## Abstract

We use data from a large US life expectancy provider to test for asymmetric information in the secondary life insurance—or life settlements—market. We compare realized lifetimes for a subsample of settled policies relative to all (settled and nonsettled) policies, and find a positive settlement-survival correlation indicating the existence of informational asymmetry between policyholders and investors. Estimates of the “excess hazard” associated with settling show the effect is temporary and wears off over approximately 8 years. This indicates individuals in our sample possess private information with regards to their near-term survival prospects and make use of it, which has economic consequences for this market and beyond.

Original language | English (US) |
---|---|

Pages (from-to) | 1143-1175 |

Number of pages | 33 |

Journal | Quantitative Economics |

Volume | 11 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1 2020 |

## All Science Journal Classification (ASJC) codes

- Economics and Econometrics

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*Quantitative Economics*,

*11*(3), 1143-1175. https://doi.org/10.3982/QE1333

**Asymmetric information in secondary insurance markets : Evidence from the life settlements market**. In: Quantitative Economics. 2020 ; Vol. 11, No. 3. pp. 1143-1175.

}

*Quantitative Economics*, vol. 11, no. 3, pp. 1143-1175. https://doi.org/10.3982/QE1333

**Asymmetric information in secondary insurance markets : Evidence from the life settlements market.** / Bauer, Daniel; Russ, Jochen; Zhu, Nan.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Asymmetric information in secondary insurance markets

