public economics lectures taxes and behavior: saving, part...

Public Economics LecturesTaxes and Behavior: Saving, Part 2

John Karl Scholz

University of Wisconsin —MadisonFall 2011

JK Scholz ()Tax Incentives and Saving 1 / 51

Figure 3 from Engen, Gale and Uccello

Observations on age-consumption (and age-wealth profiles):

Consumption is low when young: households have a desire to build upprecautionary saving.It’s higher in middle age: income rises, as does wealth. Incomeuncertainty is resolved, so the precautionary motive diminishes.High education households have steeper age-earnings profiles than lesswell educated households.Consumption declines in old age: The higher mortality probabilities forthe elderly, however, effectively makes households less patient, so theyare less willing to defer consumption because they might be dead.


Figure 5

This figure assumes retirement at age 62.

Households will deplete all wealth by age 90 or 95 and, if they survivelonger, they’ll live on their social security annuity.


Figure 6

Stochastic earnings matter.

It is not possible to make inferences about time preference rates (orr − δ) from the slope of consumption profiles when there are stochasticearnings.


Bernheim, Skinner and Weinberg (AER, 2001)

What are implications of the life-cycle model and how do these matchstylized facts about consumption?

What explains the remarkable variation in wealth observed in data?If the life-cycle model is a good representation of behavior, it impliessome specific patters we should be able to examine.

Variation in wealth

Fix income profiles (earnings, social security, pensions, etc.). The slopeof the consumption profile (a standard Euler equation representation)Et (CT+1)−Ct

Ct≈ γ

(1− 1

αt

)+ Ψ

2 σ2t+1 where γ: the intertemporal

elasticity of substitutionαt ≡ (1+r )(1−Πt+1)

1+δ where r : the real interest rate; δ: Pure rate oftime preference; Πk : : probability of dying at time k; Ψ:precautionary inclinations; σ2t+1: Variance of consumption in t+1

As long as γ 6= 0, variation in wealth is due to these factors.Consumption grows with r and falls with δ and Π.


Figure 1

There should be a positive correlation between wealth at retirementand the growth rate of consumption before or after retirement.

A falling consumption profile ⇒ low wealth at retirement. A risingprofile would imply the opposite.


Figure 2

The change in consumption at retirement.

One should see a negative correlation between retirement wealth andthe size of the consumption discontinuity at retirement.If the drop in consumption is due to work expenses falling or activitiesthat are substitutable for leisure, this should be observable.


Figure 3

Factors affecting overall consumption.

Differences in bequest motives may affect wealth (though these are notwell-observed).

Wealth may vary because of differences in income profiles.

Households with higher income replacement rates (from social securityof pensions) should have less wealth.But, higher income replacement rates may also be correlated withtastes for saving. So...Earnings replacement rates (since they are known) should not becorrelated with the size of the consumption decline at retirement, aslong as the household is not credit constrained.


Figures 4 and 5

Do consumption growth rates around retirement vary systematicallywith retirement wealth? No.

They should if pure rates of time preference, subjective survivalprobabilities, income uncertainty, or tastes of precaution vary.

There is a discontinuity income consumption at retirement. The sizeis negatively correlated with retirement saving and incomereplacement rates.

The discontinuity does not appear to be related to work expenses orincome replacement rates.Unplanned retirement does not appears to explain the consumptiondiscontinuity.There is no reason why bequest motives would lead to largerconsumption drops for low-wealth households.


Figures 4 and 5, continued

There appears to be no relationship between income replacementrates and wealth.

If people are intertemporally smoothing the marginal utility ofconsumption, it is surprising that consumption drops at retirement arenegatively related to income replacement rates, since there is nosurprise income replacement rates.

BSW argue the patterns are not consistent with forward-looking,lifecycle households. Rather, they are better understood by "rule ofthumb" behavior, mental accounting or other behavioral models.


Hurst and other thoughts

The PSID consumption data are not great.

It just provides data on food at home and food away, augmented withinformation on the value of the dwelling. They have 430 households.The only observe wealth in 1984 and 1989, so they interpolate for theintermediate years.

Hurst notes that the decline in consumption at retirement is robustacross datasets and across years, however. So the BSW results arenot an anomaly of (perhaps) less-than-ideal PSID data.

The decline, however, occurs solely in work-related expenses (clothingand transportation costs) and food (meals at home and means awayfrom home).Between the early and late 60s, spending falls for total food (10.3%),clothing (22.4%), and non-durable transportation (20.2%).Entertainment spending increases 8.7%, charity increases 40%.There is some evidence that households expect consumption to fallupon retirement. Why?


Hurst, continued

Why would there be a consumption discontinuity at retirement?

With lower opportunity cost of time, the elderly can do morenon-market production.

Hurst finds no deterioration in diet: time diaries suggest the elderlyspend more time in food production. Pay lower prices (throughcoupons) and prepare more stuff at home.The old folks shop harder!

Erik argues that lower income households do appear to have biggerconsumption declines.

I’m puzzled by this because of sharply progressive social securityreplacement rates.One will obviously see consumption discontinuities around involuntaryretirement, such as the receipt of an adverse health shock.


Are Americans Saving “Optimally” for Retirement?

John Karl Scholz, UW-MadisonAnanth Seshadri, UW-Madison

Surachai Khitatrakun, The Urban Institute

Many are skeptical that people save adequately for retirement.Bernheim: The “Baby Boomer Retirement Index:”

Saving rates will have to triple.Bernheim, Skinner, and Weinberg (2001)

Unexpected consumption drops at retirement.Moore and Mitchell (1998), Wolff (2002)

“Retirement wealth accumulation needs to be improved for the vast majority of households.”

Spendthrift American stories are common in the financial press.

Why do we care?Worry that income deficits in retirement will result in political pressure for larger transfers.

The elderly are more likely to vote than others.

Fundamental issue for the life-cycle model.Retirement saving is a big issue for the well-being of households. If the LC model can’t get this right, the power of the model would seem to be limited.Are there opportunities to improve household well-being merely by better allocating resources across time?

A lot of households worry about retirement.

Figure 1: Median DB Pension Wealth, Social Security Wealth, and Net Worth (Excluding DB Pensions) by Lifetime Earnings Decile, (1992 dollars)

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

1 2 3 4 5 6 7 8 9 10

Lifetime Household Earnings Decile

Dol

lars

Pension Social Security Wealth Net Worth

Assessing the optimality of household saving

Our strategy is straightforward.We write down a specific augmented life-cycle model. Use the model to determine optimal wealth, household-by-household in the HRS.Compare the model to observed wealth in HRS.

