1. Improving accuracy of poverty and social exclusion estimates for cities and functional urban areas
Marie Reijo, Population and Social Statistics
Ari Veijanen, Standards and Methods

2. Background, Urban Audit statistics
Urban Audit, ESS statistics on cities, towns and suburbs
Spatial units:
City, local administrative unit (LAU), at least habitants
Greater city, stretches beyond LAU
Functional urban area (FUA), city and its commuting zone
Data on several topics, e.g. demography, social aspects, economic aspects, education, environment
Data from many sources: Household income, AROPE and its component AROP collected from NSIs, EU-SILC as source
2018

3. Objectives, Finnish EU-SILC
To produce standard techniques and procedures for annual estimation for small areas from FI-SILC
To provide more accurate estimates compared with the national SILC estimates
To provide coherent estimates with the EU-SILC regional estimates ((NUTS2, NUTS3) * Degree of urbanisation)
2018

4. Background, Finnish EU-SILC
Integrated with national IDS
Four-year rotating panel design since 2010
The Finnish EU-SILC sampling and estimation design:
Two-phase stratified sampling: 1. systematic sampling by location, 2. SWOR by non-proportional allocation by strata (socio-economic status) => Fixed strata, non-fixed domains (cities, urban areas)
Using auxiliary information for calibration from TSID: e.g. direct NUTS3 population number with capital area as separated (TSID: Total statistics on income distribution)
Small sample sizes by domains (cities, urban areas) => Not accurate estimates for cities and FUAs
Rather accurate estimates for NUTS2 and NUTS3
2018

5. Cities(LAUs) and FUAs by municipality districts
2018

6. Sample sizes and SILC AROP and AROPE estimates for cities (LAUs)
City
AROPE
AROP n % CV
95%CL_L
95%CL_U
FI001C2
2 365
12.9
1.644
8.1
1.066
6.0445
FI002C1
921
19.2
6.768
15.6
6.432
FI003C1
740
25.8
9.429
16.5
6.429
FI004C3
723
18.7
7.469
13.9
5.540
9.3151
FI005C1
1 195
11.2
4.523
7.0082
5.9
2.402
2.8172
8.8930
FI006C1
732
11.5
5.025
7.1266
3.7
1.748
1.1258
6.3094
FI007C2
448
11.6
7.907
6.0948
9.7
7.198
4.4661
FI008C3
510
22.1
15.575
18.4
14.400
FI009C1
536
25.0
18.698
15.745
Others
16 648
15.3
0.387
11.8
0.344
Total
24 818
15.7
0.218
0.190
2018

7. Sample sizes and SILC AROP and AROPE estimates for urban areas (FUA)% CV
95%CL_L
95%CL_U
FI001L3
5 868
11.6
0.673
6.8
0.420
5.5229
8.0641
FI002L3
1 868
16.4
3.173
12.7
2.820
9.4269
FI003L4
1 578
19.9
3.987
13.5
2.811
FI004L4
1 015
15.6
4.986
12.0
3.856
8.1771
FI007L2
760
12.2
4.922
7.8193
9.9
4.324
5.7996
FI008L2
782
17.0
8.485
14.3
7.710
8.8295
FI009L2
792
24.6
13.523
18.9
11.452
Others
12 155
16.7
0.614
12.9
0.549
Total
24 818
15.7
0.218
11.5
0.190
FI001K2
4 338
0.924
6.7
0.530
5.2693
8.1231
2018

8. SILC and TSID estimates for cities (LAUs), persons in total
2018

9. SILC and TSID estimates for FUAs, persons aged 15-24 estimates
2018

10. SAE estimation, estimator selection
Generalized regression estimators GREG, design based model assisted estimation:
Characteristics: small bias; small variance, if not small domains; MSE close to variance
Exploitation of domain population data
Unplanned and non-fixed domains (cities, urban areas): mixed models with fixed and random effects (domain)
Especially MLGREG-D as method (generalised linear mixed model (GLMM) within generalised linear regression model framework (binary distribution), ML estimation method in model fitting.
Approximate variance estimation method (≈ Poisson sampling due to unplanned domain/strata, approximate variance estimates)
SAE -method characteristics, see e.g. Lehtonen and Pahkinen 2004
2018

11. SAE estimation, estimation phases
EU-SILC sample k ∈ s: information on PIN, household, strata, weights, measured study variables s(y) (AROPE, AROP, JOBLESS, MATDEP)
Total Statistics on Income Data, TSID k ∈ U: information on PIN, auxiliary variables
Merging EU-SILC and TSID data at unit level
Modelling y by sample units k ∈ s by assisting model: specifying final model, fitting and diagnosing, getting parameters β
Calculating predictions ŷk for all units, TSID k ∈ U, by using β for s(y)
Calculating residuals ê k = Y k – Ŷ k for EU-SILC k ∈ s
Calculating domain GREG estimates for output variables
Evaluation of estimates: incl. variance estimates and comparisons with initial estimates
2018

