Illicit Trade and the Korean Economy

Annex A. Construction of the GTRIC for products infringing Korean IPRs

Construction of GTRIC-p

Korean GTRIC-p is constructed in three steps.

• For each product category, the seizure percentages for sensitive goods are formed.

• 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 product seizure frequencies

$w_q$ is the seized value of product type $q$ infringing Korean residents’ IPR from any provenance economy in a given year. The relative seizure frequency (seizure percentages) of good $q$, denoted below as ${\eta }_q$, is then defined by:

${\eta }_q=\frac{w_q}{{\sum }_q{w}_q}, \mathrm{s}\mathrm{u}\mathrm{c}\mathrm{h}\mathrm{ }\mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t}\mathrm{ }\sum _q{\eta }_q=1$

Step 2: Measuring product-specific counterfeiting factors

$e_q$ is the global sales value (exports plus domestic sales) of all Korean branded products of type $q$, so that $E=\sum _q{e}_q$is defined as the global registered sales by Korean manufacturing industries of all sensitive goods.

The share of good $q$ in Korean total sales, denoted by ${\varsigma }_q,$ is therefore given by:

${\varsigma }_q=\frac{e_q}{E}, \mathrm{s}\mathrm{u}\mathrm{c}\mathrm{h}\mathrm{ }\mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t}\mathrm{ }\sum _q{\varsigma }_q=1$

The counterfeiting factor of product category $q$, denoted$C_q$, is then determined as the following.

$C_q=\frac{{\eta }_q}{{\varsigma }_q}$

The counterfeiting factor reflects the sensitivity of infringements of Korean trademarks and patents occurring in a particular product category, relative to its share in Korean global sales. These constitute the foundation for forming GTRIC-p.

Step 3: Establishing Korean GTRIC-p

GTRIC-p is constructed from a transformation of the counterfeiting factor; it measures the relative proneness with which Korean trademarks and patents in different types of product categories are subject to counterfeiting and piracy. The transformation of the counterfeiting factor is based on two main assumptions, described in OECD/EUIPO (2016[2]):

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

• The second (A2) acknowledges that the assumption A1 may not be entirely correct. For instance, the fact Korean IPR infringing goods are detected more frequently in certain categories could imply that differences in counterfeiting factors across products merely reflect that some goods infringing Korean IPRs are easier to detect than others, or that some of these goods, for one reason or another, have been specially targeted by customs worldwide. The counterfeiting factors of product categories with lower counterfeiting factors could therefore underestimate actual counterfeiting and piracy intensities in these cases.

In accordance with assumptions A1 and A2, GTRIC-p for products infringing Korean IPRs traded worldwide 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, 2008[9]).

In addition, 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 unsusceptible 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:

$c_q=\mathrm{l}\mathrm{n}(C_q+1)$

Assuming that the transformed counterfeiting factor can be described by a left-truncated normal distribution with $c_k\ge 0$; then, following Hald (1952), the density function of GTRIC-p is given by:

$h_{LTN}\left(c_q\right)=\{<!--\; --> \begin{array}{c}0 if{c}_q\le 0 \\ \frac{h\left(c_q\right)}{{\int }_0^{\infty }h\left(c_q\right) d{c}_q} if{c}_q\ge 0\end{array}$

where $h\left(c_q\right)$ is the non-truncated normal distribution for $c_k$, specified as:

$h\left(c_q\right)=\frac{1}{\sqrt{2\pi {\sigma }_q^2}}\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{1}{2}{\left(\frac{c_q-{\mu }_q}{{\sigma }_q}\right)}^2\right)$

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

Construction of GTRIC-e

GTRIC-e is constructed in three steps.

• For each destination economy, the seizure percentages are calculated.

