Old, Sick, Alone and Poor: A Welfare
Analysis of Old-Age Social Insurance
Programs
R. Anton Braun
Federal Reserve Bank of Atlanta

Karen A. Kopecky
Federal Reserve Bank of Atlanta

Tatyana Koreshkova
Concordia University and CIREQCIGS End of Year Macro Conference
December 26 2014

Motivation•

All societies must deal with the fact that some individuals
will end up old, sick, alone and poor.

•Why?
•Some individuals enter retirement with low wealth.

•Significant risks after retirement.
• Longevity• Medical expenses• Long-term care expenses• Spousal death•
BKK (2014)

These risks are correlated.

Motivation•

Poverty among retirees is a challenge for society.

•Poor retirees often cannot self-insure by re-entering the laborforce.

•Questions:•

Is there a role for social insurance (SI) for the aged?

•What is a good program?

BKK (2014)

U.S. Social Security Program (SS)•Biggest SI program for retirees in U.S.

•SS outlays were 4.8% of GDP in 2011 and are growing.

•A large macroeconomics literature finds that a U.S.-style, payas-you-go, public pension program is bad public policy:••Bad in dynamically efficient OLG models(Auerbach and Kotlikoff, 1987).

•

Bad in dynastic models(Fuster, Imrohoroglu and Imrohoroglu, 2007).

•Bad when individuals face life-time earnings risk
(Conesa and Krueger, 1999).

•

Bad when the economy is open (Hong and Rios, 2007).

Strongest argument in favor of SS:•BKK (2014)

It is even more costly to remove(Nishiyama and Smetters, 2007).

Is there a role for social insurance?

It would be a mistake to conclude from these results that there is norole for society to provide insurance to retirees.

BKK (2014)

Means-tested Social Insurance (MTSI) for Retirees•U.S. also offers means-tested social insurance (MTSI) toretirees.

•Some MTSI programs for U.S retirees are:•

BKK (2014)•Medicaid•

Supplemental Social Security Income•

Food Stamps•

Housing and energy assistance programs

We assess these programs using a quantitative model ofthe U.S. economy and find that they are highly valued.

Means-tested Social Insurance (MTSI) for Retirees
MTSI is valuable:•

It provides good insurance against longevity risk.

•

It is particularly effective in insuring against: medical expenses,
nursing home expenses, spousal death and low lifetime earnings.

Why?
•The transfers induced by the means-test line up well with states
where demand for the insurance is highest.

•It is cheap••

BKK (2014)

Largest program is Medicaid: expenditures for the aged are0.6% of GDP.
Second largest program is SSI: outlays for the aged are 0.3%of GDP.

Quantitative Model of U.S. Economy: Overview•

Full-lifecycle, OLG, GE model•

Households•

become active at age 21 (period = 2 years)•

While working:••••

BKK (2014)

are married couples
differ by education status of members
face uncertainty over male and female’s labor productivity
choose consumption, savings, female labor supply

Quantitative Model of U.S. Economy: Overview•Households•

retire exogenously at age 65•

While retired:• married, widows, widowers• have uncertain••••

health status
medical expenses
nursing home expenses
death (foreseen 1 period in advance)• choose consumption, savings• die with certainty at age 100BKK (2014)

Quantitative Model of U.S. Economy: Overview

Assuming retirees foresee their death 1 period in advance
allows us to:•

Capture high OOP expenses of HRS retirees in last yearof life. (3.4 times larger than other years.)•Eliminate accidental bequests. (They muddle welfare effects of policy changes.)•

Reproduce finding of Porterba et al. (2012). (Many HRS
individuals die with very low levels of assets.)••

BKK (2014)

46% have less than $10,000 in financial assets
50% have zero home equity

Quantitative Model of U.S. Economy: Overview

Exogenous risks faced by retirees:•Survival and health status••

Stochastic functions of age, sex, marital status, and previous
health status

Medical expenses•

Do not affect household utility•

Stochastic function of age, sex, marital status, current healthstatus and death•

Stochastic component consists of both••

BKK (2014)

acute shocks
a small probability but large expense “nursing home”
shockQuantitative Model of U.S. Economy: Overview•

