Long‐term care policy with lazy rotten kids

• DOI: http://doi.org/10.1111/jpet.12237
• Published date: 01 June 2017
• Date: 01 June 2017

Received: 16 August 2016 Accepted: 9 November2016

DOI: 10.1111/jpet.12237

ARTICLE

Long-term care policy with lazy rotten kids

Helmuth Cremer1Kerstin Roeder2

1Universityof Toulouse

2Universityof Augsburg

HelmuthCremer, ToulouseSchool of Economics,

Universityof Toulouse Capitole, Toulouse,France

(helmuth.cremer@tse-fr.eu).

KerstinRoeder, University of Augsburg, Augs-

burg,Germany (kerstin.roeder@wiwi.uni-

augsburg.de).

Financialsupport from the Chaire Marché des

risquesetcreationdevaleurofthe FdR/SCOR is

gratefullyacknowledged. An earlier version of

thispaper was circulated under the title “Long-

termcare and lazy rotten kids.” We thank Subir

Chakrabarti,Justina Klimaviciute, Henry Mak,

andPanu Poutvaara for their insightful remarks.

Wealso thank the referees for their constructive

andhelpful suggestions.

This paper studies the determination of informal long-term care

(LTC) provided by children in a scenario which is somewhere in

between perfect altruism and selfish exchanges. Parentsare altruis-

tic but children are purely selfish, and neither side can make credible

commitments. The model is based on Becker’s “rotten kid” specifica-

tion except that it explicitly accounts for the sequence of decisions.

In Becker’s world, with a single good efficiency is achieved.We show

that when family aid is introduced the outcome is likely to be inef-

ficient. Still, the rotten kid mechanism is at work and ensures that

a positive level of LTC is provided as long as the bequest motive is

operative. We identify the inefficiencies by comparing the laissez-

faire (subgame perfect) equilibrium to the first-best allocation. We

first assume that families are identical ex ante and then consider the

case where dynasties differ in wealth. We study how the provision of

LTCcan be improved by public policies. Interestingly, crowding out

of private aid by public LTCis not a problem in this setting. With an

operative bequest motive, public LTC will have no impact on private

aid. More amazingly still, when the bequest motive is (initially) not

operative, public insurancemay even enhance the provision of infor-

mal aid.

1INTRODUCTION

Long-termcare (LTC) concerns people who depend on help to carry out daily activities such as eating, bathing, dressing,

going to bed, getting up, or using the toilet (OECD, 2011, p. 39). It is deliveredinformally by families—mainly spouses,

daughters, and step-daughters—and, to a lesser extent, formally by care assistants, who are paid under some form of

employment contract (OECD,2011, chapter 3). Formal care is given at home or in an institution (such as care centers

and nursing homes). The governments of most industrialized countries are involvedin either the provision or financing

of LTCservices, or often both, although the extent and nature of their involvement differs widely across countries.1

In the future, the demand for formal LTCservices by the population is likely to grow substantially.LTC needs start to

rise exponentially from around the age of 80 years. The number of persons aged 80 years and aboveis growing faster

than any other segment of the population. As a consequence, the number of dependent elderly at the European level

(EU–27) is expected to grow from about 21 million people in 2007 to about 44 million in 2060 (European Commission,

1Forexample Germany, Japan, and Luxembourg have introduced a universal social insurance scheme for LTC.Countries such as Canada or the United King-

dom,by contrast, rely on means-tested public programs (OECD, 2011, p. 216). In the United states, means-tested LTCbenefits are provided through Medicaid.

Journal of Public Economic Theory.2017;19:583–602. wileyonlinelibrary.com/journal/jpet c

2017 Wiley Periodicals,Inc. 583

584 CREMER AND ROEDER

2009). We thus anticipate increasing pressure on resources demanded to provideLTC services for the frail elderly,and

this pressure will be on the three institutions currently financing and providing LTCservices: the state, the market, and

the family.2

Toassess the adequacy of LTCfinancing and provision and to make projections, it is important to assess the extent to

whichcountries will be able inthe future to rely on the informalprovision of care. Most seniors with impairments reside

in their home or that of their relatives, and they rely largely on volunteer care from family members.3An important

feature that is often neglected is the real motivation for family solidarity.For long, we have adopted the fairy tale view

of children helping their dependent parents with joy and dedication, what we call pure altruism. We now increasingly

realize that family solidarity is often based on forced altruism (social norm) or on strategic considerations (e.g., Canta

& Pestieau, 2013; Cox,1987; Cox & Rank, 1992).