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

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

Step 1: Measuring seizure intensities for each destination economy

$w_d$ is the registered seized value of all types of goods infringing Korean residents’ IPR exported to destination economy $d$ from any provenance economy at a given year. ${\eta }_d$is the relative seizure intensity (seizure percentage) of all products infringing Korean trademarks and patents that are shipped to country $d$, in a given year:

${\eta }_d=\frac{w_d}{{\sum }_d{w}_d}\text{, such that} {\sum }_d{\eta }_d=1$

Step 2: Measuring destination-specific counterfeiting factors

$e_d$ is defined as the global registered sales value of Korean branded or patented products (exports plus domestic manufacturing sales) shipped to $d$ (including Korea) and $E=\sum _d{e}_d$ is the global value of Korean sales of sensitive goods to all destination economies.

The share of sales to destination economy $d$ in Korean global sales of sensitive goods, denoted ${\varsigma }_d$, is then given by:

${\varsigma }_d=\frac{e_d}{E}, \mathrm{s}\mathrm{u}\mathrm{c}\mathrm{h}\mathrm{ }\mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t}\mathrm{ }\sum _d{\varsigma }_d=1$

From this, the economy-specific counterfeiting factor is established by dividing the seizure intensity for economy d by the share of total sales of sensitive goods to d:

$C_d=\frac{{\eta }_d}{{\varsigma }_d}$

Step 3: Establishing GTRIC-e

GTRIC-e is constructed from a transformation of the counterfeiting factor; it measures the relative proneness with which counterfeit products infringing Korean trademarks and patents are shipped to a given destination economy. The transformation of the counterfeiting factor is based on two main assumptions, described in (OECD/EUIPO, 2016[2]):

• The first assumption (A3) is that the frequency with which any counterfeit Korean branded or patented article shipped to a particular destination economy is detected and seized by customs is positively correlated with the actual amount of counterfeit and pirated Korean products exported to that location; and

• The second assumption (A4) acknowledges that assumption A3 may not be entirely correct. For instance, a high seizure intensity of products infringing Korean IPRs in a particular destination economy could be an indication that the destination economy implements a particular customs profiling scheme, or that these products are specially targeted for investigation by customs in that locale. The role some destination economies with low seizure intensities of Korean IPR infringing products play regarding actual counterfeiting and piracy activity could therefore be underrepresented by the index and lead to an underestimation of the scale of counterfeiting activities and piracy targeting Korean branded or patented products there.

Following assumptions A3 and A4, GTRIC-e for products infringing Korean IPRs 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, 2008[9]).

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

The transformed general counterfeiting factor across destination economies on which GTRIC-e is based is therefore given by applying logarithms onto economy-specific general counterfeit factors (Verbeek, 2008[9]):

$c_d=\mathrm{l}\mathrm{n}(C_d+1)$

In addition, following GTRIC-p it is assumed that GTRIC-e follows a truncated normal distribution with $c_d\ge 0$ for all $d.$ Following Hald (1952[10]), the density function of the left-truncated normal distribution for $c_d$ is given by:

$i_{LTN}\left(c_d\right)=\{<!--\; --> \begin{array}{c}0 if{c}_d\le 0 \\ \frac{i\left(c_d\right)}{{\int }_0^{\infty }i\left(c_d\right) d{c}_d} if{c}_d\ge 0\end{array}$

where $i\left(c_d\right)$ is the non-truncated normal distribution for $c_d$ specified as:

$i\left(c_d\right)=\frac{1}{\sqrt{2\pi {\sigma }_d^2}}\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{1}{2}{\left(\frac{c_d-{\mu }_d}{{\sigma }_d}\right)}^2\right)$

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

Construction of GTRIC

The combined index of GTRIC-e and GTRIC-p, denoted GTRIC, is an index that approximates the relative proneness for goods associated with Korean residents’ IPR in a given product category and a given destination economy to be counterfeit and/or pirated.

Step 1: Establishing proneness for products and destination economies

The general proneness of Korean trademarks and patents to be counterfeit or pirated in product category $q$, is denoted by${ P}_q$, and is given by GTRIC-p, so that:

$P_q=H_{LTN}\left(c_q\right)$

where $H_{LTN}\left(c_q\right)$ is the cumulative probability function of $h_{LTN}\left(c_q\right)$.

