Analysis of Poverty Data by Small Area Estimation

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/).

• Foreword xv Preface xviiAcknowledgements xxiiiAbout the Editor xxvList of Contributors xxvii1 Introduction on Measuring Poverty at Local Level Using Small Area Estimation Methods 1Monica Pratesi and Nicola Salvati1.1 Introduction 11.2 Target Parameters 21.2.1 Definition of the Main Poverty Indicators 21.2.2 Direct and Indirect Estimate of Poverty Indicators at Small Area Level 31.3 Data-related and Estimation-related Problems for the Estimation of Poverty Indicators 51.4 Model-assisted and Model-based Methods Used for the Estimation of Poverty Indicators: a Short Review 71.4.1 Model-assisted Methods 71.4.2 Model-based Methods 12References 15Part I DEFINITION OF INDICATORS AND DATA COLLECTION AND INTEGRATION METHODS2 Regional and Local Poverty Measures 21Achille Lemmi and Tomasz Panek2.1 Introduction 212.2 Poverty – Dilemmas of Definition 222.3 Appropriate Indicators of Poverty and Social Exclusion at Regional and Local Levels 232.3.1 Adaptation to the Regional Level 232.4 Multidimensional Measures of Poverty 252.4.1 Multidimensional Fuzzy Approach to Poverty Measurement 252.4.2 Fuzzy Monetary Depth Indicators 262.5 Co-incidence of Risks of Monetary Poverty and Material Deprivation 302.6 Comparative Analysis of Poverty in EU Regions in 2010 312.6.1 Data Source 312.6.2 Object of Interest 312.6.3 Scope and Assumptions of the Empirical Analysis 322.6.4 Risk of Monetary Poverty 322.6.5 Risk of Material Deprivation 332.6.6 Risk of Manifest Poverty 372.7 Conclusions 38References 393 Administrative and Survey Data Collection and Integration 41Alessandra Coli, Paolo Consolini and Marcello D’Orazio3.1 Introduction 413.2 Methods to Integrate Data from Different Data Sources: Objectives and Main Issues 433.2.1 Record Linkage 433.2.2 Statistical Matching 463.3 Administrative and Survey Data Integration: Some Examples of Application in Well-being and Poverty Studies 503.3.1 Data Integration for Measuring Disparities in Economic Well-being at the Macro Level 513.3.2 Collection and Integration of Data at the Local Level 533.4 Concluding Remarks 56References 574 Small Area Methods and Administrative Data Integration 61Li-Chun Zhang and Caterina Giusti4.1 Introduction 614.2 Register-based Small Area Estimation 634.2.1 Sampling Error: A Study of Local Area Life Expectancy 634.2.2 Measurement Error due to Progressive Administrative Data 654.3 Administrative and Survey Data Integration 684.3.1 Coverage Error and Finite-population Bias 684.3.2 Relevance Error and Benchmarked Synthetic Small Area Estimation 704.3.3 Probability Linkage Error 754.4 Concluding Remarks 80References 81Part II IMPACT OF SAMPLING DESIGN, WEIGHTING AND VARIANCE ESTIMATION5 Impact of Sampling Designs in Small Area Estimation with Applications to Poverty Measurement 85Jan Pablo Burgard, Ralf Münnich and Thomas Zimmermann5.1 Introduction 855.2 Sampling Designs in our Study 875.3 Estimation of Poverty Indicators 905.3.1 Design-based Approaches 905.3.2 Model-based Estimators 925.4 Monte Carlo Comparison of Estimation Methods and Designs 965.5 Summary and Outlook 105Acknowledgements 106References 1066 Model-assisted Methods for Small Area Estimation of Poverty Indicators 109Risto Lehtonen and Ari Veijanen6.1 Introduction 1096.1.1 General 1096.1.2 Concepts and Notation 1106.2 Design-based Estimation of Gini Index for Domains 1116.2.1 Estimators 1116.2.2 Simulation Experiments 1146.2.3 Empirical Application 1166.3 Model-assisted Estimation of At-risk-of Poverty Rate 1176.3.1 Assisting Models in GREG and