Does Publicly Provided Home Care Substitute for Family Care?

By Liliana E.Pezzin, Peter Kemper, and

James Reschovsky;Journal of Human Resources, Summer 1996, v. 31, n.3.

Presented by Mark L. Trueman

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Introduction• Elderly population in U.S. expected to double by 2030. Demand for

long term care (LTC) increasing.• Types of LTC for the poor:

– In kind, by unpaid “informal” caregivers (IC).– Institutional arrangements: e.g., nursing homes (N)- thru

Medicaid.– “Formal” home care (FC)- Subsidy. Limited.

• Concern: subsidies may increase LTC expenditures w/o lowering nursing home use.

• Purpose of paper: gain a better understanding of the extent to which public subsidy of formal home care substitutes for family care.

• Key feature: estimate how living arrangement (LA) choices and hours of IC (HIC)/LA differ in presence/ absence of public subsidy program.

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Decompose the Effects of Subsidy (FC)

1. Direct effect (aka “hours effect”): the induced marginal change in behavior of informal caregivers :

• change in hours of IC to individuals in a given LA, weighted by probability of choosing a particular LA.

2. Indirect effect (aka “LA effect”): change in the probability of choosing a specific LA:

• this change in probability is weighted by E(HIC/ LA).

* Note: Policy making may be more effective in countering the direct effects- tailor interventions through case management guidelines on IC and respite care.

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Theoretical Model• Max U=U(X, L, F; τ) s.t. an “arrangement specific budget constraint”

– X is a vector of private goods, or a composite commodity– L is leisure– F is a measure of disabled, elderly person’s functioning; May be produced in:

• Community setting: Either Separate/ Joint households– Requires Compensatory LTC: either HFC or HIC where H is hours– F = F(HFC, HIC ; D) where D is the level of disability

• Institution: Nursing home services (N), exclusively– F = F(N; D)

– τ is a taste parameter- captures family preferences for privacy and independence (affects utility of LA options)

• Step 1: Choose optimal X, L, and F/ on each LA

– { X*, L*, F*; H*FC, H*IC } are the cond’l commodity and input demands. • Step 2: Compare values, then choose type of care (IC and/or FC; or N) and LA (separate/ joint households)

which maximizes overall utility, U*.– Let j = index of LA options:

• j = 0, independent living (separate household)• j = 1, shared living (joint “intergenerational” household)• j = 2, institutional living (nursing home)

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Theoretical Model Continued• By substitution, we get a set of indirect utility functions, Vj , where:

– I = family’s unearned income– PIC = shadow price of informal caregiving time– PFC = price of formal home care– PN = price of nursing care– Px = 1 (nummeraire)

• V0 = V0(I, PIC, PFC) = U*[X0*, L0*, F0*(HIC,0*, HFC,0*; D); τ]

• V1 = V1(I, PIC, PFC) = U*[X1*, L1*, F1*(HIC,1*, HFC,1*; D); τ]

• V2 = V2(I, PN) = U*[X2*, L2*, F2*(N; D); τ]

• Chosen living arrangement will be:– j* = argmax[Vj(I, PIC, PFC, PN; t, D)] for j = 0,1, 2

• Implied (conditional) demands:– HIC* = HIC(I, PIC, PFC, PN; D/ j*)– HFC* = HFC(I, PIC, PFC, PN; D/ j*)– N* = N (I, PIC, PFC, PN; D/ j*)

• Eq’n (2) implies that a subsidy program that reduces PFC affects family’s conditional demand functions but also LA choices.

• əE(HIC)/ əPFC = Σ{ə E(HIC / j)/ əPFC * Prob(j) + [əProb(j)/ əPFC]* E(HIC / j)

(1)

(2)

Direct Effect + Indirect EffectOverall Effect = (3)j

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Channeling Experiment & Data• National test of expanded public financing of home care, 1982-1985.

• Aim: Test whether a managed system of home and community based services could be a cost effective alternative to institutionalization.

• 5 communities/ 6,236 eligible applicants

• individuals channeled into one of 3 groups, which had case managers (CMs)

– Group 1/ “Basic”: CMs determine needs/ services under existing system (i.e., limited grants, $, to finance home care services)

– Group 2/ “Financial”: Direct provision of home care subject to a CM’s authorization & cost limits >>>> substantial increase in use of HFC ($$$)!

– Group 3/ Control Group

• Screening interviews to establish eligibility (disability & unmet need) & follow-up interviews to collect data (service use, LA, # of “visiting”/ “resident” hrs.).

• Average age: 79, most w/ multiple functional limitations.

• Average monthly income: < $ 530.

• At 1-Year follow-up interview: 28% died; 15% nonrespondents; 57% analyzed.