Social insurance (SI) includes••••

SI financed (along with government expenditures) by••••
BKK (2014)means-tested social insurance program (Medicaid/other old-age SI)
progressive PAYG social security program (includes
spousal and survivor benefits)
Medicare (expenses are net of Medicare benefits, include Medicare earnings tax)

progressive income taxes
payroll tax
proportional capital income tax

No private insurance and no uncollateralized borrowing

Working Household’s Preferences

Utility function of a working-age household is1−σ1−γ(c/(1+χ))lUW (c, lf , s) = 2+ ψ(s) f− φ(s)I(lf < 1)1−σ1−γ•lf is non-market time of the female member•

preferences vary across education types s ≡ (sm , sf )•1 − χ ∈ [0, 1] is the degree of joint consumption•φ(s)I(lf < 1) is the utility cost of female labor force
participation

BKK (2014)

Retired Household’s Preferences

Utility function of a retired household is
N(d)−1 1−σR
N(d)−1 c/(1 + χ)
U (c, d) = 21−σ1−γl+ ψR (d) f1−γ

•1 − χ ∈ [0, 1] is the degree of joint consumption•N(d) is the number of household members given themarital status d ∈ {married, widow, widower}.

BKK (2014)

Retired Household’s Problem
Retired household solves
V(j, a, ē, h, εM , d, d ′ ) = max′ UR (c, d)c,a+βEh P
2′πj (d ′′ |h ′ , d ′ )V(j + 1, a′ , ē, h ′ , εM, d ′ , d ′′ )|h, εMd ′′ =0

subject to ...
ageassetsaverage earnings
health statushousehold medical expense shocks
marital status

BKK (2014)jaē ≡ {ēm , ēf }h ≡ {hm , hf }εM ≡ {εM,1 , εM,2 }d ∈ {0, 1, 2}i

Retired Household’s Problem
Retired household solves
V(j, a, ē, h, εM , d, d ′ ) = max′ UR (c, d)c,a+βEh P
2′πj (d ′′ |h ′ , d ′ )V(j + 1, a′ , ē, h ′ , εM, d ′ , d ′′ )|h, εMd ′′ =0i

subject toc > 0,a ′ > 0,c + M + a′ = a + yR − TyR + T rR .

BKK (2014)M ≡ Φ(j, h, εM , d, d ′ )medical expensesyR ≡ S(ē, d) + (1 − τc )raincomeTyR ≡ τRy ((1 − τc )ar, S(ē, d), d, M)

income taxes

T rR

means-tested SI transfer

Retired Household’s Problem•

The means-tested SI transfer function represents both Medicaid
and other means-tested SI tranfers.

•It also captures the following features of Medicaid:••

Medicaid requires copays.

•copays are capped.

Copays ⇒ even retirees on means-tested SI face some medical
expense risk.

BKK (2014)

Retired Household’s Problem
Means-tested SI transfers to retirees are given by dRT r ≡ max y + ϕM − IR , cd + M − IR , 0
where IR ≡ a + yR − TyR is cash-in-hand.
Medical!
Expenses Transfers > 0No copay
c=cTransfers > 0Copay

No Transfersc>yc<c<y

BKK (2014)

Cash in handCompetitive Equilibrium

We consider a steady-state competitive equilibrium of asmall open economy.

BKK (2014)

A Few Comments About the Calibration•Stochastic components of the earnings and medical expense
processes are not Gaussian.

•The earnings process includes an additional low earnings state
which helps us•••reproduce SS income distribution
improve model’s matching of bottom tail of earnings distribution

The medical expense process includes a large NH shock whichhelps us••

BKK (2014)

capture the risk of a large and persistent NH shock
improves model’s matching of upper tail of the medical expense distribution

A Few Comments About the Calibration•We calibrate the model to reproduce this demographic structure:100
healthy, single males

unhealthy, single males

80

Percent

60

healthy, married males

unhealthy, married males
healthy, single females

healthy, married females

40
unhealthy, married females

200
BKK (2014)

unhealthy, single females

6570758085
Age9095

A Few Comments About the Calibration•Age 65 marital distribution attained with a spousal deathevent at age 65.

•

The likelihood of the death event is decreasing with maleaverage earnings.

•Targets the marital distribution by permanent income inthe data.

BKK (2014)

A Few Comments About the Calibration•Consumption Floors:•Workers: c is 15% of average male earnings or $7,100
in year 2000 dollars.

•Retirees: cd is very similar across marital groups andis approximately 16% of average male earnings or$7,600 in year 2000 dollars.

•Means-test income thresholds: yd ≈ 2cd chosen somodel reproduces take-up rates.

