International trade in goods - methodology for indices

Background and definitions

International trade in goods statistics are an important data source for many public and private sector decision-makers at international, European Union and national level. For example, at European Union level, international trade data are extensively used for multilateral and bilateral negotiations within the framework of the common trade policy, to define and implement anti-dumping policy, to evaluate the progress of the Single Market or the integration of European economies. In the private sector, businesses can use international trade data to carry out market research and define their commercial strategy. Moreover, they constitute an essential source for the compilation of balance of payments statistics and national accounts.

In addition to the detailed monthly data, users of trade statistics need short-term indicators which are easy to use in macroeconomic analysis, such as seasonally adjusted series and indices. As trade flows are expressed in current value (with prices referring to the reference period concerned), indices help to distinguish between price changes (unit value index) and volume changes (volume index). Unit value indices, on the one hand, allow to approximate the evolution of import and export prices. Volume indices, on the other hand, measure the development in the volume of trade expressed in constant prices of a base year.

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Data sources

Indices are based on the intra-EU and extra-EU trade data at the most detailed level, namely by combined nomenclature (CN) 8-digit and by partner country. Trade in goods data are provided to Eurostat by the EU Member States, within 40 days after the reference month for extra-EU trade, and 70 days after the reference month for intra-EU trade.

The calculation of the Eurostat unit value indices starts from the original data, at the CN 8-digit elementary level, without aggregation over partners or products. These source data include the following data elements: reference period, reporting country, flow, partner country, product (CN 8-digit), trade value in euros, quantity expressed in net mass, and quantity expressed in supplementary units. For some of the CN codes, two measurement units may be used, net mass (tonnes) and supplementary unit, such as ’number of items’. In such cases, two types of unit value can be calculated: per tonne and per supplementary unit. In the compilation of the unit value index, the supplementary measurement unit is used as the primary one.

Treatment of discontinuity

Changes in product classification codes or geographical definitions over time can affect the calculation of indices significantly. It is thus crucial to manage these changes properly to ensure accurate comparisons between consecutive years.

In case there is a change in the combined nomenclature between two years, the products are combined to produce an aggregate with the same definition in both years. The same approach is followed when there are changes in the geographical definition of countries.

The types of changes in both product and country classifications can be grouped as follows:

Merge of several codes into a single code;
Split of a code into several codes;
Double: merge + split several codes into several codes;

In case of a merge (1), the codes of the year (y-1) are combined to form one single code and the values and quantities are summed up.
If a code is split (2), the code of the year (y-1) is replaced by the codes of the year (y) and the average unit value of the year (y-1) is attributed to each of these codes.
When there are merge and split (3), firstly the codes are merged (sum of values and quantities) and then the codes are split attributing the average unit value to each of them.

Treatment of outliers

Unusual movements of the unit value can be natural (e.g caused by specific economic events) but can also be caused by errors. Abnormal changes in the unit values can lead to an unreliable index. In order to assess the validity of data with a view to using these data for the calculation of unit value indices, the quality of the source data is checked by applying two main tests, a yearly and a monthly test. The items eliminated by these tests are flagged and later on the concerned unit value indices (at CN 8-digit level) are corrected by replacing them by the median unit value indices of similar products.

The yearly test is based on the hypothesis that, given the general level of inflation, the price of a product cannot vary significantly from one year to another.

For this purpose, a comparison is made between the unit value of the current year and the average unit value of the previous year. This comparison is done for products at CN 8 level for the same reporting country, flow (import or export) and partner country. A data item is rejected if the ratio is outside of the range [0.25; 4.0]. This means that a unit value is not accepted if it is 4 times higher or 4 times lower than the average unit value in the previous year. For energy products, the range is extended to [0.20; 6.0]. The formula is as follows:

\[ 0.25 < \frac{u(y, m, i)}{U(y-1, i)} < 4.0 \]

Where:
u(y, m, i) = unit value of product i for month m of year y ;
U(y-1,i) = average unit value of product i for year y-1 ;

