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1 ADVERSE SELECTION AND THE MARKET FOR ANNUITIES Oded Palmon * Avia Spivak ** Current version: August 19, 2002 * Department of Finance and Economics, Rutgers University, NJ. ** Department of Economics, Ben-Gurion University, Beer-Sheva 84105, Israel. We thank Jeff Brown, Estelle James, Olivia Mitchell, Dan Peled, Eithan Sheshinski, Ben Sopranzetti, John Wald, Mark Warshawski, David Wettstein and participants of seminars at Bar-Ilan, Hebrew and Rutgers Universities for helpful Comments.
2 Abstract Adverse selection is often blamed for the thinness of the annuities market. We study alternative types of annuity contracts that differ in the survival information structure, and explore their welfare implications. We show that, in principle, it is preferable to contract before the survival information is revealed, i.e., the deferred annuities equilibrium is better than the adverse selection equilibrium of immediate annuities. Quantitatively, however, the two arrangements are very close in terms of expected welfare. Our simulations show a welfare loss of around one percent for annuitants using the immediate annuities adverse selection market, relative to the first best allocation. We conclude that adverse selection is not the cause for the thinness of the annuities market. Key words: adverse selection, annuities, insurance, information, Social Security reform, Defined Benefits, Defined Contribution. JEL Classification: H55, G22, G28
3 ADVERSE SELECTION AND THE MARKET FOR ANNUITIES 1. Introduction Several studies document that annuities markets are susceptible to adverse selection. 1 Annuity contracts promise to pay their owners predetermined monthly installments as long as they live. 2 The later individuals purchase annuity contracts, the more likely are they to be informed about their longevity prospects. Several studies attribute the small size of the annuity market to adverse selection. 3 The recent interest in the functioning of private annuities markets partly stems from its policy implications. A frequently mentioned advantage of the universality of Social Security programs is the avoidance of the adverse selection problem. 4 The magnitude of the adverse selection problem is thus of special interest in the context of the public debate regarding the partial privatization of the Social Security system. 5 Assessing the magnitude of the adverse selection problem is also important for the welfare implications of the recent move from Defined Benefit (DB) pension plans to 1 See, for example, Poterba (2001) and Finkelstein and Poterba (2002). The lower mortality rates of annuitants, compared with those for the general population, are also evident in, among others, Mitchell, Poterba, Warshawsky and Brown (1999). 2 Other variations on the contract include joint survivorship, guaranteed ten-year payments, etc. 3 Akerloff (1970) introduced the process by which a market may disappear due to asymmetric information. Eichenbaum and Peled (1987), among others, imply that asymmetric information may be a major reason for the small size of the annuity market. Warshawsky (1988) and Friedman and Warshawsky (1990) indicate that a bequest motive and the low yields on the assets in which insurance companies are allowed to invest may contribute to the small size of the annuity market. 4 Stiglitz (1988, p. 332) states: Adverse selection may provide part of the explanation for high premiums charged for annuities. The government, however, can force all individuals to purchase the insurance, and thus avoid the problem of adverse selection. 5 Kotlikoff-Smetters-Walliser (1998) discuss the impact of adverse selection on social security privatization. Their discussion relates opting out of the system to income and age, and is not based on information..
4 Defined Contribution (DC) pension plans. DB pension plans are usually contracted at a relatively young age, when insureds have little private information regarding their survival probabilities. Thus, these contracts should be more immune to the adverse selection problem than DC plans that allow each participant to choose between lump sum and annuity distributions at the time of retirement. 6 Assessing the importance of adverse selection is the main objective of this paper. We assess the qualitative and quantitative effects of adverse selection under four alternative types of annuity contracts. These contracts differ in the availability, to the insured and the insurer, of the information that may help predict the insured s longevity. We rank the welfare associated with these contracts and discuss the policy implications of this ranking. While the qualitative analysis reviews several alternatives to limit the harmful effects of asymmetric information, the quantitative analysis obtains measures of its importance by simulating standard consumer behavior under adverse selection in annuity markets. Our simulations indicate that adverse selection increases the price of annuity by between one percent and seven percent, as compared to the no-adverse selection case. The induced welfare loss is even smaller. Mitchell, Poterba, Warshawsky and Brown (1999) show that the cost of an annuity in the US exceeds its fair actuarial value by 6 to 10 percent if the annuitants life tables are used. They note that these margins include marketing costs, corporate overhead and profits, in addition to the impact of adverse selection. James and Vittas (1999) find similar figures in an international comparison. Our simulated results are within these bounds. Our study also explains why, in contrast to other insurance 6 Poterba (2001) shows that a requirement to annuitize at least a fraction of the accumulation in DC plans may also mitigate the impact of adverse selection. 2
5 markets, asymmetric information should not be detrimental to the existence of the annuities market. The rest of the paper is organized as follows. In section 2 we present the four types of annuity contracts. In section 3 we compare the insured s expected utility under the four types of annuity contracts. In Section 4 we present simulations that evaluate the effect of adverse selection under our four contract types. In Section 5 we present the multiperiod model and simulate its asymmetric information equilibrium. Section 6 deals with the impacts of the existence of a bequest motive and of a Social Security system. Section 7 concludes the paper. The Appendix includes the more technical aspects of the analysis. 2. Contract in Annuity Markets We assume that at a young age insureds believe that their expected longevity equals the population s average. However, their information at the time of retirement is more precise. We consider four alternative types of annuity contracts. The precommitment annuity contract is initiated at a young age, before the information on longevity is revealed. It corresponds to a deferred annuity contract, a DB plan or the existing Social Security system. In contrast, the second and third annuity contracts are initiated at the time of retirement (similar to a DC plan or the proposed privatized element of the Social Security system). The public information annuity contract is assumed to be initiated when information regarding the insured s survival probabilities is known to both the insured and to the insurer (i.e., information is also symmetric). The asymmetric information annuity contract is assumed to be initiated when this information is known only to the insured. In the partial redemption contracts insureds initiate the contract at a young age when they do not 3
6 know their survival probability (as in a DB plan). However, at the time of retirement, when they know these probability, they may redeem part of their annuity subject to some penalty. 7 Our insureds live for two periods, and consume at the end of each period, at dates t=1,2. In the first period they lives with certainty, but their survival probability through period 2 is q < 1. We assume two types of insureds: high survival type and low survival type (denoted as H-insureds and L-insureds, respectively) with q H > q L and (q H +q L )/2= ½. 8 At date t=0 insureds only know that they can be of either type with a probability of ½, but between t=0 and t=1 they finds out their type. C 1 and C 2 denote consumption levels at the end of periods 1 and 2, respectively. The insureds maximize a time separable expected utility u(c), u >0, u < 0, u (0)=, with a time preference factor β < 1. It is assumed that they derive utility from consumption at date t=2 only if they survive, indicating the absence of a bequest motive. 9 The interest rate is denoted by r. The exposition and interpretation of our results are simplified by assuming that β(1+r)=1. 10 Thus, the insured s expected utility is: u(c 1 )+qβ u(c 2 ), where q is the probability known to the insured at the time the allocation is made. At t=0 insureds use the probability q=0.5, while at t=1 they use the probabilities q H or q L according to their type. Under the public information contract insurers know the type information of each insured at t=1, and are allowed to 7 The redemption plan also adds a liquidity option which is valuable for meeting the contingency of unexpected expenditures. This issue is not explored explicitly in the current paper. 8 The equal type probabilities maximize the variance of the type distribution. Thus, it is a conservative assumption for demonstrating that the asymmetric information problem does not have a major effect. 9 The absence of a bequest motive is consistent with the findings in Altonji et al. (1997). It also simplifies the initial presentation. In Section 6 we incorporate a bequest motive and demonstrate that our main results are robust to this change. 4
7 use it in determining premiums. In contrast, under the asymmetric information and partial redemption contracts insurers either do not have the information or are not allowed to use it. The premium set by the insurance company depends on its information structure and on the behavior of the insureds. We assume that competition in the insurance market guarantees that insurers balance actuarially. Insureds can use two assets as saving vehicles: a regular, non-annuitized, financial asset D and an annuity A, with the respective prices P D and P A. The annuity pays out one consumption unit in the second period contingent upon survival, while the non-annuitized financial asset pays out one consumption unit unconditionally. Assuming competition between insurers and no overhead costs, P D =1/(1+r) and P A =q/(1+r), where q is the insurer s estimate of the survival probability. The price of the annuity is lower than that of the non-annuitized financial asset, because q<1 11 ; hence, the only rationale for holding a non-annuitized asset in a two-period model is the desire to leave a bequest in the event of death before t=2. 12 Thus, in a two-period model in which a bequest motive is absent, insureds annuitize all their wealth. We thus simplify the presentation in this paper by ignoring the non-annuitized asset in all two-period models in which individuals have no bequest motive. Next we present, for each of the four contract types the information structure, the annuity contract and the resulting consumption levels. 10 This assumption implies that an individual who lives with certainty would choose identical consumption levels at dates t=1 and t=2. 11 Formally, q<1, hence P A <P D, so an annuity is always purchased. 12 In a multi period model individuals may purchase a non-annuitized asset to generate a decreasing consumption pattern. 5
