# Annex A. Methodological notes

## A.1. Primary and secondary markets

In order to distinguish fake products counterfeiters intended to sell on the primary market from those intended for sale on the secondary market, the price gap between both types of counterfeits is calculated. For each seizure specified in the WCO and DG TAXUD databases, customs authorities report the infringed trademark, the declared value of goods, the quantity seized and the product’s HS code. This allows the unit value of each seized “product type-brand” pair to be determined (brand would include the associated trademark or patent). These unit values can then serve as a proxy for the retail prices of fake goods.

For each type of product associated with a given trademark or patent, the prices of seized goods are used to estimate a confidence interval that contains the actual retail price of the corresponding genuine item. Counterfeit items whose unit price, calculated as described above, is higher than or included in this interval are then classified as intended for sale on the primary market. Those whose price is below this interval are classified as targeting the secondary market.

Formally, let ${\text{s}}_{\text{c}}$ and ${\stackrel{\mathrm{-}}{\text{s}}}_{\text{c}}$ denote, respectively, the import value and quantity of any custom seizure of counterfeit products, with the range of customs seizures and their total number. then refers to the unit value of each custom seizure and can serve as a proxy for their unit price. Let ${p}_{bp}=\left(\sum _{c\in \left\{bp\right\}}{p}_{c}\right)/{N}_{bp}$ defines the (unweighted) price average of any type of product $p$ associated with the brand or patent $b$, with ${N}_{bp}$ the total number of custom seizures reported for this “product category-brand” combination. The standard deviation of this price is denoted ${\sigma }_{bp}$.

${X}_{c}$ is defined as a dichotomous (binary) variable that takes the value of 0 if the fake goods included in the seized shipment were intended to be sold on the primary market, or 1 if they were intended to be sold on the secondary market. In accordance with the arguments mentioned in the main text, ${X}_{c}$ is assumed to be defined as follows:

It follows that the share of products sold on the primary market can be calculated by product category, ${\tau }_{p}^{1}$, and/or for the entire mass of fake imports, and is given by:

For example, Figure A A.1 shows the price distribution of fake shoes of brand X that were seized by global customs between 2014 and 2016. Using the methodology outlined, this indicates that most fake X shoes with prices lower than USD 121 were destined for the secondary market, while those with values higher than USD 121 (observations in the middle and on the right-hand side of the distribution) were targeted at the primary market.

## A.2. Construction of GTRIC-p

GTRIC-p is constructed of four steps:

• For each reporting economy, the seizure percentages for sensitive goods are formed.

• For each product category, aggregate seizure percentages are formed, taking the reporting economies’ share of total sensitive imports as weights.

• From these, a counterfeit source factor is established for each industry, based on the industries’ weight in terms of total trade.

• Based on these factors, the GTRIC-p is formed.

### Step 1: Measuring reporter-specific product seizure intensities

and are, respectively, the seizure and import values of product type k (as registered according to the HS on the two-digit level) in economy i from any provenance economy in a given year. Economy i’s relative seizure intensity (seizure percentages) of good k, denoted below as , is then defined as:

, such that

is the range of sensitive goods (the total number of goods is given by K) and is the range of reporting economies (the total number of economies is given by N).

### Step 2: Measuring general product seizure intensities

The general seizure intensity for product k, denoted , is then determined by averaging seizure intensities, , weighted by the reporting economies’ share of total sensitive imports in a given product category, k. Hence:

,

The weight of reporting economy i is given by:

where is i’s total registered import value of sensitive goods ()

### Step 3: Measuring product-specific counterfeiting factors

is defined as the total registered imports of sensitive good k for all economies and is defined as the total registered world imports of all sensitive goods.

The world import share of good k, denoted , is therefore given by:

, such that

The general counterfeiting factor of product category k, denoted , is then determined as the following:

The counterfeiting factor reflects the sensitivity of product infringements occurring in a particular product category, relative to its share in international trade. These are based on the seizure percentages calculated for each reporting economy and constitute the foundation of the formation of GTRIC-p.

### Step 4: Establishing GTRIC-p

GTRIC-p is constructed from a transformation of the general counterfeiting factor and measures the relative propensity to which different types of product categories are subject to counterfeiting and piracy in international trade. The transformation of the counterfeiting factor is based on two main assumptions:

• The first assumption (A1) is that the counterfeiting factor of a particular product category is positively correlated with the actual intensity of international trade in counterfeit and pirated goods covered by that chapter. The counterfeiting factors must thus reflect the real intensity of actual counterfeit trade in the given product categories.

