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Economic Brief

November 2020, EB20-12

Lifespan Inequality and Social Security Reform
By John Bailey Jones and John Mullin

What does lifespan inequality mean for Social Security reform? Using a
life-cycle model in which the rich tend to outlive the poor, the researchers
analyze how various reforms affect the trade-off between distributing lifetime Social Security benefits more equally and encouraging society’s most
productive members to work longer. They find that social welfare is maximized when benefits are independent of lifetime earnings, the payroll tax
cap remains near its current level, and benefits are made less dependent
on the age at which they are initially claimed.
A common proposal for stabilizing the U.S. Social
Security system is to increase the system’s normal
retirement age (NRA). An intuitively appealing
feature of this proposal is that it counters the
trend toward longer lives — a major cause of
Social Security’s financial difficulties — by delaying the age at which full benefits start. A less
appealing aspect of the proposal is that it likely
would have a disproportionately negative effect
on the poor because the longevity gap between
the rich and poor in the United States is large
and growing,1 which means that the poor tend
to receive fewer years of Social Security benefits
than the rich. Consequently, a one-year increase
in the NRA could diminish the lifetime benefits
received by the poor by a greater proportion than
those received by the rich. While this concern can
be mitigated by changing the progressivity of the
Social Security benefit formula, a more general
question remains: If high-income workers live
longer than low-income workers, shouldn’t they
work longer as well?2

EB20-12 – Federal Reserve Bank of Richmond

Economists have developed an extensive set of
tools for analyzing questions about the fairness
and efficiency of government tax-and-transfer
policies, including Social Security. Standard
economic models of optimal fiscal policy start
with the premise that policies should be chosen to maximize social welfare, subject to some
constraints. Social welfare, in turn, depends
on the welfare or “utility” of society’s individuals. All other things remaining the same, social
welfare in these models increases when income
is transferred from the rich (who have relatively
low marginal utilities of consumption) to the
poor (who have relatively high marginal utilities
of consumption). But, of course, all other things
do not necessarily stay the same. Except in very
special cases (involving “lump-sum” taxes and
transfers), government tax-and-transfer programs alter individuals’ incentives and thereby
affect labor-leisure and spending-saving decisions that can change the size of the overall
economic pie. In 1971, James Mirrlees’s seminal

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paper highlighted the tension between equalizing
consumption and encouraging work by the most
productive.3 In a more recent (2010) contribution,
Helmuth Cremer, Jean-Marie Lozachmeur, and Pierre
Pestieau analyzed the trade-offs associated with
public pension programs when beneficiaries have
a variety of survival probabilities.4 With such heterogeneous mortality, “consumption equalization”
becomes a tricky concept because equal per-period
consumption implies larger lifetime transfers to
people who live longer.
In a recent working paper, John Bailey Jones of the
Richmond Fed and Yue Li of the University at Albany
extend this research by building a heterogeneousagent, life-cycle model of Social Security to analyze
the implications of lifespan inequality for Social
Security reform.5 They find that, relative to the Social Security policies currently in place, policies that
would maximize social welfare would reduce work incentives in order to redistribute resources from high
earners to low earners. More specifically, quantitative
experiments with their calibrated model show that
welfare is maximized when benefits are independent
of lifetime earnings, the payroll tax cap is kept roughly
unchanged from current levels, and when benefits
are made less dependent on the age at which they
are initially claimed. In their model, additional gains
are provided by eliminating taxes on Social Security
benefits and by removing the Social Security “earnings test,” which reduces the benefits of younger
claimants who continue to work.
The Model
The researchers extend the framework used by Selahattin Imrohoroğlu of the University of Southern California and Sagiri Kitao of the University of Tokyo to
incorporate a richer treatment of health, mortality, education, and wages.6 In the extended model, individuals make labor-leisure choices while facing uncertain
prospects for their health, wages, medical spending,
and mortality — the distributions of which vary by
their levels of education. The government collects
income, payroll, and consumption taxes and provides
Social Security, Medicare, disability insurance, and
means-tested social insurance. Individuals can con-

