The Household Survey In The German Census 2011

Transcription

1 The Household Survey In The German Census 2011 Wolf Bihler, Dr. Andreas Berg NTTS Bruxelles, 22 th of February 2011

2 Objectives Two Objectives: Estimation of over- and under-coverage of the German population registers and therefore indirectly the official number of people living in every municipality over inhabitants. Statistical correction of population register data Population=people in registers-overcoverage+undercoverage Results for demografic variables will be enumerated from corrected population registers Estimation of variables, not available in registers (for instance employment, migration) 2

3 Sampling frame

4 Sampling frame Address and building register (AGR) by AGR contains data from municipalities population registers, georeferenced data and data from the German Federal Employment Agency unit address Address with non-zero probability to be drawn: only addresses of residences exclusive sensitive addresses (addresses relevant for sampling) 4

5 Sampling frame Addresses relevant for sampling: Non-sensitive special addresses Addresses from population registers if positively tested as a residence address Addresses, found in the geo-referenced data and as well from sources related to the German Federal Employment Agency Addresses, only from one of the latter sources but positively tested as a residence address 5

6 Sampling frame Special addresses addresses sensitive addresses Nonsensitive addresses AGR 27,7 Mill. Addresses Population register addresses 19,1 Mill. addresses non population Register addresses addresses Sampling frame 19,9 Mill. addresses 6

7 Requirements for sampling design Sampling unit address; all individuals living at a drawn address will be surveyed Only in this way over- and undercoverage can be identified after comparing with existing people in the population registers Enumeration unit is the individual size (People living with first or secondary addresses): 7,853 Mill. (9,6% of the official number of people living in Germany by ) 7

8 Requirements for sampling design Precision requirements and regional units determined by law need to be kept in mind for results Research project managed by Uni Trier/GESIS Mannheim: Recommendations for sampling method 8

9 Stratification

10 Stratification Classical method with well-known theory carried out on two stages Stratification variables First stage -> regional Stratification Second stage -> Classes of address size Allocation on the base of the official number of people living in Germany by

11 Special addresss vs Non special addresses Split because of different concepts Relatively small number of nonsensitive special addresses 11

12 Stratification, first stage Example: NUTS 2, 3 Recommendation of the sampling project for the German Census 2011, Demands from Rheinland-Pfalz, large cities, precision restrictions 12

13 Precision restrictions Regarding total number of inhabitants: Municipalities with more than inhabitants and city districts of cities with more than inhabitants: relative coefficient of variation <=0,5% Regarding other variables: precision restrictions as well on NUTS 3 level and for Verbandsgemeinden in Rheinland-Pfalz 13

14 Precision restrictions => practical implementation: for Gemeindeverbände in Rheinland-Pfalz in general: relative coefficient of variance <=0,5% 14

15 Sampling points Regional stratification into Sampling Points (SMP s) Districts of cities with more than inhabitants (Typ 0) Municipalities from inhabitants (Typ 1) Gemeindeverbände and remains of Gemeindeverbände respectively with more than Einwohner (Typ 2) NUTS 3 remains(typ 3) 15

16 Number of sampling points by states and smp type Smp type State Total Baden-Württemberg Bayern Berlin Brandenburg Bremen Hamburg Hessen Mecklenburg-Vorpommern Niedersachsen Nordrhein-Westfalen Rheinland-Pfalz Saarland Sachsen Sachsen-Anhalt Schleswig-Holstein Thüringen Total

17 Example: Kreis Alzey-Worms Sampling Point Smp type Inhabitants Alzey VG Alzey-Land VG Eich VG Monsheim VG Westhofen VG Wöllstein VG Wörrstadt Osthofen

18 Stratification, second stage Within every sampling point stratification regarding 8 address size classes (registered people first and secondary residence), uniform number of individuals within each class 18

19 Household Survey Census Wiesbaden Address sizes Addresses Registered individuals No. From to registered individuals Population fraction Population expected fraction Total Total % Total Total Total % , ,2 37, , , ,0 37, , , ,0 37, , , ,0 37, , , ,0 37, , , ,0 37, , , ,0 37, , or more ,9 37, ,8 Total 42, ,2 301, ,0 Erwarteter relativer Standardfehler für die Einwohnerzahl: 0,13% Sonderanschriften , ,6 19

20 Allocation of the size Allocation of the sample size to the strata Microcensus: proportional allocation => choose a form of allocation accounting for different variances between the strata 20

21 Optimal Allocation Sum of squared expected relative coefficients of variation of the population (first and secondary residences from the AGR) need to be minimized for cross-classifications of sampling points and address size classes 21

22 Constraints Enumeration unit is the individual, sampling unit is address Number of people to be drawn (expected value) defined beforehand 22

23 Constraints Recommendation of the research project Optimal Allocation with box constaints Lower and upper sample fraction bounds Municipality size from to inhabitants Sampling fraction Lower bound Upper bound % 50% % 40% or more 2% 40% 23

