1. Poverty Estimation in Small Areas Agne Bikauskaite European Conference on Quality in Official Statistics (Q2014) Vienna, 3-5 June 2014

2. Data: The population size N = 3000 The sample size n = 300 Number of mutually exclusive strata H = 7 The income of individuals (y h1,..., y hN ) The auxiliary information (x 1i,..., x ji,..., x Ji ) 1000 simple random samples

3. Income distribution

4. Data: The population size N = 3000 The sample size n = 300 Number of mutually exclusive strata H = 7 The income of individuals (y h1,..., y hN ) The auxiliary information (x 1i,..., x ji,..., x Ji ) 1000 simple random samples

5. Strata size Number of strataPopulation sizeStrata size 1 49650 2 33333 3 17718 4 11912 5 929 6 79479 7 98999 Total 3000300

6. Stratified Sampling The sample design probability when element i belongs to stratum h is The sampling weight for selected person i from the h stratum is

7. Estimated parameters The Average Income The Poverty Line The Headcount Index The Poverty Gap Index

8. The Average Income The average income in strata h is The average income estimate is

9. The Poverty Line The Poverty Line is defined as 60 per cent of the median equivalent disposable income The Poverty Line estimate is

10. The Headcount Index The headcount index is defined as the number of persons below the poverty line divided by the population number The Headcount index estimate is

11. The Poverty Gap The poverty gap G is defined as an amount of difference between poverty line and income value y of i th person living in poverty or social exclusion The poverty gap estimate

12. The Poverty Gap Index The poverty gap index is a proportion of the poverty gap and the poverty line The poverty gap index estimate is

13. Population

14. What is Small Area?

15. Sampling in Small Areas

16. Direct and Indirect Estimates Direct Estimates: –Not using auxiliary information –Using auxiliary information from the same area Indirect Estimates: –Using auxiliary information from adjacent areas

17. Simulated Estimation Methods The Horvitz-Thompson (HT) The Generalised Regression (GREG) The Synthetic (S)

18. The Absolute Relative Bias The Absolute Relative Bias (ARB) assessed the accuracy of the estimates

19. The Horvitz-Thompson estimator The sum estimate is

20. The ARB of the average income estimates Stratum Horvitz-Thompson estimate’s ARB (%) Generalised Regression estimate’s ARB (%) Synthetic estimate’s ARB (%) Population -0.064475440.098310539-0.08398375 1 -0.3211974-0.31518106-0.34310121 2 -0.02643092-0.014056-0.06902109 3 0.4655713930.5517990550.403882282 4 -0.81562095-0.88208503-0.65375062 5 0.4857153320.5108412720.492216146 6 -0.1417938-0.13401672-0.14913289 7 0.0792527930.0909450550.188597999

21. The ARB of the headcount index estimates Stratum Horvitz-Thompson estimate’s ARB (%) Generalised regression estimate’s ARB (%) Synthetic estimate’s ARB (%) Population 0.363963290.1476656640.152247869 1 -3.51959494-3.7958481-3.8266288 2 1.4684931511.1920298881.003491015 3 4.6447619054.7571445435.058255185 4 2.8597826092.6010869572.877924901 5 -2.80634921-2.90370419-1.68042706 6 -0.63675717-0.78252971-0.8622043 7 1.3440970791.0683577861.298860988

22. ARB of the poverty gap index estimate Stratum Horvitz-Thompson estimate’s ARB (%) Generalised regression estimate’s ARB (%) Synthetic estimate’s ARB (%) Population -0.1594528-0.35543944-0.41065525 1 -1.37126072-1.59705543-1.57592157 2 -0.9619282-1.23793553-1.64985282 3 -0.49766038-0.6453229-0.69178013 4 -1.21749012-1.2989069-1.45047831 5 -0.73358855-0.956284860.02299011 6 0.7029895530.4776107190.357964671 7 0.196259620.023796320.278143276