Model Calibration 1176.3.2 Generalized Regression Estimation 1196.3.3 Model Calibration Estimation 1206.3.4 Simulation Experiments 1226.3.5 Empirical Example 1236.4 Discussion 1246.4.1 Empirical Results 1246.4.2 Inferential Framework 1256.4.3 Data Infrastructure 125References 1267 Variance Estimation for Cumulative and Longitudinal Poverty Indicators from Panel Data at Regional Level 129Gianni Betti, Francesca Gagliardi and Vijay Verma7.1 Introduction 1297.2 Cumulative vs. Longitudinal Measures of Poverty 1307.2.1 Cumulative Measures 1307.2.2 Longitudinal Measures 1317.3 Principle Methods for Cross-sectional Variance Estimation 1317.4 Extension to Cumulation and Longitudinal Measures 1337.5 Practical Aspects: Specification of Sample Structure Variables 1347.6 Practical Aspects: Design Effects and Correlation 1367.6.1 Components of the Design Effect 1367.6.2 Estimating the Components of Design Effect 1387.6.3 Estimating other Components using Random Grouping of Elements 1397.7 Cumulative Measures and Measures of Net Change 1407.7.1 Estimation of the Measures 1407.7.2 Variance Estimation 1417.8 An Application to Three Years’ Averages 1417.8.1 Computation Given Limited Information on Sample Structure in EU-SILC 1417.8.2 Direct Computation 1447.8.3 Empirical Results 1457.9 Concluding Remarks 146References 147Part III SMALL AREA ESTIMATION MODELING AND ROBUSTNESS8 Models in Small Area Estimation when Covariates are Measured with Error 151Serena Arima, Gauri S. Datta and Brunero Liseo8.1 Introduction 1518.2 Functional Measurement Error Approach for Area-level Models 1538.2.1 Frequentist Method for Functional Measurement Error Models 1548.2.2 Bayesian Method for Functional Measurement Error Models 1568.3 Small Area Prediction with a Unit-level Model when an Auxiliary Variable is Measured with Error 1568.3.1 Functional Measurement Error Approach for Unit-level Models 1578.3.2 Structural Measurement Error Approach for Unit-level Models 1608.4 Data Analysis 1628.4.1 Example 1: Median Income Data 1628.4.2 Example 2: SAIPE Data 1658.5 Discussion and Possible Extensions 169Acknowledgements 169Disclaimer 170References 1709 Robust Domain Estimation of Income-based Inequality Indicators 171Nikos Tzavidis and Stefano Marchetti9.1 Introduction 1719.2 Definition of Income-based Inequality Measures 1729.3 Robust Small Area Estimation of Inequality Measures with M-quantile Regression 1739.4 Mean Squared Error Estimation 1769.5 Empirical Evaluations 1769.6 Estimating the Gini Coefficient and the Quintile Share Ratio for Unplanned Domains in Tuscany 1809.7 Conclusions 183References 18510 Nonparametric Regression Methods for Small Area Estimation 187M. Giovanna Ranalli, F. Jay Breidt and Jean D. Opsomer10.1 Introduction 18710.2 Nonparametric Methods in Small Area Estimation 18810.2.1 Nested Error Nonparametric Unit Level Model Using Penalized Splines 18910.2.2 Nested Error Nonparametric Unit Level Model Using Kernel Methods 19110.2.3 Generalized Responses 19210.2.4 Robust Approaches 19210.3 A Comparison for the Estimation of the Household Per-capita Consumption Expenditure in Albania 19510.4 Concluding Remarks 202References 202Part IV SPATIO-TEMPORAL MODELING OF POVERTY11 Area-level Spatio-temporal Small Area Estimation Models 207María Dolores Esteban, Domingo Morales and Agustín Pérez11.1 Introduction 20711.2 Extensions of the Fay–Herriot Model 20911.3 An Area-level Model with MA(1) Time Correlation 21211.4 EBLUP and MSE 21411.5 EBLUP of Poverty Proportions 21511.6 Simulations 21611.6.1 Simulation 1 21611.6.2 Simulation 2 21711.7 R Codes 22011.8 Concluding Remarks 220Appendix 11.A: MSE Components 22111.A.1 Calculation of g1(𝜽) 22111.A.2 Calculation of g2(𝜽) 22111.A.3 Calculation of g3(𝜽) 222Acknowledgements 224References 22412 Unit Level Spatio-temporal Models 227Maria Chiara Pagliarella and Renato Salvatore12.1 Unit Level Models 23012.2 Spatio-temporal Time-varying Effects Models 23212.3 State Space Models with Spatial Structure 23412.4 The Italian EU-SILC Data: an Application with the Spatio-temporal Unit Level Models 23612.5 Concluding Remarks 239Appendix 12.A: Restricted Maximum Likelihood Estimation 240Appendix 12.B: Mean Squared Error Estimation of the Unit Level State Space Model 241References 24213 Spatial Information and Geoadditive Small Area Models 245Chiara Bocci and Alessandra Petrucci13.1 Introduction 24513.2 Geoadditive Models 24713.3 Geoadditive Small Area Model for Skewed Data 24813.4 Small Area Mean Estimators 25013.5 Estimation of the Household Per-capita Consumption Expenditure in Albania 25113.5.1 Data 25113.5.2 Results 25313.6 Concluding Remarks and Open Questions 258Acknowledgement 259References 259Part V SMALL AREA ESTIMATION OF THE DISTRIBUTION FUNCTION OF INCOME AND INEQUALITIES14 Model-based Direct Estimation of a Small Area Distribution Function 263Hukum Chandra, Nicola Salvati and Ray Chambers14.1 Introduction 26314.2 Estimation of the Small Area Distribution Function 26414.3 Model-based Direct Estimator for the Estimation of the Distribution Function of Equivalized Income in the Toscana, Lombardia and Campania Provinces of Italy 26814.4 Final Remarks 275References 27615 Small Area Estimation for Lognormal Data 279Emily Berg, Hukum Chandra and Ray Chambers15.1 Introduction 27915.2 Literature on Small Area Estimation for Skewed Data 28015.3 Small Area Predictors for a Unit-Level Lognormal Model 28215.3.1 The Linear Unit-Level Mixed Model 28215.3.2 A Synthetic Estimator 28315.3.3 A Model-Based Direct Estimator 28515.3.4 An Empirical Bayes Predictor 28615.4 Simulations 28715.4.1 Comparison of Synthetic, TrMBDE, and EB Predictors 28715.4.2 Bias and Robustness of the EB Predictor 29115.4.3 Comparison of Lognormal and Gamma Distributions 29115.5 Concluding Remarks 294Appendix 15.A: Mean Squared Error Estimation for the Empirical Best Predictor 295References 29616 Bayesian Beta Regression Models for the Estimation of Poverty and Inequality Parameters in Small Areas 299Enrico Fabrizi, Maria Rosaria Ferrante and Carlo Trivisano16.1 Introduction 29916.2 Direct Estimation 30016.3 Small Area Estimation of the At-risk-of-poverty Rate 30216.3.1 The Model 30216.3.2 Data Analysis 30416.4 Small Area Estimation of the Material Deprivation Rates 30516.4.1 The Model 30516.4.2 Data Analysis 30616.5 Joint Estimation of the At-risk-of-poverty Rate and the Gini Coefficient 30816.5.1 The Models 30816.5.2 Data Analysis 31016.6 A Short Description of Markov Chain Monte Carlo Algorithms and R Software Codes 31216.7 Concluding Remarks 312References 31317 Empirical Bayes and Hierarchical Bayes Estimation of Poverty Measures for Small Areas 315John N. K. Rao and Isabel Molina17.1 Introduction 31517.2 Poverty Measures 31617.3 Fay–Herriot Area Level Model 31717.4 Unit Level Nested Error Linear Regression Model 31917.4.1 ELL/World Bank Method 31917.4.2 Empirical Bayes Method 32117.4.3 Hierarchical Bayes Method 32217.5 Application 32317.6 Concluding Remarks 324References 324Part VI DATA ANALYSIS AND APPLICATIONS18 Small Area Estimation Using Both Survey and Census Unit Record Data 327Stephen J. Haslett18.1 Introduction 32718.2 The ELL Implementation Process and Methodology 32918.2.1 ELL: Implementation Process 32918.2.2 ELL Methodology: Survey