W HY

DO THE OF

E LDERLY S AVE ? T HE ROLE

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 September 2009

Why do the Elderly Save? Sept. 2009 – p. 1/37

Overview What do we do? Estimate a structural model of savings after retirement allowing for heterogeneity in: medical expenses life expectancy What are we trying to understand? The saving of the elderly: Many elderly individuals keep lots of assets. High income individuals deplete their assets more slowly than low income individuals.

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Figure 1: AHEAD data (unbalanced panel) Why do the Elderly Save? Sept. 2009 – p. 3/37

Figure 2: AHEAD data (unbalanced panel) Why do the Elderly Save? Sept. 2009 – p. 4/37

Mortality bias Sample composition changes: High income people and women live longer

+

→

In an unbalanced panel, this causes observed assets to increase with age

Why do the Elderly Save? Sept. 2009 – p. 5/37

Figure 3: Median assets by birth cohort, AHEAD data Why do the Elderly Save? Sept. 2009 – p. 6/37

Contributions Estimate medical expenses using better data (from the AHEAD) and more flexible functional forms. Medical expenses rise quickly with age and PI. Construct and estimate a rich model of saving. Reasonable parameter estimates Model fits the data extremely well. Find that medical expenses and social insurance are important in understanding the elderly’s savings. Results are robust to: including a bequest motive making medical expenditures endogenous Why do the Elderly Save? Sept. 2009 – p. 7/37

Model Singles only, abstract from spousal survival. Households maximize total expected lifetime utility. Flow utility from consumption (CRRA). Utility can vary with health. Rational expectations. Beliefs about mortality rates, health cost distribution, etc., are estimated from the data. Bequest motive. Functional form follows De Nardi (2004): bequests are a luxury good.

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Uncertainty Health status: age-, gender- and permanent-income-specific Markov chain. Survival: function of gender, age, health status, and permanent income. Medical expenses: has both deterministic and stochastic components, deterministic component a function of gender, age, health status, and permanent income. Income: deterministic function of gender, age, and permanent income.

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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.

Transfers support a consumption floor: bt = max{0, cmin + mt − [at + yn (rat + yt ), τ )]}.

Borrowing constraint: at+1 ≥ 0. Why do the Elderly Save? Sept. 2009 – p. 10/37

Recursive formulation (

c1−ν Vt (xt , g, I, ht , ζt ) = max [1 + δht ] t ct ,xt+1 1−ν   + βsg,h,I,t Et Vt+1 (xt+1 , g, I, ht+1 , ζt+1 ) ) (xt − ct + k) (1−ν) + β(1 − sg,h,I,t )θ 1−ν xt = cash-on-hand = at + yn (rat + yt , τ ) + bt − mt g = gender;

I = permanent income

ht = health status (0 ⇒ bad, 1 ⇒ good) ζt = persistent health cost shock Why do the Elderly Save? Sept. 2009 – p. 11/37

Method of simulated moments Match median assets by permanent income quintile, cohort and age. 101 moment conditions. Correct for cohort-effects and mortality bias – rich people live longer – by: using cohort-specific moments and initial conditions allowing mortality rates to depend on permanent income and gender

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AHEAD data Household heads aged 70 or older in 1993/4 Consider only the retired singles Follow-up interviews in 1995/6, 1998, 2000, 2002, 2004, 2006 Asset data begins in 1996 (1994 asset data faulty), uses 2,688 individuals Use full, unbalanced panel

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Results from first step estimation

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Figure 4: Average medical expenses, AHEAD data Why do the Elderly Save? Sept. 2009 – p. 15/37

Income Quintile bottom second third fourth top

Healthy Unhealthy Healthy Unhealthy Male Male Female Female 7.6 8.4 9.3 10.5 11.3

5.9 6.6 7.4 8.4 9.3

12.8 13.8 14.7 15.7 16.7

10.9 12.0 13.2 14.2 15.1

All 11.1 12.4 13.1 14.4 14.7

Men Women

9.7 14.3

Healthy Unhealthy

14.4 11.6 Table 1: Life expectancy at age 70 Why do the Elderly Save? Sept. 2009 – p. 16/37

Results from second step estimation

Why do the Elderly Save? Sept. 2009 – p. 17/37

Benchmark (1)

Health (2)

Bequests (3)

All (4)

ν: coeff. relative risk aversion

3.81 (0.50)

3.75 (0.47)

3.84 (0.55)

3.66 (0.55)

β: discount factor

0.97 (0.04)

0.97 (0.05)

0.97 (0.05)

0.97 (0.04)

0.0 NA

-0.21 (0.18)

0.0 NA

-0.36 (0.14)

2,663 (346)

2,653 (337)

2,665 (353)

2,653 (337)

θ: bequest intensity

0.0 NA

0.0 NA

2,360 (8,122)

2,419 (1,886)

k: bequest curvature (in 000s)

NA NA

NA NA

273 (446)

215 (150)

82.3 87.4%

80.6 88.5%

81.5 85.4%

77.5 90.5%

Parameter

δ: pref. shifter, good health cmin : consumption floor

Overidentification statistic P-value

Table 2: Estimated Structural Parameters Why do the Elderly Save? Sept. 2009 – p. 18/37

Figure 5: Median assets by cohort and PI quintile: data and benchmark model Why do the Elderly Save? Sept. 2009 – p. 19/37

Distribution of bequests: data and model

10000

.9 .8 .7 .6 .5 0

.1

.2

.3

.4

probability

.6 .5 .4 0

.1

.2

.3

probability

.7

.8

.9

1

No Bequest Motive

1

Bequest Motive

30000

100000 value of assets

300000

1000000

10000

30000

100000 value of assets

300000

1000000

Figure 6: Cumulative distribution function of assets held 1 period before death: data and model. Legend: solid line is model, lighter line is data.

