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Social Choice and Welfare

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24-10-2016 | Original Paper

The political choice of social long term care transfers when family gives time and money

Authors: Philippe De Donder, Marie-Louise Leroux

Published in: Social Choice and Welfare | Issue 3-4/2017

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Abstract

We develop a model where families consist of one parent and one child, with children differing in income and all agents having the same probability of becoming dependent when old. Young and old individuals vote over the size of a social long term care transfer (LTC hereafter) program, which children complement with help in time or money to their dependent parent. Dependent parents have an intrinsic preference for help in time by family members. We first show that low (resp., high) income children provide help in time (resp. in money), whose amount is decreasing (resp. increasing) with the child’s income. The middle income class may give no family help at all, and its elderly members would be the main beneficiaries of the introduction of social LTC transfers. We then provide several reasons for the stylized fact that there are little social LTC transfers in most countries. First, social transfers are dominated by help in time by the family when the intrinsic preference of dependent parents for the latter is large enough. Second, when the probability of becoming dependent is lower than one third, the children of autonomous parents are numerous enough to oppose democratically the introduction of social LTC transfers. Third, even when none of the first two conditions is satisfied, the majority voting equilibrium may entail no social transfers, especially if the probability of becoming dependent when old is not far above one third. This equilibrium may be local (meaning that it would be defeated by the introduction of a sufficiently large social program). This local majority equilibrium may be empirically relevant whenever new programs have to be introduced at a low scale before being eventually ramped up.

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OECD (2011, chapter 7) provides a detailed taxonomy of public LTC systems within the OECD. For broader surveys on long term care, see Brown and Finkelstein (2011) and Cremer et al. (2009).

It is also associated with the desire of most people to remain in their own homes for as long as possible. Recent polling by the Canadian Life and Health Insurance Association, reported in Frank (2012) found that 77 percent of Canadians would prefer to stay in their homes as they age. See also Torjman (2013).

The same assumption is made by Nuscheler and Roeder (2013), which we cover in Sect. 1.1. Costa Font et al. (2014) contrast ex ante financing of LTC (such as insurance) with ex post financing (such as transfers, as in our model). They find that most OECD countries’ LTC spending is financed by close to a fifty-fifty mix of ex-ante and ex-post funding sources or that the spending relies heavily on ex-post funding sources. They also obtain that OECD countries view the two forms of funding as substitutes rather than complements.

Sloan et al. (1997) find little empirical support for the hypothesis that care giving by children is motivated by the prospect of receiving bequests from their parents. Kopczuk and Lupton (2007) also find no empirical evidence of strategic bequests.

We are interested in how much (more) young agents help their parent in case of dependency, so that any help to a non-dependent parent can be subsumed in the existing model. Note that we also assume away (so-called descending) altruism from parents to children to focus on help by children to parents. In the appendix, we show that introducing descending altruism would not change children preferences toward the tax rate, while parents (both autonomous and dependent) would prefer a lower value of the tax rate. Introducing descending altruism would then bias our results toward even less public LTC transfers.

Pestieau and Sato (2006, 2008) make the same assumption, although it remains implicit in their setting. This assumption requires that we assume away saving, strategic interactions between parents and children (such as exchanges of help for bequests) and that the size of the public LTC program is chosen at each period. See footnote 4 for the lack of strategic motivations for family help, and footnote 14 for a defence of the last assumption above.

Finkelstein et al. (2013) show that the marginal utility from consumption varies with health status.

We leave for future research the case where old agents differ in income, and where children and parental income within a family are correlated.

We can either assume that $v(d,e)<0$ or subtract a constant term large enough in the definition of $U_{Y}^{D}$ to make sure that $ U_{Y}^{N}>U_{Y}^{D}$. Note that this does not affect our analysis, since children do not choose to make their parent dependent or not.

Assuming away labor income tax distortions biases the model in favor of the introduction of social LTC transfers (since distortions would decrease the most-preferred value of $\tau $ of agents).

Alternatively, we could have assumed that the benefit b decreases linearly with the child’s income w. This would have generated the same kind of redistributive effects.

This formulation is made not only for analytical convenience, but also because it is more consistent with the empirical results than the alternative formulation where net income is $(1-\tau )w(1-e)$. The latter formulation means that the marginal cost of e decreases with $\tau $, while the marginal cost of $\tau $ decreases with e, so that e and $\tau $ could be complements rather than substitutes in our approach. Sloan et al. (2002), Houtven and Norton (2004) and Charles and Sevak (2005) find that informal care is a substitute for home health care, nursing home care, hospital care and physician visits.

