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Adverse Selection in Reinsurance Markets

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Abstract

This paper looks for evidence of adverse selection in the relationship between primary insurers and reinsurers. We test the implications of a model in which informational asymmetry—and therefore, its negative consequences—decline over time. Our tests involve a data panel consisting of U.S. property-liability insurance firms that reported to the National Association of Insurance Commissioners during the period 1993–2012. We find that the amount of reinsurance, insurer profitability, and insurer credit quality all increase with the tenure of the insurer–reinsurer relationship.

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Notes

  1. Jean-Baptiste and Santomero (2000).

  2. Reinsurance contracts are typically written for either a fixed term or on a “continuous until cancelled” basis. Consequently, long-term implicit contracts result either from repeated contracting (where an expiring fixed contract is effectively renewed by rolling over into another contract) or as a result of non-cancellation of a continuous contract (see the definition for “Expiration” from the Guy Carpenter glossary located at http://bit.ly/guycarpenter).

  3. Industry executives generally believe that long-term reinsurance relationships are important. Jean-Baptiste and Santomero provide theoretical grounding for this belief, showing that long-term relationships play an important role in mitigating adverse selection.

  4. An anonymous reviewer suggested an alternative view of these hypotheses. Specifically, changes in contract length could be caused by reinsurance experience, relationships, and increased profitability, rather than the other way around. Furthermore, there could be an omitted variable correlated with both demand and profit that causes them to appear to be correlated with sustainability and reinsurer focus. We recognize the possibility of such biases; we may not be able to firmly say that the causality runs in the favoured direction, except to say that it is based on the rigorous theoretical framework provided by Jean-Baptiste and Santomero.

  5. Rothschild and Stiglitz (1976) demonstrate that adverse selection may be mitigated through contract design, in which insureds self-select based upon price and coverage. Jean-Baptiste and Santomero’s theory seeks a better solution, since, as they note, the Rothschild and Stiglitz result is not first-best. Therefore, Jean-Baptiste and Santomero take the cedant–reinsurer relationship as given and rely instead upon relationship sustainability as the mechanism that separates risk types in the long run. Moreover, their analysis suggests that contingent pricing schemes (loss-sensitive contracts and large deductibles) decrease in importance as the length of the cedant/reinsurer relationship increases (as is implied by our empirical results). A researcher with access to a reinsurer’s proprietary book of business, including pricing and contract design information, could potentially test the sensitivity of our results to the relationship assumption and estimate the combined effect of contract design a priori and sustainability ex post.

  6. For example see Kunreuther and Pauly (1985), D’Arcy and Doherty (1990), Hendel and Lizzeri (2003), de Garidel-Thoron (2005), and Cohen (2012).

  7. When considering the learning and asymmetric information literature, the study closest to ours is by Cohen (2012). Cohen uses a unique panel data set of an Israeli auto insurer’s transactions with repeat customers. She finds that (1) repeat customers with good (bad) claims histories are more likely to stay with (flee from) the same insurer, and (2) the insurer and customers with good claims histories both benefit; the insurer earns higher profit whereas the customers enjoy lower premiums. Although we (unlike Cohen) lack data on earned premiums for cedants, the notion that cedants enjoy lower reinsurance premiums is implicit in Hypothesis 1; the reason why cedants demand more reinsurance as the expected length of the relationship increases is because reinsurance becomes less expensive as the costs of adverse selection are mitigated.

  8. Rubinstein and Yaari (1983).

  9. Doherty and Smetters (2005).

  10. See Cohen and Siegelman (2010) for an excellent survey of the empirical literature on the disentangling of moral hazard and adverse selection.

  11. For example see Cummins (2008).

  12. Bouriaux and MacMinn (2009).

  13. For example in the forms of so-called “big data” and data analytics; see McAfee and Brynjolfsson (2012).

  14. In our unbalanced panel consisting of 34,111 firm-years, 72 percent of these observations involve group affiliates, whereas the remaining observations involve unaffiliated single companies (see Table 1).

  15. For example Mayers and Smith (1990), Garven and Lamm-Tennant (2003), Cole and McCullough (2006).

  16. Total ceded reinsurance is defined in the numerator of Eq. (1) as the sum of reinsurance ceded internally (to group affiliates) and externally (to unaffiliated reinsurers). In the denominator, total business premiums written is defined as direct premiums written plus the sum of reinsurance assumed internally (from group affiliates) and externally (from unaffiliated companies).

  17. Unlike authorized reinsurers, unauthorized reinsurers typically do not post letters of credit. Thus, AM Best and regulators provide insurers with less “surplus relief” in their solvency ratings because unauthorized reinsurers are believed to have higher counterparty credit risk than authorized reinsurers, other things equal. However, since unauthorized reinsurers are legitimate risk transfer agents from the cedant’s perspective, we include both authorized and unauthorized reinsurers in our sample, and use a variable called PercentAuthorized (which measures the percentage of reinsurance premiums ceded to authorized reinsurers) as a control variable in our reinsurance demand equation.

  18. Since the standard deviation of the reinsurer count distribution will be zero if the cedant always cedes reinsurance to the same group of reinsurers, we add 1 to the standard deviation so as to ensure that there never is division by zero.

