1. Enumeration using frozen versions (based on slides produced by Peter Stoltze, Chief Consultant, Statistical Methods, SD)

2. Foundation of the Statistics
Definition of the population is essential in relation to interpretation of the statistics
If we do not have a firm grip on the population, everything else is unimportant!
SBR is central in this respect
Updated by administrative sources
Updated by information from different Statistical Divisions
a benefit for all Statistical Divisions

3. Definition of the Population (1)
Population of interest is the collection of objects in which we are interested
Example: All businesses in Ukraine
Target population is the section of the population of interest that we, for practical reasons, must confine ourselves to observe
Example: All businesses with at least 10 employees
Sampling frame is the data representation of the target population available to us – it is from here that the sample is drawn
Example: Extracts from SBR

4. Definition of the Population (2)
Sample
Sampling frame
Target population
Population of interest

5. Frame Imperfections
The difference between the target population and the sampling frame is due to the fact, that our registers are not perfect
Over-coverage: Businesses which are included in the sampling frame, but ought not to be included
Can be discovered during data collection
Example: The business went bankrupt long before the starting date of the reference period
Under-coverage: Businesses which ought to be included in the sample frame, but are not included
Can be discovered, if we have knowledge of the area via other sources

6. Estimation based on an updated population
Design weights are sacred
Selection probabilities are sacred
The handling of stratum changes should be conducted by calibration and domain-estimation
Estimation may account for cut-off sampling

7. Dynamic Frame Population
Current version
Historic version
Time t+2
Time t+1
Time t t
t+1
t+2

8. Frozen Frame Population
Current version
Historic version
Frozen version
Time t+4
Time t+2
Time t+3
Time t
Time t+1 t
t+1
t+2

9. Population at Estimation stage
Current version
Historic version
Frozen version
Sample
Estimation of structural survey
Estimation of short-term survey t
t+1
t+2

10. SBS statistics (all kind) (1)
Purpose:
Give information about the structure
Be able to compare across statistics
When: Year t (a period) or Ultimo t (a point in time)
Based on: A survey
100 % Big enterprises
50 % ? Medium sized enterprises
25 % ? Small enterprises
0 % ? Micro enterprises
divided eventually into sub-strata
The survey is drawn on the basis of a frozen SBR version 15th Nov year t
The survey is carried through during e.g. Marts-June t+1

11. SBS statistics (2)
New information on Year t requires updating of frozen SBR
What ?
All active enterprises and other units, as e.g. LKAU, (during the year t) have to be in the frozen version
All relevant changes/corrections (and that is changes related to the Year t and not t+1) have to be in the frozen version
but be aware of eventually bias – not only information from surveys has to be taken in
what could be the sources for updating SBR? for the year t?
When ?
Before the first SBS statistic is produced
Hopefully it is also when the information is available
Hvordan skal det fortolkes, at ikke kun information fra surveys skal indarbejdes.

12. SBS statistics (3) And now to the Enumeration
The sample was drawn 15th Nov t
The new frozen version is formed ddmmyy year t+1?
Principle: At the estimation stage we discover, that a unit selected in stratum ha with π = 0.1 has moved to stratum hb
We then have to believe that 9 other (unobserved) units from ha have made a similar move
Instead of changing the selection probabilities, the combination Activity*Size are regarded as domains, and calibration is conducted on the basis of these new domains

13. SBS statistics (4) And what does that mean?
(The table has been removed because it is not as simple as it was shown
Regression analysis has to be used
What is important is to know about the population at the time for enumeration!
See theory!!)

14. SBS statistics (5) A few names:
Horwitz-Thompson estimat or pi-expansion
the sum of design-weights over the sample within a stratum has to sum to the size of the stratum
Calibration can be implemented in the form of regression estimator
SD uses SCB CLAN survey (a collection of Swedish macros to SAS -
but other possibilities exist, e.g. package Survey to R by Thomas Lumley
google: "regression estimator sampling", "model assisted survey sampling" or "SCB CLAN survey"

15. SBS statistics (6) Problems
How do you get to know the ‘correct’ population when the frozen version 2 is formed?
How do you distribute between strata?
But it is risky only to include information from surveys
New units should not be included in the sample
Deceased units has to be placed in the stratum for deceased units so they get a weight, but it could be tricky to estimate the size (and depends whether the information is from the survey and not from the population (frozen version)

16. STS statistics (1) Purpose:
Give information about development
When: Quarter x Year t+1 (a period) or Ultimo quarter x Year t+1 (a point in time)
Based on: A survey
100 % Big enterprises, 50 % ? Medium sized enterprises, 25 % ? Small enterprises and 0 % ? Micro enterprises
divided into sub-strata
The survey is drawn on the basis of a frozen SBR version 15th Nov year t
The survey is carried through during April t+1, July t+1, October t+1 and January t+2

17. STS statistics (2) What is the problem?
What about new enterprises? In year t (from 15th Nov to 31st Dec)
What about any change from 31st Dec year t and to April, July, … t+1(2)?

18. STS statistics (2) What is the solution? Two possibilities
keep the frozen version and look at changes
Disadvantage: this does not take into account new enterprises
Advantage: easy
make new frozen versions for each quarter (or even use the actual version of SBR*) and continue as for SBS
Disadvantages:
time consuming
what is the sources for producing new versions
and to this those mentioned for SBS
Advantage: More correct description of the development
Either possibilities makes it possible to compare SBS and STS
* But it is important to know the whole population and be able to distribute to strata

19. Frozen versions Statistics Denmark
SBS year t
Version 1 (Temporary: t+1 5th Match (Turnover/Employees 15th Match)
Version 2 (Temporary: t+1 5th Sept. (Turnover/Employees 15th Sept.))
Version 3 (Final: t+1 5th Dec. (Turnover/Employees 15th Dec.))
STS 1st quarter year t+1
Version 1 (Temporary: t+1 5th May (Turnover/Employees 15th May)
Version 2 (Final: t+1 5th Aug. (Turnover/Employees 15th Aug.))
Samples might be drawn from any version before enumenation