8 Contract 1: Full precommitment. Each insured purchases at date t=0 the consumption for dates t=1 and t=2, denoted as C 1 and C 2. Consumption at t=0 takes place with certainty, but at date t= 2 it is contingent upon the survival of the insured. The timing of information arrival and individual actions are summarized in the following time line: t=0 t=1 t=2 Purchases Type is Consumes C 1 Longevity Consumes C 2 an annuity revealed is revealed if survives Because the type information is not known at the time the contract is made, at date t=0, both insureds and insurers use ½ (the average survival probability) as the relevant probability in calculating the expected utility, the budget constraint, and the annuity price. All insureds buy the same annuity amount, and thus the annuity price is: P A =0.5/(1+r). Recall that all of the second period consumption is bought as an annuity. The insured s problem is thus: max u(c 1 )+0.5β u(c 2 ) s.t. C 1 +P A C 2 =W, where W is the wealth at the beginning of period 1. Later, we normalize the units and set W=1. The conditions for the insured s optimal consumption imply that the standard result of equal consumption in both periods exists. Hence we obtain: (1) C 1 = C 2 =1/(1+0.5/(1+r)) = C PR. The expected utility of this contract, denoted by EUpr, is: 6
9 (2) EUpr = (1+0.5β)u(C PR ). Contract 2: Public information The timing of information arrival and individual actions under this contract is: t=0 t=1 t=2 Type is Purchases Consumes C 1 Longevity Consumes C 2 revealed an annuity is revealed if survives to insured and insurer Annuities are purchased when both insureds and insurers know the survival probabilities. Insurers thus charge each insured an actuarially fair premium. Insurers use q H for the H-insureds and q L for the L-insureds. Thus, an i- (i =H, L) insured solves the following maximization problem: (3) max u (C 1i )+q i βu(c 2i ) s.t. C 1i + C 2i q i /(1+r) = 1 i= H, L The solution for each type is a fixed lifetime consumption level. However, the fixed consumption level of L-insureds exceeds the corresponding level for H-insureds: (4) C 1i = C 2i =1/(1+q i /(1+r)), i= H, L. Insurers have two budget constraints, one for each type of insureds, which are identical to the respective budget constraints (and they balance actuarially for each type). 7
10 Contract 3: Adverse selection - asymmetric information The equilibrium under this contract is assumed to be a pooling equilibrium, where insurers cannot distinguish between the two types of insureds. In this equilibrium insurers cannot observe the total quantities of annuities bought by each individual (from various insurers), and thus a separating equilibrium (in which annuity prices are positively related to the total quantities purchased) is not possible. Although not modeled explicitly, income variation may also hinder the insurers ability to infer the type of market behavior. 13 The timing of information arrival and individual actions under the asymmetric information contract is: t=0 t=1 t=2 Type is Purchases Consumes C 1 Longevity Consumes C 2 revealed an annuity is revealed if survives to insured, but insurer cannot use it Insureds decide on their purchases after their types are revealed. However, insurers cannot condition the premium on the insured s type due to asymmetric information or legal constraints. Thus, insurers charge all insureds an equal annuity price, q AD, which reflects a weighted average of the survival probabilities. The weights for q H and q L are C 2H and C 2L, respectively. Note that in such pooling equilibrium, the L- insureds subsidize the H-insureds because the annuity price is higher than the fair price for L-insureds, while it is lower than the fair price for H-insureds. 13 Abel (1986), likewise, uses a pooling equilibrium. Eichenbaum and Peled (1987) use a Rothschild- Stiglitz quantity-constrained separating equilibrium. 8
11 Consequently, L-insureds purchase less annuity than H-insureds, raising the weighted average q AD and causing it to exceed ½. In that case, the insured s problem is: max u(c 1i )+q i βu(c 2i ) s.t. C 1i + C 2i q AD /(1+r) = 1 i= H, L. The Langrangean for this case is: L i = u(c 1i )+q i βu(c 2i )-λ i [C 1i + C 2i q AD /(1+r) -1], i= H, L. The first order conditions for obtaining the maximum are: u (C 1i )= λ i (5) u (C 2i )= λ i q AD /q i C 1i + C 2i q AD /(1+r) = 1 i= H, L. Because q L < q AD < q H, C 2L /C 1L < C 2H / C 1H. Furthermore, because all insureds face the same budget constraint, C 2L <C 2H. Note that the consumption levels are always strictly positive because u (0) is assumed to be unbounded. In addition to these first order conditions, competition implies that the equilibrium solution should satisfy the zero profit condition for the insurer: π=(q AD /(1+r))(0.5C 2L +0.5C 2H )- (q L 0.5C 2L +q H 0.5C 2H )/(1+r)=0. The annuities C 2L and C 2H are purchased at the same price P A = q AD /(1+r). The first term in the above expression represents the revenue of the insurer, while the second term represents his expected capitalized expenses. Equivalently: (6) q AD = q L C C 2L 2L + q + C H C 2H 2H 9
12 A positive C 2L implies that q AD <1 even if q H =1. As explained above, as long as q AD <1, the annuity contract strongly dominates the non-annuitized financial investment. The fundamental reason for the preference of annuities is the absence of the bequest motive. That is, under the non-annuitized investment individuals who die prior to the end of their planning horizon leave unintended bequests. This special feature of the annuity market is also the basis for the existence of a non-trivial equilibrium, where all agents participate in the annuities market. Definition: A participating adverse selection equilibrium is an annuity price P A and annuity purchases C 2L >0, C 2H >0, such that conditions (5) and (6) are met. Proposition 1: There exists a participating adverse selection equilibrium. Proof: Insureds prefer to annuitize all their savings. (When q AD =1, they are indifferent). It is well known that the demand for consumption functions C 1L, C 1H, C 2L and C 2H are continuous in q AD, hence the insurer s profit function π is continuous in q AD. For q AD = q L, the insurer breaks even on the L-insureds and loses on the H- insureds, hence π <0. Similarly, for q AD = q H, the insurer breaks even on the H- insureds and profits on the L-insureds (because C 2L >0), hence π >0. The proposition then follows by the continuity of the profit function in q AD. 14 The method used in the proof indicates that the proposition holds for any distribution of survival probabilities. Proposition 1 contrasts with the well-known result of Akerloff (1970) for the non-existence of equilibrium in the market for lemons, the seminal contribution to the asymmetric information literature. In Akerloff s case the equilibrium fails because 14 In the pathological case q H =1 (and thus q L =0), there also exists a trivial equilibrium where q AD =1, and C 2L =0. 10
13 the insurer loses regardless of the premium he charges. When the insurer tries to raise the premiums in order to break even, low risk insureds leave the market at a sufficiently fast rate so as to frustrate the insurer s attempt for achieving an actuarial balance. The process of attempting to achieve actuarial balance ends when the price of insurance is prohibitively high, driving the demand for insurance and the profit to zero. In contrast, in the absence of a bequest motive, the demand for annuities by all insureds is positive and bounded away from zero for any q AD < 1, even if it is very close to 1. This positive demand guarantees that insurers can achieve an actuarial surplus for some q AD s and keeps the equilibrium q AD away from 1 (and strictly below q H in our model). These different behavior patterns reveal a fundamental difference between annuity insurance and traditional insurance. In the former, every dollar invested in annuity yields more than a dollar invested in a non-annuitized asset because only the insureds who survive share the total returns. 15 As compared with the non-annuitized asset, the annuity contract is a first order stochastic improvement. Annuity insurance eliminates wasting resources on unintended bequests and thus moves out the insured s budget constraint. In contrast, in the traditional insurance market all insureds share the cost. Thus, the insurance contract replaces a random variable with its expected value, a second order stochastic improvement. This reasoning may not hold with the introduction of a bequest motive, as we show in Section This interpretation of annuities is similar to the tontine, an arrangement for sharing bequests among survivors that was popular in France before the Revolution. We thank Olivia Mitchell for pointing this out to us. 11
14 Contract 4: Partial redemption. The timing of information arrival and individual actions under the partial redemption contract is: t=0 t=1 t=2 Purchases Type is May partially Consumes C 1 Longevity Consumes C 2 an annuity revealed redeem the is revealed if survives to insured, the annuity but insurer cannot use it At date t=0, insureds purchase the contract (C 1, C 2 ). At date t=1, after they find out their type, they may redeem some or all of the second period consumption and use the proceeds to increase the first period consumption. The annuity price at t=0 reflects an adjusted survival probability q R0, while the refund t=1 is priced using another adjusted survival probability, q R1.. In order to prevent arbitrage, q R0 > q R1. Equivalently, insureds pay a redemption fine of (q R0 -q R1 )/q R0 percent. Insureds plan ahead to redeem part of their C 2 if the low probability type is realized, but to retain all of C 2 if the high probability type is realized. Therefore (C 1,C 2 ) is the planned consumption in case the H type is realized, and (C 1L,C 2L ) is the planned consumption in the event that the L type is realized. The insured thus solves: max ½[u(C 1 )+βq H u(c 2 )] +½[u(C 1L )+βq L u(c 2L )] s.t. C 1 + C 2 q R0 /(1+r) = 1 C 1L + C 2L q R1 /(1+r) = C 1 + C 2 q R1 /(1+r) C 2L < C 2 The individual maximizes the expected utility from the two states of nature, subject to three constraints. The first budget constraint is related to the purchase at date t=0, and the second to the redemption at date t=1. The third constraint states that agents 12
