Preface |
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xiii | |
List of Figures |
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xvii | |
List of Tables |
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xxi | |
1 Poverty Rate |
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1 | (36) |
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1 | (6) |
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1.1.1 Median and Percentiles |
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3 | (1) |
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1.1.2 Populations and Samples |
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4 | (3) |
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7 | (5) |
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1.2.1 Poverty-Rate Curves |
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8 | (4) |
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12 | (2) |
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14 | (6) |
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19 | (1) |
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1.A Appendix. Programming Notes |
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20 | (17) |
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20 | (3) |
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1.A.2 Estimating a Quantile |
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23 | (2) |
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1.A.3 Summarising the Weights |
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25 | (2) |
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1.A.4 Some Auxiliary Functions |
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27 | (2) |
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1.A.5 Plotting a Set of Curves |
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29 | (2) |
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1.A.6 Final Touch in a Diagram |
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31 | (4) |
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1.A.7 Countries in EU-SILC |
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35 | (2) |
2 Statistical Background |
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37 | (16) |
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2.1 Replications. Fixed and Random |
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37 | (1) |
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2.2 Estimation. Sample Quantities |
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38 | (2) |
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2.2.1 Weighted Sample Median |
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39 | (1) |
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2.3 Sampling Variation. Bootstrap |
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40 | (5) |
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2.4 Horvitz-Thompson Estimator |
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45 | (2) |
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2.5 Fragility of Unbiasedness and Efficiency |
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47 | (2) |
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2.5.1 Lognormal Distribution |
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48 | (1) |
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49 | (4) |
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49 | (3) |
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2.A.2 Moments of the Lognormal Distribution |
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52 | (1) |
3 Poverty Indices |
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53 | (44) |
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53 | (7) |
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56 | (4) |
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3.2 Relative and Log-Poverty Gaps |
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60 | (3) |
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3.3 Lorenz Curve and Gini Coefficient |
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63 | (10) |
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73 | (2) |
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75 | (1) |
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3.5 Income Inequality. Kernels, Scores and Scaling |
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75 | (2) |
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77 | (20) |
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3.A.1 Negative Values of eHI |
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77 | (3) |
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80 | (2) |
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3.A.3 More on Poverty Indices |
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82 | (5) |
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3.A.4 Lorenz Curve and Gini Coefficient |
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87 | (4) |
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91 | (2) |
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93 | (4) |
4 Mixtures of Distributions |
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97 | (38) |
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97 | (3) |
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100 | (2) |
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102 | (11) |
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4.3.1 Exploration of the Fitted Probabilities |
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104 | (6) |
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4.3.2 Results for Several Countries |
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110 | (3) |
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113 | (3) |
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4.5 Components as Clusters |
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116 | (5) |
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120 | (1) |
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4.A Appendix. Programming Notes |
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121 | (14) |
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4.A.1 EM Algorithm for Mixtures of Normal Distributions |
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121 | (10) |
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131 | (1) |
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132 | (3) |
5 Regions |
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135 | (40) |
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135 | (2) |
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137 | (5) |
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5.3 Small-Area Estimation |
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142 | (4) |
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5.4 Using Auxiliary Information |
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146 | (2) |
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148 | (8) |
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5.5.1 Composite Estimation of the Poverty Rates |
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150 | (6) |
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156 | (2) |
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158 | (2) |
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160 | (1) |
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5.A.1 Estimation of Region-Level (Co-)Variances |
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160 | (1) |
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5.A.2 Report Card for Austria and Its Regions |
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161 | (1) |
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161 | (14) |
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5.B.1 Composite Estimation |
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168 | (2) |
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5.B.2 Multivariate Composition |
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170 | (3) |
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173 | (2) |
6 Transitions |
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175 | (40) |
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175 | (7) |
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6.2 Absolute and Relative Rates of Transition |
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182 | (4) |
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6.3 Substantial Transitions |
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186 | (5) |
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6.4 Partial Scoring of Transitions |
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191 | (3) |
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6.5 Transitions over Several Years |
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194 | (3) |
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197 | (6) |
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6.A Appendix. Programming Notes |
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203 | (12) |
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6.A.1 National Panel Databases |
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203 | (4) |
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6.A.2 Rates of Transition |
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207 | (8) |
7 Multivariate Mixtures |
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215 | (36) |
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7.1 Multivariate Normal Distributions |
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215 | (2) |
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7.1.1 Finite Mixtures of Normal Distributions |
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216 | (1) |
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217 | (1) |
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218 | (9) |
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227 | (3) |
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7.5 Mixture Models for the Countries in EU-SILC |
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230 | (2) |
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232 | (2) |
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7.7 Confusion and Separation |
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234 | (2) |
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236 | (1) |
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7.A.1 What Can Go Wrong in Iterations of EM |
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236 | (1) |
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237 | (14) |
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245 | (2) |
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7.B.2 Stability of Income |
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247 | (2) |
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249 | (2) |
8 Social Transfers |
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251 | (34) |
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8.1 Capacity of Social Transfers |
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251 | (3) |
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8.2 Impact of Social Transfers |
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254 | (7) |
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8.3 Potential and Effectiveness |
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261 | (3) |
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8.4 Nonparametric Regression |
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264 | (8) |
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8.4.1 Smoothing Sequences |
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270 | (2) |
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272 | (2) |
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8.A Appendix. Programming Notes |
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274 | (11) |
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8.A.1 Nonparametric Regression |
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277 | (4) |
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8.A.2 Graphics for Nonparametric Regression |
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281 | (4) |
9 Causes and Effects. Education and Income |
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285 | (42) |
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9.1 Background and Motivation |
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285 | (2) |
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9.2 Definitions and Notation |
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287 | (3) |
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9.2.1 Treatment-Assignment Mechanism |
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288 | (2) |
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9.3 Missing-Data Perspective |
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290 | (3) |
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9.4 Propensity and Matched Pairs |
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293 | (3) |
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9.4.1 Regression as an Alternative |
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294 | (2) |
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296 | (12) |
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9.5.1 Results for Other Countries |
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304 | (1) |
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9.5.2 Regression of Outcome on Treatment and Background |
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305 | (2) |
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9.5.3 Potential Versions of Variables |
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307 | (1) |
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9.A Appendix. Programming Notes |
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308 | (19) |
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9.A.1 Second-Level Functions |
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313 | (9) |
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9.A.2 Graphics for the Balance Diagnostics |
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322 | (5) |
Epilogue |
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327 | (4) |
Bibliography |
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331 | (10) |
Subject Index |
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341 | (12) |
Index of User-Defined R Functions |
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353 | |