T2 - Evidence from the life settlements market

AU - Bauer, Daniel

AU - Russ, Jochen

AU - Zhu, Nan

N1 - Funding Information: Unsurprisingly, allowing the heterogeneity between the two groups to converge with time since settlement (t) can generate the observed patterns from Figure. To illustrate, we generalize equation () to allow for dependence on t in the unobserved heterogeneity ?i: 10?t(i)=?i(t)?B?Cx0+t. The panels in part (f) of Figure plot the multiplicative and additive excess hazard for the S relative to the N group under assumption (), where we set ?i(t)|{i?N} to one and let ?i(t)|{i?S} start at 0.6 and linearly increase to one at time 10. Similar to part (a) versus (b), adding frailty with positive variance does not substantially change the pattern. The resulting shape is similar to Figure, although this is not a like for like comparison due to differences in the definition of the N(ot settled) and the R(emaining) comparison group. In order to replicate the trends in Figure as closely as possible, we need to choose ?i(t)|{i?S} starting at roughly 0.44 and linearly increasing to one at approximately time 8.5, as shown in the panels (g) of Figure. The resulting patterns?and also the relative magnitudes?are reminiscent of so-called select-and-ultimate life tables in actuarial studies that capture selection effects due to underwriting. To illustrate, in the panels in part (h) of Figure, we plot the multiplicative and additive excess hazard, respectively, for a preferred male life underwritten at age 75 as a function of time since underwriting relative to ultimate hazard rates based on the Society of Actuaries 2001 Commissioner's Standard Ordinary (CSO) preferred life table. Here, the ?selection effect? comes from the underwriting process allowing insurers to use lower hazard rates in the select period, so the origin for the deviation is not an informational asymmetry. The relevant analogy is that insurers will only have information on the policyholder's health state at the point of sale (time of underwriting), and the relevance of this information dissipates as time progresses, producing the converging pattern. Thus, all-in-all, while there are several possible aspects contributing to the informational asymmetry, the pattern over time is most in line with policyholders adversely selecting on private information regarding their near-term survival prospects. Identifying the origin of the informational asymmetry is a difficult problem since different explanations have similar empirical implications, particularly the positive risk-coverage relationship we observe (Chiappori and Salani? ()). In our setting, there are a number of ways how asymmetric information can affect the transactions, including: (i)Selection on persistent unobservables: There exists a permanent hidden characteristic that affects both mortality and the proclivity to settle. (ii)Hidden actions (moral hazard): Settling leads individuals to adjust their behavior (relative to when retaining their policy). (iii)Settlement process: If bidders imperfectly account for hidden information, the positive relationship may arise from the transaction process (?winner's curse?). (iv)Selection on temporary unobservables: There exists a temporary hidden characteristic that affects both mortality and the proclivity to settle. However, different mechanisms for asymmetric information lead to different risk-coverage patterns over time. In what follows, we discuss and evaluate these explanations by appraising of whether they will yield the empirical pattern. We consider a simulation experiment, where we assume individual i's hazard is of the form: 8?t(i)=?i?B?Cx0+t, where B?Cx0+t is a basic Gompertz form for baseline mortality and ?i is a random variable associated with unobserved heterogeneity. We simulate 50,000 independent lifetimes, with 25,000 individuals that settled (S) and 25,000 that did not settle (N), using starting age x0=70, Gompertz parameters B=0.0003 and C=1.07 (Dickson, Hardy, and Waters ()), and making different assumptions on (the conditional distribution of) ?i within the two groups S and N. We then determine the multiplicative and additive excess hazard ?(t) and ?(t), respectively, for members of the S group following the same procedure as in Section, and compare the results to Figure. We show results for a single simulation in Figure, panels (a) through (d), (f), and (g). We carried the experiment out several times obtaining virtually identical results. Multiplicative and additive excess hazard. Panels (a) through (d), (f) and (g): Monte-Carlo experiment according to Equation () and 25,000 lives in the settled (S) and non-settled (N) groups based on various specifications. Panel (a): ?i|{i ? N}=1 and ?i|{i ? S}=0.6; panel (b): ?i|{i ? N}=?(1,0.2), and ?i|{i ? S}=0.6 ? ?(1,0.2), where ?(a,b) stands for a random variable that follows a Gamma distribution with mean a and standard deviation b; panel (c): ?i|{i ? N}=?(1,0.4), and ?i|{i ? S}=0.6 ? ?(1,0.2); panel (d): ?i|{i ? N}=?(1,1), and ?i|{i ? S}=0.6 ? ?(1,0.2); panel (f): ?i(t)|{i ? N}=1 and ?i(t)|{i ? S}=0.6 + 0.04 ? t, 0 ? t ? 10; panel (g): ?i(t)|{i ? N}=1 and ?i(t)|{i ? S}=0.44 + 0.066 ? t, 0 ? t ? 8.5. Panel (e): Monte-Carlo experiment on the settlement process, see Appendix C for details. Panel (h): at age 75 as a function of time since underwriting for the Society of Actuaries 2001 Commissioner's Standard Ordinary (CSO) preferred life table. Policyholders heterogeneity can be the root cause for an informational asymmetry. As we discuss in the context of our simple model in Section, policyholder characteristics will influence the decision to settle (via the parameter ?) and may also be related to their propensity to survive. While heterogeneity in wealth is not likely to deliver the observed result, risk aversion presents a viable explanation. Indeed, persistently higher risk aversion may directly increase the incentive to settle or it may lead individuals to hold more (relinquishable) life insurance in the first place, but may also positively affect survival prospects, for example, by limiting engagement in risky activities or more engagement in preventative health care. To illustrate the impact of persistent unobserved heterogeneity, consider the simulation experiment outlined above with different assumptions on ?i conditional on being in the N(ot-settled) and S(ettled) groups. A necessary condition for the negative settlement-mortality relationship right at settlement as observed in Figure is 9E[?i|{i?S}]<E[?i|{i?N}]. To see this, note that the multiplicative excess hazard at settlement is ?