15 cannot purchase additional annuity at t=1, they can only redeem it. The rationale for the partial redemption contract is that, as long as q R1 < q R0, it imposes on the insured the cost of using the information revealed at date 1, and thus limits the effect of adverse selection. Additionally, as long as q R1 > q L, the option to redeem some of the second period consumption mitigates the subsidy to H-insureds at the expense of L- insureds that is inherent in a pooling equilibrium. The equilibrium consumption levels should also satisfy the insurer s zero profit condition: 1/2(C 1 +C 1L )+1/2 [q H C 2 +q L C 2L ] /(1+r) =1. More technically, the insured maximizes the following Langrangean: L= [u(c 1 )+βq H u(c 2 )] + [u(c 1L )+βq L u(c 2L )] - λ [C 1 + C 2 q R0 /(1+r) - 1] - µ [C 1L + C 2L q R1 /(1+r) - C 1 - C 2 q R1 /(1+r)], C 2L < C The first order Kuhn-Tucker conditions for a maximum are: u (C 1 )= λ µ u (C 2 )< λq R0 /q H µq R1 /q H (inequality implies C 2L =C 2 ) u (C 1L )=µ u (C 2L )> µq R1 /q L (inequality implies C 2L =C 2 ) C 1 + C 2 q R0 /(1+r) = 1 C 1L + C 2L q R1 /(1+r) = C 1 + C 2 q R1 /(1+r) C 2L < C 2. It is possible to show that C 2L =C 2 if and only if q R1 < q L. 16 To simplify the notation, we multiplied the objective function by 2, a linear transformation of the utility that does not alter the outcome of the maximization problem. 13
16 It should be noted that the partial redemption contract is identical to the asymmetric information contract when q R0 = q R1. In this case both are equal to q AD. The insured can fully annuitize his wealth, and then redeem as much as he wants at no penalty (because q R0 = q R1 ). Thus, because q H> q AD =q R1 >q L, the inequality constraint C 2L < C 2 is not binding in this case. We can also see the equivalence of the partial redemption and asymmetric information contracts in this case by noting that for the first order conditions, λ Η =λ µ, and λ L =µ. At the other end of the spectrum, for q R0 = 0.5 and q R1 < q L, the insured is at the corner solution C 2L = C 2 and C 1L = C 1. Thus, in this case, the partial redemption contract is identical to the precommitment contract. 3. Hierarchy of the Contract Types In the previous section we presented four types of annuity contracts, where the partial redemption contract includes the precommitment and asymmetric information as two extreme cases. In this section we rank the utility level of the consumer under these contract types. This ranking and the simulations presented in the following sections should help policy makers evaluate the welfare loss due to adverse selection that is generated by alternative annuity contracts. We evaluate the expected utility of the insured, derived from consumption in periods 1 and 2, from the vantage point of date 0, before the information on the type is revealed to insureds. Our first result is general and strong, stating the superiority of precommitment contract to any other contract: Proposition 2: The precommitment contract is superior to any other equilibrium contract. Proof: Let C ti denote the consumption at time t and state i of the other equilibrium. The expected utility of the consumption under that equilibrium, denoted by EU other, is: 14
17 EU other = 0.5(u(C 1H ) + u(c 1L )) + 0.5β(q H u(c 2H ) + q L u(c 2L )). The consumption path satisfies the budget constraint of the insurer: 0.5(C 1H + C 1L ) (q H C 2H + q L C 2L ) /(1+r) =1 Let C 1 = 0.5C 1H + 0.5C 1L and C 2 = q H C 2H + q L C 2L be the respective averages of the two-period consumption levels. If we replace the consumption in both states of nature by their average for both periods, they satisfy the budget constraint and are preferred to the original consumption because of risk aversion: EU(C 1,C 2 ) = u(c 1 ) +0.5βu(C 2 )=u(0.5c 1H + 0.5C 1L )+ 0.5βu(q H C 2H + q L C 2L ) > 0.5(u(C 1H ) + u(c 1L )) + 0.5β(q H u(c 2H ) + q L u(c 2L )) = EU other. Note that C C 2 /(1+r) = 1. Thus, by its optimality, C PR is preferred to (C 1,C 2 ). Hence: EUpr > EU(C 1,C 2 ) > EU other. It follows that precommitment contract is preferred to all other contracts, namely, public information, asymmetric information and partial redemption. The reason for this result is that precommitment provides insurance both against the uncertainty of the insured s type and her longevity. This result is reminiscent of Hirshleifer s (1971) model, where the revelation of information reduces welfare because it destroys the insurance markets. 17 Eckwert and Zilcha (2000) stress the same point. 17 Sheshinski (1999) also concludes that early contracting is preferred to annuitizing at retirement. However, he focuses on the optimal retirement age and the unintended bequest of individuals who die prior to their retirement date. In our model, retirement age is given exogenously, and no one dies prior to that date. 15
18 Asymmetric information vs. public information The disadvantage of the asymmetric information contract is that all insureds pay the high premium that the insurer has to charge because of the relatively high consumption of the H-insureds. However, some subsidization of the H-insureds at the expense of the L-insureds is also an advantage of the asymmetric information contract because it provides some insurance against the uncertainty of the type. No such insurance is provided by the public information contract. The simulations we present in the next section indicate that there is no clear hierarchy between these two contractual arrangements. In the standard example of the CRRA (Constant Relative Risk Aversion) utility function u(c) = [1/(1-γ)]C 1-γ, where γ > 0 is the measure of relative risk aversion, the ordering depends on γ. For low levels of γ, the public information contract is preferred, while for high levels of γ the asymmetric information contract is preferred. The break-even point is obtained at a level of γ close to two from below, such as The impact of changes in γ on the expected utility of the asymmetric information contract, relative to that of the public information contract, has the following intuition. The allocation under the public information contract is independent of γ. In contrast, the difference between C 2H and C 2L, and thus the cost of an annuity under the asymmetric information contract, are negatively related to γ. As γ increases, the difference shrinks and the asymmetric information contract dominates the public information contract. Because γ is empirically found to be more than 2 in many empirical studies (see Kocherlakota (1996)), the asymmetric information contract should be preferred by the insureds to the public information contract. 16
19 Partial redemption vs. asymmetric information, precommitment and public information As explained above, the consumption allocation under the partial redemption contract depends on the fine for redemption. When the fine for redemption is prohibitive, the equilibrium is characterized by q R0 = 0.5 and q R1 < q L, and is identical to that under the precommitment contract. When the fine is zero, the equilibrium becomes the asymmetric information equilibrium, with q R0 = q R1 = q AD > 0.5. We know from Proposition 2 that from the insured s viewpoint the best option is the prohibitive fine (equivalent to the precommitment contract). The simulations support the intuition that the expected utility is increasing with the fine, or equivalently, that the expected utility is decreasing with q R0. Empirical regularity: EUrd is a decreasing function in q R0. We can summarize the hierarchy of schemes in the following: Proposition 3: For γ > 2, EUpr > EUrd > EUad > EUpi. This ordering of the four contractual arrangements have practical implications concerning the value of information. The best contract is initiated before the information is known, without the ability to renege once the information is received. The second best contract is initiated before the information is known, but also allows the redemption of some of the annuity. The third best contract is initiated when the 18 In some other applications the critical value is 1. In these cases, the underlying mechanism is the equality of the substitution and income effects under the log-utility case. 17
20 information may be used by the insured, but not by the insurer. The worst contract is when both the insured and the insurer use the information on the insured s type. One application of Proposition 3 concerns medical and genetic information that may contain relevant information on survival probability. Another example is the use of unisex tables for annuity insurance. Annuity providers in the US are not allowed to charge gender-based premiums for annuities that are issued within a qualified pension plan, although life tables vary significantly across genders. 19 Our analysis justifies this practice. Even if the information is known to the insurer, for γ > 2, welfare is higher when the insurer cannot use gender information. Notice that the criterion used is the expected utility of the fetus before its gender is known. Otherwise, this policy involves income redistribution between genders, and the welfare implications are less evident. 4. Simulation of the Two Period Model In this section we present the behavior of insureds as well as market equilibria under the alternative contracts. We also present measures for welfare loss due to deviation from the ideal contract - the precommitment at date 0. The simulations of the twoperiod model are useful for investigating the hierarchy of alternative plans that cannot be ordered based on theoretical considerations. They also illustrate the quantitative impact of adverse selection, although this will be further investigated in a more realistic multi-period model in the next section. Our basic example is the CRRA utility function u(c)= [1/(1-γ)]C 1-γ, where γ >0 is the measure of relative risk aversion. We simplify the presentation by assuming 19 For other policies, the ability to issue gender-based premiums is regulated by state law and varies across states. 18
ADVERSE SELECTION AND THE MARKET FOR ANNUITIES. Oded Palmon * Avia Spivak ** Current version: May 16, 2001
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text:
- Back to Top
- OverviewJump to Overview
- FeaturesJump to Features
- WarrantyJump to Warranty
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Breedlove Discovery Dreadnought with Sitka Spruce Top Acoustic-Electric Guitar
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subset: commoncrawl


