“How powerful is demography? The serendipity theorem revisited” comment on De la Croix et al. (2012)
“How powerful is demography? The serendipity theorem revisited” comment on De la Croix et al. (2012)
复制标题
“人口统计学有多强大？重新审视偶然性定理”De la Croix 等人的评论（2012）
DOI：
10.1007/s00148-016-0587-y
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发表时间：
2016
影响因子：
6.1
通讯作者：
S. Felder
中科院分区：
文献类型：
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作者：
S. Felder
萨缪尔森的偶然性定理（Int Econ Rev 16（3）：531-538，1975）指出，“最黄金的黄金法则”稳态均衡可以通过具有资本积累的竞争性两阶段重叠世代经济获得，只要最优增长率占上风。De la克鲁瓦et al.（J Popul Econ 25：899-922，2012）扩展了该定理的范围，表明它也适用于风险寿命。在此基础上，我们引入医疗费用作为老年生存概率的决定因素来证明该定理。然而，偶然性定理的原始版本以及所有扩展版本都未能证明二阶条件一般都满足。尽管如此，与De la克鲁瓦et al.（J Popul Econ 25：899-922，2012）不同，我们可以排除到达老年的概率为零或一的角解的存在。如果考虑到在死亡和生命效用之间随机化的选项，则零生存概率的情况变得无关紧要。如果生存的边际成本在增加，那么确定性生存就被排除了。因此，最优生存概率表示内部解。此外，我们证明了最优生存概率的统计寿命的价值是积极的，等于其边际成本。
Samuelson’s (Int Econ Rev 16(3):531-538, 1975) serendipity theorem states that the “goldenest golden rule” steady-state equilibrium can be obtained by a competitive two-period overlapping generation economy with capital accumulation, provided that the optimal growth rate prevails. De la Croix et al. (J Popul Econ 25:899-922, 2012) extended the scope of the theorem by showing that it also holds for risky lifetime. With this note, we introduce medical expenditure as a determinant of the probability of surviving to old age to prove the theorem. The original as well as all extended versions of the serendipity theorem, however, fail to prove that second-order conditions are satisfied in general. Still, unlike De la Croix et al. (J Popul Econ 25:899-922, 2012), we can exclude the existence of corner solutions where the probability of reaching old age is zero or one. The zero survival probability case becomes irrelevant if the option to randomize between death and life utility is taken into account. Survival with certainty is ruled out if the marginal cost of survival is increasing. Hence, the optimal survival probability represents an interior solution. Furthermore, we show for the optimal survival probability that the value of a statistical life is positive and equal to its marginal cost.