(HS) product code and the type of inspection that was conducted, if any. Importing firms are identified by their unique tax identification number. We further restrict the data to imports of products that will be consumed in Serbia and exclude imports that are temporary, for inward processing or for re-export. We report results from a 2013-16 sub-sample of the data that maintains a consistent classification of HS10 products.<sup>17</sup> We define the shipment _type_ at the level of the origin country ( _o_ ), importing firm ( _f_ ), and HS10 product ( _k_ ).<sup>18</sup> We aggregate these data to the _ofkt_ level, where _t_ represents a calendar year. Our primary interest is in the relationship between current-year inspection rates in an _ofk_ triplet and the numbers of shipments in the same triplet that were observed by the agency in the previous year. To study this relationship flexibly, we create bins of different lagged shipment frequencies and estimate the effects of dummy variables attached to each frequency bin. Our frequency bins have observations with 0, 1, 2, 3-5, 6-10, 11-100, and 100+ lagged shipments, respectively.<sup>19</sup> A key outcome for each shipment is whether or not it is inspected. In Serbia, each shipment is subject to six classes of documentary and/or physical inspections.<sup>20</sup> We collapse this detail, determining only whether a shipment underwent any kind of inspection, or was not inspected.<sup>21</sup> The primary outcome variable we study is the inspection rate, which is

> 17We observe similar results at the HS6 level for this sub-sample and for HS6 estimates over the entire sample. An earlier version of this paper, Hillberry _et al._ (2020), reports results using the entire data set at the HS6 level. Those specifications did not include the additional risk variables that we include here.

> 18The only firm about which we have information in our data is the importing firm _f_ . The agency’s risk model would also incorporate into its analysis the identity of other firms in the supply chain, including the (foreign) exporting firm and the firms involved in transportation of the goods. While not ideal, the absence of data on the other firms involved in the transaction may not be as problematic as it might seem, since importing firms often maintain stable supply chains. Carballo _et al._ (2014) provide some evidence on this point, showing that Peruvian importers have a median of only 1 exporter per HS10 product-origin country pair, and an average of only 1 _._ 279 exporters.

19Our chosen binning strategy provides considerable flexibility at the low end of the frequency distribution. We also tried an alternative binning strategy that shifted flexibility towards the middle of the distribution and found similar (unreported) results.

> 20We exclude from the data shipments that are never inspected due to their product characteristics: trade in natural gas or electricity transported through pipelines and electrical power lines. These shipments are distinct from shipments that are not subjected to physical inspections through a determination of the customs agency (type 1).

> 21One class of inspections in the data are _documentary_ inspections that include no physical inspection. On the grounds that purely documentary inspections may be relatively unobtrusive, we experimented with treating shipments subject only to documentary inspections as ‘not inspected.’ Purely documentary ship-

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