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Some of you might remember Nvidia GTX 970 lawsuit that was filed against Nvidia, the lawsuit was filed in February 2015 for the false advertising of its popular graphics card, GTX 970. That Nvidia GTX 970 lawsuit has been settled, and it is not in favor of the company.
The settlement is going to be costly for the company. Nvidia has reached a settlement with the the plaintiffs, and according to the settlement, Nvidia will have to pay back a certain amount of money to all the GTX 970 owners.
The Nvidia GTX 970 lawsuit is mainly centered around three allegations.
- The GTX 970 was marketed as a card with 4 GB of video memory, whereas the card actually has 3.5 GB of RAM, with the remaining 0.5 GB being a much slower "spillover segment" that is decoupled from the main RAM.
- The GTX 970 was marketed as a card with 64 render output processors, whereas the card actually has 56 render output processors.
- The GTX 970 was marketed as a card with an L2 cache capacity of 2,048 KB, whereas the card actually has a 1,792 KB L2 cache.
Now these differences are going to cost $30 to every single member of the settlement class.
However, this settlement is not only limited to Plantiffs as the settlement class is defined as any US resident or entity who purchased GTX 970 in US. Those who purchased the graphics card can get their $30 from Nvidia, ASUS, EVGA, Gigabyte or any authorized retailer before August 24, 2016.
GTX 970 is the most popular card among users on Steam, according to Valve's monthly hardware survey. According to the survey 5% of the respondents indicated that GTX 970 is the graphics card of their choice.
What do you think of Nvidia GTX 970 Lawsuit settlement? Is $30 too much for a 0.5 GB difference in memory or is it less? Let us know in the comments.
Source: US District Court.


