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Statistical Demography and Forecasting

✍ Scribed by Juha Alho, Bruce Spencer


Publisher
Springer
Year
2005
Tongue
English
Leaves
431
Series
Springer Series in Statistics
Edition
1
Category
Library

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✦ Synopsis


Sustainability of pension systems, intergeneration fiscal equity under population aging, and accounting for health care benefits for future retirees are examples of problems that cannot be solved without understanding the nature of population forecasts and their uncertainty. Similarly, the accuracy of population estimates directly affects both the distributions of formula-based government allocations to sub-national units and the apportionment of political representation. The book develops the statistical foundation for addressing such issues. Areas covered include classical mathematical demography, event history methods, multi-state methods, stochastic population forecasting, sampling and census coverage, and decision theory. The methods are illustrated with empirical applications from Europe and the U.S. For statisticians the book provides a unique introduction to demographic problems in a familiar language. For demographers, actuaries, epidemiologists, and professionals in related fields, the book presents a unified statistical outlook on both classical methods of demography and recent developments. To facilitate its classroom use, exercises are included. Over half of the book is readily accessible to undergraduates, but more maturity may be required to benefit fully from the complete text. Knowledge of differential and integral calculus, matrix algebra, basic probability theory, and regression analysis is assumed. Juha M. Alho is Professor of Statistics, University of Joensuu, Finland, and Bruce D. Spencer is Professor of Statistics and Faculty Fellow at the Institute for Policy Research, Northwestern University. Both have contributed extensively to statistical demography and served in advisory roles and as statistical consultants in the field.