• The second assumption (A2) acknowledges that the assumption may not be entirely correct. For instance, the fact that infringing goods are detected more frequently in certain categories could imply that differences in counterfeiting factors across products merely reflect that some goods are easier to detect than others or that some goods, for one reason or another, have been specially targeted for inspection. The counterfeiting factors of product categories with lower counterfeiting factors could, therefore, underestimate actual counterfeiting and piracy intensities in these cases.

In accordance with assumption A1 (positive correlation between counterfeiting factors and actual infringement activities) and assumption A2 (lower counterfeiting factors may underestimate actual activities), GTRIC-p is established by applying a positive monotonic transformation of the counterfeiting factor index using natural logarithms. This standard technique of linearisation of a non-linear relationship (in the case of this study between counterfeiting factors and actual infringement activities) allows the index to be flattened and gives a higher relative weight to lower counterfeiting factors (see Verbeek, 2000).

In order to address the possibility of outliers at both ends of the counterfeiting factor index (i.e. some categories may be measured as particularly susceptible to infringement even though they are not, whereas others may be measured as insusceptible although they are), it is assumed that GTRIC-p follows a left-truncated normal distribution, with GTRIC-p only taking values of zero or above.

The transformed counterfeiting factor is defined as:

Assuming that the transformed counterfeiting factor can be described by a left-truncated normal distribution with ; then, following Hald (1952), the density function of GTRIC-p is given by:

where is the non-truncated normal distribution for specified as:

The mean and variance of the normal distribution, here denoted and , are estimated over the transformed counterfeiting factor index, , and given by and . This enables the calculation of the counterfeit import propensity index (GTRIC-p) across HS chapters, corresponding to the cumulative distribution function of .

## A.3. Construction of GTRIC-p

GTRIC-e is also constructed in four steps:

• For each reporting economy, the seizure percentages for provenance economies are calculated.

• For each provenance economy, aggregate seizure percentages are formed, taking the reporting economies’ share of total sensitive imports as weights.

• From these, each economy’s counterfeit source factor is established, based on the provenance economies’ weight in terms of total trade.

• Based on these factors, the GTRIC-e is formed.

### Step 1: Measuring reporter-specific seizure intensities from each provenance economy

is economy i’s registered seizures of all types of infringing goods (i.e. all k) originating from economy j in a given year in terms of their value. is economy i’s relative seizure intensity (seizure percentage) of all infringing items that originate from economy j, in a given year:

such that

where is the range of identified provenance economies (the total number of exporters is given by J) and is the range of reporting economies (the total number of economies is given by N).

### Step 2: Measuring general seizure intensities of each provenance economy

The general seizure intensity for economy j, denoted , is then determined by averaging seizure intensities, , weighted by the reporting economy’s share of total imports from known counterfeit and pirate origins.1 Hence:

,

The weight of reporting economy i is given by:

, such that

### Step 3: Measuring partner-specific counterfeiting factors

is defined as the total registered world imports of all sensitive products from j,2 and is the total world import of sensitive goods from all provenance economies.

The share of imports from provenance economy j in total world imports of sensitive goods, denoted , is then given by:

, such that

From this, the economy-specific counterfeiting factor is established by dividing the general seizure intensity for economy j with the share of total imports of sensitive goods from j.

### Step 4: Establishing GTRIC-e

Gauging the magnitude of counterfeiting and piracy from a provenance economy perspective can be undertaken in a similar fashion as for sensitive goods. Hence, a general trade-related index of counterfeiting for economies (GTRIC-e) is established along similar lines and assumptions:

• The first assumption (A3) is that the intensity by which any counterfeit or pirated article from a particular economy is detected and seized by customs is positively correlated with the actual amount of counterfeit and pirate articles imported from that location.

• The second assumption (A4) acknowledges that assumption A3 may not be entirely correct. For instance, a high seizure intensity of counterfeit or pirated articles from a particular provenance economy could be an indication that the provenance economy is part of a customs profiling scheme, or that it is specially targeted for investigation by customs. The importance that provenance economies with low seizure intensities play regarding actual counterfeiting and piracy activity could, therefore, be under-represented by the index and lead to an underestimation of the scale of counterfeiting and piracy.

As with the product-specific index, GTRIC-e is established by applying a positive monotonic transformation of the counterfeiting factor index for provenance economies using natural logarithms. This follows from assumption A3 (positive correlation between seizure intensities and actual infringement activities) and assumption A4 (lower intensities tend to underestimate actual activities). Considering the possibilities of outliers at both ends of the GTRIC e-distribution (i.e. some economies may be wrongly measured as being particularly susceptible sources of counterfeit and pirated imports, and vice versa), GTRIC-e is approximated by a left-truncated normal distribution as it does not take values below zero.