Karagyozova and Siegelman (2012) review the empirical literature on relative risk aversion. They report several studies which find a coefficient of relative risk aversion lower than one. Hansen and Singleton (1983) evaluate it to be between [0.35, 1]; Holt and Laury (2002) elicit the distribution of coefficients of relative risk aversion and find that $64\,\%$ of respondents had a coefficient comprised between 0.15 and 0.97. Chetty (2006) finds that “using 33 sets of estimates of wage and income elasticities, the mean implied value of (the coefficient of relative risk aversion) is 0.71, with a range of 0.15 to 1.78 in the additive utility case.” Assumption 2 is then reasonable.

The alternative assumption that the result of a vote would hold for decades does not seem reasonable to us. The literature on the political economy of pensions often assumes that voting takes place once and for all (see for instance, Casamatta et al. (2000) and Cremer et al. (2007)), but this assumption is a pis-aller to explain the emergence of pay-as-you-go social transfer schemes in the absence of altruism. The presence of altruism in our model makes the unpalatable assumption of voting once and for all not necessary.

The boundaries of this “middle class” are obtained analytically by (i) setting $V_{Ye}=0$ for $f=e=0$ and solving for $ w<\beta $ (to obtain its lowerbound), and (ii) by setting $V_{Yf}=0$ for $ f=e=0$ and solving for $w>\beta $ (to obtain its upperbound). All figures are based on the following assumptions: $u(x)=2\sqrt{x},$ $v(d,e)=ln[d+\beta e]$, $\pi =0.5$, ${\bar{w}}=5$, $T=2$, ${\bar{p}}=4$, $\beta =5$. In Fig. 1, we assume moreover that $\tau =0$ and $\alpha =1$.

Proceeding simultaneously proves much easier to obtain the individually optimal amounts of $\tau $, e and f than proceeding sequentially and using the envelope theorem, because of the frequent corner solutions for the variables.

In order to focus on empirically relevant situations and not to multiply cases, we assume from now on that no young agent with a dependent parent most prefers $\tau _{Y}^{*}\ge 1$, which could in theory occur in our setting with untaxed labor income $w(T-1)$. This condition is satisfied if

$$\begin{aligned} wu^{\prime }\left( w\left( T-1\right) \right) >\alpha \frac{{\bar{w}}}{\pi }\phi ^{\prime }\left( {\bar{p}}+ \frac{{\bar{w}}}{\pi }\right) . \end{aligned}$$

Figs. 2 and 3 differ only in the value of $\alpha $. In both figures, all agents prefer either $\tau ^{*}>0$ or $f^{*}>0$. The curve $\beta e^{*}(0,w)$ (as in Fig. 1) is only depicted here to allow the comparison with $\tau ^{*}{\bar{w}}/\pi $ when $\tau ^{*}$ is set at its most-preferred level for individual w.

The case where $\beta >{\bar{w}}/\pi $ is available upon request but not reported here since the majority chosen value of $\tau $ is zero in that case.

Assuming that they throw a dice to determine which value of $\tau $ to vote for would not affect our results. Alternatively, we could assume that autonomous parents vote in favor of the best alternative for their child, that is for $\tau ^{*}=0$. In that case, no group forms a majority by itself with $0<\pi <1$, and the necessary condition for $\tau ^{*}>0$ becomes $\pi >1/2$, a more stringent condition than the one we obtain after Lemma 1.

We assume throughout the paper that dependency does not prevent old agents from voting (because of cognitive issues, for instance). If all dependent agents were prevented from voting, the Condorcet winning value of the tax rate would be zero if $F({\bar{w}}/\pi )<1/2\pi $ (which always holds if $\pi <1/2$), thanks to an alliance of young agents with autonomous parents, and of young agents with dependent parents and $w\ge {\bar{w}}/\pi $. If $F(\bar{w }/\pi )>1/2\pi $, then the Condorcet winning value of $\tau $ is positive, and the decisive voter is a young agent with a dependent parent and a productivity $w<{\bar{w}}/\pi $ such that $F^{-1}(w)=1/2\pi $.

It is easy to show, using the implicit function theorem on (1), that $\breve{w}$ decreases with $\pi $.

The assumption mentioned in footnote 17 implies that this threshold is lower than 1.

The assumption mentioned in footnote 17 implies that $f^{*}(\tau ,w)=0$ for $\tau >{\tilde{\tau }}$ with ${\tilde{\tau }}<1$.

It is immediate that $f^{*}(0,{\bar{w}}/\pi )<{\bar{w}}/\pi .$

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Title: The political choice of social long term care transfers when family gives time and money
Authors: Philippe De Donder
Marie-Louise Leroux
Publication date: 24-10-2016
Publisher: Springer Berlin Heidelberg
Published in: Social Choice and Welfare / Issue 3-4/2017
Print ISSN: 0176-1714
Electronic ISSN: 1432-217X
DOI: https://doi.org/10.1007/s00355-016-0999-3

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