(0)=?0S?0=E[?i|{i?S}]P(i?S)?E[?i|{i?S}]+P(i?N)?E[?i|{i?N}], and similarly the additive excess hazard at settlement is ?(0)=?0S??0=B?Cx0?P(i?N)?(E[?i|{i?S}]?E[?i|{i?N}]). The two panels (b) in Figure provide the multiplicative and additive excess hazard when assuming ?i|{i?N} is Gamma distributed with mean 1 and standard deviation 0.2, and when an individual in the settled group exhibits a 40% lower hazard rate throughout her lifetime (?i|{i?S}?0.6??i|{i?N}). The plots look similar to the situation when assuming there is no conditional heterogeneity, that is, ?i|{i?N}=1 and ?i|{i?S}=0.6, provided in panels (a). In particular, we observe a flat shape for the multiplicative excess hazard and a diverging shape for the additive excess hazard, in contrast to Figure. Hence, selection on persistent heterogeneity with identically distributed frailty factors does not appear to yield the observed pattern. However, different patterns can emerge from differences in higher-order moments. Indeed, for a flat heterogeneous hazard, ?t(i)=?i, by expanding the moment-generating function of ?i: ?tS/N?P(?i>t|{i?S/N})=E[?i|{i?S/N}]?t?E[?i2|{i?S/N}]+12t2?E[?i3|{i?S/N}]+?, so an increasing pattern in the quotient ?(t)=?tS/?t or the difference ?(t)=?tS??t must stem from differences in the conditional moments, particularly from E[?i2|{i?N}] exceeding E[?i2|{i?S}]. The intuition is as follows: While individuals in the S group have a lower hazard on average, individuals in the N group show a higher dispersion; thus, after the individuals with the lowest hazard realizations in the N group deceased, the distribution of the N group conditional on having survived until time t becomes closer and closer to the distribution of survivors in S. An example may be more risk-averse individuals in S showcasing lower?but also a more concentrated distribution of?mortality. To illustrate, for the two panels (c) in Figure, we use the same conditional distribution for the settled subgroup (?i|{i?S}) as before but now double the standard deviation for the frailty factor in the nonsettled subgroup (?i|{i?N}) to 0.4. As is evident from the plot, we now observe a slightly increasing multiplicative excess hazard but the increase in variance is not sufficient to overturn the decreasing pattern in the additive excess hazard, which originates from the underlying Gompertz form. In part (d), we repeat the exercise but now further increase the standard deviation of ?i|{i?N} to one. In this case, we do observe an increasing shape similar to Figure. However, a standard deviation of one for the unobserved heterogeneity?conditional on observables, including the underwriter's estimated hazard?is a relatively extreme assumption. Indeed, this assumption would imply a chance of close to 40% that the true hazard of individuals in the N group is less than half of the estimated hazard, and a chance of close to 14% that the true hazard is more than twice the estimated hazard. Thus, even though differences in the conditional distributions in theory could generate the observed pattern, it seems rather unlikely that persistent unobserved heterogeneity is the sole driver. In the present context, ?moral hazard? may take the form of healthier lifestyle choices after relinquishing the life insurance coverage, seeking improved medical care using the proceeds from settling, or other positive changes in health-related behavior. If permanent changes in behavior were the sole driver for the informational asymmetry, two policyholders with exactly the same observable characteristics but only differing in their settlement decision should display exactly the same hazard rate right up until settlement, and we would expect to see a diverging relationship thereafter. In particular, if there were differences in care or in lifestyle, we would arguably expect (at least) a persistent effect on the hazard?in contrast to the subsiding pattern we identify in Figure. However, if settlement is driven by the need of funds for treatment of an acute medical condition, it is conceivable that the effect of settling is immanent. And once the condition is treated, mortality may revert to population levels. To probe for this explanation, we rerun our regression analysis focusing on relatively healthy individuals. More precisely, we repeat the exercise for the 32,317 individuals in the full dataset with a mortality multiplier of less than 150% (the corresponding closed dataset comprises 7122 cases), thus excluding the individuals that were rated as very impaired. Columns [E] and [F] of Table show the results with and without time trend, respectively. For the Settled-and-Observed variable, the point estimate of the coefficient in the specification without time trend ([E]) barely changes, although standard errors increase given the smaller sample size. We observe some decrease in the slope of the time trend from 0.22 in the baseline analysis [D] to about 0.15 in specification [F], with an accompanying decrease in the intercept so that the duration of the effect roughly remains the same. Hence, while we see some relevance of the treatment of acute conditions, it appears that the observed pattern still emerges when considering only relatively healthy individuals. [E] [F] [G] [H] [I] [J] [K] [L] 1/14??014?0(t)dt 0.0000 0.0000 0.6171 0.0198 0.0193 0.0140 0.0230 0.5818 Estimated hazard, ??t(i) 0.5651 0.5749 0.8386 0.8961 0.8948 0.8914 0.8787 0.8384 (0.0735) (0.0734) (0.0265) (0.0102) (0.0102) (0.0104) (0.0097) (0.0267) Underwriting date, ln(1+DOUi) 0.2492 0.2500 ?0.0134 0.2712 0.2683 0.3032 0.2480 ?0.0150 (0.0735) (0.0734) (0.1754) (0.0285) (0.0285) (0.0289) (0.0260) (0.1753) Age at underwriting, ln(1+AUi) 5.2342 5.1351 0.5243 0.5753 0.5822 0.6273 0.5364 0.5246 (0.7582) (0.7579) (0.2089) (0.0849) (0.0849) (0.0874) (0.0843) (0.2097) Sex, SEi ?0.0037 ?0.0081 ?0.0943 ?0.1008 ?0.1006 ?0.1012 ?0.0735 ?0.0960 (0.0436) (0.0436) (0.0582) (0.0198) (0.0198) (0.0199) (0.0197) (0.0583) Smoker, SMi,1 0.6537 0.6481 0.4004 0.3611 0.3610 0.3757 0.3112 0.4019 (0.0917) (0.0917) (0.1153) (0.0431) (0.0432) (0.0434) (0.0435) (0.1155) ?Aggregate? smoking status, SMi,2 0.2394 0.2373 0.2550 0.2217 0.2223 0.2124 0.2250 0.2637 (0.1184) (0.1184) (0.1614) (0.0550) (0.0550) (0.0557) (0.0551) (0.1618) Face Value, ln(1+ln(1+FV)) ?1.1458 ?1.1223 (0.3412) (0.3721) Settled-and-Observed, SaOi ?0.1225 ?0.3922 ?0.2847 ?0.0886 ?0.3673 ?0.3835 ?0.1111 (0.0342) (0.1307) (0.1509) (0.0201) (0.0620) (0.0664) (0.0525) Small Face Value ? Settled-and-Observed, ?0.2054 (0.1747) Medium Face Value ? Settled-and-Observed, ?0.3473 (0.1552) Large Face Value ? Settled-and-Observed, ?0.1907 (0.2006) Settled-and-Observed ? trend, 0.1524 0.2094 0.1701 0.1638 0.0711 0.2308 SaOi?ln(1+t) (0.0709) (0.1023) (0.0355) (0.0372) (0.0326) (0.1026) Log-likelihood value ?46,659.58 ?46,657.25 ?13,472.47 ?133,986.91 ?133,975.36 ?132,337.92 ?132,918.00 ?13,471.36 If life settlement companies imperfectly account for missing information in their pricing, the winner's curse can yield a negative settlement-mortality correlation (Thaler ()). More precisely, a wedge could arise from brokers forwarding shorter LEs to LS companies or policyholders picking the highest among several bids for their policy, although it is not clear whether or not the LE from our provider was actually used in the settlement process. Consider the following thought experiment in opposition to this explanation: Suppose there are several identically distributed LE estimates with different associated multipliers but the broker only forwards the one with the highest multiplier and the ?winning? LS company prepares a bid on this basis; now, assuming the multiplier is simply a relatively high random realization, the multiplicative excess hazard will be constant over time at a level below one and the additive excess hazard will necessarily need to diverge to sustain this constant multiplicative trend. The panels in part (e) of Figure show the multiplicative and additive excess hazard for a Monte Carlo implementation of this thought experiment in the context of our dataset (see Appendix C for details), which is congruent with the predictions but in contrast to the pattern depicted in Figure. Thus, again, the dynamic pattern does not sustain this explanation as the sole driver. Unsurprisingly, allowing the heterogeneity between the two groups to converge with time since settlement (t) can generate the observed patterns from Figure. To illustrate, we generalize equation () to allow for dependence on t in the unobserved heterogeneity ?i: 10?t(i)=?i(t)?B?Cx0+t. The panels in part (f) of Figure plot the multiplicative and additive excess hazard for the S relative to the N group under assumption (), where we set ?i(t)|{i?N} to one and let ?i(t)|{i?S} start at 0.6 and linearly increase to one at time 10. Similar to part (a) versus (b), adding frailty with positive variance does not substantially change the pattern. The resulting shape is similar to Figure, although this is not a like for like comparison due to differences in the definition of the N(ot settled) and the R(emaining) comparison group. In order to replicate the trends in Figure as closely as possible, we need to choose ?i(t)|{i?S} starting at roughly 0.44 and linearly increasing to one at approximately time 8.5, as shown in the panels (g) of Figure. The resulting patterns?and also the relative magnitudes?are reminiscent of so-called select-and-ultimate life tables in actuarial studies that capture selection effects due to underwriting. To illustrate, in the panels in part (h) of Figure, we plot the multiplicative and additive excess hazard, respectively, for a preferred male life underwritten at age 75 as a function of time since underwriting relative to ultimate hazard rates based on the Society of Actuaries 2001 Commissioner's Standard Ordinary (CSO) preferred life table. Here, the ?selection effect? comes from the underwriting process allowing insurers to use lower hazard rates in the select period, so the origin for the deviation is not an informational asymmetry. The relevant analogy is that insurers will only have information on the policyholder's health state at the point of sale (time of underwriting), and the relevance of this information dissipates as time progresses, producing the converging pattern. Thus, all-in-all, while there are several possible aspects contributing to the informational asymmetry, the pattern over time is most in line with policyholders adversely selecting on private information regarding their near-term survival prospects. To demonstrate the quantitative impact of our results on life settlement transactions, we provide example calculations based on our proportional hazards regression results. More precisely, we are looking to quantify the average difference of LE estimates and policy valuations for an individual that decided to settle their policy relative to an individual that walked away from the transaction. We face three difficulties. First, as discussed in Section, our regression estimates are based on analyses of the known closed policies relative to the remaining policies, with the latter including a mix of closed and nonclosed cases. Since we are interested in the direct closed versus nonclosed comparison, we adjust our point estimate based on different parameter values of the (unknown) proportion of closed policies in the full sample p. More precisely, we inflate the coefficient ? based on the analysis in Appendix A.3 (equation (A.6)). Second, our regressions give us estimates for the overall impact, but not for a specific individual. Hence, we rely on US population mortality data to evaluate the impact on average policyholders at different ages that are roughly in line with the aggregate statistics from our dataset (ages 70, 75, and 80). And, third, as pointed out at the end of Section, unobserved heterogeneity may yield a prediction bias for LEs calculated based on survival regression estimates. Since we are mainly interested in the difference of LE estimates between the settled and the nonsettled group, we accept this limitation and refer to Liu () for possible