tinue working while receiving Social Security benefits,
but they may face financial incentives to retire.
In the context of the model, the researchers solve
the problem that a social planner would face when
attempting to maximize the expected lifetime utility of a newborn, prior to knowing the newborn’s
endowed characteristics. This optimization criterion,
which is standard in the literature, implicitly assigns
an equal weighting to all individuals in a society.
The criterion also provides a reasonable means of
overcoming the problems associated with periodby-period analysis in a setting where agents have
heterogeneous mortality.
After calibrating the model to reflect the current
state of the U.S. economy and Social Security policies, the researchers evaluate potential reforms.
To focus their analysis on policy trade-offs, they
evaluate only “parametric” reforms that leave Social
Security’s overall footprint unchanged. In particular,
they limit their analysis to policy changes that do
not change aggregate Social Security expenditures,
revenues, or general government budget balances.
The researchers consider three categories of parametric reforms:
1. Changes to the Social Security payroll tax rate and
changes to the cap on taxable payroll earnings;
2. Changes to the formula converting people’s
earnings histories into their baseline benefits,
known as their primary insurance amount (PIA);
3. Changes to the trade-off between the age at
which people first receive their Social Security
benefits — and thus the length of the benefit
stream — and the size of the annual benefit.

All of the reforms they study have appeared before
as proposals — some enacted, some rejected. The
first two categories of reforms affect how Social
Security payroll taxes and benefits depend on wage
realizations and work decisions. The third category
affects how benefits depend on the age at which
individuals initially claim Social Security benefits.
Increases in the NRA can be interpreted as a special

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case of this type of reform. This trade-off is formally
embodied in the early retirement penalties and delayed
retirement credits, which decrease or increase annual
benefits, respectively.

Because people can simultaneously work and receive
benefits, their work decisions and claiming decisions may appear to be disconnected under current
policies. This is not the case, however, for three main
reasons. First, the rate at which earnings translate
into Social Security benefits is an increasing function of the age at which the benefits are claimed — a
mechanism that creates an incentive to work more
years before retirement. Second, benefits received
by nonretirees can be reduced due to the Social
Security earnings test — a mechanism that creates
a work disincentive by penalizing people who claim
benefits while still working.7 And third, Social Security benefits tend to push beneficiaries into higher
marginal tax brackets — another work disincentive.
Each category of reforms embodies the canonical
trade-off between income redistribution and productive efficiency. Under the assumption that Social
Security’s overall footprint stays the same, raising
the payroll tax cap allows for a lower tax rate, but
that lower rate applies to a broader range of earnings. This reduces taxes for most workers but raises
marginal tax rates for the most productive workers.
Linking Social Security benefits to lifetime earnings increases the incentive to work, but it reduces
transfers from high earners to low earners. Raising
the penalty for claiming benefits at an early age creates a work incentive, but it punishes people with
shorter lifespans.
Policy Implications
As a general principle, the researchers find that,
relative to the Social Security policies currently in
place, the policies that would maximize welfare
would reduce work incentives in order to redistribute resources from high to low earners. Under these
policies, the PIA would be independent of lifetime
earnings, and differences in benefits due to differences in claiming ages would be smaller, while the
cap on taxable earnings would remain at more or