12. Modelling s(y), final model
Auxiliary variables 𝑧k’ = (zIk,….,zJk)’ are as follows:
sum of earned income (amount/10000)
sum of unemployment benefits (amount/10000)
des1,…, des7 = number of persons in decile groups
age10-14, …, age80-84, age85+ = number of persons in ages groups
sum of AROP persons
number of males
number of persons with earned income
number of persons with unemployed benefits
sum of equivalence scale units (of household-dwellings)
d𝑜𝑚𝑎𝑖𝑛 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠 𝑑 for cities and FUAs are used as random terms.
2018

13. Modelling s(y), final model
Generalized linear mixed model, especially binary logistic model (logit model) fitted separately for all s(y): k ∈ s:
𝐸𝑚( 𝛾𝑖𝑘 𝑢𝑑 )= 𝑒𝑥𝑝⁡(𝑧𝑘′(𝛽𝑖+𝑢𝑖𝑑) 1+𝑒𝑥𝑝⁡(𝑧𝑘′(𝛽𝑟+𝑢𝑟𝑑)
2018

14. Construction GREG estimators
Construction GREG estimators (predictions ŷ𝑘 and residuals ek = yk− ŷ𝑘 are incorporated into the GREG estimators) known
domain sizes :
𝑡 𝑑𝐺𝑅𝐸𝐺= 𝑘∈𝑈𝑑 ŷ𝑘 + 𝑘∈𝑠𝑑 𝜔𝑘(𝑦𝑘−ŷ𝑘)
where 𝜔𝑘= 1 𝜋𝑘 ,
𝑠𝑑=𝑠 ⌒ 𝑈𝑑 𝑎𝑛𝑑 𝑑=1,…,𝐷
2018

15. Variance for GREG 𝑉( 𝑡 𝑑i, HT) = 𝑘∈𝑠𝑑 𝑙∈𝑠𝑑 (𝑎𝑘𝑎𝑙−αkl) 𝑦𝑘y𝑙
An unbiased estimator for the design variance of the HT estimator of a domain total is:
𝑉( 𝑡 𝑑i, HT) = 𝑘∈𝑠𝑑 𝑙∈𝑠𝑑 (𝑎𝑘𝑎𝑙−αkl) 𝑦𝑘y𝑙
Where αk and αl are design weights and 𝛼 𝑘𝑙 is the inverse of the second –order inclusion probability 𝜋𝑖 𝑘𝑙 . Usually the equation is impractical. But under the assumption of Poisson sampling, the probabilities 𝜋𝑖 𝑘𝑙 are 𝜋𝑖 𝑘 * 𝜋𝑖 𝑙 for k not l. Then the double sum is easy to calculate. To apply the equation in the case of MLGREG estimation model residuals have been substituted for the original y-values.
2018

16. AROPE, GREG estimates for cities (LAUs)
2018

17. AROP, GREG estimates for cities (LAUs)
2018

18. JOBLESS, GREG estimates for cities (LAUs)
2018

19. MATDEP, GREG estimates for cities (LAUs)
2018

20. AROPE, GREG estimates for FUAs
2018

21. AROP, GREG estimates for FUAs
2018

22. JOBLESS, GREG estimates for FUAs
2018

23. MATDEP, GREG estimates for FUAs
2018

24. AROPE and AROP GREG estimates for cities
SILC % CV
≈ Bias
≈ Error
FI001C2
14.1
4.101
12.9
1.644
1.2
2.844 10
4.182
8.1
1.066
-3.0
4.066
FI002C1
16.3
6.779
19.2
6.768
-2.9
9.668
15.1
5.344
15.6
6.432
-0.3
6.732
FI003C1
21.7
7.323
25.8
9.429
-4.1
13.529
12.7
9.713
16.5
6.429
-0.9
7.329
FI004C3
7.713
18.7
7.469
-2.2
9.669
13.6
7.643
13.9
5.540
7.740
FI005C1
14.9
5.451
11.2
4.523
3.7
8.223
6.8
7.008
5.9
2.402
5.402
FI006C1
15.2
4.964
11.5
5.025
8.725
5.2
10.462
1.748
-3.2
4.948
FI007C2
11.9
7.908
11.6
7.907
0.3
8.207
7.729
9.7
7.198
-0.7
7.898
FI008C3
21.3
6.217
22.1
15.575
-0.8
16.375
18.6
5.192
18.4
14.400
8.2
22.600
FI009C1
25.5
7.141 25
18.698
0.5
19.198
16.1
7.457
15.745
8.6
24.345
Others
15.3
0.387
11.8
0.344
Total
15.7
0.218
0.190
2018

