Annex A. Methodological notes

Step 1: Measuring reporter-specific product seizure intensities

${\tilde{v}}_i^k$ and ${\tilde{m}}_i^k$ 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 ${\gamma }_i^k$ is then defined as:

${\gamma }_i^k=\frac{{\tilde{v}}_i^k}{\sum _{k=1}^{\stackrel{-}{K}}{\tilde{v}}_i^k}$, such that $\sum _{k=1}^{\stackrel{-}{K}}{\gamma }_i^k=1$ $\forall i \in \{1,\dots ,\stackrel{-}{N}$}

$k=\{1,\dots ,\stackrel{-}{K}\}$ is the range of sensitive goods (the total number of goods is given by K) and $i=\{1,\dots ,\stackrel{-}{N}\}$ 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 ${\mathbf{\Gamma }}^{\mathit{k}}$, is then determined by averaging seizure intensities, ${\gamma }_i^k$, weighted by the reporting economies’ share of total sensitive imports in a given product category, k. Hence:

${\mathrm{\Gamma }}^k=\sum _{i=1}^{\stackrel{-}{N}}{\omega }_i{\gamma }_i^k$ , $\forall k \in \{1,\dots , \stackrel{-}{K}\}$

The weight of reporting economy i is given by:

${\omega }_i=\frac{{\tilde{m}}_i^k}{\sum _{i=1}^{\stackrel{-}{N}}{\tilde{m}}_i^k}$

where ${\tilde{m}}_i$ is i’s total registered import value of sensitive goods ($\sum _{i=1}^{\stackrel{-}{n}}{\omega }_i=1$)

Step 3: Measuring product-specific counterfeiting factors

${\tilde{M}}_i^k=\sum _{i=1}^N{\tilde{m}}_i^k$ is defined as the total registered imports of sensitive good k for all economies and $\tilde{M}= \sum _{k=1}^{\stackrel{-}{K}}{\tilde{M}}^k$ is defined as the total registered world imports of all sensitive goods.

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

$s^k=\frac{{\tilde{M}}^k}{\tilde{M}}$, such that $\sum _{k=1}^{\stackrel{-}{K}}{s}^k=1$

The general counterfeiting factor of product category k, denoted ${CP}^k$, is then determined as the following:

${CP}^k=\mathrm{ }\frac{{\mathrm{\Gamma }}^k}{s^k}$

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 likelihood that different product categories will be subject to counterfeiting and piracy in international trade. The transformation of the counterfeiting factor is based on two main assumptions:

• Assumption (A1): 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.

• Assumption (A2): This acknowledges that the assumption A1 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 (Verbeek, 2000[17]).

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:

${cp}^k=\mathrm{l}\mathrm{n}({CP}^k+1)$

Assuming that the transformed counterfeiting factor can be described by a left-truncated normal distribution with ${cp}^k\ge 0$, then, following Hald (1952[18]), the density function of GTRIC-p is given by:

$f_{LTN }\left({cp}^k\right)=\left\{\begin{array}{c} 0 if {cp}^k \le 0\\ \frac{f \left({cp}^k\right)}{{\int }_0^{\infty }f \left({cp}^k\right)d{cp}^k} if {cp}^k\ge 0\end{array}\right\}$

where $f\left({cp}^k\right)$ is the non-truncated normal distribution for ${cp}^k$ specified as:

$f\left({cp}^k\right)=\frac{1}{\sqrt{2\pi {\sigma }_{cp}^2}} exp\left(-\frac{1}{2} \left(\frac{\left({cp}^k\right)- {\mu }_{cp}}{{\sigma }_{cp}}\right)²\right)$

The mean and variance of the normal distribution, here denoted ${\mu }_{cp}$ and ${\sigma }_{cp}^2$, are estimated over the transformed counterfeiting factor index, ${cp}^k$, and given by ${\widehat{\mu }}_{cp}^2$ and ${\sigma }_{cp}^2$. This enables the calculation of the counterfeit import propensity index (GTRIC-p) across HS codes, corresponding to the cumulative distribution function of ${cp}^k$.

