Herve Le Bras is director of studies at the School of Higher Education in the Social Sciences and director of research at the National Institute of Demographic Studies in Paris.

"I heartily recommend The Nature of Demography to all who see demography an autonomous scientific discipline with a strong core of theory--rather than just a body of techniques, the application of general statistics to demographic data. It should be consulted regularly and seriously by anyone trying to use or develop demographic theory. It can be read with profit more than once in order to begin to absorb Le Bras' deep and coherent vision of our discipline."--Thomas K. Burch, Canadian Studies in Population "The Nature of Demography would be best suited to numerate readers with an existing knowledge of basic demographic theory and methods. The book contains a fascinating overview of the current state of demography, its methodological history and links to other disciplines. It effectively conveys the continuing evolution of the discipline."--Rebecca Kippen, Economic Record "The Nature of Demography is a firm addition to the current handbooks in demography, serving as an advanced textbook for scientists to obtain the necessary fresh and critical mindset, which, in my view, could best be read after a more general introduction to demography. I am pretty sure it will change our way of looking at demography and its nature."--F. Janssen, European Journal of Population

• 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 Hagerstrand'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

Herve Le Bras is director of studies at the School of Higher Education in the Social Sciences and director of research at the National Institute of Demographic Studies in Paris.

"I heartily recommend The Nature of Demography to all who see demography an autonomous scientific discipline with a strong core of theory--rather than just a body of techniques, the application of general statistics to demographic data. It should be consulted regularly and seriously by anyone trying to use or develop demographic theory. It can be read with profit more than once in order to begin to absorb Le Bras' deep and coherent vision of our discipline."--Thomas K. Burch, Canadian Studies in Population "The Nature of Demography would be best suited to numerate readers with an existing knowledge of basic demographic theory and methods. The book contains a fascinating overview of the current state of demography, its methodological history and links to other disciplines. It effectively conveys the continuing evolution of the discipline."--Rebecca Kippen, Economic Record "The Nature of Demography is a firm addition to the current handbooks in demography, serving as an advanced textbook for scientists to obtain the necessary fresh and critical mindset, which, in my view, could best be read after a more general introduction to demography. I am pretty sure it will change our way of looking at demography and its nature."--F. Janssen, European Journal of Population

• 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 Hagerstrand'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