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Experiment Fix preference parameters at baseline estimates, vary other parameters. Eliminating out-of-pocket medical expenditures has a big effect on savings.

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Figure 7: Benchmark and model with no medical expenditures Why do the Elderly Save? Sept. 2009 – p. 22/37

Endogenous medical expenditure model Retirees receive utility from Medical goods: utility depends on age, health, shocks. Consumption of other goods (as before). Medical expenditure does not affect health and/or survival. Most studies find variations in medical expenditures have little effect on health outcomes.

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Additional moment conditions In addition to matching asset profiles, we also match: mean and 90th percentile of medical spending, conditional on age and permanent income 1st and 2nd autocorrelations of logged medical spending

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Results for endogenous expenditure model Flow utility: 1 1−ν 1 u(ct , mt , ht , ζt , ξt , t) = ct + µ(t, ht , ζt , ξt ) mt1−ω , 1−ν 1−ω

where: mt =medical expenditures; µ(·)= medical “preference shifter”. Estimated parameters: ν = 2.15; ω = 3.19; β = 0.99. Model fits asset and medical expenditure data well. Medical spending is still important: Eliminating out-of-pocket medical expenditures still has a big effect on savings. Why do the Elderly Save? Sept. 2009 – p. 25/37

Figure 8: Benchmark and model with no medical expenditures Why do the Elderly Save? Sept. 2009 – p. 26/37

Conclusions Model fits data well with reasonable preference parameter values. Key elements include: heterogeneous lifespans medical expenses that rise with age and PI consumption floor Results are robust to: including a bequest motive making medical expenditures endogenous

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Figure 9: Average income, AHEAD data Why do the Elderly Save? Sept. 2009 – p. 28/37

Constraints in detail


xt+1 = max{xt − ct + y r(xt − ct ) + yt+1 , τ − mt+1 , cmin }, yt+1 = y(g, h, I, t + 1), xt ≥ cmin , ct ≤ x t , ln(mt+1 ) = m(g, ht+1 , t + 1, I) + σ(g, ht+1 , I, t + 1)ψt+1 , Why do the Elderly Save? Sept. 2009 – p. 29/37

ψt+1 = ζt+1 + ξt+1 .

Income Healthy Unhealthy Healthy Unhealthy Quintile Male Male Female Female bottom second third fourth top

10.1 13.7 17.8 23.3 27.8

bottom second third fourth top

0.6 0.9 1.3 2.0 2.6

Percentage living to age 85 6.9 35.7 28.6 9.3 41.1 34.1 12.3 46.4 40.2 16.6 51.7 45.5 21.2 57.1 49.9 Percentage living to age 95 0.4 6.3 5.1 0.6 7.9 6.7 0.9 9.6 8.4 1.4 11.6 10.2 2.0 13.8 11.8

All 28.8 35.3 38.9 45.2 46.5 5.0 6.7 7.8 9.5 10.0

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Method of simulated moments: details Consider household i of birth cohort c in calendar year t, belonging to the q th permanent income quintile. Let aqct denote the model-predicted median asset level. Moment condition for GMM criterion function:


E I{ait ≤ aqct } − 1/2 | q, c, t, hh i alive at t = 0.

Convert into an unconditional moment:   E I{ait ≤ aqct } − 1/2 × I{qi = q} × I{ci = c}  × I{hh i alive at t} t = 0.

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Econometric problem 1: cohort effects Older HHs are born in earlier years and have lower lifetime incomes ⇒ understate asset growth and saving. Our solution: Cohort- and permanent income-specific moments; cohort-specific initial conditions.

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Econometric problem 2: mortality bias Sample composition changes: High PI people and women live longer.

+

→

In an unbalanced panel, this causes observed assets to increase with age Our solution: Allow mortality rates to depend on permanent income and gender.

Why do the Elderly Save? Sept. 2009 – p. 33/37

Figure 10: Median assets by birth cohort, AHEAD data Why do the Elderly Save? Sept. 2009 – p. 34/37

Endogenous medex: recursive formulation (

1−ω c1−ν m t V (t, at , g,ht , I, ζt , ξt ) = max + µ(t, ht , ζt , ξt ) t ct ,mt ,at+1 1 − ν 1−ω )   + βsg,h,I,t Et V (t + 1, at+1 , g, ht+1 , I, ζt+1 , ξt+1 ) ,

subject to: at+1 = at + yn (rat + yt ) + b(t, at , g, ht , I, ζt , ξt ) − ct − mt q(t, ht ),

and other constraints. Why do the Elderly Save? Sept. 2009 – p. 35/37

Medical expenditures: data and model .9 .8 .7 .6 .5 0

.1

.2

.3

.4

probability

.6 .5 .4 0

.1

.2

.3

probability

.7

.8

.9

1

Endogenous Medical Expenditure

1

Exogenous Medical Expenditure

500

1500

3750 10000 medical expenses

27500

75000

500

1500

3750 10000 medical expenses

27500

75000

Figure 11: Cumulative distribution function of medical expenses: data and the exogenous (left panel) and endogenous (right panel) medical expenditure models. Legend: solid line is model, lighter line is data. Why do the Elderly Save? Sept. 2009 – p. 36/37

Figure 12: Median consumption by cohort and PI quintile: benchmark model Why do the Elderly Save? Sept. 2009 – p. 37/37