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Living Arrangements : Unmarried Persons

40%

41%

19%

Independent Living

Shared Living

Institution

Living Arrangements: Married Persons

70%

19%

11%

Independent Living

Shared Living

Institution

Informal Care: Avg. # of "Visiting" Hours(Living Arrangement: Independent)

0

2

4

6

8

10

Unmarried Persons Married Persons

Informal Care: Avg. # of "Resident" Hrs.(Living Arrangement: Shared)

25

26

27

28

29

30

Unmarried Persons Married Persons

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Empirical Model (1)• Eq’n (2) counterparts of LA choice & HIC:

– Vijt* = ßj0 + ΣßjgTig,t + ΣßjmAim,t-1 + ΣßjkZik,t-1 + εijt (4)– ln HICijt = γj0 + Σ γjgTig,t + Σ γjkZik,t-1 + μijt (5)

– Vijt* = latent variable, value to family i choosing jth LA, at time t,

• Where:– ln HICijt = ln of IC hours in family i, choosing jth LA, at time t,– t is at 1- year follow up evaluation; t-1 is at initial screening,– T is a (1 X g) vector of dummies for treatment status (“basic”, “financial”)– Z is a (1 X k) vector of variables proxying remaining elements which affect family’s utility & cond’l demand functions:

(I,PIC, PN, D). Preexperimental measures of family’s economic, demographic, & health status, prior service use, and “site” dummies.

– A is a (1 X m) vector capturing family’s transactions costs and τ (prior LA)

– Assumes εijt and μijt are distributed BVN (0,0,σε2, σμ

2,ρ) where ρ is the correlation between LA choices and hours of informal care (HIC).

• ß and γ are the vectors of coefficients to be estimated in the model.

• Vijt* is an indicator of which of the “j” LA alternatives is chosen.• An elderly person will be observed in a particular LA, V ijt = 1 iff Vit* falls into a particular

interval αj-1 < Vit* < αj .• [αj] is a vector of (J +1= 2+1=3) thresholds in the latent variable index, where α0=0.

g m k

g k

“HFC: subsidy”

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Empirical Model (2)• Model is operationalized by assuming that LA choices can be

ordered in hierarchy corresponding to higher levels of assistance:– Independent, shared, institutional living

• Eq’n (4) reduces to an ordered probit model.– Elderly person will attempt to live independently as long as possible,

until a threshold is reached; then switches.

• Probability of any level Vit* is chosen is given by:– Prob [Vijt = 1] = Φ[ (αj –β'Yi)/ σε] - Φ[ (αj-1 –β'Yi)/ σε] (6)

• Φ(•) represents a cdf,• Y is a matrix of all nonstochastic explanatory variables in eq’n (4),• Assumes and σε = 1.

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Empirical Model (3)• Use a 2-step estimation procedure that provides estimates of

the effects of Channeling on LA choices and IC provision.– Step 1: £ = Π Π [Φ(αj –β'Yi) - Φ(αj-1 –β'Yi)]Vijt (7)– Step 2: Estimate the effect on HIC / LA choices by applying OLS to

a new version of Eq’n (5):• E(ln HICit/ j) = γj0 + Σ γjgTig,t + Σ γjkZik,t-1 + bjλij + μijt* where,

– HIC represents either “visiting” or “resident” care hrs,– bjλij is a selectivity bias correction due to nonrandom selection of LA choice.

• Model is estimated separately for each person’s marital status at time of follow-up, t.– Married/ unmarried have substantially different endowments of

potential care. Presence of spouse affects role of others/incentives.– We expect unmarried to be more responsive to intervention.

(8)

i j

g k

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Results: LA Choices (1)

• Rows 1 and 2 coefficients represent Channeling’s impact on Vit*, after controlling for differences in preexperimental LA.

• Financial intervention increased probability of being in more independent LA.

• Married folks have lower threshold value by which they will switch LA.

Table 2Maximum Likelihood Ordered Probit Estimatesof the LA Choice Models

Variables Unmarried Married

Basic Intervention (0.053) 0.090

Financial Intervention (0.215) (0.008)

Threshold (a1) 1.348 0.773

Log likelihood 5,176 1,964

Sample Size 4,421 1,905

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Results: LA Choices (2)

• Table 3 shows predicted probabilities of each LA choice in presence and absence of each interventions (from equation (6)).

• Financial interventions effect on LA choices of unmarried individuals was substantial.

Table 3LA Predicted Probabilities

Basic Intervention Financial InterventionVariables Treatment Control Difference Treatment Control Difference

Unmarried Independent living 0.407 0.390 0.017 0.450 0.379 0.071 Shared living 0.399 0.403 (0.004) 0.391 0.415 (0.024) Institution 0.194 0.206 (0.012) 0.158 0.205 (0.047)

Married Independent living 0.651 0.681 (0.030) 0.729 0.726 0.003 Shared living 0.212 0.199 0.013 0.178 0.180 (0.002) Institution 0.137 0.120 0.017 0.093 0.094 (0.001)

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Results: HIC/LA choice (1)

• Table 4 presents estimated experimental impacts on HIC, adjusted for LA choices: Eq’n (8).

