Backcasting manual : 2025 edition.
Date: 2025-07-24
Institutions: Eurostat
Subjects: EU statistics, economic activity, economic statistics, regulation (EU), statistical method, user guide, value chain

Backcasting manual 
2025 edition

M A N UA L S   A N D 
G U I D E L I N E S

Backcasting manual  2025 edition

Manuscript completed in June 2025

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Contents

Contents 

1. Introduction

2. Main changes from original NACE Rev. 2 to NACE Rev. 2.1 

3. Assignment of new activity codes in the business register

3.1 The top-down method 

3.2 Enterprise-level observations broken down by (groups of) activities 

3.2.1 Applying an ideal intermediary classification 
3.2.2 Suboptimal intermediary classification  

3.3 Imputing unobserved enterprise activities 

3.3.1 Deterministic imputation 
3.3.2 Stochastic imputation 
3.3.3 Imputing multiple weighted values per unit 

3.4 Treating units formerly outside the frame 

3.5 Automated recoding in business registers: guidance and practical experience 

4. Backcasting approaches 

4.1 Use of a key 

4.2 Microdata approach 

4.3 Aggregate approach 

4.4 Defining characteristics of the microdata and aggregate approaches  

5

7

10

14

14

15
15
16

17
18
18
18

19

19

20

20

20

21

23

4.5 Comparison of the microdata and aggregate approaches in an empirical example      23 

5. Application of the microdata approach 

25

5.1 Full replication of the production system 

5.2 Backcasting using aggregation matrices 

25 

25

 
5.3 Adaptation of the microdata approach to random samples 

5.4 Backcasting time series of sample surveys 

6. Application of the aggregate approach using conversion coefficients

6.1 Ad hoc conversion coefficient estimators 

6.2 Ordinary least squares coefficient estimator 

6.3 The benchmark/interpolation method  

7. Statistical disclosure control in the context of parallel dissemination 

7.1 Introduction 

7.2 Problem description  

7.3 Protection of the backcasted data – suppression  

7.4 Protection of the backcasted data – other methods  

7.5 Conclusions  

List of symbols 

Glossary 

References 

ANNEX: Statistical disclosure control when publishing by two NACE versions  

1. Problem description

1.1 Introduction 

1.2 Derivation through differencing 

1.3 Current best methods 

2. Assumptions

2.1 Intruder knowledge 

2.2 Granularity 

3. Double reporting: two cases

3.1 Backcasting 

3.1.1 Suppression 
3.1.2 Perturbative methods 
3.1.3 Rounding 
3.1.4 Table redesign 

3.2 Direct double tabulation 

4. Conclusion

Bibliography related to the literature review 

29

29

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32

33

36

38

38

38

39

40

40

41

43

45

48

49

49

49

50

51

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1

Introduction

1Introduction

In October 2022, the European Commission (‘the Commission’) updated the common statistical classification of 
economic activities in the European Union (NACE). This took place by means of Commission Delegated Regulation 
(EU) 2023/137 [1] (the ‘NACE Rev. 2.1 Delegated Act’), which established NACE Revision 2 Update 1 (‘NACE Rev. 2.1’), 
thus updating NACE Revision 2 (‘NACE Rev. 2’) which has been applied to European statistics since 2008. The NACE 
Rev. 2 classification was established in Regulation (EC) No 1893/2006 [2] (‘the NACE regulation’) which replaces the 
previous NACE version (NACE Rev. 1.1) [3]. The NACE regulation also empowers the Commission to update its Annex I 
(which contains the codes and headings of the NACE Rev. 2 categories) to take account of technological or economic 
developments or to align it with other economic and social classifications.  

The transition from NACE Rev. 2 to NACE Rev. 2.1 requires that national statistical institutes (NSIs) backcast existing 
statistical time series (i.e. that they re-express them in terms of NACE Rev. 2.1) applying the most appropriate methods. 
Backcasting is a statistical technique that can be applied to historical statistics reported according to a classification 
- preferably in in such a way that consistency is preserved - to render backwards predictions of the same statistics
expressed in terms of a new version of the same classification (1). The length of the NACE Rev. 2.1 backcasting periods
has been set out for a number of statistical domains in Commission Implementing Regulation (EU) 2024/1840 [5] (the
‘NACE Rev. 2.1 Implementing Act’):

•
•

for short-term business statistics, data will be backcast retrospectively until the 2021 reference period;
for global value chain statistics, data will be backcast retrospectively until the 2021-2023 reference period.

Taken together with additional requirements which may progressively be put in place through other legal acts, this 
means that there is a high demand in Europe for methodological guidance in applying backcasting techniques to 
maintain coherent time series. This demand is similar to the one observed at the global level [6].

There are several possible procedures that could be used to apply a revised classification to historical time series. They 
can be divided into two main approaches:

• Recoding statistical units and thereafter recalculating the statistics (the microdata approach);
• Converting published series by applying conversion coefficients to the statistics (the aggregate approach).

Both of these approaches are described in this manual. The presentations of the methods are not intended to be 
exhaustive or prescriptive, as the choice depends on many factors such as: 

• The kind of statistics to be backcasted (raw data, aggregates, indices, growth rates…).
• The availability and quality of microdata based on the old version of the classification.

(1)  Also see [4] for a discussion on the importance of backcasting and the sensitivity of time series with respect to different methods to cope with the changes to 
classifications when producing long time series.

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1

Introduction

• The availability of microdata or aggregated data double coded according to both the old and the new versions of the

classification.

• The number of reference periods for which double coded data are available.
• The frequency of the existing time series.
• The frequency and the level of detail required for the backcasted series.
• Cost/effectiveness considerations.
• Human resource constraints (IT staff and skilled statisticians).
• Timeliness considerations.
• The ease of reconciliation of potential breaks in backcasted time series.

The methods described in the current manual can be applied to backcasting of time series for statistical units which 
are economic entities (enterprises, local units, kind-of-activity units). With the necessary adaptations, they may also be 
applicable to other statistical units (such as individuals or households).

The methods assume that all the units recorded in the Statistical Business Register (referred to as the ‘business register’ 
below) are double coded according to the old and new versions of the classification for at least one point in time using 
the same information on the activity description for the double coding approach. Further details on the double coding 
strategy are described in the Handbook on implementation of NACE Rev. 2.1 in Business registers [7]. 

Regarding the changeover to NACE Rev. 2.1:

•

•

Article 2 of the NACE Rev. 2.1 Delegated Act [1] requires that NACE Rev. 2.1 should be applied to data transmissions
(to Eurostat) relating to reference periods from 1 January 2025 (with application delayed to later years for a number
of statistical domains)
the NACE Rev. 2.1 Implementing Act [5] stipulates that:
‘In order to serve the needs of business statistics producers and to ensure the authoritative role of the statistical 
business registers, national statistical business registers and the EuroGroups Register should provide users with 
double coding according to both original NACE Rev. 2 and NACE Rev. 2.1 for at least the reference year 2025. 

Double coding for additional years or other supporting methods may be put in place at national level based on 
an agreement with national users.'

Good practice of NSIs includes informing the users of statistics about the changes in classification of economic 
activities and publishing a timetable for the release of recalculated time series (as well as the period for which double 
reporting of time series according to NACE Rev. 2 and NACE Rev. 2.1 is foreseen) for selected variables in both NACE 
versions. This has been done for a number of business statistics domains through the NACE Rev. 2.1 Implementing Act. 
When backcasting, different special circumstances have to be taken into account:

• Consideration has to be paid to exogenous shocks (2).
• For parallel dissemination of the same time series according to the two different versions of NACE (be it based on

double coding or on backcasting), additional statistical disclosure risks might arise.

• Double coding in business registers will often result in a heightened scrutiny of the units therein. Thus, errors might
be spotted for how a unit has been encoded in the old version of the classification. This will normally be corrected
directly in the business register, but when carrying out the analysis necessary for backcasting, one will have to keep
track of which data are based on ‘uncorrected’ entries and which data are based on ‘corrected’ entries.

(2) A general methodological aspect of backcasting is that if double coded years affected by exogeneous shocks (i.e. severe financial shocks and crises, 
pandemics, etc.) are used as a basis, there is a high likelihood of obtaining estimates which cannot be extrapolated. Hence, two specific approaches should be 
considered: 

•

•

Backcasting for years unaffected by an exogenous shock should not be based on double coded years affected by an exogenous shock.

Backcasting for years affected by an exogenous shock should be based on double coded years affected by the same exogenous shock.

For comparable data within the European Statistical System, a coordinated approach among countries and the different concerned statistical areas within a 
country is recommendable.  

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Backcasting manual

1

Introduction

The current manual is partly based on the backcasting manual prepared by Eurostat in 2009 [8] and considers the 
experiences of NSIs in backcasting NACE Rev. 1.1 time series in terms of NACE Rev. 2. It has, however, gone through a 
considerable overhaul in order to arrive at a common conceptual framework (including cohesive notation as well as an 
improved analysis of the defining characteristics of the microdata and aggregate approaches).  Moreover, a chapter on 
statistical disclosure control has been introduced to highlight the specific risks associated with the parallel publication 
of statistics broken down by two versions of a classification.

The manual is organised as follows:

• Chapter 2 presents the main changes introduced by NACE Rev. 2.1. The presentation is mainly quantitative, in order to

highlight the number of categories involved in any reclassification.

• As noted above, the various backcasting methods presented in detail in this manual all presuppose that the business
register  is double coded according to the old and the new classification for at least one point in time. Therefore,
before proceeding to present the backcasting methods, Chapter 3 describes several methods for reclassification of
statistical units in a statistical business register.

• Thereafter, Chapter 4 provides an overview of the main approaches for backcasting of statistical time series (the
microdata approach, the aggregate approach and a combination of both) and their respective advantages and
disadvantages. For completeness, the ‘key method’ is also described, which however is of only limited applicability in
the context of NACE Rev. 2.1.

• A more detailed description of the main approaches based on experiences of NSIs are provided in Chapters 5

(microdata approach) and 6 (aggregate approach).

• Finally, Chapter 7 discusses the statistical disclosure risks that arise due to the parallel dissemination of the same time
series. Therein, it is noted that the statistical disclosure control (SDC) treatment must be performed at the national
level since microdata (normally not transmitted to Eurostat for business statistics) are needed to evaluate whether
individual units are identifiable. Moreover, it is concluded that whenever possible, priority should be given to the
dissemination of data according to the newer version of the classification (while restricting dissemination of data
according to the older version).

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1

Introduction

2Main changes from 

original NACE Rev. 2 to 
NACE Rev. 2.1

The main changes introduced by NACE Rev. 2.1 are the following:

• NACE Rev. 2 division 45 ‘Trade and repair of motor vehicles and motorcycles’ has been removed and the activities

moved to NACE Rev. 2.1 divisions 46 ‘Wholesale trade’, 47 ‘Retail trade’ and 95 ‘Repair and maintenance’.

• Retail trade: online and in-store sales have been merged – the means of sale is no longer considered.
•

Intermediation services: NACE Rev. 2.1 groups and classes for intermediation service activities have been created in
existing NACE Rev. 2 divisions and groups.

• NACE Rev. 2 Section J ‘Information and communication activities’ has been split into NACE Rev. 2.1 sections J

‘Publishing, broadcasting, and content production and distribution activities’ and K ‘Telecommunication, computer
programming, consulting, computing infrastructure and other information service activities’.

Table 1 gives an overview of the impact of the changes on the number of sections, divisions, groups and classes of 
the new version of NACE. A detailed overview of the main changes in NACE Rev. 2.1 compared to NACE Rev. 2 are 
described in the NACE Rev. 2.1 publication [9]. 

10

Backcasting manual

Main changes from original
NACE Rev. 2 to NACE Rev. 2.1

2

TABLE 1
Number of categories in original NACE Rev. 2 and in NACE Rev. 2.1

NACE level

NACE Rev.2

NACE Rev.2.1

Difference

Sections (1 letter)

Divisions (2 digits)

Groups (3 digits)

Classes (4 digits)

21

88

272

615

22

87

287

651

+1

–1

+15

+36

The NACE Rev. 2 – NACE Rev. 2.1 correspondence table [10] is the starting point for establishing the link between 
the old and the new classification. Table 2, which is based on Version 1.05 of the NACE Rev. 2 – NACE Rev. 2.1 
correspondence table [11] provides statistics on the types of correspondences. Examples 1a and 1b below illustrate two 
of the different types of correspondences.

The correspondence tables helps users to understand the relationship between the old and new NACE categories, 
discern the scope of changes and understand how update 1 to NACE Revision 2 affects the comparability over time 
of statistics based on NACE. The correspondence table provides the framework for calculation of the conversion 
coefficients. The conversion coefficient concept is defined in the glossary of this manual (cf. page 46). 

