Dynamic population models:
Saved in:
| Format: | Electronic eBook |
|---|---|
| Language: | English |
| Published: |
Dordrecht
Springer
c2006
|
| Series: | The Springer series on demographic methods and population analysis
17 |
| Subjects: | |
| Online Access: | UBG01 UBR01 UPA01 Volltext Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 231-239) and indexes |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 9781402052293 9781402052309 |
| DOI: | 10.1007/1-4020-5230-8 |
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| adam_text | CONTENTS
Preface xi
List of Tables and Figures xiii
1. Population Models With Constant Rates 1
1.1. Introduction 1
1.2. Some Basic Concepts 1
1.3. The Basic Life Table 3
1.4. Multiple Decrement and Cause Eliminated Life Tables 7
1.5. Stable Population Models 9
1.5.1. Continuous Stable Models 9
1.5.2. Discrete Stable Models 12
1.6. Multistate Life Tables 14
1.6.1. Scalar Multistate Equations 14
1.6.2. Matrix Multistate Equations 16
1.6.3. Multistate Expectancies and Summary Measures 19
1.7. The Multistate Stable Population 20
1.8. Summary 22
1.9. Exercises 23
2. Convergence to Stability 27
2.1. Introduction 27
2.2. Conditions for Stability 27
2.3. The Speed of Convergence 29
2.4. Some Explicit Analyses of Convergence 33
2.4.1. Convergence in 2 x 2 Leslie Models 34
2.4.2. Convergence in a 3 x 3 Leslie Model 34
2.4.3. Convergence in a Two Living State Multistate Model 37
2.5. Summary 40
2.6. Exercises 41
3. Population Momentum 43
3.1. Introduction 43
3.2. Momentum As a Demographic Phenomenon 43
3.2.1. The Basic Dynamics 43
3.2.2. Momentum and Aging 46
v
vi CONTENTS
3.3. Momentum Under Gradual Declines to Stationarity 50
3.4. Spatial Momentum 51
3.4.1. Spatial Momentum in Two Region Models
Without Age 52
3.4.2. Decomposing Total Multistate Population
Momentum 53
3.5. Summary 57
3.6. Exercises 57
4. Demographic Change at the Margin 59
4.1. Introduction 59
4.2. Marginal Change in Fixed Rate Models 59
4.2.1. Changes in Stable Population Measures 60
4.2.2. Changes in Stable Population Characteristics 62
4.3. Recognizing Age Dependent Growth 63
4.4. Connections Between Populations Having the Same
Vital Rates 65
4.5. Marginal Change in Dynamic Populations 67
4.5.1. Derivatives of Aggregate Demographic Measures 67
4.5.2. Marginal Change and Stabilization 70
4.6. A Spectral Decomposition of Marginal Change 72
4.7. Summary 74
4.8. Exercises 75
5. Longevity and Dynamic Mortality 79
5.1. Introduction 79
5.2. An Overview of Changes in Human Mortality 79
5.3. A Third Analytical Perspective: The Wedge Period 82
5.4. Period Cohort Considerations 82
5.4.1. The Period Cohort Contrast in Mortality 82
5.4.2. Average Cohort Life Expectancy 83
5.5. A Shifting Gompertz Mortality Change Model 85
5.5.1. The Bongaarts Feeney Approach 85
5.5.2. Relationships in a Shifting Gompertz Model 89
5.6. Models of Constant Mortality Decline Over Time 92
5.6.1. Three Models With Linearly Changing Mortality 92
5.6.2. Gaps and Lags Between Period and Cohort Life
Expectancies 94
5.6.3. The Modal Age At Death 96
5.7. Summary 98
5.8. Exercises 99
CONTENTS vii
6. Timing Effects on Fertility, Marriage, and Divorce 101
6.1. Introduction 101
6.2. The Period Cohort Contrast 101
6.3. The Bongaarts Feeney Approach 103
6.4. Average Cohort Fertility 105
6.5. Comparing the Bongaarts Feeney and ACF Approaches 106
6.5.1. Timing Effects in Selected Models 107
6.5.2. Timing Effects in the United States, 1917 97 107
6.6. Examining Parity Specific Period TFRs 110
6.7. A Diminishing Population Whose Every Cohort More Than
Replaces Itself 112
6.8. Timing Effects on First Marriage 113
6.8.1. Measuring Timing Effects on First Marriage 114
6.8.2. Timing Effects on First Marriage in England and Wales
and the United States 115
6.9. Timing Effects on Divorce 116
