Long-Term Care, Altruism and Socialization

For instance, the average cost of institutional LTC for old persons in France is about 35,000 euros per year (OECD 2006), while the yearly price of a nursing home in the United States ranges between $40,000 and $75,000 (see Taleyson 2003).

See Pestieau and Ponthiere (2011) for a survey.

On old-age dependency risks, see Kemper and Murtaugh (1991).

Large loading factors for LTC insurance may be caused by adverse selection.

Our article differs from Canta and Pestieau (2012), who focus on a dynamic economy composed of traditional and opportunistic agents under exogenous transition probabilities.

In that framework, individuals can neither save resources for their old days nor purchase private LTC insurance. The reason why we make those assumptions lies in individual misperception of LTC risks in the real world (Finkelstein and McGarry 2003) and in the underdevelopment of private LTC insurance markets. Those facts motivate us to develop a baseline model that focuses on a provision of LTC either by the family or by the State. The possibility of self-insurance through private savings is discussed in Section 6.1 below.

We assume here no risk about the length of life, which is a significant simplification. See Ponthiere (2010) on the interactions of life expectancy with the socialization process.

The implications of introducing savings are discussed in Section 6.1.

For simplicity, we abstract here from family altruism oriented towards children.

Assuming a single input in the production of old-age welfare leads us to abstract here from the choice between formal and informal aid. However, given that our focus is on crowding out by the State that simplification is benign.

Fixing to either 0 or 1 is an obvious simplification, but which has only minor effects on our results. We will discuss later on the influence of that assumption on our findings.

Assuming a physical effort – rather than an effort in terms of time or goods – is a simplification, which is common to the literature on cultural transmission (see Bisin and Verdier 2010). That assumption ensures that there are no income effects on socialization (see infra).

For simplicity, we assume here that socialization costs are symmetric across types. As discussed in Ponthiere (2011), introducing asymmetric socialization costs can affect long-run population dynamics. However, in our context where all parents want to transmit the same trait, it is not obvious to see why some type of parents would face smaller socialization costs.

As such, we depart from Olivera (2011).

Such efforts are widespread in real life and often take the form of family stories or justifications, which are used by parents to convince their children not to behave like them. Adults who abandon their parents can try to justify that attitude by giving to their own children some reasons why they are right to do so in their particular case, even though abandoning elderly parents is not good in general.

The probability of direct vertical socialization depends here on the true proportion of young adults who help their elderly parents and not on some beliefs about that proportion. That assumption has important consequences. Clearly, if beliefs affected socialization efforts, then the overall dynamics might be modified, with a larger occurrence of multiple equilibria. Moreover, relaxing the perfect observability assumption could affect the design of the optimal policy. Section 6.2, which considers universal LTC benefits, partly relaxes the perfect observability assumption, by assuming that the government cannot identify elderly persons with non-altruistic children (see infra).

On demonstration effects, see Canta and Pestieau (2012).

See Section 7 for a discussion on various possible extensions.

As , the share lies between 0 and .

Throughout this article, we assume the interiority of optimal socialization efforts, with . This imposes some (weak) restrictions on and on the parameter . For instance, in the case of “It’s the family”, interiority conditions are and .

Otherwise, it is better not to socialize children and to let them take their egoistic trait in a costless way.

Hence, interiority conditions for are and .

We do not consider here whether such a LTC policy would emerge from voting. But there are strong reasons to believe that it would: parents of non-altruistic children are in favour, as well as young altruistic children (since it would reduce their socialization efforts). Parents of altruistic children are indifferent, and only non-altruistic children are likely to be against. Hence, assuming that , the proposal of a LTC policy would obtain the majority of votes. On voting on LTC in a more general environment with unequal wages and dependence risk, see De Donder and Pestieau (2011).

In the rest of this article, we focus on the case where , to rule out corner solutions. That restriction is not problematic since the optimal policy always satisfies that condition.

Note that the interior conditions for are necessarily weaker here than at the laissez-faire. Hence we will not pay too much attention to these in this section.

Note, however, that the reliance on non-monetary efforts limits the influence of LTC benefits on socialization, since our framework abstracts from possible income effects.

This “crowding-out” effect differs from the usual one, where public intervention only affects the behaviour of some agent of a particular type. Here, LTC benefits affect the economy by modifying socialization efforts, and hence, the partition of the population into different types. Thus the “crowding-out” effect consists here of more than changing individual behaviours: it changes (some) individuals’ type, and, as a corollary, their behaviours as well.

Note also that, if we had instead of , what would matter for the existence of crowding out would no longer be the slope of at 0, but, rather, the slope of at the (strictly positive) level of help given by type-n children.

That social objective is formally similar to the one studied in Jousten et al. (2005).

Given that the partition of the population is assumed to be fixed, we will leave aside the choice of socialization efforts and , which are set to 0.

Note that, by focusing on the best stationary equilibrium, we deliberately abstract from the transition towards the steady-state.

Given that the partition of the population is assumed to be fixed, we will leave aside the choice of socialization efforts and , which are set to 0.

As a consequence, the variables and g become irrelevant.

The influence of intergenerational composition effects on optimal policy in the context of socialization models was also highlighted in Ponthiere (2010), but in the context of choices affecting one’s welfare rather than the welfare of others.

We assume here, for simplicity, that the interest factor R equals 1.

Those strategic interactions are studied in Cremer, Gahvari, and Pestieau (2012).

Note that this assumption departs from the assumption made in Section 2, since under quasi-linear preferences.

For each agent, the optimal consumptions, aid and savings are independent from time. This is why we get rid of time indexes. We also ignore the case where , since there is then, for type a, perfect indifference between aid and savings, making indeterminate.

Indeed, under quasi-linear utility, public LTC benefits towards the elderly in need cannot be justified from the point of view of maximizing social welfare for a given q.

Indeed, as long as savings is not as good as children’s aid, even if a government could force the elderly to save, such a solution may still be dominated by a fully altruistic society.

Note that the argument made here also holds in the “It takes a village” case.

Indeed, whereas targeted LTC benefits reduced the welfare gap between having altruistic children or not, universal LTC benefits still reduces the gap (given the concavity of ), but less than the targeted ones, which pushes towards more socialization.

Here again, we abstract from time indexes.