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2 Main changes from original

NACE Rev. 2 to NACE Rev. 2.1

TABLE 2
Proportion of NACE Rev. 2 categories affected by the changes introduced by NACE 
Rev. 2.1 (by level and type of correspondence)

Type of correspondence

2-digit
categories 
(divisions)

3-digit
categories 
(groups)

4-digit
categories 
(classes)

One-to-one – 1:1 
The scope of a single NACE Rev. 2 category is completely 
identical to that of a single NACE Rev. 2.1 category  

33 (38%)

141 (52%)

354

(58%)

Many-to-one – n:1 
The joint scope of two or more NACE Rev. 2 categories 
is completely identical to that of a single NACE Rev. 2.1 
category 

One-to-many – 1:m 
The scope of a single NACE Rev. 2 category is completely 
identical to that of the joint scope of two or more NACE 
Rev. 2.1 categories 

Many-to-many – n:m 
The joint scope of two or more NACE Rev. 2 categories is 
completely identical to that of the joint scope of two or 
more NACE Rev. 2.1 categories

0 (0%)

4

(1%)

25

(4%)

0 (0%)

3

(1%)

11

(2%)

55 (63%)

124 (46%)

225

(37%)

Total 

88 (100%)

272 (100%)

615 (100%)

Example 1a: one-to-many correspondence

NACE Rev. 2 class 16.10 of is split into NACE Rev. 2.1. classes 16.11 and 16.12.

NACE Rev. 2

NACE Rev. 2.1

Class

Heading

Class

Heading

16.10

Sawmilling and planing of wood

16.11

Sawmilling and planing of wood

16.10

Sawmilling and planing of wood

16.12

Processing and finishing of wood

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Main changes from original
NACE Rev. 2 to NACE Rev. 2.1

2

Example 1b: many-to-many correspondence

NACE Rev. 2 classes 20.51, 20.52, 20.53 are merged into NACE Rev. 2.1 class 20.59, along with most (3) of the activities 
covered by NACE Rev. 2 class 20.59. The remainder of the activities covered by NACE Rev. 2 class 20.59 (4) are 
allocated to class 20.51 of NACE Rev. 2.1.

NACE Rev. 2

NACE Rev. 2.1

Class

Heading

Class

Heading

20.51

Manufacture of explosives

20.59

Manufacture of other chemical products n.e.c.

20.52

Manufacture of glues

20.59

Manufacture of other chemical products n.e.c.

20.53

Manufacture of essential oils

20.59

Manufacture of other chemical products n.e.c.

20.59

Manufacture of                                           
other chemical products n.e.c. (4)

20.51

Manufacture of liquid biofuels

20.59

Manufacture of                                          
other chemical products n.e.c. (3)

20.59

Manufacture of other chemical products n.e.c.

(3) Essentially all activities that do not concern the manufacture of biodiesel; see the ‘common content’ column of Version 1.05 of the NACE Rev. 2 – NACE Rev. 2.1 
correspondence table [11].

(4) Mainly manufacture of biodiesel, as indicated in the ‘common content’ column of Version 1.05 of the NACE Rev. 2 – NACE Rev. 2.1 correspondence table [11].

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1

Introduction

3Assignment of new 

activity codes in the 
business register

The most important prerequisite for the transition to the new classification is a double-coded statistical business 
register (5), as the quality of the backcasted data depends on the quality of the business register. Backcasting of data 
requires at least one reference period (typically one year) of double coding in the business register, according to the 
principal activity of the units. Several methods can be applied for assigning a new activity code. Subsections 3.1 
through 3.3 present relevant methods, which – depending on the information available (or possible to gather) – can be 
combined to arrive at new activity codes.

The 2021 edition of the European business statistics methodological manual for statistical business registers [12] based 
on legal requirements and national practices and the Handbook on implementation of NACE Rev. 2.1 in Business 
registers [7] both provide useful guidance on updating the activity code of statistical units.

3.1 The top-down method

The top-down method is only possible to apply in cases when sufficiently granular information (obtained by means 
of observation or modelling) concerning the share of value added per activity is available. It follows a hierarchical 
principle; the classification of a unit at the lowest level of the classification must be consistent with the classification of 
the unit at the higher levels of the structure [9]. To satisfy this condition, the process starts with the identification of the 
relevant highest level and progresses down through the levels of the classification in the following way:

Identify the section which has the highest share of the value added.

•
• Within this section: identify the division which has the highest share of the value added.
• Within this division: identify the group which has the highest share of the valued added.
• Within this group: identify the class which has the highest share of value added.

(5)  Double coding by means of direct observation of each unit is not strictly necessary. Less costly approaches could be applied to achieve double-coded units, 
such as the automated encoding described in Section 3.5. 

Model-based approaches could be considered, but would rely upon a number of assumptions, some of which would not be possible to verify empirically. 

While sample-based approaches could be used for unbiased recoding, the large number of different NACE positions that are split would render it practically 
unfeasible to obtain conversion coefficients for all of them with a reasonable amount of precision.    

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Assignment of new activity codes
in the business register

3

3.2 Enterprise-level observations broken down by (groups of) activities

The backcasting handbook [8] produced by Eurostat at the time of the changeover from NACE Rev. 1.1 to NACE Rev. 2 
suggests the use of an intermediary classification when collecting information on activities carried out by enterprises. 
The observation of (groups of) activities carried out in each unit (for instance, through using an intermediary 
classification) can, although it is demanding in terms of resources, greatly facilitate or improve backcasting. 

3.2.1 Applying an ideal intermediary classification

The ideal intermediary classification should be developed in a way that allows unambiguous identification of the 
principal activity of an enterprise according to both the old and new classifications. It is considered evident that any 
‘intermediate classification’ which meets the criterion of being unambiguous will need to be at least as granular as the 
correspondence table between the two classifications. Thus, the coarsest option for the subclasses to a NACE Rev. 2 
class will consist of those correspondence table entries that involve that class.

Letting Ai denote NACE Rev. 2 class i and Bj denote NACE Rev. 2.1 class j, we denote the correspondence table entry 
corresponding to those activities in Ai that are classified in Bj, by Ai→j. This ideal intermediary classification will allow 
the unambiguous recoding of the main activity of an enterprise for all reference periods for which it is observed. 
This includes cases when the correspondence between old and new NACE is one-to-many or many-to-many, as 
per Examples 1a and 1b above. In practice, it might however be resource-consuming to collect the necessary data. 
Example 2 below illustrates how one may proceed in case data broken down by ideal subclass are observed for a single 
reference period only. 

Example 2: Ideal intermediary classification data observed for one reference period t

Assume that classes A7 and A8 have been rearranged into classes B7 and B8, with most of the content ‘remaining in 
place’, but certain activities of A7 being classified in B8. Furthermore, assume that, for the year t during which double 
coding has been carried out, sufficiently granular observations have been made, so that data for the small group of 
activities in A7 being classified in B8 are available.
Consider a unit Eu, whose share of the value added in the double-coded year, broken down by ideal subclass, is as 
follows:

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3 Assignment of new activity codes

in the business register

Class  
(Ai)

A7

A8

Ideal subclass: 
correspondence table entry 
(Ai→j)

Observed value added in 
year t (YAi→j,t,u)

Unit-level conversion 
coefficient (CAi→Bj,u)

A7→7

A7→8

A8→8

20

20

30

20/40 = ½

20/40 = ½

30/30 = 1  

Based on these data, the class of the principal activity of Eu is A7 (value added of 40 for A7 versus 30 for A8) according to the old 
version of the classification, and B8 according to the new classification (value added 50 for B8 versus 20 for B7). By dividing the 
overall value added for the subclasses by that of the class to which they belong, we obtain conversion coefficients.

Now assume that, for year r for which backcasting is to be performed, we observe a value added of Eu of 42 for A7 and a value 
added of 20 for A8. As we do not observe data by ideal subclass, we use the unit-level conversion coefficients from year t to 
estimate the value added for subclasses A7→7, A7→8 and A8→8. Aggregated to the class level this renders a value added of 21 for 
B7 and a value added of 21+20 = 41 for B8, thus classifying the principal activity of Eu in class B8.

Class (Ai)

Observed value added 
in year r (YAi,r,u)

Ideal subclass (Ai→j)

Unit-level conversion 
coefficient – from 
year t (CAi→Bj,u)

Estimated value added 
for year r

A7

A8

42

20

A7→7

A7→8

A8→8

½

½

1

42·½ = 21

42·½ = 21

20·1 = 20

3.2.2 Suboptimal intermediary classification 

While observing ideal intermediate classification data renders recoding easy, it might be hard to achieve for more than one 
reference period. In practice, one might therefore have to take recourse to intermediate classifications defined for other 
purposes. This might be national classifications defined according to Article 4 of the NACE regulation [2], or classifications 
implicitly defined by the classification of products by activity (CPA) [13]. While more granular than the NACE, these 
intermediary classifications are nonetheless likely to be insufficiently granular to allow the unambiguous definition of certain 
categories of the new classification B. 

Example 3 below demonstrates how such data can be used to augment the data of Example 2 to render more precise 
classifications for the backcasting year r.

Example 3: Ideal intermediary classification data observed for t and suboptimal intermediary classification data 
observed for t and r

Assume that classes A7 and A8 are subdivided into classes A7.1, A7.2, A8.1 and A8.2. Furthermore, assume that on top of the 
data observed in Example 2, data broken down by those classes have been observed for all reference periods during 
which backcasting is required. For the double coding year t, assume that the data observed are as follows:

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Assignment of new activity codes
in the business register

3

Class 
(Ai)

Subclass(Ai. l)

Class (Bj)

Ideal subclass: 
correspondence 
table entry (Ai→j)

Observed value 
added in year t 
(YAi. l ,t,u) 

A7

A8

A7.1

A7.2

A8.1

A8.2

B7

B7

B8

B8

B8

A7→7

A7→7

A7→8

A8→8

A8→8

10

10

20

20

10

Unit-level 
conversion 
coefficient 
(CAi. l →Bj,u)

10/10 =  1

10/30 = 1/3

20/30  = 2/3

20/20 =  1

10/10 =  1

As seen from the above table, we can now calculate conversion coefficients based on the subclasses. Further 
assume that for year r, for which only data broken down by the suboptimal intermediary classification can be 
observed, we observe value added of 30, 12, 20, 20 for A7.1, A7.2, A8.1 and A8.2, respectively. This yields:

Class 
(Ai)

Subclass(Ai. l)

Class (Bj)

Observed 
value added 
in year r 
(YAi. l ,r,u)

Ideal subclass 
(Ai→j)

Unit-level 
conversion 
coefficients 
– from year t 
(CAi. l →Bj,u)

Estimated value 
added for year r

A7

A8

A7.1

A7.2

A8.1

A8.2

B7

B7

B8

B8

B8

30

12

10

10

A7→7

A7→7

A7→8

A8→8

A8→8

1

1/3

2/3

1

1

1·30 = 30

1/3·12 =    4  

2/3·12 =    8  

1·10 = 10

1·10 = 10  

Aggregated to the class level this renders a value added of 30+4 = 34 for B7 and a value added of 8+10+10 = 28 
for B8, thus classifying the principal activity of Eu in class B7. The more granular information has thus resulted in a 
different classification. As this is due to the structural changes being possible to observe at a detailed level, it is likely 
to be closer to what would have been recorded in case the true value added for A7→8 had been observed.

3.3 Imputing unobserved enterprise activities

Given that the detailed recording of (groups of) activities in business registers may be resource-consuming for the 
statistical units themselves as well as for the entity in charge of the business register, it may often be the case that 
the data available for the reference periods other than t are limited to the class (or, in case a national classification is 

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3 Assignment of new activity codes

in the business register

available, subclass) of the unit. This would render the procedures described in subsection 3.2 impossible to apply. In the 
below example, methods that may be applied also under such, more restrictive, conditions are illustrated.

Throughout subsection 3.3 we well assume that enterprise Eu :
• has a turnover of 62 in year r and 70 in year t;
• has its principal activity classified in NACE Rev. 2 class A7 in years r and t;
•

is reclassified as having a principal activity in NACE Rev. 2.1 class B8 in year t.

This is thus the same situation as in Example 2 – but without any granular data beyond the NACE Rev. 2 and NACE Rev. 
2.1 classes being observed.

For r, there are various options for imputing the unobserved NACE Rev. 2.1 class of the principal activity of Eu.

3.3.1 Deterministic imputation

Option 1: Assume stability: classifying the principal activity of Eu in B8 also for r.
Option 2. Use conversion coefficients

• Calculate the overall turnover Yu for each unit u, and
• Aggregate to totals YAi→j,t for all units that are double coded (in year t) as having their principal activity in NACE Rev. 2

class Ai  and NACE Rev. 2.1 class Bj  in and

 = YAi→j,t/YAi,t indicating (under the assumption that this feature is

• Aggregate further to totals YAi,t  for all NACE Rev. 2 classes.
Use the totals to obtain conversion coefficients CAi→Bj
time-invariant and independent of unit turnover) the proportion of all units having principal activities classified in NACE 
Rev. 2 class Ai in year r that would have their principal activities classified in NACE Rev. 2.1 class Bj for year r.
Let us assume that the above calculations render the conversion coefficients CA7→B7,
indicating that most (82%) units having a principal activity classified in NACE Rev. 2 class A7 have their principal activity 
classified in NACE Rev. 2.1 class B7. Based on the class Ai of the principal activity of unit Eu in year r, assign (also for year r) 
the class Bj for which the value of with the largest. In our example, this would be class B7. While this has the advantage 
of rendering the ‘most likely’ NACE Rev. 2.1 class for each unit, activities in scope of the ideal subclass A7→8 are missed 
out – leading to an underreporting for class B8 due to what could be referred to as ‘mode bias’ or ‘winner-takes-all bias’.