remedies, for example, by relying on the so-called retransformation method. Table presents results for US male policyholders, where we rely on two different approaches to adjust the baseline mortality for settlement: A time-constant effect assumption as in equation () with results shown in the bottom part of the table, and an effect that weakens and wears off over eight years according to the time trend in our regression model with results shown in the top part of the table. As pointed out at the end of Section, our estimates for the adjustment are consistent for the cumulative hazard rates independently of its genesis. We determine the LE according to equation () for the adjusted and the unadjusted rates, and we report the LE change in percent. In addition, we report the percentage change in value for a whole-life insurance policy that was purchased 10 years prior with a constant face value, constant annual premiums, and using an interest rate of 4%. Appendix B presents additional results for female policyholders as well as for additive specifications of the excess hazard. Proportion of closed policies (p) 24.5% 30% 40% 50% 60% 70% Proportional hazards; time-weakening effect Age 70 (nonadjusted LE 13.93, value 0.2092) Difference in LE (%) 2.51 2.65 2.95 3.32 3.81 4.48 Difference in value (%) ?8.21 ?8.67 ?9.63 ?10.85 ?12.44 ?14.62 Age 75 (nonadjusted LE 10.48, value 0.2520) Difference in LE (%) 3.87 4.08 4.54 5.12 5.88 6.93 Difference in value (%) ?9.71 ?10.25 ?11.40 ?12.86 ?14.76 ?17.36 Age 80 (nonadjusted LE 7.50, value 0.3024) Difference in LE (%) 6.00 6.34 7.06 7.97 9.17 10.83 Difference in value (%) ?11.33 ?11.97 ?13.33 ?15.05 ?17.30 ?20.40 Proportional hazards; time-constant effect Age 70 (nonadjusted LE 13.93, value 0.2092) Difference in LE (%) 5.48 5.89 6.79 8.03 9.81 12.62 Difference in value (%) ?14.64 ?15.70 ?18.09 ?21.35 ?26.03 ?33.33 Age 75 (nonadjusted LE 10.48, value 0.2520) Difference in LE (%) 6.19 6.65 7.68 9.08 11.11 14.31 Difference in value (%) ?13.44 ?14.43 ?16.64 ?19.64 ?23.98 ?30.78 Age 80 (nonadjusted LE 7.50, value 0.3024) Difference in LE (%) 6.93 7.44 8.59 10.16 12.44 16.03 Difference in value (%) ?11.90 ?12.77 ?14.74 ?17.41 ?21.28 ?27.36 The first column of the table presents results based on the observed proportion of closed policies (13,221/53,947?24.5%), so without inflating the coefficient estimate. Since the actual proportion p can only be higher, these estimates provide lower bounds for the differences between settlers and nonsettlers with identical observable characteristics. The remaining columns present results based on various assumptions of p that range from 30% to 70%. Our calculations for the time-weakening assumption suggest that the LEs for individuals that settled their policy exceed those for nonsettlers by between roughly 2.5% to 11%. In particular, for a 75-year old policyholder and assuming that the proportion of closed cases in the full sample is 50%, we obtain roughly half a year (5%) of additional LE relative to a nonsettler's LE of a little over 10 years. For the differences in value of the insurance policy, we obtain figures between roughly ?8% to ?20% for settlers relative to nonsettlers. Of course, the results are based on rather specific assumptions. Nevertheless, these magnitudes suggest that asymmetric information has an economically significant impact on the life settlements market, and should be accounted for in market operations?for example, in view of pricing and risk management. The results increase substantially if we use a time-constant adjustment. For instance, they roughly double for a 75-year old for all considered proportions p. This documents the relevance of accounting for the dynamic pattern of the excess hazard. Furthermore, as we will discuss in the next subsection, it allows us to shed some light on the nature of the informational friction. Identifying the origin of the informational asymmetry is a difficult problem since different explanations have similar empirical implications, particularly the positive risk-coverage relationship we observe (Chiappori and Salani? ()). In our setting, there are a number of ways how asymmetric information can affect the transactions, including: (i)Selection on persistent unobservables: There exists a permanent hidden characteristic that affects both mortality and the proclivity to settle. (ii)Hidden actions (moral hazard): Settling leads individuals to adjust their behavior (relative to when retaining their policy). (iii)Settlement process: If bidders imperfectly account for hidden information, the positive relationship may arise from the transaction process (?winner's curse?). (iv)Selection on temporary unobservables: There exists a temporary hidden characteristic that affects both mortality and the proclivity to settle. However, different mechanisms for asymmetric information lead to different risk-coverage patterns over time. In what follows, we discuss and evaluate these explanations by appraising of whether they will yield the empirical pattern. We consider a simulation experiment, where we assume individual i's hazard is of the form: 8?t(i)=?i?B?Cx0+t, where B?Cx0+t is a basic Gompertz form for baseline mortality and ?i is a random variable associated with unobserved heterogeneity. We simulate 50,000 independent lifetimes, with 25,000 individuals that settled (S) and 25,000 that did not settle (N), using starting age x0=70, Gompertz parameters B=0.0003 and C=1.07 (Dickson, Hardy, and Waters ()), and making different assumptions on (the conditional distribution of) ?i within the two groups S and N. We then determine the multiplicative and additive excess hazard ?(t) and ?(t), respectively, for members of the S group following the same procedure as in Section, and compare the results to Figure. We show results for a single simulation in Figure, panels (a) through (d), (f), and (g). We carried the experiment out several times obtaining virtually identical results. Multiplicative and additive excess hazard. Panels (a) through (d), (f) and (g): Monte-Carlo experiment according to Equation () and 25,000 lives in the settled (S) and non-settled (N) groups based on various specifications. Panel (a): ?i|{i ? N}=1 and ?i|{i ? S}=0.6; panel (b): ?i|{i ? N}=?