text: I have an x5a 800mz tablet currently running Android 2.1 I would like to update my tablet with the most current official android rom or a version of windows for tablets. I have rooted my device and have ROM manager. Any tips, instructions, or links to downloads would be greatly appreciated. If anyone has any version of windows on their tablet, let me know how it works. Also, is it possible to dual boot on my device? Thanks!


text:
Hazel has provided us with this fab sketch
and she has chosen the theme LOTS OF LAYERS
As you can see I have rotated the sketch and used my favourite decoupage to follow the theme.
The image and papers are both from the Polly Pickleberry CD and the sentiment is a Wild Rose Studio stamp on a Spellbinders die cut. The buttons, ribbon and lace are all from my stash.
You can just see the decoupage in this photograph along with the inside of my card
I would like to enter this card into the following challenges:
Crafty Creations Challenge 164 - Spring Greens
Party Time Tuesdays Challenge 62 - Flowers
Little Darling's Challenge 20 - Outside
Wags 'n Whiskers Challenge 76 - Say it with Flowers
Sparkles Challenge 30 - Mother's Day or Spring
Pile It On Challenge 14 - Make a Scene
C.R.A.F.T. Challenge 149 - Easter/Spring


text:
Yes, I Did Say That!
A look at who's saying what in entertainment.
I have a raging case of Linsanity. …Fans have not come down with a basketball-borne disease this intense since ... Kareem Abdul-Jabbotulism."
-- Stephen Colbert
The Comedy Central host, on Jeremy Lin, the New York Knicks sensation.
"Why don't the people at your little ranch … use all the CGI to make you go away. … You're wrecking good movies."
-- Glenn Beck
The conservative radio host, criticizing George Lucas for adding 3D to Star Wars: Episode 1 -- The Phantom Menace.
"Men are terrified of me now."
-- Michelle Dockery
The Downton Abbey star, confessing that the scene on the show where her Turkish lover, Pamuk, dies in flagrante has scared away real-life suitors.
"You're like the white Kanye West."
-- Jimmy Kimmel
The late-night TV host, to Cougar Town actress Courteney Cox, after learning she tweeted 1,211 times in her first two weeks on the microblogging service.
"Every 1 who can please turn to OWN especially if u have a Nielsen box."
-- Oprah Winfrey
The talk show host, violating Nielsen rules in a tweet urging metered viewers to watch her network. She later deleted the tweet and apologized.
"I once drove 200 miles through a hurricane evacuation zone to get laid, but I don't think I'd see 'The Vow.' "
-- Danny Zuker
The Modern Family producer, tweeting about his lack of interest in seeing the romantic film that grossed $41 million during its opening weekend.
"Pine did not even have the courtesy of picking up the telephone to tell SDB that he was ending their relationship of nine years."
-- Bryan Freedman
A lawyer for Chris Pine's former talent agency SDB Partners, in a lawsuit filed Feb. 14, demanding commissions for Pine's $1.5 million Star Trek 2 fee and $5 million fee for This Means War, among other films.
"I don't want to be some skinny minny with my tits out."
-- Adele
The singer, on how she hasn't tried to change her look to fit stereotypical expectations for a female pop star.


