Analysis of Poverty Data by Small Area Estimation
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Monica Pratesi, Department of Economics and Management, University of Pisa, Italy.
Monica's research field includes small area estimation, inference in elusive populations, nonresponse, design effect in fitting statistical models. Monica is currently involved as researcher and reference person of the DEM-UNIPI in the project EFRAME(European FRAmework for MEasuring progress) funded under the 7th FP (eframeproject.eu/).
Content
Preface xvii
Acknowledgements xxiii
About the Editor xxv
List of Contributors xxvii
1 Introduction on Measuring Poverty at Local Level Using Small Area Estimation Methods 1
Monica Pratesi and Nicola Salvati
1.1 Introduction 1
1.2 Target Parameters 2
1.2.1 Definition of the Main Poverty Indicators 2
1.2.2 Direct and Indirect Estimate of Poverty Indicators at Small Area Level 3
1.3 Data-related and Estimation-related Problems for the Estimation of Poverty Indicators 5
1.4 Model-assisted and Model-based Methods Used for the Estimation of Poverty Indicators: a Short Review 7
1.4.1 Model-assisted Methods 7
1.4.2 Model-based Methods 12
References 15
Part I DEFINITION OF INDICATORS AND DATA COLLECTION AND INTEGRATION METHODS
2 Regional and Local Poverty Measures 21
Achille Lemmi and Tomasz Panek
2.1 Introduction 21
2.2 Poverty - Dilemmas of Definition 22
2.3 Appropriate Indicators of Poverty and Social Exclusion at Regional and Local Levels 23
2.3.1 Adaptation to the Regional Level 23
2.4 Multidimensional Measures of Poverty 25
2.4.1 Multidimensional Fuzzy Approach to Poverty Measurement 25
2.4.2 Fuzzy Monetary Depth Indicators 26
2.5 Co-incidence of Risks of Monetary Poverty and Material Deprivation 30
2.6 Comparative Analysis of Poverty in EU Regions in 2010 31
2.6.1 Data Source 31
2.6.2 Object of Interest 31
2.6.3 Scope and Assumptions of the Empirical Analysis 32
2.6.4 Risk of Monetary Poverty 32
2.6.5 Risk of Material Deprivation 33
2.6.6 Risk of Manifest Poverty 37
2.7 Conclusions 38
References 39
3 Administrative and Survey Data Collection and Integration 41
Alessandra Coli, Paolo Consolini and Marcello D'Orazio
3.1 Introduction 41
3.2 Methods to Integrate Data from Different Data Sources: Objectives and Main Issues 43
3.2.1 Record Linkage 43
3.2.2 Statistical Matching 46
3.3 Administrative and Survey Data Integration: Some Examples of Application in Well-being and Poverty Studies 50
3.3.1 Data Integration for Measuring Disparities in Economic Well-being at the Macro Level 51
3.3.2 Collection and Integration of Data at the Local Level 53
3.4 Concluding Remarks 56
References 57
4 Small Area Methods and Administrative Data Integration 61
Li-Chun Zhang and Caterina Giusti
4.1 Introduction 61
4.2 Register-based Small Area Estimation 63
4.2.1 Sampling Error: A Study of Local Area Life Expectancy 63
4.2.2 Measurement Error due to Progressive Administrative Data 65
4.3 Administrative and Survey Data Integration 68
4.3.1 Coverage Error and Finite-population Bias 68
4.3.2 Relevance Error and Benchmarked Synthetic Small Area Estimation 70
4.3.3 Probability Linkage Error 75
4.4 Concluding Remarks 80
References 81
Part II IMPACT OF SAMPLING DESIGN, WEIGHTING AND VARIANCE ESTIMATION
5 Impact of Sampling Designs in Small Area Estimation with Applications to Poverty Measurement 85
Jan Pablo Burgard, Ralf Münnich and Thomas Zimmermann
5.1 Introduction 85
5.2 Sampling Designs in our Study 87
5.3 Estimation of Poverty Indicators 90
5.3.1 Design-based Approaches 90
5.3.2 Model-based Estimators 92
5.4 Monte Carlo Comparison of Estimation Methods and Designs 96
5.5 Summary and Outlook 105
Acknowledgements 106
References 106
6 Model-assisted Methods for Small Area Estimation of Poverty Indicators 109
Risto Lehtonen and Ari Veijanen