(1,0.2), and ?i|{i ? S}=0.6 ? ?(1,0.2), where ?(a,b) stands for a random variable that follows a Gamma distribution with mean a and standard deviation b; panel (c): ?i|{i ? N}=?(1,0.4), and ?i|{i ? S}=0.6 ? ?(1,0.2); panel (d): ?i|{i ? N}=?(1,1), and ?i|{i ? S}=0.6 ? ?(1,0.2); panel (f): ?i(t)|{i ? N}=1 and ?i(t)|{i ? S}=0.6 + 0.04 ? t, 0 ? t ? 10; panel (g): ?i(t)|{i ? N}=1 and ?i(t)|{i ? S}=0.44 + 0.066 ? t, 0 ? t ? 8.5. Panel (e): Monte-Carlo experiment on the settlement process, see Appendix C for details. Panel (h): at age 75 as a function of time since underwriting for the Society of Actuaries 2001 Commissioner's Standard Ordinary (CSO) preferred life table. Policyholders heterogeneity can be the root cause for an informational asymmetry. As we discuss in the context of our simple model in Section, policyholder characteristics will influence the decision to settle (via the parameter ?) and may also be related to their propensity to survive. While heterogeneity in wealth is not likely to deliver the observed result, risk aversion presents a viable explanation. Indeed, persistently higher risk aversion may directly increase the incentive to settle or it may lead individuals to hold more (relinquishable) life insurance in the first place, but may also positively affect survival prospects, for example, by limiting engagement in risky activities or more engagement in preventative health care. To illustrate the impact of persistent unobserved heterogeneity, consider the simulation experiment outlined above with different assumptions on ?i conditional on being in the N(ot-settled) and S(ettled) groups. A necessary condition for the negative settlement-mortality relationship right at settlement as observed in Figure is 9E[?i|{i?S}]<E[?i|{i?N}]. To see this, note that the multiplicative excess hazard at settlement is ?(0)=?0S?0=E[?i|{i?S}]P(i?S)?E[?i|{i?S}]+P(i?N)?E[?i|{i?N}], and similarly the additive excess hazard at settlement is ?(0)=?0S??0=B?Cx0?P(i?N)?(E[?i|{i?S}]?E[?i|{i?N}]). The two panels (b) in Figure provide the multiplicative and additive excess hazard when assuming ?i|{i?N} is Gamma distributed with mean 1 and standard deviation 0.2, and when an individual in the settled group exhibits a 40% lower hazard rate throughout her lifetime (?i|{i?S}?0.6??i|{i?N}). The plots look similar to the situation when assuming there is no conditional heterogeneity, that is, ?i|{i?N}=1 and ?i|{i?S}=0.6, provided in panels (a). In particular, we observe a flat shape for the multiplicative excess hazard and a diverging shape for the additive excess hazard, in contrast to Figure. Hence, selection on persistent heterogeneity with identically distributed frailty factors does not appear to yield the observed pattern. However, different patterns can emerge from differences in higher-order moments. Indeed, for a flat heterogeneous hazard, ?t(i)=?i, by expanding the moment-generating function of ?i: ?tS/N?P(?i>t|{i?S/N})=E[?i|{i?S/N}]?t?E[?i2|{i?S/N}]+12t2?E[?i3|{i?S/N}]+?, so an increasing pattern in the quotient ?(t)=?tS/?t or the difference ?(t)=?tS??t must stem from differences in the conditional moments, particularly from E[?i2|{i?N}] exceeding E[?i2|{i?S}]. The intuition is as follows: While individuals in the S group have a lower hazard on average, individuals in the N group show a higher dispersion; thus, after the individuals with the lowest hazard realizations in the N group deceased, the distribution of the N group conditional on having survived until time t becomes closer and closer to the distribution of survivors in S. An example may be more risk-averse individuals in S showcasing lower?but also a more concentrated distribution of?mortality. To illustrate, for the two panels (c) in Figure, we use the same conditional distribution for the settled subgroup (?i|{i?S}) as before but now double the standard deviation for the frailty factor in the nonsettled subgroup (?i|{i?N}) to 0.4. As is evident from the plot, we now observe a slightly increasing multiplicative excess hazard but the increase in variance is not sufficient to overturn the decreasing pattern in the additive excess hazard, which originates from the underlying Gompertz form. In part (d), we repeat the exercise but now further increase the standard deviation of ?i|{i?N} to one. In this case, we do observe an increasing shape similar to Figure. However, a standard deviation of one for the unobserved heterogeneity?conditional on observables, including the underwriter's estimated hazard?is a relatively extreme assumption. Indeed, this assumption would imply a chance of close to 40% that the true hazard of individuals in the N group is less than half of the estimated hazard, and a chance of close to 14% that the true hazard is more than twice the estimated hazard. Thus, even though differences in the conditional distributions in theory could generate the observed pattern, it seems rather unlikely that persistent unobserved heterogeneity is the sole driver. In the present context, ?moral hazard? may take the form of healthier lifestyle choices after relinquishing the life insurance coverage, seeking improved medical care using the proceeds from settling, or other positive changes in health-related behavior. If permanent changes in behavior were the sole driver for the informational asymmetry, two policyholders with exactly the same observable characteristics but only differing in their settlement decision should display exactly the same hazard rate right up until settlement, and we would expect to see a diverging relationship thereafter. In particular, if there were differences in care or in lifestyle, we would arguably expect (at least) a persistent effect on the hazard?in contrast to the subsiding pattern we identify in Figure. However, if settlement is driven by the need of funds for treatment of an acute medical condition, it is conceivable that the effect of settling is immanent. And once the condition is treated, mortality may revert to population levels. To probe for this explanation, we rerun our regression analysis focusing on relatively healthy individuals. More precisely, we repeat the exercise for the 32,317 individuals in the full dataset with a mortality multiplier of less than 150% (the