Joint test: a) Did we write down a sensible model? And b) given the model, are people saving enough?If the approach fails, it’s hard to say whether a) or b) is the problem. A close match, however, is noteworthy for both the policy issue and for the life-cycle model.

Later in the paper we explore whether alternative models might do better and conduct sensitivity analyses.

We Build on the Large Life-Cycle Consumption LiteratureFeatures of the literature and our paper

Precautionary saving (Deaton; Carroll; Aiyagari).Asset-tested transfers (Hubbard, Skinner, Zeldes, 1995)

Medical shocks (Palumbo, 1999)We build on the fine paper of Engen, Gale, and Uccello (1999), which also addresses these issues.

The new features of our work include40 years of data on actual household earnings. These allow us to develop household-specific targets solving the dynamic programming problem for each household.We model empirically household expectations about SS, DB pension benefits, and earnings trajectoriesWe incorporate time-varying representations of the individual income tax and transfer system.

A simple, augmented life-cycle model

( )/ , subject toD

j Sj j j

j SE n U c nβ −

=

⎡ ⎤⎢ ⎥⎣ ⎦∑

{ }( , , ), ,..., ,j j j j j jy e ra T e a n j S R= + + ∈

( ) { }( ), 1,..., ,R

j j R jj S

y SS e DB e ra T j R D=

⎛ ⎞= + + + ⋅ ∈ +⎜ ⎟

⎝ ⎠∑

( ) { }( ) { }

1

1

, ,...,

, 1,...,

j j j j j j

j j j j j j

c a y a e ra j S R

c a m y a y j R D

τ

τ

+

+

+ = + − + ∈

+ + = + − ∈ +

Recursive formulation: retired households

subject to ( ) ( ) ( , , , , ),R R R R j j jy SS E DB e ra T e E a n m= + + +

( ) ,c a m y a yτ′+ + = + −

,

(2,0) ( / (2,0))

( , , , 1, ',3) ( ' | )

'( , , , , ,3) max ,(1 ) ( , , , 1, ,1) ( ' | )2

'(1 ) ( , , , 1, , 2) ( ' | )2

hj wj R R jm

R R c a hj wj R R js

wj hj R R js

g U c g

p p V e E a j m d m m

mV e E a j m p p V e E a j d m m

mp p V e E a j d m m

β

β

β

′

+⎧ ⎫⎪ ⎪

′ + Ω +⎪ ⎪⎪ ⎪

= ⎨ ⎬′− + Ω +⎪ ⎪⎪ ⎪⎪ ⎪′− + Ω⎩ ⎭

∫

∫

∫

Recursive formulation: the working adult case

subject to ( , , , ),y e ra T e a j n= + +

( )' , andj jc a y a e raτ+ = + − +

1 .E E e−= +

'

' ' '1 ,

( , ) ( / ( , ))( , , , ) max ,( , , , 1) ( | )

j j j j

c a je

g A K U c g A KV e E a j V e E a j d e eβ− ′

+⎧ ⎫⎪ ⎪= ⎨ ⎬+ Φ⎪ ⎪⎩ ⎭∫

The Health and Retirement Study (HRS)

National panel study of 7,702 households (12,652 persons) in 1992.

Face-to-face interviews of 1931-1941 birth cohort and their spouses (if married).Oversamples blacks, Hispanics, and Floridians.

Follow-up telephone interviews every two years since 1992 (up to 2002).

We primarily use the 1992 survey.

Key features: social security earnings histories, fertility history, DB pension information, wealth data, and out-of-pocket medical expenses.

Our HRS SampleWe make three sample exclusions, dropping…

379 married households where one spouse refused to participate in the 1992 survey;

We lack needed information on household characteristics93 households who never worked full time;

We do not have a reasonable measure of lifetime resources

908 households where the highest earner began working fulltime before 1951.

Our model used to impute earnings is computationally more difficult with missing initial values.

Our resulting sample has 6,322 households.

Imputing Missing or Top-Coded Earnings InformationTwo problems (not created equally)

22.8 percent of respondents refused to release SS earnings records (1951-91)

Results are unchanged if we drop these hhlds (fn. 6).16 percent between 1951-79 are top-coded (we have W2 records from 1980-91).

Assume individual log-earnings process, where * indicates the latent variable

* ',0 ,0 0 ,0

* * ', , 1 , ,

, ,

{1, 2,..., }i i i

i t i t i t i t

i t i i t

y x

y y x t Tu

β ε

ρ β ε

ε α−

= +

= + + ∈

= +

Imputing Earnings, cont.Estimate with a dynamic panel Tobit model, with random effects assumption for the error termParameters:

Estimate separately for 4 groups: gender x some college. Estimates are in Appendix Table A1.

“Undoing” top-coded data:Once we have the parameter estimates, we use a Gibbs Sampling procedure to calculate the conditional expectation of top-coded observations. An analytic expression is not available.

Model parametersPreferences

Equivalence scale

Taxes (dollar amounts in thousands)

1

, if 1( ) 1

log , if =1.96 and 3

cU c

c

γ

γγ

γβ γ

−⎧≠⎪= −⎨

⎪⎩

= =

0.7( , ) ( 0.7 )j j j jg A K A K= +

( )1 11

0 2( ) , from Gouveia and Strauss (1994, 1999)a ay a y y aτ−

−⎛ ⎞= − +⎜ ⎟⎝ ⎠

Model parameters, continued

Transfers

Household Earnings Expectations

Estimate parameters for 6 groups: married (one earner), married (two earner), and single, by 2 education statuses (college degree, yes or no).

Rho is .58 to .76 (sensitivity to .9)

Real return 4% (sensitivity to 5%, 7%)

[ ]( , )

max 0, (1 ) ,(1, 2)

j jg A KT c m e r a

g⎧ ⎫

= × + − + +⎨ ⎬⎩ ⎭

21 2log i

j j j je AGE AGE uα β β= + + +

1 ,j j ju uρ ε−= +

Model Parameters, continuedSocial Security

Using earnings realizations and expectations, we model social security rules.

DB PensionsWe estimate empirical DB pension functions based on years of service in pension-covered job, unionization status, and the expectations about the final-year earnings.

Out of Pocket Medical expenses (married*ed)2

0 1 2 ,t t t tm AGE AGE uβ β β= + + +2

1 , ~ (0, ),t t t tu u N ερ ε ε σ−= +

Solving the modelStart at the oldest possible date (100), solve backwards for all possible individual states of the world each period.

We construct discrete grids of feasible assets (100 points) and interpolate.We successively move backwards solving for the value function and the decision rule for assets.

Once we have all decision rules, we take the specific earnings realizations (from SS earnings records) for each household (and other characteristics) to solve for the optimal level of wealth in the 1992 HRS.