6.1 Introduction 109
6.1.1 General 109
6.1.2 Concepts and Notation 110
6.2 Design-based Estimation of Gini Index for Domains 111
6.2.1 Estimators 111
6.2.2 Simulation Experiments 114
6.2.3 Empirical Application 116
6.3 Model-assisted Estimation of At-risk-of Poverty Rate 117
6.3.1 Assisting Models in GREG and Model Calibration 117
6.3.2 Generalized Regression Estimation 119
6.3.3 Model Calibration Estimation 120
6.3.4 Simulation Experiments 122
6.3.5 Empirical Example 123
6.4 Discussion 124
6.4.1 Empirical Results 124
6.4.2 Inferential Framework 125
6.4.3 Data Infrastructure 125
References 126
7 Variance Estimation for Cumulative and Longitudinal Poverty Indicators from Panel Data at Regional Level 129
Gianni Betti, Francesca Gagliardi and Vijay Verma
7.1 Introduction 129
7.2 Cumulative vs. Longitudinal Measures of Poverty 130
7.2.1 Cumulative Measures 130
7.2.2 Longitudinal Measures 131
7.3 Principle Methods for Cross-sectional Variance Estimation 131
7.4 Extension to Cumulation and Longitudinal Measures 133
7.5 Practical Aspects: Specification of Sample Structure Variables 134
7.6 Practical Aspects: Design Effects and Correlation 136
7.6.1 Components of the Design Effect 136
7.6.2 Estimating the Components of Design Effect 138
7.6.3 Estimating other Components using Random Grouping of Elements 139
7.7 Cumulative Measures and Measures of Net Change 140
7.7.1 Estimation of the Measures 140
7.7.2 Variance Estimation 141
7.8 An Application to Three Years' Averages 141
7.8.1 Computation Given Limited Information on Sample Structure in EU-SILC 141
7.8.2 Direct Computation 144
7.8.3 Empirical Results 145
7.9 Concluding Remarks 146
References 147
Part III SMALL AREA ESTIMATION MODELING AND ROBUSTNESS
8 Models in Small Area Estimation when Covariates are Measured with Error 151
Serena Arima, Gauri S. Datta and Brunero Liseo
8.1 Introduction 151
8.2 Functional Measurement Error Approach for Area-level Models 153
8.2.1 Frequentist Method for Functional Measurement Error Models 154
8.2.2 Bayesian Method for Functional Measurement Error Models 156
8.3 Small Area Prediction with a Unit-level Model when an Auxiliary Variable is Measured with Error 156
8.3.1 Functional Measurement Error Approach for Unit-level Models 157
8.3.2 Structural Measurement Error Approach for Unit-level Models 160
8.4 Data Analysis 162
8.4.1 Example 1: Median Income Data 162
8.4.2 Example 2: SAIPE Data 165
8.5 Discussion and Possible Extensions 169
Acknowledgements 169
Disclaimer 170
References 170
9 Robust Domain Estimation of Income-based Inequality Indicators 171
Nikos Tzavidis and Stefano Marchetti
9.1 Introduction 171
9.2 Definition of Income-based Inequality Measures 172
9.3 Robust Small Area Estimation of Inequality Measures with M-quantile Regression 173
9.4 Mean Squared Error Estimation 176
9.5 Empirical Evaluations 176
9.6 Estimating the Gini Coefficient and the Quintile Share Ratio for Unplanned Domains in Tuscany 180
9.7 Conclusions 183
References 185
10 Nonparametric Regression Methods for Small Area Estimation 187
M. Giovanna Ranalli, F. Jay Breidt and Jean D. Opsomer
10.1 Introduction 187
10.2 Nonparametric Methods in Small Area Estimation 188
10.2.1 Nested Error Nonparametric Unit Level Model Using Penalized Splines 189
10.2.2 Nested Error Nonparametric Unit Level Model Using Kernel Methods 191
10.2.3 Generalized Responses 192
10.2.4 Robust Approaches 192
10.3 A Comparison for the Estimation of the Household Per-capita Consumption Expenditure in Albania 195
10.4 Concluding Remarks 202
References 202
Part IV SPATIO-TEMPORAL MODELING OF POVERTY
11 Area-level Spatio-temporal Small Area Estimation Models 207
María Dolores Esteban, Domingo Morales and Agustín Pérez
11.1 Introduction 207
11.2 Extensions of the Fay-Herriot Model 209
