The Economic Theory of Annuities

Annuities are financial products that guarantee the holder a fixed return so long as the holder remains alive, thereby providing insurance against lifetime uncertainty. The terms of these contracts depend on the information available to insurance firms. Unlike age and gender, information about individual survival probabilities cannot be readily ascertained. This asymmetric information causes market inefficiencies, such as adverse selection. Groundbreaking in its scope,The Economic Theory of Annuitiesoffers readers a theoretical analysis of the functioning of private annuity markets. Starting with a general analysis of survival functions, stochastic dominance, and characterization of changes in longevity, Eytan Sheshinski derives the demand for annuities using a model of individuals who jointly choose their lifetime consumption and retirement age. The relation between life insurance and annuities that have a bequest option is examined and "annuity options" are proposed as a response to the lack of secondary markets. This book also investigates the macroeconomic policy implications of annuities and changes in longevity on aggregate savings. Sheshinski utilizes statistical population theory to shed light on the debate of whether the surge in savings and growth in Asia and other countries can be attributed to higher longevity of the population and whether this surge is durable. This book shows how understanding annuities becomes essential as governments that grapple with insolvency of public social security systems place greater emphasis on individual savings accounts.

Preface	p. xiii
Introduction	p. 1
Brief Outline of the Book	p. 5
Short History of Annuity Markets	p. 9
References to Actuarial Finance	p. 11
Benchmark Calculations: Savings and Retirement	p. 12
Survival Functions, Stochastic Dominance, and Changes in Longevity	p. 15
Survival Functions	p. 15
Changes in Longevity	p. 18
Life Cycle Model with Longevity Risk: First Best and Competitive Equilibrium	p. 21
First Best	p. 21
Competitive Equilibrium: Full Annuitization	p. 23
Example: Exponential Survival Function	p. 25
Equivalence of Short-term, Long-term, and Deferred Annuities	p. 26
Appendix	p. 27
Comparative Statics, Discounting, Partial Annuitization, and No Annuities	p. 29
Increase in Wages	p. 29
Increase in Longevity	p. 30
Positive Time Preference and Rate of Interest	p. 32
Partial Annuitization: No Short-term Annuity Market	p. 33
Partial Annuitization: Low Returns on Annuities	p. 35
Length of Life and Retirement	p. 35
Optimum Without Annuities	p. 38
No Annuities: Risk Pooling by Couples	p. 40
Welfare Value of an Annuity Market	p. 41
Example: Exponential Survival Function	p. 42
Appendix	p. 44
Subjective Beliefs and Survival Probabilities	p. 45
Deviations of Subjective from Observed Frequencies	p. 45
Behavioral Effects	p. 45
Exponential Example	p. 47
Present and Future Selves	p. 48
Moral Hazard	p. 51
Introduction	p. 51
Comparison of First Best and Competitive Equilibrium	p. 51
Annuity Prices Depending on Medical Care	p. 54
Appendix	p. 55
Uncertain Future Survival Functions	p. 56
First Best	p. 56
Competitive Separating Equilibrium (Risk-class Pricing)	p. 59
Equilibrium with Short-term Annuities	p. 60
The Efficiency of Equilibrium with Long-term Annuities	p. 62
Example: Exponential Survival Functions	p. 65
Pooling Equilibrium and Adverse Selection	p. 67
Introduction	p. 67
General Model	p. 69
Example	p. 71
Appendix	p. 75
Income Uncertainty	p. 77
First Best	p. 77
Competitive Equilibrium	p. 78
Moral Hazard	p. 79
Life Insurance and Differentiated Annuities	p. 81
Bequests and Annuities	p. 81
First Best	p. 83
Separating Equilibrium	p. 84
Pooling Equilibrium	p. 84
Period-certain Annuities and Life Insurance	p. 87
Mixed Pooling Equilibrium	p. 90
Summary	p. 93
Appendix	p. 94
Annuities, Longevity, and Aggregate Savings	p. 97
Changes in Longevity and Aggregate Savings	p. 97
Longevity and Individual Savings	p. 98
Longevity and Aggregate Savings	p. 98
Example: Exponential Survival Function	p. 102
No Annuities	p. 103
Unintended Bequests	p. 104
Appendix	p. 106
Utilitarian Pricing of Annuities	p. 109
First-best Allocation	p. 109
Competitive Annuity Market with Full Information	p. 112
Second-best Optimum Pricing of Annuities	p. 113
Appendix	p. 116
Optimum Taxation in Pooling Equilibria	p. 118
Introduction	p. 118
Equilibrium with Asymmetric Information	p. 119
Optimum Commodity Taxation	p. 122
Optimum Taxation of Annuities	p. 125
Appendix	p. 129
Bundling of Annuities and Other Insurance Products	p. 131
Introduction	p. 131
Example	p. 132
Financial Innovation-Refundable Annuities (Annuity Options)	p. 135
The Timing of Annuity Purchases	p. 135
Sequential Annuity Market Equilibrium Under Survival Uncertainty	p. 137
Uncertain Future Incomes: Existence of a Separating Equilibrium	p. 140
Refundable Annuities	p. 144
A Portfolio of Refundable Annuities	p. 146
Equivalence of Refundable Annuities and Annuity Options	p. 147
Appendix	p. 150
References	p. 153
Index	p. 157
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