Opt

imal

Net

Wor

th

Observed Net Worth0 200,000 400,000 600,000 800,000 1000000

0

200,000

400,000

600,000

800,000

1000000

Scatterplot of Optimal and Actual Household Net Worth

Group Percentage Failing to

Meet Optimal Target

Median Deficit

(conditional on deficit)

Median Optimal Net Worth Target

Median Net Worth

Median Social

Security Wealth

Median DB Pension Wealth

All Households

15.6% $5,260 $63,116 $102,600 $97,726 $17,371

No High School Diploma

18.6% $2,632 $20,578 $36,800 $72,561 $0

High School Diploma

15.6% $5,702 $63,426 $102,885 $97,972 $21,290

College Degree

12.7% $14,092 $128,887 $209,616 $127,704 $60,752

Post College Education

13.2% $23,234 $158,926 $253,000 $129,320 $152,639

Lowest Lifetime Income Decile

30.4% $2,481 $2,050 $5,000 $26,202 $0

4th Income Decile

19.4% $4,730 $43,566 $74,710 $77,452 $18,428

7th Income Decile

9.9% $11,379 $80,402 $133,500 $133,451 $55,100

Highest Lifetime Income Decile

5.4% $25,855 $238,073 $388,629 $202,659 $123,192

Group Median Optimal Net Worth Target

Mean Optimal Net Worth Target

Median Net Worth

Median Social

Security Wealth

Median DB Pension Wealth

All Households

$63,116 $157,246 $102,600 $97,726 $17,371

No High School Diploma

$20,578 $70,771 $36,800 $72,561 $0

High School Diploma

$63,426 $139,732 $102,885 $97,972 $21,290

College Degree

$128,887 $243,706 $209,616 $127,704 $60,752

Post College Education

$158,926 $333,713 $253,000 $129,320 $152,639

Lowest Lifetime Income Decile

$2,050 $48,445 $5,000 $26,202 $0

4th Income Decile

$43,566 $123,441 $74,710 $77,452 $18,428

7th Income Decile

$80,402 $154,891 $133,500 $133,451 $55,100

Highest Lifetime Income Decile

$238,073 $463,807 $388,629 $202,659 $123,192

Correlates of Undersaving dF/dx § Standard Error

2nd Lifetime Income Decile .016 .0183rd Lifetime Income Decile -.005 .0194th Lifetime Income Decile .015 .0235th Lifetime Income Decile -.006 .0246th Lifetime Income Decile -.021 .0257th Lifetime Income Decile -.017 .0288th Lifetime Income Decile -.061** .0259th Lifetime Income Decile -.046 .02910th Lifetime Inc. Decile -.043 .034Retired .001 .011Has Pension -.003 .011Social Security Wealth -9.41e-08 1.88e-07Age -.002 .001Male -.007 .012Black -.006 .012Hispanic -.028 .015Married -.272*** .017High School Degree .004 .012College Degree -.009 .018Graduate Degree -.000 .020Self Employed -.012 .014

Figure 3: Distribution of "Saving Adequacy"Observed Minus Simulated Optimal Net Worth, Excluding DB Pensions, by Lifetime Earnings Decile (1992 dollars)

-50,000

0

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

1 2 3 4 5 6 7 8 9 10

Lifetime Earnings Decile

Diff

eren

ce [1

992$

]

10th Percentile 25th Percentile 50th Percentile 75th Percentile 90th Percentile

Median Regression of “Saving Adequacy” (Actual-Optimal Net Worth)

Coefficient Estimates Standard Error

8th Lifetime Income Decile 19,828.8*** 4,114.7 9th Lifetime Income Decile 26,526.0*** 5,185.3 10th Lifetime Income Decile 60,023.1*** 8,446.7 Has Pension -2,362.5** 985.8 Social Security Wealth 0.043* 0.023 Married 10,375.1*** 1,401.4 Self-Employed 14,226.7 4,037.4 Number of Children -30.8 224.2 Number of Grandchildren -98.2 88.6 Subjective Probability of Living > 75 11.7 16.3 Subjective Probability of Living > 85 -11.4 16.0 Subjective Probability of Bequest > $10k 16.0* 9.6 Subjective Probability of Bequest > $100k 296.9*** 31.3 Mid-Atlantic Division 1,692.6 3,747.3 East North Central Division 1,117.2 3,807.2 West North Central Division SD, NE 4,079.0 3,936.5 South Atlantic Division 1,336.2 3,759.7 East South Central Division 2,166.4 3,908.3 West South Central Division -282.1 3,963.4 Mountain Division 2,925.1 3,961.4 Pacific Division 3,736.3 3,941.6

Sensitivity Analysis: Housing and Social Security

Some believe the elderly are unwilling to use housing equity to support consumption.

Not clear this is true (Hurd, 2003).Even if it is, we like including housing in net worth. Still…

If we assume households are unwilling to use half of housing net worth to support living standards.

61.2% of households meet or exceed their targets25th (10th) percentile conditional deficit is $7,692 ($33,178)

The social security system modeled in the paper may be fiscally unsustainable.

Cut expected and actual SS benefits by 25 percent (from 1951) – 37.2 percent of households fail to meet optimal targets.

Table 4: Alternative Models and Sensitivity Analysis

Parameter Value Percentage Failing to Meet Optimal Target

Measure of Fit: 2R (in %)

Deficit Conditional on Failing to Meet

Optimal Target (1992$)

Baseline: 0.96β = , 3γ = , 4%r = 15.6 86.0 5,260

Alternative Models Naïve (save a constant fraction of Yt)

71.9 15.5 114,335

Naïve (save an income- and age-varying fraction of Yt)

75.7 15.8 160,676

Modigliani (annual consumption a function of lifetime resources)

48.7 6.5 89,129

Constant Alpha 35.1 45.2 30,411

Regression Including 41 Years of Earnings 59.4 29.2 109,212

Regression with Quadratic Terms for 41 Years of Earnings

60.2 35.3 101,229

Monte Carlo Draws on Earning Sequence 32.2 45.2 28,623

Source: Authors’ calculations as described in the text.

Does the Model Match Other Features of the Data?

Consumption tracks income.Consumption trajectories (netting out the effects of children) are hump-shaped and peak at 46 (income trajectories peak at 51).

The wealth distribution is skewed.The top 1 percent holds 17 percent of wealth (it’s 15.9 percent in the data, which is consistent with bequests playing a role in wealth accumulation).

The model can explain 22.6 percent of the 1992-2000 change in wealth.

A reduced-form regression model with X’s, 41 years of earnings, and earnings squared, accounts for 6.9%.