•Medicaid copay rate: 1 − ϕ is 20%.
Target: average OOP expenses of Medicaid recipients/average OOP expenses of all retirees = 0.46.

BKK (2014)

Assessment: Medicaid Take-Up Rates•

Consumption floor calibration••

Target: Take-up rates by marital status.
Assessment: Take-up rates by age groups.
Medicaid Take-Up Rates
Age
Marital StatusMarried
data
model
Widowsdata
model
Widowers
datamodel

BKK (2014)

65–74 75–84

85+

0.07
0.05

0.07
0.07

0.11
0.12

0.22
0.21

0.19
0.23

0.24
0.25

0.19
0.17

0.15
0.16

0.19
0.17

Findings•

What are the welfare effects of removing MTSI?

•Welfare is measured as an equivalent % variation in lifetime consumption.

•Assumption:

BKK (2014)•Absent MTSI society provides a Townsendian consumption floor•

Largest consumption floor that all households, indexedby education, agree on.

Welfare effects of removing MTSI
When MTSI is removed from our baseline economy•Ex-ante newborn welfare falls

Economy Baseline
Welfare, %Ex-anteBKK (2014)-4.87

Welfare effects of removing MTSI
When MTSI is removed from our baseline economy•High school educated HH dislike MTSI removal the most

EconomyBaseline

Welfare, %Ex-ante-4.87
By HH education type (female, male):high school, high school-6.04
high school, college-2.87
college, high school-1.53
college, college
0BKK (2014)

Welfare effects of removing MTSIWhen MTSI is removed from our baseline economy•

Welfare of all types indexed by male permanent earnings quintilefalls
EconomyBaseline

Welfare, %Ex-ante-4.87
By male permanent earnings:
quintile 1-7.55
quintile 2-5.43
quintile 3-4.42
quintile 4-3.65
quintile 5-1.82
BKK (2014)

Welfare effects of removing MTSI

Why are welfare gains so large and so broadly based?

•BKK (2014)

Compare baseline economy to•economy with no medical expenses•

economy with no earnings risk

Roles of medical expenses and life-time earnings risk
When medical expenses are absent•Ex-ante welfare continues to fall when MTSI is removed but now
disagreement among types
EconomyBaseline

WelfareEx-ante-4.87
By HH education type (female, male):high school, high school-6.04
high school, college-2.87
college, high school-1.53
college, college
0BKK (2014)

No MedicalExpenses
-0.26
-0.34
-0.16
0.03
0.05

Roles of medical expenses and life-time earnings risk
When earnings risk is absent•Welfare of all types now rises when MTSI is removed

EconomyNo Medical No Earnings
Baseline
Expenses
Risk

WelfareEx-ante-4.87
By HH education type (female, male):high school, high school-6.04
high school, college-2.87
college, high school-1.53
college, college0

BKK (2014)

-0.26

0.64

-0.34
-0.16
0.03
0.05

0.34
1.33
1.15
1.92

Reforming MTSI for Retirees•

BKK (2014)

Given that MTSI is highly valued by HH’s in our economy
would they like to increase its scale?

Reforming MTSI for Retirees•All newborn like a 30% increase in MTSI if it is financed with ahigher payroll tax.
U.S. economy
Welfare, %Average
By household education type (female, male):high school, high school
high school, college
college, high school
college, college
Means-tested SI
take-up rates
govt. outlays, % GNP

BKK (2014)

12.9
0.75

30% upPayroll Tax
0.54
0.62
0.35
0.48
0.29
23.7
1.44

Reforming MTSI for Retirees••

Newborn households dislike 30% increase financed by a higher
income tax instead.
Disagreement over a 30% decrease (lowering income tax).
U.S. economyWelfare
AverageBy household education type (female, male):high school, high school
high school, college
college, high school
college, college
Means-tested SI
take-up rates
govt. outlays, % GNP
BKK (2014)

12.9
0.75

30% upIncome Tax

30% down
Income Tax

-0.44

0.04

-0.24
-0.91
-0.69
-1.20

-0.13
0.45
0.28
0.65

24.1
1.50

6.0
0.30

Conclusion•Removing MTSI in a quantitative model of the U.S. economy produces a large welfare loss.

•There are broad-based welfare gains if the scale of MTSIis increased by 30% financed by a payroll tax.

•If SS was removed, the fraction of retirees living off MTSI
transfers would increase significantly but all ex-ante types
would be better off.

BKK (2014)