Why Changes in PBGC and FDIC Premiums Should Not Fully Reflect Changes in Underlying Risk (With Some Application to Long-Term Private Insurance Contracts)

Abstract

The degree of risk adjustment in both FDIC and PBGC premiums appears to be much smaller than actuarially fair. We explore why this is using a stylized theoretical model of multiperiod insurance contracts in the presence of moral hazard where the risk status of insureds changes over the life of the contract. If insureds value stable premiums and there is moral hazard, we show that the optimal multiperiod insurance contract for full insurance allocates greater premiums to higher risk states, and lower premiums to lower risk states, but the optimal allocation of premiums across risk states will usually not be actuarially fair. The degree of risk adjustment rises with the extent of moral hazard and falls as risk aversion rises. We extend our analysis to examine optimal risk classification in private insurance in the presence of moral hazard, with similar results. We also discuss practical considerations that further reduce the desirability and feasibility of actuarially fair risk adjustments in premiums for the FDIC and PBGC, and show how our model extends prior work on social insurance with moral hazard.

ACKNOWLEDGMENTS

The author thanks colleagues at UGA, participants in the annual meeting of the Southern Risk and Insurance Association, members of the PBGC’s Policy, Research and Analysis Department (PRAD), two anonymous referees, and the editor for valuable comments. All remaining errors are his own.

Notes

1 For example, few informed consumers would likely buy a whole life insurance policy that could underwrite them accurately every morning, and charged them a daily premium equal to that day’s risk. Premiums for healthy individuals would be negligible, but as individuals neared death, their daily premiums would approach the sum assured under the policy.

2 By unilateral commitment, we mean that if insureds pay premiums, the insurer is obliged to honor the contract, but if insureds decline to pay the premiums, the insurer cannot compel them to do. Almost all private-sector insurance in the United States has unilateral commitment.

3 By bilateral commitment, we mean that the insurer can compel the insured to pay premiums due in terms of the policy. Social insurance is usually bilateral.

4 The author is grateful to an anonymous referee for pointing out the connection between the current article and this strand of the economics literature.

5 See Brown (2008) for a discussion.

6 The UK equivalent of the PBGC, the Pension Protection Fund (PPF), has used risk-based pricing since inception.

7 Among international deposit insurance systems, risk-rating is still rare; the FDIC is somewhat of an outlier in that it adjusts premiums for default risk at all. See Table A.1.4 of Demirgüç-Kunt et al. (2005).

8 The figures are calculated by taking the assessment (failure) rate in the right-hand column of the table and dividing it by the assessment (failure) rate in the left-hand column of panel A (panel B) of Table 1 in the “less than adequately capitalized” row.

9 The figures are calculated analogously to the method described in note 6, but using panels C and D.

10 In its final rule establishing the 2011 risk-based premium system, the FDIC (2011) highlighted that “more stable and predictable effective assessment rates [are] a feature that industry representatives said was very important” (43, with similar language again on page 59), indicating that in practice, banks attach significant weight to stable FDIC premiums. The PPF also expended significant effort in ensuring its premiums did not change too much in response to changes in credit-worthiness, suggesting that the same would be true for sponsors of DB pension funds and PBGC premiums.

11 Other choices are possible. One is a state-dependent value function of premiums, where the “cost” per dollar of premiums to insureds rises as the risk rises. This is functionally equivalent to our model.

12 Looking ahead, we note in the conclusion that the results in this article imply that an optimal premium structure that is neither forward- nor backward-looking cannot be fully actuarially fair on a lifetime basis across all policyholders simultaneously (as shown by McCarthy and Neuberger 2005b). The optimal premium structure must therefore embody some degree of unfairness, and the PBGC/FDIC must trade off this unfairness against premium smoothness in an aggregate sense. But because the trade-off depends on the distribution of underlying risks in the first period, this is a much more complex problem than the simple one we examine here. We therefore leave consideration of this important point to future work.

13 Allowing the insured to access capital markets allow them to smooth average premiums over time but would not allow them to hedge against changes in risk-based premiums in each period.

14 If the discount factor equals the interest rate, the model outcomes will be unchanged regardless of their value. Differences between the discount factor and the interest rate primarily affect the balance of insurance premiums between the first and second periods, rather than the allocation of premiums between risk states in the second period.

15 In applying the model to FDIC and PBGC premiums, insured income may depend on the risk state (for instance, if depositors abandon a risky bank). However, we assume that the costly action is nonpecuniary (i.e., c(p) lies outside the argument of the utility function). However, the insights would be exactly the same if we made the costly effort pecuniary, at the cost of more difficult algebra. We thank an anonymous referee for making this point.

16 An equivalent result that allows for prudence is presented in Appendix B. We note that Chetty (2006) also used a second- (third-) order expansion of the utility function to prove his results.

17 The insurer is assumed to always earn zero profits, meaning that the costs of moral hazard are passed directly to insureds in the form of higher average premiums.

18 We thank an anonymous referee for making the important point that our model structure is not directly applicable to term life insurance, a point we concede. Most significantly, under term life insurance, the claim only occurs once: either in the second period, or in the first period, in distinction to our model, where the claim can occur in any and all periods. Given that the economic insights of our model are common to many types of insurance—unemployment insurance, examined by Baily (1978), and a much wider class of models examined by Chetty (2006)—our results may carry forward to term life insurance where the claim only occurs once. We leave a formal proof of this assertion to future work.

19 An equivalent result that allows for prudence is presented in Appendix B. We note that Chetty (2006) also used a second- (third-) order expansion of the utility function to prove his results.