Sensitivity Analysis: Fundamental Parameters

Table 4: Alternative Models and Sensitivity Analysis

Parameter Value Percentage Failing to Meet Optimal Target

Measure of Fit: 2R (in %)

Deficit Conditional on Failing to Meet

Optimal Target (1992$)

Baseline: 0.96β = , 3γ = , 4%r = 15.6 86.0 5,260

Parameter Sensitivity of Baseline Model 1.0β = 21.1 87.7 5,483

0.93β = 11.9 83.6 5,919

5%r = 20.0 87.2 5,500

7%r = 35.9 76.7 15,955

1.5γ = 11.8 91.9 4,699

5γ = 31.6 85.9 9,087

0.9ρ = 25.8 69.1 16,103 5 percent chance of 4

years of $60,000 end of life medical expenses

20.5 85.1 4,800

Source: Authors’ calculations as described in the text.

ConclusionsWith a common formulation of the life-cycle model, we explain 86 percent of the 1992 cross-sectional variation in wealth of HRS households.

Moreover, we find 84 percent of households meet or exceed their optimal wealth targets. And the conditional deficits tend to be small.

We interpret this as a) strongly suggestive that the life-cycle model is capable of explaining life-cycle wealth accumulation and b) that the consumption changes around retirement noted by Bernheim et al. are not driven by inadequate retirement wealth accumulation.

Results are prior to the 1990s stock market run-up

Final thoughtsAre Americans saving “optimally”?

Deliberately provocative title, though we are much closer to saying “yes” than we were before doing this.

Some households in top half of lifetime income distribution are saving “too much”

Bequest motives? Heterogeneity in rates of return or deep preference parameters?

The Aftermath

CHILDREN AND HOUSEHOLD CHILDREN AND HOUSEHOLD WEALTH

John Karl Scholz, UW-MadisonAnanth Seshadri, UW-Madison

April 2011 (the paper has a July 2009 date, but we’re revising)

Why Do We Carey

The “replacement rate” concept ignores children. The replacement rate concept ignores children. Children are one reason why wealth is more dispersed than earnings.dispersed than earnings.Children (for better or worse!) are ubiquitous.

In this paper we marry a model of endogenous fertility In this paper we marry a model of endogenous fertility with a model of life-cycle consumption.

So utility is a function of consumption and the quality and quantity of children.

Unlike our previous paper, we focus only on married l 1992couples in 1992.

The Paper Examines the Effects of Children on Wealth AccumulationChildren on Wealth Accumulation

We showWe showChildren are important to understanding wide wealth disparities.Children have a much larger effect than asset tests associated with cash and near-cash means-tested transfers.Takeaway point: adults in families with children grow y p gaccustomed to lower standards of living than adults in otherwise equivalent families.

Children Do Not Appear in the Most Closely Related LiteraturesClosely Related Literatures

Explain the wealth distribution.pLife Cycle Model: Modigliani & Brumberg (1954)Buffer Stock Framework: Deaton (1991)Precautionary Savings: Aiyagari (1991)y g y g ( )Bequests: De Nardi (2004)Variation in Time Preference: Krusell and Smith (1998)

Explain low wealth of the very poor.Explain low wealth of the very poor.Variation in Time Preference: Lawrance (1991), Time-Inconsistent Preferences: Laibson (1997) Effect of Safety Net: Hubbard Skinner and Zeldes (1995)ec o Sa e y Ne : ubba d S e a d e des ( 995)

Common theme: Given an earnings distribution, what is the implied wealth distribution? The studies typically find that the concentration of wealth (absent bequests) implied by models is ( q ) p ylower than in the data.

The Health and Retirement Study (HRS)The Health and Retirement Study (HRS)

National panel study of 7,702 households (12,652 p y , ( ,persons) in 1992.

Face-to-face interviews of 1931-1941 birth cohort and th i (if i d)their spouses (if married).Oversamples blacks, Hispanics, and Floridians.

Follow-up telephone interviews every two years since 1992 (up to 2002).

We primarily use the 1992 survey.

Key features: social security earnings histories, fertility history, DB pension information, wealth data, and out-of-pocket medical expenses.

Table 1: Variation in Age of Last Birth, Earnings, and Net Worth by Number of Children for Married Couples, Weighted 1992 Datap , g

Percentage of

Total

Mean Age When

Last Child

Mean %age

Earnings

MedianNet

Worth

Mean Net

Worth

Mean UndiscountedLifetime Earnings (1992

dollars)Number

f Total Population

Last Child is Born

EarningsAfter Last

Child is Born

Worth Worth dollars)of Children

0 3.1 Not Applicable

Not Applicable

$192,000 $316,952 $1,775,255

1 6.5 29.6 84.2 134,200 282,528 1,728,8102 24 9 31 0 82 7 182 000 327 299 1 854 4702 24.9 31.0 82.7 182,000 327,299 1,854,4703 22.4 32.1 79.5 163,155 322,252 1,816,2244 17.1 33.5 75.5 132,000 259,855 1,644,5185 9.7 34.7 73.0 118,800 239,207 1,560,7376 6.3 35.3 71.1 98,580 205,403 1,498,221

7 or more 10.1 37.4 66.7 73,100 182,037 1,343,040All

Married100.0 32.9 77.4 142,885 280,549 1,696,928

Married Couples

Figure 1: Net Worth in 1992 as a Percentage of Summed,Real Lifetime Earnings By Family Size Married Couples HRS Data

13.0

Real Lifetime Earnings, By Family Size, Married Couples, HRS Data

10 0

11.0

12.0

etim

e Ea

rnin

gs

8.0

9.0

10.0

Net

Wor

th to

Life

6.0

7.0

8.0

n of

the

Rat

io o

f

4.0

5.0

0 1 2 3 4 5 6 7

Med

ian

0 1 2 3 4 5 6 7+Number of Children

Table 2: Variation in Net Worth, Fertility and Earnings by Lifetime Earnings Deciles, Married Couples, 1992 Data, Weighted

Married CouplesLifetime Earnings

Median 1992

Mean 1992

Mean Number

Mean Age of Head Mean %age of Earnings

Decile Net Worth Net Worth of Children When Last Child is Born

After Last Child is Born

Lowest $33,000 $109,006 4.6 35.5 68.62 65,400 159,462 4.2 33.7 73.63 87,500 165,335 3.8 32.4 77.84 105,286 211,178 3.6 32.7 77.5

Middle 126,200 201,292 3.7 32.4 78.06 135 000 233 372 3 5 32 5 77 86 135,000 233,372 3.5 32.5 77.87 175,456 290,330 3.3 31.8 79.68 203,852 317,147 3.3 32.8 78.69 261,000 438,408 3.3 32.5 80.3, ,

Highest 433,800 680,671 3.1 33.1 82.1All Married

Couples142,885 280,549 3.7 32.9 77.4

Notes: Authors’ calculations from 1992 data

11Figure 2: Median Age-Log Earnings Profiles by Family Size, Married Couples

10.5

1gs

10og

Ear

ning

9.5Lo

9

20 30 40 50 60Age

0 12 34 56 7+

The Descriptive Data Suggest…

There are several possible mechanisms through which There are several possible mechanisms through which children affect wealth accumulation.