6.9.1. Measuring Timing Effects on Divorce 118
6.9.2. Timing Effects on Divorce in the United States 119
6.10. Summary 120
6.11. Exercises 121
7. Dynamic Birth Death (Multi Age) Models 123
7.1. Introduction 123
7.2. Models Where the Age Specific Rates Are Implicit 123
7.2.1. Considering Models With a Constant
Generation Length 124
7.2.2. Cyclical Models With a Constant Generation
Length 126
7.2.3. Intergenerational Relationships in a Simple Model
With Sinusoidal Births 128
7.3. Metastability, A Closed Form Extension of Stability 132
7.3.1. Deriving the Discrete Metastable Model 132
7.3.2. The Continuous Metastable Model 135
7.3.3. Modeling Fertility Transitions and Their Associated
Momentum 138
7.4. Intrinsically Dynamic Models, An Alternative Extension
of Stability 142
7.4.1. The Two Age Group Intrinsically Dynamic Model 143
7.4.2. The Three Age Group Intrinsically Dynamic Model 146
7.4.3. The n Age Group Intrinsically Dynamic Model 148
7.4.4. IDM Birth Trajectories 149
viii CONTENTS
7.4.5. Observed Populations as IDM Populations 150
7.4.6. Transitions and Momentum in IDM Populations 150
7.5. Finding Rates Consistent With a Known Birth Trajectory 152
7.5.1. Hyperstable Models 153
7.5.2. Models With Proportional Rates 155
7.6. Summary 155
7.7. Exercises 156
8. Dynamic Multistate Models 161
8.1. Introduction 161
8.2. Cohort Multistate Models With Proportional Transfer Rates 161
8.2.1. Relationships in Proportional Transfer Rate (PTR) Models 162
8.2.2. PTR Models With 2 Living States 165
8.2.3. Hierarchical PTR Models 166
8.2.4. A PTR Model of Marriage, Divorce, and Remarriage 170
8.3. Multistate Metastable Models 172
8.4. Multistate Intrinsically Dynamic Models 174
8.4.1. The Restricted Two Living State Uniform Growth Model 174
8.4.2. Additional Two Living State Models 178
8.4.3. The Restricted No Growth IDM With Three Living States 180
8.4.4. The Restricted Uniform Growth IDM With n Living
States 181
8.5. Multistate Hyperstability 181
8.5.1. Deriving the Multistate Hyperstable Equations 181
8.5.2. Relationships Between the Multi Age and Multistate
Hyperstable Models 184
8.5.3. A Further Examination of the Dynamic Two Living State
Model 185
8.6. Finding Rates Consistent With Multistate Population
Distributions 188
8.6.1. Estimating Multistate Arrays Through Iterative
Proportional Fitting 189
8.6.2. Estimating Multistate Rates By the Relative State
Attraction (RSA) Method 190
8.6.3. Evaluating the IPF and RSA Approaches 193
8.7. Summary 196
8.8. Exercises 197
9. Dynamic Models With Multiple Ages and States 203
9.1. Introduction 203
9.2. The Multi Age and State Hyperstable (MASH) Model 204
CONTENTS ix
9.2.1. Specifying the MASH Model 204
9.2.2. An Illustrative Application 207
9.3. The Multi Age and State Metastable (MASM) Model 209
9.4. Summary and Overview 212
9.4.1. Chapter Summary 212
9.4.2. Overview and Recapitulation 212
9.5. Exercises 214
Appendix A Matrices and Their Eigenstructure 217
Appendix B Selected Answers to Exercises 221
Appendix C Index of the Principal Symbols Used 225
References 231
Author Index 241
Subject Index 245
|
| adam_txt |
CONTENTS
Preface xi
List of Tables and Figures xiii
1. Population Models With Constant Rates 1
1.1. Introduction 1
1.2. Some Basic Concepts 1
1.3. The Basic Life Table 3
1.4. Multiple Decrement and Cause Eliminated Life Tables 7
1.5. Stable Population Models 9
1.5.1. Continuous Stable Models 9
1.5.2. Discrete Stable Models 12
1.6. Multistate Life Tables 14
1.6.1. Scalar Multistate Equations 14
1.6.2. Matrix Multistate Equations 16
1.6.3. Multistate Expectancies and Summary Measures 19
1.7. The Multistate Stable Population 20
1.8. Summary 22
1.9. Exercises 23
2. Convergence to Stability 27
2.1. Introduction 27
2.2. Conditions for Stability 27
2.3. The Speed of Convergence 29
2.4. Some Explicit Analyses of Convergence 33