The transformed general counterfeiting factor across provenance economies on which GTRIC-e is based is therefore given by applying logarithms onto economy-specific general counterfeit factors (see, for example, Verbeek, 2000):

In addition, following GTRIC-p, it is assumed that GTRIC-e follows a truncated normal distribution with for all j. Following Hald (1952), the density function of the left-truncated normal distribution for is given by:

where is the non-truncated normal distribution for specified as:

The mean and variance of the normal distribution, here denoted and , are estimated over the transformed counterfeiting factor index, , and given by and . This enables the calculation of the counterfeit import propensity index (GTRIC-e) across provenance economies, corresponding to the cumulative distribution function of .

## A.4. Construction of GTRIC

In the OECD (2008) and OECD-EUIPO (2016) studies, propensities to import infringing goods from different trading partners were developed using seizure data as a basis. The usage of data is maximised by applying a generalised approach in which the propensities for products to be counterfeit and for economies to be sources of counterfeit goods were analysed separately. This increased the data coverage of both products and provenance economies significantly, which increases the robustness of the overall estimation results. Unfortunately, it also reduced the detail of the analysis, meaning that counterfeit trade patterns specific to individual reporting economies, for both product types and trading partners, were not simultaneously accounted for; this introduced bias into the results. On balance, given the large scope of the analysis, the advantages of increasing data coverage can be viewed as outweighing the biases.

This approach combines the two indices: GTRIC-p and GTRIC-e. In this regard, it is important to emphasise that the index resulting from this combination does not account for differences in infringement intensities across different types of goods that may exist between economies. For instance, imports of certain counterfeit and pirated goods could be particularly large from some trading partners and small from others. An index taking such “infringement specialisation”, or concentration, into account is desirable and possible to construct; but it would require detailed seizure data. The combined index, denoted GTRIC, is, therefore, a generalised index that approximates the relative propensities to which particular product types, imported from specific trading partners, are counterfeit and/or pirated.

### Establishing propensities for product and provenance economy

In this step, the propensities to contain counterfeit and pirated products will be established for each trade flow from a given provenance economy and in a given product category.

The general propensity of importing infringed items of HS category k, from any economy, is denoted , and be given by GTRIC-p so that:

where is the cumulative probability function of .

Furthermore, the general propensity of importing any type of infringing goods from economy j is denoted , and given by GTRIC-e, so that:

where is the cumulative probability function of .

The general propensity of importing counterfeit or pirated items of type k originating from economy j is then denoted and approximated by:

Therefore, , , with denoting the minimum average counterfeit export rate for each sensitive product category and each provenance economy.3 It is assumed that .

## A.5. Calculating the absolute value

is the fixed point, i.e. the maximum average counterfeit import rate of a given type of infringing good, k, originating from a given trading partner, j.

can be applied onto propensities of importing infringing goods of type j from trading partner k (). As a result, a matrix of counterfeit import propensities C is obtained.

with dimension J x K

The matrix of world imports is denoted by M. Applying C on M yields the absolute volume of trade in counterfeit and pirated goods.

In particular, the import matrix M is given by:

with dimension n x J x K

Each element is defined by economy i’s unique import matrix of good k from trading partner j.

with dimension J x K

Hence, the element denotes i’s imports of product category k from trading partner j, where , , and .

Denoted by , the product-by-economy percentage of counterfeit and pirated imports can be determined as the following:

Total trade in counterfeit and pirated goods, denoted by the scalar TC, is then given by:

where is a vector of one with dimension nJ x 1, and is a vector of one with dimension K x 1. Then, by denoting total world trade by the scalar , the value of counterfeiting and piracy in world trade, sTC, is determined by:

## References

Hald, A. (1952), Statistical Theory with Engineering Applications, John Wiley and Sons, New York.

Verbeek, M. (2000), A Guide to Modern Econometrics, Wiley.

## Notes

← 1. This is different than the economy’s share of total imports of sensitive goods used to calculate GTRIC-p.

← 2. This is different than the total imports of sensitive goods as used in calculation of GTRIC-p.

← 3. According to the OECD (2008) methodology, these factors were applied to all provenance economies and all HS modules in order to account for counterfeit and pirated exports of products and/or from provenance economies that were not identified. This assumption is relaxed in this study, given the overall good data quality.

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