Family size is correlated with lifetime earnings.Like many others, we take the earnings process as being exogenous.

The number of children varies with lifetime income. Those with more children have children later in life so children Those with more children have children later in life, so children are present in the household for a larger portion of adults’ working years.

Of course children eat resourcesOf course, children eat resources.The upshot, with uncertainty in earnings, health, and lifespan, the timing of fertility affects consumption decisions.

A Permanent Income Model (for intuition it’s no longer in the paper!)intuition – it s no longer in the paper!)

bj ( )/T

jβ∑T T

j jc y∑ ∑subject to ( )

0max /j

j j jj

n U c nβ=∑

0 0(1 ) (1 )j j

j ji i

c yr r= =

=+ +∑ ∑

• Optimal consumption (assuming CRRA

⎛ ⎞⎜ ⎟

⎛ ⎞

preferences) is given by

[ ][ ] /

/0

(1 )(1 )(1 )

Tjj j

j j jT jjj

n yc r

rn rγ

γ ββ =

⎜ ⎟⎛ ⎞⎜ ⎟= +⎜ ⎟⎜ ⎟ ++ ⎝ ⎠⎜ ⎟

⎜ ⎟

∑∑

0 (1 ) jj r=

⎜ ⎟+⎝ ⎠∑

• The family size adjustment (the first term in parentheses) is quantitatively important

Household Consumption over the Life-Cycle (couple w/ 5 children)

0.7( 0.7 ) ; .03; 0.97; 3j j jn A K r β γ= + = = =This model, however, yields too

2

2.2 little dispersion in wealth. The poor save nothing. The wealthy save too

1 4

1.6

1.8 wealthy save too little, relative to the data. We need a richer model with

1

1.2

1.4precautionary saving, credit constraints, and uncertainty in

0.820 30 40 50 60 70 80 90

Age of household head

uncertainty in earnings, lifespan, and longevity.

Assessing the Effect of Children on Wealth A l tiAccumulation

We write down a specific augmented life-cycle model with endogenous fertility.

Precautionary saving; asset-tested transfers; medical shocks.40 f d t t l h h ld i 40 years of data on actual household earnings.

These allow us to develop household-specific targets solving the dynamic programming problem for each household.

W d l i i ll h h ld i b SS DB We model empirically household expectations about SS, DB pension benefits, and earnings trajectoriesWe incorporate time-varying representations of the individual income tax and transfer system.

We then do counterfactual simulations, examining the effects on individual decisions of altering (demographic) effects on individual decisions of altering (demographic) characteristics of households.

A Life-Cycle Model with Endogenous Fertility

W d l f tilit d i i i th i it f B k• We model fertility decisions in the spirit of Becker and Barro (1988)

• Assume all children are born at a specific date (B) 27• Assume all children are born at a specific date (B) 27.• Children are attached to parents for 18 years.Household’s decision problem isHousehold s decision problem is

1 7

( ) ( ) ( ) ( ) ( )D B

j S j S k j Sj j

j S j BE U c d f U c d f bβ β β

+− − −

= =

⎡ ⎤+ + Φ⎢ ⎥

⎣ ⎦∑ ∑

( ) { }17 wherekc fc a y a e ra j B Bτ+ + = + − + ∈ +

The budget constraint when children are around is( ) { }1 , ,..., 17 ,k

j j j j j j jc fc a y a e ra j B Bτ++ + = + − + ∈ +

( ) { }{ }

1 , ,..., 17 , where

(1 ) ( , , , ), ,..., .j j j j j j j

j j j j j j

c fc a y a e ra j B B

y f e ra T e a j n j S R

τ

κ++ + = + + ∈ +

= − + + ∈where

{ }(1 ) ( , , , ), ,...,κ= − + + ∈j j j j j jy f e ra T e a j n j S R

Each child requires κ of the parent’s earnings (think of these as indirect time costs)

The Endogenous Fertility Model, cont.g y ,

d(f) denotes the utility from quantity of children, f, which is increasing and concave.

The indirect time cost, κ, implies that higher-earning households will have fewer children.households will have fewer children.

The model now has three extra choice variablesThe model now has three extra choice variablesThe fertility rate, f, consumption per child, cj

k, and bequests, b.

The budget constraint for retired households is the same as it was for our earlier paper.

Solving the Model

: ( ) ( ) ( ),k k

j j jc U c b f U c′ ′=

( )VT⎡ ⎤ ∂∂1

( ) , 0< <11cU c

γ

γγ

−

=

First Order Condition for fertility choice

11

( ): ( ) ( ) ( ) ( )k BB B B B

VTf U c c e b f EV b f Ef f

κ ++

⎡ ⎤ ∂∂′ ′+ − = +⎢ ⎥∂ ∂⎣ ⎦

ii 10 1

1( ) ,0 1bb f b f b

γ−= < <

Functional FormsFunctional Forms1

( ) , 0< <1cU cγ

γ−

=

10 1

( ) , 0 11

( ) ,0 1b

U c

b f b f b

γγ−

= < <0 1( ) ,0 1b f b f b< <

ParametersMost of the parameters come from our earlier paper, “Are Americans Saving ‘Optimally’…”. Relative to h kthis prior work,

We need to specify 4 new parameters, κ, γ, b1, and b0.

We take κ the time cost of children from Haveman We take κ, the time cost of children, from Haveman and Wolfe (1995). They calculate that a child reduces a mother’s time in the paid labor force by 9.5 percent of earnings, so we set κ = 0.095.

For the remaining three parameters we use the structure of the model, the assumed value of the equivalence scale, and the model, the assumed value of the equivalence scale, and a restriction that the model must match the fertility rate of the median family to tie down the remaining parameters.γ= 0 48 b =0 53 and b =0 64γ= 0.48, b1=0.53, and b0.=0.64.