• Overall, there is no evidence that the intervention had a significant impact on conditional hours of care, net of its impact thru LA.

• Strong & significant effect of the LA correction term on both visiting & resident hours for the unmarried sample.

• Authors assert that it is important to control for the endogeneity of the LA choices when analyzing use of LTC.

Table 4OLS Estimates of HIC/ LA Choice

Visiting Hrs. Resident Hrs.

UNMARRIEDIndependent living Basic treatment (0.127) N/A Financial treatment (0.203) N/A LA correction ( lambda) (1.127) N/A Adjusted R-sqd 0.115 N/A Sample size 1,029 N/AShared living Basic treatment 0.050 (0.077) Financial treatment 0.009 (0.104) LA correction ( lambda) 0.460 (0.515) Adjusted R-sqd 0.097 0.147 Sample size 1,059 271MARRIEDIndependent living Basic treatment (0.042) 0.009 Financial treatment (0.109) 0.182 LA correction ( lambda) (0.832) 0.575 Adjusted R-sqd 0.072 0.090 Sample size 680 173Shared living Basic treatment 0.248 0.207 Financial treatment 0.178 0.591 LA correction ( lambda) 0.868 0.824 Adjusted R-sqd 0.043 0.153 Sample size 187 52

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Results: HIC/LA choice (2)

• The coefficients in the previous table were used to find the predicted hours in table 5, based on Eq’n (8).

• Greater reductions in informal care are observed for those receiving more generous financial intervention.

Table 5Predicted Hours of Visiting & Resident Informal Care by LA Choice- Unmarried Sample

Basic Intervention Financial Intervention

Treatment Control Difference Treatment Control Difference

Visiting hours Independent 8.6 10.3 1.7 8.1 11.9 3.8

(2.3) (2.5)

Shared living 5.6 5.1 0.5 6.1 5.5 0.6(0.8) (0.9)

Resident hours Shared living 37.5 41.5 4.0 35.0 42.9 7.9

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Results: Overall, Direct, & Indirect Program Effects (1)

• Table 6 presents the results of a simulation: an experimental analog of Eq’n (3):

əE(HIC)/ əPFC = Σ{ə E(HIC / j)/ əPFC * Prob(j) + [əProb(j)/ əPFC]* E(HIC / j)}

Overall Effect = Direct (or Hours) Effect + Indirect (LA) Effect• For each individual:

– calculate predicted probability of choosing each LA, P-hat, assuming treatment, then control status; average of these predictions: E[Prob (j)].

– calculate predicted hours of visiting and resident care, HIC-hat, each would receive had he/she chosen each LA, according to the estimated hours equation; average of these predictions: E(H IC

/ j) in the presence and absence of each treatment

• Overall program impact is given by: (1/N) Σ Σ (PTifHT

ICif – PCifHC

ICif) (9)• LA effect is given by (1/N) Σ (PT

if – PCif) HC

ICif (10)• Hours effect is given by (1/N) Σ (HT

if – HCif) PC

ICif (11)

j

i

j i

i

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Table 6Decomposition of Overall Treatment Effect into Direct (Hours) Effects and Indirect (LA) Effects- Unmarried Sample

Visiting Resident

Hours Hours Total

BASIC INTERVENTIONHours effect Independent living 0.4 0.0 0.4 Shared living 0.2 1.6 1.4 Total 0.2 1.6 1.8Living arrangement effect Independent living 0.1 0.0 0.1 Shared living 0.0 0.2 0.2 Total 0.1 0.2 0.1Overall effect 0.1 1.7 1.9

FINANCIAL INTERVENTIONHours effect Independent living 1.0 0.0 1.0 Shared living 0.2 2.9 2.7 Total 0.8 2.9 3.7Living arrangement effect Independent living 0.6 0.0 0.6 Shared living 0.1 0.9 1.0 Total 0.5 0.9 0.4Overall effect 0.3 3.8 4.1

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Conclusions• Public home care provision results in:

– only small reductions in overall amount of care provided by informal caregivers to unmarried persons;

– No reductions for married persons.

• Implication: benefits of such programs will flow primarily to disabled elderly recipients rather than to informal caregivers.

• Decomposition suggests that the direct effect on hours of care assuming no change in LA, is likely to dominate any overall effect of subsidized care.

• Policymakers concerned with potential substitution should focus their attention on specific measures designed to minimize caregiver’s behavioral responses rather than on discouraging effects due to LA choices.

• Channeling financial intervention had both sizable and statistically significant effects on LA decisions of unmarried persons.

– Increased probability of living independently by 7.1% relative to control group.

– Increase was associated with corresponding significant reduction in probabilities of living with others (2.4%) and of living in a nursing home (4.7%)

• The more generous intervention appears to have enabled unmarried elderly persons with disabilities to live more independently.

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Questions Raised

• Are the benefits from increased independence and associated quality of life sufficient to justify the cost of expanded public home care coverage for this group?

• If so, can the targeting of benefits to unmarried persons be justified on equity grounds?