1. Challenges in small area estimation of poverty indicators
Risto Lehtonen, Ari Veijanen, Maria Valaste
(University of Helsinki) , and Mikko Myrskylä (Max Planck Institute for Demographic Research, Rostock)
Ameli 2010 Conference, February 2010, Vienna

2. Outline
Background
Material and methods
Results
Discussion
References

3. EU/FP7 Project AMELI
Advanced Methodology for European Laeken Indicators ( )
The project is supported by European Commission funding from the Seventh Framework Programme for Research
DoW: The study will include research on data quality including
Measurement of quality
Treatment of outliers and nonresponse
Small area estimation
The measurement of development over time

4. Material and methods
Investigation of statistical properties (bias and accuracy) of estimators of selected Laeken indicators for population subgroups or domains and small areas
Method: Design-based Monte Carlo simulation experiments based on real data
Data: Statistical register data based on merging of administrative register data at the unit level (Finland)

5. Laeken indicators based on binary variables
At-risk-of poverty rate
Direct estimators
Horvitz-Thompson estimators HT
Indirect estimators
Model-assisted GREG and MC estimators
Model-based EBLUP and EB estimators
Modelling framework
Generalized linear mixed models GLMM
Lehtonen and Veijanen (2009)
Rao (2003), Jiang and Lahiri (2006)

6. Laeken indicators based on medians or quantiles
Indicators based on medians or quantiles of cumulative distribution function of the underlying continuous variable
Relative median at-risk-of poverty gap
Quintile share ratio (S20/S80 ratio)
Gini coefficient
Direct estimators DEFAULT
Synthetic estimators SYN
Expanded prediction SYN estimators EP-SYN
Composite estimators COMP
Simulation-based methods

7. Generalized linear mixed models

8. Design-based GREG type estimators for poverty rate

9. Model-based estimators for poverty rate

10. Poverty gap for domains
Relative median at-risk-of poverty gap
Poverty gap in domain d describes the difference between the poor people's median income and the at-risk-of-poverty threshold t

11. Estimators of poverty gap

12. Estimators of poverty gap

13. Estimators of poverty gap

14. Estimators of poverty gap

15. MSE estimation for direct estimator DEFAULT

16. MSE estimation for SYN estimator

17. Monte Carlo simulation
Fixed finite population of 1,000,000 persons
D = 70 domains of interest
Cross-classification of NUTS 3 with sex and age group (7x2x5)
Y-variables
Equivalized income (based on register data)
Binary indicator for persons in poverty
X-variables (binary or continuous variables)
house _owner (binary)
education_level (7 classes) and educ_thh
lfs_code (3 classes) and empmohh
socstrat (6 classes)
sex_class and age_class (5 age classes)
NUTS3

18. Sampling designs SRSWOR sampling Stratified SRSWOR
Sample size n = 5,000 persons
Stratified SRSWOR
Stratification by education level of HH head
H = 7 strata
Unequal inclusion probabilities
Design weights vary between strata
Min: 185, Max: 783
K = 1000 independent samples

19. Quality measures of estimators
Design bias
Absolute relative bias ARB (%)
Accuracy
Relative root mean squared error
RRMSE (%)

22. Discussion: Poverty rate
Indirect design-based estimator MLGREG
Design unbiased
Large variance in small domains
Small variance in large domains
Indirect model-based estimator EB
Design biased
Small variance also in small domains
Accuracy: EB outperformed MLGREG
Might be the best choice at least for small domains unless it is important to avoid design bias

23. Discussion: Poverty gap
Direct estimator DEFAULT
Small design bias but large variance
Indirect model-based SYN
Very large bias but small variance
Indirect model-based EP-SYN based on expanded predictions
Much smaller bias and variance than in SYN
Composite (DEFAULT with EP-SYN)
Small domains: good compromise
Large domains: bias can still dominate the MSE

25. Thank you for your attention!