=0.82 and  CA7→B8

=0,18 , thus

3.3.2 Stochastic imputation

.

The conversion coefficients defined in 3.3.1 could be used to randomly assign the NACE Rev. 2.1 class for period r. This 
would be done by selecting, for each unit with the principal activity classified in Ai in year r, class Bj as the principal 
activity with probability CAi→Bj
Using the example of 3.3.1, we would, for each unit with the principal activity classified in A7, in year r, select class B7 
with probability 82% (and thus select class B8 with probability 18%).
This will render a distribution that is more likely to hold at the population level – but at the unit level, the principal 
activity might be altogether different from the class (in our example, assuming stability over time, we would have an 
expected  rate of misclassification of 1-0.82²-0.18² = 0.30 (whereas it would be 1-0.82 = 0.18 if deterministic imputation 
is applied). 

3.3.3 Imputing multiple weighted values per unit

To preserve the overall distribution, without making any random ‘jumps’, imputation could take place at the level of the 
ideal subclasses, partitioning the turnover for each unit according to the conversion coefficients (e.g. as was done by 

18

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Assignment of new activity codes
in the business register

3

the Swiss Federal Statistical Office [14]). For Eu, the turnover (62) for r would thus be split into YA7→B7,r,u = 62·0.82 = 50.8
and YA7→B8,r,u = 62·0.18 = 11.2. This will generate data with a granularity comparable to that of Example 2. If subclass data
are used, this could generate data of a granularity corresponding to that of Example 3.

The risk of an artificial change of the structure of activities carried out by an enterprise is higher if conversion 
coefficients are applied to all activities of an enterprise at detailed level. If the conversion coefficients are applied 
directly to the principal activity of an enterprise, that risk is lower (albeit still present). If (when applying the conversion 
coefficients) the principal activity of the enterprise in year r is changed it is recommended to make the same change for 
the same enterprise for the years r-1, r-2, … unless there is any information about changes (prior to r) in the activities.

3.4 Treating units formerly outside the frame

There might be specific cases where backcasting cannot be carried out for a unit. For example, consider a unit which is 
in the frame according to NACE Rev. 2.1 but was outside the frame according to NACE Rev. 2. In this case, a conversion 
coefficient may be unavailable, in which case this unit should be treated as new. The same logic applies in the rare 
cases where units leave the frame because of the changeover to NACE Rev. 2.1; the backcasting is simply applied 
only to those units which remain or enter. This issue could be solved either at the microdata level, using a ‘nearest 
neighbour’ procedure [15], or by moving to the aggregate level and base the extrapolation on group averages.

3.5 Automated recoding in business registers: guidance and practical 
experience

To facilitate the recoding of statistical units during the changeover from NACE Rev. 1.1 to NACE Rev. 2, Statistics Estonia 
[16] created software with a user interface that enabled reclassification of activities on unit level as well as on local
kind-of-activity unit level over the period of 8 years (with all previous years recoded using probabilistic methods). This
method was used together with traditional ways of manual reclassification using all available information, such as a
special business register survey, a questionnaire for newly registered enterprises, the PRODCOM survey etc.

Buiten, Kampen and Vergouw [17] suggest the development of automatic recoding procedures (essentially based on 
stochastic imputation as described in 3.3.2 above) for units that ceased to exist before the moment of the new NACE 
implementation. 

Building the experience from the changeover from NACE Rev. 1.1 to NACE Rev. 2, as well as on recent technological 
developments, the Handbook on implementation of NACE Rev. 2.1 in Business Registers [7] describes computer 
aided coding systems, automatic coding with text recognition systems and other advanced tools that can be used in 
recoding statistical units. In addition, innovative machine-learning approaches for the automatic coding of statistical 
units according to NACE were discussed at the 11th European Conference on Quality in Official Statistics (Q2024) [18], 
[19], [20], [21]. 

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1

Introduction

4Backcasting 

approaches

4.1 Use of a key

The ‘key method’ (based on the use of a recoding ‘key’ [17]) is the most straightforward and simple of the four 
methods described in this report. This method directly recodes statistics to the revised classification. Thereby, it assures 
a straightforward relationship between the old and the new results, since the old data are simply transferred into new 
classification. Changes in the outcomes are transparent and can easily be documented and communicated to users. 

However, the key method can only be applied if there are only one-to-one or many-to-one changes from the old 
to the new classification. This limits its applicability considerably, as one-to-many and many-to-many relationships 
between NACE Rev. 2 and NACE Rev. 2.1 categories are highly prevalent (as shown in Table 2). The key method will 
therefore not be further discussed in this manual.

4.2 Microdata approach

In this manual, we use the term microdata approach to denote those backcasting methods which are based on:

• establishing (by means of observation or estimation) NACE Rev. 2.1 codes for each unit (6) for each of the reference

periods in scope of the backcasting exercise;

• subsequently recompiling statistics (broken down by NACE Rev. 2.1 position) – typically by means of the same

methods as when the corresponding original statistics (i.e. statistics broken down by NACE Rev. 2 position) were
calculated.

The microdata approach ensures consistency between the different backcasted time series, as they are all based upon 
the same set of statistical units (in the sense that the principal activity assigned to a given statistical unit remains the 
same across all time series [8]). Moreover, to the extent that it is based on high-quality microdata (e.g. observations as 
opposed to estimates) for multiple reference periods, it has a potential to very well reflect structural changes of the 
economy.

(6) Direct observation (or other kinds of ‘manual’ treatment) of each unit is not mandatory under the microdata approach. The applications presented in this 
manual do typically interpolate (or extrapolate) with various degrees of complexity in terms of the interpolation (or extrapolation) model applied. Moreover, 
they are sometimes sample-based – meaning that even for periods where the NACE Rev. 2.1 codes are recorded, they are only recorded for a sample for the 
units.

In theory, no unit-level observations of the new version of the classification would be needed – as long as good models can be established. In the case of the 
NACE, the NACE Rev. 2.1 implementing act [5] guarantees the availability of double-coded business register data for 2025; this information greatly facilitates 
backcasting.    

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Backcasting approaches 

4

The main disadvantage of the microdata approach is that the resource (and response burden) requirements increase 
proportionally to the extent that it requires observed (possibly even re-reported) or manually imputed microdata for all 
reference periods in scope. Thus, mainly variants of the microdata approach that are less labour (and burden) intensive 
are likely to be applied in practice [4]. Moreover, in cases where imputation has been done ‘manually’ – for instance 
using expert knowledge – during the compilation phase for certain time series, consistency issues would arise even for 
this approach [17]. 

4.3 Aggregate approach

In this manual, we use the term aggregate approach to denote those backcasting methods which are based on:

• establishing (by means of observations – be it at the unit level or at the population level) model parameters
• applying those parameters directly to the time series in scope.

Thus, while those methods frequently involve making observations at the unit level (which will invariably be the case 
for NACE Rev. 2.1 given that double coding in business registers is mandatory for 2025), no attempt is normally made to 
establish unit level NACE Rev. 2.1 codes for those reference periods where the principal activity has not been observed 
for a unit.

Most approaches only require unit-level values to have been observed (or modelled) for one (or a few) reference 
periods. They typically involve the establishing of conversion coefficients. These coefficients:

• may be constant or varying over time as determined by means of an implicit or explicit model;

• may be the same for all variables or be variable-specific.

These coefficients are subsequently applied to the statistics based on NACE Rev. 2 to estimate the same statistics 
broken down by NACE Rev. 2.1. In case the conversion coefficients are presumed to be constant over time, the task of 
estimating them will be easier – but they would not capture those structural changes in the economy which may take 
place within NACE Rev. 2 classes [8]. In case the conversions coefficients are the same for all variables, inconsistencies 
will arise; variable-specific conversion coefficients are hence recommended. 

Technically, conversion coefficients, as defined in this manual, are only directly applicable in case the statistics in 
questions are additive (i.e. concerning quantities such as totals or frequencies). For other statistics (such as indices), the 
conversion coefficients have to be applied to those of their components that are additive (thus requiring that additional 
information is available on file).

Example 4

For simplicity, assume that NACE Rev. 2 class A1 has been split into NACE Rev. 2.1 classes B1 and B2, and that the 
entire population consists of only two units (E1 and E2) and that both of them are classified in the NACE Rev. 2 class 
A1. Further assume that these units have been reclassified into B1 and B2, respectively, with observations of turnover, 
number of employees and value added as per the below table:

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4

Backcasting approaches 

Statistical Unit 
(Eu)

E1

E2

Total

Old class (Ai,t,u)

New class (Bj,t,u)

Turnover

Employees

A1

A1

B1

B2

300

150

450

3 900

2 000

5 900

Conversion 
coefficient 
)
(CAi→Bj

65/115

50/115

Value 
added

65

50

115

Further assume that the we for year r (for which backcasting is to be carried out) have observed the very same total 
values:

Old class (Ai)

A1

Turnover at time r

Employees at time r

Value added in year r

450

5 900

115

As we do not have any observed (or imputed) microdata, we apply the same set of conversion coefficients to all 
variables, which thus renders:

New class (Bi)

Turnover

Employees

Value added

B1

B2

CA1→B1

·450=254

CA1→B2

·450=196

CA1→B1

·5 900=3 335

CA1→B2

·5 900=2 565

CA1→B1

·115=65

CA1→B2

·115=50

If, on the other hand, observations (or individual modelling) would have been carried out at the level of the 
statistical unit, the above totals might rather have rendered the following unit-level estimates for year r (i.e. the very 
same values as in year t):

New class (Bi)
B1

B2

Turnover

Employees

Value added

300

150

3 900

2 000

65

50

The estimated for total turnover and employees in NACE Rev. 2.1 classes B1 and B2 for year r would thus be radically 
different from the true values (owing to the fact that – in this example – the number of employees and the 
turnover are not proportional to the value added). To mitigate this risk, it is necessary to calculate variable-specific 
conversion coefficients for every variable (or group of variables, in case they follow the same pattern) [8].

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Backcasting approaches 

4

One advantage of the aggregate approach is that it requires less efforts (and response burden) for unit-level 
observation (and reporting) and ‘manual’ imputation. Moreover, the problems outlined in 3.3 above (forcing the 
selection of a single NACE Rev. 2.1 class for units whose NACE Rev. 2 class is split) are treated in a streamlined way. 
Interpolation (linear or more sophisticated) over time becomes easier to achieve for the same reason.

The main disadvantage of the aggregate approach is that there is a risk of a loss of information about the real structure 
of the data. The impact (in relative terms of this lack of precision) on the backcasted time series increases with its 
granularity and length. However, any direct comparisons with the microdata approach should be made on the basis 
of the same set of observed data. When the set of observed data is the same, the microdata approach would only 
be preferable in case the modelling approach at unit level is reliable (which may be the case if analytical efforts are 
applied). Otherwise, the microdata approach may introduce more bias or variation.

Sometimes, the aggregate approach is the only one possible to apply – in particular for domains other than business 
statistics, since it might be the case that microdata might not be able to establish even for NACE Rev. 2, let alone for 
NACE Rev. 2.1. 

4.4 Defining characteristics of the microdata and aggregate 
approaches 

At times, it can be hard to discern between the microdata and aggregate approaches. The general criterion for whether 
it is one or the other method that is applied is what is being modelled – unit-level data or aggregates. 

• The microdata approach is considered to be applied if new classification codes are established for each unit (by

means of observation or estimation) – and statistics subsequently are recompiled based on the units.

• The aggregate approach is considered to be applied if the values (frequencies or variables) of unobserved statistics
by classification category are being estimated – be it (as is usually the case) in other time periods or (in particular in
the case of sampling) for population-level statistics in the same time period.

Admittedly, there are some borderline cases here: 

•

•

If the full set of microdata are observed for all time periods for which backcasting is to be performed, then the
estimation task merely consists of aggregating the observed microdata, meaning that not much (if any) modelling
is taking place at the level of the statistical unit. However, as no aggregate modelling is not taking place either, this is
still considered to be a method following the microdata approach.
If microdata are observed for a number of (say 2-3) reference periods, but modelling for the reference periods are
based on parameters that (while estimated based on the microdata observed) are applied to directly estimate
unobserved statistics, then the method used is rather to be considered as following the aggregate approach

Moreover, there are some cases which combine both features. They are said to follow a ‘combined approach’. For 
instance, modelling at the microdata level may take place for those reference periods where microdata of good quality 
are available for the old version of the classification, while modelling at the level of statistics is performed for earlier 
reference periods. This approach may also be applied to minimise the unit-level modelling efforts for the reference 
periods in the more distant past.