23. The GREG estimator The sum estimate

24. The ARB of the average income estimates Stratum Horvitz-Thompson estimate’s ARB (%) Generalised Regression estimate’s ARB (%) Synthetic estimate’s ARB (%) Population -0.064475440.098310539-0.08398375 1 -0.3211974-0.31518106-0.34310121 2 -0.02643092-0.014056-0.06902109 3 0.4655713930.5517990550.403882282 4 -0.81562095-0.88208503-0.65375062 5 0.4857153320.5108412720.492216146 6 -0.1417938-0.13401672-0.14913289 7 0.0792527930.0909450550.188597999

25. The ARB of the headcount index estimates Stratum Horvitz-Thompson estimate’s ARB (%) Generalised regression estimate’s ARB (%) Synthetic estimate’s ARB (%) Population 0.363963290.1476656640.152247869 1 -3.51959494-3.7958481-3.8266288 2 1.4684931511.1920298881.003491015 3 4.6447619054.7571445435.058255185 4 2.8597826092.6010869572.877924901 5 -2.80634921-2.90370419-1.68042706 6 -0.63675717-0.78252971-0.8622043 7 1.3440970791.0683577861.298860988

26. ARB of the poverty gap index estimate Stratum Horvitz-Thompson estimate’s ARB (%) Generalised regression estimate’s ARB (%) Synthetic estimate’s ARB (%) Population -0.1594528-0.35543944-0.41065525 1 -1.37126072-1.59705543-1.57592157 2 -0.9619282-1.23793553-1.64985282 3 -0.49766038-0.6453229-0.69178013 4 -1.21749012-1.2989069-1.45047831 5 -0.73358855-0.956284860.02299011 6 0.7029895530.4776107190.357964671 7 0.196259620.023796320.278143276

27. The Synethetic estimator The sum estimate is

28. The ARB of the average income estimates Stratum Horvitz-Thompson estimate’s ARB (%) Generalised Regression estimate’s ARB (%) Synthetic estimate’s ARB (%) Population -0.064475440.098310539-0.08398375 1 -0.3211974-0.31518106-0.34310121 2 -0.02643092-0.014056-0.06902109 3 0.4655713930.5517990550.403882282 4 -0.81562095-0.88208503-0.65375062 5 0.4857153320.5108412720.492216146 6 -0.1417938-0.13401672-0.14913289 7 0.0792527930.0909450550.188597999

29. The ARB of the headcount index estimates Stratum Horvitz-Thompson estimate’s ARB (%) Generalised regression estimate’s ARB (%) Synthetic estimate’s ARB (%) Population 0.363963290.1476656640.152247869 1 -3.51959494-3.7958481-3.8266288 2 1.4684931511.1920298881.003491015 3 4.6447619054.7571445435.058255185 4 2.8597826092.6010869572.877924901 5 -2.80634921-2.90370419-1.68042706 6 -0.63675717-0.78252971-0.8622043 7 1.3440970791.0683577861.298860988

30. ARB of the poverty gap index estimate Stratum Horvitz-Thompson estimate’s ARB (%) Generalised regression estimate’s ARB (%) Synthetic estimate’s ARB (%) Population -0.1594528-0.35543944-0.41065525 1 -1.37126072-1.59705543-1.57592157 2 -0.9619282-1.23793553-1.64985282 3 -0.49766038-0.6453229-0.69178013 4 -1.21749012-1.2989069-1.45047831 5 -0.73358855-0.956284860.02299011 6 0.7029895530.4776107190.357964671 7 0.196259620.023796320.278143276

31. The mean estimate’s variance

32. The Jack-Knife method The Jack-Knife method’s idea is to divide stratified sample into mutually exclusive subgroups. The modified sampling weights

33. The Jack-Knife variance estimator Then the Jack-Knife variance estimator of estimated parameter is

34. Conclusions: Poverty parameters estimation Different estimation methods for large and for small areas The Synthetic method for poverty estimation in small areas If auxiliary information from adjacent areas is not available then the most appropriate estimation method is Horvitz-Thompson

35. Conclusions: Variances estimation of the estimated parameters Large ARBs The best results of estimation are given by the Horvitz-Thompson method Applying Jack-Knife method precision of the estimates increases when the group size is extremely small