Analysis of Poverty Data by Small Area Estimation

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(theta) 221 11.A.2 Calculation of g2(theta) 221 11.A.3 Calculation of g3(theta) 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 beta 395 20.4.3 Empirical Bayes Estimator of theta i 395 20.4.4 Limited Translation Empirical Bayes Estimator of theta 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