Formal home health care, informal care and family decision making by Byrne, Goeree, Hiedemann & Stern (2009)

presented by Matthias Kredler Macro Reading Group UC3M

3 October 2012

presented by Matthias Kredler Macro Reading Group UC3M Formal home health care, informal care and family decision making

Motivation Facts: Population is rapidly aging in rich economies. Disabled elderly need substantial amounts of care. Care imposes substantial financial and/or time costs on families. Family is important provider of (“informal”) care, but paid (“formal”) care is becoming more important. ⇒ Important to understand families’ care decisions. This paper: Estimates a game-theoretic model of families’ care decisions. Evaluates policy options using this model.

presented by Matthias Kredler Macro Reading Group UC3M Formal home health care, informal care and family decision making

Environment and notation

Static game: Each family consists of one parent household (index i = 0) and I child households (i = 1, . . . , I ). The parent household consists of one or two persons ⇒ index: j = m (mother), j = p (father). Each child household consists of one or two persons ⇒ index: k = c (child), k = s (spouse). aij ∈ {0, 1}, aik ∈ {0, 1} indicate if j ,k exists in household i. The decision unit is the household, i.e. there are I + 1 players.

presented by Matthias Kredler Macro Reading Group UC3M Formal home health care, informal care and family decision making

Data: observed variables Health and Retirement Study (HRS), AHEAD sample, wave 1993 (no nursing-home residents!): Exogenous variables: Y0 : parent household’s income q: price of formal care in parents’ state pXi : local (general) price index for household i wik : child/spouse ik’s wage (imputed) Wi : other characteristics of household i

Endogenous variables: tijk : time spent by family member ik on informal care for parent j Lik : leisure of family member ik ¯ total amount of formal care H: ˜ i = 1 iff household i paid for formal care H u0j = 1 iff parent j says (s)he’s happy

[Consumption spending Xi is residually determined] presented by Matthias Kredler Macro Reading Group UC3M Formal home health care, informal care and family decision making

Data: care decisions

presented by Matthias Kredler Macro Reading Group UC3M Formal home health care, informal care and family decision making

Model: Health The mother’s physical well-being Qm is given by (analogous for father): I I X X X 2 2 Qm = a0p αm0p (tm0p +γtm0p )+ aik αmik (tmik +γtmik )+µ Hi +Zm , i=1 k∈c,s

i=0

where αmik is the quality of care from child/spouse ik for the mother (m), which is exponential-linear function of observables whose form has to be estimated, Hi is household i’s contribution to formal home health care (in time units), γ and µ are other coefficients that measure the effects of care, Zm = exp(Xm0 βz ): baseline health, a function of observables. presented by Matthias Kredler Macro Reading Group UC3M Formal home health care, informal care and family decision making

Preferences Parents’ utility U0 (measured by the discrete variable u0 ) is X X a0j ln Qj + β20 εX 0 ln X0 + a0k ln L0k + U0 =β0 + β10 j∈m,p

X

+

k∈m,p

a0k a0j (β40k + εt0jk )tj0k + εu0 ,

j,k∈m,p;j6=k

and child household i’s utility is X X Ui =β11 a0j ln Qj + εXi ln Xi + aik β31 εLik ln Lik + j∈m,p

+

X X

k∈c,s

aik a0j (β4jik + εtjik )tjik .

k∈c,s j∈m,p

[α, β’s: parameters, depend on elderly and caregiver characteristics if indexed by ijk; ε’s: shocks] presented by Matthias Kredler Macro Reading Group UC3M Formal home health care, informal care and family decision making

Constraints

1

All households face budget constraints of the form pXi Xi + qHi ≤ Yi , where household income Yi is government transfers Pand asset income for the P elderly, gross labor income k∈c,s aik wik (1 − Lik − j∈m,p tjik ) minus taxes for the young

⇒ Can back out Xi from budget constraint for all households. 2

From the elderly’s time constraint, back out L0k = 1 − tj0k .

presented by Matthias Kredler Macro Reading Group UC3M Formal home health care, informal care and family decision making

Equilibrium and first-order conditions

Nash equilibrium: 1 2

The elderly choose (H0 , tj0k ) to maximize U0 , each young household chooses (Hi , tjik , Lik ) to maximize Ui

given each other’s actions. A typical first-order condition – the one for children’s Hi – reads relative price effectiveness of H

z}|{ µ

×

β21 Qm |{z}

child’s marginal benefit from Qj

presented by Matthias Kredler Macro Reading Group UC3M Formal home health care, informal care and family decision making

=

z}|{ q pXi

×

εXi Xi |{z}

marginal benefit of Xi

Methodology Have data on families n = 1, . . . , N. Simple model:

This paper:

max{ln Cn + βεn ln Ln }

Cn ,Ln

Given {Xni }i=0,...,I , households choose Yni ⇒ Nash equilibrium

s.t. Cn pn ≤ wn (1 − Ln ) where εn = exp(σηn ), ηn ∼ N (0, 1) FOC:

FOCs: εn = (≤)f (Xn , Yn ; θ)

Cn wn εn β = L pn | {z n} |{z} MRS

rel. price

⇒ Can read off shocks εn needed to fulfill household’s FOCs (given θ and the observed characteristics/actions)

red: endogenous observables, blue: exogenous observables, orange: parameters, green: unobservables. presented by Matthias Kredler Macro Reading Group UC3M Formal home health care, informal care and family decision making

Maximum-likelihood estimation

For a given parameter vector θ: 1 2

3

Obtain shock vector εn for each family n from the FOCs. Read off the likelihood of shock vector εn from joint log-normal distribution (make adjustments for inequalities in FOCs) ⇒ obtain log-likelihood Ln (Yn |Xn ; θ). Add up log-likelihood of all families: X L(Y |X ; θ) = Ln (Yn |Xn ; θ). n=1,...,N

Search for global maximizer θ∗ of L.

presented by Matthias Kredler Macro Reading Group UC3M Formal home health care, informal care and family decision making

Results: predicted care decisions

presented by Matthias Kredler Macro Reading Group UC3M Formal home health care, informal care and family decision making

Results: caregiving motives

Baseline health Zm , and thus care needs, 1 2

are not significantly affected by ADL (activities of daily living) problems, and baseline health improves with age.

Informal care is somewhat effective in raising well-being, formal care isn’t. Remove gender differences in care effectiveness and burden ⇒ Men give as much care as women ⇒ Lower opportunity costs are not the reason why most caregivers are women.

presented by Matthias Kredler Macro Reading Group UC3M Formal home health care, informal care and family decision making

Policy experiments

The authors study various policy experiments that subsidize different forms of care. Almost all policies have essentially no effects on behavior. Reasons: 1 2 3

Many families are at corner solutions. Both formal and informal care have little influence on well-being. The model predicts essentially zero formal care.

presented by Matthias Kredler Macro Reading Group UC3M Formal home health care, informal care and family decision making