4.5 Comparison of the microdata and aggregate approaches in an 
empirical example  

Statistics Austria [22] evaluated possible differences between the two approaches for specific aggregates of structural 
business statistics (SBS). Every single unit in the Business Register was double coded 5 years back. That allowed the 
microdata approach to be applied. For the aggregate approach, conversion matrices were calculated for 3 years using 
the main SBS variables calculated previously by the microdata approach. The correlation between the conversion 

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4

Backcasting approaches 

coefficients for different variables were analysed. A lower correlation was observed between the variables than 
between the years. The average conversion coefficients (across 3 years) were calculated for the variables persons 
employed and turnover that were used for backcasting of all the other variables applying the one or the other 
depending on their correlation with the target variable. Brunauer and Haitzmann [22] recommend using several 
conversion coefficients calculated on the basis of different variables. They also observe that the aggregate approach 
may create biases at the more granular levels of NACE where the number of units observed per category is very small. 
For such cases, the microdata approach would be more suitable.

24

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1

Introduction

5Application of the 

microdata approach

In this chapter, we describe the microdata approach for backcasting time series (short-term statistics (STS) and 
structural business statistics (SBS) etc.) based on the business register. For such time series, the quality of the 
backcasted data clearly depends on the quality of the business register, in particular on a correctly defined principal 
activity of the statistical units therein.

As all units are coded according to the old and new classifications, there is an exact relationship between the old 
and new results (in the sense that marginal frequencies/totals are preserved for positions representing the same 
content). In practice however, the outcome may be less transparent. In cases where outlier treatment, imputation for 
nonresponse etc. has been applied on a variable-by-variable basis, the differences between the old and new results 
are not completely related to the recoding as such. In such cases, an aggregate that has a one-to-one relationship (in 
terms of the old and new versions of the classification) may have different frequencies, totals or averages. For instance, 
differences may occur in cases where imputation for non-response is based on the average of the responding units 
belonging to a specific NACE heading. Analysing, documenting and communicating the effects of changes between 
the old and new versions of a classification is more complex in such cases [17].

5.1 Full replication of the production system

For backcasting of time series of SBS and Inward Foreign Affiliates in 2009, Statistics Estonia [23] used the method 
similar to the one described in 5.2 below. As the double reporting was a non-recurrent action, it was decided to create 
a parallel/dual SBS production system, with duplicate data files and tools according to both NACE versions in use. The 
system included a full cycle of data production, i.e. microdata editing, imputation, data aggregation and preparation for 
publication.

5.2 Backcasting using aggregation matrices

Statistics Netherlands [17] presents the concept of aggregation matrices for microdata backcasting. An aggregation 
matrix I consist of zeros and ones and classifies the units u = (1,....,Nt) into the old and new classification codes at time 
t, where IAi,u,t=1  if unit u has a principal activity classified in Ai at time t,  and IAi,u,t=0 if unit u does not have its principal 
activity classified therein at time t. For the new classification, the binary variable IBi,u,t is defined similarly.
The frequencies can be expressed as follows:

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25

5

Application of the microdata approach

                 f

,
A t
i

=

                 f

,
B t
i

=

N
t

=/

u

N
t

=/

u

I

1

A u t
,
,
i

I

1

B u t
,
,
i

(1)

(2)

Defining Yu,t as the observed value of variable Y for unit u at time t, the totals of that variable in the old and new 
classifications can be formulated as:

                                             Y

=/
=/
Dividing (3) and (4) by the corresponding frequencies (1) and (2) yields the corresponding arithmetic means.

I Y ,
u t
B

I Y ,
u t
A

Y
B

=

=

N
t

N
t

i u t
,
,

i u t
,
,

A

u

u

1

1

i t
,

i t
,

                                                                                        (3)

                                                                                        (4)

Example 5

Assume that the old classification A corresponds to new classification B as follows:

Old class (Ai)

New class (Bi)

A1
A1
A2
A2
A2

B1
B2
B3
B4
B5

Further assume that there are Nt =10 enterprises (units E1,…,E10) for which the values of variable Yu,t are known for 
each enterprise Eu.

26

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Application of the microdata approach

5

Old class (Ai)

New class (Bi)

Enterprise (Eu)

Variable (Yu,t)

A1

A1

A1
A1
A1
A2
A2
A2
A2
A2

B1

B1

B1
B2
B2
B3
B4
B4
B5
B5

E1

E2

E3
E4
E5
E6
E7
E8
E9
E10

The aggregation matrix IA, t for the old classification can be defined as follows: 

Enterprise (Eu)

IA1,t,u

E1
E2
E3
E4
E5
E6
E7

E8
E9
E10

1

1

1

1

1

0

0

0

0

0

and, similarly, the aggregation matrix IB, t for the new classification is defined as: 

4

2

8

12

17

2

5

8

19

14

IA2,t,u

0

0

0

0

0

1

1

1

1

1

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27

5

Application of the microdata approach

Enterprise (Eu)
E1
E2
E3
E4
E5
E6
E7
E8
E9
E10

IB1,t,u
1

1

1

0

0

0

0

0

0

0

IB2,t,u
0

0

0

1

1

0

0

0

0

0

IB3,t,u
0

0

0

0

0

1

0

0

0

0

IB4,t,u
0

0

0

0

0

0

1

1

0

0

IB5,t,u
0

0

0

0

0

0

0

0

1

1

The frequency is the sum of each column in the aggregation matrix: 

fA₁,t = 5, fA₂,t = 5, fB₁,t = 3, fB₂,t = 2, fB₃,t = 1, fB₄,t = 2 and fB₅,t = 2. 
To backcast the variable Y broken down by the new classification B one could simply multiply the transposed 
aggregation matrix IB, t  with the vector Yt. To obtain the means within each class, the sum needs to be divided by 
the previously calculated frequencies.

New class (Bi)

B1
B2
B3
B4
B5

Backcast YBi t
(1∙4)+(1∙2)+(1∙8)+(0∙12)+(0∙17)+(0∙2)+(0∙5)+(0∙8)+(0∙19)+(0∙14) = 14

(0∙4)+(0∙2)+(0∙8)+(1∙12)+(1∙17)+(0∙2)+(0∙5)+(0∙8)+(0∙19)+(0∙14) =29

(1∙4)+(1∙2)+(1∙8)+(0∙12)+(0∙17)+(1∙2)+(0∙5)+(0∙8)+(0∙19)+(0∙14) =  2

(1∙4)+(1∙2)+(1∙8)+(0∙12)+(0∙17)+(0∙2)+(1∙5)+(1∙8)+(0∙19)+(0∙14) = 13

(1∙4)+(1∙2)+(1∙8)+(0∙12)+(0∙17)+(0∙2)+(0∙5)+(0∙8)+(1∙19)+(1∙14) =33

The results are as follows:

New class (Bi)

B1
B2
B3
B4
B5

Total

Variable (YBi t)
14

Backcast

Frequency  (fBi t)
3

29

2

13

33

91

2

1

2

2

10

Mean (YBi t  /  fBi t)
14/3 =   4.67

29/2 =14.5

2/1 =   2

13/2 =   6.5

33/2 =16.5

91/10 =   9.1

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Application of the microdata approach

5

For t, this merely replicates the already observed double-coded information in a circumspect way. To make practical 
use of the aggregation matrices for t, they could be used for extrapolation over time to other reference periods r 
(where double coded microdata are lacking). Apart from the issue of changes to the frame (units not present at 
time r), this also relies upon changes to the principal activity of a given unit being relatively rare. Alternatively, as 
presented in 5.4 below, they could be used for extrapolation from a sample to the population as a whole. As further 
discussed by Statistics Netherlands [17], the aggregation matrices could also be used as building blocks for the 
conversion coefficients applied under the aggregate approach.

5.3 Adaptation of the microdata approach to random samples

According to the definition of Chapter 4, the microdata approach requires recoding (through a combination of 
modelling, manual imputation or direct observation/data collection) of all statistical units for every reference period for 
which backcasting is to be carried out. The statistics are thereafter recompiled using the new NACE codes of the same 
statistical units repeating the same methodology.

In practice, however, it might be the case that the statistics (organised by NACE Rev. 2) have, while using the business 
register as the (sampling) frame, been based on a (cross-sectional or longitudinal/panel) sample survey. In that case, 
backcasting based on microdata will entail using recoded data for the sample, and establishing estimates based on 
NACE Rev. 2.1 using the survey weights (typically the inverse inclusion probabilities), using the same procedure as for 
the original. Thus, the method is based on the same use of microdata as for the old version of the classification – but, 
for the variables specific to the survey in question, these microdata do not cover all units in the business register. In 
case of a census, the inconsistency issues referred to previously may be less pronounced, since true outliers are typically 
self-representative and not in need of any treatment. When adapting to sample surveys on the other hand, even true 
outliers cannot be left untreated, as this would perturb estimates, requiring that outlier treatment is performed (on 
either the survey weights or the observed values). When backcasting based on such data, there may be differences 
between statistics based on different versions of the classification that are not completely attributable to recoding. 

To the extent possible, conversion coefficient estimates should be established on the basis of the fully recoded 
business register. If this is not possible, methods ensuring that the frequencies by NACE Rev. 2 are not stochastic should 
preferably be employed. This is to avoid conversion coefficients that are estimated via ratios between two stochastic 
variables (7).  

5.4 Backcasting time series of sample surveys

Along the lines of the adaptation outlined in 5.3 above, Statistics Netherlands [17] presents a method based on the 
recoding of a random sample of units, acknowledging that ‘…measurements of the new classification at the level of 
the population will be lacking…’. This method was used to compute time series according to the new classification 
on the basis of microdata using aggregation matrices (as defined in 5.2 above). The methods were applied to an STS 
sample survey related to the change from NACE Rev. 1.1 to NACE Rev. 2. The unit-level data were observed for of a 
sample of  nt units for u =(1,...,nt) and, therefore, the estimators of frequencies, totals and means used the sample 
inclusion probabilities.

The inclusion probabilities of the businesses (based on the old version A of the classification) can differ substantially 
from those that would have been optimal in a sampling design based on the new version B of the classification. 
However, it is nonetheless those probabilities that have to be used for estimating the quantities broken down by 
classification category according to the new classification B. Letting πu,t  denote the inclusion probability of unit u at 
time t, the Horvitz-Thompson estimator for totals of class Bi is equal to

(7)  Even if the numerator and denominators are both unbiased estimators, the ratio is normally a biased estimator – and moreover, in particular in the case of 
small denominator (i.e. infrequent NACE Rev. 2 classes) its variability would be very high.

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5

Application of the microdata approach

t /
=
Y
B
While unbiased, this estimator might have a high uncertainty for classes in A that are split into smaller classes in B. 
Ideally, one could compute the aggregation matrix at several points in time. However, this may be too demanding as it 
would require double-coding for multiple periods. Instead, it is more practical to compute the aggregation matrix only 
once, and re use the resulting B classification (at time t) also for the backcasting reference periods:

                                                                              (5)

I

u t
,

n
t

=

u

1

i t
,

,

Y
u t
,
i u t r
B

,

u /
=
   Y
B

i r
,

n

r

u

=

1

I

Y
i u t r
B

,

,

u r
,

u r
,

                                                                            (6)

To mitigate the issue of low precision for splits into smaller classes, one might consider methods such as Micro 
Decomposition Analysis, which attempts to backcast not only at the level sample observations, but also for granular 
statistics of the statistical population as a whole [8], [24]. As is always the case, the appropriateness of such methods will 
(in contrast to mainly design-based approaches such as the one presented above) depend on the validity of the model 
assumptions made.

Example 6

This example builds upon Example 5 (see 5.2 above), in which the aggregation matrix concept is introduced, 
adapting it to the sample survey setting. Assume that out of the Nt=10 units of the population, a sample of nt =5 
units has been drawn by means of simple random sampling. Under this design, the probability for a given unit u 
to be selected into the sample of time t is equal to πu,t = nt / Nt =5/10= 0.5 for each u. We furthermore assume that, 
based on this sample design, we have randomly drawn units E1, E2, E5, E7 and E10. Therefore, the available information 
now becomes as follows:

Old class (Ai)

New class (Bi)

Enterprise (Eu)

Variable Yt

A1
A1
A1
A2
A2

B1
B1
B2
B4
B5

The aggregation matrix of the new classification now is:

Enterprise (Eu)

E1
E2
E5
E7
E10

B1

1

1

0

0

0

B2

0

0

1

0

0

E1
E2
E5
E7
E10

B3

0

0

0

0

0

4

2

17

5

14

B5

0

0

0

0

1

B4

0

0

0

1

0

30

Backcasting manual

  
 
Application of the microdata approach

5

To calculate the totals of the corresponding variable in B one could multiply the aggregation matrix of B, displayed 
above, with the scalar 1/ πu,t= 1⁄0.5=2. The transpose of this matrix can then be multiplied with the Yu,t vector to 
obtain:

New class (Bi)

B1
B2
B3
B4
B5

Backcast (ỸBi,t)
(1∙4∙2)+(1∙2∙2)+(0∙17∙2)+(0∙5∙2)+(0∙14∙2)= 12

(0∙4∙2)+(0∙2∙2)+(1∙17∙2)+(0∙5∙2)+(0∙14∙2)= 34

(0∙4∙2)+(0∙2∙2)+(0∙17∙2)+(0∙5∙2)+(0∙14∙2)=   0

(0∙4∙2)+(0∙2∙2)+(0∙17∙2)+(1∙5∙2)+(0∙14∙2)= 10

(0∙4∙2)+(0∙2∙2)+(0∙17∙2)+(0∙5∙2)+(1∙14∙2)= 28

The results are as follows:

New class (Bi)

B1
B2
B3
B4
B5
Total

Backcast (ỸBi,t)
12

34

0

13

28

87

Even though the sampling fraction is very high, the precision is largely depending on the absolute sample size per 
class, as can be seen from the considerable differences in relative terms between ỸBi,t here and the essentially directly
observed values of ỸBi,t in Example 5. While the overall sample size would be considerable larger, it might very well be
the case that the sample size is low for classes A1 and A2. In situations where frequencies are low, but the expected 
totals are high, it is thus (as is customary for business surveys) advisable to employ probability proportional to size 
sampling (possibly with ‘take all’ strata for larger units). 