The monthly test is based on the assumption that the change in the price of a product compared with the closest month available will not differ significantly from the average (median) change in the price of similar products. The methodology for identifying similar groups of products is explained in the following paragraph, “ The blocks”. The unit value change is compared with the median unit value change of the group of similar products at SITC 3 digit level of the same flow (import or export), reporting country and partner country. The item is accepted if the result belongs to the range [0.5; 2]. If the result is outside this range, the data item is provisionally rejected and a similar comparison is made for the month (m-2). The data item is accepted if it passes one of these two tests. If it passes neither test, the data item is considered as an outlier which will be corrected. The comparison can be expressed by the formula: \[ 0.5 < \frac{u(y, m)/u(y, m_{-1})}{\text{Median}_{\text{block}}[u(y, m)/u(y, m_{-1})]} < 2.0 \]

Where:
u(y,m) = unit value of the item i for month m of year y
m = current month
m-1 = month (m-1)

The blocks

Groups of similar products are created regularly using the data of three consecutive years before the current year. All the data at CN 8-digit level are grouped by Standard International Trade Classification (SITC) 3-digit using correspondence tables, separately for intra- and extra EU trade. For each SITC 3-digit group, a specific number of combinations (15 for intra- and 10 for extra EU trade) of flow (import or export) x reporting country x partner country with the highest trade value during three previous years are selected and form the “blocks” of similar products. The trade value for each combination is a sum of the trade values of the CN8 products belonging to the same SITC 3 group of the same reporting country and partner country. The remaining combinations in each SITC 3-digit group form the residual block. The blocks are formed once per year and are used for the treatment of the data for the 12 months of a given reference year.

The blocks are used for detection of errors in the monthly test, and for the corrections of the errors detected as described in the previous section. Two medians are calculated for each block, namely the median of unit value change between the closest months of the same year Median_block ⌊u(y,m/u(y,m_-1)⌋ to detect the errors in the monthly test and the median unit value change between the reporting month and the monthly average of the previous year u(y,m,i)/U(y-1,i) for the correction of errors (outliers) detected by all the validation tests.

The median of the unit value change between the current month and the monthly average of the previous year calculated for each block using the items accepted by the validation tests, replace the unit value changes of the products at CN 8 level (of the same block) identified as abnormal by both tests. When an item is rejected by the validation tests, it is assumed that the erroneous unit value is caused by an error in the quantity of the product. Therefore, the original trade value of the product is kept.

Indices calculation

Three types of indices are commonly used in the analysis of the general evolution of a set of products: Laspeyres, Paasche and Fisher. A Laspeyres unit value index shows the unit value development using base period quantity weights, while a Paasche unit value index shows the unit value development using current-period quantity weights. A Fisher unit value index is the geometric mean of the Laspeyres index and the Paasche index and represents a kind of compromise correcting for the upward bias of the Laspeyres index and the downward bias of the Paasche index.

1. Calculation of the unit value index (UVI). Steps for the Fisher indices calculation:

Definition of components:

Monthly value and quantities:

v(y,m,i) = value of trade in item 'i' for month 'm' of year 'y'

q(y,m,i) = quantity of trade in item 'i' for month 'm' of year 'y'

The average values and average quantities of the previous year

\[\left\{\begin{matrix}V(y-1,i)=\frac{1}{12}\sum_{m=1}^{12}v(y-1,m,i)\\Q(y-1,i)=\frac{1}{12}\sum_{m=1}^{12}q(y-1,m,i)\end{matrix}\right.\]

The unit values of the reference year (defined by trade value divided by quantity) and the average unit values of the previous year.

\[u(y,m,i)=\frac{v(y,m,i)}{q(y,m,i)} \quad \text{&} \quad U(y-1,i) = \frac{V(y-1,i)}{Q(y-1,i)}\]

The result table looks like the following table:

Table 1: Calculation of the Laspeyres, Paasche and Fisher unit value indices.

