receiving GasyNet’s valuation advice.<sup>21</sup> In robustness exercises we consider other declaration characteristics: the log of the initially declared value, the log of the initially declared weight, the initial unit price relative to median import unit price and the initial hypothetical tax revenue loss (using as reference price the median import price). Summary statistics on all customs outcomes and declaration characteristics are shown in Appendix Tables A3 and A4.

# **4 Identifying Deviant Declarations**

Our identification of declarations suspect of corruption relies on detecting deviations from official rules in the assignment of incoming declarations to customs inspectors. Recall from Section 2 that, according to official rules, incoming declarations should be randomly assigned to inspectors conditional on their productivity. For each inspector, the likelihood of being assigned any given declaration is proportional to her productivity. These rules imply that the process of assigning declarations to inspectors follows a multinomial distribution. Each declaration is assigned to one of _Kt_ possible inspectors, where _Kt_ is the total number of inspectors active in semester _t_ , with corresponding probabilities _p_ 1 _t_ , _p_ 2 _t_ ,. . . ., _pKt_ .<sup>22</sup> These probabilities sum up to 1 because the _Kt_ outcomes are mutually exclusive and can be thought of as reflecting inspectors’ relative productivity in semester _t_ . An inspector that is more productive will, on average, handle more declarations than a less productive inspector. Because the marginal distribution of a multinomial distribution is binomial, for each inspector _i_ , the probability of receiving _xibt_ import declarations from the _Kt_ total number of declarations _nbt_ (where _nbt_ = � _xibt_ ) registered by broker _b_ in semester _t_ is given by the _i_ =1 binomial probability mass function: _P_ ( _xibt|pit, nbt_ ) = � _xnibtbt_ � _p_<sup>_x_</sup> _it_<sup>(1</sup><sup>_−pit_)</sup><sup>_nbt−xibt_.</sup>

Based on these rules, the share of all declarations that a given inspector handles in a given semester, which we refer to as her inspection share (analogous to the concept of market share in industrial organization), is expected to vary across inspectors, as it depends on their productivity. However, for a given inspector, it should not vary systematically across brokers, unless inspector assignment performed by the IT system did not follow official rules — i.e., was manipulated. All inspectors should have, for a given broker, an inspection share close to their average inspection share.

To assess whether this is indeed the case we consider the import declarations registered by a specific

> 21These variables are supposed to be predetermined from the point of view of the inspectors handling the declaration since they are not the ones lodging the declaration on behalf of the importer, nor are they in charge of issuing a risk score or making the first inspection channel recommendation.

> 22The probability of observing a particular distribution ( _x_ 1 _bt, x_ 2 _bt, ..., xkbt_ ) of declarations of a given broker _b_ across _Kt_ inspectors 1 _,_ 2 _, ..., k_ in semester _t_ (where � _xibt_ = _nbt_ , the total number of declarations in semester _t_ registered by broker _b_ ) _i_ =1 given their productivities ( _p_ 1 _t, p_ 2 _t, ..., pkt_ ) is:

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