Long-term Care, Home Health Care, and Informal Care David 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)

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 X i, contributions to paid help for the parent H i, leisure L ik, time spent caring for each parent t ipk and t ifk, 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-L ik -Σ j t ijk.

The coefficients β 1i, β 2i, β 3ik, and β 4jik are deterministic functions of observed child characteristics The errors ε Xi, ε Lik, and ε tijk are functions of unobserved child characteristics It is assumed that β 1i ≥0, β 2i ≥0, β 3ik ≥0, ε Xi ≥0, and ε Lik ≥0,

Budget Constraint For each child,

Budget Constraint We estimate Y i and s using CPS data and allow it to vary across states For the parent, the budget constraint is Y 0 +G 0 ≥p X0 X 0 +qH 0 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(qH 0 -qH) ≥ p X0 X 0 1 ≥L 0k +t 0jk

Consumption For each child and parent, we can solve for X i using the budget constraint to get

Formal Care Payments For each player other than the parent, the set of FOCs for H i is

Formal Care Payments If ∂U i / ∂H i <0, then FOC implies

Formal Care Payments If ∂U i / ∂H i =0, then FOC implies

Informal Care Hours The FOCs for t ijk depend on H i. If H i >0,

Informal Care Hours If H i =0,

Leisure

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 ,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

Empirical specification β 30k and β 4j0k can not be identified separately because the parents’ leisure time is determined jointly with their caregiving time. Thus, we set β 30k =0 with no loss in generality. Increasing all of the β terms by the same proportion has no effect on choices. Thus, we set β 2i =1.

Empirical Specification

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 β 4i >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 β 4i <0.

Estimates with Variation in log α and β 4 (Parent Characteristics) VariableEstimate on log α Estimate on logZ Estimate on β 4 Estimate on log β 1 Constant-5.089**-3.203**-4.186**-0.722** Age/ **-3.121** Education-0.020** White Married 0.331** #ADLs-0.165**-0.287**-0.280** Mother0.353** Spouse Characteristics Age/ ** #ADLs-0.095**

Estimates with Variation in log α and β 4 (Child Characteristics) VariableEstimate on log α Estimate on β 4 Estimate on log β 1 Estimate on log β 3 Constant-0.752**-5.333** 1.113** 0.346** Age/ ** 9.933** Male 0.389** Biological Biological* Male ** Education ** Married 0.401* ** #Kids 0.053**-0.317** Oldest

Estimates with Variation in log α and β 4 (Other Parameters) VariableEstimateVariableEstimate logμ **logσ ηt 0.890** γ **logσ u ** logβ **ρLρL logσ ηX ρtρt logσ ηL 0.221

Goodness-of-fit Results

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.