Knowing the foundation of family assistance is very important to see how it will react to the emergence of private

or public schemes of LTCinsurance. For example, the introduction of LTC social insurance is expected to crowd out

family solidarity based on pure altruism (e.g., Cremer,Gahvari, & Pestieau, 2013). On the other hand, where “solidar-

ity” is based on strategic exchanges crowding out is expectedto be less significant. Its precise extent is then likely to

dependon the specific way these interfamily exchanges are determined. The existing literature (e.g., Bernheim, Shleifer,

& Summers, 1985) concentrateson strategic bequest type models with full commitment leading to efficient bargaining.

In reality,this appears to be a rather strong assumption.4

In this paper, we study the determination of informal care in a scenario which is somewhere in between perfect

altruism and selfish exchanges.Parents are perfectly altruistic toward their children but children act in a purely selfish

wayand neither side can make credible commitments (which would open the possibility of efficient bargaining as in the

strategic bequest setting). We concentrate on this pattern of exchanges,even though we do not claim that all families

interactin the way described in our model. In reality, a wide variety of patterns of intrafamily exchangesis likely to exist.

The determination of the equilibrium and the policy design should then be studied in a setting where different types of

family exchangepatterns coexist; see the Conclusion for a more detailed discussion.

Our model is based on a pattern of exchangeswhich has been widely considered in the literature, namely, Becker’s

(1974, 1991) “rotten kid” theorem (see also Bergstrom, 1989, 1996), exceptthat we explicitly account for the sequence

of decisions (like Bruce & Waldman, 1990).5In Becker’s world, with a single good this setting yields an efficient out-

come, even in the absence of commitment and when a child is purely selfish. In other words, the selfish child chooses

its actions so as to maximize the family’s income and thereby internalizes all effects of his actions onhis parent’s utility.

This is what we shall refer to as the “rotten kid mechanism.” Weshow that when family aid (and LTCservices in general)

are introduced the outcome is likely to be inefficient. This is particularly true when parents value their children’s care

more than the market substitutes.6Still, the rotten kid mechanism is at work and ensures that a positive levelof aid is

provided as long as the bequest motive is operative.We study how the inefficiency can be corrected by public policies.

In the first part of the paper,we assume that families are identical ex a nte. In the second part, we turn our attention to

the case where dynasties differ in wealth.

The design of public policy has to account for the (in)efficiencies of informal aid. The conventional wisdom is that

public policy often creates or at least enhances such inefficiencies through crowding out (e.g., Norton, 2000). In our

setting, however,the relationship between public LTC and family aid is more complex.As long as the bequest motive is

operative, children do providesome informal aid to their parents, but its level is too low except when the full impact of

2Fora more in-depth discussion of the three institutions and their advantages and disadvantages in financing LTC, see the overviewby Cremer, Pestieau,and

Ponthière(2012).

3Acrossthe OECD, more than one in 10 adults over 50 years provides informal care (OECD, 2011, p. 13).

4Arrondel and Masson (2006) provide an excellent summary of the empirical literature which tests the exchange-motivatedmodels. The early literature

seemed to endorse the strategic type of models. However,as more and better data became available, the more recent literature has shed doubts on the

relevanceof exchange-based models. It shows that they do not offer a convincing alternative to parent’s altruism as motivation of private transfers.

5Althoughthe rotten kids framework has been widely studied it has not previously been used to analyze policy design.

6Itwas already pointed out by Bergstrom (1989) that Becker’s rotten kid theorem holds if there is one commodity (money), the parent is an effective altruist

andchooses after the child (for this, see also Hirshleifer, 1977), and the model is static. For a summary, see also Laferrère and Wolff(2006).