Optimal Social Security with Imperfect Tagging

AuthorOliver Denk,Jean‐Baptiste Michau
Publication Date01 Jul 2018
DOIhttp://doi.org/10.1111/sjoe.12250
©The editors of The Scandinavian Journal of Economics 2017.
Scand. J. of Economics 120(3), 717–762, 2018
DOI: 10.1111/sjoe.12250
Optimal Social Security with Imperfect
Tagging*
Oliver Denk
OECD, FR-75775 Paris Cedex 16, France
oliver.denk@oecd.org
Jean-Baptiste Michau
Ecole Polytechnique, FR-91128 Palaiseau Cedex, France
jean-baptiste.michau@polytechnique.edu
Abstract
Workers are exposed to the risk of permanent disability. We rely on a dynamic mechanism
design approach to determine how imperfect information on health should optimally be
used to improve the trade-off between inducing the able to work and providing insurance
against disability. The government should offer back-loaded incentives and exploit the
information revealed by the gap between the age at which disability occurs and the age
of eligibility to disability benefits. Furthermore, the able who are (mistakenly) tagged
as disabled should be encouraged to work until some early retirement age.
Keywords: Disability insurance; dynamic mechanism design; optimal social insurance
JEL classification:E62; H21; H55; J26
I. Introduction
Two of the most pressing issues in public finance across industrialized
nations are the rising costs of providing disability insurance and pensions
to an aging population. In fact, these two problems are closely related, as
disability insurance is often used as a stepping stone towards retirement
(Autor and Duggan, 2006; Li and Maestas, 2008). Furthermore, both the
disability insurance and pension programs can be seen as complementary
ways of providing insurance to workers against the risk that they lose
their ability to earn income from labor. Indeed, in the US, these two
*We are grateful to Joseph Altonji, Nick Barr, Tim Besley, Raj Chetty, David Cutler, Giulio
Fella, Mikhail Golosov, Henrik Kleven, Guy Laroque, Emmanuel Saez, Jeremy Sandford,
Monica Singhal, two anonymous referees, and seminar participants at Berkeley, CREST,
Harvard, the London School of Economics, and EEA/ESEM 2011 (Oslo) for useful comments
and suggestions. The findings, interpretations, and conclusions expressed in the paper are those
of the authors and do not necessarily represent the views of the OECD.
718 Optimal social security with imperfect tagging
programs are the main pillars of the “Social Security” system that is
meant to provide security against the risk of being unable to work.
The disability insurance program relies on imperfect information on
health to provide a decent income to those who are likely to be truly
disabled. However, it is clearly not possible to provide perfect insurance
against the disability risk, as some agents who are truly disabled fail to
qualify. Thus, systematic eligibility to old-age pensions beyond a certain
age is justified as another, complementary, way of providing insurance.
Indeed, this is what motivated Bismarck to invent pension programs as
early as 1889.1
In 2007, the US Social Security system provided income to almost
50 million individuals for a total cost of US$585 billion (4.2 percent of
gross domestic product, GDP), of which nine million received disability
benefits2for a total cost of US$99 billion (0.7 percent of GDP) (United
States Social Security Administration, 2008). By contrast, in 2007, the
total cost of unemployment insurance was only US$32 billion, about a
third of the size of the disability insurance program. Most European
countries have even larger disability insurance programs (as a share of
their GDP). Despite these gigantic numbers and the potentially large
welfare implications of the disability risk (Chandra and Samwick, 2006),
very little is known about the optimal design of insurance against this
risk.
To approach this problem, we rely on a framework that incorporates
two important dimensions. First, we have a dynamic set-up to capture the
fact that disability could potentially hit any worker at any age. Second,
we assume that medical impairments can only be imperfectly observed by
the government. This assumption is hard to dispute given that almost 70
percent of workers receiving disability insurance payments fall into the
following three categories: mental disorders (33.4 percent), musculoskeletal
system and connective tissue such as back pain (26.4 percent), and nervous
system and sense organs (9.5 percent). Therefore, our contribution is to
characterize the optimal provision of insurance against the disability risk
in a life-cycle framework with imperfectly observable health. However,
we restrict ourselves to the risk of permanent disability. Our aim is to
uncover the key qualitative and quantitative features that must be satisfied
by an optimal policy.
1Of course, there is also a leisure component to the provision of pensions which will be
captured by our theoretical framework.
2Of those, seven million were disabled workers, which represents about 4.4 percent of the
population between the ages of 25 and 64. The other beneficiaries are the spouses and children
of disabled workers.
©The editors of The Scandinavian Journal of Economics 2017.
O. Denk and J.-B. Michau 719
Let us now describe our theoretical framework. At any age, a worker
faces the risk of being hit by an irreversible disability shock. The
government would like to provide insurance against disability while
inducing the able to work up to a general retirement age. To enhance
the provision of insurance, the government could rely on its imperfect
information on health by giving higher consumption to those who seem
to be unable to work. More precisely, those who seem to be in poor
health are “tagged”3as disabled and therefore eligible for this higher
consumption level. Thus, the only information that the government has
about the health of an individual is whether or not this individual has
been awarded a tag.
Importantly, tagging is imperfect and some classification errors are
unavoidable. Hence, some workers who are able to work are awarded the
tag, while others who are truly disabled are rejected. Recognizing this
problem, the government still wants to provide the able and tagged with
incentives to work. Thus, the optimal allocation of resources is found by
setting up a dynamic mechanism design problem where the able, whether
tagged or not, are induced to work until some retirement age to be
determined. Inducing the tagged to participate is costly, because they
face a strong temptation to claim to be disabled. Hence, they should be
induced only to work up to an early retirement age.4
The first-order conditions to the planner’s problem provide a number of
qualitative insights. First, as in some other dynamic contracting problems,
the optimal allocation is characterized by back-loaded incentives. The
reward for participation is higher for more experienced workers. Not only
does it induce the old to participate, it also induces the young who
are motivated by the prospect of high consumption once they will have
accumulated a lot of work experience. Therefore, the consumption of
participating workers increases with age and jumps upward when a tag
is awarded.
A more fundamental insight is that, when an agent stopped working
before being awarded the tag, the optimal policy exploits the difference
between the age at which this agent stopped working (i.e., the age at
which he claimed to be disabled) and the age at which he was awarded
the tag. The idea is that someone who claims to be disabled is likely
to say the truth if he becomes tagged shortly after stopping to work but
3The term was originally introduced by Akerlof (1978), who performed the first analysis of
the optimal use of tagging in the design of welfare programs.
4As we argue in the text, such an early retirement age could be seen as a “health-dependent
retirement age”. However, it should be emphasized that this retirement age depends on health
as observed by the government but only applies to the able, who are, by definition, in good
health.
©The editors of The Scandinavian Journal of Economics 2017.

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