11.3 An Area-level Model with MA(1) Time Correlation 212
11.4 EBLUP and MSE 214
11.5 EBLUP of Poverty Proportions 215
11.6 Simulations 216
11.6.1 Simulation 1 216
11.6.2 Simulation 2 217
11.7 R Codes 220
11.8 Concluding Remarks 220
Appendix 11.A: MSE Components 221
11.A.1 Calculation of g1(¿¿¿¿) 221
11.A.2 Calculation of g2(¿¿¿¿) 221
11.A.3 Calculation of g3(¿¿¿¿) 222
Acknowledgements 224
References 224
12 Unit Level Spatio-temporal Models 227
Maria Chiara Pagliarella and Renato Salvatore
12.1 Unit Level Models 230
12.2 Spatio-temporal Time-varying Effects Models 232
12.3 State Space Models with Spatial Structure 234
12.4 The Italian EU-SILC Data: an Application with the Spatio-temporal Unit Level Models 236
12.5 Concluding Remarks 239
Appendix 12.A: Restricted Maximum Likelihood Estimation 240
Appendix 12.B: Mean Squared Error Estimation of the Unit Level State Space Model 241
References 242
13 Spatial Information and Geoadditive Small Area Models 245
Chiara Bocci and Alessandra Petrucci
13.1 Introduction 245
13.2 Geoadditive Models 247
13.3 Geoadditive Small Area Model for Skewed Data 248
13.4 Small Area Mean Estimators 250
13.5 Estimation of the Household Per-capita Consumption Expenditure in Albania 251
13.5.1 Data 251
13.5.2 Results 253
13.6 Concluding Remarks and Open Questions 258
Acknowledgement 259
References 259
Part V SMALL AREA ESTIMATION OF THE DISTRIBUTION FUNCTION OF INCOME AND INEQUALITIES
14 Model-based Direct Estimation of a Small Area Distribution Function 263
Hukum Chandra, Nicola Salvati and Ray Chambers
14.1 Introduction 263
14.2 Estimation of the Small Area Distribution Function 264
14.3 Model-based Direct Estimator for the Estimation of the Distribution Function of Equivalized Income in the Toscana, Lombardia and Campania Provinces of Italy 268
14.4 Final Remarks 275
References 276
15 Small Area Estimation for Lognormal Data 279
Emily Berg, Hukum Chandra and Ray Chambers
15.1 Introduction 279
15.2 Literature on Small Area Estimation for Skewed Data 280
15.3 Small Area Predictors for a Unit-Level Lognormal Model 282
15.3.1 The Linear Unit-Level Mixed Model 282
15.3.2 A Synthetic Estimator 283
15.3.3 A Model-Based Direct Estimator 285
15.3.4 An Empirical Bayes Predictor 286
15.4 Simulations 287
15.4.1 Comparison of Synthetic, TrMBDE, and EB Predictors 287
15.4.2 Bias and Robustness of the EB Predictor 291
15.4.3 Comparison of Lognormal and Gamma Distributions 291
15.5 Concluding Remarks 294
Appendix 15.A: Mean Squared Error Estimation for the Empirical Best Predictor 295
References 296
16 Bayesian Beta Regression Models for the Estimation of Poverty and Inequality Parameters in Small Areas 299
Enrico Fabrizi, Maria Rosaria Ferrante and Carlo Trivisano
16.1 Introduction 299
16.2 Direct Estimation 300
16.3 Small Area Estimation of the At-risk-of-poverty Rate 302
16.3.1 The Model 302
16.3.2 Data Analysis 304
16.4 Small Area Estimation of the Material Deprivation Rates 305
16.4.1 The Model 305
16.4.2 Data Analysis 306
16.5 Joint Estimation of the At-risk-of-poverty Rate and the Gini Coefficient 308
16.5.1 The Models 308
16.5.2 Data Analysis 310
16.6 A Short Description of Markov Chain Monte Carlo Algorithms and R Software Codes 312
16.7 Concluding Remarks 312
References 313
17 Empirical Bayes and Hierarchical Bayes Estimation of Poverty Measures for Small Areas 315
John N. K. Rao and Isabel Molina
17.1 Introduction 315
17.2 Poverty Measures 316
17.3 Fay-Herriot Area Level Model 317
17.4 Unit Level Nested Error Linear Regression Model 319
17.4.1 ELL/World Bank Method 319
17.4.2 Empirical Bayes Method 321
17.4.3 Hierarchical Bayes Method 322
17.5 Application 323
17.6 Concluding Remarks 324
References 324
Part VI DATA ANALYSIS AND APPLICATIONS
18 Small Area Estimation Using Both Survey and Census Unit Record Data 327
Stephen J. Haslett