Backcasting manual

31

1

Introduction

6Application of the 

aggregate approach using 
conversion coefficients

Conversion coefficients are factors (based on empirical measures or modelling) determining how data are reallocated 
from the old to the new version of a classification – either at unit level (as illustrated in Chapter 3) or at aggregate level 
(as illustrated in 4.3; see also [25] for a real-life example from industrial production).

In the practical experiences of NSIs (see e.g. [17]) there are several ways to estimate the conversion coefficients:

• based on frequencies (the proportion of the number of units for a given position in the old classification reclassified

to a given position of the new classification);

• based on the proportions by which a target variable is redistributed;
• by means of a least squares estimator based on the target variable (for the complex relations like many-to-many and

when several years are double-coded). 

The advantage of the latter method over the two other ad hoc estimators is that more observation points are used to 
estimate the conversion coefficients. 

6.1 Ad hoc conversion coefficient estimators

Example 7

Consider the following empirical data:

32

Backcasting manual

Application of the aggregate approach using
conversion coefficients

6

Old class (Ai)

Unit (Eu)

Persons employed

Turnover

New class (Bi)

A1
A1
A1
A1
Totals

E1
E2
E3
E4

5

6

3

6

20

150

200

50

250

650

B1
B2
B1
B2

The conversion coefficients  between the corresponding classes of new and old classifications are estimated as 
follows:

CA1→B1
CA1→B1
CA1→B1

=2/4 =0.5 and CA1→B1
= 8/20 =0.4 and CA1→B2
= 200/650 =0.3 and CA1→B2

=2/4 =0.5 for the number of enterprises,

= 12/20 =0.6 for the number of persons employed,

= 450/650 =0.7 for the turnover.

Variable

Old class

New class 

Number of enterprises

Number of persons employed

Turnover

A1

A1

A1

B1

0.5

0.4

0.3

B2

0.5

0.6

0.7

The conversion coefficients estimated for all activities can be put together in the form of a matrix, with one row for each 
category in the old version of the classification, and one column for each category in the new version. Considering the 
differences depending on which variable is used, a conversion matrix is constructed separately for each of the variables 
(including frequencies).

6.2 Ordinary least squares coefficient estimator

Statistics Netherlands [17] presents an alternative conversion coefficient estimator, based on the ordinary least squares 
(OLS) approach. This allows the conversion coefficients to be based on data that fluctuate over time. They should 
therefore in principle (assuming the model holds) be superior to the ad hoc ones. The OLS approach allows the 
conversion coefficients to be based on more observation periods (minimising the total sum of squares of the difference 
between the estimated and observed aggregates of Y) leading to potentially better estimates (assuming that the 
model assumptions hold) than what can be obtained by ad hoc estimators based on merely taking totals across the 
time periods for which aggregate data have been observed.

Under this approach, the target variable consists of the observed totals in the new classification. The independent 
variable is constructed as a sparse matrix including the values of the observed totals in for each position Ai of the old 
classification (replicated for each position Bj in the new classification).

Backcasting manual

33

6 Application of the aggregate approach using 

conversion coefficients

We assume that double coding has been made for time t and for k reference periods back, i.e. for reference periods t, 
t-1, t-2, …, t-k.

We let YAi, t denote the totals of the variable for each of the |A| classes of the old classification A. Similarly, we let YBi,t
denote the totals of the variable for each of the |B| classes of the new classification B.

Generally, the OLS equation would be formulated as follows (8).

J
Y

Y
Y

,
B t k
1

-

-

,
B t k
2
h

Y

|

B

-

B t k
,
|
h
Y
Y
B t
,
2
h

,
B t
1

J

KKKKKKKKKKKKKKKKKKKKKKKKKK

N

OOOOOOOOOOOOOOOOOOOOOOOOOO

Y
B t
,
|
B
|
P
L
Totals
(new classification)

=

KKKKKKKKKKKKKKKKKKKKKKKKKK

L

-

,
A t k
1
0
h
0
h
Y
,
A t
1
0
h
0

0

Y

-

,
A t k
1
h
0
h
0
Y
A t
,
1
h
0

A

-
t k

Y
A
|

g
g
g
g
g
g
g
g
g
Totals (old classification)

,
|
0
h
0
h
Y
A
|
0
h
0

,
|

t

A

g
g
j
g
j
g
g
g
g

0
0
h

Y
A
|

,
|

-
t k

A

h
0
0
h
Y
A
|

A

,
|

t

N

OOOOOOOOOOOOOOOOOOOOOOOOOO

P

=

C
C

A
1

"

B
1

"

B
2

A
1
h

C

A
|

A

|

"

B
1

h

J

KKKKKKKKKKKKKKKK

A
|

"

C
B
L
B
|
|
A
Conversions
coefficients

N

OOOOOOOOOOOOOOOO

P

|

Letting j denote the number of correspondences involving category Bj, k must be equal to the maximum number 
(across all values of j) of j in order to arrive at a sufficient number of degrees of freedom to estimate  the vector of 
conversion coefficients. Moreover, care must be taken to ensure that, for each i, the sum (across all values of j) of the 
conversion coefficients equals 1. This is achieved by requiring that k≥1, i.e. that double coding takes place for more than 
a year. The precision of the OLS estimator increases as k increases. This has to be balanced against the cost for double 
coding. Experience has shown k=2 (i.e. a period of double coding of three years) to be optimal in this regard [17].

Example 8

Consider a highly simplified classification (A) consisting of two categories that are split into the three categories of a 
new classification (B) consisting of three categories as illustrated in Figure 1.

FIGURE 1
Many to many correspondences between two versions of a classification

A1

A2

(8)  For completeness it should be noted that:

B1

B2

B3

•

•

•

34

The equation presented does not represent the complete regression model as the error term is missing. It is presented here only to allow a visual 
illustration of the ‘mapping’ of the available information between the old and the new classification. 

While it is possible to let the conversion coefficients be time-dependent, the equations used in this chapter assume time-invariant conversion coefficients.

The matrix presented consists of |A|·|B| columns (and |B|·(k+1) rows), which then are multiplied with a vector of conversion coefficients of length |A|·|B|. 
However, the actual number of correspondences between A and B is typically lower; only the subset of the |A|·|B| theoretically possible correspondences
that are represented in the correspondence table between A and B should be considered. As noted by Buiten, Kampen and Vergouw [17], the other 
elements must be dropped from the vector with conversion coefficients, as should the corresponding columns be from the matrix.

Backcasting manual

Application of the aggregate approach using
conversion coefficients

6

Assume that we have the double-coded data for 3 years (t, t-1, t-2) and that we based on this have observed the 
following aggregates for variable Y:

Old class (Ai)

New class (Bi)

Year

t-2

t-1

t

YA1

1 334

1 437

1 570

YA2

499

590

609

YB1

330

396

449

YB2

880

942

1 005

YB3

623

689

725

The input data used in the OLS equation are the following:

Class totals 

of Y for B

Class totals of Y for A

YB1,t-2

YB2,t-2

YB3,t-2

YB1,t-1

YB2,t-1

YB3,t-1

YB1,t

YB2,t

YB3,t

330

880

623

396

942

689

449

1005

725

1334

0

0

0

1334

0

0

1437

0

0

1334

0

0

1437

0

0

1570

0

1570

0

0

1437

0

0

1570

0

0

499

0

0

590

0

0

609

0

0

0

499

0

0

590

0

0

609

0

0

499

0

0

590

0

0

0

609

Inserting the data in any statistical software (9), we obtain the following OLS estimates:  

(9)  The ‘lm’ function in R was used in the calculation here, but any statistical software would yield the same estimates.

Backcasting manual

35

6 Application of the aggregate approach using 

conversion coefficients

Conversion coefficients

ĈA1→B1 = 0.041

ĈA1→B2 = 0.649

ĈA1→B3 = 0.310

ĈA2→B1 = 0.589

ĈA2→B2 = 0.004

ĈA2→B3 = 0.406

These can be further used to obtain the backcasted totals in the new classification.

6.3 The benchmark/interpolation method 

The experience of Statistics Netherlands of using the aggregate approach when backcasting time series for STS [17] is 
briefly summarised below.  

According to the benchmarking/interpolation method, conversion coefficients are calculated for two different points in 
time, after which the coefficients for the time points between them are derived by interpolation using the aggregate 
approach. This method decreases the set of assumptions that have to hold as well as problems of inconsistencies 
between the old and new totals. However, it does require (for both reference periods) the availability of microdata 
according to the old version of the classification, as well microdata for the new version (typically obtained by double 
coding). 

These double-coded periods are called the benchmark periods. From a theoretical point of view, it might appear ideal 
to have conversion coefficients calculated for every point of the time series but in practice this may will be too resource 
demanding. The optimal benchmark periods are to be determined by subject matter experts. First of all, the microdata 
for the benchmarking periods are recoded to the new classification. After that, two sets of conversion coefficients are 
obtained to convert the aggregated estimates from the initial to the revised classification. For the periods between the 
two benchmark periods, the coefficients could be obtained via linear interpolation (10).

Example 9

To illustrate the way of obtaining the coefficients by linear interpolation, consider the data starting from t-3 
(beginning of the historical time series) to t (end of the historical time series). Also assume that the activities 
classified in class A1 of the old classification are split into two new activities classified in classes B1 and B2 and the 
number of enterprises is distributed as follows:

(10) A spline interpolation could also be employed in case the number of available periods is greater than 2.

36

Backcasting manual

Application of the aggregate approach using
conversion coefficients

6

Old class

A1

Time

t-3

t-2

t-1

t

B1
5

6

5

8

B2
3

6

5

12

Using the ad hoc estimator based on the proportion of variable number of enterprises, the conversion coefficients 
can be calculated for each year (year-by-year estimates). As this would be demanding in resources to be done 
across many reference periods, the linear interpolation of the conversion coefficients of the first and last reference 
periods could alternatively be employed. Whenever the implicit assumption of linear evolution does not hold, the 
linear interpolation will render conversion coefficients that are different from those obtained by means of direct 
observation. In this example, this can be seen for t-2 and t-1:

Old class

Year

Yearly data

Linear interpolation

Conversion coefficient estimates (ĈAi→Bj

) based on

B1

0.625

0.500

0.500

0.400

B2

0.375

0.500

0.500

0.600

t-3

t-2

t-1

t

Average

0.506

0.494

Total

1

1

1

1

1

B1

0.625

0.550

0.475

0.400

B2

0.375

0.450

0.525

0.600

0.513

0.488

Total

1

1

1

1

1

A1

For improving the quality of the conversion coefficients, it is recommended to extend the period of double coding, 
for instance by another year, in order to allow for the application of the new classification time to stabilise, and to have 
the coefficients calculated on the basis of data which has already undergone some corrections. In addition, for some 
classes, the evolution between the two benchmark periods might not have been linear (the potential consequences 
of which are shown in example 9). For these special cases, a non-linear interpolation method could be used. In such 
cases, expert opinions are needed to recommend an assumed evolution between the benchmark periods [17].

A possible variation of the method described consists of combining the conversion coefficients determined for the 
two benchmark periods into a single set and then apply these ‘pooled’ conversion coefficients to all the periods of the 
time series. Just as for the aggregate approach, the assumption of a constant conversion coefficient over certain time 
periods does not always hold [17].

Backcasting manual

37

6 Application of the aggregate approach using 

conversion coefficients

7Statistical disclosure control 

in the context of parallel 
dissemination

7.1 Introduction

The revision of the classification of economic activities (NACE) poses a clear conflict of interest between the need of 
data users for extended time series (thus requiring a long period for which data will be available on the basis of both 
versions of the classification) and the right of respondents to be protected against the disclosure of their data. In this 
chapter, the problem of efficient protection of confidential data, when data are published in parallel according to NACE 
Rev. 2.1 and NACE Rev. 2, is briefly introduced (more details in the annex). The problem of parallel publication was 
identified by Statistics Estonia, who report [16] using manual checking (presumably along the lines of what is described 
in section 3 below) to address the issue during the changeover from NACE Rev. 1.1 to NACE Rev. 2.  

7.2 Problem description 

Publishing data broken down by the two classifications for the same reference period creates the opportunity 
to calculate differences at a lower level than either of the classifications. Moreover, thanks to the high-quality 
correspondence table, the nature of the activities of entities moving between categories is well-defined. These implicit 
cells also need protection. 

