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The Nature of Demography
Hervé Le Bras

Book Description | Reviews
Introduction [HTML] or [PDF format]

TABLE OF CONTENTS:

Preface xi
Acknowledgments xiii

Introduction 1

Part I: Individuals 7

Chapter 1: Mortality 9
1.1 The Survival Curve 9
1.2 Estimating the Survival Function by the Kaplan-Meier Method 10
1.3 Mean Length of Life and Life Expectancy 12
1.4 Deaths and Probabilities of Dying 13
1.5 Life Tables 15
1.6 Comparison of Mortality and Instantaneous Probabilities 16
1.7 Instantaneous Rates of Mortality 18
1.8 Exponential Functions: Gompertz, Makeham,Weibull 20
1.9 Model Life Tables 22
1.10 Life Insurance and Annuities 24
1.11 Appendix 26

Chapter 2: Fertility 29
2.1 Measures of Fertility in the Absence of Mortality 29
2.2 Gini and Fecundability 32
2.3 Models of Reproduction 32
2.4 Variation in Fecundability with Age, Intrauterine Mortality, and Permanent Sterility 34
2.5 Natural Fertility 35
2.6 Fertility Controls 37
2.7 Effect on Fertility of Age at Marriage 38
2.8 Length of Nonsusceptible Period after Live Births and Fertility 39
2.9 Contraception 42
2.10 Induced Abortion 43
2.11 Probabilities of Having Another Child and Parity 45
2.12 Laws of Fertility 46
2.13 The Coale-Trussell Formula 48
2.14 Male Fertility 50

Chapter 3: Censoring 52
3.1 Incomplete Observations of Fertility and Mortality 52
3.2 Independence of Fertility and Mortality: Consistency of the Estimation 54
3.3 Censored Data: The Case of Mortality 56
3.4 Multiple Life Tables 59
3.5 Cause-Specific Mortality 60
3.6 Double Censoring 62
3.7 Grouped Data 67
3.8 Method and Critique of Estimation by the Principle of Indifference 69
3.9 Estimating Rates in the Case of Censoring 71
3.10 Appendix 73

Chapter 4: Period and Cohort Approaches 77
4.1 The Lexis Plane 77
4.2 The Fictitious or "Synthetic" Cohort 82
4.3 In the Absence of Double Classification 86
4.4 Double-Period Censoring 88
4.5 Independence of Period Data 89
4.6 Period Indices 90
4.7 Appendix 92

Chapter 5: Interpreting Period Variations in Fertility 93
5.1 First Examples of Change in Reproductive Behavior 94
5.2 The Logic of Changes in Tempo 97
5.3 Principle of a Fertility Simulation (France 1955-87) 100
5.4 Reconstitution of the Fertility Processes at the Start and End of the Transition 101
5.5 The Transition between the Two Models of Fertility 105
5.6 Reconstitution of Fertility Change, 1955-87: Two Experiments 106
5.7 Reconstitution Combining the Change in Final Completed Fertility and in Timing 109
5.8 Rules of Interpretation 112
5.9 Replacement of Generations 113
5.10 Appendix 114

Chapter 6: Timing Changes and Period Mortality 117
6.1 Mortality Decline Envisaged as a Delaying of Deaths 117
6.2 Mortality Decline as an Elimination of Causes of Death 119
6.3 Elimination of a Cause of Death: A More Detailed Account 120
6.4 A Numerical Example of Both Methods
(Delays and Elimination of Causes) 121
6.5 Specifying the Reference Mortality 124
6.6 Unifying the Viewpoints: The Repartition Function of the Deaths 126
6.7 The Two Models Compared 127
6.8 Appendix 131

Part II: Populations 137

Chapter 7: Forecasts, Projections, and Prospects 139
7.1 The Laws of Population 140
7.2 Raymond Pearl and the Logistic Law 142
7.3 The Beginnings of the Component Method 146
7.4 Alfred Lotka and Stable Populations 147
7.5 The Unification of Demography 149
7.6 The Mechanism of Component Projection 150
7.7 Implementing Population Projections: An Example 152
7.8 Retroprojections 154
7.9 The Demographic Feedback Loop 156

Chapter 8: Stable Populations andWeak Ergodicity 158
8.1 Weak Ergodicity of Nonnegative Matrices 158
8.2 Projection Using Components and Matrices 161
8.3 Stable Populations 163
8.4 Stationary Populations 165
8.5 Migration and Multiregional Projection 166
8.6 The Renewal Equation 167
8.7 Convergence of the Fertility Model 168
8.8 Weak Ergodicity: The Continuous Version 169
8.9 Overlapping Generations 172
8.10 Branching Processes 174

