How Long Do We Live? (eBook)

Foreword 6
Contents 9
How long do we live? Demographic models and reflections on tempo effects: An introduction 14
1 Background 14
2 Overview of the monograph 16
References 21
I. Theoretical basis for the mortality tempo effect 22
Estimating mean lifetime 23
1 Methods 24
2 Results 27
3 Conclusion 35
Acknowledgements 36
References 36
Appendix A 37
Appendix B 38
The quantum and tempo of life-cycle events 40
1 Introduction 40
2 Background: age-specific event rates 41
3 Period quantum and tempo measures of the 2nd kind 43
4 Period quantum and tempo measures of the 1st kind 57
5 Conclusion 67
References 69
Appendix A: Relationship between the completed fertility rate and the weighted average of tempo-adjusted period total fertility rates 73
Appendix B: Comparison of measures of the 1st and 2nd kind 74
II. Critiques, extensions and applications of the mortality tempo effect 77
Demographic translation and tempo effects: An accelerated failure time perspective 78
1 Introduction 78
2 Fertility 80
3 Mortality 88
4 Discussion 98
Acknowledgments 100
References 100
Lifesaving, lifetimes and lifetables 102
1 Introduction 102
2 How saving a life alters life expectancy 104
3 Individual lifetimes 106
4 The triangle of turbulence 108
5 How large is the distortion? 109
6 Considerations about true life expectancy 110
7 A model of stretched lifetimes 112
8 Quantum and tempo vs. proportions and increments 112
9 Directions for research 113
Acknowledgements 115
References 116
Tempo and its tribulations 117
1 Tempo 117
2 Measures 119
3 Representation of M 121
4 The moving average 124
5 Period counts of deaths 127
6 Current latent conditions 128
7 Total fertility 131
References 135
Tempo effects in mortality: An appraisal 137
1 Introduction 137
2 The existence of tempo e.ects in mortality 139
3 Bongaarts and Feeney’s tempo-adjusted life expectancy 142
4 Evaluating Bongaarts and Feeney’s proportionality assumption 143
5 Bongaarts and Feeney’s de.nition of changes in period mortality conditions 147
6 Assessing indicators of period mortality conditions 152
7 Conclusion 157
Acknowledgments 158
References 158
Increments to life and mortality tempo 161
1 Time-discrete increments to life 161
2 Empirical results: Swedish females, 1751-2002 162
3 Time-continuous cohort-indexed increments to life 163
4 Time-continuous period-indexed increments to life 166
5 Relation between cohort and period increments to life 167
6 Robustness of the Bongaarts-Feeney tempo adjustment formula 170
7 Increments to life and mortality tempo: mixed models 171
8 Conclusion 172
Acknowledgements 173
References 173
Mortality tempo versus removal of causes of mortality: Opposite views leading to different estimations of life expectancy 174
1 Introduction 174
2 Decreasing mortality as a sign of delay in deaths 175
3 Decreasing mortality as a change in the causes of death 177
4 Removing one cause of death: deeper insights 178
5 A numerical example of the two methods 179
6 Which life table is the reference table? 181
7 Unifying the two views: the repartition function of the delays by age and duration 183
8 Which is the best model? A discussion of the two methods 185
References 189
Appendix A: Deaths and survivors of age x in t after the removal of a mortality cause in t = 0 189
Appendix B: Demonstrating the strong properties of the two methods 191
Appendix C: Fixed and variable delays 194
Tempo effect on age-specific death rates 197
1 Introduction 197
2 Intuitive visual explanation 198
3 Mathematical presentation 201
4 Discussion 203
Acknowledgments 205
References 205
Appendix 206
Mortality tempo-adjustment: Theoretical considerations and an empirical application 208
1 Introduction 208
2 How mortality tempo a.ects period life expectancy 211
3 Why life expectancy di.erences between western and eastern Germany call for tempo-adjustment 215
4 Trends in tempo-adjusted life expectancy in western and eastern Germany 220
5 Discussion 223
References 229
Appendix 234
III. Comparison of period and cohort measures of longevity 239
Five period measures of longevity 240
1 Introduction 240
2 Definitions of period longevity measures 241
3 Results 242
4 Discussion 244
5 Conclusion 247
Acknowledgements 247
References 247
Found in translation? A cohort perspective on tempo-adjusted life expectancy 249
1 Introduction 249
2 Proof of exact cohort translation 251
3 Discussion 253
4 Conclusion 259
Acknowledgements 260
References 260
IV. Conclusions 262
Afterthoughts on the mortality tempo effect 263
1 Do tempo adjusted period longevity measures reflect current mortality conditions? 263
2 Conclusion 268
References 269
Turbulence in lifetables: Demonstration by four simple examples 270
1 Introduction 270
2 Saving infant lives for one year 271
3 Saving infant lives for three years 273
4 Saving infant lives for two years on average 273
5 Saving everyone’s life for one year 274
6 Discussion 277
Acknowledgements 278
Appendix 279
Two proofs of a recent formula by Griffith Feeney 280
1 Introduction 280
2 Proof by Jutta Gampe 280
3 Proof by Anatoli Yashin 281
References 281