24 Household Survey Census Wiesbaden Address sizes Addresses Registered individuals No. From to registered individuals Population fraction Population expected fraction Total Total % Total Total Total % , ,2 37, , , ,0 37, , , ,0 3, , , ,0 37, , , ,0 37, , , ,0 37, , , ,0 37, , or more ,9 37, ,729 9,8 Total 42, ,2 301, ,093 3,0 Erwarteter relativer Standardfehler für die Einwohnerzahl: 0,13% Sonderanschriften , ,6 24

25 Household survey Census Verbandsgemeinde Monsheim (Kreis Alzey-Worms) Address sizes Addresses Registered individuals No. From to registered individuals Population fraction Population expected fraction Total Total % Total Total Total % , ,0 1, , ,0 1, , ,0 1, , ,1 1, , ,9 1, , ,2 1, , ,6 1, ,7 8 6 or more ,0 1, ,6 Total 3, ,9 10, ,225 22,2 Erwarteter relativer Standardfehler für die Einwohnerzahl: 0,16% Sonderanschriften 25

26 Sampling points not to be included in the optimization process Allocation of the sample size Fixed sample fraction of 5% for all strata of Gemeindeverbände (with the exception of strata in Rheinland-Pfalz of SMP type 2) and NUTS 3 remains 26

27 Example: Kreis Alzey-Worms Sampling Point Smp type Inhabitants Alzey 1 17,732 VG Alzey-Land 2 24,382 VG Eich 2 12,488 VG Monsheim 2 10,124 VG Westhofen 2 11,721 VG Wöllstein 2 11,851 VG Wörrstadt 2 28,177 Osthofen (Stadt) 3 8,283 27

28 Optimal allocation algorithm Due to several different constraints the classical formula for optimal allocation need to be modified. Implementation of an algorithm developed by University of Trier and GESIS Mannheim Programmed in R 28

29 Special addresses No sampling point allocation but aggregation on NUTS 3 level Uniform sample fraction 10% Constraint: At least 2 addresses need to be drawn 29

30 Household survey Census Wiesbaden Address sizes Addresses Registered individuals No. From to registered individuals Population fraction Population expected fraction Total Total % Total Total Total % , ,2 37, , , ,0 37, , , ,0 37, , , ,0 37, , , ,0 37, , , ,0 37, , , ,0 37, , or more ,9 37, ,729 9,8 Total 42, ,2 301, ,093 3,0 Erwarteter relativer Standardfehler für die Einwohnerzahl: 0,13% Special addresses ,8 2, ,6 30

31 Implementation

32 Implementation normal addresses Drawing of normal addresses in SAS using proc SURVEYSELECT Number of sample addresses determined by optimal allocation algorithm Simple random sampling without replacement in every stratum Output: Address-ID s of sampled addresses (household survey/post enumeration survey) for marking in AGR 32

33 Implementation non-sensitive special addresses Drawing of non-sensitive special addresses in SAS with proc SURVEYSELECT Number of addresses to be drawn determined by 10%-rule Systematic sampling within each stratum (here: NUTS 3) Sorting of addresses within each stratum by address size (Avoiding extreme sampling errors) 33

34 Performance Drawing of addresses in SAS using procedure proc SURVEYSELECT Normal addresses 15 sec Special addresses under 1 sec 34

35 Household survey Census Wiesbaden Address sizes Addresses Registered individuals No. From to registered individuals Population fraction Population expected fraction Total Total % Total Total Total % , ,2 37, , , ,0 37, , , ,0 37, , , ,0 37, , , ,0 3, , , ,0 37, , , ,0 37, , or more ,9 37,720 3,697 3,729 9,8 Total 42, ,2 301,602 9,075 9,093 3,0 Expected relative coefficient of variance for total number of inhabitants: 0,13% Non-sensitive special addresses ,8 2, ,6 35

36 Household survey Census Verbandsgemeinde Monsheim (Kreis Alzey-Worms) Address sizes Addresses Registered individuals No. From to registered individuals Population fraction Population expected fraction Total Total % Total Total Total % , ,0 1, , ,0 1, , ,0 1, , ,1 1, , ,9 1, , ,2 1, , ,6 1, ,7 8 6 or more ,0 1, ,6 Zus. 3, ,9 10,543 2,337 2,225 22,2 Expected relative coefficient of variance for total number of inhabitants : 0,16% Non-sensitive special addresses 36

37 Household survey Census Buxtehude Address sizes Addresses Registered individuals No. From to registered individuals Population fraction Population expected fraction Total Total % Total Total Total % , ,2 5, , , ,9 5, , , ,0 5, , , ,0 5, , ,9 5, , ,7 5, , ,2 5, , or more ,0 5,186 1,357 2,074 26,2 Zus. 10, ,0 41,322 4,234 4,957 10,2 Expected relative coefficient of variance for total number of inhabitants : 0,54% Non-sensitive special addresses 37

