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Analysis of Poverty Data by Small Area Estimation

Monica Pratesi (Editor)
ISBN: 978-1-118-81500-7
472 pages
December 2015
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Description

A comprehensive guide to implementing SAE methods for poverty studies and poverty mapping

There is an increasingly urgent demand for poverty and living conditions data, in relation to local areas and/or subpopulations. Policy makers and stakeholders need indicators and maps of poverty and living conditions in order to formulate and implement policies, (re)distribute resources, and measure the effect of local policy actions.

Small Area Estimation (SAE) plays a crucial role in producing statistically sound estimates for poverty mapping. This book offers a comprehensive source of information regarding the use of SAE methods adapted to these distinctive features of poverty data derived from surveys and administrative archives. The book covers the definition of poverty indicators, data collection and integration methods, the impact of sampling design, weighting and variance estimation, the issue of SAE modelling and robustness, the spatio-temporal modelling of poverty, and the SAE of the distribution function of income and inequalities. Examples of data analyses and applications are provided, and the book is supported by a website describing scripts written in SAS or R software, which accompany the majority of the presented methods.

Key features:

  • Presents a comprehensive review of SAE methods for poverty mapping
  • Demonstrates the applications of SAE methods using real-life case studies
  • Offers guidance on the use of routines and choice of websites from which to download them

Analysis of Poverty Data by Small Area Estimation offers an introduction to advanced techniques from both a practical and a methodological perspective, and will prove an invaluable resource for researchers actively engaged in organizing, managing and conducting studies on poverty.

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Table of Contents

Foreword xv

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(𝜽) 221

11.A.2 Calculation of g2(𝜽) 221

11.A.3 Calculation of g3(𝜽) 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 𝛽 395

20.4.3 Empirical Bayes Estimator of 𝜃i 395

20.4.4 Limited Translation Empirical Bayes Estimator of 𝜃i 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

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