W HY DO THE E LDERLY S AVE ?T HE ROLE OF M EDICAL E XPENSES Mariacristina De Nardi Federal Reserve Bank of Chicago and NBER Eric French Federal Reserve Bank of Chicago John Bailey Jones University at Albany, SUNY December 2009 Why do the Elderly Save? Sept. 2009 – p. 1/46
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WHY DO THE ELDERLY SAVE? THE ROLE
OF MEDICAL EXPENSES
Mariacristina De NardiFederal Reserve Bank of Chicago and NBER
Eric FrenchFederal Reserve Bank of Chicago
John Bailey JonesUniversity at Albany, SUNY
December 2009
Why do the Elderly Save? Sept. 2009 – p. 1/46
Overview
What do we do?Estimate a structural model of savingsafter retirement allowing for heterogeneity in:
medical expenseslife expectancy
What are we trying to understand? The saving of theelderly:
Many elderly individuals keep lots of assets.High income individuals deplete their assets moreslowly than low income individuals.
Why do the Elderly Save? Sept. 2009 – p. 2/46
Figure 1: AHEAD data (unbalanced panel)
Why do the Elderly Save? Sept. 2009 – p. 3/46
Figure 2: AHEAD data (unbalanced panel)
Why do the Elderly Save? Sept. 2009 – p. 4/46
Why our model?
Data show considerable heterogeneity inlife expectancymedical expenses
By:agegenderpermanent incomehealth
Why do the Elderly Save? Sept. 2009 – p. 5/46
Heterogeneity implications
For saving behaviorDifferential mortality⇒ heterogenous saving rates,with high PI people and women saving more.Medical expenses rise quickly with age⇒ keep assetsfor old age.Medical expenses rising with PI⇒ high PI people saveat higher rate.
Why do the Elderly Save? Sept. 2009 – p. 6/46
Heterogeneity implications: continued
For observed sample:mortality biasSample composition changes: High PI people andwomen live longer
+ →In an unbalanced panel, this causes observed assets toincreasewith age
Why do the Elderly Save? Sept. 2009 – p. 7/46
How we do it
First step: estimate mortality and medical expenses as afunction of age, gender, health and permanent income.
Second step: use first step results to estimate our modelwith method of simulated moments.
Why do the Elderly Save? Sept. 2009 – p. 8/46
Contributions
Estimate medical expenses using better data and moreflexible functional forms.
Medical expenses rise quickly with age and PI.
Estimate mortality probabilities by age, gender, permanentincome, and health.
Variation is large.
Find that medical expenses and social insurance areimportant in understanding the elderly’s savings.
Results are robust to:including a bequest motivemaking medical expenditures endogenous
Why do the Elderly Save? Sept. 2009 – p. 9/46
Related literature (subset)
Hubbard et al. (1994, 1995), Palumbo (1999)
Scholz et al. (2006)
Hurd (1989); De Nardi (2004); Kopczuc and Lupton(2007); Dynan et al. (2002); Ameriks et al. (2009).
Why do the Elderly Save? Sept. 2009 – p. 10/46
Model
Singles only,abstract from spousal survival.
Householdsmaximize total expected lifetime utility.
Flow utility from consumption (CRRA). Utility can varywith health.
Rational expectations.Beliefs about mortality rates, healthcost distribution, etc., are estimated from the data.
Bequest motive.Functional form follows De Nardi (2004):bequests are a luxury good.
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Income
yt = y(g, h, I, t),
g = gender,h = health,I = permanent income.
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Uncertainty
Health status: age-, gender- andpermanent-income-specific Markov chain.
Survival: function of gender, age, health status, andpermanent income.
Medical expenses:
ln(mt) = m(g, ht, I, t) + σ(g, ht, I, t)ψt,
ψt = ζt + ξt,
ζt = AR(1) shock,ξt = white noise shock.
Why do the Elderly Save? Sept. 2009 – p. 13/46
Constraints
Budget constraint:
at+1 = at + yn(rat + yt, τ) + bt −mt − ct.
yn(.) = post-tax income;yt = “non-interest” income;τ = tax parameters;bt = government transfers;mt = medical expenses.
Table 2: Estimated Structural ParametersWhy do the Elderly Save? Sept. 2009 – p. 25/46
Figure 5: Median assets by cohort and PI quintile: data and bench-
mark model
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Mortality bias
Figure 6: Left panel→ AHEAD data; right panel→ benchmark
model
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Bequests
Bequest motives are large for the richest people, but veryimprecisely estimated.
They do not improve the model’s fit.They do not not change other parameters.
This doesnot mean bequests are unimportant:
The estimated bequest motive implies that the richbequeath 88 cents of every dollar.Our data set does not contain many rich people.
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Distribution of bequests: data and model0
.1.2
.3.4
.5.6
.7.8
.91
10000 30000 100000 300000 1000000value of assets
prob
abili
ty
Bequest Motive
0.1
.2.3
.4.5
.6.7
.8.9
1
10000 30000 100000 300000 1000000value of assets
prob
abili
ty
No Bequest Motive
Figure 7: Cumulative distribution function of assets held 1 period
before death. Left, model with bequest motives. Right:
model without. Solid line: model, lighter line: data.
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Experiments
Fix preference parameters at baseline estimates, vary otherparameters.
Eliminating out-of-pocket medical expenditures has a bigeffect on savings.
Eliminating medical expense risk has a small effect.
Lowering the consumption floor by 20% has a big effect onsavings, even for the rich.
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Figure 8: Benchmark and model with no medical expenditures
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Figure 9: Benchmark and model with no medical expense risk
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Figure 10: Benchmark and model with the consumption floor re-
duced by 20%
Why do the Elderly Save? Sept. 2009 – p. 33/46
Making medical expenditures endogenous
Retirees receive utility from medical goods.
Medical expenses do not affect health and/or survival:RAND experiment (Brook et al., 1983); Fisher et al. (2003);Finkelstein and McKnight (2005); Khwaja (2009).
Why do the Elderly Save? Sept. 2009 – p. 34/46
Endogenous medical expenditure model
Flow utility:
u(ct,mt, ht, ζt, ξt, t) =1
1 − νc1−νt +µ(t, ht, ζt, ξt)
1
1 − ωm1−ω
t ,
µ(·) : medical “preference shifter”mt : total medical expendituresq(t, ht)mt : out-of-pocket medical expenditures
Transfers: set to guarantee a minimum level of utility, andthus depend onµ(·):
b(t, at, g, ht, I, ζt, ξt) = max{0, b∗(t, at, g, ht, I, ζt, ξt)}.
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Expanded estimation
In addition to matching asset profiles, we now match:
mean and90th percentile of medical spending,conditional on age and permanent income
1st and2nd autocorrelations of logged medical spending