1. New estimation system in Danish Intrastat Mr Søren Rich, Senior Adviser, Statistics Denmark
ESTP course 'Advanced issues in international trade in goods statistics‘ Eurostat, Luxembourg, 3 April 2014

2. Overview Background The old estimation system
A need for a single new estimation system
The new estimation system
Experience from using the new estimation system

3. Background Good and early access to VAT data in Denmark
In the past, VAT data have been used extensively in estimation of intra-EU adjustments …
… and a good and extensive validation of VAT/Intrastat differences at PSI level has taken place
However, contents of VAT had changed in recent years…
… and a review of old practice and the two-string estimation system was needed.
New system developed

4. The old estimation system (1)
Two systems, both using a bottom-up approach in the estimation
A FLASH estimation system for estimation of missing trade in the aggregated statistics (latest month)
The system forecasts using a growth rate approach, calculating growth rates using data from PSIs in same 4-digit NACE group
Estimates both non-response and below threshold trade
Use the face value of Intrastat and check for partial non-response is only done manually for the largest and most obvious examples of underreported value.
A system for estimation of missing trade in the releases of detailed statistics. The system is named MESTER (M for the Danish word for VAT (Moms) and ESTer for estimation)…

5. The old estimation system (2)
MESTER takes an approach where each month is handle independently and where VAT is used extensively to compensate for missing Intrastat.
Estimates both non-response and below threshold trade
If Intrastat is missing, VAT value is applied and if VAT is larger than Intrastat a partial non-response adjustment is added:
in arrivals the adjustment is calculated as 43 per cent of the Intrastat/VAT difference – in dispatches the correction factor is 53 per cent.
no adjustments are made if Intrastat value is higher than VAT.
the correction factors are based on a survey of revision patterns in Intrastat and VAT. However, the correction factors have not been updated in recent years.

6. The old estimation system (3)
MESTER needs a good validation of differences between VAT/Intrastat to work properly…
The prerequisite for the partial non response practice in MESTER has been a good and extensive validation of VAT/Intrastat differences at PSI level…
... so that that large differences between VAT/Intrastat had been validated and that remaining differences was caused by underreporting in Intrastat.
But validation of VAT/Intrastat in recent years has pointed toward that in most cases Intrastat turn out to be correct: the differences are mainly explained by wrongful declaration of VAT or that the VAT value include transactions which is not part of Intrastat, i.e. triangular trade, installation services, etc….
… this change could be caused by change of VAT reporting behavior or gradually change in contents of the VAT statements.

7. Need for a single estimation system
Two systems with different methodology can create revisions when the compilation of a specific reference month change from one to the other estimation system
Too inadequate handling of underreported trade (partial non-response) in FLASH
Too ‘efficient’ estimation of underreported trade (partial non-response) in MESTER…
A single system with a common methodology was needed…

8. The new estimation system: The basic principles
We use Intrastat if it is available, but we check for underreported Intrastat or partial non response
If we historically have a good and stable relation between Intrastat and VAT for a specific PSI, then we will used VAT in case of missing Intrastat
In case of unstable relation between Intrastat and VAT, a limited range of forecast tools are applied, based on the optimal set of input data.
All EU traders are divided in 3 groups, according to the availability of Intrastat:
Exempted enterprises
Intrastat PSIs with short period of historical Intrastat data available (less than 13 months historical Intrastat)
Intrastat PSIs with long period of historical Intrastat data available (13 or more months with historical Intrastat)

9. Below threshold trade
In cases of exempted trader (below threshold traders), we use the reported VAT value of the enterprises in question
In case of voluntary Intrastat declarations, we use the value of Intrastat
In case of missing VAT declarations (small enterprises can declare VAT at quarterly or semi-annual basis), we forecast the missing VAT
In cases of traders above the threshold without any historical Intrastat – mostly enterprises which have not yet become Intrastat PSIs – we also use the value from VAT statements.

10. Estimation of non-response
We divide all the PSI with non-response according to the availability of Intrastat:
Intrastat PSIs with short period of historical Intrastat data available (less than 13 months historical Intrastat)
Intrastat PSIs with long period of historical Intrastat data available (13 or more months with historical Intrastat)
This is done to group the PSIs according to the estimation methods, which can produce the best results:
ad 1): We use a fixed effect model
ad 2): We use the fixed effect model or corrected VAT in case of stable relationship between VAT and Intrastat.

11. Estimation of non-response: Fixed effect model (1)
We have tested various panel estimation models and regression models as forecast methods for missing Intrastat.
Our analyses have shown that a fixed effect model produce the best prediction of Intrastat.
Fixed effect models are regression models where the constant term is dependent on the incoming independent (explanatory) variables, e.g. the dependent variable can be modelled by…

12. Estimation of non-response: Fixed effect model (2)
Yi = Xij βj + εi i = 1,…,n where Yi is the dependent variable Xij are the independent variables (character or numeric variables) β1 ,…, βp are fixed effect parameters and ε1 ,…, εn are independent identical normal-distributed stochastic variables with mean 0 and variance σ2.