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

${\tilde{v}}_i^j$ 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. ${\gamma }_i^j$ is economy i’s relative seizure intensity (seizure percentage) of all infringing items that originate from economy j, in a given year:

${\gamma }_i^j=\frac{{\tilde{v}}_i^j}{\sum _{j=1}^{\stackrel{-}{J}}{\tilde{v}}_i^j}$ such that $\sum _{j=1}^{\stackrel{-}{J}}{\gamma }_i^j=1$ $\forall i \in \{1,\dots ,\stackrel{-}{N}$}

Where $j=\{1,\dots ,\stackrel{-}{J}\}$ is the range of identified provenance economies (the total number of exporters is given by J) and $i=\{1,\dots ,\stackrel{-}{N}\}$ 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 ${\mathrm{\Gamma }}^j$, is then determined by averaging seizure intensities, ${\gamma }_i^j$, weighted by the reporting economy’s share of total imports from known counterfeit and pirate origins.1 Hence:

${\mathrm{\Gamma }}^j=\sum _{i=1}^{\stackrel{-}{N}}{\omega }_i{\gamma }_i^j$ , $\forall j \in \{1,\dots , \stackrel{-}{J}\}$

The weight of reporting economy i is given by:

${\omega }_i=\frac{{\tilde{m}}_i^j}{\sum _{i=1}^{\stackrel{-}{N}}{\tilde{m}}_i^j}$, such that $\sum _{i=1}^{\stackrel{-}{N}}{\omega }_i=1$

Step 3: Measuring partner-specific counterfeiting factors

${\stackrel{-}{M}}_i^j=\sum _{i=1}^N{\stackrel{-}{m}}_i^j$ is defined as the total registered world imports of all sensitive products from j,2 and $\stackrel{-}{M}=\mathrm{ }\sum _{j=1}^{\stackrel{-}{J}}{\stackrel{-}{M}}^j$ 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 $s^j$, is then given by:

$s^j=\frac{{\stackrel{-}{M}}^j}{\stackrel{-}{M}}$, such that $\sum _{j=1}^{\stackrel{-}{J}}{s}^j=1$

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

${CE}^j=\mathrm{ }\frac{{\mathrm{\Gamma }}^j}{s^j}$

Step 4: Establishing GTRIC-e

Gauging the magnitude of counterfeiting and piracy from a provenance economy perspective can be done 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:

• Assumption (A3): 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.

• Assumption (A4): This 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[17])):

$c{e}^j=\mathit{ln}(C{E}^j+1)$

In addition, following GTRIC-p, it is assumed that GTRIC-e follows a truncated normal distribution with $c{e}^j\ge 0$ for all j. Following Hald (1952[18]), the density function of the left-truncated normal distribution for $c{e}^j$ is given by:

$g_{LTN}\left(c{e}^j\right)=\left\{\begin{array}{c}\begin{array}{c}0\\ \end{array}\\ \frac{g\left(c{e}^j\right)}{{\int }_0^{\infty }g\left(c{e}^j\right)dce}\end{array}\right.\hspace{1em}\begin{array}{c}\begin{array}{c}if\hspace{0.33em}c{e}^j\le 0\\ \\ \\ if\hspace{0.33em}c{e}^j\ge 0\end{array}\\ \end{array}$

where $g\left(c{e}^j\right)$ is the non-truncated normal distribution for $c{e}^j$ specified as:

$g\left(c{e}^j\right)=\frac{1}{\sqrt{2\pi {\sigma }_{ce}^2}}\mathit{exp}\left(-\frac{1}{2}{\left(\frac{c{e}^j-{\mu }_{ce}}{{\sigma }_{ce}}\right)}^2\right)$

The mean and variance of the normal distribution, here denoted ${\mu }_{ce}$ and ${\sigma }_{ce}^2$, are estimated over the transformed counterfeiting factor index, $c{e}^j$, and given by ${\stackrel{̑}{\mu }}_{ce}$ and ${\stackrel{̑}{\sigma }}_{ce}^2$. This enables the calculation of the counterfeit import propensity index (GTRIC-e) across provenance economies, corresponding to the cumulative distribution function of $c{e}^j$.

Establishing likelihoods for product and provenance economy

In this step, for each trade flow from a given provenance economy and for a given product category the likelihoods of containing counterfeit and pirated products will be established.

The general propensity for an economy to export infringed items of HS category k is denoted $P^k$, and given by GTRIC-p, so that:

$P^k=F_{LTN}\left(c{p}^k\right)$

where $F_{LTN}\left(c{p}^k\right)$ is the cumulative probability function of $f_{LTN}\left(c{p}^k\right)$.

Furthermore, the general likelihood of importing any type of infringing goods from economy j is denoted as ${P^j}_{}$, and given by GTRIC-e, so that:

$P^j=G_{LTN}\left(c{e}^j\right)$

where $G_{LTN}\left(c{e}^j\right)$ is the cumulative probability function of $f_{LTN}\left(c{e}^j\right)$.

The general probability of importing counterfeit or pirated items of type k originating from economy j is then denoted $P^{jk}$ and approximated by:

$P^{jk}=P^k{P}^j$

Therefore, $P^{jk}\in [{\epsilon }_p{\epsilon }_e;1)$, $\forall j,k$, with ${\epsilon }_p{\epsilon }_e$ denoting the minimum average counterfeit export rate for each sensitive product category and each provenance economy,3 it is assumed that ${\epsilon }_p={\epsilon }_e=0.05$.