Chapter 9: Equilibrium and Fluctuations 178
9.1 Approximations of Fluctuations 178
9.2 A Zero Growth Rate for Mexico from 2000 180
9.3 The Hidden Constraint of Stable Populations: Stable Equivalent Populations 182
9.4 Fluctuation in the Size of a Professional Population 184
9.5 Populating a New Neighborhood and Modeling the Household Life Cycle 189
9.6 Mathematical Model, Projection, or Microsimulation 191
9.7 An Example of a New Neighborhood's Population 192
9.8 Out-Migrants and Immigrants 198

Chapter 10: Economics and Population 200
10.1 The Self-Regulating Model of Historical Populations 201
10.2 The Easterlin and Samuelson Models 204
10.3 From Regulation to Chaos 209
10.4 Malthus: Population and Subsistence 210
10.5 Macroscopic Models: Economic Growth and Population Growth 213
10.6 The Malthusian Model 214
10.7 The Bosrupian Model: Exogenous Population Growth 215
10.8 Endogenous Technological Progress and Population Growth 217
10.9 Appendix 218

Chapter 11: Life Cycles and Old-Age Pensions 220
11.1 Equilibrium over the Life Cycle and the Funding Principle 220
11.2 Funded Pension Systems 224
11.3 Accounting Equilibrium and Pay-As-You-Go (Unfunded) Pension Systems 226
11.4 Golden Paths, Golden Rule 228
11.5 Outside the Golden Rule 230
11.6 Economize or Breed? 232
11.7 The Return to Education 235
11.8 The Quantity and Quality of Children: Gary Becker's Model 236

Part III: Space and Networks 239

Chapter 12: The Marriage Market 241
12.1 Marital Attraction 242
12.2 Social Squeeze on Marriage 243
12.3 Dances and Circles 245
12.4 The Marriage Circles under the Microscope 247
12.5 The Model of Marriage Squeeze by Age 251
12.6 The Age Squeeze and the Distributions 253
12.7 Oversized Cohorts, Nuptiality Crises 257
12.8 Nuptiality and Undersized Cohorts 260
12.9 Individual Risk 262
12.10 Equivalence between Number of Individual Ties and Speed of the Group Process 265
12.11 Networks of Ties 266
12.12 Imbalances in the Micromodel of the Marriage Market 268
12.13 Pairings 269
12.14 Appendix 272

Chapter 13: The Laws of Migration 274
13.1 The Gravity or Pareto Law of Marital Distance 274
13.2 Migration as an Allocation Process 276
13.3 A Concrete Example of Migration under the Gravity Law 277
13.4 Explaining the Variations in the Exponent for Distance 281
13.5 General Simulation of Internal Migration 282
13.6 Migration Balances and Chaos 284
13.7 The Attraction of the Neighborhoods of Paris and
Intervening Opportunities 288
13.8 H¨agerstrand's Networks 291
13.9 Attraction of the Railway Stations and City Center 292
13.10 Paris in Rings 294
13.11 Immigration to Paris: A Narrative 296
13.12 Simulation of Urban Immigration 297

Chapter 14: The Four Forms of Internal Migration 304
14.1 The Four Forms of Migration 304
14.2 The Alonso Model 306
14.3 Constant Elasticities 307
14.4 The Alonso Model as an Individual Process 308
14.5 The Model's Inconsistencies 309
14.6 Find the Mistake 311
14.7 Saving the Spirit of the Model 312
14.8 Determining Inflows and Outflows Ex Post 313
14.9 The Entropy Model as a Process 314
14.10 The Value of Conceptual Migration Models 315
14.11 Appendix 317

Chapter 15: Densities 321
15.1 Examples of Rank-Size Distributions 323
15.2 Explaining the Rank-Size Rule: Gibrat and Simon 324
15.3 Communes and Agglomerations 327
15.4 Models of Spatial Population Distribution 330
15.5 Models of the Distribution of Stellar Matter: Curdling and L´evy Flights 332
15.6 Christaller's Central Places 334
15.7 Fractal Relations and Density Thresholds 335
15.8 The Multifractal Model 338
15.9 The Generality of the Multifractal Model 340
15.10 Appendix 341

Conclusion 345
References 351
Index 359

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File created: 4/17/2014

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