where ���� is a measure of the value of imports of HS 4-digit product _k_ from country _i_ at time _t_ , ���� is an indicator that product _k_ is overseen by the FVA, �� is an indicator variable that takes the value of 1 in the period from July 2014 onwards when the reform is in place and 0 otherwise, and ��� and ��� are fixed effects at the product-country and country-year levels, respectively.<sup>41</sup> This equation serves as a D-i-D specification because the ��� term sweeps out the ���� fixed effects, and ��� sweeps out the �� fixed effects.<sup>42</sup> The coefficient of interest is �, which is positive if the effect of the FVA reforms on imports of FVA products is positive.

A first key challenge in estimating a specification like Equation (4) is the question of whether or not the non-FVA products are suitable as a control group for the FVA products. Ideally, we would have a set of products with similar characteristics that are not subject to control by the FVA. Such products could serve as the control group against which we could evaluate developments in the FVA products. But because the FVA has comprehensive authority over plant and animal-based food products as well as animals and feed (and none over most non-food manufactured goods), there are very few products that are near enough in product characteristic space to serve as credible controls.<sup>43</sup> One exception concerns the set of products known as food contact materials, which are subject to FVA import license I007. Food contact materials (cutlery, food packaging materials, etc.) have near neighbors in product characteristic space that are not subject to oversight by the FVA because they do not regularly come into contact with food. We estimate Equation (4) for the entire set of imported products, but also for a narrower set of food contact materials and the control group of neighbor products (defined as HS 4-digit products belonging to the same HS 2- digit chapters as those of FVA’s food contact materials).

A second key challenge with Equation (4) is that its estimate of � will be biased if imports at the _kit_ level are subject to time-varying shocks that are correlated with treatment status (i.e., with ������). The most plausible sources of these shocks would be export supply shocks in foreign countries. In order to address this challenge, we exploit global data on international trade flows from WITS to measure these shocks directly. We construct for each origin country’s its world export supply of product _k_ at time _t_ , ������ (where world export supply does not include exports to FYR Macedonia), following Hummels et al. (2014). Because FYR Macedonia is a small country, developments in FYR Macedonia are very unlikely

> 41 One might expect to see product-country of origin time-varying tariff rates enter into Equation (4) as a determinant of imports. Tariffs applied to imports of FVA products are remarkably stable over our period of study.  Less than 1.5 percent of HS-10 digit tariff lines saw changes in MFN tariffs during the period of our sample.  Given the inclusion of product-country of origin fixed effects in Equation (4), it is not useful to add these virtually stable tariffs as controls.

> 42 Equation (4) is a more stringent specification than a more standard D-i-D equation which would include in levels the two variables that enter the interaction term, ���� and ��.

> 43 In other settings, the structure of international trade statistics can offer a quite good set of controls.  For example, Hillberry and McCalman (2016) study antidumping orders in the United States using untreated products within still rather narrow product groups (HS4) as controls for products within the same HS4 that become subject to an antidumping order.

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