2.4.1. Convergence in 2 x 2 Leslie Models 34
2.4.2. Convergence in a 3 x 3 Leslie Model 34
2.4.3. Convergence in a Two Living State Multistate Model 37
2.5. Summary 40
2.6. Exercises 41
3. Population Momentum 43
3.1. Introduction 43
3.2. Momentum As a Demographic Phenomenon 43
3.2.1. The Basic Dynamics 43
3.2.2. Momentum and Aging 46
v
vi CONTENTS
3.3. Momentum Under Gradual Declines to Stationarity 50
3.4. Spatial Momentum 51
3.4.1. Spatial Momentum in Two Region Models
Without Age 52
3.4.2. Decomposing Total Multistate Population
Momentum 53
3.5. Summary 57
3.6. Exercises 57
4. Demographic Change at the Margin 59
4.1. Introduction 59
4.2. Marginal Change in Fixed Rate Models 59
4.2.1. Changes in Stable Population Measures 60
4.2.2. Changes in Stable Population Characteristics 62
4.3. Recognizing Age Dependent Growth 63
4.4. Connections Between Populations Having the Same
Vital Rates 65
4.5. Marginal Change in Dynamic Populations 67
4.5.1. Derivatives of Aggregate Demographic Measures 67
4.5.2. Marginal Change and Stabilization 70
4.6. A Spectral Decomposition of Marginal Change 72
4.7. Summary 74
4.8. Exercises 75
5. Longevity and Dynamic Mortality 79
5.1. Introduction 79
5.2. An Overview of Changes in Human Mortality 79
5.3. A Third Analytical Perspective: The Wedge Period 82
5.4. Period Cohort Considerations 82
5.4.1. The Period Cohort Contrast in Mortality 82
5.4.2. Average Cohort Life Expectancy 83
5.5. A Shifting Gompertz Mortality Change Model 85
5.5.1. The Bongaarts Feeney Approach 85
5.5.2. Relationships in a Shifting Gompertz Model 89
5.6. Models of Constant Mortality Decline Over Time 92
5.6.1. Three Models With Linearly Changing Mortality 92
5.6.2. Gaps and Lags Between Period and Cohort Life
Expectancies 94
5.6.3. The Modal Age At Death 96
5.7. Summary 98
5.8. Exercises 99
CONTENTS vii
6. Timing Effects on Fertility, Marriage, and Divorce 101
6.1. Introduction 101
6.2. The Period Cohort Contrast 101
6.3. The Bongaarts Feeney Approach 103
6.4. Average Cohort Fertility 105
6.5. Comparing the Bongaarts Feeney and ACF Approaches 106
6.5.1. Timing Effects in Selected Models 107
6.5.2. Timing Effects in the United States, 1917 97 107
6.6. Examining Parity Specific Period TFRs 110
6.7. A Diminishing Population Whose Every Cohort More Than
Replaces Itself 112
6.8. Timing Effects on First Marriage 113
6.8.1. Measuring Timing Effects on First Marriage 114
6.8.2. Timing Effects on First Marriage in England and Wales
and the United States 115
6.9. Timing Effects on Divorce 116
6.9.1. Measuring Timing Effects on Divorce 118
6.9.2. Timing Effects on Divorce in the United States 119
6.10. Summary 120
6.11. Exercises 121
7. Dynamic Birth Death (Multi Age) Models 123
7.1. Introduction 123
7.2. Models Where the Age Specific Rates Are Implicit 123
7.2.1. Considering Models With a Constant
Generation Length 124
7.2.2. Cyclical Models With a Constant Generation
Length 126
7.2.3. Intergenerational Relationships in a Simple Model
With Sinusoidal Births 128
7.3. Metastability, A Closed Form Extension of Stability 132
7.3.1. Deriving the Discrete Metastable Model 132
7.3.2. The Continuous Metastable Model 135
7.3.3. Modeling Fertility Transitions and Their Associated
Momentum 138
7.4. Intrinsically Dynamic Models, An Alternative Extension
of Stability 142
7.4.1. The Two Age Group Intrinsically Dynamic Model 143
7.4.2. The Three Age Group Intrinsically Dynamic Model 146
7.4.3. The n Age Group Intrinsically Dynamic Model 148
7.4.4. IDM Birth Trajectories 149
viii CONTENTS
7.4.5. Observed Populations as IDM Populations 150
7.4.6. Transitions and Momentum in IDM Populations 150
7.5. Finding Rates Consistent With a Known Birth Trajectory 152
7.5.1. Hyperstable Models 153
7.5.2. Models With Proportional Rates 155
7.6. Summary 155
7.7. Exercises 156