less its current value. Collectively, this group of
reforms would cause both earnings and employment to fall by 1 percent to 2 percent.
However, the researchers show that more than half
of the declines in earnings and employment could
be reversed by eliminating the earnings test and
the taxation of benefits.8 Adding these reforms also
results in larger welfare gains. Because the earnings
test and taxation of benefits apply only to older
workers, whose elasticity of labor supply is especially
high, eliminating them is an especially effective way
to encourage work.9 Removing these provisions
uncouples claiming decisions from retirement decisions; under the joint reforms, almost everyone in
the model claims benefits at age sixty-two.
The researchers also consider how heterogeneous
mortality affects Social Security reform in the face of
changing demographic patterns. They construct a
hypothetical “2050-demographics” scenario characterized by longer lifespans, lower population
growth, and a heightened dependence of mortality on education. They find that the Social Security
system that would maximize welfare in the 2050
demographic environment would be quite similar
to the one that would maximize welfare today. In
both cases, the PIA would be independent of individual earnings; the payroll tax cap would be higher
in the 2050 scenario, but claiming adjustments
would remain roughly the same in both scenarios.
Although increased longevity suggests that larger
claiming adjustments are needed to promote
longer careers, increased longevity also implies that
the adjustments needed to induce claiming delays
(and longer careers) are smaller. The net effect is
that the optimal claiming adjustments are smaller
than in the current demographic environment, but
only slightly so.
Within the literature on parametric Social Security
reforms, the researchers’ main contribution is to
consider a broad set of reforms simultaneously and
quantitatively while accounting for heterogeneity in income, health, and mortality. While it has

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been long recognized that heterogeneous mortality
affects the lifetime progressivity of Social Security,
and multiple studies have sought to quantify this
effect, there has been relatively little progress in
quantifying its implications for optimal policies.
The researchers believe that there are a number
of promising avenues along which to extend their
framework. The first would be to add marriage and
spousal benefits to their model. A second would be
to consider the entire tax and transfer system rather
than just Social Security. Jones and Li’s results suggest that incorporating a greater degree of heterogeneity into such analyses — in place of some of
the demographic simplifications that are commonly
used — may have important policy implications.
John Bailey Jones is a senior economist and research
advisor and John Mullin is an economics writer in
the Research Department at the Federal Reserve
Bank of Richmond.

Jessie Romero, “The Mortality Gap,” Econ Focus, Third/Fourth
Quarter 2016, vol. 21, no. 3–4, pp. 18–21.


 n analysis of the policy implications of changing life expecA
tancies for Social Security can be found in National Academies
of Sciences, Engineering, and Medicine, The Growing Gap in
Life Expectancy by Income: Implications for Federal Programs and
Policy Responses, Washington, D.C.: The National Academies
Press, 2015.


J . A. Mirrlees, “An Exploration in the Theory of Optimum
Income Taxation,” Review of Economic Studies, April 1971, vol.
38, no. 2, pp. 175–208.


 elmuth Cremer, Jean-Marie Lozachmeur, and Pierre Pestieau,
“Collective Annuities and Redistribution,” Journal of Public
Economic Theory, February 2010, vol. 12, no. 1, pp. 23–41.


J ohn Bailey Jones and Yue Li, “Social Security Reform with
Heterogeneous Mortality,” Federal Reserve Bank of Richmond
Working Paper No. 20-09, July 2020.


S elahattin Imrohoroğlu and Sagiri Kitao, “Social Security
Reforms: Benefit Claiming, Labor Force Participation, and
Long-Run Sustainability,” American Economic Journal: Macroeconomics, July 2012, vol. 4, no. 3, pp. 96–127.


S ocial Security benefits withheld because of the earnings test
are credited to future benefits. Beneficiaries who are unaware
of this provision, however, will view the earnings test as a pure
tax, as will individuals who lack liquid assets. See, for example,
Gary V. Engelhardt and Anil Kumar. “Taxes and the Labor
Supply of Older Americans: Recent Evidence from the Social
Security Earnings Test,” National Tax Journal, June 2014, vol. 67,
no. 2, pp. 443–458.


T his reform was recommended in John Bailey Jones and Yue
Li, “The Effects of Collecting Income Taxes on Social Security
Benefits,” Journal of Public Economics, March 2018, vol. 159,
pp. 128–145.


 n analysis of the role of labor supply elasticity in Social
Security reform can be found in Eric French, “The Effects of
Health, Wealth, and Wages on Labour Supply and Retirement
Behaviour,” Review of Economic Studies, April 2005, vol. 72,
no. 2, pp. 395–427.

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Federal Reserve Bank of Richmond and include the
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Views expressed in this article are those of the authors
and not necessarily those of the Federal Reserve Bank
of Richmond or the Federal Reserve System.

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