Long-term Care, Home Health Care, and Informal Care David Byrne, Michelle Goeree, Bridget Hiedemann, and Steven Stern October 2005

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)


Joint modelling of care and labor force participation

• Ettner (1996)


Intergenerational transfers and household formation

• Hoerger, Picone and Sloan (1996)

• Pezzin and Schone (1999)

Game theoretic


• 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



Focus on single caregiver

• Cantor (1983)

• Stoller and Earl (1983)

• Horowitz (1985)

• Barber (1989)


• Miller and Montgomery (1990)


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


• If ∂Ui/ ∂Hi<0, then FOC implies

pmj j

j

i

iXiiXi

Q

aQ

q

QXp

,

0

2

1

where


• 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

Qq

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


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.


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**


(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


(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.

Documents

Long-term Care, Home Health Care, and Informal Care David Byrne, Michelle Goeree, Bridget Hiedemann, and Steven Stern October 2005