For the purpose of this calculation, the base year is the previous year y-1, which means that the base year changes every year. This approach ensures that the indices calculation aligns with changes in trade patterns and is less sensitive to abnormalities in the base period. The Laspeyres and Paasche monthly indices formulae are:

\[\left\{\begin{matrix}uvi_{Laspeyres}(y,m)=\sum_{i=1}^{n}w_L(y-1,i)\left(\frac{u(y,m,i)}{U(y-1,i)}\right)\\\quad uvi_{Paasche}(y,m)=\left[\sum_{i=1}^{n}w_P(y,m,i)\left(\frac{u(y-1,i)}{U(y,m,i)}\right)\right]^{-1}\end{matrix}\right.\]

\[\text{Where:}\left\{\begin{matrix}\;w_L(y-1,i)=\frac{V(y-1,i)}{\sum_{j=1}^{n}V(y-1,j)}\\w_P(y,m,i)=\frac{v(y,m,i)}{\sum_{j=1}^{n}v(y,m,j)}\end{matrix}\right.\]

These two formulae can also be written as follows:

\[\left\{\begin{matrix}uvi_{Laspeyres}(y,m)=\frac{\sum_{i=1}^{n}u(y,m,i)\times Q(y-1,i)}{\sum_{j=1}^{n}V(y-1,j)}\\uvi_{Paasche}(y,m)=\frac{\sum_{i=1}^{n}v(y,m,i)}{\sum_{j=1}^{n}U(y-1,j)\times q(y,m,i)}\end{matrix}\right.\]

From the Laspeyres and Paasche monthly indices, one can calculate the Fisher monthly:

\[ uvi_{Fischer}(y,m) = \sqrt{(uvi_{Laspeyres}(y,m) \times uvi_{Paasche}(y,m)} \]

The volume Fischer index is then simply derived as IVOL (y,m) = IVAL / uvi_Fischer(y,m) where IVAL = v(y,m,i) / V(y-1,i)

Indices for different product classifications are calculated using the trade data at CN 8-digit level and corresponding tables:

\[\begin{matrix}CN-8\:digit\rightarrow SITC-5\:digit\rightarrow SITC-3\:digit\\CN-8\:digit\rightarrow SITC-5\:digit\rightarrow BEC-3\:digit\\CN-8\:digit\rightarrow CPA-4\:digit\rightarrow CPA-3\:digit\end{matrix}\]

Indices for higher levels of classifications are calculated using the same method as described above, weighting the individual unit value indices at CN 8-digit level by their trade values.

The annual unchained Fisher indices (UVI_Fisher) are chained accoring to the following formula, where yn is the period for which the chained index is calculated and y0 is the base year:

\[UVI^{yn}_{y0}=UVI^{y1}_{y0}\times UVI^{y2}_{y1}\times\cdots\quad\cdots\times UVI^{yn}_{yn-1}\]

UVI_yo^yn is a chained unit value index for a year yn with the reference year y0

UVI_yn-1^yn is an unchained annual unit value index for a year yn with the reference year yn-1

Notes to the article

Statistical procedures

In extra-EU trade, goods may be transferred from an EU Member State to a non-EU country, or the other way round, under customs control, and then returned to the country of departure. The EU legislation requires these movements to be classified under specific statistical procedures derived from customs procedures. For instance, this breakdown allows users to distinguish between goods permanently imported and goods imported to be transformed in the EU before being re-exported. The data transmitted by national statistical authorities to Eurostat allow different types of export and import to be identified according to their statistical procedure.

Revisions

EU Members States are required to transmit new data files on a monthly basis, which often include also revisions for previous periods. The unit value and volume indices are recalculated every month, taking into account the latest revisions. They are also recalculated for past years in case of important revisions provided by the Member States.

Confidentiality

One of the ways in which confidentiality is treated in the data is to allocate trade to a special geographic or product code, in order to disguise the origin or destination. The Eurostat index calculation system uses only the public data, i.e. data after the suppression due to confidentiality. Therefore the final indices are, on the one hand, consistent with the other trade indicators but on the other hand, affected by the camouflage.