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Empirical Economics

Erschienen in:

12.05.2023

Multiple dimensions of private information in life insurance markets

verfasst von: Xi Wu, Li Gan

Erschienen in: Empirical Economics | Ausgabe 5/2023

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Abstract

A growing amount of literature has shown the unavailability of a positive correlation between insurance coverage and ex post risk, even though the risk-related adverse selection is confirmed by other evidence. Such puzzles are suggested to be attributed to the coexistence of multi-dimensional private information. This paper develops a method to identify the risk-related private information in this case. To illustrate, we apply data from US life insurance market. Categorizing individuals’ heterogeneous insurance preferences into different groups and using joint maximum likelihood estimation of a mixture density model, we detect a positive correlation between individual mortality and insurance coverage within each group. This result is consistent with the conventional theory regarding the private information of adverse selection.

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Cohen and Siegelman (2010) review and evaluate the recent literature in this field.

Note that similar to Finkelstein and McGarry (2006), we cannot exclude the effect of this preference-related private information by just controlling a few proxy variables related to it. The reason has been analyzed before.

Recall that we mentioned that one potential but impractical method to identify risk-related private information in the presence of multi-dimensional private information is to control for a full set of proxy variables to the second type of private information. In contrast, our method only requires a subset of proxy variables.

We find many life insurance policies being lapsed or purchased during this eight-year time window. To avoid the mortality risk measured in our analysis not necessarily being the same as the risk for an insurer (e.g., the policyholder dies after her lapsation), we only keep the sample whose insurance status has never changed since 2000 and obtain the same conclusion. Results are available upon request.

According to the current literature, there are two dimensions of private information. One is risk-related, which is both positively correlated to insurance ownership and ex post risk, thus generating a positive correlation between the error terms; the other one is preference-related, denoted as H, which is positively correlated to insurance ownership but negatively related to ex post risk. As shown in Eq. (6), the effect of H has been absorbed into constant terms by assuming it is categorical; we therefore justify the correlation between \(u_{k}^{*}\) and \(v_{k}^{*}\) reflects the presence of the risk-related private information, after conditional on the risk classifications by insurance companies.

Appendix 1 presents the details for the case in which the probability of both mortality and insurance purchase being equal to one when insurance preferences are divided into two types.

We also extend the observation window for mortality to 2014 and obtain similar results.

A different approach to measure the ex post risk is to work on age-sex-race adjusted mortality instead of working on the binary variable of dying. As suggested in Gan et al(2005), this method calculates each individual’s updated survival possibility based on whether he or she has died. For simplicity, we employ the binary variable as the record of the occurrence of insured event in the rest of our analysis.

One well-known potential problem with self-perceived risk is that individuals have a propensity to report Figs. 0, 50, and 100 (Hurd and McGarry, 2002; Gan et al. 2005). These focal responses suggest that individual subjective probabilities on subsequent mortality can only serve as a noisy proxy for private information.

We also exclude, respectively, proxies for risk attitudes, the number of years of education, individuals' employment status, and financial conditions. For each of these four specifications, same conclusions can be obtained. Results are presented in Appendix 2.

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Titel: Multiple dimensions of private information in life insurance markets
verfasst von: Xi Wu
Li Gan
Publikationsdatum: 12.05.2023
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 5/2023
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-023-02424-8

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