FIGURE 2
Changes between NACE Rev. 2 and NACE Rev. 2.1 concerning classes 10.89 and 11.07

10.89

11.07

Old NACE

New
NACE

10.89

11.07

38

Backcasting manual

Statistical disclosure control in the context of parallel 
dissemination

7

Figure 2 shows an example where some activities that were classified in NACE class 10.89 (manufacture of other food 
products n.e.c.) in the old NACE were moved to class 11.07 in the new NACE (manufacture of soft drinks and bottled 
waters) as detailed in Version 1.05 of the NACE Rev. 2 – NACE Rev. 2.1 correspondence table [11]. Any publication broken 
down by the old NACE classes would only show values for classes 10.89 and 11.07, and any publication broken down 
by the new NACE classes would only show values for the classes 10.89 and 11.07. However, if publication takes place for 
the same reference period, this will implicitly also publish data on the activities that moved from 10.89 to 11.07 (the grey 
box), just by taking the difference between totals/frequencies for NACE Rev. 2 class 10.89 and the same quantity for 
the corresponding NACE Rev. 2.1 class. This difference concerns a well-defined activity: production of plant-based milk 
substitutes (e.g. coconut, rice, almond, soya-based beverages). It should be checked whether the implicit cell needs 
protection against disclosure risk.   

7.3 Protection of the backcasted data – suppression 

The disclosure protection method generally employed is suppression. For applying it in the current case, the following 
basic assumptions are made:  

• Data based on the old NACE classification have already been protected and published
• Confidential data in the tables based on the old NACE are suppressed
• Suppression is considered also for confidential data in the tables based on the new NACE.

Applying suppression also to the tables based on the new NACE has to take into account:

• the need for protection of the new NACE table itself
•
•

for the cells that remain the same in terms of scope, new NACE must follow the protection of the old
for the cells for which the scope has changed, differencing between the old and the new NACE has to be prevented.

First, the need for protection of the confidential data in the table based on NACE Rev. 2.1 table has to be determined on 
its own (using standard statistical disclosure control methods and tools). Thereafter, the process depends on the relation 
between the cells in the tables, according to the correspondence tables.  

• One-to-one relations, continuity: the NACE category moved 1-to-1 to the new NACE. The confidentiality status of

these cells for the new NACE should follow the old NACE.

• Two-to-two, simple restructuring: high risk of differencing. This is the example shown in Figure 2. Several checks are

necessary, see the annex.

• Many-to-many: complex restructuring: lower risk of differencing due to complexity. Check the protection of

dominant entities.

• One-to-many relations: split. It should be considered that the sum of the split cells has been published (or

suppressed) in the old NACE.

• Many-to-one relations: merge. The new cell is the sum of several old cells. The protection of the old cells has to be

respected.

The annex contains more details on this process. Please note that the analysis has to be done on the categories that 
actually appear in the tables. This is particularly important in the case of groupings or breakdowns which are not part of 
the NACE hierarchy. 

Suppression from 2025 onwards 

From the 2025 reference year onwards, the completeness of the statistics structured by the new NACE shall have 
priority over those structured by the old NACE. The data according to the new NACE classification will be protected and 
first and publication of the old NACE data will be conditional on checking if the comparison with the published new 
NACE data will not disclose information about entities moving between NACE categories.  

Backcasting manual

39

7 Statistical disclosure control in the context of parallel 

dissemination

7.4 Protection of the backcasted data – other methods 

Perturbation (adding random noise) or rounding could be alternatives to suppression. The advantage of these methods 
is that they can be applied without any detailed analysis on dominant businesses at the microdata level. In the case of 
backcasting, it has to still be considered that data structured by the old NACE have already been published. For cells 
with identical scope, the published value should remain, or the suppression should be kept. Moreover, the margin for 
perturbation or rounding has to be put higher than usual, as there are known ‘exact’ numbers that can be used to get 
closer to the real value. 

Applying perturbation or rounding from 2025 onwards on all data (both by the old and the new NACE), has the 
advantage that is shows complete tables, without suppression (obviously with some loss of precision). 

It must be noted though that there is currently little experience with the application of perturbation and rounding 
methods in business statistics, and in particular in magnitude tables (although these are classical disclosure control 
methods that appear in the available handbooks). This makes it difficult to offer detailed guidance on what parameters 
to choose and how to communicate with respondents and users.  

The annex offers some more details on these possible alternatives. 

7.5 Conclusions 

It will be difficult to apply suppression in a strict way to the backcasted data on the new NACE. The restrictions render 
the application of standard tools insufficient; additional steps are required, which also need manual intervention. On 
top of that, the user value will be low, as many cells will have to be suppressed. 

Perturbation methods could be a good alternative, especially for backcasted data which will be estimated through 
modelling; by their nature backcasted data are less precise. Concrete application of perturbation requires the selection 
of specific methods, approaches and parameters. These experiences could lead to more detailed guidance in the 
future. 

40

Backcasting manual

1

Introduction

List of symbols

For simplicity, the below table only lists the same concept once. Aggregate or more detailed variations thereof (as giv-
en by dropped or added indices) are thus not presented separately. As an example, the unit-specific conversion coeffi-
cient symbol (CAi→Bj,u) is not presented.

Symbol

Meaning

|A|

Ai

|B|

Bi

Ai→j

Ai.ℓ

CAi→Bj

Eu

fAi,t

fBi,t

IAi,u,t

IBi,u,t

k

Nt

Number of distinct categories (at the level of interest) of the old classification A

Class i of the old classification A

Number of distinct categories (at the level of interest) of the new classification B

Class i of the new classification B

Ideal subclass j to class i of the old classification A

Subclass ℓ to class i of the old classification A

Conversion coefficient (proportion of class i of the old classification A that is assigned to class 
j of the new classification B)

Statistical unit u

Number of units classified (at time t) in category i of the old classification A

Number of units classified (at time t) in category i of the new classification B

Indicator variable equal to 1 if unit u is classified (at time t) in category  i of the old classifi-
cation A (and 0 otherwise)

Indicator variable equal to 1 if unit u is classified (at time t) in category  i of the new classifi-
cation B (and 0 otherwise)

Number of periods (in addition to t) for which double coding is carried out

Number of statistical units in the population at time t

Backcasting manual

41

List of symbols

nt

r

t

YAi,t

YBi,t

Yu,t

π u,t

Number of statistical units in the sample (drawn for backcasting purposes) during reference 
period at time t

Period (year) for which backcasting is to be carried out

Reference period of the changeover, typically the first reference year of application of the 
new classification.

The observed total of variable Y for class i of the old classification A at time t (obtained as 
the sum of the values of the corresponding indicator variable IAi,u, t multiplied by the ob-
served values Yu,t)
The observed total of variable Y for class i of the new classification B at time t (obtained as 
the sum of the values of the corresponding indicator variable IBi, u, t multiplied by the ob-
served values Yu, t)

The observed value of variable Y for unit u at time t

Sample inclusion probability of unit u at time t

42

Backcasting manual

1

Introduction

Glossary

Aggregate approach

Aggregate matrix

Backcasting

Conversion coefficients

Conversion matrix

Correspondence table

Double coding

This approach attempts to impute backcasted statistics (according to the 
new version of a classification) by applying conversion coefficients directly 
on the statistics (according to the old version of the classification).

Sparse matrix composed of binary (dummy) variables indicating category 
membership for each category i (of a classification) and unit u (of a sample 
or a statistical population).

In general, backcasting refers to forecasting (or extrapolating) backwards 
in time. This is typically done by applying forecasting methods to a 
time series – but in reverse chronological order, starting from the end 
and going towards the beginning of the time period of interest. In the 
context of statistical classifications (such as NACE), a criterion assigned 
a high importance when selecting among backcasting methods is that 
the backcasted time series (expressed in terms of the new version of a 
classification) should be consistent with the already published time series 
(expressed in terms of the old version of the same classification).

Factors used to reallocate data (either at the aggregate level for each 
classification category or at the level of each statistical unit) from the old 
version of a classification to the new version. In their simplest form, they 
correspond to (estimated) relative frequencies – with non-zero values in 
principle only possible for those pairs of positions that are represented in 
correspondence table entries.

A matrix consisting of all conversion coefficients across all (relevant) pairs of 
categories of the old and new classifications.

A correspondence table defines the relationship between the categories 
of two classifications (or two versions of the same classification). It typically 
only contains pairs of categories with common content.

The recording of the category in which some feature (such as the principal 
activity) of a statistical unit falls according to different versions of a 
classification (or, more generally: according to two different classifications).

Backcasting manual

43

Glossary

Key method

Microdata approach

This approach uses a recoding ‘key’ with which a classification at the most 
granular level is directly recoded to the revised classification. This method 
can only be applied if there are only one-to-one, or many-to-one changes 
from the old to the new classification.

This approach attempts to impute (typically the new version of the 
classification) at the level of the statistical unit. Based on these microdata, 
backcasted statistics (according to the new version of a classification) are 
obtained by means of aggregation (typically by applying the same methods 
as for the old classification).

Nearest neighbour imputation

Consists in finding the ‘closest neighbour’ enterprise that carries out the 
same activities in the reference period t of double-coding.

Top-down method

A classification method whereby classification of the characteristics of a 
unit is made starting at the highest hierarchical level of a classification, and 
thereafter proceeding to classify at lower hierarchical levels.

44

Backcasting manual

1

Introduction

References

[1] Commission Delegated Regulation (EU) 2023/137 of 10 October 2022 amending Regulation (EC) No 1893/2006 
of the European Parliament and of the Council establishing the statistical classification of economic activities 
NACE Rev. 2 (OJ L 19, 20.1.2023, p. 5-42)
http://data.europa.eu/eli/reg_del/2023/137/oj

[2] Regulation (EC) No 1893/2006 of the European Parliament and of the Council of 20 December 2006 establishing 
the statistical classification of economic activities NACE Revision 2 and amending Council Regulation (EEC) 
No 3037/90 as well as certain EC Regulations on specific statistical domains (OJ L 393, 30.12.2066, p. 1-39)
https://data.europa.eu/eli/reg/2006/1893/oj

[3] Commission Regulation (EC) No 29/2002 of 19 December 2001 amending Council Regulation (EEC) No 3037/90 
on the statistical classification of economic activities in the European Community (OJ No L 6, 10.1.2002, p. 3)
https://data.europa.eu/eli/reg/2002/29/oj

[4] Josef Richter 2010: Statistical environment of INFORUM models – Update of the changes ahead with special 
emphasis on the implications of backcasting
https://europa.eu/!TC9Wqw

[5] Commission Implementing Regulation (EU) 2024/1840 of 27 June amending Commission Implementing Reg-
ulations (EU) 2020/1197, (EU) 2022/918 and (EU) 2022/1092, as regards references to the statistical classification 
of economic activities NACE Revision 2 established by Regulation (EC) No 1893/2006 of the European Parliament 
and of the Council (OJ L, 2024/1840, 4.7.2024)
http://data.europa.eu/eli/reg_impl/2024/1840/oj

[6] UN 2018: Handbook on Backcasting (draft)
https://unstats.un.org/unsd/nationalaccount/aeg/2018/M12_8iiib_Backcasting.pdf

[7] Eurostat 2023: Handbook on implementation of NACE Rev. 2.1 in Business registers
https://europa.eu/!w78WKW

[8] Eurostat 2009: Backcasting Handbook NACE Rev. 1.1 to NACE Rev. 2
https://europa.eu/!7xyg6N

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45

References

[9] Eurostat 2025: NACE Rev. 2.1 – Statistical classification of economic activities in the European Union
https://doi.org/10.2785/155339

[10] Eurostat 2024: NACE Rev. 2 – NACE Rev. 2.1 correspondence tables
https://europa.eu/!HVrtvx

[11] Eurostat 2024: NACE Rev. 2 – NACE Rev. 2.1 correspondence table Version 1.05
https://europa.eu/!6WdjDm

[12] Eurostat 2021: European business statistics methodological manual for statistical business registers
https://doi.org/10.2785/093371

[13] Regulation (EC) No 451/2008 of the European Parliament and of the Council of 23 April 2008 establishing a new statistical 
classification of products by activity (CPA) and repealing Council Regulation (EEC) No 3696/93 (OJ L 145, 4.6.2008, p. 65-226) 
http://data.europa.eu/eli/reg/2008/451/oj

[14] Federal Statistical Office 2012: Use of conversion keys for NOGA 2002-2008. Methodology Report
https://www.bfs.admin.ch/bfs/en/home/statistics/catalogues-databases.assetdetail.348788.html

[15] Jiahua Chen and Jun Shao 2000: Neighbour Imputation for Survey Data. Journal of Official Statistics, 16 (2), 113-131
https://www.scb.se/contentassets/ca21efb41fee47d293bbee5bf7be7fb3/nearest-neighbor-imputation-for-survey-
data.pdf (accessed on 3 February 2025).

[16] Statistics Estonia 2009: Implementation of the NACE Rev. 2 Regulation with regard to the data covering 
periods before its entry into force
https://europa.eu/!hHdRcW

[17] Gert Buiten, Jan Kampen and Sidney Vergouw 2009: Producing historical time series for STS-statistics in NACE Rev.2: 
https://www.cbs.nl/nl-nl/achtergrond/2009/03/producing-historical-time-series-for-sts-statistics-in-nace-rev-2

[18] Thomas Faria, Nathan Randriamanana and Tom Seimandi, 2024: Retaining strategies 
for an economic activity codification model. Paper presented at the Q2024 conference
https://airdrive.eventsair.com/eventsairwesteuprod/production-leading-public/e8c086593cf4446ea5b18d5a1af13903
(accessed on 21 May 2025).

