Analysis of Poverty Data by Small Area Estimation

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