corresponding closed dataset comprises 7122 cases), thus excluding the individuals that were rated as very impaired. Columns [E] and [F] of Table show the results with and without time trend, respectively. For the Settled-and-Observed variable, the point estimate of the coefficient in the specification without time trend ([E]) barely changes, although standard errors increase given the smaller sample size. We observe some decrease in the slope of the time trend from 0.22 in the baseline analysis [D] to about 0.15 in specification [F], with an accompanying decrease in the intercept so that the duration of the effect roughly remains the same. Hence, while we see some relevance of the treatment of acute conditions, it appears that the observed pattern still emerges when considering only relatively healthy individuals. [E] [F] [G] [H] [I] [J] [K] [L] 1/14??014?0(t)dt 0.0000 0.0000 0.6171 0.0198 0.0193 0.0140 0.0230 0.5818 Estimated hazard, ??t(i) 0.5651 0.5749 0.8386 0.8961 0.8948 0.8914 0.8787 0.8384 (0.0735) (0.0734) (0.0265) (0.0102) (0.0102) (0.0104) (0.0097) (0.0267) Underwriting date, ln(1+DOUi) 0.2492 0.2500 ?0.0134 0.2712 0.2683 0.3032 0.2480 ?0.0150 (0.0735) (0.0734) (0.1754) (0.0285) (0.0285) (0.0289) (0.0260) (0.1753) Age at underwriting, ln(1+AUi) 5.2342 5.1351 0.5243 0.5753 0.5822 0.6273 0.5364 0.5246 (0.7582) (0.7579) (0.2089) (0.0849) (0.0849) (0.0874) (0.0843) (0.2097) Sex, SEi ?0.0037 ?0.0081 ?0.0943 ?0.1008 ?0.1006 ?0.1012 ?0.0735 ?0.0960 (0.0436) (0.0436) (0.0582) (0.0198) (0.0198) (0.0199) (0.0197) (0.0583) Smoker, SMi,1 0.6537 0.6481 0.4004 0.3611 0.3610 0.3757 0.3112 0.4019 (0.0917) (0.0917) (0.1153) (0.0431) (0.0432) (0.0434) (0.0435) (0.1155) ?Aggregate? smoking status, SMi,2 0.2394 0.2373 0.2550 0.2217 0.2223 0.2124 0.2250 0.2637 (0.1184) (0.1184) (0.1614) (0.0550) (0.0550) (0.0557) (0.0551) (0.1618) Face Value, ln(1+ln(1+FV)) ?1.1458 ?1.1223 (0.3412) (0.3721) Settled-and-Observed, SaOi ?0.1225 ?0.3922 ?0.2847 ?0.0886 ?0.3673 ?0.3835 ?0.1111 (0.0342) (0.1307) (0.1509) (0.0201) (0.0620) (0.0664) (0.0525) Small Face Value ? Settled-and-Observed, ?0.2054 (0.1747) Medium Face Value ? Settled-and-Observed, ?0.3473 (0.1552) Large Face Value ? Settled-and-Observed, ?0.1907 (0.2006) Settled-and-Observed ? trend, 0.1524 0.2094 0.1701 0.1638 0.0711 0.2308 SaOi?ln(1+t) (0.0709) (0.1023) (0.0355) (0.0372) (0.0326) (0.1026) Log-likelihood value ?46,659.58 ?46,657.25 ?13,472.47 ?133,986.91 ?133,975.36 ?132,337.92 ?132,918.00 ?13,471.36 If life settlement companies imperfectly account for missing information in their pricing, the winner's curse can yield a negative settlement-mortality correlation (Thaler ()). More precisely, a wedge could arise from brokers forwarding shorter LEs to LS companies or policyholders picking the highest among several bids for their policy, although it is not clear whether or not the LE from our provider was actually used in the settlement process. Consider the following thought experiment in opposition to this explanation: Suppose there are several identically distributed LE estimates with different associated multipliers but the broker only forwards the one with the highest multiplier and the ?winning? LS company prepares a bid on this basis; now, assuming the multiplier is simply a relatively high random realization, the multiplicative excess hazard will be constant over time at a level below one and the additive excess hazard will necessarily need to diverge to sustain this constant multiplicative trend. The panels in part (e) of Figure show the multiplicative and additive excess hazard for a Monte Carlo implementation of this thought experiment in the context of our dataset (see Appendix C for details), which is congruent with the predictions but in contrast to the pattern depicted in Figure. Thus, again, the dynamic pattern does not sustain this explanation as the sole driver. Unsurprisingly, allowing the heterogeneity between the two groups to converge with time since settlement (t) can generate the observed patterns from Figure. To illustrate, we generalize equation () to allow for dependence on t in the unobserved heterogeneity ?i: 10?t(i)=?i(t)?B?Cx0+t. The panels in part (f) of Figure plot the multiplicative and additive excess hazard for the S relative to the N group under assumption (), where we set ?i(t)|{i?N} to one and let ?i(t)|{i?S} start at 0.6 and linearly increase to one at time 10. Similar to part (a) versus (b), adding frailty with positive variance does not substantially change the pattern. The resulting shape is similar to Figure, although this is not a like for like comparison due to differences in the definition of the N(ot settled) and the R(emaining) comparison group. In order to replicate the trends in Figure as closely as possible, we need to choose ?i(t)|{i?S} starting at roughly 0.44 and linearly increasing to one at approximately time 8.5, as shown in the panels (g) of Figure. The resulting patterns?and also the relative magnitudes?are reminiscent of so-called select-and-ultimate life tables in actuarial studies that capture selection effects due to underwriting. To illustrate, in the panels in part (h) of Figure, we plot the multiplicative and additive excess hazard, respectively, for a preferred male life underwritten at age 75 as a function of time since underwriting relative to ultimate hazard rates based on the Society of Actuaries 2001 Commissioner's Standard Ordinary (CSO) preferred life table. Here, the ?selection effect? comes from the underwriting process allowing insurers to use lower hazard rates in the select period, so the origin for the deviation is not an informational asymmetry. The relevant analogy is that insurers will only have information on the policyholder's health state at the point of sale (time of underwriting), and the relevance of this information dissipates as time progresses, producing the converging pattern. Thus, all-in-all, while there are several possible aspects contributing to the informational asymmetry, the pattern over time is most in line with policyholders adversely selecting on private information regarding their near-term survival prospects. Publisher Copyright: Copyright © 2020 The Authors. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/7/1

