Dynamic Population Models

Some Basic Concepts......Page 15
The Basic Life Table......Page 17
Multiple Decrement and Cause Eliminated Life Tables......Page 21
Continuous Stable Models......Page 23
Discrete Stable Models......Page 26
Scalar Multistate Equations......Page 28
Matrix Multistate Equations......Page 30
Multistate Expectancies and Summary Measures......Page 33
The Multistate Stable Population......Page 34
Summary......Page 36
Exercises......Page 37
Conditions for Stability......Page 41
The Speed of Convergence......Page 43
Some Explicit Analyses of Convergence......Page 47
Convergence in a 33 Leslie Model......Page 48
Convergence in a Two Living State Multistate Model......Page 51
Summary......Page 54
Exercises......Page 55
The Basic Dynamics......Page 57
Momentum and Aging......Page 60
Momentum Under Gradual Declines to Stationarity......Page 64
Spatial Momentum......Page 65
Spatial Momentum in Two Region Models Without Age......Page 66
Decomposing Total Multistate Population Momentum......Page 67
Summary......Page 70
Exercises......Page 71
Marginal Change in Fixed Rate Models......Page 73
Changes in Stable Population Measures......Page 74
Changes in Stable Population Characteristics......Page 76
Recognizing Age-Dependent Growth......Page 77
Connections Between Populations Having the Same Vital Rates......Page 79
Derivatives of Aggregate Demographic Measures......Page 81
Marginal Change and Stabilization......Page 84
A Spectral Decomposition of Marginal Change......Page 86
Summary......Page 88
Exercises......Page 89
An Overview of Changes in Human Mortality......Page 93
The Period-Cohort Contrast in Mortality......Page 96
Average Cohort Life Expectancy......Page 97
The Bongaarts-Feeney Approach......Page 99
Relationships in a Shifting Gompertz Model......Page 103
Models of Constant Mortality Decline Over Time......Page 105
Three Models With Linearly Changing Mortality......Page 106
Gaps and Lags Between Period and Cohort Life Expectancies......Page 108
The Modal Age At Death......Page 110
Summary......Page 112
Exercises......Page 113
The Period-Cohort Contrast......Page 115
The Bongaarts-Feeney Approach......Page 117
Average Cohort Fertility......Page 119
Comparing the Bongaarts-Feeney and ACF Approaches......Page 120
Timing Effects in the United States, 1917--97......Page 121
Examining Parity-Specific Period tfrs......Page 124
A Diminishing Population Whose Every Cohort More Than Replaces Itself......Page 126
Timing Effects on First Marriage......Page 127
Measuring Timing Effects on First Marriage......Page 128
Timing Effects on First Marriage in England and Wales and the United States......Page 129
Timing Effects on Divorce......Page 130
Measuring Timing Effects on Divorce......Page 132
Timing Effects on Divorce in the United States......Page 133
Summary......Page 134
Exercises......Page 135
Models Where the Age-Specific Rates Are Implicit......Page 137
Considering Models With a Constant Generation Length......Page 138
Cyclical Models With a Constant Generation Length......Page 140
Intergenerational Relationships in a Simple Model With Sinusoidal Births......Page 142
Deriving the Discrete Metastable Model......Page 146
The Continuous Metastable Model......Page 149
Modeling Fertility Transitions and Their Associated Momentum......Page 152
Intrinsically Dynamic Models, An Alternative Extension of Stability......Page 156
The Two Age Group Intrinsically Dynamic Model......Page 157
The Three Age Group Intrinsically Dynamic Model......Page 160
The n-Age Group Intrinsically Dynamic Model......Page 162
IDM Birth Trajectories......Page 163
Transitions and Momentum in IDM Populations......Page 164
Finding Rates Consistent With a Known Birth Trajectory......Page 166
Hyperstable Models......Page 167
Summary......Page 169
Exercises......Page 170
Cohort Multistate Models With Proportional Transfer Rates......Page 175
Relationships in Proportional Transfer Rate (PTR) Models......Page 176
PTR Models With 2 Living States......Page 179
Hierarchical PTR Models......Page 180
A PTR Model of Marriage, Divorce, and Remarriage......Page 184
Multistate Metastable Models......Page 186
The Restricted Two Living State Uniform Growth Model......Page 188
Additional Two Living State Models......Page 192
The Restricted No Growth IDM With Three Living States......Page 194
Deriving the Multistate Hyperstable Equations......Page 195
Relationships Between the Multi-Age and Multistate Hyperstable Models......Page 198
A Further Examination of the Dynamic Two Living State Model......Page 199
Finding Rates Consistent With Multistate Population Distributions......Page 202
Estimating Multistate Arrays Through Iterative Proportional Fitting......Page 203
Estimating Multistate Rates By the Relative State Attraction (RSA) Method......Page 204
Evaluating the IPF and RSA Approaches......Page 207
Summary......Page 210
Exercises......Page 211
Introduction......Page 217
Specifying the MASH Model......Page 218
An Illustrative Application......Page 221
The Multi-Age and State Metastable (MASM) Model......Page 223
Overview and Recapitulation......Page 226
Exercises......Page 228
Matrices and Their Eigenstructure......Page 231
Selected Answers to Exercises......Page 235
Index of the Principal Symbols Used......Page 239
References......Page 245
Author Index......Page 254
Subject Index......Page 257