inspector _i_ should have for broker _j_ if random assignment was abided by _Sibt_<sup>_logit_</sup> , and construct estimates of excess interaction _ESibt_<sup>_logit_</sup> , as the difference between the two.<sup>30</sup> To estimate _Sibt_<sup>_logit_</sup> we use a binomial logit model with all controls shown in Equation (4). To estimate _Sibt_<sup>_logit_</sup> we use a binomial logit model that mimics random assignment given by Equation (4) including only day of the week fixed effects in the vector of declaration characteristics. Confidence intervals for _Sibt_<sup>_logit_</sup> and _Sibt_<sup>_logit_</sup> are constructed using the Krinsky and Robb [1986] simulation method.<sup>31</sup> Estimates of _ESibt_<sup>_logit_</sup> (the difference between _Sibt_<sup>_logit_</sup> and _Sibt_<sup>_logit_</sup> ) are therefore driven by broker fixed effects and declaration characteristics other than the day of the week when it was registered.

This procedure has three advantages relative to our first procedure. To start with, it accommodates alternative explanations - such as differences in work schedule and specialization in specific products - for frequent pairings of the same broker with the same inspector. Second and related, it allows us to obtain consistent estimators for broker fixed effects and to test whether they are significant and have explanatory power. Third, by using Bayesian estimation methods and applying shrinkage, we account for the fact that, in a small sample, one might expect some inspector-broker pairs to exhibit apparent excessive interaction even under the null hypothesis.<sup>32</sup> Note that we estimate one logit model per inspector per semester, resulting in a total of 116 different models. Panel B of Table 1 shows the prevalence of non-random assignment in Toamasina based on the measures of excess interaction from inspector-specific binomial logits. For 10.1 percent of declarations the (final) inspector handling them interacts significantly more frequently with a broker than would be predicted based on conditional random assignment. For these declarations the fixed effect of the broker registering them is individually significant in the inspector-specific binomial logit model. We also use a likelihood ratio test to assess whether broker fixed effects are jointly significant in each inspector-semester specific binomial logit model.<sup>33</sup> The results of these tests are reported at the bottom of Panel B in Table 1. On average across semesters, broker fixed effects are jointly significant for close to half the inspectors.

> 30One difference relative to the calibration procedure is that here we use estimates of _Sibt_<sup>_logit_</sup> instead of observed _Sibt_ which facilitates hypothesis testing. Namely, it allows to test the significance of broker fixed effects using likelihood ratio tests.

> 31This simulation method draws a set of parameters from a Normal distribution centered around the point estimates with a covariance matrix equal to the estimated covariance matrix. These parameters are used to calculate assignment probabilities to each inspector for each declaration. Taking the average of these probabilities across all declarations registered by broker _b_ yields the share that is expected to be assigned to inspector _i_ : _Sibt_<sup>_logit_</sup> in the model with all controls and _Sibt_<sup>_logit_</sup> in the model that mimics random assignment. The difference between _Sibt_<sup>_logit_</sup> and _Sibt_<sup>_logit_</sup> gives _ESibt_<sup>_logit_</sup> for each iteration. This simulation method is repeated 1,000 times. For such large number of iterations, the simulated distribution of assignment probabilities approximates the real distribution of assignment probabilities. This simulation method provides (i) the point estimate for _ESibt_<sup>_logit_</sup> obtained as the average of _ESibt_<sup>_logit_</sup> across the 1,000 iterations and (ii) an indicator for whether _ESibt_<sup>_logit_</sup> is significantly larger than 0 (i.e., whether _Sibt_<sup>_logit_</sup> is significantly larger than _Sibt_<sup>_logit_</sup> ).

> 32In principle, random inspector-specific logit models would be preferable to the standard logit models we estimate as they would allow random broker effects and productivity parameters. We tried to estimate such models but failed to obtain convergence, as in the case of the multinomial logit models, possibly due to parameter proliferation.

> 33In order to conduct these tests, we estimate a third type of logit model with all controls but excluding _only_ broker fixed effects. This ensures that the significance of these fixed effects can be assessed by comparing estimates from this third type of logit model to those from the model with all controls (including broker fixed effects).

15