Tham khảo tài liệu 'the annuity puzzle economic of annuities_2', khoa học xã hội, kinh tế chính trị phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 80 Chapter 10 particular the individual typically has some influence on the outcome. Thus the probability q which was taken as given may be regarded to some extent at least as influenced by individual decisions that involve costs and efforts. The potential conflict that this type of moral hazard raises between social welfare and individual interests is very clear in this context. Since V V an increase in q decreases the first-best expected utility. On the other hand in a competitive equilibrium V1 V2 and hence an increase in q may be desirable. CHAPTER 9 Pooling Equilibrium and Adverse Selection Introduction For a competitive annuity market with long-term annuities to be efficient it must be assumed that individuals can be identified by their risk classes. We now wish to explore the existence of an equilibrium in which the individuals risk classes are unknown and cannot be revealed by their actions. This is called a pooling equilibrium. Annuities are offered in a pooling equilibrium at the same price to all individuals assuming that nonlinear prices which require exclusivity as in Rothschild and Stiglitz 1979 are not feasible . Consequently the equilibrium price of annuities is equal to the average longevity of the annuitants weighted by the equilibrium amounts purchased by different risk classes. This result has two important implications. One the amount of annuities purchased by individuals with high longevity is larger than in a separating efficient equilibrium and the opposite holds for individuals with low longevities. This is termed adverse selection. Two adverse selection causes the prices of annuities to exceed the present values of expected average actuarial payouts. The empirical importance of adverse selection is widely debated see for example Chiapori and Salanie 2000 though its presence is visible. For example from the data in Brown et al. 2001 one can derive survival rates for males and females born in 1935 distinguishing between the overall .
