Why Do Countries Import Fakes?

Annex A. Estimating the share of fake goods sold in the primary and secondary markets

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 fakes is calculated. For each seizure specified in the database, the customs authorities report the declared value of goods, the quantity seized, the product’s HS code, and the infringed trademark. This allows the unit value of each seized “product type-brand” pair (brand would include the associated trademark) to be determined. These unit values can then serve as a proxy for the retail prices of the fake goods. For each type of product associated with a given trademark, 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, are 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 $s_c$ and ${\mathrm{s}̅}_c$denote, respectively, the import value and quantity of any custom seizure of counterfeit products, with 𝑐 ∈ {1, … , 𝑁} the range of customs seizures, and N their total number. $p_c= s_c/{\mathrm{s}̅}_c$ then refers to the unit value of each custom seizure and can serve as a proxy for their unit price. Let $p_{bp}= {\sum }_{c \in \{<!--\; -->bp\}}{p}_c/N_{bp}$ } defines the (unweighted) price average of any type of product $\text{p}$ associated with the brand $\text{b}$, with $N_{bp}$the total number of custom seizures reported for this “product category - brand” combination. The standard deviation of this price is denoted ${\mathrm{\sigma }}_{bp}$.

$X_c$ 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:

$X_c=\{<!--\; -->\begin{array}{c}=0 if p_c\in \left[p_{bp}- \frac{1.96 \times {\mathrm{\sigma }}_{bp }}{\sqrt{N_{bp}}};{max}_{c \in \{<!--\; -->bp\}} p_c\right]\\ =1 if p_c\in \left[{{min }_{c \in \{<!--\; -->bp\}} p_c ; p}_{bp}- \frac{1.96 \times {\mathrm{\sigma }}_{bp }}{\sqrt{N_{bp}}}\right]\end{array} \forall c\in \{<!--\; -->bp\}$

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

${\mathrm{\tau }}_p^1={\sum }_b^{}{\sum }_c^{}{X}_c{s}_c/{\sum }_b^{}{\sum }_c^{}{s}_c ; \forall c\in \{<!--\; -->bp\}$