8. Dynamic Multistate Models 161
8.1. Introduction 161
8.2. Cohort Multistate Models With Proportional Transfer Rates 161
8.2.1. Relationships in Proportional Transfer Rate (PTR) Models 162
8.2.2. PTR Models With 2 Living States 165
8.2.3. Hierarchical PTR Models 166
8.2.4. A PTR Model of Marriage, Divorce, and Remarriage 170
8.3. Multistate Metastable Models 172
8.4. Multistate Intrinsically Dynamic Models 174
8.4.1. The Restricted Two Living State Uniform Growth Model 174
8.4.2. Additional Two Living State Models 178
8.4.3. The Restricted No Growth IDM With Three Living States 180
8.4.4. The Restricted Uniform Growth IDM With n Living
States 181
8.5. Multistate Hyperstability 181
8.5.1. Deriving the Multistate Hyperstable Equations 181
8.5.2. Relationships Between the Multi Age and Multistate
Hyperstable Models 184
8.5.3. A Further Examination of the Dynamic Two Living State
Model 185
8.6. Finding Rates Consistent With Multistate Population
Distributions 188
8.6.1. Estimating Multistate Arrays Through Iterative
Proportional Fitting 189
8.6.2. Estimating Multistate Rates By the Relative State
Attraction (RSA) Method 190
8.6.3. Evaluating the IPF and RSA Approaches 193
8.7. Summary 196
8.8. Exercises 197
9. Dynamic Models With Multiple Ages and States 203
9.1. Introduction 203
9.2. The Multi Age and State Hyperstable (MASH) Model 204
CONTENTS ix
9.2.1. Specifying the MASH Model 204
9.2.2. An Illustrative Application 207
9.3. The Multi Age and State Metastable (MASM) Model 209
9.4. Summary and Overview 212
9.4.1. Chapter Summary 212
9.4.2. Overview and Recapitulation 212
9.5. Exercises 214
Appendix A Matrices and Their Eigenstructure 217
Appendix B Selected Answers to Exercises 221
Appendix C Index of the Principal Symbols Used 225
References 231
Author Index 241
Subject Index 245 |
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| index_date | 2024-07-02T17:39:16Z |
| indexdate | 2024-07-09T20:58:02Z |
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| series | The Springer series on demographic methods and population analysis |
| series2 | The Springer series on demographic methods and population analysis |
| spelling | Dynamic population models by Robert Schoen Dordrecht Springer c2006 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier The Springer series on demographic methods and population analysis 17 Includes bibliographical references (p. 231-239) and indexes Mathematisches Modell Population Mathematical models Schön, Robert Sonstige oth Erscheint auch als Druck-Ausgabe, Hardcover 1-402-05229-4 The Springer series on demographic methods and population analysis 17 (DE-604)BV046949235 17 https://doi.org/10.1007/1-4020-5230-8 Verlag Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015666376&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dynamic population models The Springer series on demographic methods and population analysis Mathematisches Modell Population Mathematical models |
| title | Dynamic population models |
| title_auth | Dynamic population models |
| title_exact_search | Dynamic population models |
| title_exact_search_txtP | Dynamic population models |
| title_full | Dynamic population models by Robert Schoen |
| title_fullStr | Dynamic population models by Robert Schoen |
| title_full_unstemmed | Dynamic population models by Robert Schoen |
| title_short | Dynamic population models |
| title_sort | dynamic population models |
| topic | Mathematisches Modell Population Mathematical models |
| topic_facet | Mathematisches Modell Population Mathematical models |
| url | https://doi.org/10.1007/1-4020-5230-8 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015666376&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV046949235 |
| work_keys_str_mv | AT schonrobert dynamicpopulationmodels |