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Strong point: price is fair, very nice and friendly staff.
Sleeping quality: bad - very noisy outside, bad bed and water running out easily from the Air C machine. bathrooms also not very nice (funny smells sometimes...)
Little far from the beach (1.5 km walking), typical italian breakfast (croissant, yogurt, cookies...)
- Free Wifi
- Breakfast included


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Anonymous on 12/03/2010
Checked in to hotel on 11/30/2010 after 3PM, entered the room and as I was relaxing on the bed I saw a bug crawling. I had never seen this type of bug but checked the internet for a picture of a bed bug and made the Id. Started checking the bed for signs and found several dead bugs and live ones in the seams of the bed. Reported the infestation to front desk and they moved me to another room. I checked the bed in that room and it did not appear to be infested. The next day someone inquired abo
ut my find, asking if I had seen any bedbugs in the room I was in. I had not but I did see quite a few in the original room that I had. Hopefully they will take the proper steps to rid this property of these pests as that is a creepy feeling, I am just glad that I saw them before I turned in for the night.
Anonymous on 11/07/2010
We arrived on November 6, 2010 in the mid day and noticed there was plastic covers on the mattresses, but didn't really thing anything of it. When we were getting ready to go to bed at approximately 12:30am we pulled the sheets back and found a dead bug. We compared it to a picture on the Internet and it looked like a bed bug. We decided to leave and while gathering our luggage, one was crawling on the wall just inches from our belongings. There were no comforters on the beds and there was clean
ing staff in rooms at 12:30am. The manager refused to refund the money and got in an argument with us when confronted. You could definitely tell they knew the reason we were leaving but tried to cover it up to not let the other costumers know but we informed them on our way out. DONT STAY HERE!
13 bedbug reports near this address:
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The Action Congress of Nigeria (ACN) yesterday denied the Presidency's claim that progressive governors stole President Goodluck Jonathan's plan by visiting Borno State ahead of him.
It described as insulting the Presidency's reaction to last week's visit of the progressive governors to Borno State.
In a statement in Abuja yesterday by its National Publicity Secretary, Alhaji Lai Mohammed, the party said the presidency is disoriented.
ACN said: ''There is no doubt that the visit of the governors was a knock-out for the waffling presidency. Now punch-drunk, the clearly disoriented Presidency has resorted to blaming the courageous and trail-blazing governors whose only offence is that they dared to show solidarity for the people of Borno and Yobe, the two states that have been worst-hit by the Boko Haram crisis.
''These governors dismissed the Presidency's shameless attempt to scare them away from Borno with a cooked security report. They walked around the volatile Maiduguri market without bullet proof vests or helmets, to the chagrin of the President and Commander-in-Chief, who has opted to hide behind the Aso Rock fortress.''
ACN said for the Presidency to choose to denigrate the governors and accuse them of crass opportunism is the height of irresponsibility.
It added: ''Most laughable is the accusation that the governors pre-empted the visit of President Jonathan to Borno. Who did the Presidency inform of his impending visit? When did it become the business of governors to tailor their movement to that of the President? Where has the President been since 2011 when he assumed office after his election? What took him so long to visit a troubled part of the country, especially since he claimed to have received a pan-Nigeria mandate?
''The truth is that the President was so embarrassed by the visit of the governors that he quickly packaged his own visit.
"Instead of quietly licking its wounds, the presidency opted to dance naked in the market square by accusing those who blazed the trail, who showed the way to a clueless and visionless Federal Government.
''Irrespective of what the Presidency may say, the beleaguered people of Borno and Yobe appreciate the solidarity of their fellow Nigerians, as shown by the governors' visit. The people of Nigeria also appreciate the courage and compassion of the governors. Anyone trying to denigrate the visit is attracting more love for the governors and public opprobrium for the Presidency.''
ACN denied playing politics with the killing of the Commissioner of Police of Kwara State.
It said the fact that the killing of such a top security chief sends a wrong signal about the state of the country's security, cannot be faulted by any right-thinking person.
''How are we playing politics by calling for reinforced security for those whose responsibility it is to protect others? Where is the politics in calling for the apprehension and prosecution of those behind the dastardly act? What is wrong in calling the attention of a prostrate Presidency to the worsening insecurity in the country?
''Contrary to the Presidency's statement that President Jonathan has performed well in curbing insurgency, the truth is that the Presidency – bereft of ideas on how to curb the insurgency – has instead chosen to bury its head in the sand, like the proverbial ostrich. Otherwise, it would have known that the senseless killings by Boko Haram has continued. Only on Tuesday, gunmen killed a DPO and nine others in Borno, in what has been a daily trend in recent days, despite the cease-fire concocted by a desperate and clueless Federal Government,'' the party said.