  19. As a robustness check, we also calculate a reinsurance sustainability index (called Sustainability3) for 18 3-year rolling windows: 1993–1995, 1994–1996, … , 2010–2012. Since the reinsurer count distribution used for Sustainability3 is calculated over 3-year rather than 5-year rolling windows, this implies that Sustainability3 is defined over the closed interval [0,3], whereas the 5-year version of Sustainability (subsequently referred to as Sustainability5) is defined over the closed interval [0,5].

  20. Since our data are time-series in nature, autocorrelation is a potential problem. While we report heteroscedasticity and autocorrelation robust standard errors, unreported standard errors pooled by cedant were not materially different.

  21. Rothschild and Stiglitz (1976).

  22. Chiappori and Salanie (2000).

  23. We analysed numerous unreported specifications of this model and found no evidence of positive correlation in any of the models, further supporting our contention that information asymmetries are not growing over time.

  24. Here, we follow the cash flow volatility calculation method given by Cummins and Sommer (1996).

  25. We define long tail lines in the same manner as Phillips et al. (1998); that is long tail lines include Farmowners Multiple Peril, Homeowners Multiple Peril, Commercial Multiple Peril, Ocean Marine, Medical Malpractice, International, Reinsurance, Workers’ Compensation, Other Liability, Products Liability, Aircraft, Boiler and Machinery, and Automobile Liability.

  26. This interaction effect enables us to calibrate whether relationship sustainability and focus have different reinsurance demand implications for large vs small firms; we find that other things equal, reinsurance demand is positively influenced by relationship sustainability and focus, although the effect is smaller for large compared with small firms.

  27. By interacting ReinsuranceHerfindahl with GroupDummy, this allows us to differentiate somewhat between reinsurance contracts that take place within groups with reinsurance contracts that take place outside of groups.

  28. The basic intuition for squaring firm size is to determine whether there may be scale economies in risk bearing that make reinsurance marginally less attractive for large firms compared with small firms.

  29. This approach (i.e. including CedantTaxRate and CedantTaxRate2 as right-hand side variables) is consistent with approaches followed in a number of studies that have empirically investigated the implications of tax convexity for reinsurance demand; for example see Adiel (1996), Adams et al. (2008), and Kader et al. (2010).

  30. This enables us to calibrate whether the marginal effect of volatility is different at high compared with low levels of volatility; we find that other things equal, reinsurance demand is higher (lower) at higher (lower) levels of volatility.

  31. In the profitability and bankruptcy risk equations, we utilize the contemporaneous rather than 1-year lagged values for our Sustainability and Sustainability3 variables. This is appropriate since profitability and insurer rating outcomes depend upon the current status of the cedant firm’s reinsurance program.

  32. Lamm-Tennant et al. (1996).

  33. Berger et al. (1997).

  34. Thus, the reference variable for type of distribution system is the broker marketing system (see Hilliard et al. (2013)).

  35. See Bauer et al. (2013).

  36. By using both PremiumSurplusRatio and PctChgSurplus we are able to provide a more dynamic view of bankruptcy risk; that is, PremiumSurplusRatio indicates whether the cedant is currently adequately capitalized, whereas PctChgSurplus indicates where capital adequacy is either improving or deteriorating from its current level.

  37. As noted earlier, the reinsurance sustainability index based upon 5-year rolling windows (Sustainability) is a continuous variable defined over the [0,5] closed interval, whereas the reinsurance sustainability index based upon 3-year rolling windows (Sustainability3) is a continuous variable defined over the [0,3] closed interval.

  38. See Barnett and Lewis (1994) for a discussion of winsorizing and for references to the relevant statistical literature.

  39. Grace and Leverty (2010).

  40. Shumway (2001).

  41. Due to the lack of data to calculate meaningful IRIS ratios for some smaller firms, the sample for this analysis was notably smaller than the sample size for the ordered probit analysis.

  42. Since the robustness test results for Sustainability3 were not materially different from the robustness test results for Sustainability5, we only report the Sustainability5 results. Robustness test results for Sustainability3 are available from the authors upon request.

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Acknowledgements

The authors acknowledge valuable feedback and contributions from Muhammed Altuntas, Mark Browne, David Cummins, Joan Lamm-Tennant, Andrew Petersen, Alex Muermann (the guest editor), and two anonymous reviewers. Of course, we are solely responsible for any remaining errors.

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Authors and Affiliations

  1. Department of Finance, Insurance and Real Estate, Baylor University, One Bear Place #98004, Waco, 76798-8004, TX, U.S.A.

    James R Garven

  2. W.A. Franke College of Business, Northern Arizona University, 20 W. McConnell Dr., Flagstaff, 86011, AZ, U.S.A.

    James I Hilliard

  3. Risk Management and Insurance at the Robinson School of Business, Georgia State University, P.O. Box 4036, Atlanta, 30302-4036, GA, U.S.A.

    Martin F Grace

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  1. James R Garven
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  2. James I Hilliard
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Appendix

Appendix

Numerical example of the reinsurance sustainability index

Example #1:

illustration

figure b

In this first numerical example, since

  • and

it follows that SUSTAIN1=μcount1/(σcount1+1)=5/1=5.

Example #2:

illustration

figure a

In this second numerical example, since

  • and

it follows that SUSTAIN2=μcount2/(σcount2+1)=1.67/1.47=1.13.

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Garven, J., Hilliard, J. & Grace, M. Adverse Selection in Reinsurance Markets. Geneva Risk Insur Rev 39, 222–253 (2014). https://doi.org/10.1057/grir.2014.13

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