25. JOBLESS and MATDEP GREG estimates for cities
SILC % CV
≈ Bias
≈ Error
FI001C2
9.4
5.537
7.3
1.033
-2.1
3.133
3.9
10.787
2.2
0.341
-1.7
2.041
FI002C1
10.9
9.991
11.3
5.251
0.4
5.651
2.7
31.019
2.6
1.055
-0.1
1.155
FI003C1
12.9
10.121
14.7
6.533
1.8
8.333
5.6
19.264
4.4
3.148
-1.2
4.348
FI004C3
10.206
12.6
5.885
1.7
7.585
1.4
51.587
1.9
1.083
0.5
1.583
FI005C1
8.0
10.071
6.5
2.779
-1.5
4.279
39.876
0.579
0.3
0.879
FI006C1
10.6
9.548
9.7
4.537
-0.9
5.437
32.129
0.885
-0.5
1.385
FI007C2
7.4
12.693
4.9
3.196
-2.5
5.696
0.065
0.565
FI008C3
10.8
15.612
11.2
9.486
9.886
0.8
1.060
0.6
1.660
FI009C1
13.6
14.979
15.1
16.959
1.5
18.459
19.486
5.3
6.260
-2.7
8.960
Others
6.4
0.171
0.045
Total
7.6
0.120
11.5
0.190
2018

26. AROPE and AROP GREG estimates for FUAs
SILC % CV
≈ Bias
≈ Error
FI001L3
13.0
2.110
11.6
0.673
-1.4
2.073
7.2
2.663
6.8
0.420
-0.4
0.820
FI002L3
14.3
5.008
16.4
3.173
2.1
5.273
10.7
5.068
12.7
2.820
2.0
4.820
FI003L4
15.0
6.045
19.9
3.987
4.9
8.887
9.3
7.680
13.5
2.811
4.2
7.011
FI004L4
13.9
7.762
15.6
4.986
1.7
6.686
12.9
6.787
12.0
3.856
-0.9
4.756
FI007L2
16.6
4.798
12.2
4.922
-4.4
9.322
13.3
4.669
9.9
4.324
-3.4
7.724
FI008L2
6.937
17.0
8.485
10.485
15.1
4.854
7.710
-0.8
8.510
FI009L2
30.2
4.717
24.6
13.523
-5.6
19.123
18.5
5.091
18.9
11.452
0.4
11.852
FI001K2 ..
0.924
6.7
0.530
2018

27. JOBLESS and MATDEP GREG estimates for FUAs
SILC % CV
≈ Bias
≈ Error
FI001L3
7.9
3.320
6.8
0.448
-1.1
1.548
2.6
8.578
2.0
0.139
-0.6
0.739
FI002L3
8.8
7.930
9.2
2.154
0.4
2.554
2.3
21.503
2.2
0.438
-0.1
0.538
FI003L4
8.874
10.5
2.567
1.7
4.267
3.3
20.040
3.1
1.091
-0.2
1.291
FI004L4
8.7
10.147
9.3
3.337
0.6
3.937
1.0
54.062
1.4
0.587
0.987
FI007L2
7.2
10.731
4.6
1.784
-2.6
4.384
0.2
0.026
0.3
0.326
FI008L2
14.328
8.2
4.606
5.206
1.3
54.799
0.663
0.1
0.763
FI009L2
12.0
13.211
13.8
11.712
1.8
13.512
7.3
16.907
5.0
4.353
-2.3
6.653
FI001K2 ..
7.5
0.627
0.046
2018

28. AROPE GREG estimates for LAUs and SILC estimates for densely-populated areas (DB100=1) by NUTS2, persons
2018

29. AROPE GREG estimates for LAUs and SILC estimates for densely-populated areas (DB100=1) by NUTS3, persons
2018

30. Conclusions
Smaller bias, but increased variance in some domains (accuracy close to variance), overall accuracy improves by GREG -estimators
AROPE accuracy increases clearly in domains with smallest samples sizes, e.g. FI007C2, FI008C2, FI009C2, FI007L2, FI008L2, FI009L2, among them especially FUAs.
For other domains with higher sample sizes AROPE accuracy improvement is not so significant due to variance increase, which however is moderate, especially for FI001C2
AROP variance increase is marked for some cities
MATDEP variances are high
Coherence with the NUTS2 (and NUTS3) estimates for LAUs from the EU-SILC data could be better (e.g. FI1B).
2018

31. Conclusions
Rather stable variables and processes for updating estimates for LAUs and FUAs annually, assisting model for variable selection should be tested by annual SILC data
Further development, procedures are not complete
Techniques, models and parameters tests are further needed for:
- other regions, e.g. rural areas and thinly-populated areas
- inclusion of geographic areas (NUTS2) for estimation
- other SILC variables, subjective type in particular
- estimates by classification variables
Data users’ needs
2018

32. Many thanks for your attendance !
2018