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from Wiktionary, Creative Commons Attribution/Share-Alike License
- n. The portion of the infrastructure that carries communication signals from the main system to the end users' home or business.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
- n. the last walk of a condemned person to the execution place
Sorry, no etymologies found.
Sorry, no example sentences found.


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The Brubeck Collection at the University of the Pacific in Stockton, California is an unsuspected font of information concerning the US during the Cold War and Civil Rights eras. Created by pianist Dave Brubeck ("Take Five") and his wife Iola, it is one of the largest jazz archival collections. The staff and faculty have digitized large portions of the audio collection, worked carefully with history and conservatory faculty to integrate the Collection into undergraduate learning, created multiple exhibits focusing on Brubeck's connection to social justice (including a talk and oral history program at the 2012 Monterey Jazz Festival), and sponsored yearly research travel grants to use the Collection. Veronica Wells, Access Services and Music Librarian, has aggressively promoted the use of all music collections to Conservatory faculty and to the music library community. Michael Wurtz, Archivist of the Brubeck Collection, manages the Collection from accession to accessibility. He has curated exhibits for local and nationwide use, managed a Grammy grant for digitization, and continues to work closely with the donors. Patrick Langham is a musician and jazz studies professor who encourages his students to use the library's music collection and the Brubeck Collection in his jazz history and composition classes.
Available at: http://works.bepress.com/veronica-wells/10/


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WHO launches app for the care of children in hospital
The WHO e-Pocketbook is now available in Russian
WHO is launching a new app to support health workers when attending children in hospital.The Children at Hospital app, now available in Russian on the Apple App Store, provides clinical guidelines for the care of children throughout their stay in hospital.
Designed for doctors, nurses and other health workers responsible for the care of children, these guidelines focus on the management of major causes of childhood mortality, including:
- neonatal illness, including low birth weight, prematurity, sepsis, perinatal asphyxia and congenital anomalies;
- pneumonia and other breathing problems, including bronchiolitis, asthma and tuberculosis;
- diarrhoea, acute and chronic;
- fever, including malaria, meningitis, septicaemia and rheumatic fever;
- severe acute malnutrition;
- surgical problems, including trauma and burns.
The app includes guidance on the stages of management for every child: triage and emergency treatment, history and examination, laboratory investigations, supportive care and monitoring, discharge planning and follow-up.
With this app all guidelines can be viewed offline. The app contains some user-friendly features like interactive links, a search function, the possibility for viewing illustrations in full size by tapping, and formulas for medication dosage.


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34, Woman, Single
Nairn, United Kingdom
Degree dating site member
Looking for:
31 - 63 years
Within 1017 kms
Long-term dating
My self-introduction
I am a cheerful, kind, pretty, sporty, witty and tender woman. I am able to value every moment of life and like giving my smiles to other people. I am a sweet-tempered, feminine, optimistic and happy lady! I enjoy traveling very much. I am keen on active way of life. I am very romantic, caring, loyal, sincere, loving, understanding respectful and faithful when it comes to a relationship. i love music, movies, cooking, swimming, reading, gardening and likes to exercise to keep very active.
What I am doing with my life
im just taken it easy as anything is possible in this life.
Things I like about myself
respecting others, calm, faithful, caring.
My favourite outdoor activities are
tennis and volleyball
My favourite indoor activities are
cooking, reading
These topics are interesting for me
hygiene , color
I might look for you if
betray me.


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Long ago, there were items of intrigue called pens. And long ago, humans utilized these pens to write letters. These letters now exist under glass cases in museums, or in that cheap coffee table book you bought to make yourself look smart and cultured, and maybe also in your grandma's desk drawer. But that's it. Those are the only three places letters are left. They're relics, letters are. But that impulse to write to our loved ones hasn't left us yet. It hits us at 3AM when we cannot sleep, or when we need to take a minute to reflect and slow down our thoughts, and when we really need to say something.
So here they are immortalized, a museum of emails, articles and conversations and all other world contributions.


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Marvin Roy Blouin
Marvin Roy Blouin
May 26, 1938 - Dec. 3, 2017
SAUK CENTRE, Minn. - Marvin Roy Blouin, 79, Sauk Centre, died Sunday, Dec. 3, in Sauk Centre Hospital.
The memorial service will be 2 p.m. Saturday, Dec. 9, at Sauk Centre Kingdom Hall of Jehovah's Witnesses.
Arrangements by Cremation Society of Minnesota.


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The make-up free alternative to contouring…. Contouring has taken the beauty world by storm and it's not surprising as you can re-define your natural face shape within minutes. We love a bit of contour at Instant Beauty Fix but it got us thinking,..
From £39.99 (inc. VAT) £39.99 (ex. VAT)
Showing 1 to 1 of 1 (1 Pages)