Table 3: Actual and Optimal Net Worth and Children, Married Couples, weighted 1992 Data

Lifetime Earnings Decile

Median 1992 Net Worth

Median Optimal

Net WorthMean 1992 Net Worth

Mean Optimal

Net Worth

Mean Number of Children

Mean Optimal

Number of ChildrenDecile Worth Net Worth Net Worth Net Worth Children Children

Lowest $33,000 $16,684 $109,006 $69,405 4.6 4.52 65,400 43,405 159,462 107,878 4.2 4.23 87,500 58,167 165,335 133,239 3.8 4.04 105,286 72,621 211,178 150,685 3.6 3.8

Middle 126,200 93,276 201,292 162,949 3.7 3.86 135,000 107,122 233,372 197,664 3.5 3.77 175,456 127,192 290,330 243,222 3.3 3.58 203,852 183,075 317,147 269,594 3.3 3.4, , , ,9 261,000 218,950 438,408 361,473 3.3 3.3

Highest 433,800 350,986 680,671 585,261 3.1 3.2

All M i d142,885 115,148 280,549 228,073 3.7 3.7

All Married Couples

, , , ,

Source: Authors' calculations from Health and Retirement Study data, as described in the text.

1000000

800,000

t Wor

th

600,000

Opt

imal

Net

400,000

200,000

Observed Net Worth0 200,000 400,000 600,000 800,000 1000000

0

Observed Net Worth

0

Figure 3: Optimal by Actual Children, Married Couples8

106

8f C

hild

ren

46

Num

ber o

f2

4O

ptim

al N

02

0

0 1 2 3 4 5 6 7 8

The First Experiment: The Number and Timing of Children

T l h ff f h b d i i f To explore the effects of the number and timing of children on life-cycle wealth accumulation…

We give all married households 3.6 children, born at age We give all married households 3.6 children, born at age 27.

I th l t l f T bl 4 h th t th In the last column of Table 4, we show that the effect arises from changing the number of children, and not their timing.children, and not their timing.

Here, married couples get children at ages 23, 26, 29, and 0.6 of a child arrives at 33.

F l h ld k h b f h ld Fractional children make the aggregate number of children in the simulations match the aggregate in the population.

Altering the number and timing of children increases wealth of low-income households and reduces the dispersion of net worth.

Table 4: The Effects of Eliminating Variation in the Number and Timing of Children, Married Couples, weighted 1992 HRS data

Baseline No Variation in Kids

Lifetime Median Credit

Constrained Median Credit

Constrained

Median Optimal Net Worth, No

Variation in Earnings Decile Net Worth Until Age… Net Worth Until Age… Timing

Lowest $16,684 37 $26,452 26 $27,485 2 43,405 35 64,859 28 65,2833 58 167 33 74 506 29 73 0493 58,167 33 74,506 29 73,0494 72,621 32 80,563 29 81,032

Middle 93,276 30 86,384 30 87,3646 107,122 29 103,625 31 104,9507 127,192 28 112,849 31 113,0498 183,075 30 155,967 32 156,0499 218,950 31 187,489 33 188,263

Highest 350,986 33 266,379 34 265,830Highest 350,986 33 266,379 34 265,830All Married

Couples115,148 31 109,624 30 108,094


Children or the Safety Net?yIt is straightforward in the context of our model to eliminate the safety net and examine the effect of eliminate the safety net and examine the effect of doing so on wealth accumulation.

The structure of the safety net is very similar to Hubbard, Ski d Z ld (1995)Skinner, and Zeldes (1995).

Their consumption floor (for a single parent with two children) is $7,000 (in 1984$), ours (in 1984) is roughly $6,300.

A similar fraction of the population receives benefitsA similar fraction of the population receives benefits.25.3% of no HS diploma people get transfers in 1980 (their average age is 44) – 23.7% of households 40-49 in PSID get transfers in 1984. There is a similar close correspondence in 1990.

We model precisely the actual SS system (it is less clear what they do, but they may assign a fixed benefit based on age).

In contrast to the conclusions of HSZ (1995), the means-tested transfer system has an almost imperceptible effect on

optimal wealth accumulation in a life-cycle model with children.Table 5: Effects of the Transfer System on Optimal Median Net Worth and Children, Married Couples, weighted 1992 HRS data

Lifetime Earnings

Optimal Net Worth,

Endogenous Optimal

Optimal Net Worth,

Endogenous Fertility, No

Optimal Fertility,

No

Optimal Net

Worth, No

Optimal Net Worth, No

Children, NoEarnings Decile

Endogenous Fertility

Optimal Fertility

Fertility, No Transfers

No Transfers

No Children

Children, No Transfers

Lowest $16,684 4.5 $23,125 4.2 $39,586 $89,208 2 43,405 4.2 55,579 4 65,600 118,5043 58 167 4 0 67 467 3 9 79 372 141 2073 58,167 4.0 67,467 3.9 79,372 141,2074 72,621 3.8 78,476 3.8 96,375 144,589

Middle 93,276 3.8 97,296 3.7 103,282 154,5676 107,122 3.7 110,048 3.6 138,399 162,354, , , ,7 127,192 3.5 128,882 3.5 170,577 198,7618 183,075 3.4 183,864 3.4 220,391 245,4639 218,950 3.3 219,463 3.3 265,084 280,945

Hi h t 350 986 3 2 351 193 3 2 396 706 409 384Highest 350,986 3.2 351,193 3.2 396,706 409,384All Married

Couples115,148 3.7 119,362 3.7 151,029 183,049


Why Are There Such Stark Differences Between HSZ (1995) and Our Results?

The approaches have similar transfer systems, social security benefits, and similar numbers of households y ,receive transfers.

HSZ h d d l h ff f h ldHSZ, however, do not model the effects of children.As we’ve seen, low-income families have more children.

Not accounting for children is critical as shown in the last two columns of the previous table, which replicates the HSZ resultsreplicates the HSZ results.

Why Do Asset- and Income-Tested Transfers Have Such a Small Effect on a s e s ave Suc a S a ec oOptimal Wealth Accumulation?

40% of households in the lowest lifetime income decilehave SS replacement rates above the consumption floor.

For the remaining 60%, SS and DB pensions replace, on average, 55% of income in the 5 years prior to retirement. Retirement consumption relative to consumption when 5 children are in the house would optimally be 50% lower (given our equivalence scale).

Children, therefore, can largely account for the low asset accumulation of households in the lowest lifetime income deciles.

HSZ (1995) appear to find very large effects of the income- and asset-tested transfer system because they fail to account for the role of children.

It is worth noting…g

Compared to HSZ, our results imply a larger positive effect of transfer programs on

ti d h lfconsumption, and hence welfare.Our results suggest poor households have few assets in part due to commitments to their children.in part due to commitments to their children.

Transfer programs increase consumption.If we assumed no variation in family size, cutting transfers would have increased asset accumulation transfers would have increased asset accumulation, thereby leading to a smaller overall effect on consumption and welfare.