18.1 Introduction 327
18.2 The ELL Implementation Process and Methodology 329
18.2.1 ELL: Implementation Process 329
18.2.2 ELL Methodology: Survey Regression, Contextual Effects, Clustering, and the Bootstrap 331
18.2.3 Fitting Survey-based Models 334
18.2.4 Residuals and the Bootstrap 335
18.2.5 ELL: Linkages to Other Related Methods 338
18.3 ELL - Advantages, Criticisms and Disadvantages 339
18.4 Conclusions 344
References 346
19 An Overview of the U.S. Census Bureau's Small Area Income and Poverty Estimates Program 349
William R. Bell, Wesley W. Basel and Jerry J. Maples
19.1 Introduction 349
19.2 U.S. Poverty Measure and Poverty Data Sources 351
19.2.1 Poverty Measure and Survey Data Sources 351
19.2.2 Administrative Data Sources Used for Covariate Information 354
19.3 SAIPE Poverty Models and Estimation Procedures 356
19.3.1 State Poverty Models 357
19.3.2 County Poverty Models 363
19.3.3 School District Poverty Estimation 368
19.3.4 Major Changes Made in SAIPE Models and Estimation Procedures 372
19.4 Current Challenges and Recent SAIPE Research 374
19.5 Conclusions 375
References 376
20 Poverty Mapping for the Chilean Comunas 379
Carolina Casas-Cordero Valencia, Jenny Encina and Partha Lahiri
20.1 Introduction 379
20.2 Chilean Poverty Measures and Casen 381
20.2.1 The Poverty Measure Used in Chile 381
20.2.2 The Casen Survey 382
20.3 Data Preparation 383
20.3.1 Comuna Level Data Derived from Casen 2009 383
20.3.2 Comuna Level Administrative Data 387
20.4 Description of the Small Area Estimation Method Implemented in Chile 391
20.4.1 Modeling 394
20.4.2 Estimation of A and ¿¿¿¿ 395
20.4.3 Empirical Bayes Estimator of ¿¿¿¿i 395
20.4.4 Limited Translation Empirical Bayes Estimator of ¿¿¿¿i 395
20.4.5 Back-transformation and raking 396
20.4.6 Confidence intervals for the poverty rates 396
20.5 Data Analysis 397
20.6 Discussion 399
Acknowledgements 401
References 402
21 Appendix on Software and Codes Used in the Book 405
Antonella D'Agostino, Francesca Gagliardi and Laura Neri
21.1 Introduction 405
21.2 R and SAS Software: a Brief Note 406
21.3 Getting Started: EU-SILC Data 409
21.4 A Quick Guide to the Scripts 410
21.4.1 Basics of the Scripts 410
21.4.2 A Quick guide to Chapter 5 (Impact of Sampling Designs in Small Area Estimation with Applications to Poverty Measurement) 412
21.4.3 A Quick guide to Chapter 6 (Model-assisted Methods for Small Area Estimation of Poverty Indicators) 412
21.4.4 A Quick Guide to Chapter 7 (Variance Estimation for Cumulative and Longitudinal Poverty Indicators from Panel Data at Regional Level) 414
21.4.5 A Quick Guide to Chapter 8 (Models in Small Area Estimation when Covariates are Measured with Error) 415
21.4.6 A Quick Guide to Chapter 9 (Robust Domain Estimation of Income-based Inequality Indicators) 416
21.4.7 A Quick Guide to Chapter 10 (Nonparametric Regression Methods for Small Area Estimation) 417
21.4.8 A Quick Guide to Chapter 11 (Area-level Spatio-temporal Small Area Estimation Models) 418
21.4.9 A Quick Guide to Chapter 12 (Unit Level Spatio-temporal Models) 419
21.4.10 A Quick Guide to Chapter 13 (Spatial Information and Geoadditive Small Area Models) 420
21.4.11 A Quick guide to Chapter 14 (Model-based Direct Estimation of a Small Area Distribution Function) 422
21.4.12 A Quick Guide to Chapter 16 (Bayesian Beta Regression Models for the Estimation of Poverty and Inequality Parameters in Small Areas) 423
21.4.13 A Quick Guide to Chapter 17 (Empirical Bayes and Hierarchical Bayes Estimation of Poverty Measures for Small Areas) 424
21.4.14 A Quick Guide to Chapter 18 - (Small Area Estimation Using Both Survey and Census Unit Record Data: Links, Alternatives, and the
Central Roles of Regression and Contextual Variables) 425
References 426
Author Index 427
Subject Index 431