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The Queen of All Media has got it all: a nationally syndicated TV talk show, best-selling books, Radio Hall of Fame honors, her own jewelry line and, between hubby "Big Kev" Hunter and son "Lil Kev," a busy family life. So how does she keep it all together? "With a lot of cooperation from big Kevin and little Kevin. Our son is in fourth grade now, he's nine years old. And I was just talking to my husband—his office is across the hall from mine here at the TV studio—and I said, 'What are we going to have to dinner tonight?'" Wendy Williams tells host Ceslie Armstrong. "I was going to shop at Costco, maybe. I want to know why you did not eat yesterday's dinner. I made cube steaks and a little asparagus. He said, 'I just wasn't in the mood.' I said, 'What about the night before?'—I made sloppy Joe's—'What was the problem there?' He said, 'You put in too much garlic.' Well, you know what? Last night we went out after the VMAs. And I hadn't gotten much sleep the night before so I said, 'I don't want to stay at the restaurant. Can we agree on take-out?' He said, 'Yes, there's this great place up the street that makes great teriyaki.' The point is, he has learned to cooperate."
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New Video links:
Charles reads from
Canadian Content
click here
Charles is featured on Creative Mornings Vancouver:
Christmas in July
click here
New books:
Splendid Crow Booklet &
Here Follows a Collection of Little People
Charles Van Sandwyk's work is now on four pages. Please click on the links above to see watercolours, etchings, books or ephemera.
Charles Noel van Sandwyk was born in Johannesburg, South Africa in 1966. In 1977, he emigrated with his family to Vancouver, Canada. By the early 1980's, he was selling his drawings and watercolours in a style reminiscent of the old prints and paintings which hung in the family home.
He studied graphic design at Capilano University in North Vancouver. Upon completion in 1986, the wanderlust of younger years sent him travelling to the South Pacific. He discovered the Fiji Islands, and fell in love with a remote island and its inhabitants.
In that same year, he won an Alcan award for his limited edition book
A Selection of Neighbourly Birds
, illustrated with etchings and printed on an antique intaglio press. This first attempt at publishing prompted a passionate venture into the world of hand-made and private press books and prints.
His watercolours, etchings and books are now collected across North America and Europe. The National Library of Canada has maintained an archive on his work since 1986, and in 1992 purchased the original drawings and paintings for his children's book
The Parade to Paradise
. The book
Wee Folk
won Juror's Choice award at the 1994 Seattle Book Fair.
In 1995, he was involved in a motorcar accident in Fiji. In the recovery ward of the Lautoka Hospital he had a wonderous dream about an island sanctuary populated by strange creatures. It was a very gentle and healing dream with a depth he had never before experienced. Immediately upon waking, he set to work sketching the visions while they were fresh in his mind's eye. This dream became
Sketches from the Dream Island of Birds
Charles illustrated three books for the Folio Society in London, England: Andrew Lang's
Blue Fairy Book
in 2002 and Kenneth Grahame's
Wind in the Willows
in 2005 which was the winner of the Grand Prix in the Printing World Awards 2006 for the finest achievement in British Printing, and
Alice in Wonderland
Charles' own books are designed, written, and illustrated by himself, and he oversees every step of their publication.


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Kadayawan Festival 2016, a non-working holiday in Davao City, when we went motorbiking around Samal Island (official name: Island Garden City of Samal or IGACOS). Wanting to make the most out of my temporary work assignment in Davao, I was guided by my cousin and his friends in exploring this paradise down south. That it was my first time to set foot in Samal made me more eager and excited to discover what the island has to offer.
Here's our experience in exploring Samal Island by motorbike...
Hagimit Falls
Hagimit Falls, located in Barangay Peñaplata, was our first stop during the motorbike tour. Hagimit is one of the most popular tourist attractions in Samal Island. It is comprised of several short cascades along Benoling River.
Entrance to Hagimit is Php40.00 for adults and Php20.00 for children 7 years old and below. A series of concrete steps will lead you to the river and the falls down below.
Cottages and tables are available for rent. There's also a sari-sari store selling snacks and drinks. Since we already bought some food from the Public Market earlier, we just rented a table and some chairs.
After eating our late breakfast, we soaked on the the cold and cascading waters. It was a very refreshing treat to jumpstart our Samal adventures.
From Hagimit Falls we followed the coastal road going south until we reached the Acantilado Cliff. We parked in an open area where there are a few makeshift tables and chairs and a stall selling food and drinks.
The cliff offers a panoramic coastal view. But this is not the main attraction of Acantilado.
Acantilado is actually a spot for cliff jumping. We witnessed two daredevils jump off the cliff with a height of about 40 meters.
None of us are brave enough to take the dare though, so after taking a few photos, we moved on to our next destination.
Tagbaobo Falls
We headed back towards the north direction and then made a right turn upon reaching Barangay Anonang proper. The interior roads were already unpaved and with some hilly portions. Upon reaching Barangay Tagbaobo we asked some locals for directions until we finally made it to Magongawong Falls more popularly known as Tagbaobo Falls.
After paying the entrance fee of we followed the short trail going down to the falls.There were no other tourists around as Tagbaobo Falls is not that known compared to Hagimit.
We thoroughly enjoyed our time here as we had the falls all to ourselves. Of course, we did not let the chance pass without dipping on the cool water as the falls has a shallow but wide basin.
Bamboo poles were also installed as makeshift bench facing the falls and also as safety barrier to the next tier.
Canibad Beach
From Tagbaobo we traversed the island's interior rough roads heading northwest until we reach the white sand Canibad Beach.It faces mainland Davao del Norte and due to its remote location is less popular compared to the beaches on the opposite side of Samal.
Canibad still has a raw feel, with a few resorts mostly consist of native huts and cottages. It is not that commercialize yet and I love its quiet and rustic ambiance.
The waves were strong but it did not prevented us from enjoying the beach. Along with a few other tourists, we took our time soaking on the rolling waves.
Monfort Bat Colony
After having our fill of waterfalls and beach, our last stop for the day was the Monfort Bat Colony. Located in Barangay Tambo, Babak District, it is only a few kilometers away from the Babak Port.
In 2010, Monfort Bat Cave was officially recognized by the Guinness World Record as the largest single colony of Geoffrey's Rousette fruit bats. Trip Advisor also ranked it as #3 of the Top 9 Attractions of Samal Island.
The bat cave is 75 meter long and its ceilings and walls has been the home of 2.3 million Rousette fruit bats.
Entrance Fee is Php100.00 for adults and Php40.00 for kids 4-15 years of age. The owner, Norma Monfort, fenced the property and hired security guards to protect it from bat hunters. Because of her conservation efforts, she was recognized as a Disney Worlwide Conservation Fund Hero in 2011.
As the sun was already about to set, we went back to the port. We were just in time as the ferry bound for Davao City is already about to depart. Though we were all tired after a day-long exploration, we thouroughly enjoyed it and did have a great time with our Samal Island adventures.
Friday, March 10, 2017
Davao del Norte: Around Samal Island by Motorbike
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