There are indeed differences in net worth by family size in the HRSworth by family size in the HRS

Table 6: Correlates of Household Net Worth, Married Couples, 1992 HRS DataDependent Variable: Net Worth OLS Median Regression OLS Median RegressionConstant -306,180 -182,395 -378,306 -202,598

(91 741)*** (37 893)*** (96 233)*** (38 021)***(91,741)*** (37,893)*** (96,233)*** (38,021)***High School Graduate 40,234 13,073 47,544 14,350

(17,891)** (4,805)*** (17,938)*** (6,042)**College Degree 58,987 51,811 57,090 52,002

(26,668)** (11,840)*** (26,681)** (13,521)***Post-College Degree 129,288 81,925 127,863 73,548

(29,732)*** (16,800)*** (29,735)*** (19,304)***(29,732) (16,800) (29,735) (19,304)Age 7,244 3,590 7,862 3,663

(1,518)*** (665)*** (1,539)*** (579)***Has a Defined Benefit Pension -161,840 -29,466 -153,614 -24,108

(14,733)*** (5,638)*** (14,847)*** (8,784)***African-American -86,256 -37,732 -92,098 -35,270

(21,259)*** (5,815)*** (21,258)*** (7,677)***Hispanic -71,204 -15,204 -86,735 -17,534

(25,429)*** (7,468)** (25,660)*** (7,874)**Number of Children -6,384 -2,601

(2,902)** (828)***Number of Children * Bottom Lifetime Income Quintile 3,753 246

(4,009) (808)Number of Children * 2nd Lifetime Income Quintile -5 157 -3 876Number of Children 2nd Lifetime Income Quintile -5,157 -3,876

(4,376) (1,006)***Number of Children * Middle Lifetime Income Quintile -13,670 -7,514

(4,292)*** (1,499)***Number of Children * 4th Lifetime Income Quintile -20,705 -8,267

(5,064)*** (3,099)***Number of Children * Highest Lifetime Income Quintile -12,902 -4,936

(6,105)** (3,232)All regressions include annual earnings between ages 18 and 65Observations 4,201 4,201 4,201 4,201R-squared 0.24 0.24Standard errors in parentheses, * significant at 10%; ** significant at 5%; *** significant at 1%

In ClosingThe augmented life-cycle model with a Barro-Becker-style model of fertility choice does a nice job matching the joint distribution of children and wealthdistribution of children and wealth.Children increase the consumption of families when they are being supported by their parents.

Replacing the actual number (and timing) of children with the sample averages by marital status results in a change in optimal median net worth from $16 186 to $26 232 and from $68 007 to $99 462 in worth from $16,186 to $26,232, and from $68,007 to $99,462 in mean net worth in the lowest lifetime income decile.Our approach does not require heterogeneity in discount rates to

t th di t ib ti f lth generate the distribution of wealth. Children, and not income- and asset-tested transfers or discount rate differences we believe, are central to understanding the skewness of the wealth distribution and low asset accumulation of low-income households.

Health and Wealth in a Life Cycle Model

John Karl Scholz and Ananth Seshadri

University of Wisconsin-Madison and NBER and University of

Wisconsin-Madison

October 2011

Motivation

• Health and consumption decisions are intertwined.

— Health affects wealth.

— Wealth/income affects health.

— Unobserved factors likely affect both.

• But there is a strong link between income and longevity.

— We think there is more to learn about the links between health, con-

sumption, and wealth.

Objective

• To explain the joint distribution of health and wealth across households

• To understand differences in longevity across households

• To analyze the effect of policy on health, wealth and longevity

What we do

• We formulate a life-cycle model, solved household-by-household, wherehealth investments (including time-use decisions) can affect longevity.

— By modeling investments in health, we endogenize life-tables (longevity).

— We model the process of health production starting at the beginning

of working life (following Grossman)

• Model complementarities between consumption and health in preferences

• The framework allows us to analyze the effect of policy changes on healthinvestments and life tables.

Descriptive Evidence

• We use data from three waves of the Health and Retirement Study, 1998,

2000, and 2002. Given these waves, the sample includes

— The AHEAD cohort, born before 1924;

— The CODA cohort, born between 1924 and 1930;

— The original HRS cohort, born between 1931 and 1941;

— And the War Baby cohort, born between 1942 and 1947.

Economic Environment

• Households derive utility from consumption, health and leisure

E

⎡⎣ ∞Xj=S

βj−SnjU(cj/nj, lj, hj)

⎤⎦— c: Consumption

— l: Leisure

— h: Stock of health

— n: Number of adult equivalents

— E: Expectation over earnings shocks (before retirement) and health

shocks (throughout life)

Figure 1:

Figure 2: Health Capital Depreciates

Figure 3:

Figure 4:

• Households spend an indivisible amount of time ω working each period

and spend 1 − ω on either leisure or on activities that augment health

investments.

• The household possesses a health stock and investments in the healthstock prolong life. The accumulation process of the stock of health is

given by

hj+1 = f(mj, ij) + (1− δh)hj + εj, j ∈ {S, ..}

• The probability of surviving into the next period is given by Ψ(h).

— As h goes to ∞, Ψ(h) converges to 1.

— Ψ(h) = 0 for h ≤ 0. As h goes to zero, the household dies.

• Utility when dead is normalized to 0.

Retired Household’s Dynamic Programming Problem

A retired household between ages R andD obtains income from social security,

defined benefit pensions, and preretirement assets. The dynamic programming

problem at age j for a retired household is given by

V (eR,ER, a, j, h) = max½nU(c/n, 1− i, h) + βΨ(h)

ZV (eR,ER, a, j + 1, h

0)dΞ(ε)¾

subject to

y = SS(ER) +DB(eR) + ra+ TR(eR,ER, a, j, n)

c+ a0 +moop = y + a− τ(SS(ER),DB(eR) + ra)

h0 = F (M(moop), i) + (1− δh)h+ ε

Working Household’s Dynamic Programming Problem

A working household between the ages S and R obtains income from labor

earnings and preretirement assets. The dynamic programming problem at age

j for a working household is given by

V (e,E−1, a, j, h) = max½nU(c/n, 1− ω − i, h) + βΨ(h)

ZV (e0, E, a0, j + 1, h0)dΞ(ε)

subject to

y = e+ ra+ T (e, a, j, n)

c+ a0 +moop = y + a− τ(e+ ra)

h0 = F (M(moop), i) + (1− δh)h+ ε

Model Parameterization and Calibration

• Preferences

U(c, h) =[λ³cηl1−η

´ρ+ (1− λ)hρ]

1−γρ

1− γ.

