kids 0.053** -0.317**
Oldest -0.048 0.245
Estimates with Variation in log α and β4
(Other Parameters)
Variable Estimate Variable Estimate
logμ -10.153** logσηt 0.890**
γ -5.846** logσu 11.974**
logβ0 12.155** ρL 0.900
logσηX -0.037 ρt 0.900
logσηL 0.221
Goodness-of-fit Results
Family Size df
Mean Residual
Chi-Sq Stat Censored
# Censored Obs
Normalized Stat
Time Help1 155 -0.02 5.78E+17 457.70 66 17.192 737 0.00 8.08E+01 80.81 0 -17.093 994 0.00 1.39E+02 139.08 0 -19.174 605 0.01 6.51E+05 1678.43 242 30.86
Financial Help1 308 1.03 7.73E+05 194.17 21 -4.592 285 0.75 1.66E+06 222.69 28 -2.613 350 0.14 3.36E+06 176.01 19 -6.584 220 0.07 5.57E+05 84.25 11 -6.47
Leisure2 744 -0.01 197.75 190.16 3 -14.363 994 0.07 447.65 447.65 0 -12.254 605 0.11 780.03 777.68 2 4.96
Policy Experiments
• Provide a subsidy of qF to each parent that must be used for formal care (formal care stamps)
• Provide a subsidy of F to each child for each unit of time she provides informal care
• Provide a subsidy of F for each dollar spent on formal care (reduction in the price of formal care)
• Provide a lump sum of F to the parent• Increase the income limit for Medicaid• Provide a subsidy of qF to each parent for each
ADL problem that must be used for formal care.