[19] Jacob Kasche, Wictoria Widén, Kira Gylling and  Gustaf Strandell, 2024: A Potential Quality Assurance of the Re-coding 
to NACE Rev. 2.1, Combining LLMs and Manual Coding. Paper presented at the Q2024 conference
https://airdrive.eventsair.com/eventsairwesteuprod/production-leading-public/b1336b8903de440283f1ed530dec34ac
(accessed on 21 May 2025).

[20] Jaroslav Sixta, Michal Čigáš and Jan Fojtík, 2024: Updating of Statistical Register by Web Scraping. Paper
presented at the Q2024 conference
https://airdrive.eventsair.com/eventsairwesteuprod/production-leading-public/aa8e753af9e943b1aa7fac3d766e7408
(accessed on 21 May 2025).

46

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References

[21] Athanassia Chalimourda, Lorenz Helbling and Mathias Constantin 2024: Improving efficiency in assignment 
and quality control of NACE codes combining innovative methodologies with human expertise. Paper presented 
at the Q2024 conference                                                                                                                                                                                      
https://airdrive.eventsair.com/eventsairwesteuprod/production-leading-public/c3c9280bb0704067948634a3a7a26682 
(accessed on 21 May 2025).

[22] Monika Brunauer and Martin Haitzmann 2009: Backcasting Methods at Statistics Austria, Comparison of the Micro 
and Macro Approach on basis of the Structural business statistics 2005 to 2007. Results within the scope of NACE Revision 2  
https://europa.eu/!ywGrFc

[23] Statistics Estonia 2009: Support the set-up of double reporting and backcasting for NACE Rev. 2 in structural business 
statistics and inward foreign affiliates statistics                                                                                                                                                 
https://europa.eu/!kdxrCk

[24] Brandon Sacco, 2024: Projecting the Past: Micro-based Backcasting Methods in Business Statistics 
through Micro Decomposition Analysis                                                                                                                                                                                                   
https://nso.gov.mt/wp-content/uploads/Projecting-the-Past-Micro-Based-Backcasting-Methods-in-Business-
Statistics-through-Micro-Decomposition-Analysis.pdf

[25] Olivia Hellberg 2010: Backcasting Swedish industrial production. Paper presented 
at the August 2010 Workshop on Survey Sampling Theory and Methodology                                                                                                                             
https://europa.eu/!dJnrrr

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1

Introduction

ANNEX: Statistical 
disclosure control 
when publishing by 
two NACE versions 

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1. Problem description

1.1 Introduction

The changeover from NACE Rev. 2 to NACE Rev. 2.1 poses a clear conflict of interest between the need of data users for 
extended time series, thus requiring a period for which data will be available both on the basis of the old and on the 
basis of the new classification (as set out in the NACE Rev. 2.1 implementing act [5]), and the right of respondents to be 
protected against the disclosure of their data. The problem arises from the fact that small transitions from one category 
to another can be easily disclosed through differencing.

Publishing data broken down by the two classifications for the same reference period creates the opportunities 
to calculate differences at a lower level than either of the classifications. Moreover, thanks to the high-quality 
correspondence table, the nature of the activities of entities concerned is well-defined. These implicit cells also need 
protection.

FIGURE A
Changes between NACE Rev. 2 and NACE Rev. 2.1 concerning classes 10.89 and 11.07

NACE Rev.2

NACE            
Rev. 2.1

10.89

10.89

11.07

11.07

Figure A shows an example where some activities that were classified in NACE Rev. 2 class 10.89 ‘Manufacture of other 
food products n.e.c.’ were moved to NACE Rev. 2.1 class 11.07 ‘Manufacture of soft drinks and bottled waters’. The 
publication broken down by NACE Rev. 2 only shows classes 10.89 and 11.07, and similarly, the publication by NACE 
Rev. 2.1 only shows the classes 10.89 and 11.07. However, if publication takes place for the same reference period, this 
will implicitly also publish data on the activities that moved from 10.89 to 11.07 (the striped box), as information (such 
as totals and frequencies) on those activities can be obtained by merely taking the difference between (the totals or 
frequencies) of NACE Rev. 2 class 10.89 and (the same attribute for) NACE Rev. 2.1 class 10.89. As can be seen from the 
‘common content’ column in version 1.05 pf the NACE Rev. 2 – NACE Rev. 2.1 correspondence table [11], this difference 
concerns a well-defined activity: production of plant-based milk substitutes. It should therefore be checked whether 
the implicit cell needs protection against disclosure risk.

1.2 Derivation through differencing

The problem outlined above can be illustrated in terms of different quantities (such as totals, frequencies and averages).

Totals (e.g. turnover):

 and YB10.89

If YA10.89
Frequencies (e.g. number of enterprises):

 are published, then YA10.89 →B11.07

 can be derived as YA10.89

.
– YB10.89

If fA10.89

 and fB10.89

 are published, then fA10.89 →B11.07

 can be derived as fB10.89

.
– fB10.89

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National practices as to whether frequencies such as fA10.89
such frequences as public. However, even if those frequencies are considered public, the situation may be different for 
 .
the frequency of the more granular ideal subclass  A

 could be confidential. Some countries consider 

 and fB10.89

10.89 →11.07

Averages (e.g. average turnover):

 and ȲB10.89

If ȲA10.89
 are published and their frequencies fA10.89
are easily derived (as the products between frequencies and averages). 
Thereby, ȲA10.89 →11.07

 can be derived as (YA10.89

) / fA10.89→B11.07

 and fB10.89

– YB10.89

 .

 are also published, then the totals YA10.89

 and YB10.89

1.3 Current best methods

Following a literature review (presented at the end of this text), it is assessed that this particular statistical disclosure 
control issue has not been given explicit attention in any normative text in the past. In view of the apparent lack of 
available advice, the present text outlines possible methods for balancing user needs against statistical confidentiality 
requirements.

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A

2. Assumptions 

2.1 Intruder knowledge

In analysing the disclosure risk, assumptions have to be made about the information that a possible intruder (someone 
that deliberately tries to disclose the protected values) has. In the framework of this analysis, we will assume that the 
intruder has perfect knowledge on the delineation of the statistical unit and its economic activity. The correspondence 
tables, describing the changes between the two versions of the classification, are public. 

We assume that the old and the new NACE codes (11) are coherent for each reference period, this is, the conversion 
matrix only has values in line with the correspondence tables [10]. There are no transitions for other reasons (for 
instance the correction of errors) (12).

The situation is not the same for all domains in business statistics. Some domains, like structural business statistics (SBS) 
publish detailed tables by NACE and publish detailed values. Other domains, for instance short-term statistics (STS), 
use a much more aggregate NACE classification and use rounded index numbers. The latter type of domain has lower 
disclosure risk. The analysis below concerns more the SBS type of data.

This annex does not use any domain specific knowledge, for instance on specific activities that do not, or even cannot, 
occur in a country. Such knowledge, certainly if potential intruders can also be expected to have this knowledge, 
changes the analysis of disclosure risks. Another type of domain specific knowledge is on the sensitivity of the 
information. In the analysis in this annex the worst-case scenario is assumed: all the information is highly sensitive. But 
some pieces of information might be actually public and constitute no real disclosure risk.

2.2 Granularity

Countries frequently use national versions (national classifications of economic activities as per Article 4 of the NACE 
regulation [2]) that are more detailed than the NACE classification. National dissemination including specific national 
breakdowns should also be considered as available to potential intruders. Thus, for countries disseminating according 
to a national version, the national correspondence tables have to be considered. The use of national versions will not be 
mentioned in the remainder of this text, but the same principles as the ones set out below remain directly relevant to 
those versions as well.

Moreover, even in the case of one-to-one correspondences at the class level, there may be unforeseen disclosure risks owing 
to the fact that entire classes may move between higher levels (groups, divisions or even sections). In the present text, 
the fact that the NACE is a hierarchical classification is disregarded (for simplicity). The focus is thus only on the disclosure 
risks occurring because of content moving between headings at the same hierarchical level (such as classes). While the 
text remains equally valid for disclosure risks at any single level (and could thus be transposed to apply to e.g. divisions), 
simultaneous disclosure risks – at different hierarchical levels – are not considered.

(11) For readability, the terms ‘old NACE’ and ‘new NACE’ are used where the discussion is generic (and could even involve any other classification that changes).

(12) If the NACE code is established from weighted underlying NACE codes (in line with chapter 3.3 of the manual), there is the risk of transitions not in line with 
the correspondence tables.

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3. Double reporting: two cases

From the perspective of statistical disclosure control, there are two distinct cases:

•  Backcasting
•  Direct double tabulation

Backcasting concerns the case where data according to the old NACE have already been published, and the new NACE 
is not directly available for the statistical units. The data according to the new NACE are estimated with a modelling 
procedure.

Direct double tabulation concerns the case where both the old and the new NACE are available in the statistical 
business register and no modelling is required. The protection approach is still open for data to be produced according 
to both versions of the NACE. 

3.1 Backcasting

Backcasting is relevant for the reference periods up to the point in time for which the new NACE is not yet available 
in the statistical production environment. Data based on the old NACE classification have already been protected 
and published. It is assumed that these data will not be revised and that countries have applied suppression for the 
protection of the data (which is the case for most countries and most domains). The already published data based on 
the old NACE put a restriction on the publication of backcasted data based on the new NACE. The data on the bases of 
the new NACE have to be protected, without breaking the protection of the already published data. In this case, data 
published according to the old NACE is given and cannot be changed. Backcasted data produced according to new 
NACE must be checked for confidentiality also considering the data published according to old NACE. 

What are the options for protecting the backcasted data? Suppression is still by far the most prevalent method for the 
protection of business statistics against disclosure risk. This will therefore be the first option to analyse. The conclusion 
of the discussion of this method is that it will be difficult to apply and that it will lead to a low user value, due to the 
many suppressions. The following alternative solutions will be examined: perturbative methods, rounding and table 
redesign.

The alternatives to suppression, like perturbative methods and rounding, are mentioned in the handbooks on statistical 
disclosure control. These protection methods are, however, not in common use yet. A reason might be that it feels 
wrong to deliberately reduce the quality of data. One has to bear in mind, however, that statistical data is rarely 
absolute. Both sampling and non-sampling errors have to be considered. The imprecision introduced by perturbation 
or rounding could be small relative to the errors inherent in the statistical production process and may even have the 
benefit for users that it eliminates perceived precision in reporting that is not supported by the effective accuracy of 
the underlying data.

The backcasted data are published with more than the usual delay. The disclosure risk is lower for historical data, as 
it gets more difficult to establish the statistical units and their characteristics. Moreover, the sensitivity of the data 
decreases; there is a lower probability that anyone would be interested in data disclosure and that disclosure would be 
harmful for the statistical units. 

Also, the modelling procedure used in backcasting the data offers some protection against disclosure, assuming that 
the parameters of the backcasting model are not published.

3.1.1 Suppression

The identification of problematic cells, the cells that need protection, in the backcasted data follows the basic rules. The 
following has to be taken into account:

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•  the need for protection of the new NACE table itself;
•  for the cells that remain the same in terms of scope, new NACE must follow the protection of the old;
•  for the cells for which the scope has changed, differencing between the old and the new NACE has to be prevented. 

The first step in the process is to produce a table on the new NACE with a continuous variable (13). The choice of the 
continuous variable is strategic, as the pattern of protection for this variable will be reused for the protection of the other 
continuous variables. For instance, the domain at hand has the continuous variables turnover, value added, number of 
employees and profit. For the analysis of the protection the variable turnover is chosen. Turnover is well correlated with 
value added and number of employees and a good indicator of the size of the business. At the end, the confidentiality 
pattern for turnover is applied to the other continuous variables (14).

Preliminary step

(1) 

(2) 

Calculation of a table for the new NACE classification for a continuous variable: example turnover

Identification of confidentiality for the new NACE cells (primary and secondary confidentiality) using standard tools 
(15). The confidential cells get a flag (but the value is kept).

This step has established the necessary suppressions for the table on the new NACE, without considering that similar data 
has been published based on the old NACE. What follows are five groups of checks, depending on the relations according to 
the correspondence tables:

•  One-to-one relations, continuity: the NACE position moved 1:1 to the new NACE (not necessarily with the same NACE 

code) 

•  Two-to-two, simple restructure: high risk of differencing
•  Many-to-many: complex restructure: lower risk of differencing
•  One-to-many relations: split 
•  Many-to-one relations: merge. 

Please note that the correspondence table should be adapted to the breakdowns that are actually published. It is easy to 
just ignore the categories that are not in use. Attention should be paid to groupings or breakdowns that are not in the NACE 
hierarchy.

Check: one-to-one (continuity)

(1) 

(2) 

This check is done on the cells in the table where the position in the new NACE is the same as a position in 
the old NACE (the codes do not need to be the same due to renumbering). In the NACE Rev. 2 – NACE Rev. 2.1 
correspondence tables these are indicated as 1:1 relations (16). The value of the target variable should be the same.  