• Equivalence Scale: This is obtained from Citro and Michael (1995) and

takes the form

g(A,K) = (A+ 0.7K)0.7

• Taxes: We model an exogenous, time-varying, progressive income tax thattakes the form

τ(y) = a(y − (y−a1 + a2)−1/a1)

where y is in thousands of dollars. Parameters are estimated by Gouveia

and Strauss

• Earnings Process: The household model of log earnings (and earningsexpectations) is

log ej = αi + β1AGEj + β2AGE2j + uj

uj = ρuj−1 + j

• Transfer Programs: We model public income transfer programs using thespecification in Hubbard, Skinner and Zeldes (1995). Specifically, the

transfer that a household receives while working is given by

T = max{0, c− [e+ (1 + r)a]}whereas the transfer that the household will receive upon retiring is

T = max{0, c− [SS(ER) +DB(eR) + (1 + r)a]}

• Health production: We assume that the production of health is given byF (M(moop), i) =

³mχi1−χ

´ξ, where m =M(moop).

— We assume that total medical expenses are given by m = ζmoop

• Survival Probability : The survival function is given by the cumulativedistribution function Ψ(h) = 1− exp(−ψhθ).

• Health Shocks: At each age, we assume that there are two possible valuesfor the health shocks: εh and εl. The first shock εh corresponds to being

healthy and is set to zero.

• The parameters we calibrate are λ (the utility weight on consumption

relative to health), ρ (determines the elasticity of substitution between

consumption and health), γ (the coefficient of relative risk aversion), ψ

(the coefficient on health in the survival function), θ (the curvature of the

survival function with respect to health), ξ (the curvature of the health

production function), εl (the magnitude of the ”bad” health shock), χ

(the share parameter in health production between monetary and time

inputs), δh (the annual depreciation rate of health), and p55, p65, p75, p85and p100 (the probabilities of bad health shocks occurring at different age

intervals).

Moments

• Strategy is to determine the parameters of the model by matching uppredictions for the ‘average’ household.

— Mean net worth in 1998 (age 65.3) is $346,221

— Probability of dying age 54 : 0.62%

— Probability of dying 60-64: 4.34%





— Probability of dying 95 and older: 72.73%

— Average medical expenses age 18-44: $2,974

— Average medical expenses for ages 50-54: $4,974




— Average medical expenses for ages 80 and older: $10,511

Parameter λ ρ γ ψ θ ξ εlValue 0.81 -6.8 0.83 .0013 1.68 0.75 -15.3Parameter χ δh p55 p65 p75 p85 p100Value 0.51 0.049 0.05 0.10 0.135 0.86 0.239

Main Results

• How well does the model match net worth and medical expenses by lifetimeearnings (in quintiles)?

1998 Median Net Worth Median Medical ExpensesData Model Data Model

Bottom Lifetime Income Quintile $32,947 $24,357 $5,682 $5,963Second Quintile 63,129 49,583 6,219 6,647Middle Quintile 116,396 91,980 7,062 7,512Fourth Quintile 198,596 143,261 9,146 9,452Highest Lifetime Income Quintile 355,106 315,983 11,337 12,034

Lifetime Income and Longevity

• How well does the model explain the relationship between lifetime earnings(in quintiles) and 10 year survival probabilities?

Survival Probabilities Age 60 Age 75Data Model Data Model

Bottom Lifetime Income Quintile 0.77 0.74 0.5 0.5Second Quintile 0.82 0.79 0.52 0.51Middle Quintile 0.86 0.83 0.52 0.55Fourth Quintile 0.90 0.85 0.63 0.57Highest Lifetime Income Quintile 0.93 0.87 0.65 0.60

Short-run Effect of Medicare on Survival Probabilities

Age 60 Age 75

Baseline Model No Medicare Baseline Model No Medicare

Bottom Income Quintile 0.74 0.73 0.50 0.49Second Lifetime Quintile 0.79 0.77 0.51 0.50Middle Lifetime Quintile 0.83 0.82 0.55 0.54Fourth Lifetime Quintile 0.85 0.85 0.57 0.57Highest Income Quintile 0.87 0.86 0.60 0.59

Consistent with evidence from Finkelstein and McKnight (2008)!

But the Long-Run Effect of Medicare Survival Probabilities isDifferent

Age 60 Age 75

Baseline Model No Medicare Baseline Model No Medicare

Bottom Lifetime Income Quintile 0.74 0.66 0.50 0.43Second Quintile 0.79 0.72 0.51 0.47Middle Quintile 0.83 0.79 0.55 0.50Fourth Quintile 0.85 0.83 0.57 0.56Highest Lifetime Income Quintile 0.87 0.86 0.60 0.59

Long run Impact of Eliminating Medicare on Assets

• What is the impact of eliminating medicare on wealth and health accu-mulation?

1998 Median Net Worth Median Medical Exp.Lifetime Income Model No Medicare Model No MedicareBottom Quintile $24,357 $56,472 $5,963 $2,332Second Quintile 49,583 75,786 6,647 4,147Middle Quintile 91,980 121,213 7,512 6,231Fourth Quintile 143,261 182,093 9,452 8,139Highest Quintile 315,983 342,104 12,034 11,234

Comparison with Exogenous Medical Expenses

• Standard Modeling approach - Medical expenses follow a stochastic process

— Hubbard, Skinner and Zeldes (1995) argue that Medicare has a very

large effect on wealth accumulation

1998 Median Net WorthEndogenous Health Exogenous Health

Lifetime Income Model No Medicare Model No MedicareBottom Quintile $24,357 $56,472 $23,405 121,283Second Quintile 49,583 75,786 47,485 166,392Middle Quintile 91,980 121,213 85,406 230,485Fourth Quintile 143,261 182,093 147,403 312,251Highest Quintile 315,983 342,104 321,506 564,304

• With endogenous life expectancies, Medicare has smaller impact on wealth

— Households can choose not to spend on medical care later in life when

hit with a bad shock

— This option is not available when medical expenses are exogenous

Impact of ρ = 0 (consumption health substitutability)Net Worth

1998 Median Net WorthBaseline Model (ρ = −6.8) ρ = 0

Bottom Quintile $24,357 51,372Second Quintile 49,583 112,175Middle Quintile 91,980 166,835Fourth Quintile 143,261 334,506Highest Quintile 315,983 534,012

Conclusion

• The model accounts for a large fraction of the variation in medical ex-penses and assets at the household level

• Consumption decisions and asset accumulation are interrelated. Comple-mentarity between consumption and health are important in understanding

wealth differences

• Policy can have meaningful long-term impact on life tables

• Medicare (means tested transfers) have a smaller impact on asset accu-mulation in the long run when wealth and health can adjust

• When consumers have (some) control over when to die, the poor do nottend to engage in as much precautionary savings when the transfer pro-

gram is eliminated.

— Consistent with evidence from developing economies without safety

nets.

public economics lectures taxes and behavior: saving, part...

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