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Behavioral Biases and Long-Term Care Insurance: A Political Economy Approach

Philippe De Donder and Marie-Louise Leroux


We develop a model where individuals all have the same probability of becoming dependent and vote over the social long-term care insurance contribution rate before buying additional private insurance and saving. We study three types of behavioral biases, all having in common that agents under-weight their dependency probability when taking private decisions. Sophisticated procrastinators anticipate their mistake when voting, while optimistic and myopic agents have preferences that are consistent across choices. Optimists under-estimate their own probability of becoming dependent but know the average probability, while myopics underestimate both. Sophisticated procrastinators attain the first-best allocation, while myopics and optimists insure too little and save too much. Myopics and optimists more (resp., less) biased than the median are worse off (resp., better off), at the majority-voting equilibrium, when private insurance is available than when it is not.

JEL codes: H55; I13; D91

A previous version of this paper has been presented at the 2012 Venice Summer Institute Workshop on “The Economics of Long-Term Care” under the title “A Political Economy Approach to Long-Term Care with Sophisticated or (In)Consistently Myopic Voters”.


Proof of proposition 3

The preferred tax rate of a type S individual is denoted by and, if positive, is such that

Assuming that the most-preferred saving amount is positive when , the first-order condition for saving eq. [8] holds with equality and we can rewrite the above expression as

so that is such that Plugging this equality into eq. [8], we obtain that

If , we then obtain that the FOC for a, eq. [9] is negative for all a, so that . This in turn guarantees that , since we have assumed that . If , a is a perfect substitute to s (eqs. [8] and [9] are equivalent), so that we can assume w.l.o.g. that which in turn guarantees that . □


We thank our discussant and three anonymous referees for their suggestions. Financial support from the Chaire “Marché des risques et création de valeur” of the FdR/SCOR is gratefully acknowledged. The usual caveat applies.


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  1. 1

    Public LTC programs provide either cash benefits or in-kind services, which depend on the needs and on the financial resources of the user. Since benefits never totally cover the total cost of dependency, individuals have an incentive to complement public LTC coverage with private insurance. From now on, we use the term of “social insurance” for all such public programs. They include Medicaid in the US and the APA in France.

  2. 2

    For surveys on long-term care, see Brown and Finkelstein (2011) and Cremer et al. (2009).

  3. 3

    See and the references mentioned there. See also the related Dunning–Kruger effect where agents mistakenly rate their ability much higher than average.

  4. 4

    To be fair, a non-negligible fraction of respondents over-estimated their risk in this study. Also, comparing responses on subjective survival probabilities with actual ones, Hamermesh (1985) shows that middle aged individuals tend to under-estimate their survival probability to ages below 70 years old but over-estimate it for ages above 70. Ludwig and Zimper (2007) obtain similar results. Since the prevalence of dependency increases sharply with age, especially after 70, these misperceptions may lead to over-estimations of the dependency risk. We discuss in the conclusion how over-estimation by some agents would affect our results.

  5. 5

    Cremer and Roeder (2012) take a normative perspective and examine whether misperception of individual LTC risks and private insurance market loading costs can justify social LTC insurance and/or subsidization of private insurance. Although they use the term of myopia, their agents are indeed optimistic since they correctly estimate the average dependency rate in the economy. They differ in their degree of bias, income and dependency risk, with the latter two positively and perfectly correlated.

  6. 6

    See Mayhew et al. (2010) and Rickayzen (2007). It is also called an enhanced life annuity (Levantesi and Menzietti 2012). This product is currently available in the US. We model DLAs for two reasons. First, the instrument is interesting by itself: OECD (2011) considers that it is one of “the most promising private sector innovations”, while Mayhew et al. (2010) state that “DLAs could make an important contribution to LTC planning.” Second, as shown below, by varying , we can cover the case where private insurance is available () and where it is not ().

  7. 7

    This assumption allows us to obtain explicit formulations for the optimal allocation (Section 3) and the one most-preferred by myopic agents (Section 5). Our results would hold qualitatively more generally provided that and These assumptions reflect the observations that, for any consumption level, individuals are worse off if dependent than if autonomous, but have higher needs (i.e. higher marginal utility from consumption). The latter assumption may be disputed (see, for instance, Finkelstein et al. 2013), since some goods may substitute or complement good health. Observe that if dependent people do not have higher marginal utility than when autonomous, the lack of demand for LTC insurance is not puzzling at all.

  8. 8

    We assume that the transfer received by agents when old is determined by the contribution rate implemented when they were young. Since any change in the current contribution rate only affects the future payments received by the currently young agents, agents vote only when young. Alternatively, we could have studied an overlapping-generation model with a pay-as-you-go LTC insurance, where variations in impact both the (currently) young and the old agents. In that case, old agents would either be indifferent as to the value of (if autonomous at the time of voting), or favor the maximum value of (if dependent). As for young agents, their preference would depend on the perceived link between current contribution and future transfer. Such considerations are well known in the political economy literature on pensions (see Sjoblom 1985), and we abstract from them here.

  9. 9

    In the rest of the paper, we assume that no agent is totally myopic, that is to say, they all believe that they have at least a very small chance of becoming dependent: for all. This is a reasonable assumption that allows to simplify our analysis since we can disregard any discontinuity in saving or voting behavior when . In the conclusion, we discuss how our results would be affected if some agents over-estimated their risk, .

  10. 10

    See O’Donoghue and Rabin (2003) and Thaler and Sunstein (2003) for a discussion of the “new paternalism” approach linked to the rise of behavioral economics. See Salanie and Treich (2009) for a paternalistic social planner in a context where agents misperceive risks.

  11. 11

    For the justification of this approach, see the first paragraph in Section 3.

  12. 12

    We assume that is large enough that agents can obtain their most-preferred insurance level by buying annuities and without overshooting their most-preferred saving level.

  13. 13

    We assume w.l.o.g. that , since DLAs are equivalent to saving when .

  14. 14

    Recall from Section 4 that savings and social insurance are substitutes for all agents when , so that

  15. 15

    Unlike for myopics, obtaining explicit formulations for the most-preferred saving and insurance amounts of optimists would require to specify a functional form for the utility function.

  16. 16

    They are available upon request to the authors.

  17. 17

    As for type M, we assume w.l.o.g. that , since DLAs are equivalent to saving when .

Published Online: 2013-5-28

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