13. Estimation of non-response: Fixed effect model (3)
Having tested different models, the following model is considered to provide the best description of the data material by the use of the following set of dependent variables (Xij j = 1 … p):
Model: FORECAST= Level + UHO + MOMS + UHO*YM_NUM
UHO (PSI identifier), character variable, a dummy variable is created for each value of UHO with the value 1 for the current UHO and the value 0 for all others,
MOMS, numeric variable, the observed VAT
YM_NUM, numeric time variables, here only the values 1, 2, 13 and 14 are used, i.e. the current month (14), the previous month (13) and the two corresponding months of the previous year (1 and 2).

14. Estimation of non-response: Fixed effect model (4)
That is, FORECAST is modelled as a function of the independent variables UHO (the PSI), MOMS (the reported VAT) and UHO*YM_NUM (the interplay of PSI and year/month). The estimation uses the current month, the previous month and the two corresponding months of the previous year.

15. Estimation of non-response: Fixed effect model (5)
The estimation is done using the SAS procedure PROC MIXED
The fixed effect model makes the best prediction when VAT is available for the month with missing Intrastat value and when Intrastat is available in the two corresponding months of the previous year.
Because of less good results for Intrastat PSIs with short period of historical Intrastat data available, we are planning to look at these possibility to introduce trend-correction methods for these PSI.

16. Estimation of non-response: Stable relation between VAT and Intra (1)
Some PSI has a very stable relationship between Intrastat and VAT. In these cases VAT value can be a good proxy for a missing Intrastat value.
All PSI with non-response where long series of historical Intrastat and VAT data are available, we test for stable relationship.
This is done using a simple linear regression model:
I = +β V+ ε
where I is the dependent variable, Intrastat value, V is the independent variable, VAT value,  is a constant, i.e. the intercept value, β is parameter giving the slope of the linear relation and e is a independent identical normal-distributed stochastic variable with mean 0 and variance σ2.

17. Estimation of non-response: Stable relation between VAT and Intra (2)
To detect stable relation we rank the PSIs according to their individual value of the coefficient of determination R2. In case of the simple linear regression the R2 is simply the square of the sample correlation coefficient between Intrastat and VAT. R2 will have a value between 0 and 1, and the greater value, the greater is the correlation.  
In case of high value of R2 and   1 and   0 then Intrastat = VAT and VAT value can be applied in case of missing Intrastat. In case of   1 and   0 then Intrastat can be calculated at  + V.
In case that both   1 and   0 no stable relationship exists.

18. Estimation of non-response: stable relation between VAT and Intra (3)
  1
  1
  0
VAT value V is used
Compare VAT value V with predicted value of fixed effect model*
  0
 + V is used, but the estimate is compared with predicted value of fixed effect model*
Use panel estimation with fixed effect model
* A manual check of the largest adjustments will be carried out

19. Partial non-response test
All month where a PSI has reported Intrastat are checked for potential partial non-response. Declarations of each PSI is tested for outliers (small values) using this score function:
(Monthly obs. – Q2 value)
(Q3 value – Q1 value)
where Q2 is the median value of the PSI and Q1 and Q3 is lower and upper quartiles at PSI level. The test is done on
monthly Intrastat values and
monthly values of the Intrastat/VAT relation
In cases where both outlier tests indicates a low value, an adjustment equal to the differences between VAT and Intrastat (if VAT > Intrastat) is added to the reported value of Intrastat.

20. False nil declarations
Sometimes PSIs are wrongly declaring zero trade (nil declarations) to avoid penalties for late reporting or to avoid the burden of reporting.
To adjust for this, all monthly nil declarations are matched with the corresponding VAT declarations at PSI level.
In the cases where the VAT or Intrastat data has not been corrected in our VAT/Intrastat Quality Control System, an adjustments of Intrastat is made if a positive value has been declared in the VAT declaration.
The false nil declarations identified in the estimation system are checked afterwards in the Quality Control System.

21. Experience gained from using the new estimation system
The new estimation system, called ESTER (as in ESTimation) was introduced in October 2012 in the monthly production of 2012 data.
The system has also been used for revising
The system has resulted in an expected lowering of intra-EU arrivals of 2 per cent and 1 per cent of intra-EU dispatches, producing a minor data break between 2008 and 2009.
The new system has lowered the level of revisions compared with the old estimation system.

22. Implementation of complete data compilation system
In connection with the development of new estimation system, Statistics Denmark has also redesigned the system for compilation of the statistics. This has resulted in:
consolidation of the basic data extracted for the compilation
more coherent and user friendly system for the data compilation
more coherency in the data deliveries to Eurostat, Balance of Payment/National Account and our own dissemination
and the One Button system!!...

23. The One Button system
”We have custom made your key board so it only includes the buttons, which is strictly necessary for your job. Smart, right?”

24. The end
Thanks a lot for your attention!
Mr Søren Rich,