The one-to-one cells are compared by confidentiality status. The confidentiality status in the new NACE should be 
in line with the confidentiality status in the old NACE: 

(a) If both cells are not confidential, no action needed

(b) If both cells are confidential, no action needed

(c) If the old NACE cell is confidential and new NACE is not confidential: the new NACE cell should be marked as    

confidential. This is a case of secondary confidentiality in the old NACE, as the same rules were used to 
establish primary confidentiality. It should be checked whether the newly suppressed cell in the new NACE 
needs additional protection against differencing.

(13) The protection of frequency tables is similar but is easier as it does not need checking on the dominance of entities.

(14) Protecting the continuous variables independently produces a disclosure risk because of the correlation between them.

(15) Primary confidentiality: publication of a value would allow direct disclosure because it concerns too few units, or one or two units are dominant. Secondary 
confidentiality: additional protection needed to prevent the calculation of primary confidential cells through differencing.

(16) See column J of Version 1.05 of the NACE Rev. 2 – NACE Rev. 2.1 correspondence table [11] 

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(d) If the old NACE cells is not confidential and the new NACE is confidential: the new NACE should be published. 
Also, here the difference in confidentiality status must be due to secondary confidentiality. This implies that 
the secondary confidentiality of the new NACE has the be repaired on this point. This can only be done 
manually.

Check: two-to-two (simple restructuring)

(1) 

(2) 

(3) 

This check is done on the cells in the table where two positions in the new NACE (B1 and B2) consist of the same 
activities as two positions in the old NACE (A1 and A2), but some activities move from the one to the other. NACE 
Rev. 2 – NACE Rev. 2.1  correspondence tables, these are indicated as 2:2 relations. The sum of the target variable 
should be the same (YA1
There are two cases inside. Case 1: the activities of A1 are split over B1 and B2, whereas all activities of A2 go to B2 only 
(it is the case demonstrated in Figure A, YA1

). In this case the following actions must be taken:

 ≥ YB1, and YA2 ≤ YB2

). 
 = YB1 + YB2

 + YA2

(a) if A1 and B1 are not confidential, then the confidentiality of the difference YA1

If the difference is confidential, then B1 is confidential (17).

–YB1 should be checked. 

(b) if A2 and B2 are not confidential, then the confidentiality of the difference YA2

If the difference is confidential, then B2 is confidential.

–YB2 should be checked. 

(c) if A1 and A2 are not confidential, then if either B1 or B2 is confidential, the other should also be confidential.
(d) if A1 or A2 is confidential, then at least one of (B1, B2) should be confidential.

Case 2: both A1 and A2 are split over B1 and B2. This case is inherently safer, as the difference consists of two 
unknown categories. There is a problem if one the contributions is a-priori known to be empty, because the 
specific activity does not exist in the country. In that case, the problem changes effectively to the case 1 above. If 
one of the categories contains a dominant entity, then its protection should be verified. The following actions must 
be taken:

(a) if A1 and A2  are not confidential, then if either B1 or B2 is confidential, the other should also be confidential.
(b) if A1 or B2  is confidential, then at least one of (B1, B2) is confidential.

Check: many-to-many (complex restructuring)

The scenarios get too complex to analyse. If the numbers are still low (up to four to four), domain knowledge can be 
valuable. If it is somehow evident that some flows do not exist in the country, the case could effectively be reducible one of 
the other cases.

The complexity is in itself an advantage, as that will also go for a potential intruder. It is advisable to check whether one or 
two very dominant entities are involved in the restructuring. If that is the case, it should be checked whether they are well 
protected. 

Check: one-to-many (split)

From the correspondence tables it can be established which cells from the old NACE have been split in two or more cells in 
the new NACE. Figure B shows the example where one category of the old NACE is split into two or more categories in the 
new NACE. The total of the new categories 35.11 (Production of electricity from non-renewable sources), 35.12 (Production 
of electricity from renewable sources) and 35.16 (Storage of electricity) has been published (or suppressed) in the old NACE 
35.11 (Production of electricity), and that should be considered in the treatment of the new categories. 

(a) 

(b) 

If the cell in the old NACE is confidential, at least two cells in the new NACE have to be suppressed. 

If the cell in the old NACE is not confidential and one of the split cells is confidential, at least one further cell should    
be suppressed.

(17) If the difference is empty it can be considered as safe.

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FIGURE B
One old activity (35.11) is split into three new activities (35.11, 35.12 and 35.16) 
Old

35.11

New

35.11

35.12

35.16

Check: many-to-one (merge)

A merger of NACE categories is the opposite of a split. Two or more categories in the old NACE are combined to one 
category in the new NACE. The treatment in the old NACE has to be protected in the new NACE:

(a) 

(b) 

If all categories were published in the old NACE, the merged category has to be published in the new NACE. 
If it was suppressed, then it must be due to a secondary suppression. An alternative secondary suppression has to 
be found.

If one or more categories were suppressed in the old NACE, it has to be checked whether publishing the new 
NACE would break the protection by differencing. If that is the case, the merged new NACE category has to be 
suppressed (and it has to be checked whether this suppression needs further protection).

3.1.2 Perturbative methods

The application of perturbative methods in the case of backcasting also has to take into account what data has already 
published on the basis of the old NACE. For all the one-to-one correspondences (18) the original values and suppressions in 
the table by the old NACE have to be kept (as published value or suppressed). The perturbation only concerns the cells with 
changes. 

The level of perturbation should be aligned with the interval that is left in the suppression. Suppression seems to offer some 
kind of absolute protection, because the cell is not published, but further analysis shows that you can always establish an 

interval for the true value (see Table A).

TABLE A
Turnover in NACE Section E in 2021 and 2022 for Luxembourg 
NACE Rev. 2 position

E Water supply; sewerage, waste management and remediation activities

36 Water collection, treatment and supply

37 Sewerage

38 Waste collection, treatment and disposal activities; materials recovery

39 Remediation activities and other waste management services

2021

355.64

64.06

c

275.63

c

2022

405.60

84.77

c

301.44

c

In this example both columns have two confidential cells. For the year 2021 the total turnover for sewerage and remediation 
can be calculated by subtracting all non-confidential values from the total Water supply etc. This gives the value 15.95 (and 
19.39 for 2022). Knowing also that the protection only works, if the confidential cells are a bit balanced, we can already 

(18) The cells that are identical in value, although not 1 to 1 according to the correspondence tables, make it possible to identify categories (hidden cells as in 
Figure B for example) with zero value through differencing. Depending on the perturbative method used, this could produce non-zero differences. The best 
would be that the identical values get perturbed in the same way (as is the case with some methods).

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establish that the real values are somewhere between 5 and 10 for 2021 (and 7.5 and 12.5 for 2022). If that is sufficient 
protection in this case, perturbation with a margin of about 10 would be just as safe (19). Obviously, it would not make much 
sense to publish the decimal categories with this level of perturbation. This implies some loss of information, but the great 
advantage is that the complete table can be published (as long as the original suppressions are respected). 

The standard perturbation tools can be used on the full table, and then for the 1-1 cells, the values have to be replaced by 
the already published values or the suppression. 

3.1.3 Rounding

More or less the same requirements hold for rounding as for perturbation: All 1-1 cells should be kept as original and the 
level of rounding should be in line with the uncertainty interval left by suppression. For the example in Table A, rounding to 
multiples of 10 would be reasonable (20).

There are several rounding approaches. Simple rounding gives in some situations additional information which can allow 
more precise estimation of the rounded values. For instance, in the case that a total of two values has a higher rounded 
value than the total of the two subcategories. 

Rounding can be implemented on the full table, and then the 1-1 cells are copied in as original value or suppression.

Perturbation and rounding are both relatively easy to implement. The advantage of rounding is, that it is more conventional, 
so that it will be accepted easier by both producers and users. The disadvantage of rounding is that it is more predictable, so 
that it requires a bit more loss of details to have sufficient protection.

3.1.4 Table redesign

Table redesign, notably the reduction of dimensions of the table, is an appropriate alternative for the presentation of data 
where lots of cells have to be suppressed. Examples could be the gregation of size classes, or even the total suppression of 
size class as a stratifying variable. Also, the NACE could be published only at a higher level of aggregation. The advantage 
is that tables will appear more complete. The disadvantage is that it effectively leads to less information available to the 
users. From a protection point of view, a higher level of aggregation is usually better, because the data in the cells will be 
based on more entities. From the changes in the NACE itself, reducing tables to a higher level does not per se simplify the 
confidentiality issue, as many changes occur also at the higher levels of aggregation. 

At the European level the integration of data becomes more difficult if tables are redesigned in different ways by different 
countries. 

3.2 Direct double tabulation

At least for 2025, and perhaps for more years, it will be feasible to directly publish according to the two classifications, as 
both versions of the NACE code are required to be available in the statistical business register. The big difference with 
backcasting is that no data has been published yet, so the whole protection strategy is still open. As a general rule, the 
completeness of the newer version of the NACE has priority over the older. Therefore, a similar analysis would have to be 
done as described above, but preparing and protecting tables for the new NACE first. 

The order or priority of the new NACE relative to the old NACE is particularly relevant in the case where the data will be 
protected through suppression. In the case of perturbation or rounding, the order or priority does not matter. This is an 
advantage, as new tables can be added to the publication set from a certain dataset, without the need to analyse the risk of 
breaking the protection of already published tables.

(19) It is probably good to be generous with the margin for perturbation, as in the case of backcasting several exact totals are known. 

(20) Also, in the case of rounding, it has to be considered that several exact values are known.

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A

The application of perturbation or rounding for the new NACE will be easier, as the display or suppression of values for 
the 1:1 cells from the publication of the old NACE no longer have to be followed. From a user perspective this has the 
advantage that tables will be complete.

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A Statistical disclosure control when publishing by two 

NACE versions 

4. Conclusion

Statistical disclosure control is a responsibility of the statistical authority of each Member State and specific national 
rules might apply. Strict application of the dominant protection method (suppression) is complex in the case of 
publishing two versions of the NACE for the same reference period. Standard tools are of limited use and additional 
steps with manual intervention are required. Moreover, the process will result in many suppressions, thus generating a 
low user value.

Perturbation or rounding could be good alternatives. These are classical disclosure control methods that appear in the 
available handbooks. There is, however, little experience with these methods in business statistics. This makes it difficult 
to offer detailed guidance on what parameters to choose and how to communicate with respondents and users. 

The decision how to protect data broken down by NACE Rev. 2.1 from 2025 onwards should be based on what 
brings the best trade-off between protection and user value in the long term. The basic arguments are known, but 
different users might have different priorities, and it also requires active communication to explain the advantages and 
disadvantages of the different approaches. 

It is paramount to generate and share experience with alternatives to suppression. Microdata are necessary for the 
analysis of disclosure risks. Sharing between producers of some safe microdata creates the possibility of replicating 
results and of involving others.

58

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Bibliography

Bibliography related to the literature review

All known handbooks on statistical disclosure control having been published since 2000:

1. Anco Hundepool, Josep Domingo-Ferrer, Luisa Franconi, Sarah Giessing, Eric Schulte Nordholt, Keith Spicer and
Peter-Paul de Wolf 2012: Statistical Disclosure Control  
https://doi.org/10.1002/9781118348239

2. Anco Hundepool, Josep Domingo-Ferrer, Luisa Franconi, Sarah Giessing, Eric Schulte Nordholt, Keith Spicer and
Peter-Paul de Wolf 2024: Handbook on Statistical Disclosure Control, Second edition
https://sdctools.github.io/HandbookSDC/ (accessed 21 May 2025).

3. George T. Duncan, Mark Elliot and Gonzalez Juan Jose Salazar 2011:  Statistical Confidentiality: Principles and 
Practice
https://doi.org/10.1007/978-1-4419-7802-8

4. Leon Willenborg and Ton Waal, 2000: Elements of Statistical Disclosure Control.
https://doi.org/10.1007/978-1-4613-0121-9

5. Pat Doyle, Julia I. Lane, Jules J. M. Theeuwes and Laura M. Zayatz (eds.) 2001: Confidentiality, Disclosure and Data 
Access: Theory and Practical Applications for Statistical Agencies. ISBN  978-0444507617.

have been reviewed (21). All handbooks contain advice on perturbation and rounding. However, none of them offers 
advice on the specific case of parallel dissemination of two versions of the same classification for the same reference 
period. A supplementary literature search did not succeed in identifying any other literature of relevance. 

(21) Handbooks 1 and 2 are basically different versions of the same document. The updates made between 1 and 2 include details on a perturbation method 
that has been recently applied in the population census (the Cell-key method).

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Backcasting manual

This publication provides guidance to producers of official 
statistics that need to produce consistent historical time series 
for an updated classification. It gives an overview of methods 
that can be used to reformulate statistics presented according to 
the old version of the classification in terms of the new 
(updated) version. All examples of the publication are based on 
the classification of economic activities in the European Union 
(NACE).

For more information
https://ec.europa.eu/eurostat/
https://ec.europa.eu/eurostat/web/metadata/classifications

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PDF: ISBN 978-92-68-28632-6