✦ Table of Contents


Preface......Page 5
Acknowledgments......Page 6
Contents......Page 7
List of Examples......Page 14
List of Figures......Page 19
1. Role of Statistical Demography......Page 22
3. Statistical Notation and Preliminaries......Page 25
1. Populations: Open and Closed......Page 30
3. Censuses and Population Registers......Page 36
4. Lexis Diagram and Classiβ€œcation of Events......Page 37
5.2. Cohort and Case-Control Studies......Page 40
5.3. Advantages and Disadvantages......Page 41
5.4. Confounding......Page 43
6. Sampling in Censuses and Dual System Estimation......Page 45
3 Sampling Designs and Inference......Page 52
1. Simple Random Sampling......Page 53
2. Subgroups and Ratios......Page 56
3.1. Introduction......Page 57
3.2. Strati.ed Simple Random Sampling......Page 58
3.3. Design Effect for Strati.ed Simple Random Sampling......Page 59
3.4. Poststrati.cation......Page 60
4.1. Why Weight?......Page 61
4.2. Forming Weights......Page 62
4.3. Non-Response Adjustments......Page 64
4.4. Effect of Weighting on Precision......Page 66
5.1. Introduction......Page 67
5.3. Single Stage Sampling without Replacement......Page 68
5.4. Multi-Stage Sampling......Page 70
5.5. Strati.ed Samples......Page 71
6. Systematic Sampling......Page 73
7.1. Central Limit Theorems......Page 74
7.2. The Delta Method......Page 76
7.3. Estimating Equations......Page 77
8.1. Jackknife Estimates......Page 82
8.2. Bootstrap Estimates......Page 83
8.3. Replication Weights......Page 84
1. Exponential Distribution......Page 92
2.1. Hazards and Survival Probabilities......Page 97
2.2.1. Life Expectancy......Page 100
2.2.2. Life Table Populations and Stable Populations......Page 102
2.2.3. Changing Mortality......Page 103
2.2.4. Basics of Pension Funding......Page 105
2.3. Kaplan-Meier and Nelson-Aalen Estimators......Page 106
2.4. Estimation Based on Occurrence-Exposure Rates......Page 109
3. Estimating Survival Proportions......Page 112
4.1. Poisson Process Model of Childbearing......Page 114
4.2. Summary Measures of Fertility and Reproduction......Page 117
4.3.1. Cohort Fertility is Smoother......Page 122
4.3.2. Adjusting for Timing......Page 124
4.3.3. Effect of Parity on Pure Period Measures......Page 125
4.4. Multiple Births and Effect of Pregnancy on Exposure Time......Page 127
5. Poisson Character of Demographic Events......Page 128
6. Simulation of Waiting Times and Counts......Page 130
5 Regression Models for Counts and Survival......Page 138
1.1. Exponential Family......Page 139
1.3. Maximum Likelihood Estimation......Page 140
1.4. Numerical Solution......Page 141
1.5. Inferences......Page 142
1.6. Diagnostic Checks......Page 143
2.1. Interpretation of Parameters and Goodness of Fit......Page 144
2.2. Examples of Logistic Regression......Page 145
2.3. Applicability in Case-Control Studies......Page 150
3.1. Interpretation of Parameters......Page 151
3.2. Examples of Poisson Regression......Page 152
3.3. Standardization......Page 154
3.4. Loglinear Models for Capture-Recapture Data......Page 157
4. Overdispersion and Random Effects......Page 159
4.2. Marginal Models for Overdispersion......Page 160
4.3. Random Effect Models......Page 161
5. Observable Heterogeneity in Capture-Recapture Studies......Page 164
6. Bilinear Models......Page 167
7. Proportional Hazards Models for Survival......Page 171
8. Heterogeneity and Selection by Survival......Page 175
9. Estimation of Population Density......Page 177
10. Simulation of the Regression Models......Page 179
6 Multistate Models and Cohort-Component Book-Keeping......Page 187
1.1. Numerical Solution Using Runge-Kutta Algorithm......Page 188
1.2. Extension to Multistate Case......Page 189
1.3.1. Heterogeneity Attributable to Duration......Page 193
1.3.2. Forms of Duration-Dependence......Page 194
1.3.3. Aspects of Computer Implementation......Page 195
1.4. Nonparametric Intensity Estimation......Page 196
1.5. Analysis of Nuptiality......Page 198
1.6. A Model for Disability Insurance......Page 200
2.1. Matrix Formulation......Page 201
2.2. Stable Populations......Page 204
2.3. Weak Ergodicity......Page 206
3.2. Parametric Models......Page 207
3.2.2. Bilinear Models......Page 208
4. Demographic Functionals......Page 210
6. Markov Chain Models......Page 212
1. Trends, Random Walks, and Volatility......Page 219
2. Linear Stationary Processes......Page 222
2.1.1. De.nition and Basic Properties......Page 223
2.1.2. ARIMA Models......Page 224
2.1.3. Practical Modeling......Page 227
2.2.1. Stationary Processes......Page 231
2.2.2. Integrated Processes......Page 232
3.1. Differencing......Page 237
3.2. Regression......Page 239
3.3. Structural Models......Page 240
4. Heteroscedastic Innovations......Page 241
4.1. Deterministic Models of Volatility......Page 242
4.2. Stochastic Volatility......Page 243
8 Uncertainty in Demographic Forecasts: Concepts, Issues, and Evidence......Page 247
1.2. Whelpton’s Legacy......Page 249
1.3. Do We Know Better Now?......Page 252
2.1. Age-Speci.c Mortality......Page 255
2.2. Cause-Speci.c Mortality......Page 257
3.2.1. Error Classi.cations......Page 259
3.3.1. Classes of Parametric Models......Page 261
3.3.2. Data Period Bias......Page 262
3.4. Feedback Effects of Forecasts......Page 263
3.5.1. Uncertainty in Terms of Subjective Probabilities......Page 265
3.5.2. Frequency Properties of Prediction Intervals......Page 269
3.6.1. Expert Arguments......Page 270
3.6.2. Scenarios......Page 271
4. Practical Error Assessment......Page 272
4.1. Error Measures......Page 273
4.2. Baseline Forecasts......Page 274
4.3.1. An Error Model for Growth Rates......Page 277
4.3.2. Second Moments......Page 278
4.3.3. Predictive Distributions for Countries and the World......Page 280
4.4. Random Jump-Off Values......Page 282
4.4.1. Jump-Off Population......Page 283
4.4.2. Mortality......Page 284
5. Measuring Correlatedness......Page 285
1. Tornqvist Β¨ s Contribution......Page 290
2.1. Regression with a Known Covariance Structure......Page 292
2.2. Random Walks......Page 295
2.3. ARIMA(1,1,0) Models......Page 297
3. Forecast as a Database and Its Uses......Page 298
4. Parametrizations of Covariance Structure......Page 299
4.1. Effect of Correlations on the Variance of a Sum......Page 300
4.2. Scaled Model for Error......Page 301
4.3. Structure of Error in Migration Forecasts......Page 304
5.1. Births......Page 305
5.2. General Linear Growth......Page 306
6. Simulation Approach and Computer Implementation......Page 308
7.1. Altering a Distributional Form......Page 310
7.2.1. Use of Seeds......Page 313
7.2.2. Sorting Techniques......Page 314
1. Introduction......Page 317
2.1. Effects on Mortality Rates......Page 318
2.3. Effects on Evaluation of Past Population Forecasts......Page 319
3. Use of Demographic Analysis to Assess Error in U.S. Censuses......Page 320
4. Assessment of Dual System Estimates of Population Size......Page 321
5.1. A Probability Model for the Census......Page 324
5.2. Poststrati.cation......Page 325
5.3. Overview of Error Components......Page 326
5.4. Data Error Bias......Page 329
5.5.1. Synthetic Estimation Bias and Correlation Bias......Page 330
5.5.2. Poststrati.ed Estimator......Page 331
5.6. Estimation of Correlation Bias in a Poststrati.ed Dual System Estimator......Page 333
5.7. Estimation of Synthetic Estimation Bias in a Poststrati.ed Dual System Estimator......Page 335
6.1. Overview......Page 337
6.2. Computation......Page 338
1.1. Adjustment Factor for Mortality Change......Page 348
1.2. Sampling Variation in Pension Adjustment Factors......Page 350
1.3. The Predictive Distribution of the Pension Adjustment Factor......Page 351
2. Fertility Dependent Pension Bene.ts......Page 353
3. Measuring Sustainability......Page 356
4. State Aid to Municipalities......Page 358
5. Public Liabilities......Page 360
5.2. Wealth in Terms of Random Returns and Discounting......Page 361
5.3. Random Public Liability......Page 362
1. Introduction......Page 365
2. Small Area Analysis......Page 366
3.1. Theoretical Construction......Page 367
3.1.1. Apportionment of the U.S. House of Representatives......Page 368
3.1.2. Rationale Behind Allocation Formulas......Page 369
3.2. Effect of Inaccurate Demographic Statistics......Page 370
3.3. Beyond Accuracy......Page 371
4.1. Introduction......Page 372
4.2. Decision Theory for Statistical Agencies......Page 374
4.3. Loss Functions for Small Area Estimates......Page 378
4.4.1. Apportionment......Page 380
4.4.2. Redistricting......Page 381
4.5.1. Effects of Overand Under-Allocation......Page 382
4.5.2. Formula Nonoptimality......Page 383
5. Comparing Risks of Adjusted and Unadjusted Census Estimates......Page 384
5.1. Accounting for Variances of Bias Estimates......Page 385
6. Decision Analysis of Adjustment for Census Undercount......Page 386
7. Cost-Bene.t Analysis of Demographic Data......Page 388
References......Page 392
Author Index......Page 418
Subject Index......Page 426


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