Optimal Social Insurance with Endogenous Health*

• DOI: http://doi.org/10.1111/sjoe.12359
• Date: 01 April 2020
• Published date: 01 April 2020

Scand. J. of Economics 122(2), 464–493, 2020

DOI: 10.1111/sjoe.12359

Optimal Social Insurance with Endogenous

Health*

Tobias Laun

National Institute of Economic Research, SE-103 62 Stockholm, Sweden

tobias.laun@konj.se

Abstract

In this paper, I analyze optimal insurance against unemployment and disability in a private

information economy with endogenous health and search effort. Individuals can reduce the

probability of becoming disabled by exerting preventioneffort. I show that the optimal sequence

of consumption is increasing for a working individual and constant for a disabled individual.

During unemployment,decreasing benefits are not necessarily optimal. The prevention constraint

implies increasing benefits while the search constraint demands decreasing benefits while being

unemployed. However, if individuals respond sufficiently to search incentives, the latter effect

dominates the former and the optimal consumption sequence is decreasing during unemployment.

Keywords: Disability insurance; optimal contracts; unemployment insurance

JEL classification:D86; E24; H53; J65

I. Introduction

The question of how a government should insure workers against

unemployment and disability is a recurring and controversial theme in

the public policy debate. In the last 20 years, many developed countries

have reformed their unemployment insurance programs in order to decrease

costs for the government and to make people return to employment.

These changes have often included a decrease in benefits, if the worker

is unemployed longer than a certain amount of time. While these reforms

obviously increase the incentives of unemployed workers to find new

employment, they might at the same time decrease the incentives of the

long-term unemployed to remain in the labor force at all.

Substitution between social insurance programs is indeed a common

phenomenon according to, for example, Larsson (2006) and Karlstr¨om et al.

(2008). Using the coal boom and bust as a natural experiment, Black et al.

(2002) demonstrate that participation in a disability program increases when

*I thank the three anonymous referees for their insightful comments. I also thank the seminar

participants at SSE, IIES, ETH Z¨urich, Uppsala University, and SED for their helpful comments

and suggestions. Financial suppor t from the Jan Wallander and Tom Hedelius Foundation and

the Riksbankens Jubileumsfond is gratefully acknowledged.

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The editors of The Scandinavian Journal of Economics 2019.

T. Laun 465

the value of being in the labor force decreases. Autor and Duggan (2003)

show that disability insurance is often (mis)used as an alternative insurance

channel during unemployment. Given that the literature has largely focused

on the two systems in isolation, it is useful to integrate disability and

unemployment insurance in a joint model and to study their interaction and

implications for optimal policy.

In order to receive disability insurance benefits, an individual either

has to falsely claim to be unable to work or has to become actually

unemployable. The former is a well-known moral hazard problem and

is also taken into account in this paper. However, the idea that strict

unemployment insurance systems can reduce incentives for individuals to

remain in the labor force has, to my knowledge, not yet been formally

investigated. This moral hazard problem is the main focus of this paper.

To study this issue, I combine unemployment and disability insurance in

one framework and assume that the probability of becoming disabled is

endogenous. Individuals, whether employed or unemployed, can exert a so-

called prevention effort, which is costly in terms of utility. In so doing,

they increase the probability of remaining healthy, and hence staying in the

labor force, for one more period.1

By combining these two moral hazard problems, I am able to study the

optimal design of unemployment insurance when individuals have to exert

effort in order to remain in the labor force. In this framework, I am also able

to analyze how unemployment and disability benefits should depend on the

employment history. In this sense, combining unemployment and disability

insurance yields more than just the sum of its parts. For example, disability

benefits dependent on employment history allow the government to use

disability benefits not only to provide incentives for preventing disability but

also as an additional way of creating search incentives for the unemployed

individual.

An unemployed individual has the option of exercising search effort,

which increases the probability of finding employment in the next period.

Both the prevention and the search effort are costly in terms of utility.

Disability is assumed to be an absorbing state.2The government’s goal is

to minimize the expected discounted cost of providing the individual with a

certain level of utility. I first consider the full information case in which the

government can observe effort levels and the individual’s state of health and

1It turns out that this prevention effort, and not the possibility to falsely claim to be disabled, is

driving the main results.

2In reality, very few individuals leave disability insurance and return to the labor force. In

the United States, the number is currently around 1 percent of disability benefits recipients. See

Table 56 in theAnnual Statistical Report on the Social Security Disability Insurance Program,

2016 (https://www.ssa.gov/policy/docs/statcomps/di asr/2016/di asr16.pdf ).

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The editors of The Scandinavian Journal of Economics 2019.