38 State Address Population sizes and sampling fractions for states Normal addresses Person Population addresses Residents expected Residents realized Sampling fraction addresses Proportion of residents expected Proportion of residents realized SH 857, ,763 76,280 2,86, , % 9.67% 9.65% HH 264,780 1,750,708 6,784 62,416 62, % 3.57% 3.54% NI 2,343,781 8,177, , , , % 9.85% 9.83% HB 148, ,811 4,063 28,136 28, % 4.24% 4.34% NW 4,084,030 18,146, ,514 1,487,655 1,487, % 8.20% 8.20% HE 1,519,560 6,333, , , , % 11.59% 11.58% RP 1,253,844 4,150, , , , % 13.31% 13.32% BW 2,553,507 10,697, ,235 1,135,841 1,135, % 10.62% 10.62% BY 3,102,221 12,840, ,153 1,165,681 1,166, % 9.08% 9.08% SL 318,532 1,058,720 41, , , % 12.36% 12.34% BE 310,273 3,451,337 7, , , % 3.60% 3.55% BB 671,536 2,547,525 74, , , % 11.70% 11.69% MV 391,046 1,666,991 30, , , % 8.53% 8.55% SN 902,723 4,209,897 90, , , % 8.76% 8.78% ST 618,954 2,325,709 75, , , % 10.42% 10.44% TH 570,327 2,245,224 48, , , % 8.69% 8.67% Total 19,910,826 83,226,209 1,948,371 7,759,228 7,756, % 9.32% 9.32% 38

39 State Address Population sizes and sampling fractions for states Non-sensitive special addresses Person Population addresses Residents expected Residents realized Sampling fraction addresses Proportion of residents expected Proportion of residents realized SH , ,284 3, % 10.01% 9.31% HH , ,949 2, % 10.16% 11.16% NI 2,479 92, ,514 9, % 10.28% 10.00% HB 150 7, % 10.70% 9.85% NW 3, , ,252 2, % 10.22% 10.13% HE 1,516 60, ,029 6, % 9.97% 10.32% RP , ,072 4, % 11.95% 11.07% BW 3, , ,067 12, % 10.06% 9.22% BY 3, , ,137 17, % 10.92% 10.68% SL , , % 9.72% 9.83% BE , ,159 3, % 10.08% 9.66% BB , ,125 2, % 11.32% 10.52% MV , ,110 2, % 18.86% 20.19% SN , ,741 6, % 10.13% 10.98% ST , ,891 3, % 9.70% 10.12% TH , ,186 2, % 12.25% 10.77% Total 19, ,037 2, ,355 99, % 10.54% 10.30% 39

40 sizes and sampling fractions for states Totals State Address Population Person Population addresses Residents expected Residents realized Sampling fraction addresses Proportion of residents expected Proportion of residents realized SH 857,898 2,993,573 76, , , % 9.68% 9.64% HH 265,036 1,769,900 6,810 64,365 64, % 3.64% 3.63% NI 2,346,260 8,270, , , , % 9.85% 9.84% HB 148, ,722 4,079 28,983 29, % 4.32% 4.40% NW 4,087,803 18,344, ,899 1,507,907 1,507, % 8.22% 8.22% HE 1,521,076 6,394, , , , % 11.57% 11.57% RP 1,254,694 4,192, , , , % 13.30% 13.30% BW 2,556,883 10,837, ,574 1,149,908 1,148, % 10.61% 10.60% BY 3,105,309 13,006, ,488 1,183,818 1,183, % 9.10% 9.10% SL 318,827 1,068,930 41, , , % 12.34% 12.32% BE 310,769 3,492,597 7, , , % 3.68% 3.62% BB 671,954 2,575,126 74, , , % 11.69% 11.68% MV 391,255 1,678,176 30, , , % 8.60% 8.63% SN 903,573 4,266,553 90, , , % 8.78% 8.81% ST 619,508 2,355,514 76, , , % 10.41% 10.44% TH 570,798 2,271,234 48, , , % 8.73% 8.69% Total 19,930,373 84,188,246 1,950,420 7,860,583 7,856, % 9.34% 9.33% 40

41 Post enumeration survey Post enumeration survey for quality assessment of the official number of population drawn immediately after household survey as a sub sample Large municipalities from inhabitants Design similar to household survey, aggregation of address size strata if needed Sub-sample fraction 5% uniformly in every strata 41

42 Post enumeration survey Smaller municipaltities with less than inhabitants Stratification regarding 2 municipality size classes (less than 2,000 inhabitants/ more than 2,000 inhabitants) Within each municipality size class stratification analogous to household survey with few additional aggregation possibilities of SMPs For each (combined) SMP sample size 0.3 % of the official number of inhabitants by Allocation of sample size (addresses) uniformly to the address size classes of a (combined) SMP s 42

43 Outlook

44 Outlook What else need to be done? Additional sampling of newly detected addresses in the AGR after (carried out April 2011) Most important source is another data supply of the population registers by Probably small numbers, simple design to be proposed Estimation and Calculation of errors Implementation of recommendations from research project Partial implementation of small area estimators Two parts: First preliminary results, 18 months after due date Final results, 24 months after due date 44

45 Thank you for your attention! Questions? Andreas Berg, Wolf Bihler,