Furthermore, the general proneness of all Korean trademarks and patents to be infringed and shipped to economy $d$ is denoted by${ P}_d$, and is given by GTRIC-e, so that:

$P_d=I_{LTN}\left(c_d\right)$

where $I_{LTN}\left(c_d\right)$ is the cumulative probability function of $i_{LTN}\left(c_d\right)$.

The general proneness of Korean residents’ IPR to be counterfeit or pirated in a given product category $q$ and to be shipped to a given destination d from any provenance economy is then denoted by $P_{kd}$ and approximated by:

$P_{qd}=P_q\times P_d$

Therefore, $P_{qd}\in \left[{\epsilon }_q{\epsilon }_d ;1\right]$, $\forall k,d$, with ${\epsilon }_q{\epsilon }_d$ denoting the minimum average counterfeit export rate for each sensitive product category and each destination economy. It is assumed that ${\epsilon }_q={\epsilon }_d=0.05$.

Step 2: Calculating the absolute value

$\beta$ is the fixed point, i.e. the maximum average counterfeit rate of Korean trademarks and patents for a given product type $q$, shipped to a given trading partner, $d$. $\beta$ can therefore be applied onto the proneness of Korean-related IPRs of type $q$ to be counterfeit and shipped to destination partner $d$ ($\beta \times P_{qd}$).

As a result, a matrix of counterfeit import propensities $\mathrm{\Lambda }$ is obtained.

$\mathrm{\Lambda }=\left(\begin{array}{ccc}\beta P_{11}& \beta P_{12}& \beta P_{1Q}\\ \beta P_{21}& \ddots & \\ \beta P_{dq}& \\ \ddots & \\ \beta P_{D1}& \beta P_{DQ}\end{array}\right)$ with dimension $D \times Q$

The matrix of Korean global sales is denoted by $E$. Applying $\mathrm{\Lambda }$ on $E$yields the absolute volume of counterfeit and pirated trade in products that infringe Korean residents’ IPR. In particular, the sales matrix $E$ is given by:

$E=\left(\begin{array}{ccc}{e}_{11}& e_{12}& e_{1Q}\\ e_{21}& \ddots & \\ e_{dq}& \\ \ddots & \\ e_{D1}& e_{DQ}\end{array}\right)$ with dimension $D \times Q$

Hence, the element $e_{dq}$ denotes Korean sales of products in category $q$ to destination $d$, including the Korean, with $d=\left[1,\dots , D\right]$and $q=\left[1,\dots , Q\right]$.

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

$\mathrm{{\rm Z}}=\mathrm{\Lambda }\mathrm{\text{'}}\mathrm{E}÷\mathrm{E}$

Total trade in counterfeit and pirated goods that infringe Korean trademarks and patents, denoted by the scalar$\mathrm{ }\mathrm{T}\mathrm{\Lambda }$, is then given by:

$\mathrm{T}\mathrm{\Lambda }={\mathrm{I}}_1\mathrm{\text{'}}\mathrm{{\rm Z}}{\mathrm{I}}_2$

where ${\mathrm{I}}_1$ is an identity matrix with dimension $D \times 1$, and ${\mathrm{I}}_2$ is an identity matrix with dimension $Q \times 1$.

Then, by denoting global Korean sales by the scalar$\mathrm{ }\mathrm{T}\mathrm{E}={\mathrm{I}}_1\mathrm{\text{'}}\mathrm{{\rm Z}}{\mathrm{E}}_2$, the share of counterfeit and pirated products infringing Korean residents’ IPR in Korean global manufacturing sales, ${\varsigma }_{\mathrm{T}\mathrm{\Lambda }}$, is determined by:

${\varsigma }_{\mathrm{T}\mathrm{\Lambda }}=\frac{\mathrm{T}\mathrm{\Lambda }}{\mathrm{T}\mathrm{E}}$