Multidimensional Mathematical Demography

Contributors

Preface

Acknowledgments


1 Multidimensional Mathematical Demography: An Overview


1. Introduction


2. Recent Developments in Multistate Demographic Models


3. The Conference on Multidimensional Mathematical Demography


4. Organization of the Volume


5. Conclusions and Next Steps


2 Multidimensional Population Analysis with Incomplete Data


1. Introduction


2. Data Requirements and Data Availability


3. Modeling the Data in the Account


4. Parameter Estimation from Available Data


5. Numerical Applications


6. Conclusion


3 Model Schedules in Multistate Demographic Analysis: The Case of Migration


1. Synthetic Model Migration Schedules: I. The Correlational Perspective


2. Synthetic Model Migration Schedules: II. The Relational Perspective


3. Concluding Remarks


4 Multistate Life Table Methodology: A Probabilist Critique


1. Introduction


2. The Markov Chain Model


3. Integration Hypotheses


4. Occurrence/Exposure Rates


5. Other Observational Plans


6. Sampling and Heterogeneity


5 Statistical Methods for Markov-Generated Increment-Decrement Life Tables with Polynomial Gross Flow Functions


1. Introduction


2. Model Specification


3. Age-Specific Methods for Occurrence/Exposure Rates


4. Marital Dissolution and Remarriage in Sweden: Application and Comparison of Methods


5. Application of the Methods to Survivorship Proportions


6. Concluding Comments


6 Transition Probability Estimation in Increment-Decrement Life Tables: Using Mobility Data from a Census or a Survey


1. Introduction


2. Approach A: Estimation from Mobility Rates


3. Approach B: Estimation from Transition Proportions


4. A Brief Comparison of the Two Alternative Approaches


5. Conclusion


7 Generalizing the Life Table Model to Incorporate Interactions between the Sexes


1. Introduction


2. Life Table Models


3. A TWOFIDS Model for the United States/California 1970


4. Conclusion

Appendix: The TWONUP First Marriage Matrix

Appendix: Input Data for the TWOFIDS Model


8 Multiregional Population Projections by Place of Previous Residence


1. Introduction


2. Stationary and Stable Population Distributions


3. Multiregional Population Projections by Place of Birth


4. Multiregional Population Projections by Place of Previous Residence


5. Native-Dependent Multiregional Population Projections


6. Conclusion

Appendix A: Native-Independent Multistate Projection: Biregional Model

Appendix B: Separation Factors


9 Multiregional Age-Structured Populations with Changing Rates: Weak and Stochastic Ergodic Theorems


1. Introduction


2. The Formalism of Multiregional Population Models


3. Weak Ergodic Theorems for Multiregional Populations Models


4. Stochastic Ergodic Theorems


5. Relative Rates of Convergence


6. Extensions and Applications


10 High- and Low-Intensity Model of Mobility


1. Introduction


2. The High- and Low-Intensity Model of Mobility


3. Solution of the Model


4. Verification of the Model


5. Implementation of the Model


6. A Possible Extension

Appendix


11 Increment-Decrement Life Tables and Semi-Markovian Processes from a Sample Path Perspective


1. Introduction


2. Defining Basic Probabilities on Sample Paths


3. Semi-Markovian Processes


4. Parametric Forms of One-Step Transition Matrices, Competing Risks, and Likelihood Functions


5. One-Step Transition Matrices and Multiple Decrement Life Tables


6. The Kolmogorov Differential Equations


7. Integral Equations for Age-Dependent Semi-Markov Processes


8. Numerical Algorithms for Solving Renewal-Type Equations


12 Population Heterogeneity in Demographic Models


1. Introduction


2. Duration Models and Unobservables


3. Sensitivity of Parameter Estimates


4. Qualitative Properties of Mixtures


5. Estimation in Mixture Models


6. Performance of the EM Algorithm and Revised Estimates for the Kiefer-Neumann Data


7. Discussion and Conclusions

Index

Participants