Y1 - 2020/7/1

N2 - We use data from a large US life expectancy provider to test for asymmetric information in the secondary life insurance—or life settlements—market. We compare realized lifetimes for a subsample of settled policies relative to all (settled and nonsettled) policies, and find a positive settlement-survival correlation indicating the existence of informational asymmetry between policyholders and investors. Estimates of the “excess hazard” associated with settling show the effect is temporary and wears off over approximately 8 years. This indicates individuals in our sample possess private information with regards to their near-term survival prospects and make use of it, which has economic consequences for this market and beyond.

AB - We use data from a large US life expectancy provider to test for asymmetric information in the secondary life insurance—or life settlements—market. We compare realized lifetimes for a subsample of settled policies relative to all (settled and nonsettled) policies, and find a positive settlement-survival correlation indicating the existence of informational asymmetry between policyholders and investors. Estimates of the “excess hazard” associated with settling show the effect is temporary and wears off over approximately 8 years. This indicates individuals in our sample possess private information with regards to their near-term survival prospects and make use of it, which has economic consequences for this market and beyond.

UR - http://www.scopus.com/inward/record.url?scp=85088120715&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85088120715&partnerID=8YFLogxK

U2 - 10.3982/QE1333

DO - 10.3982/QE1333

M3 - Article

AN - SCOPUS:85088120715

VL - 11

SP - 1143

EP - 1175

JO - Quantitative Economics

JF - Quantitative Economics

SN - 1759-7323

IS - 3

ER -