Regression, Contextual Effects, Clustering, and the Bootstrap 33118.2.3 Fitting Survey-based Models 33418.2.4 Residuals and the Bootstrap 33518.2.5 ELL: Linkages to Other Related Methods 33818.3 ELL – Advantages, Criticisms and Disadvantages 33918.4 Conclusions 344References 34619 An Overview of the U.S. Census Bureau’s Small Area Income and Poverty Estimates Program 349William R. Bell, Wesley W. Basel and Jerry J. Maples19.1 Introduction 34919.2 U.S. Poverty Measure and Poverty Data Sources 35119.2.1 Poverty Measure and Survey Data Sources 35119.2.2 Administrative Data Sources Used for Covariate Information 35419.3 SAIPE Poverty Models and Estimation Procedures 35619.3.1 State Poverty Models 35719.3.2 County Poverty Models 36319.3.3 School District Poverty Estimation 36819.3.4 Major Changes Made in SAIPE Models and Estimation Procedures 37219.4 Current Challenges and Recent SAIPE Research 37419.5 Conclusions 375References 37620 Poverty Mapping for the Chilean Comunas 379Carolina Casas-Cordero Valencia, Jenny Encina and Partha Lahiri20.1 Introduction 37920.2 Chilean Poverty Measures and Casen 38120.2.1 The Poverty Measure Used in Chile 38120.2.2 The Casen Survey 38220.3 Data Preparation 38320.3.1 Comuna Level Data Derived from Casen 2009 38320.3.2 Comuna Level Administrative Data 38720.4 Description of the Small Area Estimation Method Implemented in Chile 39120.4.1 Modeling 39420.4.2 Estimation of A and 𝛽 39520.4.3 Empirical Bayes Estimator of 𝜃i 39520.4.4 Limited Translation Empirical Bayes Estimator of 𝜃i 39520.4.5 Back-transformation and raking 39620.4.6 Confidence intervals for the poverty rates 39620.5 Data Analysis 39720.6 Discussion 399Acknowledgements 401References 40221 Appendix on Software and Codes Used in the Book 405Antonella D’Agostino, Francesca Gagliardi and Laura Neri21.1 Introduction 40521.2 R and SAS Software: a Brief Note 40621.3 Getting Started: EU-SILC Data 40921.4 A Quick Guide to the Scripts 41021.4.1 Basics of the Scripts 41021.4.2 A Quick guide to Chapter 5 (Impact of Sampling Designs in Small Area Estimation with Applications to Poverty Measurement) 41221.4.3 A Quick guide to Chapter 6 (Model-assisted Methods for Small Area Estimation of Poverty Indicators) 41221.4.4 A Quick Guide to Chapter 7 (Variance Estimation for Cumulative and Longitudinal Poverty Indicators from Panel Data at Regional Level) 41421.4.5 A Quick Guide to Chapter 8 (Models in Small Area Estimation when Covariates are Measured with Error) 41521.4.6 A Quick Guide to Chapter 9 (Robust Domain Estimation of Income-based Inequality Indicators) 41621.4.7 A Quick Guide to Chapter 10 (Nonparametric Regression Methods for Small Area Estimation) 41721.4.8 A Quick Guide to Chapter 11 (Area-level Spatio-temporal Small Area Estimation Models) 41821.4.9 A Quick Guide to Chapter 12 (Unit Level Spatio-temporal Models) 41921.4.10 A Quick Guide to Chapter 13 (Spatial Information and Geoadditive Small Area Models) 42021.4.11 A Quick guide to Chapter 14 (Model-based Direct Estimation of a Small Area Distribution Function) 42221.4.12 A Quick Guide to Chapter 16 (Bayesian Beta Regression Models for the Estimation of Poverty and Inequality Parameters in Small Areas) 42321.4.13 A Quick Guide to Chapter 17 (Empirical Bayes and Hierarchical Bayes Estimation of Poverty Measures for Small Areas) 42421.4.14 A Quick Guide to Chapter 18 - (Small Area Estimation Using Both Survey and Census Unit Record Data: Links, Alternatives, and theCentral Roles of Regression and Contextual Variables) 425References 426Author Index 427Subject Index 431

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